TSTP Solution File: SWW298+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:25:53 EDT 2023
% Result : Theorem 46.36s 45.02s
% Output : Proof 46.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 22:21:15 EDT 2023
% 0.12/0.33 % CPUTime :
% 46.36/45.02
% 46.36/45.02 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 46.36/45.02 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.36/45.02 %-----------------------------------------------------
% 46.36/45.02 ncf(matrix, plain, [(53123 ^ _2093791) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(t_a, v_n, 53119 ^ [])], (53121 ^ _2093791) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 53119 ^ []), v_ts)))], !, (29364 ^ _779327) ^ [_1303242, _1303244, _1303246] : [class_Orderings_Olinorder(_1303242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303242), _1303244), _1303246)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303242, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1303242, _1303244, _1303246)), hAPP(hAPP(c_Set_Oinsert(_1303242), _1303246), c_Orderings_Obot__class_Obot(tc_fun(_1303242, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1303242, _1303244, _1303246))], (39091 ^ _779327) ^ [_1519463, _1519465, _1519467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519463), _1519465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519463, _1519463), tc_HOL_Obool)), _1519467), hAPP(hAPP(c_Product__Type_OSigma(_1519463, _1519463), _1519465), hAPP(c_COMBK(tc_fun(_1519463, tc_HOL_Obool), _1519463), _1519465)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1519463, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1519463), _1519465), _1519467))))], (16367 ^ _779327) ^ [_1056668, _1056670] : [class_Groups_Oordered__ab__group__add__abs(_1056668), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056668), _1056670), hAPP(c_Groups_Oabs__class_Oabs(_1056668), _1056670))))], (18478 ^ _779327) ^ [] : [-(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))))], (5174 ^ _779327) ^ [_858249, _858251] : [_858251 = _858249, -(c_Set_OBex(_858251) = c_Set_OBex(_858249))], (7580 ^ _779327) ^ [_898520, _898522, _898524] : [7581 ^ _779327 : [(7584 ^ _779327) ^ [] : [_898520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7582 ^ _779327) ^ [] : [_898522 = _898524]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898520), _898522) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898520), _898524))], (24329 ^ _779327) ^ [_1202840, _1202842] : [24336 ^ _779327 : [(24339 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202842), _1202840))], (24337 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202840), _1202842)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202840), _1202842)), -(_1202840 = _1202842)], (41239 ^ _779327) ^ [_1577677, _1577679, _1577681, _1577683, _1577685, _1577687] : [-(hAPP(hAPP(c_Fun_Ocomp(_1577677, _1577679, _1577681, _1577683), _1577685), _1577687) = hAPP(_1577683, hAPP(_1577685, _1577687)))], (47430 ^ _779327) ^ [_1726297, _1726299] : [-(_1726297 = c_List_Olist_ONil(_1726299)), hBOOL(hAPP(c_List_Odistinct(_1726299), _1726297)), -(hBOOL(hAPP(c_List_Odistinct(_1726299), c_List_Obutlast(_1726299, _1726297))))], (52616 ^ _779327) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (48104 ^ _779327) ^ [_1740713, _1740715, _1740717] : [-(c_Enum_Oproduct(_1740713, _1740715, c_List_Olist_ONil(_1740713), _1740717) = c_List_Olist_ONil(tc_prod(_1740713, _1740715)))], (44015 ^ _779327) ^ [_1641999, _1642001] : [class_Complete__Lattice_Ocomplete__lattice(_1641999), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641999), _1642001)), -(c_Complete__Lattice_OSup__class_OSup(_1641999, _1642001) = hAPP(hAPP(c_Finite__Set_Ofold(_1641999, _1641999, c_Lattices_Osemilattice__sup__class_Osup(_1641999)), c_Orderings_Obot__class_Obot(_1641999)), _1642001))], (9551 ^ _779327) ^ [_934038, _934040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934038)), -(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), _934038), _934040))))], (5566 ^ _779327) ^ [_864257, _864259, _864261, _864263] : [-(hAPP(_864263, _864259) = hAPP(_864261, _864257)), _864263 = _864261, _864259 = _864257], (52840 ^ _779327) ^ [_1838693] : [-(class_Nat_Osize(tc_List_Olist(_1838693)))], (31461 ^ _779327) ^ [_1349880, _1349882, _1349884] : [class_Orderings_Owellorder(_1349880), hBOOL(hAPP(_1349882, _1349884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Orderings_Oord__class_OLeast(_1349880, _1349882)), _1349884)))], (12854 ^ _779327) ^ [_994124, _994126] : [class_Groups_Olinordered__ab__group__add(_994124), 12857 ^ _779327 : [(12864 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994124), c_Groups_Ozero__class_Ozero(_994124)), _994126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994124), hAPP(c_Groups_Ouminus__class_Ouminus(_994124), _994126)), _994126)))], (12858 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994124), hAPP(c_Groups_Ouminus__class_Ouminus(_994124), _994126)), _994126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994124), c_Groups_Ozero__class_Ozero(_994124)), _994126)))]]], (48732 ^ _779327) ^ [_1756338, _1756340, _1756342, _1756344] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1756338, tc_Nat_Onat), _1756338), c_Product__Type_Ofst(_1756338, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1756338, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1756338, 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(_1756338, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1756338, tc_Nat_Onat))), _1756340)), hAPP(hAPP(c_List_Ozip(_1756338, tc_Nat_Onat), _1756342), c_List_Oupt(_1756344, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1756344), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756338)), _1756342)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1756338, tc_Nat_Onat), _1756338), c_Product__Type_Ofst(_1756338, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1756338, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1756338, 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(_1756338, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1756338, 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(_1756338, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1756338, tc_Nat_Onat))), _1756344))), _1756340)), hAPP(hAPP(c_List_Ozip(_1756338, tc_Nat_Onat), _1756342), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756338)), _1756342))))))], (47496 ^ _779327) ^ [_1727584, _1727586] : [-(c_List_Obutlast(_1727584, _1727586) = hAPP(hAPP(c_List_Otake(_1727584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727584)), _1727586)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1727586))], (36813 ^ _779327) ^ [_1466130, _1466132, _1466134, _1466136] : [class_Orderings_Oorder(_1466130), class_Orderings_Olinorder(_1466132), c_Orderings_Oorder__class_Ostrict__mono(_1466132, _1466130, _1466134), -(c_Fun_Oinj__on(_1466132, _1466130, _1466134, _1466136))], (27196 ^ _779327) ^ [_1259244, _1259246, _1259248] : [class_Lattices_Osemilattice__sup(_1259244), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259244), _1259246), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259244), _1259246), _1259248))))], (52944 ^ _779327) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (20219 ^ _779327) ^ [_1124276, _1124278, _1124280, _1124282] : [class_Fields_Olinordered__field(_1124276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124276), c_Groups_Ozero__class_Ozero(_1124276)), _1124278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124276), _1124280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124276), _1124282), _1124278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124276), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124276), _1124280), _1124278)), _1124282)))], (45848 ^ _779327) ^ [_1690902, _1690904, _1690906, _1690908, _1690910] : [-(_1690902 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1690904, _1690906, _1690908), _1690902), _1690910) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1690906), _1690904), tc_prod(_1690906, _1690904), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690906), _1690904), c_List_Olist_ONil(_1690906)), _1690910), hAPP(c_Product__Type_Oprod_Oprod__case(_1690906, _1690904, tc_prod(tc_List_Olist(_1690906), _1690904)), hAPP(hAPP(c_COMBC(_1690906, tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904)), tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1690906), _1690904), tc_prod(tc_List_Olist(_1690906), _1690904)), tc_fun(tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904)), tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904))), _1690906), c_COMBB(tc_prod(tc_List_Olist(_1690906), _1690904), tc_prod(tc_List_Olist(_1690906), _1690904), _1690904)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690906), tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904))), tc_fun(tc_prod(tc_List_Olist(_1690906), _1690904), tc_prod(tc_List_Olist(_1690906), _1690904)), _1690906), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690906), _1690904, tc_prod(tc_List_Olist(_1690906), _1690904))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690906), tc_List_Olist(_1690906)), tc_fun(tc_List_Olist(_1690906), tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904))), _1690906), hAPP(c_COMBB(tc_List_Olist(_1690906), tc_fun(_1690904, tc_prod(tc_List_Olist(_1690906), _1690904)), tc_List_Olist(_1690906)), c_Product__Type_OPair(tc_List_Olist(_1690906), _1690904))), c_List_Olist_OCons(_1690906))))), hAPP(c_Lazy__Sequence_Oanamorph(_1690904, _1690906, _1690908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1690902), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1690908, _1690910)))], (2062 ^ _779327) ^ [_809097, _809099] : [_809099 = _809097, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809099) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_809097))], (30489 ^ _779327) ^ [_1329197, _1329199, _1329201, _1329203, _1329205] : [class_Groups_Ocomm__monoid__add(_1329197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329199), _1329201)), 30496 ^ _779327 : [(30503 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329199), _1329203), _1329201))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329199, _1329197), hAPP(hAPP(c_COMBC(_1329199, _1329197, _1329197), hAPP(hAPP(c_COMBS(_1329199, _1329197, tc_fun(_1329197, _1329197)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329197, tc_fun(_1329197, _1329197)), _1329199), c_If(_1329197)), hAPP(hAPP(c_COMBC(_1329199, _1329199, tc_HOL_Obool), c_fequal), _1329203))), _1329205)), c_Groups_Ozero__class_Ozero(_1329197))), _1329201) = c_Groups_Ozero__class_Ozero(_1329197))], (30497 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1329199), _1329203), _1329201)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329199, _1329197), hAPP(hAPP(c_COMBC(_1329199, _1329197, _1329197), hAPP(hAPP(c_COMBS(_1329199, _1329197, tc_fun(_1329197, _1329197)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1329197, tc_fun(_1329197, _1329197)), _1329199), c_If(_1329197)), hAPP(hAPP(c_COMBC(_1329199, _1329199, tc_HOL_Obool), c_fequal), _1329203))), _1329205)), c_Groups_Ozero__class_Ozero(_1329197))), _1329201) = hAPP(_1329205, _1329203))]]], (22217 ^ _779327) ^ [_1163322] : [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), _1163322))), -(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), _1163322)) = 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), _1163322))))], (41199 ^ _779327) ^ [_1576575, _1576577, _1576579, _1576581, _1576583, _1576585] : [41202 ^ _779327 : [(41205 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1576581), _1576583), hAPP(hAPP(_1576585, 41200 ^ [_1576575, _1576577, _1576579, _1576581, _1576583, _1576585]), 41201 ^ [_1576575, _1576577, _1576579, _1576581, _1576583, _1576585])))], (41203 ^ _779327) ^ [] : [-(_1576575 = hAPP(hAPP(c_Product__Type_OPair(_1576577, _1576579), 41200 ^ [_1576575, _1576577, _1576579, _1576581, _1576583, _1576585]), 41201 ^ [_1576575, _1576577, _1576579, _1576581, _1576583, _1576585]))]], -(hBOOL(hAPP(hAPP(c_member(_1576581), _1576583), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1576577, _1576579, tc_fun(_1576581, tc_HOL_Obool)), _1576585), _1576575))))], (25716 ^ _779327) ^ [_1229713] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229713) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1229713))], (15357 ^ _779327) ^ [_1038469, _1038471, _1038473, _1038475] : [class_Divides_Osemiring__div(_1038469), -(c_Divides_Odiv__class_Omod(_1038469, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038469), _1038471), _1038473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038469), _1038475), _1038473)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038469), c_Divides_Odiv__class_Omod(_1038469, _1038471, _1038475)), _1038473))], (14177 ^ _779327) ^ [_1018111, _1018113, _1018115] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018113), _1018115)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018111), _1018113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018111), _1018115)))], (9274 ^ _779327) ^ [_929531, _929533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929531)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _929531), _929533)))], (48179 ^ _779327) ^ [_1742484, _1742486, _1742488, _1742490] : [hBOOL(hAPP(c_List_Odistinct(_1742484), _1742486)), hBOOL(hAPP(c_List_Odistinct(_1742488), _1742490)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1742484, _1742488)), c_Enum_Oproduct(_1742484, _1742488, _1742486, _1742490))))], (18899 ^ _779327) ^ [_1101183, _1101185] : [c_Nat__Transfer_Ois__nat(_1101183), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1101183), _1101185)))], (33399 ^ _779327) ^ [_1387883, _1387885, _1387887, _1387889, _1387891] : [class_Fields_Ofield(_1387883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387885), _1387887)), -(hAPP(_1387889, _1387891) = c_Groups_Ozero__class_Ozero(_1387883)), 33410 ^ _779327 : [(33417 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387885), _1387891), _1387887))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387885, _1387883), _1387889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387885, tc_HOL_Obool)), _1387887), hAPP(hAPP(c_Set_Oinsert(_1387885), _1387891), c_Orderings_Obot__class_Obot(tc_fun(_1387885, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387885, _1387883), _1387889), _1387887))], (33411 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1387885), _1387891), _1387887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387885, _1387883), _1387889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387885, tc_HOL_Obool)), _1387887), hAPP(hAPP(c_Set_Oinsert(_1387885), _1387891), c_Orderings_Obot__class_Obot(tc_fun(_1387885, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387883), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387885, _1387883), _1387889), _1387887)), hAPP(_1387889, _1387891)))]]], (50084 ^ _779327) ^ [_1783398, _1783400, _1783402] : [hBOOL(hAPP(c_List_Odistinct(_1783398), _1783400)), -(hBOOL(hAPP(c_List_Odistinct(_1783398), hAPP(c_List_OremoveAll(_1783398, _1783402), _1783400))))], (13060 ^ _779327) ^ [_997546, _997548, _997550, _997552] : [class_Groups_Oordered__comm__monoid__add(_997546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997546), c_Groups_Ozero__class_Ozero(_997546)), _997548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997546), _997550), _997552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997546), _997550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997546), _997548), _997552))))], (2002 ^ _779327) ^ [_808195, _808197, _808199, _808201, _808203, _808205] : [-(c_Power_Opower_Opower(_808205, _808201, _808197) = c_Power_Opower_Opower(_808203, _808199, _808195)), _808205 = _808203, _808201 = _808199, _808197 = _808195], (13630 ^ _779327) ^ [_1007862, _1007864] : [class_Rings_Oring__1(_1007862), 13633 ^ _779327 : [(13640 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007864), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1007862), _1007864) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1007862), hAPP(c_Int_Onat, _1007864)))], (13634 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007864), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1007862), _1007864) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007862), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1007862), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1007864)))))]]], (9156 ^ _779327) ^ [_927354, _927356, _927358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927354, tc_HOL_Obool)), _927356), _927358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927354, tc_HOL_Obool)), _927356), _927358))), -(_927356 = _927358)], (6182 ^ _779327) ^ [_876705, _876707, _876709, _876711] : [class_Orderings_Oorder(_876705), _876707 = _876709, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876705), _876711), _876709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876705), _876711), _876707)))], (48945 ^ _779327) ^ [_1760692, _1760694] : [class_Orderings_Olinorder(_1760692), -(c_List_Olinorder__class_Osorted(_1760692, hAPP(hAPP(c_List_Olist_OCons(_1760692), _1760694), c_List_Olist_ONil(_1760692))))], (24271 ^ _779327) ^ [_1201930, _1201932] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201930), _1201932)), 24276 ^ _779327 : [(24279 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201932), _1201930))], (24277 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201930), _1201932)))]], -(_1201930 = _1201932)], (51574 ^ _779327) ^ [_1816053, _1816055, _1816057] : [-(c_List_Olist__ex(_1816053, _1816057, _1816055)), 51575 ^ _779327 : [(51576 ^ _779327) ^ [_1816110] : [hBOOL(hAPP(hAPP(c_member(_1816053), _1816110), hAPP(c_List_Oset(_1816053), _1816055))), hBOOL(hAPP(_1816057, _1816110))]]], (26328 ^ _779327) ^ [_1242582, _1242584, _1242586] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242582), _1242584), _1242586) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1242582), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1242582, tc_Int_Oint), _1242584), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1242586))), class_Groups_Ocomm__monoid__add(_1242582), class_Groups_Ocomm__monoid__mult(_1242582)], (27777 ^ _779327) ^ [_1272958, _1272960] : [class_Orderings_Olinorder(_1272958), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272958, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1272958), _1272960)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1272958), _1272960))], (28902 ^ _779327) ^ [_1294463, _1294465, _1294467, _1294469] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294463, tc_HOL_Obool)), _1294465), hAPP(hAPP(c_Set_Oinsert(_1294463), _1294467), _1294469)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294463, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294463, tc_HOL_Obool)), _1294465), hAPP(hAPP(c_Set_Oinsert(_1294463), _1294467), c_Orderings_Obot__class_Obot(tc_fun(_1294463, tc_HOL_Obool))))), _1294469))], (8808 ^ _779327) ^ [_920904, _920906, _920908, _920910] : [class_Rings_Olinordered__semidom(_920904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920904), hAPP(hAPP(c_Power_Opower__class_Opower(_920904), _920906), hAPP(c_Nat_OSuc, _920908))), hAPP(hAPP(c_Power_Opower__class_Opower(_920904), _920910), hAPP(c_Nat_OSuc, _920908)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920904), c_Groups_Ozero__class_Ozero(_920904)), _920910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920904), _920906), _920910)))], (52646 ^ _779327) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (34781 ^ _779327) ^ [_1420240, _1420242] : [class_Lattices_Osemilattice__inf(_1420240), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420240), _1420242), _1420242) = _1420242)], (25219 ^ _779327) ^ [_1218886, _1218888, _1218890] : [-(_1218886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25222 ^ _779327 : [(25229 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218886), _1218888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218886), _1218890))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218888), _1218890)))], (25223 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218888), _1218890)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218886), _1218888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218886), _1218890))))]]], (50727 ^ _779327) ^ [_1797639, _1797641, _1797643] : [hBOOL(hAPP(hAPP(c_member(_1797639), _1797641), hAPP(c_List_Oset(_1797639), _1797643))), 50732 ^ _779327 : [(50735 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1797639), _1797641), hAPP(c_List_Oset(_1797639), 50730 ^ [_1797639, _1797641, _1797643])))], (50733 ^ _779327) ^ [] : [-(_1797643 = hAPP(hAPP(c_List_Oappend(_1797639), 50730 ^ [_1797639, _1797641, _1797643]), hAPP(hAPP(c_List_Olist_OCons(_1797639), _1797641), 50731 ^ [_1797639, _1797641, _1797643])))]]], (49355 ^ _779327) ^ [_1767943, _1767945, _1767947, _1767949] : [class_Orderings_Olinorder(_1767943), c_List_Olinorder__class_Osorted(_1767943, _1767945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1767947), _1767949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767949), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767943)), _1767945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767943), hAPP(hAPP(c_List_Onth(_1767943), _1767945), _1767947)), hAPP(hAPP(c_List_Onth(_1767943), _1767945), _1767949))))], (37871 ^ _779327) ^ [_1488159, _1488161, _1488163, _1488165] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488159, tc_fun(_1488161, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488159, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1488161, tc_HOL_Obool), tc_fun(_1488161, tc_HOL_Obool), _1488159), hAPP(c_COMBC(_1488161, tc_fun(_1488161, tc_HOL_Obool), tc_HOL_Obool), c_member(_1488161))), _1488163)), _1488165)), -(hBOOL(hAPP(hAPP(c_member(_1488161), _1488165), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488159, tc_fun(_1488161, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488159, tc_HOL_Obool))), _1488163))))], (34965 ^ _779327) ^ [_1423705, _1423707, _1423709] : [class_Lattices_Olattice(_1423705), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423705), _1423707), _1423709)), _1423707)))], (7598 ^ _779327) ^ [_898776, _898778] : [7599 ^ _779327 : [(7602 ^ _779327) ^ [] : [_898778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7600 ^ _779327) ^ [] : [_898776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898776), _898778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34751 ^ _779327) ^ [_1419697, _1419699, _1419701] : [class_Lattices_Osemilattice__inf(_1419697), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419697), _1419699), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419697), _1419699), _1419701)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419697), _1419699), _1419701))], (38109 ^ _779327) ^ [_1493679, _1493681, _1493683, _1493685, _1493687] : [-(_1493679 = c_Orderings_Obot__class_Obot(tc_fun(_1493681, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493683, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493681, tc_fun(_1493683, tc_HOL_Obool)), _1493679), _1493685)), _1493687) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493681, tc_fun(_1493683, tc_HOL_Obool)), _1493679), hAPP(hAPP(c_COMBC(_1493681, tc_fun(_1493683, tc_HOL_Obool), tc_fun(_1493683, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493683, tc_HOL_Obool), tc_fun(tc_fun(_1493683, tc_HOL_Obool), tc_fun(_1493683, tc_HOL_Obool)), _1493681), c_Groups_Ominus__class_Ominus(tc_fun(_1493683, tc_HOL_Obool))), _1493685)), _1493687)))], (13782 ^ _779327) ^ [_1010607, _1010609, _1010611] : [class_Rings_Olinordered__ring(_1010607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010607), _1010609), _1010609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010607), _1010611), _1010611))), c_Groups_Ozero__class_Ozero(_1010607)))], (8960 ^ _779327) ^ [_923641, _923643, _923645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923641), _923643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _923645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923645), _923641)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923645), _923643))))], (41752 ^ _779327) ^ [_1589423, _1589425, _1589427] : [-(c_Hilbert__Choice_OEps(tc_prod(_1589423, _1589425), hAPP(c_Product__Type_Oprod_Oprod__case(_1589423, _1589425, tc_HOL_Obool), _1589427)) = c_Hilbert__Choice_OEps(tc_prod(_1589423, _1589425), hAPP(hAPP(c_COMBS(tc_prod(_1589423, _1589425), _1589425, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1589423, tc_fun(_1589425, tc_HOL_Obool), tc_prod(_1589423, _1589425)), _1589427), c_Product__Type_Ofst(_1589423, _1589425))), c_Product__Type_Osnd(_1589423, _1589425))))], (37941 ^ _779327) ^ [_1489921, _1489923, _1489925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1489921, _1489921), tc_HOL_Obool)), _1489923), _1489925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489921, tc_HOL_Obool)), c_Wellfounded_Oacc(_1489921, _1489925)), c_Wellfounded_Oacc(_1489921, _1489923))))], (52103 ^ _779327) ^ [_1828096, _1828098, _1828100] : [c_Relation_Osym(_1828096, _1828098), c_Relation_Osym(_1828096, _1828100), -(c_Relation_Osym(_1828096, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1828096, _1828096), tc_HOL_Obool)), _1828098), _1828100)))], (5816 ^ _779327) ^ [_871186, _871188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871186), _871188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871186), _871188))), -(_871186 = _871188)], (45490 ^ _779327) ^ [_1681423, _1681425] : [-(c_List_Olist_Olist__size(_1681423, _1681425, c_List_Olist_ONil(_1681423)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13609 ^ _779327) ^ [_1007430] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1007430)) = 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), _1007430)))], (47486 ^ _779327) ^ [_1727347, _1727349, _1727351] : [-(c_List_Obutlast(_1727347, hAPP(hAPP(c_List_Oappend(_1727347), _1727349), hAPP(hAPP(c_List_Olist_OCons(_1727347), _1727351), c_List_Olist_ONil(_1727347)))) = _1727349)], (9749 ^ _779327) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26669 ^ _779327) ^ [_1248801, _1248803] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248801), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1248803) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1248801, _1248803))], (4352 ^ _779327) ^ [_845540, _845542] : [_845542 = _845540, -(c_Orderings_Oord__class_Omax(_845542) = c_Orderings_Oord__class_Omax(_845540))], (7314 ^ _779327) ^ [_893988] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _893988), _893988)))], (5278 ^ _779327) ^ [_859891, _859893, _859895, _859897] : [-(c_List_Olistrel(_859897, _859893) = c_List_Olistrel(_859895, _859891)), _859897 = _859895, _859893 = _859891], (52644 ^ _779327) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (46760 ^ _779327) ^ [_1712434, _1712436] : [-(_1712434 = c_List_Olist_ONil(_1712436)), -(hAPP(c_List_Orotate1(_1712436), _1712434) = hAPP(hAPP(c_List_Oappend(_1712436), hAPP(c_List_Otl(_1712436), _1712434)), hAPP(hAPP(c_List_Olist_OCons(_1712436), hAPP(c_List_Ohd(_1712436), _1712434)), c_List_Olist_ONil(_1712436))))], (49671 ^ _779327) ^ [_1774639, _1774641, _1774643] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1774639), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1774639))), _1774641))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774643), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1774639))), _1774641))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1774639))), hAPP(c_List_Ofilter(tc_List_Olist(_1774639), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1774639)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774643)), c_Nat_Osize__class_Osize(tc_List_Olist(_1774639)))), c_List_Otranspose(_1774639, _1774641))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774639)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1774639)), _1774641), _1774643)))], (25343 ^ _779327) ^ [_1221209, _1221211] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221209)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221211))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221211), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221209)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13300 ^ _779327) ^ [_1001836, _1001838] : [class_Rings_Olinordered__semidom(_1001836), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001836), _1001838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001836), _1001838), c_Groups_Oone__class_Oone(_1001836)))))], (46788 ^ _779327) ^ [_1712996, _1712998, _1713000, _1713002] : [-(hAPP(hAPP(c_List_Omap(_1712996, _1712998), _1713000), hAPP(c_List_Otl(_1712996), _1713002)) = hAPP(c_List_Otl(_1712998), hAPP(hAPP(c_List_Omap(_1712996, _1712998), _1713000), _1713002)))], (29678 ^ _779327) ^ [_1309571, _1309573, _1309575] : [_1309571 = c_Orderings_Obot__class_Obot(tc_fun(_1309573, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1309573), _1309575), _1309571))], (46217 ^ _779327) ^ [_1699069, _1699071, _1699073, _1699075] : [hAPP(hAPP(c_List_Oappend(_1699069), _1699071), _1699073) = hAPP(hAPP(c_List_Oappend(_1699069), _1699071), _1699075), -(_1699073 = _1699075)], (52476 ^ _779327) ^ [_1835068, _1835070] : [class_Lattices_Odistrib__lattice(_1835068), -(class_Lattices_Odistrib__lattice(tc_fun(_1835070, _1835068)))], (3526 ^ _779327) ^ [_832607, _832609, _832611, _832613] : [-(c_Lazy__Sequence_Ohb__single(_832613, _832609) = c_Lazy__Sequence_Ohb__single(_832611, _832607)), _832613 = _832611, _832609 = _832607], (10297 ^ _779327) ^ [_946181, _946183, _946185, _946187] : [class_Rings_Olinordered__semidom(_946181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _946183), _946185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946181), c_Groups_Oone__class_Oone(_946181)), _946187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946181), hAPP(hAPP(c_Power_Opower__class_Opower(_946181), _946187), _946183)), hAPP(hAPP(c_Power_Opower__class_Opower(_946181), _946187), _946185))))], (52814 ^ _779327) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (21981 ^ _779327) ^ [_1158427, _1158429, _1158431] : [hBOOL(hAPP(_1158427, hAPP(hAPP(c_Product__Type_OPair(_1158429, _1158431), 21982 ^ [_1158427, _1158429, _1158431]), 21983 ^ [_1158427, _1158429, _1158431]))), 21986 ^ _779327 : [(21987 ^ _779327) ^ [_1158574] : [-(hBOOL(hAPP(_1158427, _1158574)))]]], (21932 ^ _779327) ^ [_1157398, _1157400, _1157402, _1157404, _1157406] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1157398, _1157400, tc_HOL_Obool), _1157402), hAPP(hAPP(c_Product__Type_OPair(_1157398, _1157400), _1157404), _1157406))), -(hBOOL(hAPP(hAPP(_1157402, _1157404), _1157406)))], (41467 ^ _779327) ^ [_1582901, _1582903, _1582905, _1582907, _1582909, _1582911, _1582913, _1582915] : [c_Finite__Set_Ofolding__image(_1582901, _1582903, _1582905, _1582907, _1582909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582903), _1582911)), c_Fun_Oinj__on(_1582903, _1582903, _1582913, _1582911), -(hAPP(hAPP(_1582909, _1582915), hAPP(c_Set_Oimage(_1582903, _1582903, _1582913), _1582911)) = hAPP(hAPP(_1582909, hAPP(c_Fun_Ocomp(_1582903, _1582901, _1582903, _1582915), _1582913)), _1582911))], (52636 ^ _779327) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (8790 ^ _779327) ^ [_920577, _920579, _920581, _920583] : [class_Rings_Olinordered__semidom(_920577), hAPP(hAPP(c_Power_Opower__class_Opower(_920577), _920579), hAPP(c_Nat_OSuc, _920581)) = hAPP(hAPP(c_Power_Opower__class_Opower(_920577), _920583), hAPP(c_Nat_OSuc, _920581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920577), c_Groups_Ozero__class_Ozero(_920577)), _920579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920577), c_Groups_Ozero__class_Ozero(_920577)), _920583)), -(_920579 = _920583)], (48550 ^ _779327) ^ [_1751315, _1751317, _1751319] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751315)), hAPP(c_List_Ofilter(_1751315, _1751317), _1751319))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751315)), _1751319))))], (17402 ^ _779327) ^ [_1074745, _1074747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074745), _1074747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1074745)), c_Int_OBit1(_1074747))))], (26683 ^ _779327) ^ [_1249084, _1249086] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1249084), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1249086) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1249084, _1249086))], (38204 ^ _779327) ^ [_1496717, _1496719, _1496721, _1496723, _1496725] : [_1496717 = c_Orderings_Obot__class_Obot(tc_fun(_1496719, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496719, tc_fun(_1496721, tc_HOL_Obool)), _1496717), hAPP(hAPP(c_COMBB(tc_fun(_1496721, tc_HOL_Obool), tc_fun(_1496721, tc_HOL_Obool), _1496719), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1496721, tc_HOL_Obool)), _1496723)), _1496725)) = c_Orderings_Otop__class_Otop(tc_fun(_1496721, tc_HOL_Obool)))], (32376 ^ _779327) ^ [_1367641, _1367643, _1367645] : [class_Orderings_Olinorder(_1367641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1367641, tc_HOL_Obool)), _1367643), _1367645)), -(_1367643 = c_Orderings_Obot__class_Obot(tc_fun(_1367641, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367641), _1367645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367641), c_Big__Operators_Olinorder__class_OMin(_1367641, _1367645)), c_Big__Operators_Olinorder__class_OMin(_1367641, _1367643))))], (15664 ^ _779327) ^ [_1044343, _1044345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1044343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1044345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044345), _1044343)), _1044345)))], (18136 ^ _779327) ^ [_1087290] : [-(c_Int_Opred(c_Int_OBit1(_1087290)) = c_Int_OBit0(_1087290))], (12033 ^ _779327) ^ [_978863, _978865] : [class_Groups_Olinordered__ab__group__add(_978863), 12036 ^ _779327 : [(12043 ^ _779327) ^ [] : [_978865 = c_Groups_Ozero__class_Ozero(_978863), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978863), _978865), _978865) = c_Groups_Ozero__class_Ozero(_978863))], (12037 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978863), _978865), _978865) = c_Groups_Ozero__class_Ozero(_978863), -(_978865 = c_Groups_Ozero__class_Ozero(_978863))]]], (17774 ^ _779327) ^ [_1080665, _1080667] : [class_Int_Onumber__ring(_1080665), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080665), hAPP(c_Int_Onumber__class_Onumber__of(_1080665), _1080667)), c_Groups_Oone__class_Oone(_1080665)) = hAPP(c_Int_Onumber__class_Onumber__of(_1080665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1080667), c_Int_OBit1(c_Int_OPls))))], (6464 ^ _779327) ^ [_880816, _880818, _880820] : [class_Orderings_Olinorder(_880816), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880816), _880818), _880820))), 6471 ^ _779327 : [(6478 ^ _779327) ^ [] : [_880820 = _880818, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880816), _880820), _880818))], (6472 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880816), _880820), _880818))), -(_880820 = _880818)]]], (52662 ^ _779327) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11573 ^ _779327) ^ [_971045, _971047, _971049, _971051, _971053] : [class_Groups_Oordered__ab__group__add(_971045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971045), _971047), _971049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971045), _971051), _971053), 11580 ^ _779327 : [(11587 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971045), _971051), _971053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971045), _971047), _971049)))], (11581 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971045), _971047), _971049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971045), _971051), _971053)))]]], (38565 ^ _779327) ^ [_1506280, _1506282, _1506284, _1506286, _1506288, _1506290] : [c_Typedef_Otype__definition(_1506280, _1506282, _1506284, _1506286, _1506288), -(hAPP(_1506286, hAPP(_1506284, _1506290)) = _1506290)], (48343 ^ _779327) ^ [_1746034, _1746036, _1746038] : [hBOOL(hAPP(hAPP(c_member(_1746034), _1746036), hAPP(c_List_Oset(_1746034), _1746038))), -(c_List_Oremdups(_1746034, hAPP(hAPP(c_List_Olist_OCons(_1746034), _1746036), _1746038)) = c_List_Oremdups(_1746034, _1746038))], (18138 ^ _779327) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (15586 ^ _779327) ^ [_1042757, _1042759, _1042761] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1042757), _1042759)), _1042761) = 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), _1042757), _1042761)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1042759), _1042761))), 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, _1042757, _1042761)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042759, _1042761))), _1042761)))], (21188 ^ _779327) ^ [_1142914, _1142916] : [class_Rings_Osemiring__1(_1142914), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1142914), _1142916) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1142914, hAPP(hAPP(c_COMBC(_1142914, _1142914, _1142914), c_Groups_Oplus__class_Oplus(_1142914)), c_Groups_Oone__class_Oone(_1142914)), _1142916, c_Groups_Ozero__class_Ozero(_1142914)))], (45512 ^ _779327) ^ [_1681861, _1681863, _1681865] : [-(hAPP(hAPP(c_List_Ozip(_1681861, _1681863), c_List_Olist_ONil(_1681861)), _1681865) = c_List_Olist_ONil(tc_prod(_1681861, _1681863)))], (47654 ^ _779327) ^ [_1730609, _1730611, _1730613, _1730615, _1730617] : [c_List_Opartition(_1730609, _1730611, _1730613) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730609), tc_List_Olist(_1730609)), _1730615), _1730617), 47657 ^ _779327 : [(47664 ^ _779327) ^ [_1730871] : [hBOOL(hAPP(hAPP(c_member(_1730609), _1730871), hAPP(c_List_Oset(_1730609), _1730617))), hBOOL(hAPP(_1730611, _1730871))], (47658 ^ _779327) ^ [_1730762] : [hBOOL(hAPP(hAPP(c_member(_1730609), _1730762), hAPP(c_List_Oset(_1730609), _1730615))), -(hBOOL(hAPP(_1730611, _1730762)))]]], (17978 ^ _779327) ^ [_1084529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084529)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084529), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47998 ^ _779327) ^ [_1738393, _1738395, _1738397, _1738399, _1738401, _1738403, _1738405] : [c_List_Olist__all2(_1738393, _1738395, _1738397, _1738399, _1738401), c_List_Olist__all2(_1738393, _1738395, _1738397, _1738403, _1738405), -(c_List_Olist__all2(_1738393, _1738395, _1738397, hAPP(hAPP(c_List_Oappend(_1738393), _1738399), _1738403), hAPP(hAPP(c_List_Oappend(_1738395), _1738401), _1738405)))], (13088 ^ _779327) ^ [_998052, _998054, _998056] : [class_Groups_Oordered__comm__monoid__add(_998052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998052), _998054), c_Groups_Ozero__class_Ozero(_998052))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998052), _998056), c_Groups_Ozero__class_Ozero(_998052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998052), _998054), _998056)), c_Groups_Ozero__class_Ozero(_998052))))], (47149 ^ _779327) ^ [_1720514] : [-(c_List_Orotate(_1720514, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1720514)))], (1928 ^ _779327) ^ [_806415, _806417] : [-(class_Int_Onumber(_806415)), _806417 = _806415, class_Int_Onumber(_806417)], (37057 ^ _779327) ^ [_1471187, _1471189, _1471191, _1471193, _1471195] : [-(c_Fun_Oinj__on(_1471187, _1471189, _1471191, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471187, tc_HOL_Obool)), _1471193), _1471195))), c_Fun_Oinj__on(_1471187, _1471189, _1471191, _1471193), c_Fun_Oinj__on(_1471187, _1471189, _1471191, _1471195), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471189, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471187, _1471189, _1471191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471187, tc_HOL_Obool)), _1471193), _1471195))), hAPP(c_Set_Oimage(_1471187, _1471189, _1471191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471187, tc_HOL_Obool)), _1471195), _1471193))) = c_Orderings_Obot__class_Obot(tc_fun(_1471189, tc_HOL_Obool))], (27396 ^ _779327) ^ [_1263798, _1263800, _1263802, _1263804] : [class_Orderings_Olinorder(_1263798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263798), _1263800), _1263802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263798), _1263802), _1263804)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263798, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1263798, _1263800), _1263802)), c_SetInterval_Oord__class_OatLeastAtMost(_1263798, _1263802, _1263804)) = c_SetInterval_Oord__class_OatLeastAtMost(_1263798, _1263800, _1263804))], (18855 ^ _779327) ^ [_1100604, _1100606] : [c_Nat__Transfer_Ois__nat(_1100604), c_Nat__Transfer_Ois__nat(_1100606), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100604), _1100606)))], (38139 ^ _779327) ^ [_1494391, _1494393, _1494395, _1494397] : [_1494395 = _1494397, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1494391, _1494393, hAPP(hAPP(c_Set_Oinsert(_1494391), _1494395), c_Orderings_Obot__class_Obot(tc_fun(_1494391, tc_HOL_Obool)))), _1494397)))], (5008 ^ _779327) ^ [_855654, _855656] : [_855656 = _855654, -(c_Nat_Osize__class_Osize(_855656) = c_Nat_Osize__class_Osize(_855654))], (6084 ^ _779327) ^ [_875130, _875132, _875134, _875136] : [class_Orderings_Oorder(_875130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875130), _875132), _875134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875130), _875136), _875132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875130), _875136), _875134)))], (53114 ^ _779327) ^ [_1841912] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _1841912), v_ts)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_n), _1841912))], (46267 ^ _779327) ^ [_1700093, _1700095, _1700097, _1700099] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700093)), hAPP(hAPP(c_List_Oappend(_1700093), _1700095), _1700097)), c_List_Olists(_1700093, _1700099)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700093)), _1700095), c_List_Olists(_1700093, _1700099))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700093)), _1700097), c_List_Olists(_1700093, _1700099)))], (4652 ^ _779327) ^ [_850224, _850226, _850228, _850230] : [-(c_Lazy__Sequence_Osmall__lazy_H(_850230, _850226) = c_Lazy__Sequence_Osmall__lazy_H(_850228, _850224)), _850230 = _850228, _850226 = _850224], (43600 ^ _779327) ^ [_1632826, _1632828] : [class_Complete__Lattice_Ocomplete__lattice(_1632826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632826), _1632828)), -(c_Complete__Lattice_OInf__class_OInf(_1632826, _1632828) = hAPP(hAPP(c_Finite__Set_Ofold(_1632826, _1632826, c_Lattices_Osemilattice__inf__class_Oinf(_1632826)), c_Orderings_Otop__class_Otop(_1632826)), _1632828))], (35511 ^ _779327) ^ [_1436437, _1436439, _1436441, _1436443] : [class_Orderings_Olinorder(_1436437), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436437, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1436437, _1436439, _1436441)), hAPP(c_SetInterval_Oord__class_OatMost(_1436437), _1436443)) = c_SetInterval_Oord__class_OatLeastAtMost(_1436437, _1436439, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1436437), _1436441), _1436443)))], (9120 ^ _779327) ^ [_926675, _926677, _926679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926675, tc_HOL_Obool)), _926677), _926679)), 9123 ^ _779327 : [(9126 ^ _779327) ^ [] : [_926677 = _926679], (9124 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926675, tc_HOL_Obool)), _926677), _926679)))]]], (37681 ^ _779327) ^ [_1484852, _1484854] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1484852, _1484854)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1484852, _1484854), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484852), c_Orderings_Otop__class_Otop(tc_fun(_1484852, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484854), c_Orderings_Otop__class_Otop(tc_fun(_1484854, tc_HOL_Obool))))], (18322 ^ _779327) ^ [] : [-(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))))))], (17846 ^ _779327) ^ [_1082171, _1082173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082171), 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)))), _1082173))), 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)))), _1082171)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1082173), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1082171))], (33618 ^ _779327) ^ [] : [-(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)))], (42892 ^ _779327) ^ [_1617095, _1617097, _1617099] : [42893 ^ _779327 : [(42894 ^ _779327) ^ [_1617171] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617095, _1617095)), _1617097), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617095, _1617095), tc_HOL_Obool), _1617171), _1617099)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617095, _1617095)), _1617097), c_Transitive__Closure_Ortrancl(_1617095, _1617099))))], (43758 ^ _779327) ^ [_1636157, _1636159, _1636161] : [class_Complete__Lattice_Ocomplete__lattice(_1636157), -(c_Complete__Lattice_OInf__class_OInf(_1636157, hAPP(hAPP(c_Set_Oinsert(_1636157), _1636159), hAPP(hAPP(c_Set_Oinsert(_1636157), _1636161), c_Orderings_Obot__class_Obot(tc_fun(_1636157, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1636157), _1636159), _1636161))], (46074 ^ _779327) ^ [_1696041, _1696043, _1696045, _1696047] : [_1696043 = c_List_Olist_ONil(_1696041), -(hAPP(hAPP(c_List_Olist__update(_1696041, _1696043), _1696045), _1696047) = c_List_Olist_ONil(_1696041))], (13122 ^ _779327) ^ [_998638, _998640, _998642, _998644, _998646] : [class_Groups_Oordered__cancel__ab__semigroup__add(_998638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998638), _998640), _998642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998638), _998644), _998646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998638), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998638), _998640), _998644)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998638), _998642), _998646))))], (44692 ^ _779327) ^ [_1660001, _1660003, _1660005, _1660007] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1660001), tc_List_Olist(_1660001), c_List_Olistrel(_1660001, _1660003)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1660001)), hAPP(hAPP(c_List_Olist_OCons(_1660001), _1660005), _1660007)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1660001), tc_HOL_Obool)))) = c_List_Oset__Cons(_1660001, hAPP(c_Relation_OImage(_1660001, _1660001, _1660003), hAPP(hAPP(c_Set_Oinsert(_1660001), _1660005), c_Orderings_Obot__class_Obot(tc_fun(_1660001, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1660001), tc_List_Olist(_1660001), c_List_Olistrel(_1660001, _1660003)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1660001)), _1660007), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1660001), tc_HOL_Obool))))))], (43754 ^ _779327) ^ [_1635948, _1635950, _1635952, _1635954, _1635956] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635948, tc_fun(_1635950, tc_HOL_Obool)), _1635952), hAPP(hAPP(c_COMBS(_1635948, tc_fun(_1635950, tc_HOL_Obool), tc_fun(_1635950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1635950, tc_HOL_Obool), tc_fun(tc_fun(_1635950, tc_HOL_Obool), tc_fun(_1635950, tc_HOL_Obool)), _1635948), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635950, tc_HOL_Obool))), _1635954)), _1635956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635950, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635950, tc_HOL_Obool), hAPP(c_Set_Oimage(_1635948, tc_fun(_1635950, tc_HOL_Obool), _1635954), _1635952))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635950, tc_HOL_Obool), hAPP(c_Set_Oimage(_1635948, tc_fun(_1635950, tc_HOL_Obool), _1635956), _1635952))))], (8948 ^ _779327) ^ [_923465] : [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), _923465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _923465)))], (51271 ^ _779327) ^ [_1809130, _1809132, _1809134] : [-(hAPP(c_List_Oset(_1809130), c_List_Oreplicate(_1809130, hAPP(c_Nat_OSuc, _1809132), _1809134)) = hAPP(hAPP(c_Set_Oinsert(_1809130), _1809134), c_Orderings_Obot__class_Obot(tc_fun(_1809130, tc_HOL_Obool))))], (52159 ^ _779327) ^ [_1829252, _1829254, _1829256] : [c_Relation_Osym(_1829252, _1829254), c_Relation_Osym(_1829252, _1829256), -(c_Relation_Osym(_1829252, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1829252, _1829252), tc_HOL_Obool)), _1829254), _1829256)))], (914 ^ _779327) ^ [_793290, _793292, _793294, _793296, _793298, _793300] : [-(c_List_Olist__ex(_793298, _793294, _793290)), c_List_Olist__ex(_793300, _793296, _793292), _793300 = _793298, _793296 = _793294, _793292 = _793290], (494 ^ _779327) ^ [_786910, _786912] : [-(c_Nitpick_Ounknown(_786910)), _786912 = _786910, c_Nitpick_Ounknown(_786912)], (5268 ^ _779327) ^ [_859742, _859744, _859746, _859748] : [-(c_Relation_Oinv__image(_859748, _859744) = c_Relation_Oinv__image(_859746, _859742)), _859748 = _859746, _859744 = _859742], (17946 ^ _779327) ^ [_1084002] : [c_Int_OPls = c_Int_OBit0(_1084002), -(c_Int_OPls = _1084002)], (45333 ^ _779327) ^ [_1676858, _1676860, _1676862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676858), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676860)), _1676862))), -(hBOOL(hAPP(hAPP(c_member(_1676860), hAPP(hAPP(c_List_Onth(_1676860), _1676862), _1676858)), hAPP(c_List_Oset(_1676860), _1676862))))], (16483 ^ _779327) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (38892 ^ _779327) ^ [_1514865, _1514867, _1514869, _1514871] : [c_Finite__Set_Ofolding__one(_1514865, _1514867, _1514869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514865), _1514871)), -(hAPP(_1514869, _1514871) = hAPP(c_Finite__Set_Ofold1(_1514865, _1514867), _1514871))], (51043 ^ _779327) ^ [_1804297, _1804299, _1804301] : [_1804299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1804297, _1804299, _1804301) = c_List_Olist_ONil(_1804297))], (6733 ^ _779327) ^ [_884804, _884806, _884808] : [class_Orderings_Olinorder(_884804), 6736 ^ _779327 : [(6737 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884804), _884806), _884808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884804), _884808), _884806))), -(_884806 = _884808)], (6747 ^ _779327) ^ [] : [6748 ^ _779327 : [(6751 ^ _779327) ^ [] : [_884806 = _884808], (6749 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884804), _884808), _884806))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884804), _884806), _884808))]]], (47873 ^ _779327) ^ [_1735644, _1735646, _1735648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1735644, tc_HOL_Obool)), _1735646), _1735648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1735644), tc_HOL_Obool)), c_List_Olistsp(_1735644, _1735646)), c_List_Olistsp(_1735644, _1735648))))], (48826 ^ _779327) ^ [_1758116, _1758118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758116)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758118))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758116), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758118)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758116)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758116)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758118))))], (14515 ^ _779327) ^ [_1024023] : [class_Rings_Osemiring__1(_1024023), c_Int_Oiszero(_1024023, c_Groups_Oone__class_Oone(_1024023))], (30055 ^ _779327) ^ [_1318280, _1318282, _1318284, _1318286, _1318288, _1318290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1318280, _1318282)), hAPP(hAPP(c_Product__Type_OPair(_1318280, _1318282), _1318288), _1318290)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool)), _1318284), _1318286))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318280, tc_fun(_1318282, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1318280, tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_fun(_1318282, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1318282, tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_fun(_1318282, tc_HOL_Obool)), _1318280), c_COMBC(_1318282, tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1318282, tc_prod(_1318280, _1318282)), tc_fun(_1318282, tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), _1318280), hAPP(c_COMBB(tc_prod(_1318280, _1318282), tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool), _1318282), c_member(tc_prod(_1318280, _1318282)))), c_Product__Type_OPair(_1318280, _1318282)))), _1318284)), hAPP(hAPP(c_COMBC(_1318280, tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_fun(_1318282, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1318282, tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_fun(_1318282, tc_HOL_Obool)), _1318280), c_COMBC(_1318282, tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1318282, tc_prod(_1318280, _1318282)), tc_fun(_1318282, tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool)), _1318280), hAPP(c_COMBB(tc_prod(_1318280, _1318282), tc_fun(tc_fun(tc_prod(_1318280, _1318282), tc_HOL_Obool), tc_HOL_Obool), _1318282), c_member(tc_prod(_1318280, _1318282)))), c_Product__Type_OPair(_1318280, _1318282)))), _1318286)), _1318288), _1318290)))], (44638 ^ _779327) ^ [_1658299, _1658301, _1658303, _1658305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658299), tc_List_Olist(_1658299))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658299), tc_List_Olist(_1658299)), _1658301), _1658303)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1658299), c_List_Olistrel1(_1658299, _1658305)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658299)), _1658301) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658299)), _1658303))], (28834 ^ _779327) ^ [_1293328, _1293330, _1293332] : [class_Groups_Ocomm__monoid__add(_1293328), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293330, _1293328), _1293332), c_Orderings_Obot__class_Obot(tc_fun(_1293330, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1293328))], (12501 ^ _779327) ^ [_987690, _987692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987692), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987690), _987692))), -(_987690 = _987692)], (18056 ^ _779327) ^ [_1085866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085866))))], (27691 ^ _779327) ^ [_1271069] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1271069)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1271069))], (33078 ^ _779327) ^ [_1381405, _1381407, _1381409] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381405, tc_Nat_Onat), _1381407), _1381409) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381405, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1381405), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1381407)), _1381409)))], (37213 ^ _779327) ^ [_1474680, _1474682, _1474684, _1474686] : [c_Fun_Oinj__on(_1474680, _1474682, _1474684, _1474686), -(hAPP(c_Set_Oimage(_1474682, _1474680, c_Fun_Othe__inv__into(_1474680, _1474682, _1474686, _1474684)), hAPP(c_Set_Oimage(_1474680, _1474682, _1474684), _1474686)) = _1474686)], (39509 ^ _779327) ^ [_1528290, _1528292, _1528294, _1528296, _1528298, _1528300, _1528302, _1528304, _1528306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528290, _1528292)), hAPP(hAPP(c_Product__Type_OPair(_1528290, _1528292), _1528294), _1528296)), _1528298)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528300, _1528302)), hAPP(hAPP(c_Product__Type_OPair(_1528300, _1528302), hAPP(_1528304, _1528294)), hAPP(_1528306, _1528296))), hAPP(c_Set_Oimage(tc_prod(_1528290, _1528292), tc_prod(_1528300, _1528302), c_Product__Type_Omap__pair(_1528290, _1528300, _1528292, _1528302, _1528304, _1528306)), _1528298))))], (15351 ^ _779327) ^ [_1038326, _1038328, _1038330, _1038332] : [class_Divides_Osemiring__div(_1038326), -(c_Divides_Odiv__class_Omod(_1038326, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038326), _1038328), _1038330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038326), _1038328), _1038332)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038326), _1038328), c_Divides_Odiv__class_Omod(_1038326, _1038330, _1038332)))], (22669 ^ _779327) ^ [_1171768, _1171770] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1171768, _1171770) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1171768, _1171770)))], (24779 ^ _779327) ^ [_1210913, _1210915, _1210917] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210913), _1210915)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210913), _1210917))), -(_1210913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210915), _1210917)))], (22647 ^ _779327) ^ [_1171339, _1171341, _1171343] : [class_Int_Onumber(_1171339), class_Orderings_Oord(_1171339), 22654 ^ _779327 : [(22661 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171339), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171341)), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171343)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171339), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171341)), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171343)) = hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171343))], (22655 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171339), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171341)), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171343))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171339), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171341)), hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171343)) = hAPP(c_Int_Onumber__class_Onumber__of(_1171339), _1171341))]]], (35613 ^ _779327) ^ [_1438814, _1438816, _1438818, _1438820, _1438822] : [class_Groups_Ocomm__monoid__mult(_1438814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438816), _1438818)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438816), _1438820)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438816, _1438814), _1438822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438816, tc_HOL_Obool)), _1438818), _1438820))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438816, _1438814), _1438822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438816, tc_HOL_Obool)), _1438818), _1438820))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438816, _1438814), _1438822), _1438818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438816, _1438814), _1438822), _1438820)))], (34629 ^ _779327) ^ [_1416751, _1416753, _1416755, _1416757, _1416759, _1416761, _1416763] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416751, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416753, tc_fun(_1416751, tc_HOL_Obool)), _1416755), _1416757)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416759, tc_fun(_1416751, tc_HOL_Obool)), _1416761), _1416763)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416753, tc_fun(_1416751, tc_HOL_Obool)), _1416755), hAPP(hAPP(c_COMBB(tc_fun(_1416759, tc_fun(_1416751, tc_HOL_Obool)), tc_fun(_1416751, tc_HOL_Obool), _1416753), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416759, tc_fun(_1416751, tc_HOL_Obool)), _1416761)), hAPP(hAPP(c_COMBC(_1416753, tc_fun(_1416759, tc_fun(_1416751, tc_HOL_Obool)), tc_fun(_1416759, tc_fun(_1416751, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1416751, tc_HOL_Obool), tc_fun(_1416751, tc_HOL_Obool)), tc_fun(tc_fun(_1416759, tc_fun(_1416751, tc_HOL_Obool)), tc_fun(_1416759, tc_fun(_1416751, tc_HOL_Obool))), _1416753), c_COMBB(tc_fun(_1416751, tc_HOL_Obool), tc_fun(_1416751, tc_HOL_Obool), _1416759)), hAPP(hAPP(c_COMBB(tc_fun(_1416751, tc_HOL_Obool), tc_fun(tc_fun(_1416751, tc_HOL_Obool), tc_fun(_1416751, tc_HOL_Obool)), _1416753), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416751, tc_HOL_Obool))), _1416757))), _1416763))))], (36104 ^ _779327) ^ [_1449567, _1449569, _1449571, _1449573, _1449575, _1449577, _1449579, _1449581, _1449583] : [c_Equiv__Relations_Oequiv(_1449567, _1449569, _1449571), c_Equiv__Relations_Oequiv(_1449573, _1449575, _1449577), c_Equiv__Relations_Ocongruent2(_1449567, _1449573, tc_fun(_1449579, tc_HOL_Obool), _1449571, _1449577, _1449581), hBOOL(hAPP(hAPP(c_member(_1449573), _1449583), _1449575)), -(c_Equiv__Relations_Ocongruent(_1449567, tc_fun(_1449579, tc_HOL_Obool), _1449571, hAPP(hAPP(c_COMBB(tc_fun(_1449573, tc_fun(_1449579, tc_HOL_Obool)), tc_fun(_1449579, tc_HOL_Obool), _1449567), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449573, tc_fun(_1449579, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1449573, _1449573, _1449577), hAPP(hAPP(c_Set_Oinsert(_1449573), _1449583), c_Orderings_Obot__class_Obot(tc_fun(_1449573, tc_HOL_Obool)))))), _1449581)))], (28626 ^ _779327) ^ [_1289427, _1289429, _1289431, _1289433] : [c_Orderings_Obot__class_Obot(tc_fun(_1289427, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1289429, _1289427, _1289431), _1289433), -(_1289433 = c_Orderings_Obot__class_Obot(tc_fun(_1289429, tc_HOL_Obool)))], (12934 ^ _779327) ^ [_995476] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _995476) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _995476))], (20973 ^ _779327) ^ [_1138583] : [c_Code__Numeral_OSuc__code__numeral(_1138583) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (52540 ^ _779327) ^ [_1835908, _1835910] : [class_Groups_Ominus(_1835908), -(class_Groups_Ominus(tc_fun(_1835910, _1835908)))], (39786 ^ _779327) ^ [_1534331, _1534333, _1534335] : [hBOOL(hAPP(hAPP(c_member(_1534331), _1534333), hAPP(c_Set_OCollect(_1534331), _1534335))), -(hBOOL(hAPP(_1534335, _1534333)))], (38714 ^ _779327) ^ [_1509904, _1509906, _1509908] : [class_Groups_Oab__semigroup__mult(_1509904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509904), _1509906)), -(_1509906 = c_Orderings_Obot__class_Obot(tc_fun(_1509904, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509904), _1509908)), -(_1509908 = c_Orderings_Obot__class_Obot(tc_fun(_1509904, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509904, tc_HOL_Obool)), _1509906), _1509908) = c_Orderings_Obot__class_Obot(tc_fun(_1509904, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1509904, c_Groups_Otimes__class_Otimes(_1509904)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509904, tc_HOL_Obool)), _1509906), _1509908)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1509904), hAPP(c_Finite__Set_Ofold1(_1509904, c_Groups_Otimes__class_Otimes(_1509904)), _1509906)), hAPP(c_Finite__Set_Ofold1(_1509904, c_Groups_Otimes__class_Otimes(_1509904)), _1509908)))], (20077 ^ _779327) ^ [_1121690, _1121692] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121690), _1121692), hAPP(c_Int_Onumber__class_Onumber__of(_1121690), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1121690)), class_Fields_Ofield__inverse__zero(_1121690), class_Int_Onumber__ring(_1121690)], (16067 ^ _779327) ^ [_1051295, _1051297, _1051299, _1051301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051297), _1051299)), -(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), _1051299), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1051301, _1051295))), _1051297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051299), _1051295))))], (23185 ^ _779327) ^ [_1181869, _1181871, _1181873, _1181875, _1181877, _1181879, _1181881] : [-(hAPP(c_Product__Type_Oapfst(_1181869, _1181871, _1181873, _1181875), hAPP(c_Product__Type_Oapsnd(_1181877, _1181873, _1181869, _1181879), _1181881)) = hAPP(hAPP(c_Product__Type_OPair(_1181871, _1181873), hAPP(_1181875, hAPP(c_Product__Type_Ofst(_1181869, _1181877), _1181881))), hAPP(_1181879, hAPP(c_Product__Type_Osnd(_1181869, _1181877), _1181881))))], (23540 ^ _779327) ^ [_1189108, _1189110, _1189112, _1189114] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1189108, _1189110)), c_Nitpick_Opair__box_OPairBox(_1189108, _1189110, _1189112, _1189114)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46146 ^ _779327) ^ [_1697316, _1697318] : [-(hAPP(hAPP(c_List_Oappend(_1697316), _1697318), c_List_Olist_ONil(_1697316)) = _1697318)], (32078 ^ _779327) ^ [_1361898, _1361900, _1361902] : [class_Lattices_Olattice(_1361898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361898), _1361900)), -(_1361900 = c_Orderings_Obot__class_Obot(tc_fun(_1361898, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361898), _1361902)), -(_1361902 = c_Orderings_Obot__class_Obot(tc_fun(_1361898, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1361898, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361898, tc_HOL_Obool)), _1361900), _1361902)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1361898), c_Big__Operators_Olattice__class_OSup__fin(_1361898, _1361900)), c_Big__Operators_Olattice__class_OSup__fin(_1361898, _1361902)))], (38531 ^ _779327) ^ [_1505682, _1505684, _1505686, _1505688, _1505690] : [c_Typedef_Otype__definition(_1505682, _1505684, _1505686, _1505688, _1505690), -(hAPP(c_Set_Oimage(_1505682, _1505684, _1505686), c_Orderings_Otop__class_Otop(tc_fun(_1505682, tc_HOL_Obool))) = _1505690)], (21474 ^ _779327) ^ [_1148803, _1148805, _1148807] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1148803, _1148805), _1148807)), 21477 ^ _779327 : [(21478 ^ _779327) ^ [_1148888] : [hBOOL(hAPP(hAPP(_1148805, _1148888), _1148807)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1148803, _1148805), _1148888)))]]], (19119 ^ _779327) ^ [_1105134, _1105136, _1105138] : [class_Fields_Olinordered__field__inverse__zero(_1105134), 19122 ^ _779327 : [(19137 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105134), _1105136), _1105138)))), 19138 ^ _779327 : [(19145 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), _1105136), c_Groups_Ozero__class_Ozero(_1105134))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), _1105138), c_Groups_Ozero__class_Ozero(_1105134)))], (19139 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), _1105136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), _1105138))]]], (19123 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105134), _1105136), _1105138))), 19128 ^ _779327 : [(19131 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), _1105138)))], (19129 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), c_Groups_Ozero__class_Ozero(_1105134)), _1105136)))]], 19132 ^ _779327 : [(19135 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), _1105138), c_Groups_Ozero__class_Ozero(_1105134))))], (19133 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105134), _1105136), c_Groups_Ozero__class_Ozero(_1105134))))]]]]], (52864 ^ _779327) ^ [_1839002] : [class_Finite__Set_Ofinite(_1839002), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1839002)))], (9765 ^ _779327) ^ [_937595, _937597] : [class_Rings_Ocomm__semiring__1(_937595), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937595), _937597), c_Groups_Oone__class_Oone(_937595)) = _937597)], (1388 ^ _779327) ^ [_799665, _799667] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799665)), _799667 = _799665, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799667)], (25668 ^ _779327) ^ [_1228925, _1228927, _1228929, _1228931, _1228933] : [class_Orderings_Olinorder(_1228925), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1228925, _1228927), _1228929) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1228925, _1228931), _1228933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228925), _1228927), _1228929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228925), _1228931), _1228933)), -(_1228927 = _1228931)], (26814 ^ _779327) ^ [_1251680, _1251682, _1251684, _1251686] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251680, tc_HOL_Obool)), _1251682), _1251684), _1251686)), -(hBOOL(hAPP(_1251682, _1251686))), -(hBOOL(hAPP(_1251684, _1251686)))], (29000 ^ _779327) ^ [_1296140] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1296140), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (10821 ^ _779327) ^ [_955618, _955620, _955622] : [class_Int_Onumber__ring(_955618), -(hAPP(c_Int_Onumber__class_Onumber__of(_955618), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955620), _955622)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955618), hAPP(c_Int_Onumber__class_Onumber__of(_955618), _955620)), hAPP(c_Int_Onumber__class_Onumber__of(_955618), _955622)))], (26290 ^ _779327) ^ [_1241742, _1241744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1241742), _1241744)), -(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)), _1241742)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241744))))], (50923 ^ _779327) ^ [_1801814, _1801816, _1801818, _1801820] : [-(c_List_Olist__ex1(_1801814, _1801816, hAPP(hAPP(c_List_Olist_OCons(_1801814), _1801818), _1801820))), 50926 ^ _779327 : [(50929 ^ _779327) ^ [] : [c_List_Olist__all(_1801814, hAPP(hAPP(c_COMBS(_1801814, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801814), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1801814), c_fNot), _1801816))), hAPP(c_fequal, _1801818)), _1801820)], (50927 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1801816, _1801818)))]], 50930 ^ _779327 : [(50933 ^ _779327) ^ [] : [c_List_Olist__ex1(_1801814, _1801816, _1801820)], (50931 ^ _779327) ^ [] : [hBOOL(hAPP(_1801816, _1801818))]]], (34931 ^ _779327) ^ [_1423128, _1423130, _1423132] : [class_Lattices_Osemilattice__inf(_1423128), 34934 ^ _779327 : [(34941 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423128), _1423130), _1423132) = _1423130, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423128), _1423130), _1423132)))], (34935 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423128), _1423130), _1423132)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423128), _1423130), _1423132) = _1423130)]]], (45647 ^ _779327) ^ [_1685717, _1685719, _1685721, _1685723, _1685725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685717), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685719)), _1685721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685717), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685723)), _1685725))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1685719, _1685723)), hAPP(hAPP(c_List_Ozip(_1685719, _1685723), _1685721), _1685725)), _1685717) = hAPP(hAPP(c_Product__Type_OPair(_1685719, _1685723), hAPP(hAPP(c_List_Onth(_1685719), _1685721), _1685717)), hAPP(hAPP(c_List_Onth(_1685723), _1685725), _1685717)))], (16333 ^ _779327) ^ [_1056161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056161), 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), _1056161)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (45715 ^ _779327) ^ [_1687358] : [class_Groups_Omonoid__add(_1687358), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687358), c_List_Olist_ONil(_1687358)) = c_Groups_Ozero__class_Ozero(_1687358))], (40394 ^ _779327) ^ [_1556242, _1556244, _1556246, _1556248, _1556250, _1556252, _1556254] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556242, _1556244, _1556246), _1556248), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1556250, tc_fun(tc_prod(_1556244, _1556246), tc_HOL_Obool)), _1556252), _1556254)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1556250, tc_fun(tc_prod(_1556242, _1556246), tc_HOL_Obool)), _1556252), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1556244, _1556246), tc_HOL_Obool), tc_fun(tc_prod(_1556242, _1556246), tc_HOL_Obool), _1556250), hAPP(c_Relation_Orel__comp(_1556242, _1556244, _1556246), _1556248)), _1556254)))], (44130 ^ _779327) ^ [_1644701, _1644703, _1644705, _1644707] : [class_Orderings_Olinorder(_1644701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1644701), _1644703)), 44140 ^ _779327 : [(44143 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644701), 44139 ^ [_1644701, _1644703, _1644705, _1644707]), _1644705))], (44141 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644701), 44139 ^ [_1644701, _1644703, _1644705, _1644707]), _1644703)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1644701), hAPP(hAPP(c_Finite__Set_Ofold(_1644701, _1644701, c_Orderings_Oord__class_Omax(_1644701)), _1644707), _1644703)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1644701), _1644705), _1644707))))], (47239 ^ _779327) ^ [_1722519, _1722521, _1722523, _1722525] : [47240 ^ _779327 : [(47241 ^ _779327) ^ [_1722616, _1722618] : [_1722519 = hAPP(hAPP(c_List_Olist_OCons(_1722521), _1722618), _1722616)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1722521), tc_List_Olist(_1722521))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722521), tc_List_Olist(_1722521)), _1722523), hAPP(hAPP(c_List_Oappend(_1722521), _1722523), _1722519))), c_List_Olexord(_1722521, _1722525))))], (45108 ^ _779327) ^ [_1671706, _1671708, _1671710, _1671712, _1671714] : [hAPP(hAPP(c_List_Omap(_1671706, _1671708), _1671710), _1671712) = hAPP(hAPP(c_List_Omap(_1671706, _1671708), _1671714), _1671712), 45111 ^ _779327 : [(45112 ^ _779327) ^ [_1671829] : [hBOOL(hAPP(hAPP(c_member(_1671706), _1671829), hAPP(c_List_Oset(_1671706), _1671712))), -(hAPP(_1671710, _1671829) = hAPP(_1671714, _1671829))]]], (35051 ^ _779327) ^ [_1425813, _1425815, _1425817, _1425819] : [class_Lattices_Odistrib__lattice(_1425813), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425813), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425813), _1425815), _1425817)), _1425819) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425813), _1425815), _1425819)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425813), _1425817), _1425819)))], (23404 ^ _779327) ^ [_1185857, _1185859, _1185861, _1185863, _1185865, _1185867] : [hBOOL(hAPP(hAPP(_1185857, _1185859), _1185861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1185863, tc_fun(_1185865, tc_HOL_Obool))), _1185857), _1185867)), -(hBOOL(hAPP(hAPP(_1185867, _1185859), _1185861)))], (29170 ^ _779327) ^ [_1299324, _1299326, _1299328, _1299330, _1299332] : [-(_1299324 = c_Orderings_Obot__class_Obot(tc_fun(_1299326, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299326, tc_fun(_1299328, tc_HOL_Obool)), _1299324), hAPP(hAPP(c_COMBB(tc_fun(_1299328, tc_HOL_Obool), tc_fun(_1299328, tc_HOL_Obool), _1299326), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299328, tc_HOL_Obool)), _1299330)), _1299332)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299328, tc_HOL_Obool)), _1299330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299326, tc_fun(_1299328, tc_HOL_Obool)), _1299324), _1299332)))], (11233 ^ _779327) ^ [_963552, _963554, _963556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963552), _963554)), 11236 ^ _779327 : [(11243 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963556), _963552)), _963554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963554), _963552))))], (11237 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963554), _963552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963556), _963552)), _963554)))]]], (36867 ^ _779327) ^ [_1467267, _1467269, _1467271, _1467273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467267), hAPP(c_Set_Oimage(_1467269, _1467267, _1467271), _1467273))), c_Fun_Oinj__on(_1467269, _1467267, _1467271, _1467273), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467269), _1467273)))], (29877 ^ _779327) ^ [_1313369, _1313371, _1313373, _1313375] : [_1313369 = _1313371, 29880 ^ _779327 : [(29887 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313373), _1313371), _1313375)), -(hBOOL(hAPP(hAPP(c_member(_1313373), _1313369), _1313375)))], (29881 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313373), _1313369), _1313375)), -(hBOOL(hAPP(hAPP(c_member(_1313373), _1313371), _1313375)))]]], (26424 ^ _779327) ^ [_1244522, _1244524, _1244526] : [-(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)), _1244522)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1244524, _1244526)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244524), _1244522), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244526), _1244522)))], (48661 ^ _779327) ^ [_1753806, _1753808] : [48663 ^ _779327 : [(48666 ^ _779327) ^ [] : [48662 ^ [_1753806, _1753808] = c_List_Olist_ONil(_1753806)], (48664 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753806)), 48662 ^ [_1753806, _1753808]), hAPP(c_List_Oset(tc_List_Olist(_1753806)), _1753808))))]], -(c_List_Otranspose(_1753806, _1753808) = c_List_Olist_ONil(tc_List_Olist(_1753806)))], (41267 ^ _779327) ^ [_1578442, _1578444, _1578446, _1578448, _1578450, _1578452, _1578454] : [-(hAPP(c_Fun_Ocomp(_1578442, _1578444, _1578446, _1578448), c_Fun_Ofun__upd(_1578446, _1578442, _1578450, _1578452, _1578454)) = c_Fun_Ofun__upd(_1578446, _1578444, hAPP(c_Fun_Ocomp(_1578442, _1578444, _1578446, _1578448), _1578450), _1578452, hAPP(_1578448, _1578454)))], (5806 ^ _779327) ^ [_871017, _871019] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871017), _871019))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871017), _871019)), -(_871017 = _871019)], (12135 ^ _779327) ^ [_980769, _980771, _980773, _980775] : [class_Rings_Ocomm__semiring(_980769), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980769), _980771), _980773)), _980775) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980769), _980771), _980775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980769), _980773), _980775)))], (38982 ^ _779327) ^ [_1516731, _1516733] : [class_Lattices_Olattice(_1516731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516731), _1516733)), -(c_Big__Operators_Olattice__class_OInf__fin(_1516731, _1516733) = hAPP(c_Finite__Set_Ofold1(_1516731, c_Lattices_Osemilattice__inf__class_Oinf(_1516731)), _1516733))], (46828 ^ _779327) ^ [_1713739, _1713741, _1713743] : [-(_1713739 = c_List_Olist_ONil(_1713741)), -(hAPP(c_List_Otl(_1713741), hAPP(hAPP(c_List_Oappend(_1713741), _1713739), _1713743)) = hAPP(hAPP(c_List_Oappend(_1713741), hAPP(c_List_Otl(_1713741), _1713739)), _1713743))], (42158 ^ _779327) ^ [_1598610, _1598612, _1598614, _1598616] : [-(c_Transitive__Closure_Otrancl(_1598610, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1598610, _1598610)), hAPP(hAPP(c_Product__Type_OPair(_1598610, _1598610), _1598612), _1598614)), _1598616)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1598610, _1598616)), hAPP(c_Set_OCollect(tc_prod(_1598610, _1598610)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598610, _1598610, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1598610, tc_fun(_1598610, tc_HOL_Obool), tc_fun(_1598610, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1598610, tc_HOL_Obool), tc_fun(_1598610, tc_HOL_Obool)), _1598610), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1598610)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1598610), c_fconj), hAPP(hAPP(c_COMBC(_1598610, tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1598610, _1598610), tc_fun(tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool), tc_HOL_Obool), _1598610), c_member(tc_prod(_1598610, _1598610))), hAPP(hAPP(c_COMBC(_1598610, _1598610, tc_prod(_1598610, _1598610)), c_Product__Type_OPair(_1598610, _1598610)), _1598612))), c_Transitive__Closure_Ortrancl(_1598610, _1598616))))), hAPP(hAPP(c_COMBC(_1598610, tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1598610, _1598610), tc_fun(tc_fun(tc_prod(_1598610, _1598610), tc_HOL_Obool), tc_HOL_Obool), _1598610), c_member(tc_prod(_1598610, _1598610))), hAPP(c_Product__Type_OPair(_1598610, _1598610), _1598614))), c_Transitive__Closure_Ortrancl(_1598610, _1598616)))))))], (45584 ^ _779327) ^ [_1684040, _1684042, _1684044] : [_1684040 = _1684042, 45587 ^ _779327 : [(45590 ^ _779327) ^ [_1684196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1684044, _1684044)), _1684196), hAPP(c_List_Oset(tc_prod(_1684044, _1684044)), hAPP(hAPP(c_List_Ozip(_1684044, _1684044), _1684040), _1684042)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1684044, _1684044, tc_HOL_Obool), c_fequal), _1684196)))], (45588 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684044)), _1684040) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684044)), _1684042))]]], (9665 ^ _779327) ^ [_936000, _936002, _936004, _936006] : [class_Rings_Olinordered__semidom(_936000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936002), _936004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936000), c_Groups_Ozero__class_Ozero(_936000)), _936006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936000), _936006), c_Groups_Oone__class_Oone(_936000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936000), hAPP(hAPP(c_Power_Opower__class_Opower(_936000), _936006), _936004)), hAPP(hAPP(c_Power_Opower__class_Opower(_936000), _936006), _936002))))], (38816 ^ _779327) ^ [_1512728, _1512730, _1512732, _1512734, _1512736] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512728, _1512730), _1512732), hAPP(hAPP(c_COMBS(_1512728, tc_fun(_1512730, tc_HOL_Obool), tc_fun(_1512730, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512730, tc_HOL_Obool), tc_fun(tc_fun(_1512730, tc_HOL_Obool), tc_fun(_1512730, tc_HOL_Obool)), _1512728), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512730, tc_HOL_Obool))), _1512734)), _1512736)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512728, _1512730), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512728, _1512730), _1512732), _1512734)), hAPP(hAPP(c_Product__Type_OSigma(_1512728, _1512730), _1512732), _1512736)))], (5024 ^ _779327) ^ [_855888, _855890] : [_855890 = _855888, -(c_Groups_Ozero__class_Ozero(_855890) = c_Groups_Ozero__class_Ozero(_855888))], (22163 ^ _779327) ^ [_1162413, _1162415] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1162413), _1162415) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1162413, _1162415)))], (44795 ^ _779327) ^ [_1663471, _1663473, _1663475, _1663477, _1663479, _1663481] : [c_List_Olistrelp(_1663471, _1663473, hAPP(hAPP(c_List_Olist_OCons(_1663471), _1663475), _1663477), hAPP(hAPP(c_List_Olist_OCons(_1663471), _1663479), _1663481)), 44798 ^ _779327 : [(44801 ^ _779327) ^ [] : [-(c_List_Olistrelp(_1663471, _1663473, _1663477, _1663481))], (44799 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1663473, _1663475), _1663479)))]]], (9985 ^ _779327) ^ [_940991, _940993, _940995] : [class_Rings_Olinordered__semidom(_940991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940991), c_Groups_Oone__class_Oone(_940991)), _940993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940991), c_Groups_Oone__class_Oone(_940991)), _940995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940991), c_Groups_Oone__class_Oone(_940991)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940991), _940993), _940995))))], (52504 ^ _779327) ^ [_1835434, _1835436] : [class_Lattices_Olattice(_1835434), -(class_Lattices_Olattice(tc_fun(_1835436, _1835434)))], (3634 ^ _779327) ^ [_834219, _834221] : [_834221 = _834219, -(c_Equiv__Relations_Oquotient(_834221) = c_Equiv__Relations_Oquotient(_834219))], (8354 ^ _779327) ^ [_912680, _912682, _912684, _912686, _912688] : [class_Rings_Olinordered__semiring__strict(_912680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912680), _912682), _912684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912680), _912686), _912688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912680), c_Groups_Ozero__class_Ozero(_912680)), _912682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912680), c_Groups_Ozero__class_Ozero(_912680)), _912686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912680), _912682), _912686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912680), _912684), _912688))))], (1618 ^ _779327) ^ [_802540, _802542] : [-(class_Groups_Ocancel__ab__semigroup__add(_802540)), _802542 = _802540, class_Groups_Ocancel__ab__semigroup__add(_802542)], (12548 ^ _779327) ^ [_988527, _988529, _988531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988527), _988529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988527), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988529), _988531))))], (46556 ^ _779327) ^ [_1707745, _1707747, _1707749, _1707751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707745), _1707747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1707749, tc_HOL_Obool)), hAPP(c_List_Oset(_1707749), hAPP(hAPP(c_List_Odrop(_1707749), _1707747), _1707751))), hAPP(c_List_Oset(_1707749), hAPP(hAPP(c_List_Odrop(_1707749), _1707745), _1707751)))))], (28598 ^ _779327) ^ [] : [-(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))))], (28760 ^ _779327) ^ [_1292065, _1292067] : [class_Lattices_Obounded__lattice__bot(_1292065), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292065), c_Orderings_Obot__class_Obot(_1292065)), _1292067) = _1292067)], (7067 ^ _779327) ^ [_889888, _889890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889888)), _889890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889888), _889890)))], (36785 ^ _779327) ^ [_1465652, _1465654, _1465656, _1465658, _1465660, _1465662] : [c_Fun_Oinj__on(_1465652, _1465654, _1465656, _1465658), hAPP(_1465656, _1465660) = hAPP(_1465656, _1465662), hBOOL(hAPP(hAPP(c_member(_1465652), _1465660), _1465658)), hBOOL(hAPP(hAPP(c_member(_1465652), _1465662), _1465658)), -(_1465660 = _1465662)], (23275 ^ _779327) ^ [_1183388, _1183390, _1183392, _1183394] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1183388, _1183390, _1183392, tc_prod(_1183390, _1183392)), _1183394), c_Product__Type_OPair(_1183390, _1183392)) = _1183394)], (12511 ^ _779327) ^ [_987808, _987810] : [12512 ^ _779327 : [(12515 ^ _779327) ^ [] : [_987808 = _987810], (12513 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987808), _987810))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987810), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (30759 ^ _779327) ^ [_1335106, _1335108, _1335110, _1335112, _1335114] : [class_Groups_Oab__group__add(_1335106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335108), _1335110)), 30766 ^ _779327 : [(30773 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335108), _1335112), _1335110))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335108, _1335106), _1335114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335108, tc_HOL_Obool)), _1335110), hAPP(hAPP(c_Set_Oinsert(_1335108), _1335112), c_Orderings_Obot__class_Obot(tc_fun(_1335108, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335108, _1335106), _1335114), _1335110))], (30767 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1335108), _1335112), _1335110)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335108, _1335106), _1335114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335108, tc_HOL_Obool)), _1335110), hAPP(hAPP(c_Set_Oinsert(_1335108), _1335112), c_Orderings_Obot__class_Obot(tc_fun(_1335108, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1335106), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1335108, _1335106), _1335114), _1335110)), hAPP(_1335114, _1335112)))]]], (9589 ^ _779327) ^ [_934626, _934628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934626)), 9592 ^ _779327 : [(9599 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934626), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _934626)), _934628)))], (9593 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _934626)), _934628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _934626), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934628))))]]], (52590 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (48734 ^ _779327) ^ [_1756543, _1756545] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1756543, _1756545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1756545), _1756543))], (15842 ^ _779327) ^ [_1047199, _1047201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1047199)), 15845 ^ _779327 : [(15852 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047201), _1047199))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047201), _1047199) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047201), _1047199)), _1047199)))], (15846 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047201), _1047199)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047201), _1047199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (35663 ^ _779327) ^ [_1440205, _1440207, _1440209, _1440211, _1440213] : [c_Equiv__Relations_Oequiv(_1440205, _1440207, _1440209), hBOOL(hAPP(hAPP(c_member(tc_fun(_1440205, tc_HOL_Obool)), _1440211), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1440205), _1440207), _1440209))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1440205, tc_HOL_Obool)), _1440213), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1440205), _1440207), _1440209))), -(_1440211 = _1440213), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440205, tc_HOL_Obool)), _1440211), _1440213) = c_Orderings_Obot__class_Obot(tc_fun(_1440205, tc_HOL_Obool)))], (15580 ^ _779327) ^ [_1042669, _1042671] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042669, _1042671)), _1042671) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36407 ^ _779327) ^ [_1458582, _1458584, _1458586] : [class_Lattices_Olattice(_1458582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458582), _1458584)), hBOOL(hAPP(hAPP(c_member(_1458582), _1458586), _1458584)), 36418 ^ _779327 : [(36425 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1458582, tc_HOL_Obool)), _1458584), hAPP(hAPP(c_Set_Oinsert(_1458582), _1458586), c_Orderings_Obot__class_Obot(tc_fun(_1458582, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1458582, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1458582, _1458584) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1458582), _1458586), c_Big__Operators_Olattice__class_OInf__fin(_1458582, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1458582, tc_HOL_Obool)), _1458584), hAPP(hAPP(c_Set_Oinsert(_1458582), _1458586), c_Orderings_Obot__class_Obot(tc_fun(_1458582, tc_HOL_Obool)))))))], (36419 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1458582, tc_HOL_Obool)), _1458584), hAPP(hAPP(c_Set_Oinsert(_1458582), _1458586), c_Orderings_Obot__class_Obot(tc_fun(_1458582, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1458582, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1458582, _1458584) = _1458586)]]], (38848 ^ _779327) ^ [_1513680, _1513682, _1513684, _1513686, _1513688] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1513680, _1513682), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513680, tc_HOL_Obool)), _1513684), _1513686)), _1513688) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1513680, _1513682), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1513680, _1513682), _1513684), _1513688)), hAPP(hAPP(c_Product__Type_OSigma(_1513680, _1513682), _1513686), _1513688)))], (6014 ^ _779327) ^ [_874013, _874015, _874017] : [class_Orderings_Oorder(_874013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874013), _874015), _874017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874013), _874017), _874015)), -(_874015 = _874017)], (52924 ^ _779327) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (23700 ^ _779327) ^ [_1191946, _1191948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1191946)), hAPP(c_Code__Numeral_Onat__of, _1191948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1191946), _1191948)))], (14471 ^ _779327) ^ [_1023402, _1023404] : [class_Divides_Osemiring__div(_1023402), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1023402), _1023404), c_Groups_Oone__class_Oone(_1023402)) = _1023404)], (49850 ^ _779327) ^ [_1778517, _1778519, _1778521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778517)), c_List_OdropWhile(_1778517, _1778519, _1778521))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778517)), _1778521))))], (22365 ^ _779327) ^ [_1166227, _1166229, _1166231, _1166233] : [class_Orderings_Olinorder(_1166227), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166227), _1166229), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166227), _1166231), _1166233)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166227), _1166231), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166227), _1166229), _1166233)))], (11737 ^ _779327) ^ [_973778, _973780] : [class_Groups_Olinordered__ab__group__add(_973778), 11740 ^ _779327 : [(11747 ^ _779327) ^ [] : [_973780 = c_Groups_Ozero__class_Ozero(_973778), -(_973780 = hAPP(c_Groups_Ouminus__class_Ouminus(_973778), _973780))], (11741 ^ _779327) ^ [] : [_973780 = hAPP(c_Groups_Ouminus__class_Ouminus(_973778), _973780), -(_973780 = c_Groups_Ozero__class_Ozero(_973778))]]], (33724 ^ _779327) ^ [_1395551] : [-(c_Wellfounded_Omeasure(_1395551) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1395551), c_Wellfounded_Oless__than))], (26852 ^ _779327) ^ [_1252408, _1252410, _1252412] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252408, tc_HOL_Obool)), _1252410), _1252412) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252408, tc_HOL_Obool)), _1252412), _1252410))], (22169 ^ _779327) ^ [_1162531, _1162533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162531), _1162533)), -(c_Divides_Odivmod__nat(_1162531, _1162533) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162531))], (19943 ^ _779327) ^ [_1119460, _1119462, _1119464, _1119466] : [class_Fields_Ofield__inverse__zero(_1119460), class_Int_Onumber(_1119460), 19950 ^ _779327 : [(19951 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119460), _1119464), _1119466), 19954 ^ _779327 : [(19961 ^ _779327) ^ [] : [_1119466 = c_Groups_Ozero__class_Ozero(_1119460), -(hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462) = c_Groups_Ozero__class_Ozero(_1119460))], (19955 ^ _779327) ^ [] : [-(_1119466 = c_Groups_Ozero__class_Ozero(_1119460)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119460), hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462)), _1119466) = _1119464)]]], (19967 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119460), _1119464), _1119466)), 19970 ^ _779327 : [(19973 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1119460), hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462)), _1119466) = _1119464], (19971 ^ _779327) ^ [] : [_1119466 = c_Groups_Ozero__class_Ozero(_1119460)]], 19974 ^ _779327 : [(19977 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1119460), _1119462) = c_Groups_Ozero__class_Ozero(_1119460)], (19975 ^ _779327) ^ [] : [-(_1119466 = c_Groups_Ozero__class_Ozero(_1119460))]]]]], (45484 ^ _779327) ^ [_1681330, _1681332] : [-(c_List_Olistrelp(_1681330, _1681332, c_List_Olist_ONil(_1681330), c_List_Olist_ONil(_1681330)))], (40797 ^ _779327) ^ [_1567003, _1567005, _1567007, _1567009] : [c_Wellfounded_Owf(_1567003, _1567005), c_Fun_Oinj__on(_1567003, _1567007, _1567009, c_Orderings_Otop__class_Otop(tc_fun(_1567003, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1567007, hAPP(c_Set_Oimage(tc_prod(_1567003, _1567003), tc_prod(_1567007, _1567007), c_Product__Type_Omap__pair(_1567003, _1567007, _1567003, _1567007, _1567009, _1567009)), _1567005)))], (11313 ^ _779327) ^ [_965155, _965157] : [class_Int_Onumber__ring(_965155), -(hAPP(c_Int_Oring__1__class_Oof__int(_965155), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _965157)) = hAPP(c_Int_Onumber__class_Onumber__of(_965155), _965157))], (28988 ^ _779327) ^ [_1295896, _1295898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295896, tc_HOL_Obool)), _1295898), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295896, tc_HOL_Obool)), _1295898))), -(_1295898 = c_Orderings_Obot__class_Obot(tc_fun(_1295896, tc_HOL_Obool)))], (24945 ^ _779327) ^ [_1214176, _1214178, _1214180, _1214182, _1214184] : [class_Divides_Osemiring__div(_1214176), -(_1214178 = c_Groups_Ozero__class_Ozero(_1214176)), -(_1214180 = c_Groups_Ozero__class_Ozero(_1214176)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214176), _1214178), _1214182)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214176), _1214180), _1214184)), 24964 ^ _779327 : [(24971 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214176), _1214182), _1214180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214176), _1214178), _1214184), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214176), _1214182), _1214178) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214176), _1214184), _1214180))], (24965 ^ _779327) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214176), _1214182), _1214178) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214176), _1214184), _1214180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214176), _1214182), _1214180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214176), _1214178), _1214184))]]], (24167 ^ _779327) ^ [_1200276, _1200278] : [_1200276 = _1200278, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200276), _1200278)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200278), _1200276)))], (5158 ^ _779327) ^ [_858015, _858017] : [_858017 = _858015, -(c_Wellfounded_Ofinite__psubset(_858017) = c_Wellfounded_Ofinite__psubset(_858015))], (29608 ^ _779327) ^ [_1308170, _1308172, _1308174, _1308176, _1308178, _1308180] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1308170, tc_fun(_1308172, tc_HOL_Obool)), _1308174), _1308176), _1308178)), -(hBOOL(hAPP(hAPP(_1308176, _1308180), _1308178))), hBOOL(hAPP(hAPP(c_member(_1308170), _1308180), _1308174))], (37793 ^ _779327) ^ [_1486751, _1486753, _1486755, _1486757] : [-(hBOOL(hAPP(hAPP(c_member(_1486751), hAPP(_1486753, _1486755)), hAPP(c_Set_Oimage(_1486757, _1486751, _1486753), c_Orderings_Otop__class_Otop(tc_fun(_1486757, tc_HOL_Obool))))))], (17604 ^ _779327) ^ [_1078049] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1078049) = c_Int_Opred(_1078049))], (28102 ^ _779327) ^ [_1279063, _1279065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1279063), hAPP(c_Nat_OSuc, _1279065))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1279063, hAPP(c_Nat_OSuc, _1279065)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1279065)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1279063, _1279065)))], (52658 ^ _779327) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (47580 ^ _779327) ^ [_1729146, _1729148, _1729150, _1729152] : [-(hBOOL(hAPP(hAPP(c_member(_1729146), _1729148), hAPP(c_List_Oset(_1729146), _1729150)))), hBOOL(hAPP(hAPP(c_member(_1729146), _1729148), hAPP(c_List_Oset(_1729146), c_List_Oremove1(_1729146, _1729152, _1729150))))], (9871 ^ _779327) ^ [_939215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _939215)), -(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, _939215))))], (30293 ^ _779327) ^ [_1324136, _1324138, _1324140] : [class_Orderings_Oord(_1324136), 30296 ^ _779327 : [(30303 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324136), _1324138), _1324140)), -(hBOOL(hAPP(hAPP(c_member(_1324136), _1324138), hAPP(c_SetInterval_Oord__class_OatMost(_1324136), _1324140))))], (30297 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324136), _1324138), hAPP(c_SetInterval_Oord__class_OatMost(_1324136), _1324140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324136), _1324138), _1324140)))]]], (45914 ^ _779327) ^ [_1692446, _1692448, _1692450, _1692452, _1692454] : [hAPP(hAPP(c_List_Oappend(_1692446), _1692448), _1692450) = hAPP(hAPP(c_List_Olist_OCons(_1692446), _1692452), _1692454), 45919 ^ _779327 : [(45922 ^ _779327) ^ [] : [-(_1692450 = hAPP(hAPP(c_List_Olist_OCons(_1692446), _1692452), _1692454))], (45920 ^ _779327) ^ [] : [-(_1692448 = c_List_Olist_ONil(_1692446))]], 45924 ^ _779327 : [(45927 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1692446), 45923 ^ [_1692446, _1692448, _1692450, _1692452, _1692454]), _1692450) = _1692454)], (45925 ^ _779327) ^ [] : [-(_1692448 = hAPP(hAPP(c_List_Olist_OCons(_1692446), _1692452), 45923 ^ [_1692446, _1692448, _1692450, _1692452, _1692454]))]]], (7318 ^ _779327) ^ [_894050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894050), _894050)))))], (1368 ^ _779327) ^ [_799415, _799417] : [-(class_Rings_Oring(_799415)), _799417 = _799415, class_Rings_Oring(_799417)], (52628 ^ _779327) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (23722 ^ _779327) ^ [_1192438, _1192440, _1192442, _1192444, _1192446] : [-(hAPP(c_New__DSequence_Opos__bind(_1192438, _1192440, _1192442, _1192444), _1192446) = hAPP(c_Lazy__Sequence_Obind(_1192438, _1192440, hAPP(_1192442, _1192446)), hAPP(hAPP(c_COMBC(_1192438, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1192440)), _1192444), _1192446)))], (21812 ^ _779327) ^ [_1155114, _1155116] : [-(_1155114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21815 ^ _779327 : [(21822 ^ _779327) ^ [] : [-(_1155116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1155114, _1155116) = 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, _1155116))), 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)), _1155116)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155114))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1155116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1155114), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1155114, _1155116)), 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), _1155116))))), c_Divides_Opdivmod(_1155114, _1155116)))))], (21816 ^ _779327) ^ [] : [_1155116 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1155114, _1155116) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155114))]]], (50814 ^ _779327) ^ [_1799747, _1799749, _1799751] : [c_List_Olist__all(_1799747, _1799749, _1799751), 50817 ^ _779327 : [(50818 ^ _779327) ^ [_1799828] : [hBOOL(hAPP(hAPP(c_member(_1799747), _1799828), hAPP(c_List_Oset(_1799747), _1799751))), -(hBOOL(hAPP(_1799749, _1799828)))]]], (48619 ^ _779327) ^ [_1752678, _1752680, _1752682] : [-(c_List_Oremdups(_1752678, hAPP(c_List_Ofilter(_1752678, _1752680), _1752682)) = hAPP(c_List_Ofilter(_1752678, _1752680), c_List_Oremdups(_1752678, _1752682)))], (21176 ^ _779327) ^ [_1142698, _1142700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142698), 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)), _1142700)), -(c_Divides_OnegDivAlg(_1142698, _1142700) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1142698), _1142700)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1142698, _1142700)))], (18514 ^ _779327) ^ [_1093758, _1093760, _1093762] : [class_Rings_Olinordered__semidom(_1093758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093758), hAPP(hAPP(c_Power_Opower__class_Opower(_1093758), _1093760), 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(_1093758), _1093762), 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(_1093758), c_Groups_Ozero__class_Ozero(_1093758)), _1093762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093758), _1093760), _1093762)))], (10075 ^ _779327) ^ [_942412, _942414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _942412)), hAPP(c_Int_Onat, _942414))), 10078 ^ _779327 : [(10081 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942412), _942414)))], (10079 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _942414)))]]], (47316 ^ _779327) ^ [_1724086, _1724088, _1724090] : [_1724086 = c_List_Olist_ONil(_1724088), -(c_List_Olast(_1724088, hAPP(hAPP(c_List_Olist_OCons(_1724088), _1724090), _1724086)) = _1724090)], (41519 ^ _779327) ^ [_1584153, _1584155, _1584157, _1584159, _1584161, _1584163, _1584165, _1584167] : [c_Finite__Set_Ofolding(_1584153, _1584155, _1584157, _1584159), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584153), _1584161)), -(hAPP(c_Fun_Ocomp(_1584155, _1584155, _1584163, hAPP(_1584157, _1584165)), hAPP(c_Fun_Ocomp(_1584155, _1584155, _1584163, hAPP(_1584159, _1584161)), _1584167)) = hAPP(c_Fun_Ocomp(_1584155, _1584155, _1584163, hAPP(_1584159, _1584161)), hAPP(c_Fun_Ocomp(_1584155, _1584155, _1584163, hAPP(_1584157, _1584165)), _1584167)))], (34333 ^ _779327) ^ [_1410172, _1410174, _1410176, _1410178] : [_1410172 = _1410174, hBOOL(hAPP(hAPP(c_member(_1410176), _1410172), _1410178)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1410176, _1410176)), hAPP(hAPP(c_Product__Type_OPair(_1410176, _1410176), _1410172), _1410174)), c_Relation_OId__on(_1410176, _1410178))))], (31171 ^ _779327) ^ [_1343865, _1343867, _1343869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343865)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343867), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1343869)), 31181 ^ _779327 : [(31187 ^ _779327) ^ [] : [-(_1343867 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 31183 ^ [_1343865, _1343867, _1343869]), 31180 ^ [_1343865, _1343867, _1343869]))], (31185 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31183 ^ [_1343865, _1343867, _1343869]), _1343869)))], (31182 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31180 ^ [_1343865, _1343867, _1343869]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1343865))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343867), _1343865) = _1343867)], (11135 ^ _779327) ^ [_961268, _961270, _961272, _961274, _961276, _961278] : [class_Rings_Oring(_961268), 11138 ^ _779327 : [(11145 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961268), _961270), _961276)), _961272)), _961274) = _961278, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), _961270), _961272)), _961274) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), _961276), _961272)), _961278))], (11139 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), _961270), _961272)), _961274) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), _961276), _961272)), _961278), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961268), _961270), _961276)), _961272)), _961274) = _961278)]]], (27460 ^ _779327) ^ [_1265082, _1265084, _1265086, _1265088] : [class_Orderings_Olinorder(_1265082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265082), _1265084), _1265086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265082), _1265086), _1265088)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265082, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1265082, _1265084, _1265086)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1265082, _1265086), _1265088)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1265082, _1265084, _1265088))], (19309 ^ _779327) ^ [_1108152, _1108154, _1108156, _1108158, _1108160] : [class_Fields_Ofield(_1108152), -(_1108154 = c_Groups_Ozero__class_Ozero(_1108152)), -(_1108156 = c_Groups_Ozero__class_Ozero(_1108152)), 19320 ^ _779327 : [(19327 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108152), _1108158), _1108156) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108152), _1108160), _1108154), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108152), _1108158), _1108154) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108152), _1108160), _1108156))], (19321 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108152), _1108158), _1108154) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108152), _1108160), _1108156), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108152), _1108158), _1108156) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108152), _1108160), _1108154))]]], (51774 ^ _779327) ^ [_1820444, _1820446] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1820444, tc_HOL_Obool), _1820446) = hAPP(c_Set_OCollect(_1820444), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820444, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1820444), c_HOL_OEx(tc_fun(_1820444, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820444, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1820444, tc_HOL_Obool), tc_HOL_Obool), _1820444), hAPP(c_COMBS(tc_fun(_1820444, 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(_1820444, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1820444, tc_HOL_Obool), tc_fun(tc_fun(_1820444, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1820444, tc_HOL_Obool))), _1820446)))), c_member(_1820444)))))], (15588 ^ _779327) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (51358 ^ _779327) ^ [_1811154, _1811156, _1811158] : [hBOOL(hAPP(hAPP(c_member(_1811154), _1811158), hAPP(c_List_Oset(_1811154), _1811156))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1811154), _1811156), _1811158)))], (946 ^ _779327) ^ [_793752, _793754, _793756, _793758, _793760, _793762, _793764, _793766] : [-(c_Wellfounded_Omax__extp(_793764, _793760, _793756, _793752)), c_Wellfounded_Omax__extp(_793766, _793762, _793758, _793754), _793766 = _793764, _793762 = _793760, _793758 = _793756, _793754 = _793752], (51235 ^ _779327) ^ [_1807947, _1807949, _1807951] : [-(c_List_Oreplicate(_1807947, hAPP(c_Nat_OSuc, _1807949), _1807951) = hAPP(hAPP(c_List_Olist_OCons(_1807947), _1807951), c_List_Oreplicate(_1807947, _1807949, _1807951)))], (12181 ^ _779327) ^ [_981857, _981859, _981861, _981863] : [class_Rings_Ocomm__semiring__1(_981857), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981857), _981859), _981861)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981857), _981863), _981861)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981857), _981859), _981863)), _981861))], (3360 ^ _779327) ^ [_829926, _829928, _829930, _829932, _829934, _829936, _829938, _829940] : [-(c_Fun_Othe__inv__into(_829940, _829936, _829932, _829928) = c_Fun_Othe__inv__into(_829938, _829934, _829930, _829926)), _829940 = _829938, _829936 = _829934, _829932 = _829930, _829928 = _829926], (11965 ^ _779327) ^ [_977811, _977813] : [class_Groups_Omonoid__add(_977811), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977811), c_Groups_Ozero__class_Ozero(_977811)), _977813) = _977813)], (16928 ^ _779327) ^ [_1066506] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066506), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066506) = _1066506)], (26986 ^ _779327) ^ [_1255277, _1255279, _1255281, _1255283] : [class_Lattices_Osemilattice__sup(_1255277), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255277), _1255279), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255277), _1255281), _1255283)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255277), _1255281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255277), _1255279), _1255283)))], (26956 ^ _779327) ^ [_1254684, _1254686, _1254688] : [class_Lattices_Olattice(_1254684), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254684), _1254686), _1254688) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254684), _1254688), _1254686))], (38992 ^ _779327) ^ [_1516888, _1516890] : [class_Orderings_Olinorder(_1516888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516888), _1516890)), -(c_Big__Operators_Olinorder__class_OMin(_1516888, _1516890) = hAPP(c_Finite__Set_Ofold1(_1516888, c_Orderings_Oord__class_Omin(_1516888)), _1516890))], (50860 ^ _779327) ^ [_1800620, _1800622, _1800624] : [c_List_Olist__all(_1800620, _1800624, _1800622), 50863 ^ _779327 : [(50864 ^ _779327) ^ [_1800701] : [hBOOL(hAPP(hAPP(c_member(_1800620), _1800701), hAPP(c_List_Oset(_1800620), _1800622))), -(hBOOL(hAPP(_1800624, _1800701)))]]], (52560 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (43299 ^ _779327) ^ [_1627065, _1627067, _1627069] : [class_Orderings_Olinorder(_1627065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627065), _1627067)), -(c_Big__Operators_Olinorder__class_OMin(_1627065, hAPP(hAPP(c_Set_Oinsert(_1627065), _1627069), _1627067)) = hAPP(hAPP(c_Finite__Set_Ofold(_1627065, _1627065, c_Orderings_Oord__class_Omin(_1627065)), _1627069), _1627067))], (51177 ^ _779327) ^ [_1806836, _1806838, _1806840] : [-(c_Predicate_Oconversep(_1806836, _1806838, c_Predicate_Oconversep(_1806838, _1806836, _1806840)) = _1806840)], (52566 ^ _779327) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (22323 ^ _779327) ^ [_1165379, _1165381] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1165379)), hAPP(c_Nat_OSuc, _1165381)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1165379))), 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)), _1165381)))))], (16679 ^ _779327) ^ [_1062272, _1062274] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062272, _1062274)) = _1062274), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1062272), _1062274) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062272, _1062274)))], (49473 ^ _779327) ^ [_1770436, _1770438, _1770440] : [_1770440 = hAPP(hAPP(c_List_Olist_OCons(_1770436), _1770438), c_List_Olist_ONil(_1770436)), -(hAPP(hAPP(c_List_Olist_OCons(_1770436), _1770438), c_List_Olist_ONil(_1770436)) = hAPP(c_List_Orev(_1770436), _1770440))], (7870 ^ _779327) ^ [_903824, _903826, _903828, _903830, _903832] : [class_Rings_Oordered__semiring(_903824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903824), _903826), _903828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903824), _903830), _903832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903824), c_Groups_Ozero__class_Ozero(_903824)), _903828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903824), c_Groups_Ozero__class_Ozero(_903824)), _903830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903824), _903826), _903830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903824), _903828), _903832))))], (48357 ^ _779327) ^ [_1746278, _1746280] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746278)), c_List_Oremdups(_1746278, c_List_Oconcat(_1746278, _1746280))) = hAPP(c_Finite__Set_Ocard(_1746278), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1746278), tc_fun(_1746278, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1746278)), _1746280)), c_List_Oset(_1746278))))], (52698 ^ _779327) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (28306 ^ _779327) ^ [_1283108, _1283110, _1283112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283108), _1283110)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283108, tc_HOL_Obool)), _1283112), _1283110)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283108), _1283112)))], (34987 ^ _779327) ^ [_1424150, _1424152, _1424154, _1424156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424150, tc_HOL_Obool)), _1424152), _1424154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424150, tc_HOL_Obool)), _1424152), _1424156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424150, tc_HOL_Obool)), _1424152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424150, tc_HOL_Obool)), _1424154), _1424156))))], (37648 ^ _779327) ^ [_1484122, _1484124, _1484126, _1484128] : [37650 ^ _779327 : [(37653 ^ _779327) ^ [] : [hAPP(_1484128, 37649 ^ [_1484122, _1484124, _1484126, _1484128]) = c_Orderings_Otop__class_Otop(tc_fun(_1484124, tc_HOL_Obool))], (37651 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484122), 37649 ^ [_1484122, _1484124, _1484126, _1484128]), _1484126)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1484122, tc_fun(_1484124, tc_HOL_Obool)), _1484126), _1484128) = c_Orderings_Otop__class_Otop(tc_fun(_1484124, tc_HOL_Obool)))], (12287 ^ _779327) ^ [_983715, _983717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983715), _983717)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983717), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983717), _983715)) = _983715)], (52784 ^ _779327) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (15433 ^ _779327) ^ [_1040070, _1040072, _1040074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040070), _1040072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040070), _1040074)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040072), _1040074))))], (45791 ^ _779327) ^ [_1689472, _1689474, _1689476, _1689478, _1689480] : [-(hAPP(hAPP(c_List_Ozip(_1689472, _1689474), _1689476), hAPP(hAPP(c_List_Olist_OCons(_1689474), _1689478), _1689480)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1689472, _1689474)), _1689472, c_List_Olist_ONil(tc_prod(_1689472, _1689474)), hAPP(hAPP(c_COMBC(_1689472, tc_fun(tc_List_Olist(_1689472), tc_List_Olist(tc_prod(_1689472, _1689474))), tc_fun(tc_List_Olist(_1689472), tc_List_Olist(tc_prod(_1689472, _1689474)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1689472, _1689474)), tc_List_Olist(tc_prod(_1689472, _1689474))), tc_fun(tc_fun(tc_List_Olist(_1689472), tc_List_Olist(tc_prod(_1689472, _1689474))), tc_fun(tc_List_Olist(_1689472), tc_List_Olist(tc_prod(_1689472, _1689474)))), _1689472), c_COMBB(tc_List_Olist(tc_prod(_1689472, _1689474)), tc_List_Olist(tc_prod(_1689472, _1689474)), tc_List_Olist(_1689472))), hAPP(hAPP(c_COMBB(tc_prod(_1689472, _1689474), tc_fun(tc_List_Olist(tc_prod(_1689472, _1689474)), tc_List_Olist(tc_prod(_1689472, _1689474))), _1689472), c_List_Olist_OCons(tc_prod(_1689472, _1689474))), hAPP(hAPP(c_COMBC(_1689472, _1689474, tc_prod(_1689472, _1689474)), c_Product__Type_OPair(_1689472, _1689474)), _1689478)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1689472), tc_List_Olist(_1689474), tc_List_Olist(tc_prod(_1689472, _1689474))), c_List_Ozip(_1689472, _1689474)), _1689480))), _1689476))], (38740 ^ _779327) ^ [_1510411, _1510413, _1510415, _1510417, _1510419, _1510421] : [hBOOL(hAPP(hAPP(c_member(_1510411), _1510413), _1510415)), hBOOL(hAPP(hAPP(c_member(_1510417), _1510419), hAPP(_1510421, _1510413))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510411, _1510417)), hAPP(hAPP(c_Product__Type_OPair(_1510411, _1510417), _1510413), _1510419)), hAPP(hAPP(c_Product__Type_OSigma(_1510411, _1510417), _1510415), _1510421))))], (10903 ^ _779327) ^ [_957101, _957103, _957105] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957101), _957103)), _957105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957103), _957105)))], (52083 ^ _779327) ^ [_1827789, _1827791] : [c_Relation_Osym(_1827789, _1827791), -(c_Relation_Osym(_1827789, hAPP(c_Relation_Oconverse(_1827789, _1827789), _1827791)))], (44514 ^ _779327) ^ [_1654148, _1654150, _1654152, _1654154, _1654156, _1654158] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654148), tc_List_Olist(_1654148))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654148), tc_List_Olist(_1654148)), hAPP(hAPP(c_List_Olist_OCons(_1654148), _1654150), _1654152)), hAPP(hAPP(c_List_Olist_OCons(_1654148), _1654154), _1654156))), c_List_Olex(_1654148, _1654158)))), 44515 ^ _779327 : [(44522 ^ _779327) ^ [] : [_1654150 = _1654154, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654148), tc_List_Olist(_1654148))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654148), tc_List_Olist(_1654148)), _1654152), _1654156)), c_List_Olex(_1654148, _1654158)))], (44516 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654148, _1654148)), hAPP(hAPP(c_Product__Type_OPair(_1654148, _1654148), _1654150), _1654154)), _1654158)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654148)), _1654152) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654148)), _1654156)]]], (46808 ^ _779327) ^ [_1713398, _1713400] : [hBOOL(hAPP(c_List_Odistinct(_1713398), _1713400)), -(hBOOL(hAPP(c_List_Odistinct(_1713398), hAPP(c_List_Otl(_1713398), _1713400))))], (51239 ^ _779327) ^ [_1808078, _1808080, _1808082, _1808084, _1808086] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1808078, _1808080, hAPP(hAPP(c_COMBC(_1808078, tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_fun(_1808080, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808080, tc_fun(tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_fun(_1808080, tc_HOL_Obool)), _1808078), c_COMBC(_1808080, tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808080, tc_prod(_1808078, _1808080)), tc_fun(_1808080, tc_fun(tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_HOL_Obool)), _1808078), hAPP(c_COMBB(tc_prod(_1808078, _1808080), tc_fun(tc_fun(tc_prod(_1808078, _1808080), tc_HOL_Obool), tc_HOL_Obool), _1808080), c_member(tc_prod(_1808078, _1808080)))), c_Product__Type_OPair(_1808078, _1808080)))), _1808082)), _1808084), _1808086)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1808080, _1808078)), hAPP(hAPP(c_Product__Type_OPair(_1808080, _1808078), _1808084), _1808086)), hAPP(c_Relation_Oconverse(_1808078, _1808080), _1808082))))], (43640 ^ _779327) ^ [_1633597, _1633599, _1633601] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1633597, tc_HOL_Obool)), _1633599), _1633601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1633597, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1633597, tc_HOL_Obool), _1633601)), _1633599)))], (17602 ^ _779327) ^ [_1078018] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1078018), c_Int_OMin) = c_Int_Opred(_1078018))], (43203 ^ _779327) ^ [_1625239, _1625241, _1625243, _1625245, _1625247] : [c_Finite__Set_Ofolding__one__idem(_1625239, _1625241, _1625243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625239), _1625245)), -(hAPP(_1625243, hAPP(hAPP(c_Set_Oinsert(_1625239), _1625247), _1625245)) = hAPP(hAPP(c_Finite__Set_Ofold(_1625239, _1625239, _1625241), _1625247), _1625245))], (15568 ^ _779327) ^ [_1042488, _1042490] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042488, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1042490)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042488, _1042490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (15477 ^ _779327) ^ [_1040932, _1040934, _1040936, _1040938] : [class_Divides_Osemiring__div(_1040932), -(c_Divides_Odiv__class_Omod(_1040932, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040932), _1040934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040932), _1040936), _1040938)), _1040936) = c_Divides_Odiv__class_Omod(_1040932, _1040934, _1040936))], (49599 ^ _779327) ^ [_1773097, _1773099, _1773101] : [-(hAPP(c_List_Orev(_1773097), hAPP(hAPP(c_List_Odrop(_1773097), _1773099), _1773101)) = hAPP(hAPP(c_List_Otake(_1773097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773097)), _1773101)), _1773099)), hAPP(c_List_Orev(_1773097), _1773101)))], (31535 ^ _779327) ^ [_1351995, _1351997, _1351999, _1352001, _1352003] : [class_Groups_Oordered__ab__semigroup__add(_1351995), class_Rings_Osemiring__1(_1351995), 31545 ^ _779327 : [(31548 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351995), hAPP(_1352001, 31544 ^ [_1351995, _1351997, _1351999, _1352001, _1352003])), _1352003))], (31546 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351997), 31544 ^ [_1351995, _1351997, _1351999, _1352001, _1352003]), _1351999)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351995), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351997, _1351995), _1352001), _1351999)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351995), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1351995), hAPP(c_Finite__Set_Ocard(_1351997), _1351999))), _1352003))))], (16724 ^ _779327) ^ [_1062915, _1062917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062915), _1062917)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062917, _1062915) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1062917), _1062915), _1062915))], (52494 ^ _779327) ^ [_1835305, _1835307] : [-(class_Finite__Set_Ofinite(tc_fun(_1835305, _1835307))), class_Finite__Set_Ofinite(_1835305), class_Finite__Set_Ofinite(_1835307)], (17450 ^ _779327) ^ [_1075619] : [c_Int_OMin = c_Int_OBit1(_1075619), -(c_Int_OMin = _1075619)], (52842 ^ _779327) ^ [_1838717, _1838719] : [-(class_Finite__Set_Ofinite(tc_sum(_1838717, _1838719))), class_Finite__Set_Ofinite(_1838717), class_Finite__Set_Ofinite(_1838719)], (43407 ^ _779327) ^ [_1629174, _1629176, _1629178] : [class_Lattices_Olattice(_1629174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629174), _1629176)), -(hBOOL(hAPP(hAPP(c_member(_1629174), _1629178), _1629176))), -(c_Big__Operators_Olattice__class_OInf__fin(_1629174, hAPP(hAPP(c_Set_Oinsert(_1629174), _1629178), _1629176)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629174, _1629174, c_Lattices_Osemilattice__inf__class_Oinf(_1629174)), _1629178), _1629176))], (45248 ^ _779327) ^ [_1674894, _1674896, _1674898] : [45250 ^ _779327 : [(45253 ^ _779327) ^ [] : [hBOOL(hAPP(_1674898, hAPP(hAPP(c_List_Onth(_1674894), _1674896), 45249 ^ [_1674894, _1674896, _1674898])))], (45251 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45249 ^ [_1674894, _1674896, _1674898]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674894)), _1674896))))]], 45254 ^ _779327 : [(45255 ^ _779327) ^ [_1675096] : [hBOOL(hAPP(hAPP(c_member(_1674894), _1675096), hAPP(c_List_Oset(_1674894), _1674896))), -(hBOOL(hAPP(_1674898, _1675096)))]]], (29554 ^ _779327) ^ [_1307164, _1307166, _1307168, _1307170] : [hBOOL(hAPP(hAPP(c_member(_1307164), _1307166), _1307168)), -(hBOOL(hAPP(hAPP(c_member(_1307164), _1307166), _1307170))), -(hBOOL(hAPP(hAPP(c_member(_1307164), _1307166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307164, tc_HOL_Obool)), _1307168), _1307170))))], (32940 ^ _779327) ^ [_1378497, _1378499, _1378501, _1378503] : [c_Finite__Set_Ofolding__one(_1378497, _1378499, _1378501), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378497), _1378503)), -(_1378503 = c_Orderings_Obot__class_Obot(tc_fun(_1378497, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1378497), hAPP(hAPP(_1378499, 32953 ^ [_1378497, _1378499, _1378501, _1378503]), 32954 ^ [_1378497, _1378499, _1378501, _1378503])), hAPP(hAPP(c_Set_Oinsert(_1378497), 32953 ^ [_1378497, _1378499, _1378501, _1378503]), hAPP(hAPP(c_Set_Oinsert(_1378497), 32954 ^ [_1378497, _1378499, _1378501, _1378503]), c_Orderings_Obot__class_Obot(tc_fun(_1378497, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1378497), hAPP(_1378501, _1378503)), _1378503)))], (43923 ^ _779327) ^ [_1640144, _1640146, _1640148] : [c_Equiv__Relations_Oequiv(_1640144, _1640146, _1640148), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640144, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1640144), _1640146), _1640148)) = _1640146)], (52920 ^ _779327) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52962 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (47102 ^ _779327) ^ [_1719564, _1719566, _1719568, _1719570] : [-(hAPP(c_List_Ofoldl(_1719564, _1719566, _1719568, _1719570), c_List_Olist_ONil(_1719566)) = _1719570)], (46391 ^ _779327) ^ [_1703194, _1703196, _1703198, _1703200, _1703202, _1703204, _1703206] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1703194, _1703194)), hAPP(hAPP(c_Product__Type_OPair(_1703194, _1703194), _1703196), _1703198)), _1703200)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703194), tc_List_Olist(_1703194))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1703194), tc_List_Olist(_1703194)), hAPP(hAPP(c_List_Oappend(_1703194), _1703202), hAPP(hAPP(c_List_Olist_OCons(_1703194), _1703196), _1703204))), hAPP(hAPP(c_List_Oappend(_1703194), _1703202), hAPP(hAPP(c_List_Olist_OCons(_1703194), _1703198), _1703206)))), c_List_Olexord(_1703194, _1703200))))], (110 ^ _779327) ^ [_780818, _780820, _780822, _780824, _780826, _780828] : [-(c_Nitpick_Oless__eq__frac(_780826, _780822, _780818)), c_Nitpick_Oless__eq__frac(_780828, _780824, _780820), _780828 = _780826, _780824 = _780822, _780820 = _780818], (18342 ^ _779327) ^ [_1090860] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1090860), 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), _1090860), _1090860))], (10737 ^ _779327) ^ [_954023, _954025, _954027] : [class_Int_Onumber__ring(_954023), class_Int_Oring__char__0(_954023), 10744 ^ _779327 : [(10751 ^ _779327) ^ [] : [_954025 = _954027, -(hAPP(c_Int_Onumber__class_Onumber__of(_954023), _954025) = hAPP(c_Int_Onumber__class_Onumber__of(_954023), _954027))], (10745 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_954023), _954025) = hAPP(c_Int_Onumber__class_Onumber__of(_954023), _954027), -(_954025 = _954027)]]], (4246 ^ _779327) ^ [_843793, _843795, _843797, _843799, _843801, _843803, _843805, _843807] : [-(c_List_Olinorder__class_Osort__key(_843807, _843803, _843799, _843795) = c_List_Olinorder__class_Osort__key(_843805, _843801, _843797, _843793)), _843807 = _843805, _843803 = _843801, _843799 = _843797, _843795 = _843793], (30435 ^ _779327) ^ [_1327108, _1327110, _1327112, _1327114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327108, tc_fun(_1327110, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1327108, tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_fun(_1327110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327110, tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_fun(_1327110, tc_HOL_Obool)), _1327108), c_COMBC(_1327110, tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327110, tc_prod(_1327108, _1327110)), tc_fun(_1327110, tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), _1327108), hAPP(c_COMBB(tc_prod(_1327108, _1327110), tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool), _1327110), c_member(tc_prod(_1327108, _1327110)))), c_Product__Type_OPair(_1327108, _1327110)))), _1327112)), hAPP(hAPP(c_COMBC(_1327108, tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_fun(_1327110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327110, tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_fun(_1327110, tc_HOL_Obool)), _1327108), c_COMBC(_1327110, tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327110, tc_prod(_1327108, _1327110)), tc_fun(_1327110, tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool)), _1327108), hAPP(c_COMBB(tc_prod(_1327108, _1327110), tc_fun(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool), tc_HOL_Obool), _1327110), c_member(tc_prod(_1327108, _1327110)))), c_Product__Type_OPair(_1327108, _1327110)))), _1327114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1327108, _1327110), tc_HOL_Obool)), _1327112), _1327114)))], (5732 ^ _779327) ^ [_870003] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _870003)], (2854 ^ _779327) ^ [_821865, _821867, _821869, _821871, _821873, _821875, _821877, _821879] : [-(c_Lazy__Sequence_Ohb__bind(_821879, _821875, _821871, _821867) = c_Lazy__Sequence_Ohb__bind(_821877, _821873, _821869, _821865)), _821879 = _821877, _821875 = _821873, _821871 = _821869, _821867 = _821865], (31491 ^ _779327) ^ [_1350352, _1350354] : [class_Complete__Lattice_Ocomplete__lattice(_1350352), c_Orderings_Oorder__class_Omono(_1350352, _1350352, _1350354), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350352), c_Inductive_Ocomplete__lattice__class_Olfp(_1350352, _1350354)), hAPP(_1350354, c_Inductive_Ocomplete__lattice__class_Olfp(_1350352, _1350354)))))], (38750 ^ _779327) ^ [_1510646, _1510648, _1510650, _1510652, _1510654, _1510656] : [hBOOL(hAPP(hAPP(c_member(_1510646), _1510648), _1510650)), 38753 ^ _779327 : [(38760 ^ _779327) ^ [] : [_1510654 = _1510656, -(hAPP(hAPP(c_Product__Type_OSigma(_1510652, _1510646), _1510654), hAPP(c_COMBK(tc_fun(_1510646, tc_HOL_Obool), _1510652), _1510650)) = hAPP(hAPP(c_Product__Type_OSigma(_1510652, _1510646), _1510656), hAPP(c_COMBK(tc_fun(_1510646, tc_HOL_Obool), _1510652), _1510650)))], (38754 ^ _779327) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1510652, _1510646), _1510654), hAPP(c_COMBK(tc_fun(_1510646, tc_HOL_Obool), _1510652), _1510650)) = hAPP(hAPP(c_Product__Type_OSigma(_1510652, _1510646), _1510656), hAPP(c_COMBK(tc_fun(_1510646, tc_HOL_Obool), _1510652), _1510650)), -(_1510654 = _1510656)]]], (34229 ^ _779327) ^ [_1407219] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1407219) = 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, _1407219)), 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))))))))], (11405 ^ _779327) ^ [_967438, _967440] : [-(_967438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967438), _967440) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967438), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _967440)))], (37971 ^ _779327) ^ [_1490492, _1490494] : [class_Lattices_Oboolean__algebra(_1490492), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1490492), hAPP(c_Groups_Ouminus__class_Ouminus(_1490492), _1490494)), _1490494) = c_Orderings_Otop__class_Otop(_1490492))], (38145 ^ _779327) ^ [_1494512, _1494514, _1494516, _1494518] : [hBOOL(hAPP(hAPP(c_member(_1494512), _1494514), c_Wellfounded_Oacc(_1494512, _1494516))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1494512, _1494512)), hAPP(hAPP(c_Product__Type_OPair(_1494512, _1494512), _1494518), _1494514)), _1494516)), -(hBOOL(hAPP(hAPP(c_member(_1494512), _1494518), c_Wellfounded_Oacc(_1494512, _1494516))))], (34971 ^ _779327) ^ [_1423812, _1423814, _1423816] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423812, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423812, tc_HOL_Obool)), _1423814), _1423816)), _1423814)))], (42192 ^ _779327) ^ [_1600183, _1600185] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1600183, _1600183), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1600183, _1600185)), c_Relation_OId(_1600183)) = c_Transitive__Closure_Ortrancl(_1600183, _1600185))], (21626 ^ _779327) ^ [_1152005, _1152007, _1152009, _1152011, _1152013] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152005, _1152007), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152009), _1152011))), -(_1152007 = 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)), _1152013)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152005, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1152007), _1152013)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1152009), _1152013)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1152007), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1152009, _1152013))), _1152011)))))], (40869 ^ _779327) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (42617 ^ _779327) ^ [_1610388, _1610390, _1610392] : [-(hAPP(c_Relation_ORange(_1610388, _1610390), _1610392) = hAPP(c_Relation_ODomain(_1610390, _1610388), hAPP(c_Relation_Oconverse(_1610388, _1610390), _1610392)))], (24655 ^ _779327) ^ [_1208502, _1208504, _1208506] : [class_Divides_Osemiring__div(_1208502), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208502), _1208504), _1208506)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208502), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208502), _1208506), _1208504)), _1208504) = _1208506)], (40249 ^ _779327) ^ [_1552151, _1552153] : [-(hAPP(c_Fun_Oid(_1552151), _1552153) = _1552153)], (46608 ^ _779327) ^ [_1709004, _1709006, _1709008, _1709010] : [-(_1709004 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1709006), _1709004), hAPP(hAPP(c_List_Olist_OCons(_1709006), _1709008), _1709010)) = hAPP(hAPP(c_List_Odrop(_1709006), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1709004), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1709010))], (47586 ^ _779327) ^ [_1729269, _1729271, _1729273, _1729275] : [-(_1729269 = _1729271), 47589 ^ _779327 : [(47596 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1729273), _1729269), hAPP(c_List_Oset(_1729273), _1729275))), -(hBOOL(hAPP(hAPP(c_member(_1729273), _1729269), hAPP(c_List_Oset(_1729273), c_List_Oremove1(_1729273, _1729271, _1729275)))))], (47590 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1729273), _1729269), hAPP(c_List_Oset(_1729273), c_List_Oremove1(_1729273, _1729271, _1729275)))), -(hBOOL(hAPP(hAPP(c_member(_1729273), _1729269), hAPP(c_List_Oset(_1729273), _1729275))))]]], (23710 ^ _779327) ^ [_1192123] : [-(c_Code__Numeral_OSuc__code__numeral(_1192123) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1192123))))], (23520 ^ _779327) ^ [_1188613, _1188615, _1188617, _1188619, _1188621, _1188623] : [-(c_Nitpick_Opair__box_OPairBox(_1188613, _1188615, _1188617, _1188619) = c_Nitpick_Opair__box_OPairBox(_1188613, _1188615, _1188621, _1188623)), _1188617 = _1188621, _1188619 = _1188623], (51501 ^ _779327) ^ [_1814603, _1814605] : [-(c_Lazy__Sequence_Oappend(_1814603, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814603), _1814605) = _1814605)], (18382 ^ _779327) ^ [_1091591, _1091593, _1091595] : [class_Rings_Olinordered__semidom(_1091591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091591), hAPP(hAPP(c_Power_Opower__class_Opower(_1091591), _1091593), 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(_1091591), _1091595), 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(_1091591), c_Groups_Ozero__class_Ozero(_1091591)), _1091595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091591), _1091593), _1091595)))], (11993 ^ _779327) ^ [_978242, _978244] : [class_Groups_Omonoid__add(_978242), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978242), _978244), c_Groups_Ozero__class_Ozero(_978242)) = _978244)], (37889 ^ _779327) ^ [_1488770] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1488770)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (4176 ^ _779327) ^ [_842726, _842728, _842730, _842732, _842734, _842736] : [-(c_List_Osublist(_842736, _842732, _842728) = c_List_Osublist(_842734, _842730, _842726)), _842736 = _842734, _842732 = _842730, _842728 = _842726], (45854 ^ _779327) ^ [_1691196, _1691198] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1691196, _1691198) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691196, _1691198)))], (12273 ^ _779327) ^ [_983433, _983435] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983433), _983435)), _983433)))], (49812 ^ _779327) ^ [_1777611, _1777613] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1777611), _1777613) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1777611)), c_List_Oembed__list(_1777613))))], (14249 ^ _779327) ^ [_1019501, _1019503, _1019505] : [class_Lattices_Oboolean__algebra(_1019501), 14252 ^ _779327 : [(14259 ^ _779327) ^ [] : [_1019503 = _1019505, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1019501), _1019503) = hAPP(c_Groups_Ouminus__class_Ouminus(_1019501), _1019505))], (14253 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1019501), _1019503) = hAPP(c_Groups_Ouminus__class_Ouminus(_1019501), _1019505), -(_1019503 = _1019505)]]], (47510 ^ _779327) ^ [_1727854, _1727856] : [-(_1727854 = c_List_Olist_ONil(_1727856)), -(hAPP(hAPP(c_List_Oappend(_1727856), c_List_Obutlast(_1727856, _1727854)), hAPP(hAPP(c_List_Olist_OCons(_1727856), c_List_Olast(_1727856, _1727854)), c_List_Olist_ONil(_1727856))) = _1727854)], (12141 ^ _779327) ^ [_980928, _980930, _980932, _980934, _980936] : [class_Rings_Osemiring(_980928), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980928), _980930), _980932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980928), _980934), _980932)), _980936)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980928), _980930), _980934)), _980932)), _980936))], (27941 ^ _779327) ^ [_1276186, _1276188, _1276190, _1276192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276186, tc_HOL_Obool)), _1276188), _1276190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276186, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1276186), _1276192), _1276188)), hAPP(hAPP(c_Set_Oinsert(_1276186), _1276192), _1276190))))], (43393 ^ _779327) ^ [_1628960, _1628962, _1628964] : [class_Lattices_Olattice(_1628960), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628960), _1628962)), -(hBOOL(hAPP(hAPP(c_member(_1628960), _1628964), _1628962))), -(c_Big__Operators_Olattice__class_OSup__fin(_1628960, hAPP(hAPP(c_Set_Oinsert(_1628960), _1628964), _1628962)) = hAPP(hAPP(c_Finite__Set_Ofold(_1628960, _1628960, c_Lattices_Osemilattice__sup__class_Osup(_1628960)), _1628964), _1628962))], (14155 ^ _779327) ^ [_1017588, _1017590, _1017592, _1017594, _1017596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017588, tc_HOL_Obool)), _1017590), _1017592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017588, tc_HOL_Obool)), _1017594), _1017596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017588, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017588, tc_HOL_Obool)), _1017590), _1017596)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017588, tc_HOL_Obool)), _1017592), _1017594))))], (17300 ^ _779327) ^ [_1072910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072910), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072910)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19981 ^ _779327) ^ [_1120055, _1120057, _1120059, _1120061] : [class_Fields_Ofield__inverse__zero(_1120055), class_Int_Onumber(_1120055), 19988 ^ _779327 : [(19989 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120055), _1120057), _1120059) = hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061), 19992 ^ _779327 : [(19999 ^ _779327) ^ [] : [_1120059 = c_Groups_Ozero__class_Ozero(_1120055), -(hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061) = c_Groups_Ozero__class_Ozero(_1120055))], (19993 ^ _779327) ^ [] : [-(_1120059 = c_Groups_Ozero__class_Ozero(_1120055)), -(_1120057 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120055), hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061)), _1120059))]]], (20005 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120055), _1120057), _1120059) = hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061)), 20008 ^ _779327 : [(20011 ^ _779327) ^ [] : [_1120057 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120055), hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061)), _1120059)], (20009 ^ _779327) ^ [] : [_1120059 = c_Groups_Ozero__class_Ozero(_1120055)]], 20012 ^ _779327 : [(20015 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120055), _1120061) = c_Groups_Ozero__class_Ozero(_1120055)], (20013 ^ _779327) ^ [] : [-(_1120059 = c_Groups_Ozero__class_Ozero(_1120055))]]]]], (5986 ^ _779327) ^ [_873547, _873549, _873551, _873553] : [class_Orderings_Oorder(_873547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873547), _873549), _873551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_873547), _873553), _873549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_873547), _873553), _873551)))], (29516 ^ _779327) ^ [_1306441, _1306443, _1306445, _1306447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306441, tc_HOL_Obool)), _1306443), _1306445)), hBOOL(hAPP(hAPP(c_member(_1306441), _1306447), _1306443)), -(hBOOL(hAPP(hAPP(c_member(_1306441), _1306447), _1306445)))], (44662 ^ _779327) ^ [_1659203, _1659205, _1659207, _1659209, _1659211, _1659213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659203), tc_List_Olist(_1659203))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659203), tc_List_Olist(_1659203)), hAPP(hAPP(c_List_Olist_OCons(_1659203), _1659205), _1659207)), hAPP(hAPP(c_List_Olist_OCons(_1659203), _1659209), _1659211))), c_List_Olistrel1(_1659203, _1659213))), 44667 ^ _779327 : [(44670 ^ _779327) ^ [] : [-(_1659207 = _1659211)], (44668 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1659203, _1659203)), hAPP(hAPP(c_Product__Type_OPair(_1659203, _1659203), _1659205), _1659209)), _1659213)))]], 44671 ^ _779327 : [(44674 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659203), tc_List_Olist(_1659203))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659203), tc_List_Olist(_1659203)), _1659207), _1659211)), c_List_Olistrel1(_1659203, _1659213))))], (44672 ^ _779327) ^ [] : [-(_1659205 = _1659209)]]], (42547 ^ _779327) ^ [_1608866, _1608868, _1608870, _1608872, _1608874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608868, _1608866)), hAPP(hAPP(c_Product__Type_OPair(_1608868, _1608866), _1608872), _1608870)), _1608874)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608866, _1608868)), hAPP(hAPP(c_Product__Type_OPair(_1608866, _1608868), _1608870), _1608872)), hAPP(c_Relation_Oconverse(_1608868, _1608866), _1608874))))], (12343 ^ _779327) ^ [_984718, _984720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _984718)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _984720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984718), _984720)))], (9427 ^ _779327) ^ [_932019, _932021, _932023] : [class_Rings_Olinordered__idom(_932019), 9430 ^ _779327 : [(9437 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _932021), _932023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932019), hAPP(c_Int_Oring__1__class_Oof__int(_932019), _932021)), hAPP(c_Int_Oring__1__class_Oof__int(_932019), _932023))))], (9431 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932019), hAPP(c_Int_Oring__1__class_Oof__int(_932019), _932021)), hAPP(c_Int_Oring__1__class_Oof__int(_932019), _932023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _932021), _932023)))]]], (5742 ^ _779327) ^ [_870153] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _870153)))], (32614 ^ _779327) ^ [_1372315, _1372317] : [class_Orderings_Olinorder(_1372315), -(c_Big__Operators_Olattice_OSup__fin(_1372315, c_Orderings_Oord__class_Omax(_1372315), hAPP(hAPP(c_Set_Oinsert(_1372315), _1372317), c_Orderings_Obot__class_Obot(tc_fun(_1372315, tc_HOL_Obool)))) = _1372317)], (18374 ^ _779327) ^ [_1091447] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091447), _1091447)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1091447)], (25365 ^ _779327) ^ [_1221603, _1221605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221605)), 25372 ^ _779327 : [(25379 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1221603), _1221605)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1221603)), hAPP(c_Int_Onat, _1221605))))], (25373 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1221603)), hAPP(c_Int_Onat, _1221605))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1221603), _1221605)))]]], (15646 ^ _779327) ^ [_1044002, _1044004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1044002)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044002), _1044004)), _1044002) = _1044004)], (28552 ^ _779327) ^ [_1287929, _1287931, _1287933] : [hAPP(hAPP(c_Set_Oinsert(_1287929), _1287931), _1287933) = c_Orderings_Obot__class_Obot(tc_fun(_1287929, tc_HOL_Obool))], (21540 ^ _779327) ^ [_1150070, _1150072] : [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), _1150070), _1150072))), 21543 ^ _779327 : [(21552 ^ _779327) ^ [] : [-(c_Divides_OposDivAlg(_1150070, _1150072) = hAPP(c_Divides_Oadjust(_1150072), c_Divides_OposDivAlg(_1150070, 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)))), _1150072)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150070), _1150072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1150072), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21544 ^ _779327) ^ [] : [21545 ^ _779327 : [(21548 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1150072), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21546 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150070), _1150072))]], -(c_Divides_OposDivAlg(_1150070, _1150072) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150070))]]], (28890 ^ _779327) ^ [_1294217, _1294219, _1294221] : [class_Orderings_Oorder(_1294217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294217), _1294219), _1294221)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1294217, _1294221, _1294219) = c_Orderings_Obot__class_Obot(tc_fun(_1294217, tc_HOL_Obool)))], (19353 ^ _779327) ^ [_1108903, _1108905] : [class_Rings_Odivision__ring(_1108903), -(_1108905 = c_Groups_Ozero__class_Ozero(_1108903)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108903), _1108905), _1108905) = c_Groups_Oone__class_Oone(_1108903))], (14165 ^ _779327) ^ [_1017833, _1017835, _1017837, _1017839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017833, tc_HOL_Obool)), _1017835), _1017837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017833, tc_HOL_Obool)), _1017837), _1017839)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017833, tc_HOL_Obool)), _1017837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017833, tc_HOL_Obool)), _1017839), _1017835)) = _1017835)], (46834 ^ _779327) ^ [_1713820, _1713822] : [hBOOL(hAPP(c_List_Odistinct(_1713820), hAPP(c_List_Orotate1(_1713820), _1713822))), -(hBOOL(hAPP(c_List_Odistinct(_1713820), _1713822)))], (37737 ^ _779327) ^ [_1485809, _1485811] : [class_Lattices_Obounded__lattice__top(_1485809), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1485809), _1485811), c_Orderings_Otop__class_Otop(_1485809)) = c_Orderings_Otop__class_Otop(_1485809))], (33824 ^ _779327) ^ [_1397798, _1397800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1397798, _1397798)), _1397800)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1397798), hAPP(c_Relation_OField(_1397798), _1397800))))], (11009 ^ _779327) ^ [_958931, _958933, _958935] : [class_Groups_Ogroup__add(_958931), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958931), hAPP(c_Groups_Ouminus__class_Ouminus(_958931), _958933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958931), _958933), _958935)) = _958935)], (35287 ^ _779327) ^ [_1431481, _1431483, _1431485] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431481, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431481, tc_HOL_Obool)), _1431483), _1431485)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431481, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431481, tc_HOL_Obool)), _1431483)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431481, tc_HOL_Obool)), _1431485)))], (17350 ^ _779327) ^ [_1073707, _1073709] : [class_Int_Onumber__ring(_1073707), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073707), c_Groups_Oone__class_Oone(_1073707)), hAPP(c_Int_Onumber__class_Onumber__of(_1073707), _1073709)) = hAPP(c_Int_Onumber__class_Onumber__of(_1073707), 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), _1073709))))], (1046 ^ _779327) ^ [_795222, _795224, _795226, _795228] : [-(c_Relation_Osym(_795226, _795222)), c_Relation_Osym(_795228, _795224), _795228 = _795226, _795224 = _795222], (3122 ^ _779327) ^ [_826189, _826191, _826193, _826195, _826197, _826199, _826201, _826203] : [-(c_Sum__Type_OPlus(_826203, _826199, _826195, _826191) = c_Sum__Type_OPlus(_826201, _826197, _826193, _826189)), _826203 = _826201, _826199 = _826197, _826195 = _826193, _826191 = _826189], (9353 ^ _779327) ^ [_930858, _930860] : [class_Rings_Olinordered__idom(_930858), 9356 ^ _779327 : [(9363 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930858), c_Groups_Ozero__class_Ozero(_930858)), hAPP(c_Int_Oring__1__class_Oof__int(_930858), _930860))))], (9357 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930858), c_Groups_Ozero__class_Ozero(_930858)), hAPP(c_Int_Oring__1__class_Oof__int(_930858), _930860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930860)))]]], (8054 ^ _779327) ^ [_907212, _907214, _907216] : [class_Rings_Olinordered__semiring__strict(_907212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907212), c_Groups_Ozero__class_Ozero(_907212)), _907214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907212), _907216), c_Groups_Ozero__class_Ozero(_907212))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907212), _907216), _907214)), c_Groups_Ozero__class_Ozero(_907212))))], (51802 ^ _779327) ^ [_1822528, _1822530, _1822532, _1822534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1822528), _1822530)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1822528), _1822532)), -(_1822532 = c_Orderings_Obot__class_Obot(tc_fun(_1822528, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1822528, _1822534, _1822530, _1822532)), 51816 ^ _779327 : [(51819 ^ _779327) ^ [_1822873] : [hBOOL(hAPP(hAPP(c_member(_1822528), _1822873), _1822532)), hBOOL(hAPP(hAPP(_1822534, 51815 ^ [_1822528, _1822530, _1822532, _1822534]), _1822873))], (51817 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822528), 51815 ^ [_1822528, _1822530, _1822532, _1822534]), _1822530)))]]], (39746 ^ _779327) ^ [_1533486, _1533488, _1533490] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533486), hAPP(c_Set_OCollect(_1533486), hAPP(hAPP(c_COMBS(_1533486, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533486), c_fdisj), _1533488)), _1533490)))), 39749 ^ _779327 : [(39752 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533486), hAPP(c_Set_OCollect(_1533486), _1533490))))], (39750 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533486), hAPP(c_Set_OCollect(_1533486), _1533488))))]]], (17970 ^ _779327) ^ [_1084373, _1084375] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1084373)), c_Int_OBit0(_1084375)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1084373), _1084375)))], (31860 ^ _779327) ^ [_1358309, _1358311] : [class_Rings_Oring__1(_1358309), hBOOL(hAPP(hAPP(c_member(_1358309), _1358311), c_Int_Oring__1__class_OInts(_1358309))), -(hBOOL(hAPP(hAPP(c_member(_1358309), hAPP(c_Groups_Ouminus__class_Ouminus(_1358309), _1358311)), c_Int_Oring__1__class_OInts(_1358309))))], (45179 ^ _779327) ^ [_1673356, _1673358, _1673360, _1673362, _1673364] : [c_Fun_Oinj__on(_1673356, _1673358, _1673360, c_Orderings_Otop__class_Otop(tc_fun(_1673356, tc_HOL_Obool))), 45182 ^ _779327 : [(45189 ^ _779327) ^ [] : [_1673362 = _1673364, -(hAPP(hAPP(c_List_Omap(_1673356, _1673358), _1673360), _1673362) = hAPP(hAPP(c_List_Omap(_1673356, _1673358), _1673360), _1673364))], (45183 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Omap(_1673356, _1673358), _1673360), _1673362) = hAPP(hAPP(c_List_Omap(_1673356, _1673358), _1673360), _1673364), -(_1673362 = _1673364)]]], (34193 ^ _779327) ^ [_1406146, _1406148, _1406150, _1406152] : [-(hAPP(c_Relation_OImage(_1406146, _1406148, _1406150), _1406152) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406146, tc_fun(_1406148, tc_HOL_Obool)), _1406152), hAPP(hAPP(c_COMBB(tc_fun(_1406146, tc_HOL_Obool), tc_fun(_1406148, tc_HOL_Obool), _1406146), c_Relation_OImage(_1406146, _1406148, _1406150)), hAPP(hAPP(c_COMBC(_1406146, tc_fun(_1406146, tc_HOL_Obool), tc_fun(_1406146, tc_HOL_Obool)), c_Set_Oinsert(_1406146)), c_Orderings_Obot__class_Obot(tc_fun(_1406146, tc_HOL_Obool))))))], (330 ^ _779327) ^ [_784282, _784284, _784286, _784288, _784290, _784292] : [-(c_Orderings_Oorder__class_Ostrict__mono(_784290, _784286, _784282)), c_Orderings_Oorder__class_Ostrict__mono(_784292, _784288, _784284), _784292 = _784290, _784288 = _784286, _784284 = _784282], (6244 ^ _779327) ^ [_877637, _877639, _877641] : [class_Orderings_Oorder(_877637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877637), _877639), _877641)), -(_877639 = _877641), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877637), _877639), _877641)))], (51049 ^ _779327) ^ [_1804408, _1804410, _1804412] : [c_List_Olist_ONil(_1804408) = c_List_Oreplicate(_1804408, _1804410, _1804412), -(_1804410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7722 ^ _779327) ^ [_901036, _901038, _901040] : [class_Rings_Oordered__cancel__semiring(_901036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901036), c_Groups_Ozero__class_Ozero(_901036)), _901038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901036), _901040), c_Groups_Ozero__class_Ozero(_901036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_901036), _901038), _901040)), c_Groups_Ozero__class_Ozero(_901036))))], (39798 ^ _779327) ^ [_1534672, _1534674, _1534676, _1534678] : [-(hAPP(c_Set_OCollect(tc_prod(_1534672, _1534674)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534672, _1534674, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1534672, tc_fun(_1534674, tc_HOL_Obool), tc_fun(_1534674, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534674, tc_HOL_Obool), tc_fun(_1534674, tc_HOL_Obool)), _1534672), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534674)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534672), c_fconj), _1534676))), _1534678))) = hAPP(hAPP(c_Product__Type_OSigma(_1534672, _1534674), hAPP(c_Set_OCollect(_1534672), _1534676)), hAPP(c_COMBK(tc_fun(_1534674, tc_HOL_Obool), _1534672), hAPP(c_Set_OCollect(_1534674), _1534678))))], (11817 ^ _779327) ^ [_975028, _975030, _975032] : [class_Groups_Oordered__ab__group__add(_975028), 11820 ^ _779327 : [(11827 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975028), _975032), _975030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975028), hAPP(c_Groups_Ouminus__class_Ouminus(_975028), _975030)), hAPP(c_Groups_Ouminus__class_Ouminus(_975028), _975032))))], (11821 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975028), hAPP(c_Groups_Ouminus__class_Ouminus(_975028), _975030)), hAPP(c_Groups_Ouminus__class_Ouminus(_975028), _975032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975028), _975032), _975030)))]]], (38902 ^ _779327) ^ [_1515030, _1515032, _1515034, _1515036] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1515030, _1515032)), hAPP(hAPP(c_Product__Type_OSigma(_1515030, _1515032), hAPP(hAPP(c_Set_Oinsert(_1515030), _1515034), c_Orderings_Obot__class_Obot(tc_fun(_1515030, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1515032, tc_HOL_Obool), _1515030), _1515036))) = hAPP(c_Finite__Set_Ocard(_1515032), _1515036))], (44977 ^ _779327) ^ [_1668102, _1668104, _1668106, _1668108] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1668104), hAPP(hAPP(c_List_Olist_OCons(_1668104), _1668106), _1668108)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668102)) = hAPP(hAPP(c_List_Onth(_1668104), _1668108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1668102)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (14723 ^ _779327) ^ [_1027036, _1027038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027036)), 14726 ^ _779327 : [(14733 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027036), _1027038)), -(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), _1027038), _1027036))))], (14727 ^ _779327) ^ [] : [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), _1027038), _1027036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027036), _1027038)))]]], (49603 ^ _779327) ^ [_1773229, _1773231, _1773233] : [-(hAPP(c_List_Orotate(_1773229, _1773231), hAPP(c_List_Orev(_1773229), _1773233)) = hAPP(c_List_Orev(_1773229), hAPP(c_List_Orotate(_1773229, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773229)), _1773233)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1773231, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773229)), _1773233)))), _1773233)))], (45072 ^ _779327) ^ [_1670877, _1670879, _1670881] : [-(hAPP(c_List_Oset(_1670877), hAPP(hAPP(c_List_Olist_OCons(_1670877), _1670879), _1670881)) = hAPP(hAPP(c_Set_Oinsert(_1670877), _1670879), hAPP(c_List_Oset(_1670877), _1670881)))], (42561 ^ _779327) ^ [_1609264, _1609266, _1609268] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1609266, _1609264)), _1609268)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1609264, _1609266)), hAPP(c_Relation_Oconverse(_1609266, _1609264), _1609268))))], (15182 ^ _779327) ^ [_1034993, _1034995, _1034997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034993)), 15188 ^ _779327 : [(15191 ^ _779327) ^ [] : [hBOOL(hAPP(_1034995, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15187 ^ [_1034993, _1034995, _1034997]), _1034993)))], (15189 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1034995, 15187 ^ [_1034993, _1034995, _1034997])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034997)), 15196 ^ _779327 : [(15197 ^ _779327) ^ [_1035282] : [hBOOL(hAPP(_1034995, _1035282)), -(hBOOL(hAPP(_1034995, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1035282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1034997), _1034993)))))]]], (48062 ^ _779327) ^ [_1739672, _1739674, _1739676] : [_1739672 = _1739674, -(c_List_Olist__all2(_1739676, _1739676, c_fequal, _1739672, _1739674))], (1248 ^ _779327) ^ [_797915, _797917] : [-(class_Rings_Olinordered__idom(_797915)), _797917 = _797915, class_Rings_Olinordered__idom(_797917)], (14761 ^ _779327) ^ [_1027614, _1027616, _1027618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027616), _1027618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027614), _1027618)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1027614), _1027616))))], (39806 ^ _779327) ^ [_1535077, _1535079, _1535081, _1535083] : [hBOOL(hAPP(hAPP(c_member(_1535077), _1535079), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535077, tc_HOL_Obool)), _1535081), hAPP(c_Set_OCollect(_1535077), _1535083)))), 39809 ^ _779327 : [(39812 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1535083, _1535079)))], (39810 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535077), _1535079), _1535081)))]]], (39057 ^ _779327) ^ [_1518212, _1518214, _1518216, _1518218, _1518220, _1518222] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518212, _1518214), hAPP(hAPP(c_Set_Oinsert(_1518212), _1518216), _1518218)), hAPP(c_COMBK(tc_fun(_1518214, tc_HOL_Obool), _1518212), hAPP(hAPP(c_Set_Oinsert(_1518214), _1518220), _1518222))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1518212, _1518214)), hAPP(hAPP(c_Product__Type_OPair(_1518212, _1518214), _1518216), _1518220)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518212, _1518214), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518212, _1518214), _1518218), hAPP(c_COMBK(tc_fun(_1518214, tc_HOL_Obool), _1518212), hAPP(hAPP(c_Set_Oinsert(_1518214), _1518220), _1518222)))), hAPP(hAPP(c_Product__Type_OSigma(_1518212, _1518214), hAPP(hAPP(c_Set_Oinsert(_1518212), _1518216), _1518218)), hAPP(c_COMBK(tc_fun(_1518214, tc_HOL_Obool), _1518212), _1518222)))))], (40050 ^ _779327) ^ [_1543771, _1543773, _1543775, _1543777] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1543771, _1543773), _1543775), _1543777) = hAPP(c_Set_OCollect(tc_prod(_1543773, _1543773)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543773, _1543773, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1543773, tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_fun(_1543773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_fun(tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_fun(_1543773, tc_HOL_Obool)), _1543773), c_COMBC(_1543773, tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543773, tc_prod(_1543771, _1543771)), tc_fun(_1543773, tc_fun(tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_HOL_Obool)), _1543773), hAPP(c_COMBB(tc_prod(_1543771, _1543771), tc_fun(tc_fun(tc_prod(_1543771, _1543771), tc_HOL_Obool), tc_HOL_Obool), _1543773), c_member(tc_prod(_1543771, _1543771)))), hAPP(hAPP(c_COMBC(_1543773, tc_fun(_1543773, _1543771), tc_fun(_1543773, tc_prod(_1543771, _1543771))), hAPP(hAPP(c_COMBB(tc_fun(_1543771, tc_prod(_1543771, _1543771)), tc_fun(tc_fun(_1543773, _1543771), tc_fun(_1543773, tc_prod(_1543771, _1543771))), _1543773), c_COMBB(_1543771, tc_prod(_1543771, _1543771), _1543773)), hAPP(hAPP(c_COMBB(_1543771, tc_fun(_1543771, tc_prod(_1543771, _1543771)), _1543773), c_Product__Type_OPair(_1543771, _1543771)), _1543777))), _1543777)))), _1543775))))], (49701 ^ _779327) ^ [_1775348, _1775350, _1775352, _1775354] : [hBOOL(hAPP(hAPP(c_member(_1775348), _1775350), hAPP(c_List_Oset(_1775348), c_List_OtakeWhile(_1775348, _1775352, _1775354)))), 49704 ^ _779327 : [(49707 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1775352, _1775350)))], (49705 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775348), _1775350), hAPP(c_List_Oset(_1775348), _1775354))))]]], (33682 ^ _779327) ^ [_1394220, _1394222] : [-(c_FunDef_Orp__inv__image(_1394220, _1394222) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))))), tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))), tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)), tc_fun(tc_fun(_1394222, _1394220), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool)), c_COMBS(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)), tc_fun(tc_fun(_1394222, _1394220), tc_fun(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), tc_fun(tc_prod(_1394220, _1394220), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool))), tc_fun(_1394222, _1394220)), c_Product__Type_OPair(tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool), tc_fun(tc_prod(_1394222, _1394222), tc_HOL_Obool)))), c_Relation_Oinv__image(_1394220, _1394222))))), c_Relation_Oinv__image(_1394220, _1394222))))], (10566 ^ _779327) ^ [_950525, _950527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _950525), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _950525), _950527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _950525))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _950527))))], (34721 ^ _779327) ^ [_1419018, _1419020, _1419022, _1419024] : [class_Lattices_Osemilattice__inf(_1419018), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419018), _1419020), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419018), _1419022), _1419024)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419018), _1419022), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419018), _1419020), _1419024)))], (15005 ^ _779327) ^ [_1031840] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031840)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031840)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031840))], (4078 ^ _779327) ^ [_841209, _841211] : [_841211 = _841209, -(c_Power_Opower__class_Opower(_841211) = c_Power_Opower__class_Opower(_841209))], (15531 ^ _779327) ^ [_1041844, _1041846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1041844, _1041846)), _1041844)))], (41087 ^ _779327) ^ [_1574592, _1574594, _1574596] : [c_Wellfounded_Oacyclic(_1574592, _1574594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574592, _1574592), tc_HOL_Obool)), _1574596), _1574594)), -(c_Wellfounded_Oacyclic(_1574592, _1574596))], (22879 ^ _779327) ^ [_1175761, _1175763, _1175765, _1175767] : [class_Orderings_Olinorder(_1175761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175761), _1175763), _1175765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175761), _1175767), _1175765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175761), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175761), _1175763), _1175767)), _1175765)))], (27566 ^ _779327) ^ [_1267327, _1267329, _1267331, _1267333, _1267335] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267327, tc_fun(_1267329, tc_HOL_Obool)), _1267331), _1267333), _1267335)), 27570 ^ _779327 : [(27573 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1267333, 27569 ^ [_1267327, _1267329, _1267331, _1267333, _1267335]), _1267335)))], (27571 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267327), 27569 ^ [_1267327, _1267329, _1267331, _1267333, _1267335]), _1267331)))]]], (9056 ^ _779327) ^ [_925471, _925473, _925475, _925477] : [class_Rings_Ocomm__semiring__1(_925471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925471), _925473), _925475)), _925477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925471), _925473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925471), _925475), _925477)))], (40044 ^ _779327) ^ [_1543463, _1543465] : [-(c_Fun_Oinj__on(tc_fun(_1543463, _1543465), tc_fun(tc_prod(_1543463, _1543465), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1543463, _1543465), tc_HOL_Obool), tc_fun(tc_prod(_1543463, _1543465), tc_HOL_Obool), tc_fun(_1543463, _1543465)), c_Set_OCollect(tc_prod(_1543463, _1543465))), hAPP(hAPP(c_COMBB(tc_fun(_1543463, tc_fun(_1543465, tc_HOL_Obool)), tc_fun(tc_prod(_1543463, _1543465), tc_HOL_Obool), tc_fun(_1543463, _1543465)), c_Product__Type_Oprod_Oprod__case(_1543463, _1543465, tc_HOL_Obool)), hAPP(c_COMBB(_1543465, tc_fun(_1543465, tc_HOL_Obool), _1543463), hAPP(c_COMBC(_1543465, _1543465, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1543463, _1543465), tc_HOL_Obool))))], (34973 ^ _779327) ^ [_1423860, _1423862, _1423864] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423860, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423860, tc_HOL_Obool)), _1423862), _1423864)), _1423864)))], (14283 ^ _779327) ^ [_1020062, _1020064] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020062), _1020064))), -(c_Nat__Transfer_Otsub(_1020064, _1020062) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51985 ^ _779327) ^ [_1825692, _1825694] : [c_Relation_Oantisym(_1825692, _1825694), -(c_Relation_Oantisym(_1825692, hAPP(c_Relation_Oconverse(_1825692, _1825692), _1825694)))], (12752 ^ _779327) ^ [_992389, _992391] : [class_Rings_Olinordered__idom(_992389), 12755 ^ _779327 : [(12762 ^ _779327) ^ [] : [_992391 = c_Groups_Ozero__class_Ozero(_992389), -(c_Groups_Osgn__class_Osgn(_992389, _992391) = c_Groups_Ozero__class_Ozero(_992389))], (12756 ^ _779327) ^ [] : [c_Groups_Osgn__class_Osgn(_992389, _992391) = c_Groups_Ozero__class_Ozero(_992389), -(_992391 = c_Groups_Ozero__class_Ozero(_992389))]]], (8504 ^ _779327) ^ [_915563] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _915563) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3096 ^ _779327) ^ [_825806, _825808, _825810, _825812] : [-(c_FunDef_Orp__inv__image(_825812, _825808) = c_FunDef_Orp__inv__image(_825810, _825806)), _825812 = _825810, _825808 = _825806], (7432 ^ _779327) ^ [_896095, _896097, _896099, _896101] : [class_Groups_Omonoid__mult(_896095), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896095), _896097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _896099), _896101)) = hAPP(hAPP(c_Power_Opower__class_Opower(_896095), hAPP(hAPP(c_Power_Opower__class_Opower(_896095), _896097), _896099)), _896101))], (49297 ^ _779327) ^ [_1766757, _1766759] : [class_Orderings_Olinorder(_1766757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1766757), _1766759)), 49304 ^ _779327 : [(49309 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1766757), c_List_Olinorder__class_Osorted__list__of__set(_1766757, _1766759))))], (49307 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766757, c_List_Olinorder__class_Osorted__list__of__set(_1766757, _1766759)))], (49305 ^ _779327) ^ [] : [-(hAPP(c_List_Oset(_1766757), c_List_Olinorder__class_Osorted__list__of__set(_1766757, _1766759)) = _1766759)]]], (53000 ^ _779327) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (53070 ^ _779327) ^ [_1841382, _1841384] : [hBOOL(_1841382), -(hBOOL(hAPP(hAPP(c_fdisj, _1841382), _1841384)))], (24441 ^ _779327) ^ [_1204738, _1204740, _1204742] : [class_Rings_Ocomm__semiring__1(_1204738), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204738), _1204740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204738), _1204740), _1204742))))], (51023 ^ _779327) ^ [_1803991, _1803993, _1803995, _1803997] : [hBOOL(hAPP(_1803991, _1803993)), -(hAPP(c_List_Ofilter(_1803995, _1803991), c_List_Oreplicate(_1803995, _1803997, _1803993)) = c_List_Oreplicate(_1803995, _1803997, _1803993))], (35189 ^ _779327) ^ [_1429133, _1429135, _1429137, _1429139] : [-(hBOOL(hAPP(hAPP(c_member(_1429133), _1429135), _1429137))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429133, tc_HOL_Obool)), _1429137), hAPP(hAPP(c_Set_Oinsert(_1429133), _1429135), _1429139)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429133, tc_HOL_Obool)), _1429137), _1429139))], (49507 ^ _779327) ^ [_1771308, _1771310, _1771312, _1771314, _1771316] : [c_List_Olist__all2(_1771308, _1771310, _1771312, hAPP(c_List_Orev(_1771308), _1771314), _1771316), -(c_List_Olist__all2(_1771308, _1771310, _1771312, _1771314, hAPP(c_List_Orev(_1771310), _1771316)))], (26540 ^ _779327) ^ [_1246652, _1246654, _1246656] : [class_Orderings_Olinorder(_1246652), 26543 ^ _779327 : [(26550 ^ _779327) ^ [] : [_1246654 = _1246656, -(hAPP(c_SetInterval_Oord__class_OatMost(_1246652), _1246654) = hAPP(c_SetInterval_Oord__class_OatMost(_1246652), _1246656))], (26544 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1246652), _1246654) = hAPP(c_SetInterval_Oord__class_OatMost(_1246652), _1246656), -(_1246654 = _1246656)]]], (26856 ^ _779327) ^ [_1252517, _1252519, _1252521, _1252523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252517, tc_HOL_Obool)), _1252519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252517, tc_HOL_Obool)), _1252521), _1252523)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252517, tc_HOL_Obool)), _1252521), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252517, tc_HOL_Obool)), _1252519), _1252523)))], (39523 ^ _779327) ^ [_1528741, _1528743, _1528745, _1528747, _1528749, _1528751] : [-(c_Product__Type_Omap__pair(_1528741, _1528743, _1528745, _1528747, _1528749, _1528751) = hAPP(c_Product__Type_Oprod_Oprod__case(_1528741, _1528745, tc_prod(_1528743, _1528747)), hAPP(hAPP(c_COMBC(_1528741, tc_fun(_1528745, _1528747), tc_fun(_1528745, tc_prod(_1528743, _1528747))), hAPP(hAPP(c_COMBB(tc_fun(_1528747, tc_prod(_1528743, _1528747)), tc_fun(tc_fun(_1528745, _1528747), tc_fun(_1528745, tc_prod(_1528743, _1528747))), _1528741), c_COMBB(_1528747, tc_prod(_1528743, _1528747), _1528745)), hAPP(hAPP(c_COMBB(_1528743, tc_fun(_1528747, tc_prod(_1528743, _1528747)), _1528741), c_Product__Type_OPair(_1528743, _1528747)), _1528749))), _1528751)))], (18590 ^ _779327) ^ [_1095294, _1095296, _1095298] : [class_Rings_Olinordered__idom(_1095294), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095294), c_Groups_Ozero__class_Ozero(_1095294)), hAPP(hAPP(c_Power_Opower__class_Opower(_1095294), _1095296), 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)))), _1095298)))))], (25440 ^ _779327) ^ [_1223028, _1223030, _1223032] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223028, _1223030) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223032, _1223030), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223030), 25443 ^ [_1223028, _1223030, _1223032])) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223030), 25444 ^ [_1223028, _1223030, _1223032])))], (22359 ^ _779327) ^ [_1166084, _1166086, _1166088, _1166090] : [class_Orderings_Olinorder(_1166084), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166084), _1166086), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166084), _1166088), _1166090)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166084), _1166088), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166084), _1166086), _1166090)))], (41129 ^ _779327) ^ [_1575207, _1575209] : [c_Nitpick_Owf_H(_1575207, _1575209), 41132 ^ _779327 : [(41135 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575207, _1575207)), _1575209))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (41133 ^ _779327) ^ [] : [-(c_Wellfounded_Oacyclic(_1575207, _1575209))]]], (50824 ^ _779327) ^ [_1799937, _1799939, _1799941] : [50826 ^ _779327 : [(50829 ^ _779327) ^ [] : [hBOOL(hAPP(_1799939, 50825 ^ [_1799937, _1799939, _1799941]))], (50827 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1799937), 50825 ^ [_1799937, _1799939, _1799941]), hAPP(c_List_Oset(_1799937), _1799941))))]], -(c_List_Olist__all(_1799937, _1799939, _1799941))], (40496 ^ _779327) ^ [_1560574] : [-(c_Wellfounded_Owf(_1560574, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1560574, _1560574), tc_HOL_Obool))))], (45028 ^ _779327) ^ [_1669612, _1669614, _1669616, _1669618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669612), _1669614)), -(hAPP(hAPP(c_List_Onth(_1669616), hAPP(hAPP(c_List_Otake(_1669616), _1669614), _1669618)), _1669612) = hAPP(hAPP(c_List_Onth(_1669616), _1669618), _1669612))], (32186 ^ _779327) ^ [_1363570, _1363572, _1363574] : [class_Lattices_Olattice(_1363570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363570), _1363572)), 32193 ^ _779327 : [(32200 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363570, tc_HOL_Obool)), _1363572), hAPP(hAPP(c_Set_Oinsert(_1363570), _1363574), c_Orderings_Obot__class_Obot(tc_fun(_1363570, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1363570, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1363570, hAPP(hAPP(c_Set_Oinsert(_1363570), _1363574), _1363572)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1363570), _1363574), c_Big__Operators_Olattice__class_OSup__fin(_1363570, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363570, tc_HOL_Obool)), _1363572), hAPP(hAPP(c_Set_Oinsert(_1363570), _1363574), c_Orderings_Obot__class_Obot(tc_fun(_1363570, tc_HOL_Obool)))))))], (32194 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363570, tc_HOL_Obool)), _1363572), hAPP(hAPP(c_Set_Oinsert(_1363570), _1363574), c_Orderings_Obot__class_Obot(tc_fun(_1363570, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1363570, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1363570, hAPP(hAPP(c_Set_Oinsert(_1363570), _1363574), _1363572)) = _1363574)]]], (46052 ^ _779327) ^ [_1695635, _1695637, _1695639, _1695641, _1695643] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695635), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695637)), _1695639)))), -(hAPP(hAPP(c_List_Olist__update(_1695637, hAPP(hAPP(c_List_Oappend(_1695637), _1695639), _1695641)), _1695635), _1695643) = hAPP(hAPP(c_List_Oappend(_1695637), _1695639), hAPP(hAPP(c_List_Olist__update(_1695637, _1695641), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1695635), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695637)), _1695639))), _1695643)))], (31245 ^ _779327) ^ [_1345346, _1345348, _1345350, _1345352] : [hBOOL(hAPP(hAPP(_1345350, _1345352), _1345348)), -(hBOOL(hAPP(hAPP(c_member(_1345346), _1345348), c_SetInterval_Oord_OatLeast(_1345346, _1345350, _1345352))))], (52766 ^ _779327) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (21156 ^ _779327) ^ [_1142278, _1142280] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1142278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1142280))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1142278), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142280))), 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))))], (33597 ^ _779327) ^ [_1391812, _1391814, _1391816] : [33599 ^ _779327 : [(33602 ^ _779327) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1391816, 33598 ^ [_1391812, _1391814, _1391816]))], (33600 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391812), 33598 ^ [_1391812, _1391814, _1391816]), _1391814)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391812, tc_Int_Oint), _1391816), _1391814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391812, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1391812), c_Int_Onat), _1391816)), _1391814)))], (18014 ^ _779327) ^ [_1085132, _1085134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085132)), c_Int_OBit1(_1085134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085132), _1085134)))], (44971 ^ _779327) ^ [_1667983, _1667985, _1667987, _1667989] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667983) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1667985), hAPP(hAPP(c_List_Olist_OCons(_1667985), _1667987), _1667989)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667983)) = _1667987)], (16698 ^ _779327) ^ [_1062550, _1062552] : [16699 ^ _779327 : [(16700 ^ _779327) ^ [_1062599] : [_1062550 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062552), _1062599)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062550, _1062552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42120 ^ _779327) ^ [_1597587, _1597589, _1597591, _1597593, _1597595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597587, _1597587)), hAPP(hAPP(c_Product__Type_OPair(_1597587, _1597587), _1597589), _1597591)), c_Transitive__Closure_Otrancl(_1597587, _1597593))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1597587, _1597587)), hAPP(hAPP(c_Product__Type_OPair(_1597587, _1597587), _1597591), _1597595)), c_Transitive__Closure_Otrancl(_1597587, _1597593))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597587, _1597587)), hAPP(hAPP(c_Product__Type_OPair(_1597587, _1597587), _1597589), _1597595)), c_Transitive__Closure_Otrancl(_1597587, _1597593))))], (29312 ^ _779327) ^ [_1301996, _1301998, _1302000, _1302002, _1302004] : [class_Groups_Ocomm__monoid__add(_1301996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301998), _1302000)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1301998, _1301996), _1302002), hAPP(hAPP(c_Set_Oinsert(_1301998), _1302004), _1302000)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301996), hAPP(_1302002, _1302004)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1301998, _1301996), _1302002), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301998, tc_HOL_Obool)), _1302000), hAPP(hAPP(c_Set_Oinsert(_1301998), _1302004), c_Orderings_Obot__class_Obot(tc_fun(_1301998, tc_HOL_Obool)))))))], (6220 ^ _779327) ^ [_877303, _877305, _877307] : [class_Orderings_Opreorder(_877303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877303), _877305), _877307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877303), _877307), _877305))], (47112 ^ _779327) ^ [_1719821, _1719823, _1719825] : [-(hAPP(c_List_Orotate1(_1719821), hAPP(c_List_Orotate(_1719821, _1719823), _1719825)) = hAPP(c_List_Orotate(_1719821, _1719823), hAPP(c_List_Orotate1(_1719821), _1719825)))], (26607 ^ _779327) ^ [_1247681] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1247681) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1247681))], (23301 ^ _779327) ^ [_1183892, _1183894, _1183896, _1183898, _1183900, _1183902, _1183904] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1183892, _1183894, _1183896, _1183898), _1183900), _1183902), _1183904) = hAPP(hAPP(_1183902, hAPP(c_Product__Type_Ofst(_1183894, _1183896), hAPP(_1183900, _1183904))), hAPP(c_Product__Type_Osnd(_1183894, _1183896), hAPP(_1183900, _1183904))))], (9180 ^ _779327) ^ [_927740, _927742, _927744] : [_927740 = _927742, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927744, tc_HOL_Obool)), _927742), _927740)))], (13336 ^ _779327) ^ [_1002660, _1002662, _1002664] : [class_Rings_Ocomm__semiring__1(_1002660), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002660), _1002662), _1002664)), _1002664) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002660), _1002662), c_Groups_Oone__class_Oone(_1002660))), _1002664))], (41740 ^ _779327) ^ [_1589125, _1589127, _1589129, _1589131] : [-(c_New__Random__Sequence_Oneg__map(_1589125, _1589127, _1589129, _1589131) = c_New__Random__Sequence_Oneg__bind(_1589125, _1589127, _1589131, hAPP(c_Fun_Ocomp(_1589127, 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(_1589127)))))), _1589125, c_New__Random__Sequence_Oneg__single(_1589127)), _1589129)))], (22501 ^ _779327) ^ [_1168684, _1168686, _1168688, _1168690, _1168692] : [class_Orderings_Olinorder(_1168684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168684), _1168686), _1168688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168684), _1168690), _1168692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168684), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168684), _1168686), _1168690)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168684), _1168688), _1168692))))], (39632 ^ _779327) ^ [_1531151, _1531153, _1531155, _1531157, _1531159] : [c_Finite__Set_Ofun__left__comm__idem(_1531151, _1531153, _1531155), -(hAPP(hAPP(_1531155, _1531157), hAPP(hAPP(_1531155, _1531157), _1531159)) = hAPP(hAPP(_1531155, _1531157), _1531159))], (7552 ^ _779327) ^ [_898135, _898137, _898139] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898135), _898137) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898139), _898137), -(_898135 = _898139), -(_898137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5334 ^ _779327) ^ [_860721, _860723] : [_860723 = _860721, -(c_Lattices_Osemilattice__sup__class_Osup(_860723) = c_Lattices_Osemilattice__sup__class_Osup(_860721))], (38792 ^ _779327) ^ [_1511855, _1511857, _1511859, _1511861] : [38793 ^ _779327 : [(38796 ^ _779327) ^ [] : [_1511861 = c_Orderings_Obot__class_Obot(tc_fun(_1511857, tc_HOL_Obool))], (38794 ^ _779327) ^ [] : [_1511859 = c_Orderings_Obot__class_Obot(tc_fun(_1511855, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1511855, _1511857), _1511859), hAPP(c_COMBK(tc_fun(_1511857, tc_HOL_Obool), _1511855), _1511861)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1511855, _1511857), tc_HOL_Obool)))], (27016 ^ _779327) ^ [_1255992, _1255994, _1255996, _1255998] : [class_Lattices_Osemilattice__sup(_1255992), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255992), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255992), _1255994), _1255996)), _1255998) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255992), _1255994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255992), _1255996), _1255998)))], (50878 ^ _779327) ^ [_1800964, _1800966, _1800968, _1800970] : [-(c_List_Olist__all(_1800964, _1800966, hAPP(hAPP(c_List_Olist_OCons(_1800964), _1800968), _1800970))), hBOOL(hAPP(_1800966, _1800968)), c_List_Olist__all(_1800964, _1800966, _1800970)], (16782 ^ _779327) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (7021 ^ _779327) ^ [_889226, _889228] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889226), _889228))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889226), hAPP(c_Nat_OSuc, _889228))), -(_889228 = _889226)], (16758 ^ _779327) ^ [_1063490, _1063492] : [class_Int_Onumber__ring(_1063490), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063490), _1063492), hAPP(c_Int_Onumber__class_Onumber__of(_1063490), c_Int_OPls)) = _1063492)], (25988 ^ _779327) ^ [_1235312, _1235314] : [25990 ^ _779327 : [(25993 ^ _779327) ^ [] : [hBOOL(hAPP(_1235314, 25989 ^ [_1235312, _1235314]))], (25991 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25989 ^ [_1235312, _1235314]), _1235312)))]], 25994 ^ _779327 : [(25995 ^ _779327) ^ [_1235462] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1235462), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235312))), -(hBOOL(hAPP(_1235314, _1235462)))]]], (18080 ^ _779327) ^ [_1086294, _1086296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086294), _1086296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086294)), c_Int_OBit0(_1086296))))], (43764 ^ _779327) ^ [_1636298, _1636300, _1636302] : [class_Complete__Lattice_Ocomplete__lattice(_1636298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636298), _1636300)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1636298), _1636302), c_Complete__Lattice_OInf__class_OInf(_1636298, _1636300)) = hAPP(hAPP(c_Finite__Set_Ofold(_1636298, _1636298, c_Lattices_Osemilattice__inf__class_Oinf(_1636298)), _1636302), _1636300))], (14175 ^ _779327) ^ [_1018054, _1018056, _1018058] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018054), _1018056)), _1018058) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018054), _1018058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018056), _1018058)))], (10835 ^ _779327) ^ [_955910] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _955910)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _955910)))], (52862 ^ _779327) ^ [_1838975, _1838977] : [-(class_Nat_Osize(tc_sum(_1838975, _1838977)))], (17874 ^ _779327) ^ [_1082762, _1082764] : [c_Int_OBit0(_1082762) = c_Int_OBit0(_1082764), -(_1082762 = _1082764)], (15778 ^ _779327) ^ [_1046289, _1046291] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046289), _1046291) = c_Groups_Oone__class_Oone(tc_Int_Oint), 15783 ^ _779327 : [(15786 ^ _779327) ^ [] : [-(_1046291 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15784 ^ _779327) ^ [] : [-(_1046289 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 15787 ^ _779327 : [(15790 ^ _779327) ^ [] : [-(_1046291 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (15788 ^ _779327) ^ [] : [-(_1046289 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (47219 ^ _779327) ^ [_1721989, _1721991, _1721993, _1721995] : [class_Complete__Lattice_Ocomplete__lattice(_1721989), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1721991, _1721989), hAPP(c_List_Oset(_1721991), _1721993)), _1721995) = hAPP(c_List_Ofoldl(_1721989, _1721991, hAPP(c_COMBC(_1721991, _1721989, _1721989), hAPP(hAPP(c_COMBB(_1721989, tc_fun(_1721989, _1721989), _1721991), c_Lattices_Osemilattice__sup__class_Osup(_1721989)), _1721995)), c_Orderings_Obot__class_Obot(_1721989)), _1721993))], (35836 ^ _779327) ^ [_1444230, _1444232, _1444234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1444230), _1444232)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444230), _1444234)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444230, tc_HOL_Obool)), _1444232), _1444234) = c_Orderings_Obot__class_Obot(tc_fun(_1444230, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1444230), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444230, tc_HOL_Obool)), _1444232), _1444234)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1444230), _1444232)), hAPP(c_Finite__Set_Ocard(_1444230), _1444234)))], (32032 ^ _779327) ^ [_1361168, _1361170, _1361172] : [class_Lattices_Olattice(_1361168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361168), _1361170)), -(_1361170 = c_Orderings_Obot__class_Obot(tc_fun(_1361168, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1361168, hAPP(hAPP(c_Set_Oinsert(_1361168), _1361172), _1361170)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1361168), _1361172), c_Big__Operators_Olattice__class_OSup__fin(_1361168, _1361170)))], (27344 ^ _779327) ^ [_1262746, _1262748, _1262750, _1262752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262746, tc_HOL_Obool)), _1262748), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262746, tc_HOL_Obool)), _1262750), _1262752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262746, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262746, tc_HOL_Obool)), _1262748), _1262750)), _1262752)))], (14123 ^ _779327) ^ [_1016827, _1016829, _1016831] : [_1016829 = _1016831, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016827), _1016829) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016827), _1016831))], (52916 ^ _779327) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (33654 ^ _779327) ^ [_1393589, _1393591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1393589), _1393591)), -(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), _1393589), _1393591)), c_Wellfounded_Oless__than)))], (24341 ^ _779327) ^ [_1203053, _1203055] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203053), _1203055)), 24346 ^ _779327 : [(24349 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203055), _1203053))], (24347 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203053), _1203055)))]], -(_1203053 = _1203055)], (52926 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (11105 ^ _779327) ^ [_960646, _960648] : [class_Rings_Olinordered__idom(_960646), -(c_Groups_Osgn__class_Osgn(_960646, c_Groups_Osgn__class_Osgn(_960646, _960648)) = c_Groups_Osgn__class_Osgn(_960646, _960648))], (15271 ^ _779327) ^ [_1036642, _1036644] : [class_Divides_Osemiring__div(_1036642), -(c_Divides_Odiv__class_Omod(_1036642, _1036644, _1036644) = c_Groups_Ozero__class_Ozero(_1036642))], (33375 ^ _779327) ^ [_1387289, _1387291, _1387293, _1387295, _1387297] : [class_Groups_Ocomm__monoid__mult(_1387289), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387291), _1387293)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387291, _1387289), _1387295), hAPP(hAPP(c_Set_Oinsert(_1387291), _1387297), _1387293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387289), hAPP(_1387295, _1387297)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387291, _1387289), _1387295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387291, tc_HOL_Obool)), _1387293), hAPP(hAPP(c_Set_Oinsert(_1387291), _1387297), c_Orderings_Obot__class_Obot(tc_fun(_1387291, tc_HOL_Obool)))))))], (5304 ^ _779327) ^ [_860274, _860276, _860278, _860280] : [-(c_Relation_OId__on(_860280, _860276) = c_Relation_OId__on(_860278, _860274)), _860280 = _860278, _860276 = _860274], (38319 ^ _779327) ^ [_1500508, _1500510, _1500512, _1500514, _1500516] : [c_Equiv__Relations_Oequivp(_1500508, _1500510), hBOOL(hAPP(hAPP(_1500510, _1500512), _1500514)), hBOOL(hAPP(hAPP(_1500510, _1500514), _1500516)), -(hBOOL(hAPP(hAPP(_1500510, _1500512), _1500516)))], (39545 ^ _779327) ^ [_1529392, _1529394, _1529396, _1529398, _1529400, _1529402, _1529404, _1529406] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529392, _1529394)), _1529396), hAPP(c_Set_Oimage(tc_prod(_1529398, _1529400), tc_prod(_1529392, _1529394), c_Product__Type_Omap__pair(_1529398, _1529392, _1529400, _1529394, _1529402, _1529404)), _1529406))), 39550 ^ _779327 : [(39553 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529398, _1529400)), hAPP(hAPP(c_Product__Type_OPair(_1529398, _1529400), 39548 ^ [_1529392, _1529394, _1529396, _1529398, _1529400, _1529402, _1529404, _1529406]), 39549 ^ [_1529392, _1529394, _1529396, _1529398, _1529400, _1529402, _1529404, _1529406])), _1529406)))], (39551 ^ _779327) ^ [] : [-(_1529396 = hAPP(hAPP(c_Product__Type_OPair(_1529392, _1529394), hAPP(_1529402, 39548 ^ [_1529392, _1529394, _1529396, _1529398, _1529400, _1529402, _1529404, _1529406])), hAPP(_1529404, 39549 ^ [_1529392, _1529394, _1529396, _1529398, _1529400, _1529402, _1529404, _1529406])))]]], (47879 ^ _779327) ^ [_1735797, _1735799, _1735801] : [hBOOL(hAPP(c_List_Olistsp(_1735797, hAPP(hAPP(c_COMBC(_1735797, tc_fun(_1735797, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735797)), _1735799)), _1735801)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1735797)), _1735801), c_List_Olists(_1735797, _1735799))))], (40255 ^ _779327) ^ [_1552255, _1552257, _1552259] : [c_Predicate_Oreflp(_1552255, _1552257), -(hBOOL(hAPP(hAPP(_1552257, _1552259), _1552259)))], (21242 ^ _779327) ^ [_1144198, _1144200] : [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(_1144200))), 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), _1144198)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1144198)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144200))))], (46590 ^ _779327) ^ [_1708575, _1708577, _1708579, _1708581] : [-(hAPP(hAPP(c_List_Oappend(_1708575), _1708577), _1708579) = _1708581), _1708577 = hAPP(hAPP(c_List_Otake(_1708575), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708575)), _1708577)), _1708581), _1708579 = hAPP(hAPP(c_List_Odrop(_1708575), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708575)), _1708577)), _1708581)], (34679 ^ _779327) ^ [_1418113, _1418115, _1418117, _1418119] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418113, tc_HOL_Obool)), _1418115), _1418117), _1418119)), -(hBOOL(hAPP(_1418115, _1418119)))], (38774 ^ _779327) ^ [_1511356, _1511358, _1511360, _1511362] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1511356, _1511358)), hAPP(hAPP(c_Product__Type_OSigma(_1511356, _1511358), _1511360), hAPP(c_COMBK(tc_fun(_1511358, tc_HOL_Obool), _1511356), _1511362))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1511356), _1511360)), hAPP(c_Finite__Set_Ocard(_1511358), _1511362)))], (33208 ^ _779327) ^ [_1383737, _1383739, _1383741] : [class_Groups_Ocomm__monoid__add(_1383737), class_Groups_Ocomm__monoid__mult(_1383737), c_Nat__Transfer_Onat__set(_1383739), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1383737), _1383741), _1383739) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1383737), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1383737, tc_Nat_Onat), _1383741), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1383739)))], (14635 ^ _779327) ^ [_1025823] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1025823))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025823)))], (36957 ^ _779327) ^ [_1469007, _1469009, _1469011, _1469013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469007), _1469009)), 36960 ^ _779327 : [(36967 ^ _779327) ^ [] : [hAPP(c_Finite__Set_Ocard(_1469011), hAPP(c_Set_Oimage(_1469007, _1469011, _1469013), _1469009)) = hAPP(c_Finite__Set_Ocard(_1469007), _1469009), -(c_Fun_Oinj__on(_1469007, _1469011, _1469013, _1469009))], (36961 ^ _779327) ^ [] : [c_Fun_Oinj__on(_1469007, _1469011, _1469013, _1469009), -(hAPP(c_Finite__Set_Ocard(_1469011), hAPP(c_Set_Oimage(_1469007, _1469011, _1469013), _1469009)) = hAPP(c_Finite__Set_Ocard(_1469007), _1469009))]]], (44462 ^ _779327) ^ [_1652703, _1652705, _1652707] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652703)), c_List_Osublist(_1652703, _1652705, _1652707)) = 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(_1652703)), _1652705)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1652707)))))], (46134 ^ _779327) ^ [_1697120, _1697122, _1697124] : [_1697120 = hAPP(hAPP(c_List_Oappend(_1697122), _1697120), _1697124), -(_1697124 = c_List_Olist_ONil(_1697122))], (14153 ^ _779327) ^ [_1017540, _1017542, _1017544] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017540, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017540, tc_HOL_Obool)), _1017542), _1017544)), _1017542)))], (17206 ^ _779327) ^ [_1071362, _1071364] : [class_Int_Onumber__ring(_1071362), class_Rings_Olinordered__idom(_1071362), 17213 ^ _779327 : [(17220 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071364), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071362), hAPP(c_Int_Onumber__class_Onumber__of(_1071362), _1071364)), c_Groups_Ozero__class_Ozero(_1071362))))], (17214 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071362), hAPP(c_Int_Onumber__class_Onumber__of(_1071362), _1071364)), c_Groups_Ozero__class_Ozero(_1071362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071364), c_Int_OPls)))]]], (35705 ^ _779327) ^ [_1441055, _1441057, _1441059, _1441061, _1441063] : [c_Finite__Set_Ofolding__one(_1441055, _1441057, _1441059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441055), _1441061)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441055), _1441063)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441055, tc_HOL_Obool)), _1441061), _1441063) = c_Orderings_Obot__class_Obot(tc_fun(_1441055, tc_HOL_Obool))), -(hAPP(hAPP(_1441057, hAPP(_1441059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441055, tc_HOL_Obool)), _1441061), _1441063))), hAPP(_1441059, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441055, tc_HOL_Obool)), _1441061), _1441063))) = hAPP(hAPP(_1441057, hAPP(_1441059, _1441061)), hAPP(_1441059, _1441063)))], (51077 ^ _779327) ^ [_1804853, _1804855, _1804857] : [-(_1804853 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1804855), c_List_Oreplicate(_1804855, _1804853, _1804857)) = _1804857)], (13628 ^ _779327) ^ [_1007805, _1007807, _1007809] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1007805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007807), _1007809)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1007805), _1007807)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1007805), _1007809)))], (194 ^ _779327) ^ [_782146, _782148, _782150, _782152] : [-(c_Nitpick_Orefl_H(_782150, _782146)), c_Nitpick_Orefl_H(_782152, _782148), _782152 = _782150, _782148 = _782146], (48419 ^ _779327) ^ [_1747616, _1747618, _1747620, _1747622] : [class_Orderings_Olinorder(_1747616), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747618)), c_List_Olinorder__class_Osort__key(_1747618, _1747616, _1747620, _1747622)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747618)), _1747622))], (47714 ^ _779327) ^ [_1732361, _1732363, _1732365, _1732367] : [class_Orderings_Olinorder(_1732361), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1732363, _1732361, _1732365), _1732367), c_List_Olist_ONil(_1732363)) = hAPP(hAPP(c_List_Olist_OCons(_1732363), _1732367), c_List_Olist_ONil(_1732363)))], (32334 ^ _779327) ^ [_1366999, _1367001, _1367003] : [class_Orderings_Olinorder(_1366999), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366999), _1367001)), hBOOL(hAPP(hAPP(c_member(_1366999), _1367003), _1367001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366999), c_Big__Operators_Olinorder__class_OMin(_1366999, _1367001)), _1367003)))], (39515 ^ _779327) ^ [_1528509, _1528511, _1528513, _1528515, _1528517, _1528519, _1528521] : [-(hAPP(c_Product__Type_Ofst(_1528509, _1528511), hAPP(c_Product__Type_Omap__pair(_1528513, _1528509, _1528515, _1528511, _1528517, _1528519), _1528521)) = hAPP(_1528517, hAPP(c_Product__Type_Ofst(_1528513, _1528515), _1528521)))], (53082 ^ _779327) ^ [_1841556, _1841558] : [hBOOL(hAPP(hAPP(c_fdisj, _1841556), _1841558)), -(hBOOL(_1841556)), -(hBOOL(_1841558))], (26127 ^ _779327) ^ [_1238081, _1238083, _1238085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238081)), 26130 ^ _779327 : [(26131 ^ _779327) ^ [_1238215] : [26133 ^ _779327 : [(26139 ^ _779327) ^ [] : [-(_1238215 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26135 ^ [_1238081, _1238083, _1238085, _1238215]), 26132 ^ [_1238081, _1238083, _1238085, _1238215]))], (26137 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26135 ^ [_1238081, _1238083, _1238085, _1238215]), _1238083)))], (26134 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26132 ^ [_1238081, _1238083, _1238085, _1238215]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1238081))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238215), _1238085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1238215), _1238081)), _1238085)))]]], (45135 ^ _779327) ^ [_1672381, _1672383, _1672385, _1672387, _1672389, _1672391] : [-(hAPP(hAPP(c_List_Omap(_1672381, _1672383), _1672385), hAPP(hAPP(c_List_Omap(_1672387, _1672381), _1672389), _1672391)) = hAPP(hAPP(c_List_Omap(_1672387, _1672383), hAPP(c_Fun_Ocomp(_1672381, _1672383, _1672387, _1672385), _1672389)), _1672391))], (22325 ^ _779327) ^ [_1165436, _1165438] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1165436)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1165438)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1165438))), 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), _1165436)), c_Int_Onat)))))], (42140 ^ _779327) ^ [_1598075, _1598077] : [-(c_Transitive__Closure_Otrancl(_1598075, _1598077) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1598075, _1598075), tc_HOL_Obool)), _1598077), hAPP(hAPP(c_Relation_Orel__comp(_1598075, _1598075, _1598075), c_Transitive__Closure_Otrancl(_1598075, _1598077)), _1598077)))], (15630 ^ _779327) ^ [_1043654, _1043656, _1043658, _1043660] : [class_Divides_Osemiring__div(_1043654), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043654), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043654), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1043654), _1043656), _1043658)), _1043658)), c_Divides_Odiv__class_Omod(_1043654, _1043656, _1043658))), _1043660) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043654), _1043656), _1043660))], (14131 ^ _779327) ^ [_1016983, _1016985, _1016987] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016985), _1016987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016983), _1016987)))], (33684 ^ _779327) ^ [_1394733, _1394735, _1394737] : [class_Orderings_Olinorder(_1394733), hAPP(_1394735, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1394733), 33689 ^ [_1394733, _1394735, _1394737]), 33690 ^ [_1394733, _1394735, _1394737])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1394733), hAPP(_1394735, 33689 ^ [_1394733, _1394735, _1394737])), hAPP(_1394735, 33690 ^ [_1394733, _1394735, _1394737])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394733), _1394737)), -(_1394737 = c_Orderings_Obot__class_Obot(tc_fun(_1394733, tc_HOL_Obool))), -(hAPP(_1394735, c_Big__Operators_Olattice_OInf__fin(_1394733, c_Orderings_Oord__class_Omin(_1394733), _1394737)) = c_Big__Operators_Olattice_OInf__fin(_1394733, c_Orderings_Oord__class_Omin(_1394733), hAPP(c_Set_Oimage(_1394733, _1394733, _1394735), _1394737)))], (44644 ^ _779327) ^ [_1658499, _1658501, _1658503, _1658505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658499), tc_List_Olist(_1658499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658499), tc_List_Olist(_1658499)), _1658501), _1658503)), c_List_Olistrel1(_1658499, hAPP(c_Relation_Oconverse(_1658499, _1658499), _1658505)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658499), tc_List_Olist(_1658499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658499), tc_List_Olist(_1658499)), _1658501), _1658503)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1658499), tc_List_Olist(_1658499)), c_List_Olistrel1(_1658499, _1658505)))))], (1528 ^ _779327) ^ [_801415, _801417] : [-(class_Finite__Set_Ofinite(_801415)), _801417 = _801415, class_Finite__Set_Ofinite(_801417)], (38237 ^ _779327) ^ [_1498341, _1498343, _1498345, _1498347] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498341, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38238 ^ [_1498341, _1498343, _1498345, _1498347])), _1498343) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498341, 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), 38238 ^ [_1498341, _1498343, _1498345, _1498347]), _1498345))), _1498347), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498341, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1498343) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498341, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1498347))], (35427 ^ _779327) ^ [_1434571, _1434573, _1434575, _1434577] : [class_Complete__Lattice_Ocomplete__lattice(_1434571), _1434573 = c_Inductive_Ocomplete__lattice__class_Olfp(_1434571, _1434575), c_Orderings_Oorder__class_Omono(_1434571, _1434571, _1434575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434571), hAPP(_1434575, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1434571), _1434573), _1434577))), _1434577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434571), _1434573), _1434577)))], (24119 ^ _779327) ^ [_1199501, _1199503] : [_1199501 = _1199503, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199501), _1199503)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199503), _1199501)))], (36716 ^ _779327) ^ [_1464447, _1464449, _1464451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464447, _1464447)), _1464449), c_Relation_OId__on(_1464447, _1464451))), 36720 ^ _779327 : [(36723 ^ _779327) ^ [] : [-(_1464449 = hAPP(hAPP(c_Product__Type_OPair(_1464447, _1464447), 36719 ^ [_1464447, _1464449, _1464451]), 36719 ^ [_1464447, _1464449, _1464451]))], (36721 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464447), 36719 ^ [_1464447, _1464449, _1464451]), _1464451)))]]], (33981 ^ _779327) ^ [_1401088, _1401090, _1401092] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1401088, tc_HOL_Obool)), _1401090), hAPP(c_Set_OPow(_1401088), _1401092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401088, tc_HOL_Obool)), _1401090), _1401092)))], (23047 ^ _779327) ^ [_1178627, _1178629, _1178631, _1178633] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1178627), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178627), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178627), _1178629), _1178631)), _1178633) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178627), _1178629), _1178633)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178627), _1178631), _1178633)))], (29392 ^ _779327) ^ [_1303829, _1303831, _1303833, _1303835] : [-(c_Sum__Type_OPlus(_1303829, _1303831, _1303833, _1303835) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1303829, _1303831), tc_HOL_Obool))), _1303833 = c_Orderings_Obot__class_Obot(tc_fun(_1303829, tc_HOL_Obool)), _1303835 = c_Orderings_Obot__class_Obot(tc_fun(_1303831, tc_HOL_Obool))], (19507 ^ _779327) ^ [_1111505, _1111507, _1111509, _1111511, _1111513] : [class_Fields_Olinordered__field(_1111505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111505), c_Groups_Ozero__class_Ozero(_1111505)), _1111507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111505), _1111507), _1111509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111505), c_Groups_Ozero__class_Ozero(_1111505)), _1111511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111505), _1111511), _1111513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111505), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111505), _1111507), _1111513)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111505), _1111509), _1111511))))], (19593 ^ _779327) ^ [_1113156, _1113158, _1113160, _1113162] : [class_Fields_Olinordered__field(_1113156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113156), _1113158), c_Groups_Ozero__class_Ozero(_1113156))), 19600 ^ _779327 : [(19607 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113156), _1113162), _1113158)), _1113160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113156), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113156), _1113160), _1113158)), _1113162)))], (19601 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113156), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113156), _1113160), _1113158)), _1113162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113156), _1113162), _1113158)), _1113160)))]]], (41934 ^ _779327) ^ [_1593596, _1593598, _1593600, _1593602, _1593604, _1593606] : [class_Rings_Ocomm__semiring__1(_1593596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593598), _1593600)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1593598, tc_HOL_Obool)), _1593602), _1593600)), 41948 ^ _779327 : [(41951 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1593596), hAPP(_1593604, 41947 ^ [_1593596, _1593598, _1593600, _1593602, _1593604, _1593606])), hAPP(_1593606, 41947 ^ [_1593596, _1593598, _1593600, _1593602, _1593604, _1593606])))], (41949 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1593598), 41947 ^ [_1593596, _1593598, _1593600, _1593602, _1593604, _1593606]), _1593602)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1593596), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1593598, _1593596), _1593604), _1593602)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1593598, _1593596), _1593606), _1593600))))], (4048 ^ _779327) ^ [_840762, _840764, _840766, _840768] : [-(c_HOL_OLet(_840768, _840764) = c_HOL_OLet(_840766, _840762)), _840768 = _840766, _840764 = _840762], (26432 ^ _779327) ^ [_1244689, _1244691, _1244693] : [class_Orderings_Olinorder(_1244689), 26435 ^ _779327 : [(26442 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244689), _1244693), _1244691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244689, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244689), _1244691)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244689), _1244693))))], (26436 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244689, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244689), _1244691)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244689), _1244693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244689), _1244693), _1244691)))]]], (18114 ^ _779327) ^ [_1086909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1086909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1086909))))], (46602 ^ _779327) ^ [_1708881, _1708883, _1708885, _1708887] : [_1708881 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1708883), _1708881), hAPP(hAPP(c_List_Olist_OCons(_1708883), _1708885), _1708887)) = hAPP(hAPP(c_List_Olist_OCons(_1708883), _1708885), _1708887))], (41085 ^ _779327) ^ [_1574557] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 41081 ^ [_1574557]), c_Int_OInteg)))], (52347 ^ _779327) ^ [_1832383, _1832385, _1832387, _1832389, _1832391] : [c_Equiv__Relations_Opart__equivp(_1832383, _1832385), hBOOL(hAPP(hAPP(_1832385, _1832387), _1832389)), hBOOL(hAPP(hAPP(_1832385, _1832389), _1832391)), -(hBOOL(hAPP(hAPP(_1832385, _1832387), _1832391)))], (9861 ^ _779327) ^ [_939063] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939063), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _939063)], (46544 ^ _779327) ^ [_1707464, _1707466, _1707468, _1707470, _1707472] : [hAPP(hAPP(c_List_Odrop(_1707464), _1707466), _1707468) = hAPP(hAPP(c_List_Olist_OCons(_1707464), _1707470), _1707472), -(hAPP(hAPP(c_List_Onth(_1707464), _1707468), _1707466) = _1707470)], (53006 ^ _779327) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (7129 ^ _779327) ^ [_890916, _890918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890916), hAPP(c_Nat_OSuc, _890918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890916), _890918))), -(_890916 = hAPP(c_Nat_OSuc, _890918))], (34249 ^ _779327) ^ [_1407884, _1407886, _1407888, _1407890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407884), _1407890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407888), _1407886))), -(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), _1407884), _1407886)), 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), _1407888), _1407890)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (11513 ^ _779327) ^ [_969530, _969532, _969534, _969536, _969538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969530), _969532)), -(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), _969532), _969534)), _969536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969530), _969534)), _969538)) = 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), _969532), _969530)), _969534)), _969536)), _969538))], (3062 ^ _779327) ^ [_825247, _825249, _825251, _825253, _825255, _825257, _825259, _825261, _825263, _825265] : [-(c_SetInterval_Oord_OatLeastLessThan(_825265, _825261, _825257, _825253, _825249) = c_SetInterval_Oord_OatLeastLessThan(_825263, _825259, _825255, _825251, _825247)), _825265 = _825263, _825261 = _825259, _825257 = _825255, _825253 = _825251, _825249 = _825247], (14386 ^ _779327) ^ [_1021840, _1021842] : [-(hBOOL(hAPP(_1021840, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1021840, _1021842)), 14394 ^ _779327 : [(14397 ^ _779327) ^ [_1022078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022078), 14393 ^ [_1021840, _1021842])), hBOOL(hAPP(_1021840, _1022078))], (14403 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1021840, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 14393 ^ [_1021840, _1021842]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (14395 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14393 ^ [_1021840, _1021842]), _1021842)))]]], (47000 ^ _779327) ^ [_1717421, _1717423, _1717425] : [-(hAPP(c_List_Otl(_1717421), hAPP(hAPP(c_List_Otake(_1717421), _1717423), _1717425)) = hAPP(hAPP(c_List_Otake(_1717421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1717423), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1717421), _1717425)))], (15363 ^ _779327) ^ [_1038612, _1038614, _1038616, _1038618] : [class_Divides_Osemiring__div(_1038612), -(c_Divides_Odiv__class_Omod(_1038612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038612), c_Divides_Odiv__class_Omod(_1038612, _1038614, _1038616)), _1038618), _1038616) = c_Divides_Odiv__class_Omod(_1038612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038612), _1038614), _1038618), _1038616))], (42567 ^ _779327) ^ [_1609403, _1609405, _1609407] : [c_Relation_Orefl__on(_1609403, _1609405, hAPP(c_Relation_Oconverse(_1609403, _1609403), _1609407)), -(c_Relation_Orefl__on(_1609403, _1609405, _1609407))], (48275 ^ _779327) ^ [_1744841, _1744843] : [c_List_Oremdups(_1744841, _1744843) = _1744843, -(hBOOL(hAPP(c_List_Odistinct(_1744841), _1744843)))], (28248 ^ _779327) ^ [_1281979, _1281981, _1281983] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281979), _1281981)), -(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(_1281979), _1281983)), hAPP(c_Finite__Set_Ocard(_1281979), _1281981))), hAPP(c_Finite__Set_Ocard(_1281979), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281979, tc_HOL_Obool)), _1281983), _1281981)))))], (49746 ^ _779327) ^ [_1776336, _1776338, _1776340, _1776342] : [-(hBOOL(hAPP(_1776336, _1776338))), -(c_List_OtakeWhile(_1776340, _1776336, hAPP(hAPP(c_List_Olist_OCons(_1776340), _1776338), _1776342)) = c_List_Olist_ONil(_1776340))], (43818 ^ _779327) ^ [_1637585, _1637587, _1637589, _1637591] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637585, tc_HOL_Obool), tc_fun(_1637587, tc_HOL_Obool)), _1637589), hAPP(hAPP(c_COMBC(tc_fun(_1637585, tc_HOL_Obool), tc_fun(_1637585, tc_fun(_1637587, tc_HOL_Obool)), tc_fun(_1637587, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637585, tc_fun(_1637587, tc_HOL_Obool))), _1637591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637585, tc_fun(_1637587, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637585, tc_HOL_Obool), _1637589)), _1637591))], (52694 ^ _779327) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (48991 ^ _779327) ^ [_1761363, _1761365, _1761367] : [class_Orderings_Olinorder(_1761363), c_List_Olinorder__class_Osorted(_1761363, _1761365), -(c_List_Olinorder__class_Osorted(_1761363, hAPP(hAPP(c_List_Odrop(_1761363), _1761367), _1761365)))], (5524 ^ _779327) ^ [_863594, _863596, _863598, _863600, _863602, _863604] : [-(c_COMBB(_863604, _863600, _863596) = c_COMBB(_863602, _863598, _863594)), _863604 = _863602, _863600 = _863598, _863596 = _863594], (6985 ^ _779327) ^ [_888620, _888622] : [6986 ^ _779327 : [(6989 ^ _779327) ^ [] : [_888620 = _888622], (6987 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888620), _888622))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888620), hAPP(c_Nat_OSuc, _888622))))], (35255 ^ _779327) ^ [_1430514, _1430516, _1430518, _1430520] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430514, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430514, tc_HOL_Obool)), _1430516), _1430518)), _1430520) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430514, tc_HOL_Obool)), _1430516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430514, tc_HOL_Obool)), _1430518), _1430520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430514, tc_HOL_Obool)), _1430520), _1430516)))], (31892 ^ _779327) ^ [_1358871, _1358873, _1358875] : [class_Orderings_Olinorder(_1358871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358871), _1358873)), hBOOL(hAPP(hAPP(c_member(_1358871), _1358875), _1358873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1358871), _1358875), c_Big__Operators_Olinorder__class_OMax(_1358871, _1358873))))], (8988 ^ _779327) ^ [_924013, _924015] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924013), _924015))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _924013), _924015)), -(_924013 = _924015)], (21023 ^ _779327) ^ [_1139346, _1139348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139346), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139348)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139346)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139348))], (45434 ^ _779327) ^ [_1680229, _1680231, _1680233] : [-(hAPP(hAPP(c_List_Omap(_1680229, _1680231), _1680233), c_List_Olist_ONil(_1680229)) = c_List_Olist_ONil(_1680231))], (39387 ^ _779327) ^ [_1525168, _1525170, _1525172, _1525174, _1525176, _1525178] : [class_Groups_Ocomm__monoid__add(_1525168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525170), _1525172)), 39397 ^ _779327 : [(39400 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525174), hAPP(_1525176, 39396 ^ [_1525168, _1525170, _1525172, _1525174, _1525176, _1525178])))], (39398 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525170), 39396 ^ [_1525168, _1525170, _1525172, _1525174, _1525176, _1525178]), _1525172)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525170, _1525168), hAPP(hAPP(c_COMBS(_1525170, tc_fun(_1525174, tc_HOL_Obool), _1525168), hAPP(hAPP(c_COMBB(tc_fun(_1525174, _1525168), tc_fun(tc_fun(_1525174, tc_HOL_Obool), _1525168), _1525170), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525174, _1525168)), _1525178)), _1525176)), _1525172) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1525170, _1525174), _1525168), hAPP(c_Product__Type_Oprod_Oprod__case(_1525170, _1525174, _1525168), _1525178)), hAPP(hAPP(c_Product__Type_OSigma(_1525170, _1525174), _1525172), _1525176)))], (7111 ^ _779327) ^ [_890597, _890599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890597)), hAPP(c_Nat_OSuc, _890599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890597), _890599)))], (4112 ^ _779327) ^ [_841736, _841738, _841740, _841742, _841744, _841746] : [-(c_List_Opartition(_841746, _841742, _841738) = c_List_Opartition(_841744, _841740, _841736)), _841746 = _841744, _841742 = _841740, _841738 = _841736], (32394 ^ _779327) ^ [_1367947, _1367949, _1367951] : [class_Orderings_Olinorder(_1367947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367947), _1367949)), -(_1367949 = c_Orderings_Obot__class_Obot(tc_fun(_1367947, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1367947, hAPP(hAPP(c_Set_Oinsert(_1367947), _1367951), _1367949)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367947), _1367951), c_Big__Operators_Olinorder__class_OMin(_1367947, _1367949)))], (21144 ^ _779327) ^ [_1142007, _1142009] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142007), hAPP(c_Nat_OSuc, _1142009)) = 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), _1142007), _1142009)))], (39306 ^ _779327) ^ [_1523416, _1523418, _1523420] : [class_Groups_Oab__semigroup__mult(_1523416), -(_1523418 = c_Orderings_Obot__class_Obot(tc_fun(_1523416, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523416), _1523418)), -(hBOOL(hAPP(hAPP(c_member(_1523416), _1523420), _1523418))), -(hAPP(c_Finite__Set_Ofold1(_1523416, c_Groups_Otimes__class_Otimes(_1523416)), hAPP(hAPP(c_Set_Oinsert(_1523416), _1523420), _1523418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1523416), _1523420), hAPP(c_Finite__Set_Ofold1(_1523416, c_Groups_Otimes__class_Otimes(_1523416)), _1523418)))], (17916 ^ _779327) ^ [_1083492, _1083494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083492), _1083494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083492)), c_Int_OBit0(_1083494))))], (21646 ^ _779327) ^ [_1152351, _1152353] : [-(c_Divides_Odivmod__int__rel(_1152351, _1152353) = 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, _1152351))), 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), _1152353)))))), 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)), _1152353))), 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)), _1152353))))), 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)), _1152353)))), 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), _1152353))), 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))))))))], (50701 ^ _779327) ^ [_1797198, _1797200, _1797202, _1797204] : [50702 ^ _779327 : [(50705 ^ _779327) ^ [] : [c_List_Olist__ex(_1797198, _1797200, _1797204)], (50703 ^ _779327) ^ [] : [c_List_Olist__ex(_1797198, _1797200, _1797202)]], -(c_List_Olist__ex(_1797198, _1797200, hAPP(hAPP(c_List_Oappend(_1797198), _1797202), _1797204)))], (11637 ^ _779327) ^ [_972072, _972074, _972076, _972078, _972080] : [class_Groups_Oordered__ab__group__add(_972072), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972072), _972074), _972076) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972072), _972078), _972080), 11644 ^ _779327 : [(11651 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972072), _972078), _972080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972072), _972074), _972076)))], (11645 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972072), _972074), _972076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972072), _972078), _972080)))]]], (48776 ^ _779327) ^ [_1757273, _1757275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757273), _1757275)), -(c_List_Oupt(_1757273, _1757275) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1757273), c_List_Oupt(hAPP(c_Nat_OSuc, _1757273), _1757275)))], (4456 ^ _779327) ^ [_847080, _847082, _847084, _847086, _847088, _847090] : [-(c_List_Oinsert(_847090, _847086, _847082) = c_List_Oinsert(_847088, _847084, _847080)), _847090 = _847088, _847086 = _847084, _847082 = _847080], (38263 ^ _779327) ^ [_1499270, _1499272] : [c_Equiv__Relations_Oequivp(_1499270, hAPP(hAPP(c_COMBC(_1499270, tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_fun(_1499270, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499270, tc_fun(tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_fun(_1499270, tc_HOL_Obool)), _1499270), c_COMBC(_1499270, tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499270, tc_prod(_1499270, _1499270)), tc_fun(_1499270, tc_fun(tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_HOL_Obool)), _1499270), hAPP(c_COMBB(tc_prod(_1499270, _1499270), tc_fun(tc_fun(tc_prod(_1499270, _1499270), tc_HOL_Obool), tc_HOL_Obool), _1499270), c_member(tc_prod(_1499270, _1499270)))), c_Product__Type_OPair(_1499270, _1499270)))), _1499272)), -(c_Equiv__Relations_Oequiv(_1499270, c_Orderings_Otop__class_Otop(tc_fun(_1499270, tc_HOL_Obool)), _1499272))], (31674 ^ _779327) ^ [_1354850, _1354852] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354850, _1354852), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354850), _1354852)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354852), _1354850)))], (48405 ^ _779327) ^ [_1747330, _1747332, _1747334] : [class_Orderings_Olinorder(_1747330), -(c_List_Olinorder__class_Osort__key(_1747332, _1747330, _1747334, c_List_Olist_ONil(_1747332)) = c_List_Olist_ONil(_1747332))], (22329 ^ _779327) ^ [_1165525, _1165527] : [class_Orderings_Olinorder(_1165525), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165525), _1165527), _1165527) = _1165527)], (15606 ^ _779327) ^ [_1043088, _1043090, _1043092] : [class_Divides_Osemiring__div(_1043088), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043088), c_Divides_Odiv__class_Omod(_1043088, _1043090, _1043092)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043088), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1043088), _1043090), _1043092)), _1043092)) = _1043090)], (19891 ^ _779327) ^ [_1118603, _1118605, _1118607, _1118609, _1118611] : [class_Fields_Ofield(_1118603), -(_1118605 = c_Groups_Ozero__class_Ozero(_1118603)), -(_1118607 = c_Groups_Ozero__class_Ozero(_1118603)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118603), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118603), _1118609), _1118605)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118603), _1118611), _1118607)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118603), _1118609), _1118607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118603), _1118611), _1118605))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118603), _1118605), _1118607)))], (39588 ^ _779327) ^ [_1530421] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1530421), c_Int_OInteg)), -(_1530421 = hAPP(c_Int_ORep__Integ, 39591 ^ [_1530421]))], (35401 ^ _779327) ^ [_1434042, _1434044, _1434046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434042, tc_HOL_Obool)), _1434044), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1434042, tc_HOL_Obool)), _1434046))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434042, tc_HOL_Obool)), _1434044), _1434046) = c_Orderings_Obot__class_Obot(tc_fun(_1434042, tc_HOL_Obool)))], (42222 ^ _779327) ^ [_1600919, _1600921, _1600923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600919, _1600919), tc_HOL_Obool)), _1600921), _1600923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600919, _1600919), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1600919, _1600921)), c_Transitive__Closure_Ortrancl(_1600919, _1600923))))], (52592 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (45141 ^ _779327) ^ [_1672591, _1672593, _1672595, _1672597, _1672599] : [-(hAPP(hAPP(c_List_Omap(_1672591, _1672593), _1672595), hAPP(hAPP(c_List_Olist_OCons(_1672591), _1672597), _1672599)) = hAPP(hAPP(c_List_Olist_OCons(_1672593), hAPP(_1672595, _1672597)), hAPP(hAPP(c_List_Omap(_1672591, _1672593), _1672595), _1672599)))], (4848 ^ _779327) ^ [_853150, _853152, _853154, _853156, _853158, _853160] : [-(c_List_Oreplicate(_853160, _853156, _853152) = c_List_Oreplicate(_853158, _853154, _853150)), _853160 = _853158, _853156 = _853154, _853152 = _853150], (3640 ^ _779327) ^ [_834304, _834306, _834308, _834310, _834312, _834314, _834316, _834318, _834320, _834322] : [-(c_Finite__Set_Ofold__graph(_834322, _834318, _834314, _834310, _834306) = c_Finite__Set_Ofold__graph(_834320, _834316, _834312, _834308, _834304)), _834322 = _834320, _834318 = _834316, _834314 = _834312, _834310 = _834308, _834306 = _834304], (39874 ^ _779327) ^ [_1536625, _1536627] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1536625, tc_HOL_Obool)), _1536627) = hAPP(c_Set_OCollect(_1536625), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536625), c_fNot), hAPP(hAPP(c_COMBC(_1536625, tc_fun(_1536625, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536625)), _1536627))))], (3002 ^ _779327) ^ [_824267, _824269, _824271, _824273, _824275, _824277] : [-(c_SetInterval_Oord_OatLeast(_824277, _824273, _824269) = c_SetInterval_Oord_OatLeast(_824275, _824271, _824267)), _824277 = _824275, _824273 = _824271, _824269 = _824267], (17146 ^ _779327) ^ [_1070438, _1070440] : [class_Int_Onumber__ring(_1070438), class_Rings_Olinordered__idom(_1070438), 17153 ^ _779327 : [(17160 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1070440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070438), c_Groups_Ozero__class_Ozero(_1070438)), hAPP(c_Int_Onumber__class_Onumber__of(_1070438), _1070440))))], (17154 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070438), c_Groups_Ozero__class_Ozero(_1070438)), hAPP(c_Int_Onumber__class_Onumber__of(_1070438), _1070440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1070440)))]]], (5356 ^ _779327) ^ [_861040, _861042] : [_861042 = _861040, -(c_Set_OCollect(_861042) = c_Set_OCollect(_861040))], (47440 ^ _779327) ^ [_1726448, _1726450, _1726452] : [-(hAPP(hAPP(c_List_Odrop(_1726448), _1726450), c_List_Obutlast(_1726448, _1726452)) = c_List_Obutlast(_1726448, hAPP(hAPP(c_List_Odrop(_1726448), _1726450), _1726452)))], (40599 ^ _779327) ^ [_1562399, _1562401, _1562403] : [c_Wellfounded_Owf(_1562399, _1562401), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562399, _1562399)), hAPP(hAPP(c_Product__Type_OPair(_1562399, _1562399), _1562403), _1562403)), _1562401))], (48700 ^ _779327) ^ [_1755418, _1755420, _1755422, _1755424] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755418)), _1755420))), c_List_Ofoldr(tc_List_Olist(_1755422), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1755422)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1755422))), _1755424, 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(_1755418)), _1755420)), c_List_Ofoldr(tc_List_Olist(_1755422), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1755422)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1755422), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1755422)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1755422)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1755422), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1755422)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1755422), tc_List_Olist(_1755422), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1755422)))), _1755424), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10905 ^ _779327) ^ [_957152, _957154] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957152), _957154)), _957152) = _957154)], (48953 ^ _779327) ^ [_1760815, _1760817] : [class_Orderings_Olinorder(_1760815), -(c_List_Olinorder__class_Osorted(_1760815, c_List_Olinorder__class_Osort__key(_1760815, _1760815, c_COMBI(_1760815), _1760817)))], (30273 ^ _779327) ^ [_1323833, _1323835] : [c_Nat__Transfer_Ois__nat(_1323833), c_Nat__Transfer_Onat__set(_1323835), 30280 ^ _779327 : [(30287 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1323833)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1323835))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1323833), _1323835)))], (30281 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1323833), _1323835)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1323833)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1323835))))]]], (46235 ^ _779327) ^ [_1699423, _1699425, _1699427, _1699429] : [_1699425 = _1699429, -(hAPP(hAPP(c_List_Oappend(_1699423), _1699425), _1699427) = hAPP(hAPP(c_List_Oappend(_1699423), _1699429), _1699427))], (14331 ^ _779327) ^ [_1020894, _1020896, _1020898] : [-(hBOOL(hAPP(_1020894, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1020896), _1020898))))), 14334 ^ _779327 : [(14337 ^ _779327) ^ [] : [hBOOL(hAPP(_1020894, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1020896)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1020898))))], (14335 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020898), _1020896)))]], 14338 ^ _779327 : [(14341 ^ _779327) ^ [] : [hBOOL(hAPP(_1020894, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14339 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020896), _1020898)))]]], (44464 ^ _779327) ^ [_1652769, _1652771, _1652773] : [-(hAPP(c_List_Olexn(_1652769, _1652771), hAPP(c_Nat_OSuc, _1652773)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1652769), tc_List_Olist(_1652769)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1652769, tc_List_Olist(_1652769)), tc_prod(_1652769, tc_List_Olist(_1652769))), tc_prod(tc_List_Olist(_1652769), tc_List_Olist(_1652769)), c_Product__Type_Omap__pair(tc_prod(_1652769, tc_List_Olist(_1652769)), tc_List_Olist(_1652769), tc_prod(_1652769, tc_List_Olist(_1652769)), tc_List_Olist(_1652769), hAPP(c_Product__Type_Oprod_Oprod__case(_1652769, tc_List_Olist(_1652769), tc_List_Olist(_1652769)), c_List_Olist_OCons(_1652769)), hAPP(c_Product__Type_Oprod_Oprod__case(_1652769, tc_List_Olist(_1652769), tc_List_Olist(_1652769)), c_List_Olist_OCons(_1652769)))), c_Wellfounded_Olex__prod(_1652769, tc_List_Olist(_1652769), _1652771, hAPP(c_List_Olexn(_1652769, _1652771), _1652773)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1652769), tc_List_Olist(_1652769))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1652769), tc_List_Olist(_1652769), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652769), tc_fun(tc_List_Olist(_1652769), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652769), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1652769), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652769), tc_HOL_Obool)), tc_List_Olist(_1652769)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1652769))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1652769)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652769), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1652769)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1652769)))), hAPP(c_Nat_OSuc, _1652773))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652769), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1652769)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1652769)))), hAPP(c_Nat_OSuc, _1652773)))))))], (52612 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (25949 ^ _779327) ^ [_1234556, _1234558] : [25951 ^ _779327 : [(25954 ^ _779327) ^ [] : [hBOOL(hAPP(_1234558, 25950 ^ [_1234556, _1234558]))], (25952 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25950 ^ [_1234556, _1234558]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1234556))))]], 25955 ^ _779327 : [(25956 ^ _779327) ^ [_1234711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1234711), _1234556)), -(hBOOL(hAPP(_1234558, _1234711)))]]], (29714 ^ _779327) ^ [_1310340, _1310342, _1310344] : [hBOOL(hAPP(hAPP(c_member(_1310340), _1310342), _1310344)), -(hAPP(hAPP(c_Set_Oinsert(_1310340), _1310342), _1310344) = _1310344)], (52640 ^ _779327) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (39692 ^ _779327) ^ [_1532428, _1532430, _1532432] : [hBOOL(hAPP(_1532428, _1532430)), -(hBOOL(hAPP(hAPP(c_member(_1532432), _1532430), hAPP(c_Set_OCollect(_1532432), _1532428))))], (36282 ^ _779327) ^ [_1455177, _1455179, _1455181, _1455183, _1455185, _1455187] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455177, tc_fun(_1455179, tc_HOL_Obool))), _1455181), _1455183), _1455185), _1455187)), 36285 ^ _779327 : [(36288 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1455183, _1455185), _1455187)))], (36286 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1455181, _1455185), _1455187)))]]], (36188 ^ _779327) ^ [_1451966, _1451968, _1451970, _1451972, _1451974, _1451976, _1451978] : [c_Equiv__Relations_Oequiv(_1451966, _1451968, _1451970), c_Equiv__Relations_Ocongruent(_1451966, tc_fun(_1451972, tc_HOL_Obool), _1451970, _1451974), hBOOL(hAPP(hAPP(c_member(tc_fun(_1451966, tc_HOL_Obool)), _1451976), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1451966), _1451968), _1451970))), 36202 ^ _779327 : [(36205 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1451972, tc_HOL_Obool)), hAPP(_1451974, 36201 ^ [_1451966, _1451968, _1451970, _1451972, _1451974, _1451976, _1451978])), _1451978))], (36203 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451966), 36201 ^ [_1451966, _1451968, _1451970, _1451972, _1451974, _1451976, _1451978]), _1451968)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1451972, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451966, tc_fun(_1451972, tc_HOL_Obool)), _1451976), _1451974)), _1451978)))], (24763 ^ _779327) ^ [_1210654] : [_1210654 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210654), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (52562 ^ _779327) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (17798 ^ _779327) ^ [_1081165, _1081167] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1081165, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081167)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1081165, 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)))), _1081167)))], (47106 ^ _779327) ^ [_1719650, _1719652, _1719654, _1719656, _1719658, _1719660] : [-(hAPP(c_List_Ofoldl(_1719650, _1719652, _1719654, _1719656), hAPP(hAPP(c_List_Olist_OCons(_1719652), _1719658), _1719660)) = hAPP(c_List_Ofoldl(_1719650, _1719652, _1719654, hAPP(hAPP(_1719654, _1719656), _1719658)), _1719660))], (37330 ^ _779327) ^ [_1477246, _1477248, _1477250, _1477252] : [class_Groups_Ocomm__monoid__add(_1477246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477248), _1477250)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477248, _1477246), _1477252), _1477250) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1477246, _1477248, c_Groups_Oplus__class_Oplus(_1477246)), _1477252), c_Groups_Ozero__class_Ozero(_1477246)), _1477250))], (9863 ^ _779327) ^ [_939092] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _939092) = _939092)], (39880 ^ _779327) ^ [_1536894, _1536896, _1536898] : [-(hAPP(c_Set_OCollect(_1536894), hAPP(hAPP(c_COMBS(_1536894, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536894), c_fimplies), _1536896)), _1536898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536894, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1536894, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1536894), _1536896))), hAPP(c_Set_OCollect(_1536894), _1536898)))], (17532 ^ _779327) ^ [_1076907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1076907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1076907))))], (128 ^ _779327) ^ [_781087, _781089, _781091, _781093, _781095, _781097, _781099, _781101] : [-(c_Nat__Transfer_Otransfer__morphism(_781099, _781095, _781091, _781087)), c_Nat__Transfer_Otransfer__morphism(_781101, _781097, _781093, _781089), _781101 = _781099, _781097 = _781095, _781093 = _781091, _781089 = _781087], (8980 ^ _779327) ^ [_923886, _923888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923886), _923888)), 8983 ^ _779327 : [(8986 ^ _779327) ^ [] : [_923886 = _923888], (8984 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _923886), _923888)))]]], (14043 ^ _779327) ^ [_1015308, _1015310, _1015312, _1015314, _1015316] : [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), _1015308), _1015310)), _1015312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015308), _1015314)), _1015316))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015316), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015308), _1015316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015308), _1015312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015314), _1015310)))], (8524 ^ _779327) ^ [_915831, _915833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _915831)), -(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), _915831), _915833))))], (37615 ^ _779327) ^ [_1483274, _1483276] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483274, tc_HOL_Obool)), _1483276), c_Orderings_Otop__class_Otop(tc_fun(_1483274, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1483274, tc_HOL_Obool)))], (17586 ^ _779327) ^ [_1077769, _1077771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077769), _1077771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1077769)), _1077771)))], (52802 ^ _779327) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (982 ^ _779327) ^ [_794298, _794300, _794302, _794304] : [-(c_Relation_Oantisym(_794302, _794298)), c_Relation_Oantisym(_794304, _794300), _794304 = _794302, _794300 = _794298], (6392 ^ _779327) ^ [_879800, _879802, _879804] : [class_Orderings_Oorder(_879800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879800), _879802), _879804)), _879802 = _879804], (48287 ^ _779327) ^ [_1745021, _1745023] : [hBOOL(hAPP(c_List_Odistinct(_1745021), _1745023)), -(c_List_Oremdups(_1745021, _1745023) = _1745023)], (48722 ^ _779327) ^ [_1756041, _1756043, _1756045] : [class_Groups_Omonoid__add(_1756041), -(hAPP(c_List_Ofoldl(_1756041, _1756041, c_Groups_Oplus__class_Oplus(_1756041), _1756043), _1756045) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1756041), _1756043), c_List_Ofoldr(_1756041, _1756041, c_Groups_Oplus__class_Oplus(_1756041), _1756045, c_Groups_Ozero__class_Ozero(_1756041))))], (31203 ^ _779327) ^ [_1344540, _1344542] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344540), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344542))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344542), _1344540)))], (4950 ^ _779327) ^ [_854795, _854797] : [_854797 = _854795, -(c_List_Olist_ONil(_854797) = c_List_Olist_ONil(_854795))], (33995 ^ _779327) ^ [_1401396, _1401398] : [hAPP(c_Set_OPow(_1401396), _1401398) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1401396, tc_HOL_Obool), tc_HOL_Obool))], (46223 ^ _779327) ^ [_1699178, _1699180, _1699182, _1699184] : [_1699182 = _1699184, -(hAPP(hAPP(c_List_Oappend(_1699178), _1699180), _1699182) = hAPP(hAPP(c_List_Oappend(_1699178), _1699180), _1699184))], (42404 ^ _779327) ^ [_1605290, _1605292, _1605294, _1605296] : [-(hBOOL(hAPP(hAPP(c_member(_1605290), _1605292), hAPP(c_Relation_ODomain(_1605290, _1605290), _1605294)))), 42407 ^ _779327 : [(42414 ^ _779327) ^ [] : [_1605292 = _1605296, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605290, _1605290)), hAPP(hAPP(c_Product__Type_OPair(_1605290, _1605290), _1605292), _1605296)), c_Transitive__Closure_Ortrancl(_1605290, _1605294))))], (42408 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605290, _1605290)), hAPP(hAPP(c_Product__Type_OPair(_1605290, _1605290), _1605292), _1605296)), c_Transitive__Closure_Ortrancl(_1605290, _1605294))), -(_1605292 = _1605296)]]], (12984 ^ _779327) ^ [_996254, _996256] : [class_Groups_Olinordered__ab__group__add(_996254), 12987 ^ _779327 : [(12994 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996254), c_Groups_Ozero__class_Ozero(_996254)), _996256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996254), c_Groups_Ozero__class_Ozero(_996254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996254), _996256), _996256))))], (12988 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996254), c_Groups_Ozero__class_Ozero(_996254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996254), _996256), _996256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996254), c_Groups_Ozero__class_Ozero(_996254)), _996256)))]]], (35585 ^ _779327) ^ [_1438092, _1438094, _1438096, _1438098, _1438100] : [class_Groups_Ocomm__monoid__add(_1438092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438094), _1438096)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438094), _1438098)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438092), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438094, _1438092), _1438100), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438094, tc_HOL_Obool)), _1438096), _1438098))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438094, _1438092), _1438100), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438094, tc_HOL_Obool)), _1438096), _1438098))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438092), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438094, _1438092), _1438100), _1438096)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1438094, _1438092), _1438100), _1438098)))], (10213 ^ _779327) ^ [_944668, _944670, _944672] : [class_Rings_Olinordered__semidom(_944668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944668), c_Groups_Oone__class_Oone(_944668)), _944670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944668), hAPP(hAPP(c_Power_Opower__class_Opower(_944668), _944670), _944672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944668), _944670), hAPP(hAPP(c_Power_Opower__class_Opower(_944668), _944670), _944672)))))], (12445 ^ _779327) ^ [_986535, _986537, _986539, _986541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986535), _986537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986539), _986541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986535), _986539)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986537), _986541))))], (46465 ^ _779327) ^ [_1705428] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1705428)), -(c_List_Onat__list(_1705428))], (9094 ^ _779327) ^ [_926211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926211)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_926211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15449 ^ _779327) ^ [_1040340, _1040342, _1040344] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1040340), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040342, _1040344)), _1040344) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1040340), _1040342), _1040344))], (22007 ^ _779327) ^ [_1159006, _1159008] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1159006, _1159008) = 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), _1159006), _1159008)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1159006, _1159008)))], (11221 ^ _779327) ^ [_963304, _963306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963304), _963306)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963306), _963304)) = _963306)], (44881 ^ _779327) ^ [_1665556, _1665558, _1665560, _1665562] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665556), tc_List_Olist(_1665556))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665556), tc_List_Olist(_1665556)), _1665558), _1665560)), c_List_Olistrel(_1665556, _1665562))), 44884 ^ _779327 : [(44887 ^ _779327) ^ [_1665785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665785), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665556)), _1665558))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1665556, _1665556)), hAPP(hAPP(c_Product__Type_OPair(_1665556, _1665556), hAPP(hAPP(c_List_Onth(_1665556), _1665558), _1665785)), hAPP(hAPP(c_List_Onth(_1665556), _1665560), _1665785))), _1665562)))], (44885 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665556)), _1665558) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665556)), _1665560))]]], (33423 ^ _779327) ^ [_1388424, _1388426, _1388428, _1388430, _1388432, _1388434] : [class_Groups_Oordered__ab__group__add(_1388424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388426), _1388428)), 33433 ^ _779327 : [(33436 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388424), c_Groups_Ozero__class_Ozero(_1388424)), hAPP(_1388430, 33432 ^ [_1388424, _1388426, _1388428, _1388430, _1388432, _1388434])))], (33434 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388426), 33432 ^ [_1388424, _1388426, _1388428, _1388430, _1388432, _1388434]), _1388428)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388426, _1388424), _1388430), _1388428) = _1388432, hBOOL(hAPP(hAPP(c_member(_1388426), _1388434), _1388428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388424), hAPP(_1388430, _1388434)), _1388432)))], (52458 ^ _779327) ^ [_1834831, _1834833] : [class_Lattices_Obounded__lattice(_1834831), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1834833, _1834831)))], (26840 ^ _779327) ^ [_1252243] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1252243) = c_Orderings_Oord__class_Omax(_1252243)), class_Lattices_Osemilattice__sup(_1252243), class_Orderings_Olinorder(_1252243)], (34132 ^ _779327) ^ [_1404535, _1404537] : [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)), _1404535), 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)), _1404537), 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)), _1404535), _1404537)), c_Int_Ointrel)))], (25650 ^ _779327) ^ [_1228618, _1228620, _1228622, _1228624, _1228626] : [class_Orderings_Olinorder(_1228618), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1228618, _1228620), _1228622) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1228618, _1228624), _1228626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228618), _1228620), _1228622)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228618), _1228624), _1228626)), -(_1228622 = _1228626)], (17000 ^ _779327) ^ [_1067816, _1067818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067816)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067816), _1067818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067816), c_Int_OPls)))], (37953 ^ _779327) ^ [_1490205] : [class_Lattices_Oboolean__algebra(_1490205), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1490205), c_Orderings_Otop__class_Otop(_1490205)) = c_Orderings_Obot__class_Obot(_1490205))], (17592 ^ _779327) ^ [_1077866, _1077868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1077866)), _1077868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077866), _1077868)))], (6963 ^ _779327) ^ [_888342, _888344] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888342), _888344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888344), hAPP(c_Nat_OSuc, _888342))))], (14569 ^ _779327) ^ [_1024817, _1024819, _1024821, _1024823] : [class_Divides_Osemiring__div(_1024817), -(_1024819 = c_Groups_Ozero__class_Ozero(_1024817)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024817), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024817), _1024819), _1024821)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024817), _1024819), _1024823)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024817), _1024821), _1024823))], (27292 ^ _779327) ^ [_1261190, _1261192, _1261194, _1261196, _1261198] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261190, tc_fun(_1261192, tc_HOL_Obool)), _1261194), hAPP(hAPP(c_COMBB(tc_fun(_1261192, tc_HOL_Obool), tc_fun(_1261192, tc_HOL_Obool), _1261190), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261192, tc_HOL_Obool)), _1261196)), _1261198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261192, tc_HOL_Obool)), _1261196), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261190, tc_fun(_1261192, tc_HOL_Obool)), _1261194), _1261198)))], (49141 ^ _779327) ^ [_1763734, _1763736, _1763738, _1763740, _1763742] : [class_Orderings_Olinorder(_1763734), c_List_Olinorder__class_Osorted(_1763734, hAPP(hAPP(c_List_Omap(_1763736, _1763734), _1763738), _1763740)), -(c_List_Olinorder__class_Osorted(_1763734, hAPP(hAPP(c_List_Omap(_1763736, _1763734), _1763738), c_List_Oremove1(_1763736, _1763742, _1763740))))], (7498 ^ _779327) ^ [_897289, _897291, _897293] : [class_Rings_Ono__zero__divisors(_897289), -(_897291 = c_Groups_Ozero__class_Ozero(_897289)), -(_897293 = c_Groups_Ozero__class_Ozero(_897289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897289), _897291), _897293) = c_Groups_Ozero__class_Ozero(_897289)], (750 ^ _779327) ^ [_790864, _790866] : [-(class_Lattices_Oab__semigroup__idem__mult(_790864)), _790866 = _790864, class_Lattices_Oab__semigroup__idem__mult(_790866)], (38499 ^ _779327) ^ [_1504686, _1504688, _1504690, _1504692, _1504694, _1504696] : [hBOOL(hAPP(hAPP(c_member(_1504686), _1504688), _1504690)), 38502 ^ _779327 : [(38509 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504686), _1504692), _1504690))), -(hAPP(c_Set_Ovimage(_1504694, _1504686, hAPP(hAPP(c_COMBC(_1504694, _1504686, _1504686), hAPP(hAPP(c_COMBC(_1504694, _1504686, tc_fun(_1504686, _1504686)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504686, tc_fun(_1504686, _1504686)), _1504694), c_If(_1504686)), hAPP(hAPP(c_COMBC(_1504694, tc_fun(_1504694, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504694)), _1504696))), _1504688)), _1504692)), _1504690) = _1504696)], (38503 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1504686), _1504692), _1504690)), -(hAPP(c_Set_Ovimage(_1504694, _1504686, hAPP(hAPP(c_COMBC(_1504694, _1504686, _1504686), hAPP(hAPP(c_COMBC(_1504694, _1504686, tc_fun(_1504686, _1504686)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1504686, tc_fun(_1504686, _1504686)), _1504694), c_If(_1504686)), hAPP(hAPP(c_COMBC(_1504694, tc_fun(_1504694, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504694)), _1504696))), _1504688)), _1504692)), _1504690) = c_Orderings_Otop__class_Otop(tc_fun(_1504694, tc_HOL_Obool)))]]], (10445 ^ _779327) ^ [_948507, _948509] : [hAPP(c_Int_Onat, _948507) = _948509, 10448 ^ _779327 : [(10455 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948507))), -(_948509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10449 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948507)), -(_948507 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948509))]]], (48880 ^ _779327) ^ [_1759114, _1759116] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1759114, _1759116) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1759114), hAPP(c_Nat_OSuc, _1759116))))], (51646 ^ _779327) ^ [_1817561, _1817563, _1817565, _1817567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1817561), _1817563)), 51649 ^ _779327 : [(51650 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1817565), hAPP(c_Set_OCollect(_1817565), hAPP(hAPP(c_COMBB(tc_fun(_1817561, tc_HOL_Obool), tc_HOL_Obool, _1817565), c_HOL_OEx(_1817561)), hAPP(hAPP(c_COMBB(tc_fun(_1817561, tc_HOL_Obool), tc_fun(_1817561, tc_HOL_Obool), _1817565), hAPP(c_COMBS(_1817561, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1817561), c_fconj), hAPP(hAPP(c_COMBC(_1817561, tc_fun(_1817561, tc_HOL_Obool), tc_HOL_Obool), c_member(_1817561)), _1817563)))), _1817567))))), 51653 ^ _779327 : [(51654 ^ _779327) ^ [_1817869] : [hBOOL(hAPP(hAPP(c_member(_1817561), _1817869), _1817563)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1817565), hAPP(c_Set_OCollect(_1817565), hAPP(hAPP(c_COMBC(_1817565, _1817561, tc_HOL_Obool), _1817567), _1817869)))))]]], (51660 ^ _779327) ^ [] : [51662 ^ _779327 : [(51665 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1817565), hAPP(c_Set_OCollect(_1817565), hAPP(hAPP(c_COMBC(_1817565, _1817561, tc_HOL_Obool), _1817567), 51661 ^ [_1817561, _1817563, _1817565, _1817567]))))], (51663 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1817561), 51661 ^ [_1817561, _1817563, _1817565, _1817567]), _1817563)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1817565), hAPP(c_Set_OCollect(_1817565), hAPP(hAPP(c_COMBB(tc_fun(_1817561, tc_HOL_Obool), tc_HOL_Obool, _1817565), c_HOL_OEx(_1817561)), hAPP(hAPP(c_COMBB(tc_fun(_1817561, tc_HOL_Obool), tc_fun(_1817561, tc_HOL_Obool), _1817565), hAPP(c_COMBS(_1817561, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1817561), c_fconj), hAPP(hAPP(c_COMBC(_1817561, tc_fun(_1817561, tc_HOL_Obool), tc_HOL_Obool), c_member(_1817561)), _1817563)))), _1817567))))))]]], (12415 ^ _779327) ^ [_985978, _985980] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _985978)), _985980) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _985978), _985980)))], (30179 ^ _779327) ^ [_1321891, _1321893, _1321895, _1321897] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321891, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1321891), _1321893), _1321895)), _1321897))), hBOOL(hAPP(hAPP(c_member(_1321891), _1321893), _1321897)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321891, tc_HOL_Obool)), _1321895), _1321897))], (18596 ^ _779327) ^ [_1095411, _1095413, _1095415] : [class_Groups_Omonoid__mult(_1095411), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095411), _1095413), 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)))), _1095415))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095411), _1095413), hAPP(hAPP(c_Power_Opower__class_Opower(_1095411), hAPP(hAPP(c_Power_Opower__class_Opower(_1095411), _1095413), _1095415)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (9611 ^ _779327) ^ [_935002, _935004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _935002)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _935002)), _935004) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _935002), _935004)))], (26655 ^ _779327) ^ [_1248535] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1248535) = 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)), _1248535)))], (5508 ^ _779327) ^ [_863360, _863362] : [_863362 = _863360, -(c_COMBI(_863362) = c_COMBI(_863360))], (29112 ^ _779327) ^ [_1298038, _1298040] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1298038), _1298040))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1298038, _1298040) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33483 ^ _779327) ^ [_1389645, _1389647, _1389649] : [class_Orderings_Olinorder(_1389645), hAPP(_1389647, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389645), 33488 ^ [_1389645, _1389647, _1389649]), 33489 ^ [_1389645, _1389647, _1389649])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389645), hAPP(_1389647, 33488 ^ [_1389645, _1389647, _1389649])), hAPP(_1389647, 33489 ^ [_1389645, _1389647, _1389649])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389645), _1389649)), -(_1389649 = c_Orderings_Obot__class_Obot(tc_fun(_1389645, tc_HOL_Obool))), -(hAPP(_1389647, c_Big__Operators_Olattice_OSup__fin(_1389645, c_Orderings_Oord__class_Omax(_1389645), _1389649)) = c_Big__Operators_Olattice_OSup__fin(_1389645, c_Orderings_Oord__class_Omax(_1389645), hAPP(c_Set_Oimage(_1389645, _1389645, _1389647), _1389649)))], (42826 ^ _779327) ^ [_1615564, _1615566, _1615568, _1615570, _1615572] : [c_Relation_Osingle__valued(_1615564, _1615564, _1615566), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615564, _1615564)), hAPP(hAPP(c_Product__Type_OPair(_1615564, _1615564), _1615568), _1615570)), c_Transitive__Closure_Ortrancl(_1615564, _1615566))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615564, _1615564)), hAPP(hAPP(c_Product__Type_OPair(_1615564, _1615564), _1615568), _1615572)), c_Transitive__Closure_Ortrancl(_1615564, _1615566))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615564, _1615564)), hAPP(hAPP(c_Product__Type_OPair(_1615564, _1615564), _1615570), _1615572)), c_Transitive__Closure_Ortrancl(_1615564, _1615566)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615564, _1615564)), hAPP(hAPP(c_Product__Type_OPair(_1615564, _1615564), _1615572), _1615570)), c_Transitive__Closure_Ortrancl(_1615564, _1615566))))], (37731 ^ _779327) ^ [_1485732] : [-(hAPP(c_Set_OPow(_1485732), c_Orderings_Otop__class_Otop(tc_fun(_1485732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1485732, tc_HOL_Obool), tc_HOL_Obool)))], (40418 ^ _779327) ^ [_1557112, _1557114, _1557116, _1557118] : [hAPP(hAPP(c_Relation_Orel__comp(_1557112, _1557112, _1557112), _1557114), _1557116) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557112, _1557112), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1557112, _1557112, _1557112), _1557114), _1557118) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557112, _1557112), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1557112, _1557112, _1557112), _1557114), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1557112, _1557112), tc_HOL_Obool)), _1557116), _1557118)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557112, _1557112), tc_HOL_Obool)))], (1408 ^ _779327) ^ [_799915, _799917] : [-(class_Complete__Lattice_Ocomplete__lattice(_799915)), _799917 = _799915, class_Complete__Lattice_Ocomplete__lattice(_799917)], (21618 ^ _779327) ^ [_1151899, _1151901] : [-(_1151899 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1151901, _1151899) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151901), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151899)))], (9268 ^ _779327) ^ [] : [-(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)))], (34635 ^ _779327) ^ [_1417153, _1417155, _1417157, _1417159, _1417161] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417153, tc_HOL_Obool)), _1417155), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417157, tc_fun(_1417153, tc_HOL_Obool)), _1417159), _1417161)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417157, tc_fun(_1417153, tc_HOL_Obool)), _1417159), hAPP(hAPP(c_COMBB(tc_fun(_1417153, tc_HOL_Obool), tc_fun(_1417153, tc_HOL_Obool), _1417157), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417153, tc_HOL_Obool)), _1417155)), _1417161)))], (31968 ^ _779327) ^ [_1360098, _1360100, _1360102] : [class_Rings_Osemiring__1(_1360098), hBOOL(hAPP(hAPP(c_member(_1360098), _1360100), c_Nat_Osemiring__1__class_ONats(_1360098))), hBOOL(hAPP(hAPP(c_member(_1360098), _1360102), c_Nat_Osemiring__1__class_ONats(_1360098))), -(hBOOL(hAPP(hAPP(c_member(_1360098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360098), _1360100), _1360102)), c_Nat_Osemiring__1__class_ONats(_1360098))))], (48738 ^ _779327) ^ [_1756617, _1756619] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1756617, _1756619)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1756617), _1756619))], (24987 ^ _779327) ^ [_1214922, _1214924, _1214926] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214922), _1214924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1214922), _1214926))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214922)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214924), _1214926)))], (16435 ^ _779327) ^ [_1057904, _1057906] : [class_Groups_Oordered__ab__group__add__abs(_1057904), -(hAPP(c_Groups_Oabs__class_Oabs(_1057904), hAPP(c_Groups_Ouminus__class_Ouminus(_1057904), _1057906)) = hAPP(c_Groups_Oabs__class_Oabs(_1057904), _1057906))], (15560 ^ _779327) ^ [_1042359, _1042361] : [15561 ^ _779327 : [(15562 ^ _779327) ^ [_1042408] : [_1042359 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042361), _1042408)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042359, _1042361) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23542 ^ _779327) ^ [_1189150, _1189152, _1189154, _1189156, _1189158, _1189160] : [-(c_Nitpick_Opair__box_Opair__box__case(_1189150, _1189152, _1189154, _1189156, c_Nitpick_Opair__box_OPairBox(_1189150, _1189152, _1189158, _1189160)) = hAPP(hAPP(_1189156, _1189158), _1189160))], (16481 ^ _779327) ^ [_1058694] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1058694), c_Int_OPls) = _1058694)], (20165 ^ _779327) ^ [_1123245, _1123247, _1123249, _1123251] : [class_Fields_Olinordered__field(_1123245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123245), _1123247), c_Groups_Ozero__class_Ozero(_1123245))), 20172 ^ _779327 : [(20179 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123245), _1123251), _1123247)), _1123249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123245), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123245), _1123249), _1123247)), _1123251)))], (20173 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123245), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123245), _1123249), _1123247)), _1123251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123245), _1123251), _1123247)), _1123249)))]]], (50568 ^ _779327) ^ [_1794786, _1794788] : [class_Enum_Oenum(_1794786), 50571 ^ _779327 : [(50578 ^ _779327) ^ [] : [hBOOL(hAPP(_1794788, 50579 ^ [_1794786, _1794788])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1794786), _1794788)))], (50572 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1794786), _1794788)), 50575 ^ _779327 : [(50576 ^ _779327) ^ [_1794912] : [-(hBOOL(hAPP(_1794788, _1794912)))]]]]], (7640 ^ _779327) ^ [_899601, _899603, _899605] : [class_Rings_Olinordered__ring__strict(_899601), 7643 ^ _779327 : [(7658 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899601), _899603), _899605)))), 7659 ^ _779327 : [(7666 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), _899603), c_Groups_Ozero__class_Ozero(_899601))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), _899605), c_Groups_Ozero__class_Ozero(_899601)))], (7660 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), _899603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), _899605))]]], (7644 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899601), _899603), _899605))), 7649 ^ _779327 : [(7652 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), _899605)))], (7650 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), c_Groups_Ozero__class_Ozero(_899601)), _899603)))]], 7653 ^ _779327 : [(7656 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), _899605), c_Groups_Ozero__class_Ozero(_899601))))], (7654 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899601), _899603), c_Groups_Ozero__class_Ozero(_899601))))]]]]], (46363 ^ _779327) ^ [_1702498, _1702500, _1702502, _1702504] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702498), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702500)), _1702502)))), -(hAPP(hAPP(c_List_Onth(_1702500), hAPP(hAPP(c_List_Oappend(_1702500), _1702502), _1702504)), _1702498) = hAPP(hAPP(c_List_Onth(_1702500), _1702504), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1702498), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702500)), _1702502))))], (8420 ^ _779327) ^ [_913949, _913951, _913953, _913955] : [class_Rings_Olinordered__semiring(_913949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913949), _913951), _913953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913949), _913955), _913953))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913949), c_Groups_Ozero__class_Ozero(_913949)), _913953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913949), _913951), _913955)))], (27010 ^ _779327) ^ [_1255849, _1255851, _1255853, _1255855] : [class_Lattices_Olattice(_1255849), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255849), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255849), _1255851), _1255853)), _1255855) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255849), _1255851), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255849), _1255853), _1255855)))], (52650 ^ _779327) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (46229 ^ _779327) ^ [_1699314, _1699316, _1699318, _1699320] : [hAPP(hAPP(c_List_Oappend(_1699314), _1699316), _1699318) = hAPP(hAPP(c_List_Oappend(_1699314), _1699320), _1699318), -(_1699316 = _1699320)], (12395 ^ _779327) ^ [_985563, _985565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985563), _985565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _985563)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _985565))))], (16742 ^ _779327) ^ [_1063218] : [class_Int_Onumber__ring(_1063218), -(c_Groups_Ozero__class_Ozero(_1063218) = hAPP(c_Int_Onumber__class_Onumber__of(_1063218), c_Int_OPls))], (24497 ^ _779327) ^ [_1205746, _1205748, _1205750, _1205752] : [class_Rings_Ocomm__semiring__1(_1205746), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205746), _1205748), _1205750)), _1205752)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205746), _1205748), _1205752)))], (46712 ^ _779327) ^ [_1711802, _1711804, _1711806] : [-(_1711802 = c_List_Olist_ONil(_1711804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711806), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711804)), _1711802))), -(hAPP(c_List_Ohd(_1711804), hAPP(hAPP(c_List_Odrop(_1711804), _1711806), _1711802)) = hAPP(hAPP(c_List_Onth(_1711804), _1711802), _1711806))], (50181 ^ _779327) ^ [_1785541, _1785543] : [-(c_Wellfounded_Owf(_1785541, c_List_Omeasures(_1785541, _1785543)))], (49567 ^ _779327) ^ [_1772457, _1772459, _1772461, _1772463, _1772465] : [-(hAPP(c_List_Ofoldl(_1772457, _1772459, _1772461, _1772463), _1772465) = c_List_Ofoldr(_1772459, _1772457, hAPP(c_COMBC(_1772457, _1772459, _1772457), _1772461), hAPP(c_List_Orev(_1772459), _1772465), _1772463))], (52438 ^ _779327) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (42458 ^ _779327) ^ [_1606491, _1606493, _1606495, _1606497] : [c_Wellfounded_Oacyclic(_1606491, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1606491, _1606491)), hAPP(hAPP(c_Product__Type_OPair(_1606491, _1606491), _1606493), _1606495)), _1606497)), 42461 ^ _779327 : [(42464 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606491, _1606491)), hAPP(hAPP(c_Product__Type_OPair(_1606491, _1606491), _1606495), _1606493)), c_Transitive__Closure_Ortrancl(_1606491, _1606497)))], (42462 ^ _779327) ^ [] : [-(c_Wellfounded_Oacyclic(_1606491, _1606497))]]], (31906 ^ _779327) ^ [_1359098, _1359100] : [class_Orderings_Olinorder(_1359098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359098), _1359100)), -(_1359100 = c_Orderings_Obot__class_Obot(tc_fun(_1359098, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1359098), c_Big__Operators_Olinorder__class_OMax(_1359098, _1359100)), _1359100)))], (17928 ^ _779327) ^ [_1083715, _1083717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083715), _1083717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083715)), c_Int_OBit0(_1083717))))], (41629 ^ _779327) ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517] : [class_Groups_Ocomm__monoid__add(_1586507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586509), _1586511)), 41639 ^ _779327 : [(41640 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586509), 41638 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517]), _1586511)))], (41645 ^ _779327) ^ [] : [41638 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517] = 41641 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517]], (41649 ^ _779327) ^ [] : [hAPP(_1586515, hAPP(_1586513, 41638 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517])) = c_Groups_Ozero__class_Ozero(_1586507)], (41647 ^ _779327) ^ [] : [-(hAPP(_1586513, 41638 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517]) = hAPP(_1586513, 41641 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517]))], (41643 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586509), 41641 ^ [_1586507, _1586509, _1586511, _1586513, _1586515, _1586517]), _1586511)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1586517, _1586507), _1586515), hAPP(c_Set_Oimage(_1586509, _1586517, _1586513), _1586511)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1586509, _1586507), hAPP(c_Fun_Ocomp(_1586517, _1586507, _1586509, _1586515), _1586513)), _1586511))], (47494 ^ _779327) ^ [_1727536, _1727538] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727536)), c_List_Obutlast(_1727536, _1727538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727536)), _1727538)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45633 ^ _779327) ^ [_1685301, _1685303, _1685305, _1685307, _1685309, _1685311] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685301, _1685303)), hAPP(hAPP(c_Product__Type_OPair(_1685301, _1685303), _1685305), _1685307)), hAPP(c_List_Oset(tc_prod(_1685301, _1685303)), hAPP(hAPP(c_List_Ozip(_1685301, _1685303), _1685309), _1685311)))), -(hBOOL(hAPP(hAPP(c_member(_1685303), _1685307), hAPP(c_List_Oset(_1685303), _1685311))))], (46140 ^ _779327) ^ [_1697215, _1697217, _1697219] : [_1697219 = c_List_Olist_ONil(_1697217), -(_1697215 = hAPP(hAPP(c_List_Oappend(_1697217), _1697215), _1697219))], (12806 ^ _779327) ^ [_993308, _993310] : [class_Groups_Oordered__ab__group__add(_993308), 12809 ^ _779327 : [(12816 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993308), _993310), c_Groups_Ozero__class_Ozero(_993308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993308), c_Groups_Ozero__class_Ozero(_993308)), hAPP(c_Groups_Ouminus__class_Ouminus(_993308), _993310))))], (12810 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993308), c_Groups_Ozero__class_Ozero(_993308)), hAPP(c_Groups_Ouminus__class_Ouminus(_993308), _993310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993308), _993310), c_Groups_Ozero__class_Ozero(_993308))))]]], (8130 ^ _779327) ^ [_908613, _908615, _908617] : [class_Rings_Olinordered__ring__strict(_908613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908613), _908615), c_Groups_Ozero__class_Ozero(_908613))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908613), _908617), c_Groups_Ozero__class_Ozero(_908613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908613), c_Groups_Ozero__class_Ozero(_908613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908613), _908615), _908617))))], (49897 ^ _779327) ^ [_1779408, _1779410, _1779412, _1779414, _1779416] : [hBOOL(hAPP(hAPP(c_member(_1779408), _1779410), hAPP(c_List_Oset(_1779408), _1779412))), -(hBOOL(hAPP(_1779414, _1779410))), -(c_List_OdropWhile(_1779408, _1779414, hAPP(hAPP(c_List_Oappend(_1779408), _1779412), _1779416)) = hAPP(hAPP(c_List_Oappend(_1779408), c_List_OdropWhile(_1779408, _1779414, _1779412)), _1779416))], (33955 ^ _779327) ^ [_1400526, _1400528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1400526), _1400528)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1400526, tc_HOL_Obool)), hAPP(c_Set_OPow(_1400526), _1400528))))], (52546 ^ _779327) ^ [_1835987, _1835989] : [-(class_Enum_Oenum(tc_fun(_1835987, _1835989))), class_Enum_Oenum(_1835987), class_Enum_Oenum(_1835989)], (12523 ^ _779327) ^ [_988044, _988046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988044), _988046)), -(_988046 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988044), 12526 ^ [_988044, _988046]))], (48832 ^ _779327) ^ [_1758269, _1758271] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758269)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758271)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758269), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758271)) = c_List_Olist_ONil(tc_Nat_Onat))], (5382 ^ _779327) ^ [_861431, _861433, _861435, _861437, _861439, _861441, _861443, _861445] : [-(c_Fun_Ocomp(_861445, _861441, _861437, _861433) = c_Fun_Ocomp(_861443, _861439, _861435, _861431)), _861445 = _861443, _861441 = _861439, _861437 = _861435, _861433 = _861431], (31251 ^ _779327) ^ [_1345461, _1345463, _1345465, _1345467, _1345469, _1345471, _1345473, _1345475] : [c_Finite__Set_Ofolding__image__simple(_1345461, _1345463, _1345465, _1345467, _1345469, _1345471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345463), _1345473)), hBOOL(hAPP(hAPP(c_member(_1345463), _1345475), _1345473)), -(hAPP(_1345471, _1345473) = hAPP(hAPP(_1345465, hAPP(_1345469, _1345475)), hAPP(_1345471, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345463, tc_HOL_Obool)), _1345473), hAPP(hAPP(c_Set_Oinsert(_1345463), _1345475), c_Orderings_Obot__class_Obot(tc_fun(_1345463, tc_HOL_Obool)))))))], (45177 ^ _779327) ^ [_1673304, _1673306, _1673308, _1673310] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673304)), hAPP(hAPP(c_List_Omap(_1673306, _1673304), _1673308), _1673310)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673306)), _1673310))], (47632 ^ _779327) ^ [_1730140, _1730142, _1730144] : [class_Orderings_Olinorder(_1730140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1730140), _1730142)), -(c_List_Olinorder__class_Osorted__list__of__set(_1730140, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1730140, tc_HOL_Obool)), _1730142), hAPP(hAPP(c_Set_Oinsert(_1730140), _1730144), c_Orderings_Obot__class_Obot(tc_fun(_1730140, tc_HOL_Obool))))) = c_List_Oremove1(_1730140, _1730144, c_List_Olinorder__class_Osorted__list__of__set(_1730140, _1730142)))], (40295 ^ _779327) ^ [_1553017, _1553019, _1553021, _1553023] : [hBOOL(hAPP(hAPP(c_member(_1553017), _1553019), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1553017, tc_HOL_Obool), _1553021))), c_Orderings_Oorder__class_Omono(tc_fun(_1553017, tc_HOL_Obool), tc_fun(_1553017, tc_HOL_Obool), _1553021), 40305 ^ _779327 : [(40308 ^ _779327) ^ [] : [hBOOL(hAPP(_1553023, 40304 ^ [_1553017, _1553019, _1553021, _1553023]))], (40306 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553017), 40304 ^ [_1553017, _1553019, _1553021, _1553023]), hAPP(_1553021, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553017, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1553017, tc_HOL_Obool), _1553021)), hAPP(c_Set_OCollect(_1553017), _1553023))))))]], -(hBOOL(hAPP(_1553023, _1553019)))], (26187 ^ _779327) ^ [_1239361, _1239363, _1239365, _1239367] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239361), _1239363)), 26190 ^ _779327 : [(26191 ^ _779327) ^ [_1239515] : [26193 ^ _779327 : [(26199 ^ _779327) ^ [] : [-(_1239515 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26195 ^ [_1239361, _1239363, _1239365, _1239367, _1239515]), 26192 ^ [_1239361, _1239363, _1239365, _1239367, _1239515]))], (26197 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26195 ^ [_1239361, _1239363, _1239365, _1239367, _1239515]), _1239365)))], (26194 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26192 ^ [_1239361, _1239363, _1239365, _1239367, _1239515]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1239363))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239361), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239515), _1239367))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239361), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239515), _1239363)), _1239367))))]]], (42182 ^ _779327) ^ [_1599946, _1599948, _1599950, _1599952] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599946, _1599946)), hAPP(hAPP(c_Product__Type_OPair(_1599946, _1599946), _1599948), _1599950)), c_Transitive__Closure_Otrancl(_1599946, _1599952))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599946, _1599946)), hAPP(hAPP(c_Product__Type_OPair(_1599946, _1599946), _1599948), _1599950)), c_Transitive__Closure_Ortrancl(_1599946, _1599952))))], (48451 ^ _779327) ^ [_1748207, _1748209, _1748211, _1748213, _1748215] : [class_Orderings_Olinorder(_1748207), -(c_List_Olinorder__class_Osort__key(_1748209, _1748207, _1748211, hAPP(hAPP(c_List_Olist_OCons(_1748209), _1748213), _1748215)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1748209, _1748207, _1748211), _1748213), c_List_Olinorder__class_Osort__key(_1748209, _1748207, _1748211, _1748215)))], (53016 ^ _779327) ^ [_1840631, _1840633, _1840635, _1840637, _1840639, _1840641] : [-(hAPP(hAPP(hAPP(c_COMBC(_1840631, _1840633, _1840635), _1840637), _1840639), _1840641) = hAPP(hAPP(_1840637, _1840641), _1840639))], (18867 ^ _779327) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47845 ^ _779327) ^ [_1735133, _1735135, _1735137] : [class_Orderings_Olinorder(_1735133), -(c_List_Oremove1(_1735133, _1735135, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1735133, _1735133, c_COMBI(_1735133)), _1735135), _1735137)) = _1735137)], (40265 ^ _779327) ^ [_1552426, _1552428] : [-(hAPP(c_Set_Oimage(_1552426, _1552426, c_Fun_Oid(_1552426)), _1552428) = _1552428)], (22161 ^ _779327) ^ [_1162384] : [-(c_Divides_Odivmod__nat(_1162384, 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)), _1162384))], (42064 ^ _779327) ^ [_1596241, _1596243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596241, _1596241), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1596241, _1596243)), hAPP(hAPP(c_Product__Type_OSigma(_1596241, _1596241), hAPP(c_Relation_OField(_1596241), _1596243)), hAPP(c_COMBK(tc_fun(_1596241, tc_HOL_Obool), _1596241), hAPP(c_Relation_OField(_1596241), _1596243))))))], (11227 ^ _779327) ^ [_963415, _963417, _963419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963415), _963417)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963419), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963417), _963415)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963419), _963417)), _963415))], (43736 ^ _779327) ^ [_1635546] : [class_Complete__Lattice_Ocomplete__lattice(_1635546), -(c_Complete__Lattice_OInf__class_OInf(_1635546, c_Orderings_Otop__class_Otop(tc_fun(_1635546, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1635546))], (42476 ^ _779327) ^ [_1606912, _1606914] : [-(c_Relation_Orefl__on(_1606912, c_Orderings_Otop__class_Otop(tc_fun(_1606912, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606912, _1606912), tc_HOL_Obool)), _1606914), c_Relation_OId(_1606912))))], (26472 ^ _779327) ^ [_1245513, _1245515] : [-(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)), _1245513)), 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), _1245515), _1245513))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1245513), _1245515))], (13806 ^ _779327) ^ [_1011140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011140)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011140), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1011140)], (36448 ^ _779327) ^ [_1459453, _1459455] : [-(c_Relation_Orefl__on(_1459453, _1459455, c_Relation_OId__on(_1459453, _1459455)))], (8754 ^ _779327) ^ [_919867, _919869] : [-(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), _919867), _919869)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919869))], (33185 ^ _779327) ^ [_1383317, _1383319, _1383321] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1383317), _1383319)), 33188 ^ _779327 : [(33189 ^ _779327) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383317, tc_Nat_Onat), _1383321), _1383319) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 33192 ^ _779327 : [(33193 ^ _779327) ^ [_1383479] : [hBOOL(hAPP(hAPP(c_member(_1383317), _1383479), _1383319)), -(hAPP(_1383321, _1383479) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33199 ^ _779327) ^ [] : [33201 ^ _779327 : [(33204 ^ _779327) ^ [] : [hAPP(_1383321, 33200 ^ [_1383317, _1383319, _1383321]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (33202 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383317), 33200 ^ [_1383317, _1383319, _1383321]), _1383319)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383317, tc_Nat_Onat), _1383321), _1383319) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (47851 ^ _779327) ^ [_1735242, _1735244, _1735246, _1735248, _1735250] : [class_Orderings_Olinorder(_1735242), 47854 ^ _779327 : [(47863 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1735244), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1735244, _1735242, _1735246), _1735248), _1735250)))), -(hBOOL(hAPP(hAPP(c_member(_1735244), _1735248), hAPP(c_List_Oset(_1735244), _1735250)))), hBOOL(hAPP(c_List_Odistinct(_1735244), _1735250))], (47855 ^ _779327) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1735244), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1735244, _1735242, _1735246), _1735248), _1735250))), 47858 ^ _779327 : [(47861 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1735244), _1735250)))], (47859 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1735244), _1735248), hAPP(c_List_Oset(_1735244), _1735250)))]]]]], (12612 ^ _779327) ^ [_989761, _989763, _989765] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989763), _989765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989761), _989763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989761), _989765)))], (18218 ^ _779327) ^ [_1088727, _1088729] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1088727)), _1088729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1088727), _1088729))), _1088729))], (44241 ^ _779327) ^ [_1647383, _1647385, _1647387, _1647389, _1647391, _1647393, _1647395, _1647397] : [c_Finite__Set_Ofolding__image__simple__idem(_1647383, _1647385, _1647387, _1647389, _1647391, _1647393), hBOOL(hAPP(c_Finite__Set_Ofinite(_1647385), _1647395)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1647385), _1647397)), -(hAPP(_1647393, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1647385, tc_HOL_Obool)), _1647395), _1647397)) = hAPP(hAPP(_1647387, hAPP(_1647393, _1647395)), hAPP(_1647393, _1647397)))], (28224 ^ _779327) ^ [_1281486, _1281488, _1281490, _1281492] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281490), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1281486, tc_fun(_1281490, tc_HOL_Obool)), _1281488), _1281492)))), 28225 ^ _779327 : [(28226 ^ _779327) ^ [_1281560] : [hBOOL(hAPP(hAPP(c_member(_1281486), _1281560), _1281488)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281490), hAPP(_1281492, _1281560)))]]], (10787 ^ _779327) ^ [_954881, _954883, _954885, _954887] : [class_Rings_Ocomm__semiring__1(_954881), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954881), _954883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954881), _954885), _954887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954881), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954881), _954883), _954885)), _954887))], (14955 ^ _779327) ^ [_1030867, _1030869] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1030867) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1030869)), 14958 ^ _779327 : [(14961 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030869)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14959 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030867))))]], 14962 ^ _779327 : [(14965 ^ _779327) ^ [] : [14966 ^ _779327 : [(14969 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030867) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (14967 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030869))))]], 14970 ^ _779327 : [(14973 ^ _779327) ^ [] : [_1030867 = _1030869], (14971 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030869)))]]], (14963 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030867)))]]], (41529 ^ _779327) ^ [_1584406, _1584408, _1584410, _1584412, _1584414, _1584416] : [c_Finite__Set_Ofolding(_1584406, _1584408, _1584410, _1584412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584406), _1584414)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584406), _1584416)), -(hAPP(c_Fun_Ocomp(_1584408, _1584408, _1584408, hAPP(_1584412, _1584416)), hAPP(_1584412, _1584414)) = hAPP(c_Fun_Ocomp(_1584408, _1584408, _1584408, hAPP(_1584412, _1584414)), hAPP(_1584412, _1584416)))], (47189 ^ _779327) ^ [_1721332, _1721334, _1721336] : [class_Lattices_Olattice(_1721332), -(c_Big__Operators_Olattice__class_OInf__fin(_1721332, hAPP(c_List_Oset(_1721332), hAPP(hAPP(c_List_Olist_OCons(_1721332), _1721334), _1721336))) = hAPP(c_List_Ofoldl(_1721332, _1721332, c_Lattices_Osemilattice__inf__class_Oinf(_1721332), _1721334), _1721336))], (3242 ^ _779327) ^ [_828041, _828043, _828045, _828047] : [-(c_Wellfounded_Omin__ext(_828047, _828043) = c_Wellfounded_Omin__ext(_828045, _828041)), _828047 = _828045, _828043 = _828041], (37269 ^ _779327) ^ [_1475944, _1475946, _1475948, _1475950, _1475952] : [class_Groups_Ocomm__monoid__add(_1475944), class_Groups_Ocomm__monoid__mult(_1475944), _1475946 = _1475948, c_Nat__Transfer_Onat__set(_1475948), 37287 ^ _779327 : [(37290 ^ _779327) ^ [] : [hAPP(_1475950, 37286 ^ [_1475944, _1475946, _1475948, _1475950, _1475952]) = hAPP(_1475952, 37286 ^ [_1475944, _1475946, _1475948, _1475950, _1475952])], (37288 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37286 ^ [_1475944, _1475946, _1475948, _1475950, _1475952])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1475944), _1475950), _1475946) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1475944), _1475952), _1475948))], (49254 ^ _779327) ^ [_1765942, _1765944, _1765946, _1765948, _1765950, _1765952] : [class_Orderings_Olinorder(_1765942), c_List_Olinorder__class_Osorted(_1765942, hAPP(hAPP(c_List_Omap(_1765944, _1765942), _1765946), _1765948)), hBOOL(hAPP(_1765950, _1765952)), -(hAPP(c_List_Ofilter(_1765944, _1765950), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1765944, _1765942, _1765946), _1765952), _1765948)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1765944, _1765942, _1765946), _1765952), hAPP(c_List_Ofilter(_1765944, _1765950), _1765948)))], (43985 ^ _779327) ^ [_1641501, _1641503, _1641505] : [class_Complete__Lattice_Ocomplete__lattice(_1641501), -(c_Complete__Lattice_OSup__class_OSup(_1641501, hAPP(hAPP(c_Set_Oinsert(_1641501), _1641503), hAPP(hAPP(c_Set_Oinsert(_1641501), _1641505), c_Orderings_Obot__class_Obot(tc_fun(_1641501, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1641501), _1641503), _1641505))], (52890 ^ _779327) ^ [_1839332, _1839334] : [-(class_Finite__Set_Ofinite(tc_prod(_1839332, _1839334))), class_Finite__Set_Ofinite(_1839332), class_Finite__Set_Ofinite(_1839334)], (29322 ^ _779327) ^ [_1302265, _1302267, _1302269] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302265), _1302267)), -(hAPP(c_Finite__Set_Ocard(_1302265), hAPP(hAPP(c_Set_Oinsert(_1302265), _1302269), _1302267)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1302265), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302265, tc_HOL_Obool)), _1302267), hAPP(hAPP(c_Set_Oinsert(_1302265), _1302269), c_Orderings_Obot__class_Obot(tc_fun(_1302265, tc_HOL_Obool)))))))], (25281 ^ _779327) ^ [_1220113, _1220115] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220113), _1220115)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220113)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220115))))], (27673 ^ _779327) ^ [_1270165, _1270167, _1270169, _1270171, _1270173, _1270175] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270165, tc_fun(_1270167, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1270169, _1270165, _1270171), _1270173)), _1270175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270169, tc_fun(_1270167, tc_HOL_Obool)), _1270173), hAPP(hAPP(c_COMBB(_1270165, tc_fun(_1270167, tc_HOL_Obool), _1270169), _1270175), _1270171)))], (28294 ^ _779327) ^ [_1282888, _1282890, _1282892] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282888), hAPP(hAPP(c_Set_Oinsert(_1282888), _1282890), _1282892))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282888), _1282892)))], (9821 ^ _779327) ^ [_938470] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _938470) = _938470)], (44727 ^ _779327) ^ [_1661070, _1661072] : [-(c_List_Olistrel(_1661070, c_Transitive__Closure_Ortrancl(_1661070, _1661072)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1661070), c_List_Olistrel1(_1661070, _1661072)))], (37825 ^ _779327) ^ [_1487334] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487334, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1487334, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1487334, tc_HOL_Obool)))], (41719 ^ _779327) ^ [_1588617, _1588619, _1588621, _1588623, _1588625, _1588627, _1588629, _1588631] : [class_Groups_Ocomm__monoid__mult(_1588617), c_Fun_Oinj__on(_1588619, _1588621, _1588623, _1588625), _1588627 = hAPP(c_Set_Oimage(_1588619, _1588621, _1588623), _1588625), 41733 ^ _779327 : [(41736 ^ _779327) ^ [] : [hAPP(_1588629, 41732 ^ [_1588617, _1588619, _1588621, _1588623, _1588625, _1588627, _1588629, _1588631]) = hAPP(hAPP(c_Fun_Ocomp(_1588621, _1588617, _1588619, _1588631), _1588623), 41732 ^ [_1588617, _1588619, _1588621, _1588623, _1588625, _1588627, _1588629, _1588631])], (41734 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588619), 41732 ^ [_1588617, _1588619, _1588621, _1588623, _1588625, _1588627, _1588629, _1588631]), _1588625)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588621, _1588617), _1588631), _1588627) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1588619, _1588617), _1588629), _1588625))], (8248 ^ _779327) ^ [_910848, _910850, _910852] : [class_Power_Opower(_910848), class_Rings_Omult__zero(_910848), class_Rings_Ono__zero__divisors(_910848), class_Rings_Ozero__neq__one(_910848), 8263 ^ _779327 : [(8272 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_910848), _910850), _910852) = c_Groups_Ozero__class_Ozero(_910848)), _910850 = c_Groups_Ozero__class_Ozero(_910848), -(_910852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8264 ^ _779327) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_910848), _910850), _910852) = c_Groups_Ozero__class_Ozero(_910848), 8267 ^ _779327 : [(8270 ^ _779327) ^ [] : [_910852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8268 ^ _779327) ^ [] : [-(_910850 = c_Groups_Ozero__class_Ozero(_910848))]]]]], (35147 ^ _779327) ^ [_1428173, _1428175, _1428177, _1428179] : [class_Lattices_Olattice(_1428173), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428173), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428173), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428173), _1428175), _1428177)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428173), _1428175), _1428179))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428173), _1428175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428173), _1428177), _1428179)))))], (17128 ^ _779327) ^ [_1070153, _1070155] : [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), _1070153)), _1070155))), _1070153 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1070155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45456 ^ _779327) ^ [_1680725, _1680727, _1680729, _1680731, _1680733] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680725)), _1680727) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680729)), _1680731), 45459 ^ _779327 : [(45468 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1680725, _1680729), _1680727), _1680731) = _1680733), hAPP(hAPP(c_List_Omap(tc_prod(_1680725, _1680729), _1680725), c_Product__Type_Ofst(_1680725, _1680729)), _1680733) = _1680727, hAPP(hAPP(c_List_Omap(tc_prod(_1680725, _1680729), _1680729), c_Product__Type_Osnd(_1680725, _1680729)), _1680733) = _1680731], (45460 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Ozip(_1680725, _1680729), _1680727), _1680731) = _1680733, 45463 ^ _779327 : [(45466 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1680725, _1680729), _1680729), c_Product__Type_Osnd(_1680725, _1680729)), _1680733) = _1680731)], (45464 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1680725, _1680729), _1680725), c_Product__Type_Ofst(_1680725, _1680729)), _1680733) = _1680727)]]]]], (37420 ^ _779327) ^ [_1479160, _1479162, _1479164, _1479166, _1479168, _1479170, _1479172] : [c_Big__Operators_Ocomm__monoid__big(_1479160, _1479162, _1479164, _1479166, _1479168), 37423 ^ _779327 : [(37430 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479162), _1479170))), -(hAPP(hAPP(_1479168, _1479172), _1479170) = _1479166)], (37424 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1479162), _1479170)), -(hAPP(hAPP(_1479168, _1479172), _1479170) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1479160, _1479162, _1479164), _1479172), _1479166), _1479170))]]], (10069 ^ _779327) ^ [_942306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _942306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _942306) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47352 ^ _779327) ^ [_1724574, _1724576, _1724578] : [-(c_List_Olast(_1724574, hAPP(hAPP(c_List_Oappend(_1724574), _1724576), hAPP(hAPP(c_List_Olist_OCons(_1724574), _1724578), c_List_Olist_ONil(_1724574)))) = _1724578)], (44709 ^ _779327) ^ [_1660509, _1660511] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1660509), tc_List_Olist(_1660509)), tc_HOL_Obool)), c_List_Olistrel(_1660509, _1660511)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1660509), c_List_Olistrel1(_1660509, _1660511)))))], (49499 ^ _779327) ^ [_1771063, _1771065, _1771067, _1771069] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771063)), _1771065) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771067)), _1771069), -(hAPP(hAPP(c_List_Ozip(_1771063, _1771067), hAPP(c_List_Orev(_1771063), _1771065)), hAPP(c_List_Orev(_1771067), _1771069)) = hAPP(c_List_Orev(tc_prod(_1771063, _1771067)), hAPP(hAPP(c_List_Ozip(_1771063, _1771067), _1771065), _1771069)))], (22347 ^ _779327) ^ [_1165834, _1165836, _1165838] : [class_Orderings_Olinorder(_1165834), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165834), _1165836), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165834), _1165836), _1165838)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165834), _1165836), _1165838))], (47760 ^ _779327) ^ [_1733344, _1733346] : [-(hBOOL(hAPP(c_List_Olistsp(_1733344, _1733346), c_List_Olist_ONil(_1733344))))], (25305 ^ _779327) ^ [_1220597] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220597), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1220597) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (28822 ^ _779327) ^ [_1293102, _1293104, _1293106, _1293108] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1293102, _1293104)), c_Sum__Type_OPlus(_1293102, _1293104, _1293106, _1293108))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1293102), _1293106)))], (4742 ^ _779327) ^ [_851589, _851591] : [_851591 = _851589, -(c_List_Orev(_851591) = c_List_Orev(_851589))], (31684 ^ _779327) ^ [_1355011, _1355013] : [31685 ^ _779327 : [(31688 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355013), _1355011))], (31686 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355011), _1355013)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1355011, _1355013))], (9280 ^ _779327) ^ [_929636, _929638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _929636), _929638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929636)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929638))))], (4058 ^ _779327) ^ [_840911, _840913, _840915, _840917] : [-(c_Enum_Osublists(_840917, _840913) = c_Enum_Osublists(_840915, _840911)), _840917 = _840915, _840913 = _840911], (16477 ^ _779327) ^ [_1058642] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1058642) = _1058642)], (33090 ^ _779327) ^ [_1381666, _1381668, _1381670] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381666, tc_Nat_Onat), _1381668), _1381670)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381666, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1381666), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1381668)), _1381670))], (29588 ^ _779327) ^ [_1307776, _1307778, _1307780, _1307782, _1307784, _1307786] : [hBOOL(hAPP(hAPP(c_member(_1307776), _1307778), _1307780)), hBOOL(hAPP(hAPP(_1307782, _1307778), _1307784)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307776, tc_fun(_1307786, tc_HOL_Obool)), _1307780), _1307782), _1307784)))], (41317 ^ _779327) ^ [_1579710, _1579712, _1579714, _1579716, _1579718, _1579720] : [c_Fun_Oinj__on(_1579710, _1579712, _1579714, _1579716), c_Fun_Oinj__on(_1579712, _1579718, _1579720, hAPP(c_Set_Oimage(_1579710, _1579712, _1579714), _1579716)), -(c_Fun_Oinj__on(_1579710, _1579718, hAPP(c_Fun_Ocomp(_1579712, _1579718, _1579710, _1579720), _1579714), _1579716))], (12323 ^ _779327) ^ [_984350, _984352, _984354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984350), _984352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984350), _984354)), 12330 ^ _779327 : [(12337 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984352), _984354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984352), _984350)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984354), _984350))))], (12331 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984352), _984350)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984354), _984350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984352), _984354)))]]], (38287 ^ _779327) ^ [_1499933, _1499935] : [-(c_Equiv__Relations_Oequivp(_1499933, _1499935)), 38292 ^ _779327 : [(38295 ^ _779327) ^ [] : [hAPP(_1499935, 38288 ^ [_1499933, _1499935]) = hAPP(_1499935, 38289 ^ [_1499933, _1499935])], (38293 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1499935, 38288 ^ [_1499933, _1499935]), 38289 ^ [_1499933, _1499935])))]], 38296 ^ _779327 : [(38299 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1499935, 38288 ^ [_1499933, _1499935]), 38289 ^ [_1499933, _1499935]))], (38297 ^ _779327) ^ [] : [-(hAPP(_1499935, 38288 ^ [_1499933, _1499935]) = hAPP(_1499935, 38289 ^ [_1499933, _1499935]))]]], (17966 ^ _779327) ^ [_1084301] : [-(c_Int_OBit0(_1084301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1084301), _1084301))], (17810 ^ _779327) ^ [_1081471] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1081471)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081471) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39222 ^ _779327) ^ [_1521909, _1521911, _1521913] : [class_Lattices_Oab__semigroup__idem__mult(_1521909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521909), _1521911)), -(_1521911 = c_Orderings_Obot__class_Obot(tc_fun(_1521909, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521909), _1521913)), -(_1521913 = c_Orderings_Obot__class_Obot(tc_fun(_1521909, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1521909, c_Groups_Otimes__class_Otimes(_1521909)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521909, tc_HOL_Obool)), _1521911), _1521913)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1521909), hAPP(c_Finite__Set_Ofold1(_1521909, c_Groups_Otimes__class_Otimes(_1521909)), _1521911)), hAPP(c_Finite__Set_Ofold1(_1521909, c_Groups_Otimes__class_Otimes(_1521909)), _1521913)))], (12602 ^ _779327) ^ [_989547, _989549, _989551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989547), _989549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989549), _989551))))], (44025 ^ _779327) ^ [_1642167, _1642169, _1642171, _1642173] : [-(_1642167 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1642169, tc_HOL_Obool), tc_HOL_Obool))), 44031 ^ _779327 : [(44034 ^ _779327) ^ [] : [c_Fun_Oinj__on(_1642169, _1642171, _1642173, 44030 ^ [_1642167, _1642169, _1642171, _1642173])], (44032 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642169, tc_HOL_Obool)), 44030 ^ [_1642167, _1642169, _1642171, _1642173]), _1642167)))]], -(c_Fun_Oinj__on(_1642169, _1642171, _1642173, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642169, tc_HOL_Obool), _1642167)))], (44084 ^ _779327) ^ [_1643593, _1643595, _1643597] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1643593, tc_HOL_Obool)), _1643595)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643593), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643593, tc_HOL_Obool), _1643595))), 44094 ^ _779327 : [(44097 ^ _779327) ^ [] : [hAPP(c_Finite__Set_Ocard(_1643593), 44093 ^ [_1643593, _1643595, _1643597]) = _1643597], (44095 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1643593, tc_HOL_Obool)), 44093 ^ [_1643593, _1643595, _1643597]), _1643595)))]], 44101 ^ _779327 : [(44105 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1643593, tc_HOL_Obool)), 44103 ^ [_1643593, _1643595, _1643597]), _1643595)))], (44107 ^ _779327) ^ [] : [44100 ^ [_1643593, _1643595, _1643597] = 44103 ^ [_1643593, _1643595, _1643597]], (44109 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643593, tc_HOL_Obool)), 44100 ^ [_1643593, _1643595, _1643597]), 44103 ^ [_1643593, _1643595, _1643597]) = c_Orderings_Obot__class_Obot(tc_fun(_1643593, tc_HOL_Obool))], (44102 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1643593, tc_HOL_Obool)), 44100 ^ [_1643593, _1643595, _1643597]), _1643595)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1643597), hAPP(c_Finite__Set_Ocard(tc_fun(_1643593, tc_HOL_Obool)), _1643595)) = hAPP(c_Finite__Set_Ocard(_1643593), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643593, tc_HOL_Obool), _1643595)))], (4988 ^ _779327) ^ [_855348, _855350, _855352, _855354, _855356, _855358] : [-(c_FunDef_OTHE__default(_855358, _855354, _855350) = c_FunDef_OTHE__default(_855356, _855352, _855348)), _855358 = _855356, _855354 = _855352, _855350 = _855348], (6706 ^ _779327) ^ [_884340, _884342, _884344] : [class_Orderings_Olinorder(_884340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884340), _884342), _884344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884340), _884344), _884342)))], (38184 ^ _779327) ^ [_1495900, _1495902, _1495904, _1495906, _1495908, _1495910] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495902, _1495904)), hAPP(hAPP(c_Product__Type_OPair(_1495902, _1495904), _1495908), _1495910)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495900, tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1495900, tc_HOL_Obool))), _1495906))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495900, tc_fun(_1495902, tc_fun(_1495904, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1495900, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_fun(_1495902, tc_fun(_1495904, tc_HOL_Obool)), _1495900), hAPP(c_COMBC(_1495902, tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_fun(_1495904, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495904, tc_fun(tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_fun(_1495904, tc_HOL_Obool)), _1495902), c_COMBC(_1495904, tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495904, tc_prod(_1495902, _1495904)), tc_fun(_1495904, tc_fun(tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_HOL_Obool)), _1495902), hAPP(c_COMBB(tc_prod(_1495902, _1495904), tc_fun(tc_fun(tc_prod(_1495902, _1495904), tc_HOL_Obool), tc_HOL_Obool), _1495904), c_member(tc_prod(_1495902, _1495904)))), c_Product__Type_OPair(_1495902, _1495904))))), _1495906)), _1495908), _1495910)))], (2302 ^ _779327) ^ [_812901, _812903, _812905, _812907] : [-(c_Orderings_Oord_Omin(_812907, _812903) = c_Orderings_Oord_Omin(_812905, _812901)), _812907 = _812905, _812903 = _812901], (46742 ^ _779327) ^ [_1712280, _1712282, _1712284] : [-(_1712280 = c_List_Olist_ONil(_1712282)), -(hAPP(c_List_Ohd(_1712282), hAPP(hAPP(c_List_Oappend(_1712282), _1712280), _1712284)) = hAPP(c_List_Ohd(_1712282), _1712280))], (43279 ^ _779327) ^ [_1626695, _1626697, _1626699] : [class_Lattices_Olattice(_1626695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626695), _1626697)), -(c_Big__Operators_Olattice__class_OSup__fin(_1626695, hAPP(hAPP(c_Set_Oinsert(_1626695), _1626699), _1626697)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626695, _1626695, c_Lattices_Osemilattice__sup__class_Osup(_1626695)), _1626699), _1626697))], (1996 ^ _779327) ^ [_808110, _808112] : [_808112 = _808110, -(c_Set_OBall(_808112) = c_Set_OBall(_808110))], (49927 ^ _779327) ^ [_1780051, _1780053, _1780055, _1780057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1780051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780053)), c_List_OdropWhile(_1780053, _1780055, _1780057)))), -(hAPP(hAPP(c_List_Onth(_1780053), c_List_OdropWhile(_1780053, _1780055, _1780057)), _1780051) = hAPP(hAPP(c_List_Onth(_1780053), _1780057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1780051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780053)), c_List_OtakeWhile(_1780053, _1780055, _1780057)))))], (15652 ^ _779327) ^ [_1044107, _1044109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1044107)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044109), _1044107)), _1044107) = _1044109)], (10367 ^ _779327) ^ [_947311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _947311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947311)))], (12774 ^ _779327) ^ [_992742, _992744, _992746] : [class_Groups_Oordered__ab__group__add(_992742), 12777 ^ _779327 : [(12784 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992742), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_992742), _992744), _992746)), c_Groups_Ozero__class_Ozero(_992742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992742), _992744), _992746)))], (12778 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992742), _992744), _992746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992742), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_992742), _992744), _992746)), c_Groups_Ozero__class_Ozero(_992742))))]]], (35627 ^ _779327) ^ [_1439175, _1439177, _1439179] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439175), _1439177)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439175), _1439179)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1439175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439175, tc_HOL_Obool)), _1439177), _1439179))), hAPP(c_Finite__Set_Ocard(_1439175), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439175, tc_HOL_Obool)), _1439177), _1439179))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1439175), _1439177)), hAPP(c_Finite__Set_Ocard(_1439175), _1439179)))], (7972 ^ _779327) ^ [_905715, _905717, _905719, _905721] : [class_Rings_Olinordered__ring__strict(_905715), 7975 ^ _779327 : [(7990 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905715), _905717), _905719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905715), _905717), _905721)))), 7991 ^ _779327 : [(7998 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905717), c_Groups_Ozero__class_Ozero(_905715))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905721), _905719))], (7992 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), c_Groups_Ozero__class_Ozero(_905715)), _905717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905719), _905721))]]], (7976 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905715), _905717), _905719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905715), _905717), _905721))), 7981 ^ _779327 : [(7984 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905719), _905721)))], (7982 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), c_Groups_Ozero__class_Ozero(_905715)), _905717)))]], 7985 ^ _779327 : [(7988 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905721), _905719)))], (7986 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905715), _905717), c_Groups_Ozero__class_Ozero(_905715))))]]]]], (12209 ^ _779327) ^ [_982428, _982430] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982428), _982430) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982430), _982428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_982428 = _982430)], (5376 ^ _779327) ^ [_861346, _861348] : [_861348 = _861346, -(c_HOL_OEx(_861348) = c_HOL_OEx(_861346))], (50987 ^ _779327) ^ [_1803297, _1803299] : [c_Wellfounded_Oacyclic(_1803297, hAPP(c_Set_OCollect(tc_prod(_1803297, _1803297)), hAPP(c_Product__Type_Oprod_Oprod__case(_1803297, _1803297, tc_HOL_Obool), c_Predicate_Oconversep(_1803297, _1803297, _1803299)))), -(c_Wellfounded_Oacyclic(_1803297, hAPP(c_Set_OCollect(tc_prod(_1803297, _1803297)), hAPP(c_Product__Type_Oprod_Oprod__case(_1803297, _1803297, tc_HOL_Obool), _1803299))))], (42296 ^ _779327) ^ [_1602804, _1602806] : [-(c_Transitive__Closure_Ortrancl(_1602804, c_Transitive__Closure_Ortrancl(_1602804, _1602806)) = c_Transitive__Closure_Ortrancl(_1602804, _1602806))], (40894 ^ _779327) ^ [_1569301, _1569303, _1569305, _1569307] : [40896 ^ _779327 : [(40899 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1569303, hAPP(_1569305, 40895 ^ [_1569301, _1569303, _1569305, _1569307]))), hAPP(_1569303, 40895 ^ [_1569301, _1569303, _1569305, _1569307])))], (40897 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1569301, 40895 ^ [_1569301, _1569303, _1569305, _1569307])))]], -(c_Wellfounded_Owf(_1569307, hAPP(c_Set_OCollect(tc_prod(_1569307, _1569307)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569307, _1569307, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1569307, tc_HOL_Obool), tc_fun(_1569307, tc_HOL_Obool), _1569307), hAPP(c_COMBS(_1569307, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569307), c_fconj), _1569301))), hAPP(hAPP(c_COMBC(_1569307, tc_fun(_1569307, _1569307), tc_fun(_1569307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569307, tc_HOL_Obool), tc_fun(tc_fun(_1569307, _1569307), tc_fun(_1569307, tc_HOL_Obool)), _1569307), c_COMBB(_1569307, tc_HOL_Obool, _1569307)), c_fequal)), _1569305))))))], (37779 ^ _779327) ^ [_1486482, _1486484, _1486486] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1486482, _1486484, c_Orderings_Obot__class_Obot(tc_fun(_1486482, tc_HOL_Obool))), _1486486))], (9967 ^ _779327) ^ [_940704] : [class_Rings_Olinordered__semidom(_940704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940704), c_Groups_Oone__class_Oone(_940704)), c_Groups_Ozero__class_Ozero(_940704)))], (9573 ^ _779327) ^ [_934388, _934390] : [_934388 = _934390, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934388) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934390))], (9337 ^ _779327) ^ [_930596, _930598] : [class_Rings_Olinordered__idom(_930596), 9340 ^ _779327 : [(9347 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _930598), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930596), hAPP(c_Int_Oring__1__class_Oof__int(_930596), _930598)), c_Groups_Ozero__class_Ozero(_930596))))], (9341 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930596), hAPP(c_Int_Oring__1__class_Oof__int(_930596), _930598)), c_Groups_Ozero__class_Ozero(_930596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _930598), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (31383 ^ _779327) ^ [_1348426, _1348428, _1348430, _1348432, _1348434] : [_1348426 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1348428, tc_HOL_Obool), _1348430), c_Orderings_Oorder__class_Omono(tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool), _1348430), hBOOL(hAPP(hAPP(c_member(_1348428), _1348432), _1348434)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1348428, tc_HOL_Obool)), _1348434), hAPP(_1348430, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1348428, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348428, tc_HOL_Obool), tc_fun(tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), tc_fun(_1348428, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1348428, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1348428, tc_HOL_Obool), tc_fun(tc_fun(_1348428, tc_HOL_Obool), tc_fun(_1348428, tc_HOL_Obool)), tc_fun(_1348428, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1348428, tc_HOL_Obool))), _1348430)), _1348434))), _1348426))))), -(hBOOL(hAPP(hAPP(c_member(_1348428), _1348432), _1348426)))], (52604 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51245 ^ _779327) ^ [_1808461, _1808463, _1808465, _1808467, _1808469] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1808463, _1808461)), hAPP(hAPP(c_Product__Type_OPair(_1808463, _1808461), _1808467), _1808469)), hAPP(c_Relation_Oconverse(_1808461, _1808463), _1808465))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1808461, _1808463, hAPP(hAPP(c_COMBC(_1808461, tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_fun(_1808463, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808463, tc_fun(tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_fun(_1808463, tc_HOL_Obool)), _1808461), c_COMBC(_1808463, tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808463, tc_prod(_1808461, _1808463)), tc_fun(_1808463, tc_fun(tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_HOL_Obool)), _1808461), hAPP(c_COMBB(tc_prod(_1808461, _1808463), tc_fun(tc_fun(tc_prod(_1808461, _1808463), tc_HOL_Obool), tc_HOL_Obool), _1808463), c_member(tc_prod(_1808461, _1808463)))), c_Product__Type_OPair(_1808461, _1808463)))), _1808465)), _1808467), _1808469)))], (9841 ^ _779327) ^ [_938765] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938765), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _938765)], (46311 ^ _779327) ^ [_1701275, _1701277, _1701279, _1701281, _1701283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701275), tc_List_Olist(_1701275))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701275), tc_List_Olist(_1701275)), _1701277), _1701279)), c_List_Olexord(_1701275, _1701281))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701275), tc_List_Olist(_1701275))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701275), tc_List_Olist(_1701275)), hAPP(hAPP(c_List_Oappend(_1701275), _1701283), _1701277)), hAPP(hAPP(c_List_Oappend(_1701275), _1701283), _1701279))), c_List_Olexord(_1701275, _1701281))))], (5110 ^ _779327) ^ [_857259, _857261, _857263, _857265, _857267, _857269] : [-(c_Relation_OImage(_857269, _857265, _857261) = c_Relation_OImage(_857267, _857263, _857259)), _857269 = _857267, _857265 = _857263, _857261 = _857259], (14483 ^ _779327) ^ [_1023582] : [class_Rings_Osemiring__1(_1023582), -(c_Int_Oiszero(_1023582, c_Groups_Ozero__class_Ozero(_1023582)))], (23063 ^ _779327) ^ [_1179000, _1179002] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1179000)), hAPP(c_Nat_OSuc, _1179002)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1179000), _1179002)))], (52702 ^ _779327) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (29802 ^ _779327) ^ [_1311957, _1311959, _1311961, _1311963, _1311965, _1311967] : [hBOOL(hAPP(hAPP(c_member(_1311957), _1311959), _1311961)), _1311963 = hAPP(_1311965, _1311959), -(hBOOL(hAPP(hAPP(c_member(_1311967), _1311963), hAPP(c_Set_Oimage(_1311957, _1311967, _1311965), _1311961))))], (47976 ^ _779327) ^ [_1737971, _1737973, _1737975, _1737977, _1737979, _1737981, _1737983] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737971)), _1737973) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737975)), _1737977), 47979 ^ _779327 : [(47988 ^ _779327) ^ [] : [-(c_List_Olist__all2(_1737971, _1737975, _1737979, hAPP(hAPP(c_List_Oappend(_1737971), _1737973), _1737981), hAPP(hAPP(c_List_Oappend(_1737975), _1737977), _1737983))), c_List_Olist__all2(_1737971, _1737975, _1737979, _1737973, _1737977), c_List_Olist__all2(_1737971, _1737975, _1737979, _1737981, _1737983)], (47980 ^ _779327) ^ [] : [c_List_Olist__all2(_1737971, _1737975, _1737979, hAPP(hAPP(c_List_Oappend(_1737971), _1737973), _1737981), hAPP(hAPP(c_List_Oappend(_1737975), _1737977), _1737983)), 47983 ^ _779327 : [(47986 ^ _779327) ^ [] : [-(c_List_Olist__all2(_1737971, _1737975, _1737979, _1737981, _1737983))], (47984 ^ _779327) ^ [] : [-(c_List_Olist__all2(_1737971, _1737975, _1737979, _1737973, _1737977))]]]]], (48505 ^ _779327) ^ [_1749913, _1749915, _1749917, _1749919] : [-(c_List_Oconcat(_1749913, hAPP(hAPP(c_List_Omap(_1749915, tc_List_Olist(_1749913)), hAPP(hAPP(c_COMBC(_1749915, tc_List_Olist(_1749913), tc_List_Olist(_1749913)), hAPP(hAPP(c_COMBB(_1749913, tc_fun(tc_List_Olist(_1749913), tc_List_Olist(_1749913)), _1749915), c_List_Olist_OCons(_1749913)), _1749917)), c_List_Olist_ONil(_1749913))), _1749919)) = hAPP(hAPP(c_List_Omap(_1749915, _1749913), _1749917), _1749919))], (9020 ^ _779327) ^ [_924558, _924560] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _924558), _924560)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924558)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924560)))], (23782 ^ _779327) ^ [_1193721, _1193723, _1193725, _1193727] : [-(c_Product__Type_Ocurry(_1193721, _1193723, _1193725, hAPP(c_Product__Type_Oprod_Oprod__case(_1193721, _1193723, _1193725), _1193727)) = _1193727)], (35009 ^ _779327) ^ [_1424756, _1424758, _1424760, _1424762] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424756, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1424756, tc_fun(_1424756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424756)), _1424758)), hAPP(hAPP(c_COMBC(_1424756, tc_fun(_1424756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424756)), _1424760)), _1424762)), -(hBOOL(hAPP(hAPP(c_member(_1424756), _1424762), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424756, tc_HOL_Obool)), _1424758), _1424760))))], (6916 ^ _779327) ^ [_887537] : [_887537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887537), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (48086 ^ _779327) ^ [_1740184, _1740186, _1740188, _1740190, _1740192, _1740194, _1740196] : [c_List_Olist__all2(_1740184, _1740186, _1740188, _1740190, hAPP(hAPP(c_List_Omap(_1740192, _1740186), _1740194), _1740196)), -(c_List_Olist__all2(_1740184, _1740192, hAPP(hAPP(c_COMBC(_1740184, tc_fun(_1740192, _1740186), tc_fun(_1740192, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1740186, tc_HOL_Obool), tc_fun(tc_fun(_1740192, _1740186), tc_fun(_1740192, tc_HOL_Obool)), _1740184), c_COMBB(_1740186, tc_HOL_Obool, _1740192)), _1740188)), _1740194), _1740190, _1740196))], (44436 ^ _779327) ^ [_1651726, _1651728] : [-(c_FunDef_Ois__measure(_1651726, _1651728))], (9941 ^ _779327) ^ [_940287] : [9942 ^ _779327 : [(9943 ^ _779327) ^ [_940344] : [hBOOL(hAPP(_940287, _940344))]], 9945 ^ _779327 : [(9948 ^ _779327) ^ [] : [-(hBOOL(hAPP(_940287, hAPP(c_Int_Onat, 9944 ^ [_940287]))))], (9946 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9944 ^ [_940287])))]]], (46522 ^ _779327) ^ [_1706991, _1706993, _1706995, _1706997] : [-(hAPP(hAPP(c_List_Otake(_1706991), _1706993), hAPP(hAPP(c_List_Odrop(_1706991), _1706995), _1706997)) = hAPP(hAPP(c_List_Odrop(_1706991), _1706995), hAPP(hAPP(c_List_Otake(_1706991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1706993), _1706995)), _1706997)))], (28676 ^ _779327) ^ [_1290355, _1290357] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290355, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1290355, tc_HOL_Obool))), _1290357) = _1290357)], (12736 ^ _779327) ^ [_992137, _992139] : [class_Rings_Olinordered__idom(_992137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992137), _992139), c_Groups_Ozero__class_Ozero(_992137))), -(c_Groups_Osgn__class_Osgn(_992137, _992139) = hAPP(c_Groups_Ouminus__class_Ouminus(_992137), c_Groups_Oone__class_Oone(_992137)))], (34715 ^ _779327) ^ [_1418875, _1418877, _1418879, _1418881] : [class_Lattices_Osemilattice__inf(_1418875), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418875), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418875), _1418877), _1418879)), _1418881) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418875), _1418877), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418875), _1418879), _1418881)))], (14195 ^ _779327) ^ [_1018479] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1018479) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018479)))], (44930 ^ _779327) ^ [_1667056, _1667058, _1667060] : [-(hAPP(hAPP(c_List_Onth(_1667056), hAPP(hAPP(c_List_Olist_OCons(_1667056), _1667058), _1667060)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1667058)], (50142 ^ _779327) ^ [_1784455, _1784457, _1784459] : [-(c_List_Omaps(_1784455, _1784457, _1784459, c_List_Olist_ONil(_1784455)) = c_List_Olist_ONil(_1784457))], (19043 ^ _779327) ^ [_1103779, _1103781, _1103783] : [class_Fields_Olinordered__field(_1103779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103779), _1103781), c_Groups_Ozero__class_Ozero(_1103779))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103779), c_Groups_Ozero__class_Ozero(_1103779)), _1103783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103779), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103779), _1103781), _1103783)), c_Groups_Ozero__class_Ozero(_1103779))))], (51901 ^ _779327) ^ [_1824154, _1824156] : [c_Equiv__Relations_Oequivp(_1824154, _1824156), 51904 ^ _779327 : [(51909 ^ _779327) ^ [] : [-(c_Predicate_Otransp(_1824154, _1824156))], (51907 ^ _779327) ^ [] : [-(c_Predicate_Osymp(_1824154, _1824156))], (51905 ^ _779327) ^ [] : [-(c_Predicate_Oreflp(_1824154, _1824156))]]], (35201 ^ _779327) ^ [_1429392, _1429394, _1429396, _1429398] : [-(hBOOL(hAPP(hAPP(c_member(_1429392), _1429394), _1429396))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429392, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1429392), _1429394), _1429398)), _1429396) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429392, tc_HOL_Obool)), _1429398), _1429396))], (16806 ^ _779327) ^ [_1064199, _1064201, _1064203] : [class_Rings_Olinordered__idom(_1064199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064199), c_Groups_Ozero__class_Ozero(_1064199)), _1064201)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064199), hAPP(c_Groups_Oabs__class_Oabs(_1064199), _1064203)), _1064201) = hAPP(c_Groups_Oabs__class_Oabs(_1064199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064199), _1064203), _1064201)))], (38133 ^ _779327) ^ [_1494276, _1494278, _1494280, _1494282] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1494276, _1494278, hAPP(hAPP(c_Set_Oinsert(_1494276), _1494280), c_Orderings_Obot__class_Obot(tc_fun(_1494276, tc_HOL_Obool)))), _1494282)), -(_1494280 = _1494282)], (26944 ^ _779327) ^ [_1254484, _1254486] : [class_Lattices_Osemilattice__sup(_1254484), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254484), _1254486), _1254486) = _1254486)], (15618 ^ _779327) ^ [_1043354, _1043356, _1043358] : [class_Divides_Osemiring__div(_1043354), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043354), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1043354), _1043356), _1043358)), _1043358)), c_Divides_Odiv__class_Omod(_1043354, _1043356, _1043358)) = _1043356)], (22223 ^ _779327) ^ [_1163437] : [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), _1163437))), -(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), _1163437)) = 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), _1163437))))], (16904 ^ _779327) ^ [_1066118, _1066120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1066118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066120, _1066118)), _1066118)))], (52774 ^ _779327) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (6494 ^ _779327) ^ [_881195, _881197, _881199] : [class_Orderings_Olinorder(_881195), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881195), _881197), _881199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881195), _881199), _881197)))], (6000 ^ _779327) ^ [_873780, _873782, _873784, _873786] : [class_Orderings_Opreorder(_873780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873780), _873782), _873784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873780), _873784), _873786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873780), _873782), _873786)))], (51352 ^ _779327) ^ [_1811041, _1811043, _1811045] : [hBOOL(hAPP(hAPP(c_List_Omember(_1811041), _1811043), _1811045)), -(hBOOL(hAPP(hAPP(c_member(_1811041), _1811045), hAPP(c_List_Oset(_1811041), _1811043))))], (52826 ^ _779327) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (51299 ^ _779327) ^ [_1809679, _1809681] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809679)), _1809681) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1809679, tc_Lazy__Sequence_Olazy__sequence(_1809679)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1809679, tc_Lazy__Sequence_Olazy__sequence(_1809679), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809679), tc_Nat_Onat), _1809679), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1809679), 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(_1809679)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809679)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1809679), _1809681)))], (5148 ^ _779327) ^ [_857866, _857868, _857870, _857872] : [-(c_List_Olexord(_857872, _857868) = c_List_Olexord(_857870, _857866)), _857872 = _857870, _857868 = _857866], (18768 ^ _779327) ^ [_1098755, _1098757, _1098759] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1098755, _1098757) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1098759, _1098757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098759), _1098755)), -(_1098755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1098759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1098757), 18775 ^ [_1098755, _1098757, _1098759])))], (18632 ^ _779327) ^ [_1096174] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1096174, 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, _1096174, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32566 ^ _779327) ^ [_1371315, _1371317, _1371319] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1371315, tc_HOL_Obool), tc_fun(_1371315, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1371315, tc_HOL_Obool), tc_fun(_1371315, tc_HOL_Obool)), _1371317), _1371319)), c_Wellfounded_Ofinite__psubset(_1371315)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1371315, tc_HOL_Obool)), _1371317), _1371319)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371315), _1371319))], (27813 ^ _779327) ^ [_1273707] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1273707)) = 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), _1273707))))], (21503 ^ _779327) ^ [_1149379, _1149381, _1149383] : [21505 ^ _779327 : [(21508 ^ _779327) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1149379, _1149381), 21504 ^ [_1149379, _1149381, _1149383]))], (21506 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1149381, 21504 ^ [_1149379, _1149381, _1149383]), _1149383)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1149379, _1149381), _1149383)))], (18620 ^ _779327) ^ [_1095994, _1095996] : [-(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), _1095994)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095996))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095994))) = 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), _1095996)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095994)))], (20683 ^ _779327) ^ [_1133176, _1133178, _1133180, _1133182] : [class_Fields_Olinordered__field__inverse__zero(_1133176), class_Int_Onumber(_1133176), 20690 ^ _779327 : [(20691 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133176), _1133178), _1133180)), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182))), 20694 ^ _779327 : [(20701 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), _1133180))), 20704 ^ _779327 : [(20711 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), _1133180), c_Groups_Ozero__class_Ozero(_1133176)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182))))], (20705 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), _1133180), c_Groups_Ozero__class_Ozero(_1133176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133176), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)), _1133180)), _1133178)))]]], (20695 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), _1133180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), _1133178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133176), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)), _1133180))))]]], (20717 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133176), _1133178), _1133180)), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)))), 20720 ^ _779327 : [(20723 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), _1133178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133176), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)), _1133180)))], (20721 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), _1133180)))]], 20724 ^ _779327 : [(20727 ^ _779327) ^ [] : [20728 ^ _779327 : [(20731 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133176), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)), _1133180)), _1133178))], (20729 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), _1133180), c_Groups_Ozero__class_Ozero(_1133176))))]], 20732 ^ _779327 : [(20735 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), hAPP(c_Int_Onumber__class_Onumber__of(_1133176), _1133182)))], (20733 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), _1133180), c_Groups_Ozero__class_Ozero(_1133176)))]]], (20725 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), _1133180))]]]]], (43838 ^ _779327) ^ [_1638248, _1638250, _1638252] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638248, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638248, tc_HOL_Obool), _1638250)), _1638252) = c_Orderings_Obot__class_Obot(tc_fun(_1638248, tc_HOL_Obool)), 43841 ^ _779327 : [(43842 ^ _779327) ^ [_1638383] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1638248, tc_HOL_Obool)), _1638383), _1638250)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638248, tc_HOL_Obool)), _1638383), _1638252) = c_Orderings_Obot__class_Obot(tc_fun(_1638248, tc_HOL_Obool)))]]], (45888 ^ _779327) ^ [_1691817, _1691819] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1691817), _1691819) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691817, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1691819), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40454 ^ _779327) ^ [_1558388, _1558390, _1558392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1558388, _1558388), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1558388, _1558388, _1558388), _1558390), _1558392)), _1558390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1558388, _1558390)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1558388, _1558392)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1558388, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1558388, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1558388, tc_HOL_Obool), tc_fun(_1558388, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1558388, _1558390))))], (34553 ^ _779327) ^ [_1415012, _1415014, _1415016, _1415018, _1415020, _1415022, _1415024, _1415026, _1415028, _1415030] : [c_Equiv__Relations_Oequiv(_1415012, _1415014, _1415016), c_Equiv__Relations_Oequiv(_1415018, _1415020, _1415022), c_Equiv__Relations_Ocongruent2(_1415012, _1415018, tc_fun(_1415024, tc_HOL_Obool), _1415016, _1415022, _1415026), hBOOL(hAPP(hAPP(c_member(_1415012), _1415028), _1415014)), hBOOL(hAPP(hAPP(c_member(_1415018), _1415030), _1415020)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415012, tc_fun(_1415024, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1415012, _1415012, _1415016), hAPP(hAPP(c_Set_Oinsert(_1415012), _1415028), c_Orderings_Obot__class_Obot(tc_fun(_1415012, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1415018, tc_fun(_1415024, tc_HOL_Obool)), tc_fun(_1415024, tc_HOL_Obool), _1415012), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415018, tc_fun(_1415024, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1415018, _1415018, _1415022), hAPP(hAPP(c_Set_Oinsert(_1415018), _1415030), c_Orderings_Obot__class_Obot(tc_fun(_1415018, tc_HOL_Obool)))))), _1415026)) = hAPP(hAPP(_1415026, _1415028), _1415030))], (43255 ^ _779327) ^ [_1626233, _1626235, _1626237, _1626239] : [class_Orderings_Olinorder(_1626233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626233), _1626235)), hBOOL(hAPP(hAPP(c_member(_1626233), _1626237), _1626235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626233), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1626233), _1626237), _1626239)), hAPP(hAPP(c_Finite__Set_Ofold(_1626233, _1626233, c_Orderings_Oord__class_Omax(_1626233)), _1626239), _1626235))))], (23059 ^ _779327) ^ [_1178945] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1178945), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1178945)], (40755 ^ _779327) ^ [_1565757, _1565759] : [c_FunDef_Oreduction__pair(_1565757, _1565759), 40758 ^ _779327 : [(40761 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565757, _1565757, _1565757), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool), tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), _1565759)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool), tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), _1565759))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool), tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), _1565759))))], (40759 ^ _779327) ^ [] : [-(c_Wellfounded_Owf(_1565757, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool), tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), _1565759)))]]], (27136 ^ _779327) ^ [_1258215, _1258217, _1258219, _1258221] : [class_Lattices_Osemilattice__sup(_1258215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258215), _1258217), _1258219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258215), _1258217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258215), _1258219), _1258221))))], (40011 ^ _779327) ^ [_1542115, _1542117] : [-(hAPP(c_Set_OPow(_1542115), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1542115, tc_HOL_Obool)), _1542117)) = hAPP(c_Set_OCollect(tc_fun(_1542115, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1542115, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1542115, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1542115, tc_HOL_Obool), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1542115, tc_HOL_Obool)), c_COMBS(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1542115, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1542115, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1542115, tc_HOL_Obool), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_fun(_1542115, tc_HOL_Obool)), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_fun(_1542115, tc_HOL_Obool)), tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1542115, tc_HOL_Obool)), c_COMBB(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1542115, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1542115, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1542115, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1542115, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1542115, tc_HOL_Obool)), _1542117)), c_Set_OPow(_1542115))))))], (19543 ^ _779327) ^ [_1112183, _1112185, _1112187] : [class_Fields_Olinordered__field(_1112183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112183), c_Groups_Ozero__class_Ozero(_1112183)), _1112185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112183), c_Groups_Ozero__class_Ozero(_1112183)), _1112187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112183), c_Groups_Ozero__class_Ozero(_1112183)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112183), _1112185), _1112187))))], (50907 ^ _779327) ^ [_1801538, _1801540, _1801542, _1801544] : [c_List_Olist__ex1(_1801538, _1801540, hAPP(hAPP(c_List_Olist_OCons(_1801538), _1801542), _1801544)), 50910 ^ _779327 : [(50917 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1801540, _1801542))), -(c_List_Olist__ex1(_1801538, _1801540, _1801544))], (50911 ^ _779327) ^ [] : [hBOOL(hAPP(_1801540, _1801542)), -(c_List_Olist__all(_1801538, hAPP(hAPP(c_COMBS(_1801538, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801538), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1801538), c_fNot), _1801540))), hAPP(c_fequal, _1801542)), _1801544))]]], (15770 ^ _779327) ^ [_1046032, _1046034] : [-(_1046032 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046034), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046032), _1046034))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046032, _1046034)))], (46112 ^ _779327) ^ [_1696725, _1696727, _1696729] : [-(hAPP(hAPP(c_List_Oappend(_1696725), _1696727), _1696729) = c_List_Olist_ONil(_1696725)), _1696727 = c_List_Olist_ONil(_1696725), _1696729 = c_List_Olist_ONil(_1696725)], (48556 ^ _779327) ^ [_1751469, _1751471, _1751473] : [-(c_List_Opartition(_1751469, _1751471, _1751473) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751469), tc_List_Olist(_1751469)), hAPP(c_List_Ofilter(_1751469, _1751471), _1751473)), hAPP(c_List_Ofilter(_1751469, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1751469, c_fNot), _1751471)), _1751473)))], (26466 ^ _779327) ^ [_1245378, _1245380, _1245382] : [class_Groups_Oordered__ab__group__add(_1245378), -(hAPP(c_Set_Oimage(_1245378, _1245378, c_Groups_Ouminus__class_Ouminus(_1245378)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1245378, _1245380, _1245382)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1245378, hAPP(c_Groups_Ouminus__class_Ouminus(_1245378), _1245382)), hAPP(c_Groups_Ouminus__class_Ouminus(_1245378), _1245380)))], (22063 ^ _779327) ^ [_1160383, _1160385, _1160387] : [-(_1160383 = hAPP(hAPP(c_Product__Type_OPair(_1160385, _1160387), hAPP(c_Product__Type_Ofst(_1160385, _1160387), _1160383)), hAPP(c_Product__Type_Osnd(_1160385, _1160387), _1160383)))], (15902 ^ _779327) ^ [_1048330, _1048332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048330)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048332)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1048330)), hAPP(c_Int_Onat, _1048332)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1048330), _1048332)))], (41301 ^ _779327) ^ [_1579388, _1579390, _1579392, _1579394, _1579396] : [c_Fun_Oinj__on(_1579388, _1579390, _1579392, c_Orderings_Otop__class_Otop(tc_fun(_1579388, tc_HOL_Obool))), c_Fun_Oinj__on(_1579394, _1579388, _1579396, c_Orderings_Otop__class_Otop(tc_fun(_1579394, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1579394, _1579390, hAPP(c_Fun_Ocomp(_1579388, _1579390, _1579394, _1579392), _1579396), c_Orderings_Otop__class_Otop(tc_fun(_1579394, tc_HOL_Obool))))], (50888 ^ _779327) ^ [_1801145, _1801147, _1801149] : [c_List_Olist__all(_1801145, _1801147, _1801149), 50891 ^ _779327 : [(50892 ^ _779327) ^ [_1801226] : [hBOOL(hAPP(hAPP(c_member(_1801145), _1801226), hAPP(c_List_Oset(_1801145), _1801149))), -(hBOOL(hAPP(_1801147, _1801226)))]]], (12101 ^ _779327) ^ [_980108, _980110, _980112, _980114, _980116] : [class_Groups_Oordered__cancel__ab__semigroup__add(_980108), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980108), _980110), _980112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980108), _980114), _980116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980108), _980110), _980114)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980108), _980112), _980116))))], (49491 ^ _779327) ^ [_1770841, _1770843, _1770845] : [-(hAPP(c_List_Orev(_1770841), hAPP(hAPP(c_List_Oappend(_1770841), _1770843), _1770845)) = hAPP(hAPP(c_List_Oappend(_1770841), hAPP(c_List_Orev(_1770841), _1770845)), hAPP(c_List_Orev(_1770841), _1770843)))], (13312 ^ _779327) ^ [_1002080, _1002082, _1002084] : [class_Int_Onumber__ring(_1002080), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002080), hAPP(c_Int_Onumber__class_Onumber__of(_1002080), _1002082)), hAPP(c_Int_Onumber__class_Onumber__of(_1002080), _1002084)) = hAPP(c_Int_Onumber__class_Onumber__of(_1002080), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002082), _1002084)))], (44053 ^ _779327) ^ [_1642741, _1642743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1642741, tc_HOL_Obool)), _1642743)), 44059 ^ _779327 : [(44062 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1642741), 44058 ^ [_1642741, _1642743]))], (44060 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642741, tc_HOL_Obool)), 44058 ^ [_1642741, _1642743]), _1642743)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1642741), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642741, tc_HOL_Obool), _1642743))))], (18354 ^ _779327) ^ [_1091062, _1091064] : [class_Rings_Olinordered__idom(_1091062), -(hAPP(c_Groups_Oabs__class_Oabs(_1091062), hAPP(hAPP(c_Power_Opower__class_Opower(_1091062), _1091064), 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(_1091062), _1091064), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (30205 ^ _779327) ^ [_1322407, _1322409, _1322411, _1322413, _1322415] : [hBOOL(hAPP(hAPP(c_member(_1322407), _1322409), _1322411)), -(hAPP(hAPP(c_Set_Oinsert(_1322413), hAPP(_1322415, _1322409)), hAPP(c_Set_Oimage(_1322407, _1322413, _1322415), _1322411)) = hAPP(c_Set_Oimage(_1322407, _1322413, _1322415), _1322411))], (29812 ^ _779327) ^ [_1312150, _1312152, _1312154, _1312156, _1312158] : [hBOOL(hAPP(hAPP(c_member(_1312150), _1312152), _1312154)), -(hBOOL(hAPP(hAPP(c_member(_1312156), hAPP(_1312158, _1312152)), hAPP(c_Set_Oimage(_1312150, _1312156, _1312158), _1312154))))], (27190 ^ _779327) ^ [_1259137, _1259139, _1259141] : [class_Lattices_Olattice(_1259137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259137), _1259139), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259137), _1259141), _1259139))))], (45488 ^ _779327) ^ [_1681392, _1681394] : [-(c_List_Osublist(_1681392, _1681394, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1681392))], (6885 ^ _779327) ^ [_887042, _887044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887042), hAPP(c_Nat_OSuc, _887044))), -(_887042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6893 ^ _779327 : [(6896 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 6892 ^ [_887042, _887044]), _887044)))], (6894 ^ _779327) ^ [] : [-(_887042 = hAPP(c_Nat_OSuc, 6892 ^ [_887042, _887044]))]]], (28802 ^ _779327) ^ [_1292746, _1292748, _1292750, _1292752] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1292746, _1292748)), c_Sum__Type_OPlus(_1292746, _1292748, _1292750, _1292752)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292746), _1292750)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292748), _1292752))], (39652 ^ _779327) ^ [_1531458, _1531460, _1531462, _1531464, _1531466, _1531468] : [-(_1531458 = c_Orderings_Obot__class_Obot(tc_fun(_1531460, tc_HOL_Obool))), 39658 ^ _779327 : [(39661 ^ _779327) ^ [] : [c_Fun_Oinj__on(_1531462, _1531464, _1531466, hAPP(_1531468, 39657 ^ [_1531458, _1531460, _1531462, _1531464, _1531466, _1531468]))], (39659 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531460), 39657 ^ [_1531458, _1531460, _1531462, _1531464, _1531466, _1531468]), _1531458)))]], -(c_Fun_Oinj__on(_1531462, _1531464, _1531466, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1531460, tc_fun(_1531462, tc_HOL_Obool)), _1531458), _1531468)))], (30189 ^ _779327) ^ [_1322099, _1322101, _1322103, _1322105] : [-(hBOOL(hAPP(hAPP(c_member(_1322099), _1322101), _1322103))), 30192 ^ _779327 : [(30199 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322099, tc_HOL_Obool)), _1322103), _1322105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322099, tc_HOL_Obool)), _1322103), hAPP(hAPP(c_Set_Oinsert(_1322099), _1322101), _1322105))))], (30193 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322099, tc_HOL_Obool)), _1322103), hAPP(hAPP(c_Set_Oinsert(_1322099), _1322101), _1322105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322099, tc_HOL_Obool)), _1322103), _1322105)))]]], (42274 ^ _779327) ^ [_1602230, _1602232, _1602234, _1602236, _1602238] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602230, _1602230)), hAPP(hAPP(c_Product__Type_OPair(_1602230, _1602230), _1602232), _1602234)), c_Transitive__Closure_Ortrancl(_1602230, _1602236))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602230, _1602230)), hAPP(hAPP(c_Product__Type_OPair(_1602230, _1602230), _1602234), _1602238)), _1602236)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602230, _1602230)), hAPP(hAPP(c_Product__Type_OPair(_1602230, _1602230), _1602232), _1602238)), c_Transitive__Closure_Ortrancl(_1602230, _1602236))))], (45308 ^ _779327) ^ [_1676295, _1676297, _1676299] : [hBOOL(hAPP(hAPP(c_member(_1676295), _1676297), hAPP(c_List_Oset(_1676295), _1676299))), -(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(_1676295)), _1676299))))], (4160 ^ _779327) ^ [_842492, _842494, _842496, _842498] : [-(c_Random_Oselect__weight(_842498, _842494) = c_Random_Oselect__weight(_842496, _842492)), _842498 = _842496, _842494 = _842492], (29546 ^ _779327) ^ [_1306979, _1306981, _1306983, _1306985] : [29547 ^ _779327 : [(29550 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306979), _1306981), _1306985))], (29548 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306979), _1306981), _1306983))]], -(hBOOL(hAPP(hAPP(c_member(_1306979), _1306981), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306979, tc_HOL_Obool)), _1306985), _1306983))))], (9379 ^ _779327) ^ [_931260, _931262, _931264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931260), _931262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931262), _931264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931260), _931264)))], (48704 ^ _779327) ^ [_1755624, _1755626, _1755628, _1755630, _1755632, _1755634] : [-(c_List_Ofoldr(_1755624, _1755626, _1755628, hAPP(hAPP(c_List_Olist_OCons(_1755624), _1755630), _1755632), _1755634) = hAPP(hAPP(_1755628, _1755630), c_List_Ofoldr(_1755624, _1755626, _1755628, _1755632, _1755634)))], (21686 ^ _779327) ^ [_1152986] : [-(_1152986 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1152986), 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)))))], (7149 ^ _779327) ^ [_891222] : [hAPP(c_Nat_OSuc, _891222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40807 ^ _779327) ^ [_1567215, _1567217, _1567219, _1567221] : [hBOOL(hAPP(c_Predicate_ORangeP(_1567215, _1567217, hAPP(hAPP(c_COMBC(_1567215, tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_fun(_1567217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567217, tc_fun(tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_fun(_1567217, tc_HOL_Obool)), _1567215), c_COMBC(_1567217, tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567217, tc_prod(_1567215, _1567217)), tc_fun(_1567217, tc_fun(tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_HOL_Obool)), _1567215), hAPP(c_COMBB(tc_prod(_1567215, _1567217), tc_fun(tc_fun(tc_prod(_1567215, _1567217), tc_HOL_Obool), tc_HOL_Obool), _1567217), c_member(tc_prod(_1567215, _1567217)))), c_Product__Type_OPair(_1567215, _1567217)))), _1567219)), _1567221)), -(hBOOL(hAPP(hAPP(c_member(_1567217), _1567221), hAPP(c_Relation_ORange(_1567215, _1567217), _1567219))))], (29094 ^ _779327) ^ [_1297791, _1297793] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297791, _1297793), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297791), _1297793))], (48816 ^ _779327) ^ [_1757903, _1757905, _1757907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757903), _1757905)), _1757907)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1757905), c_List_Oupt(_1757903, _1757907)) = c_List_Oupt(_1757903, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757903), _1757905)))], (32666 ^ _779327) ^ [_1373215, _1373217, _1373219] : [class_Orderings_Olinorder(_1373215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373215), _1373217)), -(_1373217 = c_Orderings_Obot__class_Obot(tc_fun(_1373215, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373215), _1373219)), -(_1373219 = c_Orderings_Obot__class_Obot(tc_fun(_1373215, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1373215, c_Orderings_Oord__class_Omax(_1373215), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1373215, tc_HOL_Obool)), _1373217), _1373219)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373215), c_Big__Operators_Olattice_OSup__fin(_1373215, c_Orderings_Oord__class_Omax(_1373215), _1373217)), c_Big__Operators_Olattice_OSup__fin(_1373215, c_Orderings_Oord__class_Omax(_1373215), _1373219)))], (43289 ^ _779327) ^ [_1626880, _1626882, _1626884] : [class_Lattices_Olattice(_1626880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626880), _1626882)), -(c_Big__Operators_Olattice__class_OInf__fin(_1626880, hAPP(hAPP(c_Set_Oinsert(_1626880), _1626884), _1626882)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626880, _1626880, c_Lattices_Osemilattice__inf__class_Oinf(_1626880)), _1626884), _1626882))], (38121 ^ _779327) ^ [_1494031, _1494033, _1494035, _1494037, _1494039] : [-(_1494031 = c_Orderings_Obot__class_Obot(tc_fun(_1494033, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1494033, tc_fun(_1494035, tc_HOL_Obool)), _1494031), hAPP(hAPP(c_COMBC(_1494033, tc_fun(_1494035, tc_HOL_Obool), tc_fun(_1494035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494035, tc_HOL_Obool), tc_fun(tc_fun(_1494035, tc_HOL_Obool), tc_fun(_1494035, tc_HOL_Obool)), _1494033), c_Groups_Ominus__class_Ominus(tc_fun(_1494035, tc_HOL_Obool))), _1494037)), _1494039)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494035, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1494033, tc_fun(_1494035, tc_HOL_Obool)), _1494031), _1494037)), _1494039))], (9479 ^ _779327) ^ [_932901, _932903] : [class_Int_Oring__char__0(_932901), 9482 ^ _779327 : [(9489 ^ _779327) ^ [] : [_932903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_932901), _932903) = c_Groups_Ozero__class_Ozero(_932901))], (9483 ^ _779327) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_932901), _932903) = c_Groups_Ozero__class_Ozero(_932901), -(_932903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (52922 ^ _779327) ^ [_1839707] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1839707)))], (46506 ^ _779327) ^ [_1706558, _1706560, _1706562, _1706564] : [hBOOL(hAPP(hAPP(c_member(_1706558), _1706560), hAPP(c_List_Oset(_1706558), hAPP(hAPP(c_List_Odrop(_1706558), _1706562), _1706564)))), -(hBOOL(hAPP(hAPP(c_member(_1706558), _1706560), hAPP(c_List_Oset(_1706558), _1706564))))], (34327 ^ _779327) ^ [_1409915, _1409917] : [-(c_Relation_OId__on(_1409915, _1409917) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409915, tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool)), _1409917), hAPP(hAPP(c_COMBC(_1409915, tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool), tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1409915, _1409915), tc_fun(tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool), tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool)), _1409915), c_Set_Oinsert(tc_prod(_1409915, _1409915))), hAPP(hAPP(c_COMBS(_1409915, _1409915, tc_prod(_1409915, _1409915)), c_Product__Type_OPair(_1409915, _1409915)), c_COMBI(_1409915)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1409915, _1409915), tc_HOL_Obool)))))], (50808 ^ _779327) ^ [_1799634, _1799636, _1799638] : [c_List_Olist__all(_1799634, _1799636, _1799638), -(c_List_Olist__all(_1799634, _1799636, hAPP(c_List_Orev(_1799634), _1799638)))], (10959 ^ _779327) ^ [_958040, _958042, _958044, _958046] : [class_Groups_Ocancel__semigroup__add(_958040), 10962 ^ _779327 : [(10969 ^ _779327) ^ [] : [_958042 = _958046, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958040), _958042), _958044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958040), _958046), _958044))], (10963 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958040), _958042), _958044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958040), _958046), _958044), -(_958042 = _958046)]]], (5294 ^ _779327) ^ [_860125, _860127, _860129, _860131] : [-(c_Transitive__Closure_Otrancl(_860131, _860127) = c_Transitive__Closure_Otrancl(_860129, _860125)), _860131 = _860129, _860127 = _860125], (35381 ^ _779327) ^ [_1433618, _1433620, _1433622, _1433624, _1433626] : [class_Lattices_Osemilattice__inf(_1433618), class_Orderings_Olinorder(_1433620), c_Orderings_Oorder__class_Omono(_1433620, _1433618, _1433622), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433618), hAPP(_1433622, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1433620), _1433624), _1433626))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1433618), hAPP(_1433622, _1433624)), hAPP(_1433622, _1433626)))))], (12720 ^ _779327) ^ [_991875, _991877] : [class_Rings_Olinordered__idom(_991875), 12723 ^ _779327 : [(12730 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991875), _991877), c_Groups_Ozero__class_Ozero(_991875))), -(c_Groups_Osgn__class_Osgn(_991875, _991877) = hAPP(c_Groups_Ouminus__class_Ouminus(_991875), c_Groups_Oone__class_Oone(_991875)))], (12724 ^ _779327) ^ [] : [c_Groups_Osgn__class_Osgn(_991875, _991877) = hAPP(c_Groups_Ouminus__class_Ouminus(_991875), c_Groups_Oone__class_Oone(_991875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991875), _991877), c_Groups_Ozero__class_Ozero(_991875))))]]], (10693 ^ _779327) ^ [_952943, _952945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _952943), _952945))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _952943), _952945)) = _952943)], (7005 ^ _779327) ^ [_888993, _888995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888993), _888995))), 7008 ^ _779327 : [(7015 ^ _779327) ^ [] : [_888993 = _888995, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888993), hAPP(c_Nat_OSuc, _888995))))], (7009 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888993), hAPP(c_Nat_OSuc, _888995))), -(_888993 = _888995)]]], (35553 ^ _779327) ^ [_1437378, _1437380, _1437382, _1437384] : [class_Orderings_Oorder(_1437378), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437378, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1437378, _1437380, _1437382)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1437378, _1437382, _1437384)) = c_Orderings_Obot__class_Obot(tc_fun(_1437378, tc_HOL_Obool)))], (17010 ^ _779327) ^ [_1067946, _1067948] : [17011 ^ _779327 : [(17014 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067946), c_Int_OPls))], (17012 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067946), _1067948))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067946)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067948))))], (44833 ^ _779327) ^ [_1664497, _1664499, _1664501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664497, tc_HOL_Obool)), _1664499), _1664501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1664497), tc_HOL_Obool)), c_List_Olists(_1664497, _1664499)), c_List_Olists(_1664497, _1664501))))], (5086 ^ _779327) ^ [_856889, _856891, _856893, _856895] : [-(c_List_Oupto(_856895, _856891) = c_List_Oupto(_856893, _856889)), _856895 = _856893, _856891 = _856889], (9739 ^ _779327) ^ [] : [-(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))], (9961 ^ _779327) ^ [_940609] : [class_Rings_Olinordered__semidom(_940609), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940609), c_Groups_Ozero__class_Ozero(_940609)), c_Groups_Oone__class_Oone(_940609))))], (52622 ^ _779327) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (20377 ^ _779327) ^ [_1127213, _1127215, _1127217, _1127219] : [class_Fields_Olinordered__field__inverse__zero(_1127213), class_Int_Onumber(_1127213), 20384 ^ _779327 : [(20385 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127215), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127213), _1127217), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)))), 20388 ^ _779327 : [(20395 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), c_Groups_Ozero__class_Ozero(_1127213)), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)))), 20398 ^ _779327 : [(20405 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)), c_Groups_Ozero__class_Ozero(_1127213)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127215), c_Groups_Ozero__class_Ozero(_1127213))))], (20399 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)), c_Groups_Ozero__class_Ozero(_1127213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127213), _1127215), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)))))]]], (20389 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), c_Groups_Ozero__class_Ozero(_1127213)), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127213), _1127215), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))), _1127217)))]]], (20411 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127215), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127213), _1127217), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))))), 20414 ^ _779327 : [(20417 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127213), _1127215), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))), _1127217))], (20415 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), c_Groups_Ozero__class_Ozero(_1127213)), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))))]], 20418 ^ _779327 : [(20421 ^ _779327) ^ [] : [20422 ^ _779327 : [(20425 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127213), _1127215), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219))))], (20423 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)), c_Groups_Ozero__class_Ozero(_1127213))))]], 20426 ^ _779327 : [(20429 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), _1127215), c_Groups_Ozero__class_Ozero(_1127213)))], (20427 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)), c_Groups_Ozero__class_Ozero(_1127213)))]]], (20419 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127213), c_Groups_Ozero__class_Ozero(_1127213)), hAPP(c_Int_Onumber__class_Onumber__of(_1127213), _1127219)))]]]]], (52978 ^ _779327) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (17520 ^ _779327) ^ [_1076711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076711), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1076711)), c_Int_OMin)))], (24621 ^ _779327) ^ [_1207813, _1207815, _1207817, _1207819] : [class_Divides_Osemiring__div(_1207813), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207813), _1207815), _1207817)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207813), _1207815), _1207819)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207813), _1207817), _1207819)), _1207815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207813), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207813), _1207817), _1207815)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207813), _1207819), _1207815)))], (41744 ^ _779327) ^ [_1589238, _1589240, _1589242, _1589244] : [-(c_New__Random__Sequence_Opos__map(_1589238, _1589240, _1589242, _1589244) = c_New__Random__Sequence_Opos__bind(_1589238, _1589240, _1589244, hAPP(c_Fun_Ocomp(_1589240, 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(_1589240))))), _1589238, c_New__Random__Sequence_Opos__single(_1589240)), _1589242)))], (51493 ^ _779327) ^ [_1814437, _1814439] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1814437, _1814439), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814437)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39421 ^ _779327) ^ [_1526202, _1526204, _1526206, _1526208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526202), _1526204)), 39427 ^ _779327 : [(39430 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526206), hAPP(_1526208, 39426 ^ [_1526202, _1526204, _1526206, _1526208])))], (39428 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526202), 39426 ^ [_1526202, _1526204, _1526206, _1526208]), _1526204)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1526202, _1526206)), hAPP(hAPP(c_Product__Type_OSigma(_1526202, _1526206), _1526204), _1526208)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526202, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1526206, tc_HOL_Obool), tc_Nat_Onat, _1526202), c_Finite__Set_Ocard(_1526206)), _1526208)), _1526204))], (18170 ^ _779327) ^ [_1087850, _1087852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1087850)), c_Int_OBit1(_1087852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087850), _1087852)))], (13848 ^ _779327) ^ [_1011853] : [-(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), _1011853))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23831 ^ _779327) ^ [_1194691, _1194693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1194691)), 23834 ^ _779327 : [(23841 ^ _779327) ^ [] : [_1194693 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194693), _1194691)), _1194691)))], (23835 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194693), _1194691)), _1194691)), -(_1194693 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10415 ^ _779327) ^ [_948076, _948078] : [_948076 = hAPP(c_Int_Onat, _948078), 10418 ^ _779327 : [(10425 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948078))), -(_948076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10419 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948078)), -(_948078 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948076))]]], (39876 ^ _779327) ^ [_1536688, _1536690, _1536692, _1536694] : [-(hAPP(c_Set_Ovimage(_1536688, _1536690, _1536692), _1536694) = hAPP(c_Set_OCollect(_1536688), hAPP(hAPP(c_COMBC(_1536688, tc_fun(_1536690, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1536690, tc_fun(tc_fun(_1536690, tc_HOL_Obool), tc_HOL_Obool), _1536688), c_member(_1536690)), _1536692)), _1536694)))], (20627 ^ _779327) ^ [_1132062, _1132064, _1132066, _1132068] : [class_Fields_Olinordered__field__inverse__zero(_1132062), class_Int_Onumber(_1132062), 20634 ^ _779327 : [(20635 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132062), _1132064), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))), _1132068)), 20638 ^ _779327 : [(20645 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)))), 20648 ^ _779327 : [(20655 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)), c_Groups_Ozero__class_Ozero(_1132062)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), _1132068)))], (20649 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)), c_Groups_Ozero__class_Ozero(_1132062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132062), _1132068), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))), _1132064)))]]], (20639 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), _1132064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132062), _1132068), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)))))]]], (20661 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132062), _1132064), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))), _1132068))), 20664 ^ _779327 : [(20667 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), _1132064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132062), _1132068), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))))], (20665 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))))]], 20668 ^ _779327 : [(20671 ^ _779327) ^ [] : [20672 ^ _779327 : [(20675 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132062), _1132068), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066))), _1132064))], (20673 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)), c_Groups_Ozero__class_Ozero(_1132062))))]], 20676 ^ _779327 : [(20679 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), _1132068))], (20677 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)), c_Groups_Ozero__class_Ozero(_1132062)))]]], (20669 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132062), c_Groups_Ozero__class_Ozero(_1132062)), hAPP(c_Int_Onumber__class_Onumber__of(_1132062), _1132066)))]]]]], (41439 ^ _779327) ^ [_1582223] : [-(c_Nitpick_Onum(_1582223) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1582223, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1582223)))], (38367 ^ _779327) ^ [_1501474, _1501476, _1501478, _1501480] : [-(hAPP(c_Set_Ovimage(_1501474, _1501476, _1501478), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1501476, tc_HOL_Obool)), _1501480)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1501474, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1501474, _1501476, _1501478), _1501480)))], (18817 ^ _779327) ^ [_1099806, _1099808] : [class_Rings_Odivision__ring(_1099806), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099806), _1099808), c_Groups_Oone__class_Oone(_1099806)) = _1099808)], (42583 ^ _779327) ^ [_1609725, _1609727, _1609729] : [-(hAPP(c_Relation_Oconverse(_1609725, _1609727), hAPP(c_Relation_Oconverse(_1609727, _1609725), _1609729)) = _1609729)], (37917 ^ _779327) ^ [_1489594, _1489596, _1489598, _1489600] : [-(_1489594 = c_Orderings_Obot__class_Obot(tc_fun(_1489596, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489596, tc_fun(_1489598, tc_HOL_Obool)), _1489594), hAPP(c_COMBK(tc_fun(_1489598, tc_HOL_Obool), _1489596), _1489600)) = _1489600)], (10897 ^ _779327) ^ [_956948, _956950, _956952] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956948), _956950)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956952), _956950)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956948), _956952))], (52077 ^ _779327) ^ [_1827704, _1827706] : [c_Relation_Osym(_1827704, hAPP(c_Relation_Oconverse(_1827704, _1827704), _1827706)), -(c_Relation_Osym(_1827704, _1827706))], (24299 ^ _779327) ^ [_1202356, _1202358] : [_1202356 = _1202358, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202356), _1202358)))], (52179 ^ _779327) ^ [_1829550, _1829552, _1829554] : [c_Relation_Orefl__on(_1829550, _1829552, _1829554), c_Relation_Osym(_1829550, _1829554), c_Relation_Otrans(_1829550, _1829554), -(c_Equiv__Relations_Oequiv(_1829550, _1829552, _1829554))], (41509 ^ _779327) ^ [_1583940, _1583942, _1583944, _1583946, _1583948, _1583950] : [c_Finite__Set_Ofolding(_1583940, _1583942, _1583944, _1583946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583940), _1583948)), -(hAPP(c_Fun_Ocomp(_1583942, _1583942, _1583942, hAPP(_1583944, _1583950)), hAPP(_1583946, _1583948)) = hAPP(c_Fun_Ocomp(_1583942, _1583942, _1583942, hAPP(_1583946, _1583948)), hAPP(_1583944, _1583950)))], (3922 ^ _779327) ^ [_838819, _838821, _838823, _838825] : [-(c_Big__Operators_Olattice__class_OInf__fin(_838825, _838821) = c_Big__Operators_Olattice__class_OInf__fin(_838823, _838819)), _838825 = _838823, _838821 = _838819], (50136 ^ _779327) ^ [_1784318, _1784320] : [-(c_List_Oinsert(_1784318, _1784320, c_List_Olist_ONil(_1784318)) = hAPP(hAPP(c_List_Olist_OCons(_1784318), _1784320), c_List_Olist_ONil(_1784318)))], (27873 ^ _779327) ^ [_1274848, _1274850, _1274852, _1274854] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274848, tc_HOL_Obool)), _1274850), hAPP(hAPP(c_Set_Oinsert(_1274848), _1274852), _1274854)) = hAPP(hAPP(c_Set_Oinsert(_1274848), _1274852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274848, tc_HOL_Obool)), _1274850), _1274854)))], (43449 ^ _779327) ^ [_1629816, _1629818, _1629820] : [class_Orderings_Olinorder(_1629816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629816), _1629818)), -(hBOOL(hAPP(hAPP(c_member(_1629816), _1629820), _1629818))), -(c_Big__Operators_Olattice_OInf__fin(_1629816, c_Orderings_Oord__class_Omin(_1629816), hAPP(hAPP(c_Set_Oinsert(_1629816), _1629820), _1629818)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629816, _1629816, c_Orderings_Oord__class_Omin(_1629816)), _1629820), _1629818))], (28495 ^ _779327) ^ [_1286714, _1286716, _1286718, _1286720, _1286722] : [class_Groups_Ocomm__monoid__add(_1286714), class_Groups_Oordered__ab__semigroup__add(_1286714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286716), _1286718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286716, tc_HOL_Obool)), _1286720), _1286718)), 28513 ^ _779327 : [(28516 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286714), c_Groups_Ozero__class_Ozero(_1286714)), hAPP(_1286722, 28512 ^ [_1286714, _1286716, _1286718, _1286720, _1286722])))], (28514 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286716), 28512 ^ [_1286714, _1286716, _1286718, _1286720, _1286722]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1286716, tc_HOL_Obool)), _1286718), _1286720))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286714), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1286716, _1286714), _1286722), _1286720)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1286716, _1286714), _1286722), _1286718))))], (4132 ^ _779327) ^ [_842042, _842044, _842046, _842048, _842050, _842052, _842054, _842056] : [-(c_List_Olist_Olist__case(_842056, _842052, _842048, _842044) = c_List_Olist_Olist__case(_842054, _842050, _842046, _842042)), _842056 = _842054, _842052 = _842050, _842048 = _842046, _842044 = _842042], (9865 ^ _779327) ^ [_939130] : [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, _939130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _939130)))], (7446 ^ _779327) ^ [_896406, _896408, _896410] : [class_Rings_Osemiring__1(_896406), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_896406), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _896408), _896410)) = hAPP(hAPP(c_Power_Opower__class_Opower(_896406), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_896406), _896408)), _896410))], (28276 ^ _779327) ^ [_1282587, _1282589, _1282591] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282587), _1282589)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282587), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282587, tc_HOL_Obool)), _1282589), _1282591))))], (40514 ^ _779327) ^ [_1560857, _1560859] : [-(c_Wellfounded_Owf(_1560857, hAPP(c_Wellfounded_Omeasure(_1560857), _1560859)))], (45070 ^ _779327) ^ [_1670812, _1670814, _1670816, _1670818, _1670820] : [-(hAPP(hAPP(c_List_Otake(_1670812), _1670814), hAPP(hAPP(c_List_Omap(_1670816, _1670812), _1670818), _1670820)) = hAPP(hAPP(c_List_Omap(_1670816, _1670812), _1670818), hAPP(hAPP(c_List_Otake(_1670816), _1670814), _1670820)))], (23750 ^ _779327) ^ [_1192862, _1192864, _1192866, _1192868] : [-(c_New__Random__Sequence_Opos__empty(_1192862, _1192864, _1192866, _1192868) = c_New__DSequence_Opos__empty(_1192862))], (34079 ^ _779327) ^ [_1403324, _1403326, _1403328, _1403330] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1403324), _1403326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1403324, tc_HOL_Obool)), _1403326), _1403328)), hBOOL(hAPP(_1403330, c_Orderings_Obot__class_Obot(tc_fun(_1403324, tc_HOL_Obool)))), 34094 ^ _779327 : [(34095 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1403324), 34093 ^ [_1403324, _1403326, _1403328, _1403330])))], (34099 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1403324), 34092 ^ [_1403324, _1403326, _1403328, _1403330]), 34093 ^ [_1403324, _1403326, _1403328, _1403330]))], (34103 ^ _779327) ^ [] : [hBOOL(hAPP(_1403330, hAPP(hAPP(c_Set_Oinsert(_1403324), 34092 ^ [_1403324, _1403326, _1403328, _1403330]), 34093 ^ [_1403324, _1403326, _1403328, _1403330])))], (34101 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1403330, 34093 ^ [_1403324, _1403326, _1403328, _1403330])))], (34097 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403324), 34092 ^ [_1403324, _1403326, _1403328, _1403330]), _1403328)))]], -(hBOOL(hAPP(_1403330, _1403326)))], (29176 ^ _779327) ^ [_1299447, _1299449] : [hAPP(c_Finite__Set_Ocard(_1299447), _1299449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1299449 = c_Orderings_Obot__class_Obot(tc_fun(_1299447, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299447), _1299449))], (51562 ^ _779327) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (42856 ^ _779327) ^ [_1616344, _1616346] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616344, _1616344)), hAPP(hAPP(c_Product__Type_OPair(_1616344, _1616344), 42857 ^ [_1616344, _1616346]), 42857 ^ [_1616344, _1616346])), c_Transitive__Closure_Otrancl(_1616344, _1616346)))), -(c_Wellfounded_Oacyclic(_1616344, _1616346))], (46614 ^ _779327) ^ [_1709076, _1709078, _1709080, _1709082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709076), _1709078)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709080)), _1709082))), -(hAPP(hAPP(c_List_Onth(_1709080), hAPP(hAPP(c_List_Odrop(_1709080), _1709076), _1709082)), _1709078) = hAPP(hAPP(c_List_Onth(_1709080), _1709082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709076), _1709078)))], (46355 ^ _779327) ^ [_1702239, _1702241, _1702243, _1702245, _1702247] : [-(hAPP(hAPP(c_List_Olist__update(_1702239, hAPP(hAPP(c_List_Olist_OCons(_1702239), _1702241), _1702243)), _1702245), _1702247) = c_Nat_Onat_Onat__case(tc_List_Olist(_1702239), hAPP(hAPP(c_List_Olist_OCons(_1702239), _1702247), _1702243), hAPP(hAPP(c_COMBB(tc_List_Olist(_1702239), tc_List_Olist(_1702239), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1702239), _1702241)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1702239, tc_List_Olist(_1702239)), c_List_Olist__update(_1702239, _1702243)), _1702247)), _1702245))], (13941 ^ _779327) ^ [_1013496] : [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, _1013496)))))], (45824 ^ _779327) ^ [_1690468, _1690470, _1690472, _1690474] : [-(hAPP(c_List_Olist_Olist__case(_1690468, _1690470, _1690472, _1690474), c_List_Olist_ONil(_1690470)) = _1690472)], (10997 ^ _779327) ^ [_958713, _958715, _958717] : [class_Groups_Ogroup__add(_958713), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958713), _958715), _958717)), _958717) = _958715)], (36456 ^ _779327) ^ [_1459589] : [-(c_Relation_Orefl__on(_1459589, c_Orderings_Obot__class_Obot(tc_fun(_1459589, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1459589, _1459589), tc_HOL_Obool))))], (21418 ^ _779327) ^ [_1147819] : [-(c_Divides_Oadjust(_1147819) = 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)), _1147819))))), 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)), _1147819))))), 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))))))))], (28596 ^ _779327) ^ [] : [-(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))))], (16798 ^ _779327) ^ [_1064098] : [class_Int_Onumber__ring(_1064098), -(c_Int_Oiszero(_1064098, hAPP(c_Int_Onumber__class_Onumber__of(_1064098), c_Int_OPls)))], (10564 ^ _779327) ^ [] : [-(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))))], (28750 ^ _779327) ^ [_1291931, _1291933, _1291935, _1291937] : [class_Complete__Lattice_Ocomplete__lattice(_1291931), -(_1291933 = c_Orderings_Obot__class_Obot(tc_fun(_1291935, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1291935, _1291931), _1291933), hAPP(c_COMBK(_1291931, _1291935), _1291937)) = _1291937)], (26296 ^ _779327) ^ [_1241847, _1241849] : [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)), _1241847)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1241847), _1241849)))], (25576 ^ _779327) ^ [_1226629, _1226631, _1226633] : [class_Orderings_Olinorder(_1226629), 25579 ^ _779327 : [(25586 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226629), _1226631), _1226633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1226629, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226629), _1226631)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226629), _1226633))))], (25580 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1226629, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226629), _1226631)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226629), _1226633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226629), _1226631), _1226633)))]]], (7073 ^ _779327) ^ [_889991, _889993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889991)), hAPP(c_Nat_OSuc, _889993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889991), _889993)))], (34061 ^ _779327) ^ [_1402994, _1402996, _1402998, _1403000, _1403002] : [c_Finite__Set_Ofolding__one__idem(_1402994, _1402996, _1402998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402994), _1403000)), -(_1403002 = c_Orderings_Obot__class_Obot(tc_fun(_1402994, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402994, tc_HOL_Obool)), _1403002), _1403000)), -(hAPP(hAPP(_1402996, hAPP(_1402998, _1403002)), hAPP(_1402998, _1403000)) = hAPP(_1402998, _1403000))], (46964 ^ _779327) ^ [_1716674, _1716676, _1716678] : [hBOOL(hAPP(c_List_Odistinct(_1716674), hAPP(hAPP(c_List_Oappend(_1716674), _1716676), _1716678))), 46967 ^ _779327 : [(46972 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1716674, tc_HOL_Obool)), hAPP(c_List_Oset(_1716674), _1716676)), hAPP(c_List_Oset(_1716674), _1716678)) = c_Orderings_Obot__class_Obot(tc_fun(_1716674, tc_HOL_Obool)))], (46970 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1716674), _1716678)))], (46968 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1716674), _1716676)))]]], (4068 ^ _779327) ^ [_841060, _841062, _841064, _841066] : [-(c_Enum_Oenum__the(_841066, _841062) = c_Enum_Oenum__the(_841064, _841060)), _841066 = _841064, _841062 = _841060], (16878 ^ _779327) ^ [_1065687, _1065689] : [class_Groups_Oordered__ab__group__add__abs(_1065687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065687), _1065689), c_Groups_Ozero__class_Ozero(_1065687))), -(hAPP(c_Groups_Oabs__class_Oabs(_1065687), _1065689) = hAPP(c_Groups_Ouminus__class_Ouminus(_1065687), _1065689))], (15471 ^ _779327) ^ [_1040827, _1040829, _1040831] : [class_Divides_Osemiring__div(_1040827), -(c_Divides_Odiv__class_Omod(_1040827, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040827), _1040829), _1040831), _1040829) = c_Groups_Ozero__class_Ozero(_1040827))], (48884 ^ _779327) ^ [_1759193] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1759193) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1759193))))], (46357 ^ _779327) ^ [_1702351, _1702353, _1702355, _1702357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702351), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702353)), _1702355))), -(hAPP(hAPP(c_List_Onth(_1702353), hAPP(hAPP(c_List_Oappend(_1702353), _1702355), _1702357)), _1702351) = hAPP(hAPP(c_List_Onth(_1702353), _1702355), _1702351))], (27272 ^ _779327) ^ [_1260876, _1260878, _1260880, _1260882] : [class_Lattices_Osemilattice__sup(_1260876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260876), _1260878), _1260880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260876), _1260878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260876), _1260882), _1260880))))], (46902 ^ _779327) ^ [_1715142, _1715144] : [hBOOL(hAPP(c_List_Odistinct(_1715142), _1715144)), 46905 ^ _779327 : [(46906 ^ _779327) ^ [_1715274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715142)), _1715144))), 46909 ^ _779327 : [(46910 ^ _779327) ^ [_1715401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715401), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715142)), _1715144))), -(_1715274 = _1715401), hAPP(hAPP(c_List_Onth(_1715142), _1715144), _1715274) = hAPP(hAPP(c_List_Onth(_1715142), _1715144), _1715401)]]]]], (1032 ^ _779327) ^ [_795029, _795031, _795033, _795035] : [-(c_Relation_Otrans(_795033, _795029)), c_Relation_Otrans(_795035, _795031), _795035 = _795033, _795031 = _795029], (41001 ^ _779327) ^ [_1572471] : [-(c_Wellfounded_OwfP(_1572471, hAPP(c_COMBK(tc_fun(_1572471, tc_HOL_Obool), _1572471), hAPP(c_COMBK(tc_HOL_Obool, _1572471), c_fFalse))))], (40939 ^ _779327) ^ [_1570505, _1570507, _1570509] : [-(hAPP(c_Set_Oimage(tc_prod(_1570505, _1570507), _1570505, c_Product__Type_Ofst(_1570505, _1570507)), _1570509) = hAPP(c_Relation_ODomain(_1570505, _1570507), _1570509))], (22673 ^ _779327) ^ [_1171839, _1171841, _1171843] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1171839, _1171841), _1171843)), 22676 ^ _779327 : [(22685 ^ _779327) ^ [] : [-(_1171841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22688 ^ _779327 : [(22697 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171841))), 22700 ^ _779327 : [(22703 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1171843)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22701 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1171841), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1171843))))]]], (22689 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171841)), 22692 ^ _779327 : [(22695 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1171843)), _1171841)))], (22693 ^ _779327) ^ [] : [-(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), _1171843))))]]]]], (22679 ^ _779327) ^ [] : [_1171841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1171843) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22677 ^ _779327) ^ [] : [-(_1171839 = 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), _1171843)), _1171841)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1171843)))]]], (21202 ^ _779327) ^ [_1143259, _1143261] : [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(_1143259))), 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)), _1143261))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143259) = hAPP(c_Nat_OSuc, _1143261))], (46309 ^ _779327) ^ [_1701209, _1701211, _1701213, _1701215] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701209, tc_HOL_Obool)), hAPP(c_List_Oset(_1701209), hAPP(hAPP(c_List_Olist__update(_1701209, _1701211), _1701213), _1701215))), hAPP(hAPP(c_Set_Oinsert(_1701209), _1701215), hAPP(c_List_Oset(_1701209), _1701211)))))], (45691 ^ _779327) ^ [_1686584, _1686586] : [-(c_List_Oset__Cons(_1686584, _1686586, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1686584)), c_List_Olist_ONil(_1686584)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1686584), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1686584, tc_List_Olist(_1686584), hAPP(hAPP(c_COMBC(_1686584, tc_List_Olist(_1686584), tc_List_Olist(_1686584)), c_List_Olist_OCons(_1686584)), c_List_Olist_ONil(_1686584))), _1686586))], (28520 ^ _779327) ^ [_1287273, _1287275, _1287277, _1287279] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1287273, _1287277)), c_Sum__Type_OPlus(_1287273, _1287277, _1287275, _1287279)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1287273), _1287275)), hAPP(c_Finite__Set_Ocard(_1287277), _1287279))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287273), _1287275)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287277), _1287279))], (46748 ^ _779327) ^ [_1712336, _1712338] : [-(_1712336 = c_List_Olist_ONil(_1712338)), -(hBOOL(hAPP(hAPP(c_member(_1712338), hAPP(c_List_Ohd(_1712338), _1712336)), hAPP(c_List_Oset(_1712338), _1712336))))], (31954 ^ _779327) ^ [_1359843, _1359845, _1359847] : [class_Rings_Osemiring__1(_1359843), hBOOL(hAPP(hAPP(c_member(_1359843), _1359845), c_Nat_Osemiring__1__class_ONats(_1359843))), hBOOL(hAPP(hAPP(c_member(_1359843), _1359847), c_Nat_Osemiring__1__class_ONats(_1359843))), -(hBOOL(hAPP(hAPP(c_member(_1359843), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1359843), _1359845), _1359847)), c_Nat_Osemiring__1__class_ONats(_1359843))))], (45520 ^ _779327) ^ [_1682056, _1682058] : [-(hAPP(hAPP(c_List_Otake(_1682056), _1682058), c_List_Olist_ONil(_1682056)) = c_List_Olist_ONil(_1682056))], (12461 ^ _779327) ^ [_986849, _986851, _986853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986849), _986851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986853), _986851))))], (52956 ^ _779327) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (49581 ^ _779327) ^ [_1772839, _1772841, _1772843] : [-(hAPP(c_List_Orev(_1772839), hAPP(hAPP(c_List_Olist_OCons(_1772839), _1772841), _1772843)) = hAPP(hAPP(c_List_Oappend(_1772839), hAPP(c_List_Orev(_1772839), _1772843)), hAPP(hAPP(c_List_Olist_OCons(_1772839), _1772841), c_List_Olist_ONil(_1772839))))], (47891 ^ _779327) ^ [_1736081, _1736083, _1736085] : [-(c_List_Olistsp(_1736081, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1736081, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1736081, tc_fun(_1736081, tc_HOL_Obool), tc_HOL_Obool), c_member(_1736081)), _1736083)), hAPP(hAPP(c_COMBC(_1736081, tc_fun(_1736081, tc_HOL_Obool), tc_HOL_Obool), c_member(_1736081)), _1736085))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1736081), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736081), tc_fun(tc_List_Olist(_1736081), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1736081))), c_List_Olists(_1736081, _1736083))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1736081), tc_fun(tc_List_Olist(_1736081), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1736081))), c_List_Olists(_1736081, _1736085))))], (14891 ^ _779327) ^ [_1029836, _1029838, _1029840, _1029842] : [class_Divides_Osemiring__div(_1029836), -(_1029838 = c_Groups_Ozero__class_Ozero(_1029836)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029836), _1029840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029836), _1029838), _1029842))), _1029838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029836), _1029842), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029836), _1029840), _1029838)))], (15319 ^ _779327) ^ [_1037630, _1037632, _1037634, _1037636, _1037638, _1037640] : [class_Divides_Osemiring__div(_1037630), c_Divides_Odiv__class_Omod(_1037630, _1037632, _1037634) = c_Divides_Odiv__class_Omod(_1037630, _1037636, _1037634), c_Divides_Odiv__class_Omod(_1037630, _1037638, _1037634) = c_Divides_Odiv__class_Omod(_1037630, _1037640, _1037634), -(c_Divides_Odiv__class_Omod(_1037630, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037630), _1037632), _1037638), _1037634) = c_Divides_Odiv__class_Omod(_1037630, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037630), _1037636), _1037640), _1037634))], (23083 ^ _779327) ^ [_1179523, _1179525, _1179527, _1179529] : [class_Orderings_Olinorder(_1179523), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179523), _1179525), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179523), _1179527), _1179529)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179523), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179523), _1179525), _1179527)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179523), _1179525), _1179529)))], (47078 ^ _779327) ^ [_1719098, _1719100, _1719102] : [class_Groups_Omonoid__add(_1719098), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1719098), _1719100), hAPP(c_List_Ofoldl(_1719098, _1719098, c_Groups_Oplus__class_Oplus(_1719098), c_Groups_Ozero__class_Ozero(_1719098)), _1719102)) = hAPP(c_List_Ofoldl(_1719098, _1719098, c_Groups_Oplus__class_Oplus(_1719098), _1719100), _1719102))], (17792 ^ _779327) ^ [_1081036, _1081038] : [class_Int_Onumber__ring(_1081036), -(hAPP(c_Int_Onumber__class_Onumber__of(_1081036), c_Int_Opred(_1081038)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081036), hAPP(c_Groups_Ouminus__class_Ouminus(_1081036), c_Groups_Oone__class_Oone(_1081036))), hAPP(c_Int_Onumber__class_Onumber__of(_1081036), _1081038)))], (37697 ^ _779327) ^ [_1485176] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485176), c_Orderings_Otop__class_Otop(tc_fun(_1485176, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1485176)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1485176), tc_HOL_Obool)))))], (12125 ^ _779327) ^ [_980574, _980576, _980578, _980580] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_980574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980574), _980576), _980578)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980574), _980576), _980580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980574), _980578), _980580)))], (6935 ^ _779327) ^ [_887827, _887829, _887831, _887833, _887835] : [class_Complete__Lattice_Ocomplete__lattice(_887827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887829, tc_HOL_Obool)), _887831), _887833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887827), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887829, _887827), _887833), _887835)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887829, _887827), _887831), _887835))))], (22741 ^ _779327) ^ [_1173029, _1173031] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173029)), _1173031) = 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), _1173029)), _1173031))], (52556 ^ _779327) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (49907 ^ _779327) ^ [_1779606, _1779608, _1779610, _1779612, _1779614] : [c_List_OdropWhile(_1779606, _1779608, _1779610) = hAPP(hAPP(c_List_Olist_OCons(_1779606), _1779612), _1779614), 49910 ^ _779327 : [(49913 ^ _779327) ^ [] : [hBOOL(hAPP(_1779608, _1779612))], (49911 ^ _779327) ^ [] : [-(_1779610 = hAPP(hAPP(c_List_Oappend(_1779606), c_List_OtakeWhile(_1779606, _1779608, _1779610)), hAPP(hAPP(c_List_Olist_OCons(_1779606), _1779612), _1779614)))]]], (23724 ^ _779327) ^ [_1192517, _1192519, _1192521, _1192523, _1192525] : [_1192517 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1192519, _1192521, _1192523, _1192525), _1192517) = c_Lazy__Sequence_Ohit__bound(_1192521))], (18290 ^ _779327) ^ [_1090038, _1090040] : [class_Rings_Oring__1__no__zero__divisors(_1090038), 18293 ^ _779327 : [(18300 ^ _779327) ^ [] : [_1090040 = c_Groups_Ozero__class_Ozero(_1090038), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090038), _1090040), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1090038))], (18294 ^ _779327) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1090038), _1090040), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1090038), -(_1090040 = c_Groups_Ozero__class_Ozero(_1090038))]]], (40736 ^ _779327) ^ [_1565318, _1565320, _1565322, _1565324] : [hBOOL(hAPP(hAPP(c_member(_1565318), _1565320), hAPP(c_Relation_ORange(_1565322, _1565318), _1565324))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565322, _1565318)), hAPP(hAPP(c_Product__Type_OPair(_1565322, _1565318), 40739 ^ [_1565318, _1565320, _1565322, _1565324]), _1565320)), _1565324)))], (17538 ^ _779327) ^ [_1077008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1077008)))], (45494 ^ _779327) ^ [_1681501, _1681503] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681501)), _1681503) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1681503 = c_List_Olist_ONil(_1681501))], (41689 ^ _779327) ^ [_1587988, _1587990, _1587992, _1587994, _1587996, _1587998, _1588000] : [c_Finite__Set_Ofolding__idem(_1587988, _1587990, _1587992, _1587994), -(hAPP(c_Fun_Ocomp(_1587990, _1587990, _1587996, hAPP(_1587992, _1587998)), hAPP(c_Fun_Ocomp(_1587990, _1587990, _1587996, hAPP(_1587992, _1587998)), _1588000)) = hAPP(c_Fun_Ocomp(_1587990, _1587990, _1587996, hAPP(_1587992, _1587998)), _1588000))], (45842 ^ _779327) ^ [_1690779, _1690781, _1690783, _1690785, _1690787] : [_1690779 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1690781, _1690783, _1690785), _1690779), _1690787) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690783), _1690781), c_List_Olist_ONil(_1690783)), _1690787))], (48770 ^ _779327) ^ [_1757227, _1757229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757227), _1757229))), -(c_List_Oupt(_1757227, _1757229) = c_List_Olist_ONil(tc_Nat_Onat))], (52758 ^ _779327) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (43555 ^ _779327) ^ [_1631938, _1631940, _1631942, _1631944, _1631946, _1631948] : [c_Finite__Set_Ofun__left__comm(_1631938, _1631940, _1631942), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631938), _1631944)), -(hBOOL(hAPP(hAPP(c_member(_1631938), _1631946), _1631944))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1631938, _1631940, _1631942), _1631948), hAPP(hAPP(c_Set_Oinsert(_1631938), _1631946), _1631944)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631938, _1631940, _1631942), hAPP(hAPP(_1631942, _1631946), _1631948)), _1631944))], (16417 ^ _779327) ^ [_1057557, _1057559] : [class_Rings_Olinordered__idom(_1057557), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057557), hAPP(c_Groups_Oabs__class_Oabs(_1057557), _1057559)), hAPP(c_Groups_Oabs__class_Oabs(_1057557), _1057559)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057557), _1057559), _1057559))], (42058 ^ _779327) ^ [_1596078, _1596080, _1596082, _1596084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596078, _1596078)), hAPP(hAPP(c_Product__Type_OPair(_1596078, _1596078), _1596080), _1596082)), _1596084)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596078, _1596078)), hAPP(hAPP(c_Product__Type_OPair(_1596078, _1596078), _1596080), _1596082)), c_Transitive__Closure_Otrancl(_1596078, _1596084))))], (33872 ^ _779327) ^ [_1398809, _1398811, _1398813, _1398815, _1398817] : [class_Groups_Ocomm__monoid__add(_1398809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398811), _1398813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398811, tc_HOL_Obool)), _1398815), _1398813)), 33886 ^ _779327 : [(33889 ^ _779327) ^ [] : [hAPP(_1398817, 33885 ^ [_1398809, _1398811, _1398813, _1398815, _1398817]) = c_Groups_Ozero__class_Ozero(_1398809)], (33887 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398811), 33885 ^ [_1398809, _1398811, _1398813, _1398815, _1398817]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398811, tc_HOL_Obool)), _1398813), _1398815))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398811, _1398809), _1398817), _1398813) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398811, _1398809), _1398817), _1398815))], (34869 ^ _779327) ^ [_1422068, _1422070, _1422072] : [class_Lattices_Osemilattice__inf(_1422068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422068), _1422070), _1422072)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422068), _1422072), _1422070) = _1422070)], (18608 ^ _779327) ^ [_1095733, _1095735] : [class_Rings_Oring__1(_1095733), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095733), hAPP(c_Groups_Ouminus__class_Ouminus(_1095733), c_Groups_Oone__class_Oone(_1095733))), 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)))), _1095735)) = c_Groups_Oone__class_Oone(_1095733))], (22059 ^ _779327) ^ [_1160265, _1160267, _1160269, _1160271, _1160273] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1160265, _1160267, _1160269), _1160271), _1160273) = hAPP(hAPP(_1160271, hAPP(c_Product__Type_Ofst(_1160265, _1160267), _1160273)), hAPP(c_Product__Type_Osnd(_1160265, _1160267), _1160273)))], (23548 ^ _779327) ^ [_1189288, _1189290] : [-(c_HOL_OThe(_1189288, hAPP(c_fequal, _1189290)) = _1189290)], (30541 ^ _779327) ^ [_1330401, _1330403, _1330405, _1330407, _1330409] : [hBOOL(hAPP(hAPP(c_member(_1330401), _1330403), _1330405)), -(hAPP(c_Set_Oimage(_1330401, _1330407, hAPP(c_COMBK(_1330407, _1330401), _1330409)), _1330405) = hAPP(hAPP(c_Set_Oinsert(_1330407), _1330409), c_Orderings_Obot__class_Obot(tc_fun(_1330407, tc_HOL_Obool))))], (47002 ^ _779327) ^ [_1717476, _1717478, _1717480] : [-(_1717476 = c_List_Olist_ONil(_1717478)), -(hAPP(hAPP(c_List_Otake(_1717478), hAPP(c_Nat_OSuc, _1717480)), _1717476) = hAPP(hAPP(c_List_Olist_OCons(_1717478), hAPP(c_List_Ohd(_1717478), _1717476)), hAPP(hAPP(c_List_Otake(_1717478), _1717480), hAPP(c_List_Otl(_1717478), _1717476))))], (47340 ^ _779327) ^ [_1724469, _1724471, _1724473] : [-(_1724469 = c_List_Olist_ONil(_1724471)), -(c_List_Olast(_1724471, hAPP(hAPP(c_List_Oappend(_1724471), _1724473), _1724469)) = c_List_Olast(_1724471, _1724469))], (1898 ^ _779327) ^ [_806040, _806042] : [-(class_Groups_Ominus(_806040)), _806042 = _806040, class_Groups_Ominus(_806042)], (35289 ^ _779327) ^ [_1431554, _1431556, _1431558] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431554, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431554, tc_HOL_Obool)), _1431556), _1431558)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431554, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431554, tc_HOL_Obool)), _1431556)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431554, tc_HOL_Obool)), _1431558)))], (43788 ^ _779327) ^ [_1636655, _1636657] : [class_Complete__Lattice_Ocomplete__lattice(_1636655), -(c_Complete__Lattice_OInf__class_OInf(_1636655, _1636657) = c_Complete__Lattice_OSup__class_OSup(_1636655, hAPP(c_Set_OCollect(_1636655), hAPP(hAPP(c_COMBB(tc_fun(_1636655, tc_HOL_Obool), tc_HOL_Obool, _1636655), c_HOL_OAll(_1636655)), hAPP(hAPP(c_COMBB(tc_fun(_1636655, tc_HOL_Obool), tc_fun(_1636655, tc_HOL_Obool), _1636655), hAPP(c_COMBS(_1636655, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1636655), c_fimplies), hAPP(hAPP(c_COMBC(_1636655, tc_fun(_1636655, tc_HOL_Obool), tc_HOL_Obool), c_member(_1636655)), _1636657)))), c_Orderings_Oord__class_Oless__eq(_1636655))))))], (31308 ^ _779327) ^ [_1346759, _1346761, _1346763, _1346765, _1346767, _1346769] : [c_Finite__Set_Ofolding__image__simple(_1346759, _1346761, _1346763, _1346765, _1346767, _1346769), -(hAPP(_1346769, c_Orderings_Obot__class_Obot(tc_fun(_1346761, tc_HOL_Obool))) = _1346765)], (9809 ^ _779327) ^ [_938288, _938290] : [class_Rings_Ocomm__semiring__1(_938288), -(hAPP(hAPP(c_Power_Opower__class_Opower(_938288), _938290), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _938290)], (43706 ^ _779327) ^ [_1634880, _1634882] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1634880, tc_HOL_Obool), _1634882) = hAPP(c_Set_OCollect(_1634880), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1634880, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1634880), c_HOL_OAll(tc_fun(_1634880, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1634880, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1634880, tc_HOL_Obool), tc_HOL_Obool), _1634880), hAPP(c_COMBS(tc_fun(_1634880, 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(_1634880, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1634880, tc_HOL_Obool), tc_fun(tc_fun(_1634880, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1634880, tc_HOL_Obool))), _1634882)))), c_member(_1634880)))))], (34953 ^ _779327) ^ [_1423491, _1423493, _1423495] : [class_Lattices_Olattice(_1423491), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423491), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423491), _1423493), _1423495)), _1423495)))], (45904 ^ _779327) ^ [_1692127, _1692129] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1692127, _1692129) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1692127), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1692129), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (27028 ^ _779327) ^ [_1256272, _1256274, _1256276, _1256278, _1256280] : [class_Lattices_Olattice(_1256272), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256274, _1256272)), _1256276), _1256278), _1256280) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256272), hAPP(_1256276, _1256280)), hAPP(_1256278, _1256280)))], (26278 ^ _779327) ^ [_1241511, _1241513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1241511), _1241513)), -(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)), _1241511)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241513))))], (34027 ^ _779327) ^ [_1402334, _1402336, _1402338, _1402340, _1402342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1402334, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1402336, _1402334, _1402338), _1402340)), _1402342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1402334, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1402336, tc_HOL_Obool), tc_fun(_1402334, tc_HOL_Obool), c_Set_Oimage(_1402336, _1402334, _1402338)), hAPP(c_Set_OPow(_1402336), _1402340))), hAPP(c_Set_OPow(_1402334), _1402342))))], (12614 ^ _779327) ^ [_989818, _989820, _989822, _989824] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989818), _989820)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989822), _989820)), _989824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989818), _989822)), _989820)), _989824))], (6070 ^ _779327) ^ [_874897, _874899, _874901, _874903] : [class_Orderings_Oorder(_874897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874897), _874899), _874901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874897), _874903), _874899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874897), _874903), _874901)))], (41860 ^ _779327) ^ [_1591831, _1591833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1591831), _1591833)), 41866 ^ _779327 : [(41869 ^ _779327) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41867 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591831), 41865 ^ [_1591831, _1591833]), _1591833)))]], -(hAPP(c_Finite__Set_Ocard(_1591831), _1591833) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27382 ^ _779327) ^ [_1263535, _1263537, _1263539, _1263541, _1263543] : [class_Lattices_Osemilattice__sup(_1263535), class_Orderings_Olinorder(_1263537), c_Orderings_Oorder__class_Omono(_1263537, _1263535, _1263539), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263535), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263535), hAPP(_1263539, _1263541)), hAPP(_1263539, _1263543))), hAPP(_1263539, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1263537), _1263541), _1263543)))))], (43519 ^ _779327) ^ [_1631236, _1631238, _1631240, _1631242, _1631244] : [c_Finite__Set_Ofun__left__comm(_1631236, _1631238, _1631240), -(c_Finite__Set_Ofun__left__comm(_1631242, _1631238, hAPP(hAPP(c_COMBB(_1631236, tc_fun(_1631238, _1631238), _1631242), _1631240), _1631244)))], (51069 ^ _779327) ^ [_1804761, _1804763, _1804765] : [-(_1804761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1804763, c_List_Oreplicate(_1804763, _1804761, _1804765)) = _1804765)], (3890 ^ _779327) ^ [_838351, _838353] : [_838353 = _838351, -(c_Groups_Otimes__class_Otimes(_838353) = c_Groups_Otimes__class_Otimes(_838351))], (33851 ^ _779327) ^ [_1398358, _1398360, _1398362, _1398364, _1398366] : [class_Groups_Ocomm__monoid__add(_1398358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398360), _1398362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398360, tc_HOL_Obool)), _1398364), _1398362)), 33865 ^ _779327 : [(33868 ^ _779327) ^ [] : [hAPP(_1398366, 33864 ^ [_1398358, _1398360, _1398362, _1398364, _1398366]) = c_Groups_Ozero__class_Ozero(_1398358)], (33866 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398360), 33864 ^ [_1398358, _1398360, _1398362, _1398364, _1398366]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398360, tc_HOL_Obool)), _1398362), _1398364))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398360, _1398358), _1398366), _1398364) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398360, _1398358), _1398366), _1398362))], (46249 ^ _779327) ^ [_1699672, _1699674, _1699676, _1699678, _1699680, _1699682] : [hAPP(hAPP(c_List_Oappend(_1699672), _1699674), _1699676) = _1699678, _1699680 = hAPP(hAPP(c_List_Oappend(_1699672), _1699676), _1699682), -(hAPP(hAPP(c_List_Oappend(_1699672), _1699674), _1699680) = hAPP(hAPP(c_List_Oappend(_1699672), _1699678), _1699682))], (41997 ^ _779327) ^ [_1594836, _1594838, _1594840] : [c_Wellfounded_Owf(_1594836, _1594838), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594836, _1594836)), hAPP(hAPP(c_Product__Type_OPair(_1594836, _1594836), hAPP(_1594840, hAPP(c_Nat_OSuc, 42000 ^ [_1594836, _1594838, _1594840]))), hAPP(_1594840, 42000 ^ [_1594836, _1594838, _1594840]))), _1594838))], (16776 ^ _779327) ^ [_1063805, _1063807, _1063809] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063805), _1063807)), _1063809) = 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), _1063805), _1063809)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1063807), _1063809))), 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, _1063805, _1063809)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1063807, _1063809))), _1063809)))], (38251 ^ _779327) ^ [_1498847, _1498849] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1498847, tc_HOL_Obool)), _1498849)))], (33620 ^ _779327) ^ [] : [-(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)))], (7057 ^ _779327) ^ [_889770, _889772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889770), hAPP(c_Nat_OSuc, _889772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889770), _889772))), -(_889770 = _889772)], (5852 ^ _779327) ^ [_871603, _871605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871603), _871605)), _871605 = _871603], (35141 ^ _779327) ^ [_1428000, _1428002, _1428004, _1428006] : [class_Lattices_Olattice(_1428000), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428000), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428000), _1428002), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428000), _1428004), _1428006))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428000), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428000), _1428002), _1428004)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428000), _1428002), _1428006)))))], (16940 ^ _779327) ^ [_1066721, _1066723, _1066725] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066721), _1066723)), _1066725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066721), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1066723), _1066725))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066721), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066723, _1066725))), _1066725)))], (35307 ^ _779327) ^ [_1432047, _1432049, _1432051] : [-(hAPP(c_Relation_OImage(_1432047, _1432047, c_Relation_OId__on(_1432047, _1432049)), _1432051) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432047, tc_HOL_Obool)), _1432049), _1432051))], (41746 ^ _779327) ^ [_1589301, _1589303, _1589305] : [-(hAPP(c_New__DSequence_Oneg__single(_1589301, _1589303), _1589305) = c_Lazy__Sequence_Ohb__single(_1589301, _1589303))], (22147 ^ _779327) ^ [_1162104, _1162106, _1162108] : [-(hAPP(c_Product__Type_Osnd(_1162104, _1162106), _1162108) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1162104, _1162106, _1162106), hAPP(c_COMBK(tc_fun(_1162106, _1162106), _1162104), c_COMBI(_1162106))), _1162108))], (4828 ^ _779327) ^ [_852852, _852854, _852856, _852858] : [-(c_List_Omap(_852858, _852854) = c_List_Omap(_852856, _852852)), _852858 = _852856, _852854 = _852852], (17272 ^ _779327) ^ [_1072448, _1072450, _1072452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072448), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072450)), _1072452)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38904 ^ _779327) ^ [_1515103, _1515105, _1515107, _1515109, _1515111, _1515113] : [hBOOL(hAPP(hAPP(c_member(_1515103), _1515105), _1515107)), 38907 ^ _779327 : [(38914 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515109, tc_HOL_Obool)), _1515111), _1515113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515109, _1515103), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515109, _1515103), _1515111), hAPP(c_COMBK(tc_fun(_1515103, tc_HOL_Obool), _1515109), _1515107))), hAPP(hAPP(c_Product__Type_OSigma(_1515109, _1515103), _1515113), hAPP(c_COMBK(tc_fun(_1515103, tc_HOL_Obool), _1515109), _1515107)))))], (38908 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515109, _1515103), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515109, _1515103), _1515111), hAPP(c_COMBK(tc_fun(_1515103, tc_HOL_Obool), _1515109), _1515107))), hAPP(hAPP(c_Product__Type_OSigma(_1515109, _1515103), _1515113), hAPP(c_COMBK(tc_fun(_1515103, tc_HOL_Obool), _1515109), _1515107)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515109, tc_HOL_Obool)), _1515111), _1515113)))]]], (47108 ^ _779327) ^ [_1719713, _1719715, _1719717, _1719719, _1719721, _1719723] : [-(hAPP(c_List_Ofoldl(_1719713, _1719715, _1719717, _1719719), hAPP(hAPP(c_List_Oappend(_1719715), _1719721), _1719723)) = hAPP(c_List_Ofoldl(_1719713, _1719715, _1719717, hAPP(c_List_Ofoldl(_1719713, _1719715, _1719717, _1719719), _1719721)), _1719723))], (22057 ^ _779327) ^ [_1160164, _1160166, _1160168, _1160170, _1160172, _1160174] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1160164, _1160166), _1160166, _1160168), hAPP(hAPP(c_COMBB(_1160170, tc_fun(_1160166, _1160168), tc_prod(_1160164, _1160166)), _1160172), hAPP(hAPP(c_COMBB(_1160164, _1160170, tc_prod(_1160164, _1160166)), _1160174), c_Product__Type_Ofst(_1160164, _1160166)))), c_Product__Type_Osnd(_1160164, _1160166)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1160164, _1160166, _1160168), hAPP(hAPP(c_COMBB(_1160170, tc_fun(_1160166, _1160168), _1160164), _1160172), _1160174)))], (24077 ^ _779327) ^ [_1198806, _1198808, _1198810] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198806), _1198808)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198808), _1198806))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198808), _1198810)), 24088 ^ _779327 : [(24091 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198810), _1198806))], (24089 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198806), _1198810)))]]], (46022 ^ _779327) ^ [_1694929, _1694931, _1694933, _1694935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694929)), _1694931)), _1694933)), -(hAPP(hAPP(c_List_Olist__update(_1694929, _1694931), _1694933), _1694935) = _1694931)], (39796 ^ _779327) ^ [_1534547, _1534549, _1534551, _1534553] : [-(hAPP(c_Set_OCollect(tc_prod(_1534547, _1534549)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534547, _1534549, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1534547, tc_fun(_1534549, tc_HOL_Obool), tc_fun(_1534549, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534549, tc_HOL_Obool), tc_fun(_1534549, tc_HOL_Obool)), _1534547), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534549)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534547), c_fconj), _1534551))), _1534553))) = hAPP(hAPP(c_Product__Type_OSigma(_1534547, _1534549), hAPP(c_Set_OCollect(_1534547), _1534551)), hAPP(hAPP(c_COMBB(tc_fun(_1534549, tc_HOL_Obool), tc_fun(_1534549, tc_HOL_Obool), _1534547), c_Set_OCollect(_1534549)), _1534553)))], (39754 ^ _779327) ^ [_1533681, _1533683, _1533685] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533681), hAPP(c_Set_OCollect(_1533681), hAPP(hAPP(c_COMBS(_1533681, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533681), c_fdisj), _1533683)), _1533685))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533681), hAPP(c_Set_OCollect(_1533681), _1533683))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533681), hAPP(c_Set_OCollect(_1533681), _1533685)))], (23281 ^ _779327) ^ [_1183547, _1183549, _1183551, _1183553, _1183555, _1183557, _1183559] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1183547, _1183549, _1183551, _1183553), _1183555), _1183557), _1183559) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183549, _1183551, _1183553), _1183557), hAPP(_1183555, _1183559)))], (38371 ^ _779327) ^ [_1501567, _1501569, _1501571, _1501573, _1501575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501567, tc_HOL_Obool)), _1501569), _1501571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501573, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1501573, _1501567, _1501575), _1501569)), hAPP(c_Set_Ovimage(_1501573, _1501567, _1501575), _1501571))))], (39794 ^ _779327) ^ [_1534494, _1534496] : [-(hAPP(c_Set_OCollect(_1534494), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534494), c_fNot), _1534496)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1534494, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1534494), _1534496)))], (30007 ^ _779327) ^ [_1315883, _1315885] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1315883, tc_HOL_Obool)), _1315885)), -(hBOOL(hAPP(hAPP(c_member(_1315883), _1315885), c_Orderings_Obot__class_Obot(tc_fun(_1315883, tc_HOL_Obool)))))], (50357 ^ _779327) ^ [_1789798, _1789800] : [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), _1789798), _1789800))), 50360 ^ _779327 : [(50367 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789798), _1789800))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789798, _1789800) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789800), c_Lazy__Sequence_Osmall__lazy_H(_1789798, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789800), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50361 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789798), _1789800)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789798, _1789800) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (10598 ^ _779327) ^ [_951195, _951197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951197)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _951195)), hAPP(c_Int_Onat, _951197)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_951195, _951197)))], (23496 ^ _779327) ^ [_1187791, _1187793, _1187795, _1187797, _1187799, _1187801] : [-(c_Nitpick_Opair__box_Opair__box__size(_1187791, _1187793, _1187795, _1187797, c_Nitpick_Opair__box_OPairBox(_1187791, _1187793, _1187799, _1187801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1187795, _1187799)), hAPP(_1187797, _1187801))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10757 ^ _779327) ^ [_954318, _954320, _954322] : [class_Int_Onumber__ring(_954318), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_954318), hAPP(c_Int_Onumber__class_Onumber__of(_954318), _954320)), hAPP(c_Int_Onumber__class_Onumber__of(_954318), _954322)) = hAPP(c_Int_Onumber__class_Onumber__of(_954318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _954320), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _954322))))], (38874 ^ _779327) ^ [_1514431, _1514433, _1514435, _1514437, _1514439, _1514441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514431, _1514433)), hAPP(hAPP(c_Product__Type_OPair(_1514431, _1514433), _1514435), _1514437)), hAPP(hAPP(c_Product__Type_OSigma(_1514431, _1514433), _1514439), _1514441))), 38877 ^ _779327 : [(38880 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514433), _1514437), hAPP(_1514441, _1514435))))], (38878 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514431), _1514435), _1514439)))]]], (40581 ^ _779327) ^ [_1562096, _1562098] : [c_Wellfounded_Owf(_1562096, _1562098), -(c_Wellfounded_Owf(tc_fun(_1562096, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1562096, _1562098)))], (35021 ^ _779327) ^ [_1425160, _1425162, _1425164, _1425166] : [hBOOL(hAPP(hAPP(c_member(_1425160), _1425162), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425160, tc_HOL_Obool)), _1425164), _1425166))), -(hBOOL(hAPP(hAPP(c_member(_1425160), _1425162), _1425166)))], (38176 ^ _779327) ^ [_1495334] : [-(c_Fun_Oinj__on(_1495334, tc_fun(_1495334, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1495334, tc_fun(_1495334, tc_HOL_Obool), tc_fun(_1495334, tc_HOL_Obool)), c_Set_Oinsert(_1495334)), c_Orderings_Obot__class_Obot(tc_fun(_1495334, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1495334, tc_HOL_Obool))))], (34841 ^ _779327) ^ [_1421570, _1421572, _1421574, _1421576] : [class_Lattices_Osemilattice__inf(_1421570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421570), _1421572), _1421574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421570), _1421572), _1421576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421570), _1421572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421570), _1421574), _1421576))))], (26950 ^ _779327) ^ [_1254575, _1254577, _1254579] : [class_Lattices_Osemilattice__sup(_1254575), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254575), _1254577), _1254579) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254575), _1254579), _1254577))], (35451 ^ _779327) ^ [_1435035, _1435037, _1435039, _1435041, _1435043] : [class_Orderings_Olinorder(_1435035), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435035, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435035, _1435037), _1435039)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435035, _1435041), _1435043)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435035, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1435035), _1435037), _1435041)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1435035), _1435039), _1435043)))], (37179 ^ _779327) ^ [_1474053, _1474055] : [-(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)), _1474053), _1474055))], (15463 ^ _779327) ^ [_1040671, _1040673, _1040675] : [-(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, _1040671, _1040673)), _1040675), _1040673) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1040671), _1040675), _1040673))], (51179 ^ _779327) ^ [_1806871] : [-(c_Predicate_Oconversep(_1806871, _1806871, c_fequal) = c_fequal)], (48782 ^ _779327) ^ [_1757390] : [-(c_List_Oupt(_1757390, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (21130 ^ _779327) ^ [_1141721, _1141723, _1141725, _1141727] : [class_Groups_Ouminus(_1141721), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1141723, _1141721)), _1141725), _1141727) = hAPP(c_Groups_Ouminus__class_Ouminus(_1141721), hAPP(_1141725, _1141727)))], (45040 ^ _779327) ^ [_1669929, _1669931, _1669933] : [-(c_List_Osublist(_1669929, _1669931, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1669933)) = hAPP(hAPP(c_List_Otake(_1669929), _1669933), _1669931))], (34813 ^ _779327) ^ [_1420992, _1420994, _1420996, _1420998] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420992, tc_HOL_Obool)), _1420994), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420992, tc_HOL_Obool)), _1420996), _1420998)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420992, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420992, tc_HOL_Obool)), _1420994), _1420996)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420992, tc_HOL_Obool)), _1420994), _1420998)))], (44893 ^ _779327) ^ [_1665964, _1665966, _1665968, _1665970] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665964), tc_List_Olist(_1665964))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665964), tc_List_Olist(_1665964)), _1665966), _1665968)), c_List_Olistrel(_1665964, _1665970)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665964)), _1665966) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665964)), _1665968), 44899 ^ _779327 : [(44902 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1665964, _1665964)), hAPP(hAPP(c_Product__Type_OPair(_1665964, _1665964), hAPP(hAPP(c_List_Onth(_1665964), _1665966), 44898 ^ [_1665964, _1665966, _1665968, _1665970])), hAPP(hAPP(c_List_Onth(_1665964), _1665968), 44898 ^ [_1665964, _1665966, _1665968, _1665970]))), _1665970))], (44900 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44898 ^ [_1665964, _1665966, _1665968, _1665970]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665964)), _1665966))))]]], (21944 ^ _779327) ^ [_1157678, _1157680, _1157682, _1157684, _1157686, _1157688] : [-(hAPP(c_Product__Type_Oapsnd(_1157678, _1157680, _1157682, _1157684), hAPP(hAPP(c_Product__Type_OPair(_1157682, _1157678), _1157686), _1157688)) = hAPP(hAPP(c_Product__Type_OPair(_1157682, _1157680), _1157686), hAPP(_1157684, _1157688)))], (30061 ^ _779327) ^ [_1318964, _1318966, _1318968, _1318970] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1318964, tc_fun(_1318966, tc_HOL_Obool))), _1318968), _1318970)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1318964, _1318966)), hAPP(hAPP(c_Product__Type_OPair(_1318964, _1318966), _1318968), _1318970)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1318964, _1318966), tc_HOL_Obool)))))], (21021 ^ _779327) ^ [_1139301] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1139301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1139301)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9795 ^ _779327) ^ [_938070, _938072] : [class_Groups_Omonoid__mult(_938070), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938070), c_Groups_Oone__class_Oone(_938070)), _938072) = _938072)], (7410 ^ _779327) ^ [_895713, _895715, _895717] : [class_Groups_Omonoid__mult(_895713), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895713), hAPP(hAPP(c_Power_Opower__class_Opower(_895713), _895715), _895717)), _895715) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895713), _895715), hAPP(hAPP(c_Power_Opower__class_Opower(_895713), _895715), _895717)))], (52608 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52407 ^ _779327) ^ [_1833783, _1833785, _1833787] : [hAPP(c_Set_Oimage(_1833783, _1833785, _1833787), c_Orderings_Otop__class_Otop(tc_fun(_1833783, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1833785, tc_HOL_Obool)), 52410 ^ _779327 : [(52411 ^ _779327) ^ [_1833894] : [-(hAPP(_1833787, hAPP(c_Hilbert__Choice_Oinv__into(_1833783, _1833785, c_Orderings_Otop__class_Otop(tc_fun(_1833783, tc_HOL_Obool)), _1833787), _1833894)) = _1833894)]]], (28794 ^ _779327) ^ [_1292603, _1292605, _1292607, _1292609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1292603, _1292605)), c_Sum__Type_OPlus(_1292603, _1292605, _1292607, _1292609))), 28797 ^ _779327 : [(28800 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1292605), _1292609)))], (28798 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1292603), _1292607)))]]], (48617 ^ _779327) ^ [_1752604, _1752606, _1752608, _1752610, _1752612] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752604)), hAPP(c_List_Ofilter(_1752604, _1752606), hAPP(hAPP(c_List_Omap(_1752608, _1752604), _1752610), _1752612))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752608)), hAPP(c_List_Ofilter(_1752608, hAPP(c_Fun_Ocomp(_1752604, tc_HOL_Obool, _1752608, _1752606), _1752610)), _1752612)))], (30705 ^ _779327) ^ [_1333849, _1333851, _1333853, _1333855] : [hBOOL(hAPP(hAPP(c_member(_1333849), _1333851), _1333853)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1333849, tc_Nat_Onat), _1333855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333849, tc_HOL_Obool)), _1333853), hAPP(hAPP(c_Set_Oinsert(_1333849), _1333851), c_Orderings_Obot__class_Obot(tc_fun(_1333849, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1333849, tc_Nat_Onat), _1333855), _1333853)), hAPP(_1333855, _1333851)))], (16339 ^ _779327) ^ [_1056252] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056252), 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), _1056252)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1056252)))], (47096 ^ _779327) ^ [_1719463, _1719465, _1719467] : [_1719467 = c_List_Olist_ONil(_1719463), -(hAPP(c_List_Orotate(_1719463, _1719465), _1719467) = c_List_Olist_ONil(_1719463))], (3438 ^ _779327) ^ [_831169, _831171, _831173, _831175, _831177, _831179, _831181, _831183] : [-(c_New__Random__Sequence_Oneg__map(_831183, _831179, _831175, _831171) = c_New__Random__Sequence_Oneg__map(_831181, _831177, _831173, _831169)), _831183 = _831181, _831179 = _831177, _831175 = _831173, _831171 = _831169], (47177 ^ _779327) ^ [_1721088, _1721090] : [class_Complete__Lattice_Ocomplete__lattice(_1721088), -(c_Complete__Lattice_OInf__class_OInf(_1721088, hAPP(c_List_Oset(_1721088), _1721090)) = hAPP(c_List_Ofoldl(_1721088, _1721088, c_Lattices_Osemilattice__inf__class_Oinf(_1721088), c_Orderings_Otop__class_Otop(_1721088)), _1721090))], (45323 ^ _779327) ^ [_1676622, _1676624, _1676626] : [-(hBOOL(hAPP(hAPP(c_member(_1676622), _1676624), hAPP(c_List_Oset(_1676622), _1676626)))), 45324 ^ _779327 : [(45325 ^ _779327) ^ [_1676696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676696), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676622)), _1676626))), hAPP(hAPP(c_List_Onth(_1676622), _1676626), _1676696) = _1676624]]], (7562 ^ _779327) ^ [_898247, _898249, _898251] : [7563 ^ _779327 : [(7566 ^ _779327) ^ [] : [_898249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7564 ^ _779327) ^ [] : [_898247 = _898251]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898247), _898249) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898251), _898249))], (32814 ^ _779327) ^ [_1376156, _1376158, _1376160] : [class_Orderings_Olinorder(_1376156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376156), _1376158)), -(_1376158 = c_Orderings_Obot__class_Obot(tc_fun(_1376156, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1376156, c_Orderings_Oord__class_Omin(_1376156), hAPP(hAPP(c_Set_Oinsert(_1376156), _1376160), _1376158)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376156), _1376160), c_Big__Operators_Olattice_OInf__fin(_1376156, c_Orderings_Oord__class_Omin(_1376156), _1376158)))], (4956 ^ _779327) ^ [_854880, _854882] : [_854882 = _854880, -(c_List_Olist_OCons(_854882) = c_List_Olist_OCons(_854880))], (32706 ^ _779327) ^ [_1373831, _1373833, _1373835] : [class_Orderings_Olinorder(_1373831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373831), _1373833)), 32713 ^ _779327 : [(32720 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373831, tc_HOL_Obool)), _1373833), hAPP(hAPP(c_Set_Oinsert(_1373831), _1373835), c_Orderings_Obot__class_Obot(tc_fun(_1373831, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373831, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1373831, c_Orderings_Oord__class_Omax(_1373831), hAPP(hAPP(c_Set_Oinsert(_1373831), _1373835), _1373833)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373831), _1373835), c_Big__Operators_Olattice_OSup__fin(_1373831, c_Orderings_Oord__class_Omax(_1373831), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373831, tc_HOL_Obool)), _1373833), hAPP(hAPP(c_Set_Oinsert(_1373831), _1373835), c_Orderings_Obot__class_Obot(tc_fun(_1373831, tc_HOL_Obool)))))))], (32714 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373831, tc_HOL_Obool)), _1373833), hAPP(hAPP(c_Set_Oinsert(_1373831), _1373835), c_Orderings_Obot__class_Obot(tc_fun(_1373831, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1373831, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1373831, c_Orderings_Oord__class_Omax(_1373831), hAPP(hAPP(c_Set_Oinsert(_1373831), _1373835), _1373833)) = _1373835)]]], (6696 ^ _779327) ^ [_884222, _884224, _884226] : [class_Orderings_Olinorder(_884222), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884222), _884224), _884226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884222), _884226), _884224)))], (35876 ^ _779327) ^ [_1445006, _1445008, _1445010] : [class_Lattices_Olattice(_1445006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445006), _1445008)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445006), _1445010)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445006, tc_HOL_Obool)), _1445008), _1445010) = c_Orderings_Obot__class_Obot(tc_fun(_1445006, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1445006), c_Big__Operators_Olattice__class_OSup__fin(_1445006, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445006, tc_HOL_Obool)), _1445008), _1445010))), c_Big__Operators_Olattice__class_OSup__fin(_1445006, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445006, tc_HOL_Obool)), _1445008), _1445010))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1445006), c_Big__Operators_Olattice__class_OSup__fin(_1445006, _1445008)), c_Big__Operators_Olattice__class_OSup__fin(_1445006, _1445010)))], (16615 ^ _779327) ^ [_1061133, _1061135, _1061137] : [class_Groups_Oordered__ab__group__add__abs(_1061133), 16618 ^ _779327 : [(16627 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), hAPP(c_Groups_Oabs__class_Oabs(_1061133), _1061135)), _1061137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), _1061135), _1061137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), hAPP(c_Groups_Ouminus__class_Ouminus(_1061133), _1061135)), _1061137))], (16619 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), hAPP(c_Groups_Oabs__class_Oabs(_1061133), _1061135)), _1061137)), 16622 ^ _779327 : [(16625 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), hAPP(c_Groups_Ouminus__class_Ouminus(_1061133), _1061135)), _1061137)))], (16623 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061133), _1061135), _1061137)))]]]]], (49973 ^ _779327) ^ [_1781121, _1781123, _1781125, _1781127] : [49975 ^ _779327 : [(49980 ^ _779327) ^ [] : [hBOOL(hAPP(_1781127, hAPP(hAPP(c_List_Onth(_1781123), _1781125), 49974 ^ [_1781121, _1781123, _1781125, _1781127])))], (49978 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49974 ^ [_1781121, _1781123, _1781125, _1781127]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781123)), _1781125))))], (49976 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49974 ^ [_1781121, _1781123, _1781125, _1781127]), _1781121)))]], 49983 ^ _779327 : [(49986 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1781127, hAPP(hAPP(c_List_Onth(_1781123), _1781125), _1781121))))], (49984 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1781121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781123)), _1781125))))]], -(c_List_OtakeWhile(_1781123, _1781127, _1781125) = hAPP(hAPP(c_List_Otake(_1781123), _1781121), _1781125))], (34261 ^ _779327) ^ [_1408290, _1408292, _1408294, _1408296, _1408298] : [hBOOL(hAPP(hAPP(c_member(_1408290), _1408292), hAPP(c_Relation_OImage(_1408294, _1408290, _1408296), _1408298))), 34265 ^ _779327 : [(34268 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408294), 34264 ^ [_1408290, _1408292, _1408294, _1408296, _1408298]), _1408298)))], (34266 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1408294, _1408290)), hAPP(hAPP(c_Product__Type_OPair(_1408294, _1408290), 34264 ^ [_1408290, _1408292, _1408294, _1408296, _1408298]), _1408292)), _1408296)))]]], (27218 ^ _779327) ^ [_1259689, _1259691, _1259693] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259689, tc_HOL_Obool)), _1259691), _1259693) = _1259693, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259689, tc_HOL_Obool)), _1259691), _1259693)))], (7396 ^ _779327) ^ [_895360, _895362, _895364, _895366] : [class_Groups_Oab__semigroup__mult(_895360), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895360), _895362), _895364)), _895366) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895360), _895362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895360), _895364), _895366)))], (45898 ^ _779327) ^ [_1692069, _1692071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1692069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1692071)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1692069), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1692071)) = c_List_Olist_ONil(tc_Int_Oint))], (33242 ^ _779327) ^ [_1384516, _1384518, _1384520, _1384522, _1384524] : [class_Rings_Ocomm__semiring__1(_1384516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384518), _1384520)), hBOOL(hAPP(hAPP(c_member(_1384518), _1384522), _1384520)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1384516), hAPP(_1384524, _1384522)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384518, _1384516), _1384524), _1384520))))], (27040 ^ _779327) ^ [_1256500, _1256502, _1256504, _1256506] : [hBOOL(hAPP(_1256500, _1256502)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256504, tc_HOL_Obool)), _1256500), _1256506), _1256502)))], (13800 ^ _779327) ^ [_1011031, _1011033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011031), hAPP(c_Nat_OSuc, _1011033))), _1011031)))], (47893 ^ _779327) ^ [_1736213, _1736215, _1736217, _1736219, _1736221] : [class_Orderings_Olinorder(_1736213), -(hBOOL(hAPP(hAPP(c_member(_1736213), hAPP(_1736215, _1736217)), hAPP(c_Set_Oimage(_1736219, _1736213, _1736215), hAPP(c_List_Oset(_1736219), _1736221))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1736219, _1736213, _1736215, _1736217, _1736221) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1736219, _1736213, _1736215), _1736217), _1736221))], (26671 ^ _779327) ^ [_1248840] : [c_Nat__Transfer_Onat__set(_1248840), -(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), _1248840)) = _1248840)], (15465 ^ _779327) ^ [_1040722, _1040724, _1040726] : [class_Divides_Osemiring__div(_1040722), -(c_Divides_Odiv__class_Omod(_1040722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040722), _1040724), _1040726), _1040726) = c_Groups_Ozero__class_Ozero(_1040722))], (33256 ^ _779327) ^ [_1384773, _1384775, _1384777] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384773), _1384775)), 33259 ^ _779327 : [(33260 ^ _779327) ^ [] : [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(_1384773, tc_Nat_Onat), _1384777), _1384775))), 33263 ^ _779327 : [(33264 ^ _779327) ^ [_1384941] : [hBOOL(hAPP(hAPP(c_member(_1384773), _1384941), _1384775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1384777, _1384941))))]]], (33270 ^ _779327) ^ [] : [33272 ^ _779327 : [(33275 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1384777, 33271 ^ [_1384773, _1384775, _1384777])))], (33273 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384773), 33271 ^ [_1384773, _1384775, _1384777]), _1384775)))]], -(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(_1384773, tc_Nat_Onat), _1384777), _1384775))))]]], (15636 ^ _779327) ^ [_1043821, _1043823, _1043825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1043821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043821), _1043823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1043825), _1043823)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1043825), _1043821))))], (43752 ^ _779327) ^ [_1635874, _1635876, _1635878] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635874, tc_HOL_Obool)), _1635876), _1635878) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635874, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1635874, tc_HOL_Obool)), _1635876), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1635874, tc_HOL_Obool)), _1635878), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1635874, tc_HOL_Obool), tc_HOL_Obool))))))], (3682 ^ _779327) ^ [_834991, _834993, _834995, _834997, _834999, _835001, _835003, _835005, _835007, _835009, _835011, _835013] : [-(c_Product__Type_Omap__pair(_835013, _835009, _835005, _835001, _834997, _834993) = c_Product__Type_Omap__pair(_835011, _835007, _835003, _834999, _834995, _834991)), _835013 = _835011, _835009 = _835007, _835005 = _835003, _835001 = _834999, _834997 = _834995, _834993 = _834991], (9783 ^ _779327) ^ [_937880, _937882] : [class_Groups_Omonoid__mult(_937880), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937880), _937882), c_Groups_Oone__class_Oone(_937880)) = _937882)], (49268 ^ _779327) ^ [_1766231, _1766233, _1766235] : [class_Orderings_Olinorder(_1766231), 49271 ^ _779327 : [(49284 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766231, hAPP(hAPP(c_List_Olist_OCons(_1766231), _1766233), _1766235))), 49288 ^ _779327 : [(49291 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1766231), _1766233), 49287 ^ [_1766231, _1766233, _1766235]))], (49289 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766231), 49287 ^ [_1766231, _1766233, _1766235]), hAPP(c_List_Oset(_1766231), _1766235))))]], c_List_Olinorder__class_Osorted(_1766231, _1766235)], (49272 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1766231, hAPP(hAPP(c_List_Olist_OCons(_1766231), _1766233), _1766235)), 49275 ^ _779327 : [(49276 ^ _779327) ^ [_1766399] : [hBOOL(hAPP(hAPP(c_member(_1766231), _1766399), hAPP(c_List_Oset(_1766231), _1766235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1766231), _1766233), _1766399)))], (49282 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766231, _1766235))]]]]], (23375 ^ _779327) ^ [_1185304, _1185306, _1185308, _1185310, _1185312] : [23377 ^ _779327 : [(23380 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1185310, 23376 ^ [_1185304, _1185306, _1185308, _1185310, _1185312]), _1185312))], (23378 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1185304), 23376 ^ [_1185304, _1185306, _1185308, _1185310, _1185312]), _1185308)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1185304, tc_fun(_1185306, tc_HOL_Obool)), _1185308), _1185310), _1185312)))], (49443 ^ _779327) ^ [_1769902, _1769904] : [c_List_Olist_ONil(_1769902) = hAPP(c_List_Orev(_1769902), _1769904), -(_1769904 = c_List_Olist_ONil(_1769902))], (7185 ^ _779327) ^ [_891830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _891830)), -(_891830 = hAPP(c_Nat_OSuc, 7188 ^ [_891830]))], (23889 ^ _779327) ^ [_1195617, _1195619, _1195621] : [class_Rings_Olinordered__idom(_1195617), hAPP(c_Groups_Oabs__class_Oabs(_1195617), _1195619) = hAPP(c_Groups_Oabs__class_Oabs(_1195617), _1195621), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195617), _1195619), _1195621)))], (40120 ^ _779327) ^ [_1546651, _1546653, _1546655] : [class_Lattices_Odistrib__lattice(_1546651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546651), _1546653)), -(_1546653 = c_Orderings_Obot__class_Obot(tc_fun(_1546651, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1546651), _1546655), c_Big__Operators_Olattice__class_OSup__fin(_1546651, _1546653)) = c_Big__Operators_Olattice__class_OSup__fin(_1546651, hAPP(c_Set_OCollect(_1546651), hAPP(hAPP(c_COMBB(tc_fun(_1546651, tc_HOL_Obool), tc_HOL_Obool, _1546651), c_HOL_OEx(_1546651)), hAPP(hAPP(c_COMBC(_1546651, tc_fun(_1546651, tc_HOL_Obool), tc_fun(_1546651, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546651, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1546651, tc_HOL_Obool), tc_fun(_1546651, tc_HOL_Obool)), _1546651), c_COMBS(_1546651, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546651, tc_HOL_Obool), tc_fun(_1546651, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1546651), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546651), c_fconj)), hAPP(hAPP(c_COMBC(_1546651, tc_fun(_1546651, _1546651), tc_fun(_1546651, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546651, tc_HOL_Obool), tc_fun(tc_fun(_1546651, _1546651), tc_fun(_1546651, tc_HOL_Obool)), _1546651), c_COMBB(_1546651, tc_HOL_Obool, _1546651)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1546651), _1546655))))), hAPP(hAPP(c_COMBC(_1546651, tc_fun(_1546651, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546651)), _1546653))))))], (48447 ^ _779327) ^ [_1748098, _1748100] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748098)), c_List_Oconcat(_1748098, _1748100)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1748098), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1748098))), _1748100)))], (38411 ^ _779327) ^ [_1502614, _1502616, _1502618, _1502620, _1502622, _1502624] : [-(hAPP(c_Set_Ovimage(_1502614, _1502616, _1502618), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502620, tc_fun(_1502616, tc_HOL_Obool)), _1502622), _1502624)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502620, tc_fun(_1502614, tc_HOL_Obool)), _1502622), hAPP(hAPP(c_COMBB(tc_fun(_1502616, tc_HOL_Obool), tc_fun(_1502614, tc_HOL_Obool), _1502620), c_Set_Ovimage(_1502614, _1502616, _1502618)), _1502624)))], (41057 ^ _779327) ^ [_1573645, _1573647] : [c_Wellfounded_Owf(_1573645, _1573647), -(c_Wellfounded_OwfP(_1573645, hAPP(hAPP(c_COMBC(_1573645, tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_fun(_1573645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573645, tc_fun(tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_fun(_1573645, tc_HOL_Obool)), _1573645), c_COMBC(_1573645, tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573645, tc_prod(_1573645, _1573645)), tc_fun(_1573645, tc_fun(tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_HOL_Obool)), _1573645), hAPP(c_COMBB(tc_prod(_1573645, _1573645), tc_fun(tc_fun(tc_prod(_1573645, _1573645), tc_HOL_Obool), tc_HOL_Obool), _1573645), c_member(tc_prod(_1573645, _1573645)))), c_Product__Type_OPair(_1573645, _1573645)))), _1573647)))], (13074 ^ _779327) ^ [_997799, _997801, _997803, _997805] : [class_Groups_Oordered__comm__monoid__add(_997799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997799), c_Groups_Ozero__class_Ozero(_997799)), _997801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997799), _997803), _997805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997799), _997803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997799), _997805), _997801))))], (28403 ^ _779327) ^ [_1284936, _1284938, _1284940, _1284942] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284936, tc_HOL_Obool)), _1284938), hAPP(hAPP(c_Set_Oinsert(_1284936), _1284940), _1284942)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284936, tc_HOL_Obool)), _1284938), _1284942))))], (5412 ^ _779327) ^ [_861902, _861904] : [_861904 = _861902, -(c_Orderings_Otop__class_Otop(_861904) = c_Orderings_Otop__class_Otop(_861902))], (21948 ^ _779327) ^ [_1157758, _1157760, _1157762, _1157764, _1157766, _1157768] : [hAPP(hAPP(c_Product__Type_OPair(_1157758, _1157760), _1157762), _1157764) = hAPP(hAPP(c_Product__Type_OPair(_1157758, _1157760), _1157766), _1157768), 21951 ^ _779327 : [(21954 ^ _779327) ^ [] : [-(_1157764 = _1157768)], (21952 ^ _779327) ^ [] : [-(_1157762 = _1157766)]]], (46241 ^ _779327) ^ [_1699538, _1699540, _1699542, _1699544, _1699546] : [-(hAPP(hAPP(c_List_Olist__update(_1699538, hAPP(hAPP(c_List_Olist__update(_1699538, _1699540), _1699542), _1699544)), _1699542), _1699546) = hAPP(hAPP(c_List_Olist__update(_1699538, _1699540), _1699542), _1699546))], (47310 ^ _779327) ^ [_1724032, _1724034, _1724036] : [-(_1724032 = c_List_Olist_ONil(_1724034)), -(c_List_Olast(_1724034, hAPP(hAPP(c_List_Olist_OCons(_1724034), _1724036), _1724032)) = c_List_Olast(_1724034, _1724032))], (7610 ^ _779327) ^ [_898978, _898980, _898982] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _898978)), _898980) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _898978)), _898982), -(_898980 = _898982)], (21194 ^ _779327) ^ [_1143041, _1143043, _1143045] : [-(hAPP(c_Divides_Oadjust(_1143041), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1143043), _1143045)) = 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), _1143045), _1143041)), 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)))), _1143043)), 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)))), _1143043)), _1143045))))], (34703 ^ _779327) ^ [_1418589, _1418591, _1418593, _1418595] : [class_Lattices_Osemilattice__inf(_1418589), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418589), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418589), _1418591), _1418593)), _1418595) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418589), _1418591), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418589), _1418593), _1418595)))], (46277 ^ _779327) ^ [_1700320, _1700322, _1700324, _1700326] : [-(hAPP(hAPP(c_List_Onth(_1700320), hAPP(hAPP(c_List_Oappend(_1700320), _1700322), hAPP(hAPP(c_List_Olist_OCons(_1700320), _1700324), _1700326))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700320)), _1700322)) = _1700324)], (39792 ^ _779327) ^ [_1534438, _1534440, _1534442, _1534444] : [-(hAPP(c_Set_Ovimage(_1534438, _1534440, _1534442), hAPP(c_Set_OCollect(_1534440), _1534444)) = hAPP(c_Set_OCollect(_1534438), hAPP(hAPP(c_COMBB(_1534440, tc_HOL_Obool, _1534438), _1534444), _1534442)))], (37316 ^ _779327) ^ [_1476968, _1476970, _1476972, _1476974, _1476976, _1476978] : [class_Groups_Oab__semigroup__mult(_1476968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476970), _1476972)), -(hBOOL(hAPP(hAPP(c_member(_1476970), _1476974), _1476972))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476968, _1476970, c_Groups_Otimes__class_Otimes(_1476968)), _1476976), _1476978), hAPP(hAPP(c_Set_Oinsert(_1476970), _1476974), _1476972)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1476968), hAPP(_1476976, _1476974)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476968, _1476970, c_Groups_Otimes__class_Otimes(_1476968)), _1476976), _1476978), _1476972)))], (51709 ^ _779327) ^ [_1818872, _1818874] : [-(c_Relation_Otrans(_1818872, c_Relation_OId__on(_1818872, _1818874)))], (52464 ^ _779327) ^ [_1834910, _1834912] : [class_Lattices_Olattice(_1834910), -(class_Lattices_Osemilattice__sup(tc_fun(_1834912, _1834910)))], (45814 ^ _779327) ^ [_1690236, _1690238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690236), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1690238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1690238), _1690236)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1690238))))], (33822 ^ _779327) ^ [_1397731, _1397733, _1397735] : [-(hAPP(c_Relation_OField(_1397731), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1397731, _1397731), tc_HOL_Obool)), _1397733), _1397735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397731, tc_HOL_Obool)), hAPP(c_Relation_OField(_1397731), _1397733)), hAPP(c_Relation_OField(_1397731), _1397735)))], (32226 ^ _779327) ^ [_1364510, _1364512] : [class_Orderings_Olinorder(_1364510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364510), _1364512)), -(_1364512 = c_Orderings_Obot__class_Obot(tc_fun(_1364510, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1364510), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364510), 32239 ^ [_1364510, _1364512]), 32240 ^ [_1364510, _1364512])), hAPP(hAPP(c_Set_Oinsert(_1364510), 32239 ^ [_1364510, _1364512]), hAPP(hAPP(c_Set_Oinsert(_1364510), 32240 ^ [_1364510, _1364512]), c_Orderings_Obot__class_Obot(tc_fun(_1364510, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1364510), c_Big__Operators_Olinorder__class_OMax(_1364510, _1364512)), _1364512)))], (10801 ^ _779327) ^ [_955218, _955220, _955222] : [class_Rings_Ocomm__ring__1(_955218), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955218), _955220), _955222) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955218), _955220), hAPP(c_Groups_Ouminus__class_Ouminus(_955218), _955222)))], (34225 ^ _779327) ^ [_1407066, _1407068, _1407070, _1407072] : [-(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), _1407066), _1407068)), 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), _1407070), _1407072)), 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), _1407066), _1407070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407068), _1407072))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (12257 ^ _779327) ^ [_983241] : [-(_983241 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12260 ^ _779327 : [(12267 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983241))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _983241) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12261 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983241)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _983241) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (13366 ^ _779327) ^ [_1003222, _1003224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003222), _1003224)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003222), _1003224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12275 ^ _779327) ^ [_983469, _983471, _983473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983469), _983471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983473), _983471)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983473), _983469))))], (598 ^ _779327) ^ [_788488, _788490, _788492, _788494, _788496, _788498] : [-(c_Relation_Osingle__valued(_788496, _788492, _788488)), c_Relation_Osingle__valued(_788498, _788494, _788490), _788498 = _788496, _788494 = _788492, _788490 = _788488], (14211 ^ _779327) ^ [_1018768, _1018770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018768), _1018770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018768), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018770), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (35273 ^ _779327) ^ [_1431118, _1431120, _1431122, _1431124] : [class_Orderings_Oorder(_1431118), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431118, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1431118, _1431120), _1431122)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1431118, _1431122), _1431124)) = c_Orderings_Obot__class_Obot(tc_fun(_1431118, tc_HOL_Obool)))], (46550 ^ _779327) ^ [_1707595, _1707597, _1707599] : [-(hAPP(hAPP(c_List_Odrop(_1707595), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1707595), _1707597), _1707599)) = _1707599)], (16716 ^ _779327) ^ [_1062813, _1062815] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062813), _1062815))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062813, _1062815) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1062813), _1062815), _1062815))], (29466 ^ _779327) ^ [_1305414, _1305416, _1305418, _1305420, _1305422, _1305424, _1305426, _1305428] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1305414, tc_fun(_1305416, tc_fun(_1305418, tc_HOL_Obool))), _1305420), _1305422), _1305424), _1305426)), -(hBOOL(hAPP(hAPP(hAPP(_1305422, _1305428), _1305424), _1305426))), hBOOL(hAPP(hAPP(c_member(_1305414), _1305428), _1305420))], (9823 ^ _779327) ^ [_938511, _938513] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938511), _938513), 9826 ^ _779327 : [(9829 ^ _779327) ^ [] : [-(_938513 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9827 ^ _779327) ^ [] : [-(_938511 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (36877 ^ _779327) ^ [_1467438, _1467440, _1467442, _1467444, _1467446] : [c_Fun_Oinj__on(_1467438, _1467440, _1467442, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467438, tc_HOL_Obool)), _1467444), _1467446)), 36880 ^ _779327 : [(36887 ^ _779327) ^ [] : [_1467444 = _1467446, -(hAPP(c_Set_Oimage(_1467438, _1467440, _1467442), _1467444) = hAPP(c_Set_Oimage(_1467438, _1467440, _1467442), _1467446))], (36881 ^ _779327) ^ [] : [hAPP(c_Set_Oimage(_1467438, _1467440, _1467442), _1467444) = hAPP(c_Set_Oimage(_1467438, _1467440, _1467442), _1467446), -(_1467444 = _1467446)]]], (11117 ^ _779327) ^ [_960834, _960836] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _960834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _960834), _960836)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25454 ^ _779327) ^ [_1223363, _1223365, _1223367, _1223369] : [class_Groups_Oordered__ab__group__add__abs(_1223363), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223363), hAPP(c_Groups_Oabs__class_Oabs(_1223363), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223365, _1223363), _1223367), _1223369))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223365, _1223363), hAPP(hAPP(c_COMBB(_1223363, _1223363, _1223365), c_Groups_Oabs__class_Oabs(_1223363)), _1223367)), _1223369))))], (52704 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (39499 ^ _779327) ^ [_1528005, _1528007, _1528009, _1528011, _1528013, _1528015] : [hAPP(c_Set_Oimage(_1528005, _1528007, _1528009), c_Orderings_Otop__class_Otop(tc_fun(_1528005, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528007, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528011, _1528013, _1528015), c_Orderings_Otop__class_Otop(tc_fun(_1528011, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528013, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1528005, _1528011), tc_prod(_1528007, _1528013), c_Product__Type_Omap__pair(_1528005, _1528007, _1528011, _1528013, _1528009, _1528015)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1528005, _1528011), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1528007, _1528013), tc_HOL_Obool)))], (25648 ^ _779327) ^ [_1228580, _1228582] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1228580), hAPP(c_Nat_OSuc, _1228582)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228580, _1228582))], (34331 ^ _779327) ^ [_1410133] : [-(c_Relation_OId__on(_1410133, c_Orderings_Obot__class_Obot(tc_fun(_1410133, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1410133, _1410133), tc_HOL_Obool)))], (35517 ^ _779327) ^ [_1436580, _1436582, _1436584] : [class_Orderings_Oorder(_1436580), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436580, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1436580, _1436582), _1436584)), hAPP(c_SetInterval_Oord__class_OatLeast(_1436580), _1436584)) = c_Orderings_Obot__class_Obot(tc_fun(_1436580, tc_HOL_Obool)))], (41221 ^ _779327) ^ [_1577283, _1577285, _1577287] : [-(hAPP(c_Fun_Ocomp(_1577283, _1577283, _1577285, c_Fun_Oid(_1577283)), _1577287) = _1577287)], (33993 ^ _779327) ^ [_1401344, _1401346] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1401344, tc_HOL_Obool)), _1401346), hAPP(c_Set_OPow(_1401344), _1401346))))], (34011 ^ _779327) ^ [_1401845, _1401847, _1401849] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1401845, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1401845, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1401845), _1401847)), hAPP(c_Set_OPow(_1401845), _1401849))), hAPP(c_Set_OPow(_1401845), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401845, tc_HOL_Obool)), _1401847), _1401849)))))], (38475 ^ _779327) ^ [_1504159, _1504161, _1504163, _1504165] : [hBOOL(hAPP(hAPP(c_member(_1504159), _1504161), _1504163)), -(hAPP(c_Set_Ovimage(_1504165, _1504159, hAPP(c_COMBK(_1504159, _1504165), _1504161)), _1504163) = c_Orderings_Otop__class_Otop(tc_fun(_1504165, tc_HOL_Obool)))], (4042 ^ _779327) ^ [_840677, _840679] : [_840679 = _840677, -(c_Set_OPow(_840679) = c_Set_OPow(_840677))], (34727 ^ _779327) ^ [_1419161, _1419163, _1419165, _1419167] : [class_Lattices_Olattice(_1419161), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419161), _1419163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419161), _1419165), _1419167)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419161), _1419165), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419161), _1419163), _1419167)))], (13510 ^ _779327) ^ [_1005502, _1005504] : [13511 ^ _779327 : [(13514 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005504))], (13512 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005502))]], -(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), _1005502), _1005504))))], (42641 ^ _779327) ^ [_1611078, _1611080, _1611082, _1611084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611078, _1611078)), hAPP(hAPP(c_Product__Type_OPair(_1611078, _1611078), _1611080), _1611082)), hAPP(c_Relation_Oconverse(_1611078, _1611078), c_Transitive__Closure_Otrancl(_1611078, _1611084)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611078, _1611078)), hAPP(hAPP(c_Product__Type_OPair(_1611078, _1611078), _1611080), _1611082)), c_Transitive__Closure_Otrancl(_1611078, hAPP(c_Relation_Oconverse(_1611078, _1611078), _1611084)))))], (45227 ^ _779327) ^ [_1674385, _1674387, _1674389] : [c_Fun_Oinj__on(_1674385, _1674387, _1674389, c_Orderings_Otop__class_Otop(tc_fun(_1674385, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1674385), tc_List_Olist(_1674387), hAPP(c_List_Omap(_1674385, _1674387), _1674389), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674385), tc_HOL_Obool))))], (23748 ^ _779327) ^ [_1192836] : [-(c_Quickcheck_Obeyond(_1192836, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (7147 ^ _779327) ^ [_891187] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _891187)], (52980 ^ _779327) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (16786 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (42918 ^ _779327) ^ [_1617795, _1617797, _1617799, _1617801, _1617803, _1617805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617795, _1617795)), hAPP(hAPP(c_Product__Type_OPair(_1617795, _1617795), _1617797), _1617799)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617795, _1617795), tc_HOL_Obool), _1617801), _1617803))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1617795, _1617795)), hAPP(hAPP(c_Product__Type_OPair(_1617795, _1617795), _1617799), _1617805)), _1617803)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617795, _1617795)), hAPP(hAPP(c_Product__Type_OPair(_1617795, _1617795), _1617797), _1617805)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617795, _1617795), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1617801)), _1617803))))], (30091 ^ _779327) ^ [_1319878, _1319880, _1319882, _1319884] : [hBOOL(hAPP(hAPP(c_member(_1319878), _1319884), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319878, tc_HOL_Obool)), _1319880), _1319882))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319878, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1319878, tc_fun(_1319878, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319878)), _1319880)), hAPP(hAPP(c_COMBC(_1319878, tc_fun(_1319878, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319878)), _1319882)), _1319884)))], (37709 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (21158 ^ _779327) ^ [_1142329, _1142331, _1142333] : [class_Int_Onumber__ring(_1142329), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142329), hAPP(c_Int_Onumber__class_Onumber__of(_1142329), _1142331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1142333))) = hAPP(hAPP(c_HOL_OLet(_1142329, _1142329), hAPP(hAPP(c_Power_Opower__class_Opower(_1142329), hAPP(c_Int_Onumber__class_Onumber__of(_1142329), _1142331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142333))), hAPP(hAPP(c_COMBS(_1142329, _1142329, _1142329), c_Groups_Otimes__class_Otimes(_1142329)), c_COMBI(_1142329))))], (46736 ^ _779327) ^ [_1712167, _1712169, _1712171] : [_1712167 = c_List_Olist_ONil(_1712169), -(hAPP(c_List_Ohd(_1712169), hAPP(hAPP(c_List_Oappend(_1712169), _1712167), _1712171)) = hAPP(c_List_Ohd(_1712169), _1712171))], (45976 ^ _779327) ^ [_1693774, _1693776, _1693778, _1693780, _1693782] : [hAPP(hAPP(c_List_Oappend(_1693774), _1693776), hAPP(hAPP(c_List_Olist_OCons(_1693774), _1693778), c_List_Olist_ONil(_1693774))) = hAPP(hAPP(c_List_Oappend(_1693774), _1693780), hAPP(hAPP(c_List_Olist_OCons(_1693774), _1693782), c_List_Olist_ONil(_1693774))), 45979 ^ _779327 : [(45982 ^ _779327) ^ [] : [-(_1693778 = _1693782)], (45980 ^ _779327) ^ [] : [-(_1693776 = _1693780)]]], (47574 ^ _779327) ^ [_1729093, _1729095, _1729097] : [-(hBOOL(hAPP(hAPP(c_member(_1729093), _1729095), hAPP(c_List_Oset(_1729093), _1729097)))), -(c_List_Oremove1(_1729093, _1729095, _1729097) = _1729097)], (40625 ^ _779327) ^ [_1562945, _1562947, _1562949] : [c_Wellfounded_Owf(_1562945, _1562947), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562945, _1562945)), hAPP(hAPP(c_Product__Type_OPair(_1562945, _1562945), _1562949), _1562949)), _1562947))], (40396 ^ _779327) ^ [_1556346, _1556348, _1556350, _1556352, _1556354, _1556356, _1556358] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556346, _1556348, _1556350), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1556352, tc_fun(tc_prod(_1556346, _1556348), tc_HOL_Obool)), _1556354), _1556356)), _1556358) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1556352, tc_fun(tc_prod(_1556346, _1556350), tc_HOL_Obool)), _1556354), hAPP(hAPP(c_COMBC(_1556352, tc_fun(tc_prod(_1556348, _1556350), tc_HOL_Obool), tc_fun(tc_prod(_1556346, _1556350), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1556346, _1556348), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1556348, _1556350), tc_HOL_Obool), tc_fun(tc_prod(_1556346, _1556350), tc_HOL_Obool)), _1556352), c_Relation_Orel__comp(_1556346, _1556348, _1556350)), _1556356)), _1556358)))], (12405 ^ _779327) ^ [_985788, _985790] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985788)), _985790) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985788), hAPP(c_Nat_OSuc, _985790)))], (15141 ^ _779327) ^ [_1034339, _1034341] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034339))), -(c_SMT_Oz3div(_1034341, _1034339) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034341), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1034339))))], (18092 ^ _779327) ^ [_1086520, _1086522] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086520)), c_Int_OBit0(_1086522)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086520), _1086522)))], (52095 ^ _779327) ^ [_1827980, _1827982] : [hAPP(c_Relation_Oconverse(_1827980, _1827980), _1827982) = _1827982, -(c_Relation_Osym(_1827980, _1827982))], (44376 ^ _779327) ^ [_1650398, _1650400, _1650402, _1650404] : [class_Rings_Olinordered__semidom(_1650398), 44382 ^ _779327 : [(44385 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1650398), c_Groups_Ozero__class_Ozero(_1650398)), hAPP(_1650404, 44381 ^ [_1650398, _1650400, _1650402, _1650404])))], (44383 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1650400), 44381 ^ [_1650398, _1650400, _1650402, _1650404]), _1650402)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1650398), c_Groups_Ozero__class_Ozero(_1650398)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1650400, _1650398), _1650404), _1650402))))], (38820 ^ _779327) ^ [_1512944, _1512946, _1512948, _1512950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512944), _1512946)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512948), _1512950)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1512944, _1512948)), hAPP(hAPP(c_Product__Type_OSigma(_1512944, _1512948), _1512946), hAPP(c_COMBK(tc_fun(_1512948, tc_HOL_Obool), _1512944), _1512950)))))], (50056 ^ _779327) ^ [_1783007, _1783009, _1783011] : [-(hBOOL(hAPP(hAPP(c_member(_1783007), _1783009), hAPP(c_List_Oset(_1783007), _1783011)))), -(hAPP(c_List_OremoveAll(_1783007, _1783009), _1783011) = _1783011)], (40676 ^ _779327) ^ [_1564077, _1564079, _1564081] : [hAPP(c_Relation_ORange(_1564077, _1564079), _1564081) = c_Orderings_Obot__class_Obot(tc_fun(_1564079, tc_HOL_Obool)), -(_1564081 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564077, _1564079), tc_HOL_Obool)))], (48056 ^ _779327) ^ [_1739525, _1739527, _1739529, _1739531, _1739533, _1739535] : [c_List_Olist__all2(_1739525, _1739527, _1739529, _1739531, _1739533), -(c_List_Olist__all2(_1739525, _1739527, _1739529, hAPP(hAPP(c_List_Otake(_1739525), _1739535), _1739531), hAPP(hAPP(c_List_Otake(_1739527), _1739535), _1739533)))], (10063 ^ _779327) ^ [_942213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _942213), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _942213) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10093 ^ _779327) ^ [_942714, _942716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _942714)), 10096 ^ _779327 : [(10103 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942716), _942714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _942716)), hAPP(c_Int_Onat, _942714))))], (10097 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _942716)), hAPP(c_Int_Onat, _942714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942716), _942714)))]]], (21989 ^ _779327) ^ [_1158605, _1158607, _1158609, _1158611, _1158613, _1158615] : [_1158605 = _1158607, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1158609, _1158611, _1158613), _1158615), _1158605) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1158609, _1158611, _1158613), _1158615), _1158607))], (38624 ^ _779327) ^ [_1507394, _1507396, _1507398, _1507400] : [-(c_Wellfounded_Omax__extp(_1507394, _1507396, _1507398, _1507400)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507394), _1507398)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507394), _1507400)), -(_1507400 = c_Orderings_Obot__class_Obot(tc_fun(_1507394, tc_HOL_Obool))), 38638 ^ _779327 : [(38641 ^ _779327) ^ [_1507739] : [hBOOL(hAPP(hAPP(c_member(_1507394), _1507739), _1507400)), hBOOL(hAPP(hAPP(_1507396, 38637 ^ [_1507394, _1507396, _1507398, _1507400]), _1507739))], (38639 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507394), 38637 ^ [_1507394, _1507396, _1507398, _1507400]), _1507398)))]]], (48189 ^ _779327) ^ [_1742661, _1742663, _1742665, _1742667] : [-(hAPP(c_List_Oset(tc_prod(_1742661, _1742663)), c_Enum_Oproduct(_1742661, _1742663, _1742665, _1742667)) = hAPP(hAPP(c_Product__Type_OSigma(_1742661, _1742663), hAPP(c_List_Oset(_1742661), _1742665)), hAPP(c_COMBK(tc_fun(_1742663, tc_HOL_Obool), _1742661), hAPP(c_List_Oset(_1742663), _1742667))))], (52652 ^ _779327) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (18182 ^ _779327) ^ [_1088073, _1088075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088073)), c_Int_OBit1(_1088075))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088073), _1088075)))], (52420 ^ _779327) ^ [_1834133, _1834135, _1834137, _1834139] : [hAPP(c_Set_Oimage(_1834133, _1834135, _1834137), c_Orderings_Otop__class_Otop(tc_fun(_1834133, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1834135, tc_HOL_Obool)), -(hAPP(_1834137, hAPP(c_Hilbert__Choice_Oinv__into(_1834133, _1834135, c_Orderings_Otop__class_Otop(tc_fun(_1834133, tc_HOL_Obool)), _1834137), _1834139)) = _1834139)], (43669 ^ _779327) ^ [_1634162, _1634164, _1634166] : [class_Complete__Lattice_Ocomplete__lattice(_1634162), class_Orderings_Olinorder(_1634162), 43676 ^ _779327 : [(43686 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1634162), c_Complete__Lattice_OInf__class_OInf(_1634162, _1634164)), _1634166))), 43687 ^ _779327 : [(43688 ^ _779327) ^ [_1634468] : [hBOOL(hAPP(hAPP(c_member(_1634162), _1634468), _1634164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1634162), _1634468), _1634166))]]], (43677 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1634162), c_Complete__Lattice_OInf__class_OInf(_1634162, _1634164)), _1634166)), 43681 ^ _779327 : [(43684 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1634162), 43680 ^ [_1634162, _1634164, _1634166]), _1634166)))], (43682 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634162), 43680 ^ [_1634162, _1634164, _1634166]), _1634164)))]]]]], (6416 ^ _779327) ^ [_880081, _880083, _880085] : [class_Orderings_Oorder(_880081), -(_880083 = _880085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880081), _880085), _880083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880081), _880085), _880083)))], (38409 ^ _779327) ^ [_1502530, _1502532, _1502534, _1502536, _1502538, _1502540] : [-(hAPP(c_Set_Ovimage(_1502530, _1502532, _1502534), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1502536, tc_fun(_1502532, tc_HOL_Obool)), _1502538), _1502540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1502536, tc_fun(_1502530, tc_HOL_Obool)), _1502538), hAPP(hAPP(c_COMBB(tc_fun(_1502532, tc_HOL_Obool), tc_fun(_1502530, tc_HOL_Obool), _1502536), c_Set_Ovimage(_1502530, _1502532, _1502534)), _1502540)))], (26619 ^ _779327) ^ [_1247899, _1247901, _1247903] : [class_Orderings_Oorder(_1247899), 26622 ^ _779327 : [(26629 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247899), _1247901), _1247903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247899, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1247899), _1247901)), hAPP(c_SetInterval_Oord__class_OatMost(_1247899), _1247903))))], (26623 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247899, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1247899), _1247901)), hAPP(c_SetInterval_Oord__class_OatMost(_1247899), _1247903))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247899), _1247901), _1247903)))]]], (20127 ^ _779327) ^ [] : [-(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))], (43937 ^ _779327) ^ [_1640413] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640413, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1640413, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1640413, tc_HOL_Obool)))], (38103 ^ _779327) ^ [_1493514, _1493516, _1493518, _1493520, _1493522] : [_1493514 = c_Orderings_Obot__class_Obot(tc_fun(_1493516, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493518, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493516, tc_fun(_1493518, tc_HOL_Obool)), _1493514), _1493520)), _1493522) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493518, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1493518, tc_HOL_Obool))), _1493522))], (38335 ^ _779327) ^ [] : [-(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))], (41611 ^ _779327) ^ [_1586134, _1586136, _1586138, _1586140, _1586142, _1586144] : [c_Finite__Set_Ofolding(_1586134, _1586136, _1586138, _1586140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586134), _1586142)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586134), _1586144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586134, tc_HOL_Obool)), _1586142), _1586144) = c_Orderings_Obot__class_Obot(tc_fun(_1586134, tc_HOL_Obool)), -(hAPP(_1586140, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1586134, tc_HOL_Obool)), _1586142), _1586144)) = hAPP(c_Fun_Ocomp(_1586136, _1586136, _1586136, hAPP(_1586140, _1586142)), hAPP(_1586140, _1586144)))], (23071 ^ _779327) ^ [_1179205, _1179207, _1179209, _1179211] : [class_Orderings_Olinorder(_1179205), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179205), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179205), _1179207), _1179209)), _1179211) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179205), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179205), _1179207), _1179211)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179205), _1179209), _1179211)))], (35159 ^ _779327) ^ [_1428451, _1428453] : [class_Lattices_Oboolean__algebra(_1428451), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428451), _1428453), hAPP(c_Groups_Ouminus__class_Ouminus(_1428451), _1428453)) = c_Orderings_Obot__class_Obot(_1428451))], (28688 ^ _779327) ^ [_1290559, _1290561, _1290563, _1290565] : [class_Complete__Lattice_Ocomplete__lattice(_1290559), -(_1290561 = c_Orderings_Obot__class_Obot(tc_fun(_1290563, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290563, _1290559), _1290561), hAPP(c_COMBK(_1290559, _1290563), _1290565)) = _1290565)], (18266 ^ _779327) ^ [_1089600, _1089602] : [class_Int_Onumber__ring(_1089600), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089600), hAPP(c_Int_Onumber__class_Onumber__of(_1089600), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1089602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089600), _1089602), _1089602))], (41251 ^ _779327) ^ [_1577991, _1577993, _1577995, _1577997, _1577999, _1578001, _1578003, _1578005] : [hAPP(c_Fun_Ocomp(_1577991, _1577993, _1577995, _1577997), _1577999) = hAPP(c_Fun_Ocomp(_1578001, _1577993, _1577995, _1578003), _1578005), 41254 ^ _779327 : [(41255 ^ _779327) ^ [_1578106] : [-(hAPP(_1577997, hAPP(_1577999, _1578106)) = hAPP(_1578003, hAPP(_1578005, _1578106)))]]], (52966 ^ _779327) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (16780 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17018 ^ _779327) ^ [_1068107, _1068109] : [class_Int_Onumber__ring(_1068107), class_Rings_Olinordered__idom(_1068107), 17025 ^ _779327 : [(17032 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068107), hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109)), c_Groups_Ozero__class_Ozero(_1068107)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1068107), hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109))], (17026 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068107), hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109)), c_Groups_Ozero__class_Ozero(_1068107))), -(hAPP(c_Groups_Oabs__class_Oabs(_1068107), hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1068107), hAPP(c_Int_Onumber__class_Onumber__of(_1068107), _1068109)))]]], (11458 ^ _779327) ^ [_968394, _968396, _968398] : [-(hBOOL(hAPP(_968394, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968396), _968398)))), 11461 ^ _779327 : [(11464 ^ _779327) ^ [] : [hBOOL(hAPP(_968394, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11462 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968396), _968398)))]], 11466 ^ _779327 : [(11469 ^ _779327) ^ [] : [hBOOL(hAPP(_968394, 11465 ^ [_968394, _968396, _968398]))], (11467 ^ _779327) ^ [] : [-(_968396 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968398), 11465 ^ [_968394, _968396, _968398]))]]], (18140 ^ _779327) ^ [_1087337, _1087339] : [class_Int_Onumber__ring(_1087337), class_Int_Oring__char__0(_1087337), 18147 ^ _779327 : [(18154 ^ _779327) ^ [] : [c_Int_Oiszero(_1087337, hAPP(c_Int_Onumber__class_Onumber__of(_1087337), _1087339)), -(c_Int_Oiszero(_1087337, hAPP(c_Int_Onumber__class_Onumber__of(_1087337), c_Int_OBit0(_1087339))))], (18148 ^ _779327) ^ [] : [c_Int_Oiszero(_1087337, hAPP(c_Int_Onumber__class_Onumber__of(_1087337), c_Int_OBit0(_1087339))), -(c_Int_Oiszero(_1087337, hAPP(c_Int_Onumber__class_Onumber__of(_1087337), _1087339)))]]], (15495 ^ _779327) ^ [_1041277, _1041279, _1041281] : [class_Divides_Osemiring__div(_1041277), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1041277), c_Divides_Odiv__class_Omod(_1041277, _1041279, _1041281)), _1041281) = c_Groups_Ozero__class_Ozero(_1041277))], (16275 ^ _779327) ^ [_1055168] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055168))), -(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), _1055168)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35033 ^ _779327) ^ [_1425443, _1425445, _1425447, _1425449] : [hBOOL(hAPP(hAPP(c_member(_1425443), _1425445), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425443, tc_HOL_Obool)), _1425447), _1425449))), 35036 ^ _779327 : [(35039 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425443), _1425445), _1425449)))], (35037 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425443), _1425445), _1425447)))]]], (17108 ^ _779327) ^ [_1069796, _1069798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069798)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1069796, _1069798)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1069796), hAPP(c_Int_Onat, _1069798)))], (10524 ^ _779327) ^ [_949765, _949767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _949765)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _949765), _949767)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _949765)), hAPP(c_Int_Onat, _949767)))], (1478 ^ _779327) ^ [_800790, _800792] : [-(class_Lattices_Olattice(_800790)), _800792 = _800790, class_Lattices_Olattice(_800792)], (18919 ^ _779327) ^ [_1101537, _1101539, _1101541, _1101543] : [class_Fields_Olinordered__field__inverse__zero(_1101537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101537), _1101539), _1101541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101537), c_Groups_Ozero__class_Ozero(_1101537)), _1101543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101537), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101537), _1101539), _1101543)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101537), _1101541), _1101543))))], (5894 ^ _779327) ^ [_872155, _872157, _872159] : [5895 ^ _779327 : [(5898 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_872159, _872157), _872155))], (5896 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872155), _872157)))]], 5901 ^ _779327 : [(5904 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_872159, _872157), _872155))], (5902 ^ _779327) ^ [] : [-(_872155 = _872157)]], 5907 ^ _779327 : [(5910 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_872159, _872157), _872155))], (5908 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _872157), _872155)))]], -(hBOOL(hAPP(hAPP(_872159, _872157), _872155)))], (28982 ^ _779327) ^ [_1295772, _1295774] : [class_Orderings_Oorder(_1295772), -(c_SetInterval_Oord__class_OatLeastAtMost(_1295772, _1295774, _1295774) = hAPP(hAPP(c_Set_Oinsert(_1295772), _1295774), c_Orderings_Obot__class_Obot(tc_fun(_1295772, tc_HOL_Obool))))], (39002 ^ _779327) ^ [_1517045, _1517047] : [class_Orderings_Olinorder(_1517045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517045), _1517047)), -(c_Big__Operators_Olinorder__class_OMax(_1517045, _1517047) = hAPP(c_Finite__Set_Ofold1(_1517045, c_Orderings_Oord__class_Omax(_1517045)), _1517047))], (52716 ^ _779327) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (30926 ^ _779327) ^ [_1338801, _1338803, _1338805] : [_1338801 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1338803, _1338803), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1338803, _1338803), tc_HOL_Obool)), _1338801), _1338805)))], (44466 ^ _779327) ^ [_1653060, _1653062, _1653064, _1653066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653060)), _1653062)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653060)), _1653064))), _1653062 = hAPP(hAPP(c_List_Olist_OCons(_1653060), _1653066), _1653064)], (20795 ^ _779327) ^ [_1135314, _1135316, _1135318, _1135320] : [class_Fields_Olinordered__field__inverse__zero(_1135314), class_Int_Onumber(_1135314), 20802 ^ _779327 : [(20803 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135314), _1135318), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)))), 20806 ^ _779327 : [(20813 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), c_Groups_Ozero__class_Ozero(_1135314)), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)))), 20816 ^ _779327 : [(20823 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)), c_Groups_Ozero__class_Ozero(_1135314)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135316), c_Groups_Ozero__class_Ozero(_1135314))))], (20817 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)), c_Groups_Ozero__class_Ozero(_1135314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135314), _1135316), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)))))]]], (20807 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), c_Groups_Ozero__class_Ozero(_1135314)), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135314), _1135316), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))), _1135318)))]]], (20829 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135314), _1135318), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))))), 20832 ^ _779327 : [(20835 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135314), _1135316), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))), _1135318))], (20833 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), c_Groups_Ozero__class_Ozero(_1135314)), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))))]], 20836 ^ _779327 : [(20839 ^ _779327) ^ [] : [20840 ^ _779327 : [(20843 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135314), _1135316), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320))))], (20841 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)), c_Groups_Ozero__class_Ozero(_1135314))))]], 20844 ^ _779327 : [(20847 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135314), _1135316), c_Groups_Ozero__class_Ozero(_1135314)))], (20845 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)), c_Groups_Ozero__class_Ozero(_1135314)))]]], (20837 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135314), c_Groups_Ozero__class_Ozero(_1135314)), hAPP(c_Int_Onumber__class_Onumber__of(_1135314), _1135320)))]]]]], (40668 ^ _779327) ^ [_1563810, _1563812, _1563814] : [c_Wellfounded_Owf(_1563810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563810, _1563810), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563810, _1563810), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563810, _1563810, _1563810), _1563812), _1563812)), hAPP(hAPP(c_Relation_Orel__comp(_1563810, _1563810, _1563810), _1563814), _1563812))), _1563814)), -(c_Wellfounded_Owf(_1563810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563810, _1563810), tc_HOL_Obool)), _1563812), _1563814)))], (52229 ^ _779327) ^ [_1830323, _1830325] : [c_Equiv__Relations_Opart__equivp(_1830323, _1830325), 52233 ^ _779327 : [(52238 ^ _779327) ^ [] : [-(c_Predicate_Otransp(_1830323, _1830325))], (52236 ^ _779327) ^ [] : [-(c_Predicate_Osymp(_1830323, _1830325))], (52234 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1830325, 52232 ^ [_1830323, _1830325]), 52232 ^ [_1830323, _1830325])))]]], (11289 ^ _779327) ^ [_964622, _964624, _964626] : [class_Rings_Osemiring__1(_964622), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_964622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964624), _964626)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964622), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_964622), _964624)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_964622), _964626)))], (17396 ^ _779327) ^ [_1074644, _1074646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1074644)), c_Int_OBit1(_1074646))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074644), _1074646)))], (7151 ^ _779327) ^ [_891248, _891250, _891252, _891254] : [class_Rings_Olinordered__semidom(_891248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891248), _891250), _891252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891248), c_Groups_Ozero__class_Ozero(_891248)), _891250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _891254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891248), hAPP(hAPP(c_Power_Opower__class_Opower(_891248), _891250), _891254)), hAPP(hAPP(c_Power_Opower__class_Opower(_891248), _891252), _891254))))], (4084 ^ _779327) ^ [_841294, _841296, _841298, _841300, _841302, _841304] : [-(c_Finite__Set_Ofold(_841304, _841300, _841296) = c_Finite__Set_Ofold(_841302, _841298, _841294)), _841304 = _841302, _841300 = _841298, _841296 = _841294], (47046 ^ _779327) ^ [_1718388, _1718390, _1718392] : [-(_1718388 = c_List_Olist_ONil(_1718390)), -(hAPP(c_List_Ohd(_1718390), hAPP(c_List_Orotate(_1718390, _1718392), _1718388)) = hAPP(hAPP(c_List_Onth(_1718390), _1718388), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718392, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718390)), _1718388))))], (6402 ^ _779327) ^ [_879946, _879948, _879950] : [class_Orderings_Olinorder(_879946), -(_879948 = _879950), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879946), _879948), _879950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879946), _879950), _879948)))], (27168 ^ _779327) ^ [_1258774, _1258776, _1258778] : [class_Lattices_Osemilattice__sup(_1258774), 27171 ^ _779327 : [(27178 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258774), _1258776), _1258778) = _1258778, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258774), _1258776), _1258778)))], (27172 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258774), _1258776), _1258778)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258774), _1258776), _1258778) = _1258778)]]], (52696 ^ _779327) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (14271 ^ _779327) ^ [_1019859, _1019861] : [class_Lattices_Oboolean__algebra(_1019859), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1019859), hAPP(c_Groups_Ouminus__class_Ouminus(_1019859), _1019861)) = _1019861)], (28326 ^ _779327) ^ [_1283464, _1283466, _1283468] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283464), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283464, tc_HOL_Obool)), _1283466), _1283468))), 28329 ^ _779327 : [(28332 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283464), _1283468)))], (28330 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283464), _1283466)))]]], (44476 ^ _779327) ^ [_1653320, _1653322, _1653324, _1653326, _1653328] : [hAPP(hAPP(c_List_Olist_OCons(_1653320), _1653322), _1653324) = hAPP(hAPP(c_List_Olist_OCons(_1653320), _1653326), _1653328), 44479 ^ _779327 : [(44482 ^ _779327) ^ [] : [-(_1653324 = _1653328)], (44480 ^ _779327) ^ [] : [-(_1653322 = _1653326)]]], (25686 ^ _779327) ^ [_1229232, _1229234, _1229236, _1229238, _1229240] : [class_Orderings_Olinorder(_1229232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229232), _1229234), _1229236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229232), _1229238), _1229240)), 25697 ^ _779327 : [(25706 ^ _779327) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1229232, _1229234), _1229236) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1229232, _1229238), _1229240)), _1229234 = _1229238, _1229236 = _1229240], (25698 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1229232, _1229234), _1229236) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1229232, _1229238), _1229240), 25701 ^ _779327 : [(25704 ^ _779327) ^ [] : [-(_1229236 = _1229240)], (25702 ^ _779327) ^ [] : [-(_1229234 = _1229238)]]]]], (51067 ^ _779327) ^ [_1804725, _1804727, _1804729] : [-(hAPP(c_List_Orev(_1804725), c_List_Oreplicate(_1804725, _1804727, _1804729)) = c_List_Oreplicate(_1804725, _1804727, _1804729))], (12235 ^ _779327) ^ [_982861, _982863, _982865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982861), _982863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982861), _982865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982865), _982863)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982865), _982861))))], (42178 ^ _779327) ^ [_1599851, _1599853, _1599855] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599851, _1599851)), hAPP(hAPP(c_Product__Type_OPair(_1599851, _1599851), _1599853), _1599853)), c_Transitive__Closure_Ortrancl(_1599851, _1599855))))], (24611 ^ _779327) ^ [_1207656, _1207658, _1207660] : [class_Divides_Osemiring__div(_1207656), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207656), _1207658), _1207660)), -(c_Divides_Odiv__class_Omod(_1207656, _1207660, _1207658) = c_Groups_Ozero__class_Ozero(_1207656))], (32860 ^ _779327) ^ [_1376943, _1376945, _1376947] : [class_Orderings_Olinorder(_1376943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376943), _1376945)), -(_1376945 = c_Orderings_Obot__class_Obot(tc_fun(_1376943, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376943), _1376947)), -(_1376947 = c_Orderings_Obot__class_Obot(tc_fun(_1376943, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1376943, c_Orderings_Oord__class_Omin(_1376943), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376943, tc_HOL_Obool)), _1376945), _1376947)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376943), c_Big__Operators_Olattice_OInf__fin(_1376943, c_Orderings_Oord__class_Omin(_1376943), _1376945)), c_Big__Operators_Olattice_OInf__fin(_1376943, c_Orderings_Oord__class_Omin(_1376943), _1376947)))], (47963 ^ _779327) ^ [_1737630, _1737632, _1737634, _1737636, _1737638] : [-(c_List_Olist__all2(_1737630, _1737632, _1737634, _1737636, _1737638)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737630)), _1737636) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737632)), _1737638), 47969 ^ _779327 : [(47972 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1737630, _1737632, tc_HOL_Obool), _1737634), 47968 ^ [_1737630, _1737632, _1737634, _1737636, _1737638]))], (47970 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1737630, _1737632)), 47968 ^ [_1737630, _1737632, _1737634, _1737636, _1737638]), hAPP(c_List_Oset(tc_prod(_1737630, _1737632)), hAPP(hAPP(c_List_Ozip(_1737630, _1737632), _1737636), _1737638)))))]]], (50639 ^ _779327) ^ [_1796065, _1796067, _1796069] : [c_List_Olist__ex(_1796065, _1796067, _1796069), 50643 ^ _779327 : [(50646 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1796067, hAPP(hAPP(c_List_Onth(_1796065), _1796069), 50642 ^ [_1796065, _1796067, _1796069]))))], (50644 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50642 ^ [_1796065, _1796067, _1796069]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796065)), _1796069))))]]], (32100 ^ _779327) ^ [_1362247, _1362249, _1362251] : [class_Orderings_Olinorder(_1362247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362247), _1362249)), -(_1362251 = c_Orderings_Obot__class_Obot(tc_fun(_1362247, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1362247, tc_HOL_Obool)), _1362251), _1362249)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362247), c_Big__Operators_Olinorder__class_OMax(_1362247, _1362251)), c_Big__Operators_Olinorder__class_OMax(_1362247, _1362249)) = c_Big__Operators_Olinorder__class_OMax(_1362247, _1362249))], (8736 ^ _779327) ^ [_919546, _919548, _919550] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919546), _919548)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919546), _919550)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919548), _919550))], (42250 ^ _779327) ^ [_1601605, _1601607] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601605, _1601605), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1601605, _1601607)), c_Relation_OId(_1601605)) = c_Transitive__Closure_Ortrancl(_1601605, _1601607))], (52069 ^ _779327) ^ [_1827557, _1827559] : [-(c_Relation_Osym(_1827557, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1827557, _1827557), tc_HOL_Obool)), _1827559), hAPP(c_Relation_Oconverse(_1827557, _1827557), _1827559))))], (5784 ^ _779327) ^ [_870667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870667), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49925 ^ _779327) ^ [_1780001, _1780003, _1780005] : [-(c_List_OdropWhile(_1780001, _1780003, _1780005) = hAPP(hAPP(c_List_Odrop(_1780001), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780001)), c_List_OtakeWhile(_1780001, _1780003, _1780005))), _1780005))], (23544 ^ _779327) ^ [_1189200, _1189202, _1189204, _1189206, _1189208, _1189210] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1189200, _1189202, _1189204, _1189206, c_Nitpick_Opair__box_OPairBox(_1189200, _1189202, _1189208, _1189210)) = hAPP(hAPP(_1189206, _1189208), _1189210))], (31920 ^ _779327) ^ [_1359278, _1359280, _1359282] : [class_Lattices_Olattice(_1359278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359278), _1359280)), hBOOL(hAPP(hAPP(c_member(_1359278), _1359282), _1359280)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1359278), _1359282), c_Big__Operators_Olattice__class_OSup__fin(_1359278, _1359280)) = c_Big__Operators_Olattice__class_OSup__fin(_1359278, _1359280))], (21738 ^ _779327) ^ [_1153609, _1153611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1153611)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153609, _1153611), c_Divides_OposDivAlg(_1153609, _1153611))))], (11721 ^ _779327) ^ [_973546, _973548] : [class_Groups_Ogroup__add(_973546), 11724 ^ _779327 : [(11731 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_973546) = _973548, -(c_Groups_Ozero__class_Ozero(_973546) = hAPP(c_Groups_Ouminus__class_Ouminus(_973546), _973548))], (11725 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_973546) = hAPP(c_Groups_Ouminus__class_Ouminus(_973546), _973548), -(c_Groups_Ozero__class_Ozero(_973546) = _973548)]]], (14369 ^ _779327) ^ [_1021543, _1021545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021545)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1021545), _1021543)), _1021545) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1021545), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1021543), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (42629 ^ _779327) ^ [_1610704, _1610706, _1610708, _1610710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610704, _1610704)), hAPP(hAPP(c_Product__Type_OPair(_1610704, _1610704), _1610706), _1610708)), c_Transitive__Closure_Ortrancl(_1610704, _1610710))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610704, _1610704)), hAPP(hAPP(c_Product__Type_OPair(_1610704, _1610704), _1610708), _1610706)), c_Transitive__Closure_Ortrancl(_1610704, hAPP(c_Relation_Oconverse(_1610704, _1610704), _1610710)))))], (17834 ^ _779327) ^ [_1081897, _1081899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1081897), 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)))), _1081899)), 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)))), _1081897)) = 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), _1081899), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1081897))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17694 ^ _779327) ^ [_1079427, _1079429] : [class_Int_Onumber__ring(_1079427), class_Rings_Olinordered__idom(_1079427), 17701 ^ _779327 : [(17708 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079429), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079427), hAPP(c_Int_Onumber__class_Onumber__of(_1079427), _1079429)), c_Groups_Oone__class_Oone(_1079427))))], (17702 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079427), hAPP(c_Int_Onumber__class_Onumber__of(_1079427), _1079429)), c_Groups_Oone__class_Oone(_1079427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079429), c_Int_OBit1(c_Int_OPls))))]]], (33893 ^ _779327) ^ [_1399260, _1399262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399260), _1399262)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1399260, tc_HOL_Obool)), hAPP(c_Set_OPow(_1399260), _1399262)) = 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(_1399260), _1399262)))], (5938 ^ _779327) ^ [_872756, _872758, _872760, _872762, _872764] : [class_Orderings_Oord(_872756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872758, _872756)), _872760), _872762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872756), hAPP(_872760, _872764)), hAPP(_872762, _872764))))], (31870 ^ _779327) ^ [_1358482, _1358484, _1358486] : [class_Rings_Oring__1(_1358482), hBOOL(hAPP(hAPP(c_member(_1358482), _1358484), c_Int_Oring__1__class_OInts(_1358482))), -(hBOOL(hAPP(hAPP(c_member(_1358482), hAPP(hAPP(c_Power_Opower__class_Opower(_1358482), _1358484), _1358486)), c_Int_Oring__1__class_OInts(_1358482))))], (22817 ^ _779327) ^ [_1174669, _1174671, _1174673, _1174675] : [class_Orderings_Olinorder(_1174669), 22820 ^ _779327 : [(22821 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174669), _1174673), _1174675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), _1174673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), _1174675)))], (22831 ^ _779327) ^ [] : [22832 ^ _779327 : [(22835 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), _1174675))], (22833 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), _1174673))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174669), _1174671), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174669), _1174673), _1174675))))]]], (52724 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (49519 ^ _779327) ^ [_1771560, _1771562, _1771564, _1771566, _1771568] : [c_List_Olist__all2(_1771560, _1771562, _1771564, hAPP(c_List_Orev(_1771560), _1771566), hAPP(c_List_Orev(_1771562), _1771568)), -(c_List_Olist__all2(_1771560, _1771562, _1771564, _1771566, _1771568))], (23991 ^ _779327) ^ [_1197372, _1197374, _1197376, _1197378] : [class_Divides_Osemiring__div(_1197372), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197372), _1197374), _1197376)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197372), _1197374), _1197378)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197372), _1197374), c_Divides_Odiv__class_Omod(_1197372, _1197376, _1197378))))], (51139 ^ _779327) ^ [_1806057, _1806059, _1806061, _1806063] : [-(c_Predicate_Oconversep(_1806057, _1806059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1806057, tc_fun(_1806059, tc_HOL_Obool))), _1806061), _1806063)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1806059, tc_fun(_1806057, tc_HOL_Obool))), c_Predicate_Oconversep(_1806057, _1806059, _1806061)), c_Predicate_Oconversep(_1806057, _1806059, _1806063)))], (14689 ^ _779327) ^ [_1026500, _1026502] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026500), _1026502) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14690 ^ _779327 : [(14699 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1026500), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026502), _1026500))], (14693 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026500), _1026502))], (14691 ^ _779327) ^ [] : [_1026502 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (2678 ^ _779327) ^ [_818845, _818847] : [_818847 = _818845, -(c_New__DSequence_Opos__not__seq(_818847) = c_New__DSequence_Opos__not__seq(_818845))], (39850 ^ _779327) ^ [_1536053, _1536055] : [-(hAPP(c_Set_OCollect(_1536053), hAPP(hAPP(c_COMBC(_1536053, _1536053, tc_HOL_Obool), c_fequal), _1536055)) = hAPP(hAPP(c_Set_Oinsert(_1536053), _1536055), c_Orderings_Obot__class_Obot(tc_fun(_1536053, tc_HOL_Obool))))], (8902 ^ _779327) ^ [_922578, _922580, _922582] : [class_Rings_Ocomm__semiring__1(_922578), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922578), hAPP(hAPP(c_Power_Opower__class_Opower(_922578), _922580), _922582)), _922580) = hAPP(hAPP(c_Power_Opower__class_Opower(_922578), _922580), hAPP(c_Nat_OSuc, _922582)))], (13016 ^ _779327) ^ [_996820, _996822, _996824] : [class_Groups_Oordered__comm__monoid__add(_996820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996820), c_Groups_Ozero__class_Ozero(_996820)), _996822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996820), c_Groups_Ozero__class_Ozero(_996820)), _996824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996820), c_Groups_Ozero__class_Ozero(_996820)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996820), _996822), _996824))))], (19881 ^ _779327) ^ [_1118425, _1118427, _1118429, _1118431] : [class_Fields_Ofield(_1118425), -(_1118427 = c_Groups_Ozero__class_Ozero(_1118425)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118425), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118425), _1118429), _1118427)), _1118431) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118425), _1118429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118425), _1118427), _1118431))), _1118427))], (16673 ^ _779327) ^ [_1062173, _1062175] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062173, _1062175)) = _1062175, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1062173), _1062175) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44440 ^ _779327) ^ [_1651775, _1651777, _1651779] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651775)), _1651777) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651775)), _1651779)), _1651777 = _1651779], (46526 ^ _779327) ^ [_1707125, _1707127] : [-(hAPP(hAPP(c_List_Odrop(_1707125), _1707127), c_List_Olist_ONil(_1707125)) = c_List_Olist_ONil(_1707125))], (28546 ^ _779327) ^ [_1287787, _1287789] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287787, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1287787, tc_HOL_Obool))), _1287789)))], (20129 ^ _779327) ^ [_1122527, _1122529, _1122531, _1122533] : [class_Fields_Olinordered__field__inverse__zero(_1122527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122527), _1122529), _1122531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122527), _1122533), c_Groups_Ozero__class_Ozero(_1122527))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122527), c_Groups_Ozero__class_Ozero(_1122527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122527), _1122529), _1122531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122527), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122527), _1122533), _1122529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122527), _1122533), _1122531))))], (6999 ^ _779327) ^ [_888883, _888885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888883), _888885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _888883)), hAPP(c_Nat_OSuc, _888885))))], (40825 ^ _779327) ^ [_1568010, _1568012, _1568014, _1568016] : [hBOOL(hAPP(hAPP(c_member(_1568010), _1568012), hAPP(c_Relation_ORange(_1568014, _1568010), _1568016))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568014, _1568010)), hAPP(hAPP(c_Product__Type_OPair(_1568014, _1568010), 40828 ^ [_1568010, _1568012, _1568014, _1568016]), _1568012)), _1568016)))], (39902 ^ _779327) ^ [_1538023, _1538025, _1538027, _1538029] : [_1538023 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1538025, _1538027), 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)), _1538029))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1538025), _1538023)))], (51065 ^ _779327) ^ [_1804674, _1804676, _1804678, _1804680, _1804682] : [-(hAPP(hAPP(c_List_Omap(_1804674, _1804676), _1804678), c_List_Oreplicate(_1804674, _1804680, _1804682)) = c_List_Oreplicate(_1804676, _1804680, hAPP(_1804678, _1804682)))], (11003 ^ _779327) ^ [_958822, _958824, _958826] : [class_Groups_Ogroup__add(_958822), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_958822), _958824), _958826)), _958826) = _958824)], (50185 ^ _779327) ^ [_1785638, _1785640] : [-(c_List_Omeasures(_1785638, _1785640) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1785638), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1785638, tc_List_Olist(tc_fun(_1785638, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785638, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1785638, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1785638), c_List_Omap(tc_fun(_1785638, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1785638, tc_Nat_Onat), _1785638, tc_Nat_Onat), c_COMBI(tc_fun(_1785638, tc_Nat_Onat))))), _1785640)))], (31638 ^ _779327) ^ [_1354202, _1354204] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354202, _1354204) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354202), _1354204)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354204), _1354202)))], (33634 ^ _779327) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (48824 ^ _779327) ^ [_1758077, _1758079] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1758077, _1758079))))], (39555 ^ _779327) ^ [_1529725, _1529727, _1529729, _1529731, _1529733] : [c_Finite__Set_Ofolding__one__idem(_1529725, _1529727, _1529729), hAPP(_1529731, hAPP(hAPP(_1529727, 39560 ^ [_1529725, _1529727, _1529729, _1529731, _1529733]), 39561 ^ [_1529725, _1529727, _1529729, _1529731, _1529733])) = hAPP(hAPP(_1529727, hAPP(_1529731, 39560 ^ [_1529725, _1529727, _1529729, _1529731, _1529733])), hAPP(_1529731, 39561 ^ [_1529725, _1529727, _1529729, _1529731, _1529733])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529725), _1529733)), -(_1529733 = c_Orderings_Obot__class_Obot(tc_fun(_1529725, tc_HOL_Obool))), -(hAPP(_1529731, hAPP(_1529729, _1529733)) = hAPP(_1529729, hAPP(c_Set_Oimage(_1529725, _1529725, _1529731), _1529733)))], (23470 ^ _779327) ^ [_1187299, _1187301, _1187303] : [c_Nitpick_Oless__frac(_1187299, _1187301, _1187303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1187299), c_Nitpick_Oplus__frac(_1187299, _1187301, c_Nitpick_Ouminus__frac(_1187299, _1187303)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35301 ^ _779327) ^ [_1431868, _1431870, _1431872, _1431874, _1431876] : [c_Orderings_Oorder__class_Omono(tc_fun(_1431868, tc_HOL_Obool), tc_fun(_1431870, tc_HOL_Obool), _1431872), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431870, tc_HOL_Obool)), hAPP(_1431872, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431868, tc_HOL_Obool)), _1431874), _1431876))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431870, tc_HOL_Obool)), hAPP(_1431872, _1431874)), hAPP(_1431872, _1431876)))))], (44859 ^ _779327) ^ [_1665032, _1665034, _1665036, _1665038] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665032)), hAPP(hAPP(c_List_Olist_OCons(_1665032), _1665034), _1665036)), c_List_Olists(_1665032, _1665038)))), hBOOL(hAPP(hAPP(c_member(_1665032), _1665034), _1665038)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665032)), _1665036), c_List_Olists(_1665032, _1665038)))], (23325 ^ _779327) ^ [_1184487, _1184489] : [-(c_Nitpick_Oint__lcm(_1184487, _1184489) = 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), _1184487)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184489)))))], (23712 ^ _779327) ^ [_1192157, _1192159] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1192157), _1192159) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1192157)), hAPP(c_Code__Numeral_Onat__of, _1192159))))], (23849 ^ _779327) ^ [_1194963, _1194965] : [class_Rings_Ocomm__semiring__1(_1194963), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1194963), _1194965), c_Groups_Ozero__class_Ozero(_1194963))))], (15159 ^ _779327) ^ [_1034543] : [-(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), _1034543)) = 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), _1034543))))], (52684 ^ _779327) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (24789 ^ _779327) ^ [_1211045, _1211047, _1211049] : [24790 ^ _779327 : [(24793 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211047), _1211049))], (24791 ^ _779327) ^ [] : [_1211045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211045), _1211047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211045), _1211049))))], (18368 ^ _779327) ^ [_1091314] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1091314)), 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, _1091314, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (42944 ^ _779327) ^ [_1618601, _1618603, _1618605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618601, _1618601)), _1618603), c_Transitive__Closure_Otrancl(_1618601, _1618605))), 42948 ^ _779327 : [(42951 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618601, _1618601)), _1618603), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1618601, _1618601), tc_HOL_Obool), 42947 ^ [_1618601, _1618603, _1618605]), _1618605))))], (42949 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 42947 ^ [_1618601, _1618603, _1618605])))]]], (37545 ^ _779327) ^ [_1481609, _1481611, _1481613] : [class_Lattices_Oboolean__algebra(_1481609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1481609), _1481611), _1481613) = c_Orderings_Obot__class_Obot(_1481609), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1481609), _1481611), _1481613) = c_Orderings_Otop__class_Otop(_1481609), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1481609), _1481611) = _1481613)], (26992 ^ _779327) ^ [_1255420, _1255422, _1255424, _1255426] : [class_Lattices_Olattice(_1255420), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255420), _1255422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255420), _1255424), _1255426)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255420), _1255424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255420), _1255422), _1255426)))], (40948 ^ _779327) ^ [_1570729, _1570731, _1570733, _1570735] : [40949 ^ _779327 : [(40950 ^ _779327) ^ [_1570804] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570729, _1570733)), hAPP(hAPP(c_Product__Type_OPair(_1570729, _1570733), _1570731), _1570804)), _1570735))]], -(hBOOL(hAPP(hAPP(c_member(_1570729), _1570731), hAPP(c_Relation_ODomain(_1570729, _1570733), _1570735))))], (48349 ^ _779327) ^ [_1746159, _1746161, _1746163] : [-(hBOOL(hAPP(hAPP(c_member(_1746159), _1746161), hAPP(c_List_Oset(_1746159), _1746163)))), -(c_List_Oremdups(_1746159, hAPP(hAPP(c_List_Olist_OCons(_1746159), _1746161), _1746163)) = hAPP(hAPP(c_List_Olist_OCons(_1746159), _1746161), c_List_Oremdups(_1746159, _1746163)))], (12091 ^ _779327) ^ [_979913, _979915, _979917, _979919] : [class_Groups_Oordered__cancel__ab__semigroup__add(_979913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979913), _979915), _979917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979913), _979919), _979915)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979913), _979919), _979917))))], (14821 ^ _779327) ^ [_1028594, _1028596, _1028598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028594), 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)), _1028596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028596), _1028598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028594), _1028596)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028594), _1028598))))], (42216 ^ _779327) ^ [_1600786, _1600788, _1600790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600786, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1600786, _1600786, _1600788), _1600790)), _1600790)), -(hAPP(c_Relation_OImage(_1600786, _1600786, c_Transitive__Closure_Ortrancl(_1600786, _1600788)), _1600790) = _1600790)], (10143 ^ _779327) ^ [_943509, _943511] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943509) = _943511), _943509 = hAPP(c_Int_Onat, _943511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943511))], (22787 ^ _779327) ^ [_1174110, _1174112, _1174114] : [class_Orderings_Olinorder(_1174110), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174110), _1174112), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174110), _1174112), _1174114)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174110), _1174112), _1174114))], (34621 ^ _779327) ^ [_1416588, _1416590, _1416592] : [34622 ^ _779327 : [(34625 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416588), _1416592))], (34623 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416588), _1416590))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1416588), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416588, tc_HOL_Obool)), _1416590), _1416592))))], (12367 ^ _779327) ^ [_985134, _985136] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985134), _985136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 12370 ^ _779327 : [(12373 ^ _779327) ^ [] : [-(_985136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12371 ^ _779327) ^ [] : [-(_985134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46064 ^ _779327) ^ [_1695837, _1695839, _1695841] : [-(hAPP(hAPP(c_List_Olist__update(_1695837, c_List_Olist_ONil(_1695837)), _1695839), _1695841) = c_List_Olist_ONil(_1695837))], (19905 ^ _779327) ^ [_1118850, _1118852, _1118854, _1118856] : [class_Fields_Ofield__inverse__zero(_1118850), class_Int_Onumber(_1118850), 19912 ^ _779327 : [(19913 ^ _779327) ^ [] : [_1118852 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118850), _1118854), hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856)), 19916 ^ _779327 : [(19923 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856) = c_Groups_Ozero__class_Ozero(_1118850), -(_1118852 = c_Groups_Ozero__class_Ozero(_1118850))], (19917 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856) = c_Groups_Ozero__class_Ozero(_1118850)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118850), _1118852), hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856)) = _1118854)]]], (19929 ^ _779327) ^ [] : [-(_1118852 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118850), _1118854), hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856))), 19932 ^ _779327 : [(19935 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118850), _1118852), hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856)) = _1118854], (19933 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856) = c_Groups_Ozero__class_Ozero(_1118850)]], 19936 ^ _779327 : [(19939 ^ _779327) ^ [] : [_1118852 = c_Groups_Ozero__class_Ozero(_1118850)], (19937 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1118850), _1118856) = c_Groups_Ozero__class_Ozero(_1118850))]]]]], (23446 ^ _779327) ^ [_1186792, _1186794, _1186796] : [-(c_Product__Type_Ointernal__split(_1186792, _1186794, _1186796) = c_Product__Type_Oprod_Oprod__case(_1186792, _1186794, _1186796))], (19409 ^ _779327) ^ [_1109713, _1109715, _1109717] : [class_Fields_Olinordered__field(_1109713), -(_1109715 = c_Groups_Ozero__class_Ozero(_1109713)), -(hAPP(c_Groups_Oabs__class_Oabs(_1109713), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109713), _1109717), _1109715)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109713), hAPP(c_Groups_Oabs__class_Oabs(_1109713), _1109717)), hAPP(c_Groups_Oabs__class_Oabs(_1109713), _1109715)))], (14351 ^ _779327) ^ [_1021295, _1021297] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021295)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021295)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021297)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021295)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021297))))], (46417 ^ _779327) ^ [_1704073, _1704075, _1704077, _1704079, _1704081, _1704083] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704073), tc_List_Olist(_1704073))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704073), tc_List_Olist(_1704073)), hAPP(hAPP(c_List_Oappend(_1704073), _1704075), hAPP(hAPP(c_List_Olist_OCons(_1704073), _1704077), c_List_Olist_ONil(_1704073)))), hAPP(hAPP(c_List_Oappend(_1704073), _1704079), hAPP(hAPP(c_List_Olist_OCons(_1704073), _1704081), c_List_Olist_ONil(_1704073))))), c_List_Olistrel1(_1704073, _1704083)))), 46418 ^ _779327 : [(46425 ^ _779327) ^ [] : [_1704075 = _1704079, hBOOL(hAPP(hAPP(c_member(tc_prod(_1704073, _1704073)), hAPP(hAPP(c_Product__Type_OPair(_1704073, _1704073), _1704077), _1704081)), _1704083))], (46419 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704073), tc_List_Olist(_1704073))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704073), tc_List_Olist(_1704073)), _1704075), _1704079)), c_List_Olistrel1(_1704073, _1704083))), _1704077 = _1704081]]], (18468 ^ _779327) ^ [_1093057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1093057), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1093057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1093057 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46684 ^ _779327) ^ [_1710877, _1710879, _1710881, _1710883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710877), _1710879)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710881)), _1710883))), -(hAPP(hAPP(c_List_Otake(_1710881), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710877), _1710879)), _1710883) = hAPP(hAPP(c_List_Oappend(_1710881), hAPP(hAPP(c_List_Otake(_1710881), _1710877), _1710883)), hAPP(hAPP(c_List_Otake(_1710881), _1710879), hAPP(hAPP(c_List_Odrop(_1710881), _1710877), _1710883))))], (29638 ^ _779327) ^ [_1308809, _1308811, _1308813, _1308815, _1308817, _1308819, _1308821] : [hBOOL(hAPP(hAPP(c_member(_1308809), _1308811), hAPP(hAPP(_1308813, _1308815), _1308817))), -(hBOOL(hAPP(hAPP(c_member(_1308809), _1308811), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1308819, _1308821, tc_fun(_1308809, tc_HOL_Obool)), _1308813), hAPP(hAPP(c_Product__Type_OPair(_1308819, _1308821), _1308815), _1308817)))))], (3390 ^ _779327) ^ [_830397, _830399] : [_830399 = _830397, -(c_Nitpick_ORep__Frac(_830399) = c_Nitpick_ORep__Frac(_830397))], (6278 ^ _779327) ^ [_878111, _878113, _878115] : [class_Orderings_Oorder(_878111), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878111), _878113), _878115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878111), _878113), _878115))), -(_878113 = _878115)], (47454 ^ _779327) ^ [_1726774, _1726776, _1726778] : [_1726774 = c_List_Olist_ONil(_1726776), -(c_List_Obutlast(_1726776, hAPP(hAPP(c_List_Olist_OCons(_1726776), _1726778), _1726774)) = c_List_Olist_ONil(_1726776))], (52558 ^ _779327) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (12956 ^ _779327) ^ [_995832, _995834] : [class_Rings_Oring__1__no__zero__divisors(_995832), 12959 ^ _779327 : [(12960 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995832), _995834), _995834) = c_Groups_Oone__class_Oone(_995832), -(_995834 = c_Groups_Oone__class_Oone(_995832)), -(_995834 = hAPP(c_Groups_Ouminus__class_Ouminus(_995832), c_Groups_Oone__class_Oone(_995832)))], (12970 ^ _779327) ^ [] : [12971 ^ _779327 : [(12974 ^ _779327) ^ [] : [_995834 = hAPP(c_Groups_Ouminus__class_Ouminus(_995832), c_Groups_Oone__class_Oone(_995832))], (12972 ^ _779327) ^ [] : [_995834 = c_Groups_Oone__class_Oone(_995832)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_995832), _995834), _995834) = c_Groups_Oone__class_Oone(_995832))]]], (24769 ^ _779327) ^ [_1210741, _1210743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210741), _1210743)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210743), _1210741))], (52600 ^ _779327) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52618 ^ _779327) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (45149 ^ _779327) ^ [_1672734, _1672736, _1672738, _1672740] : [-(hBOOL(hAPP(hAPP(c_member(_1672734), _1672736), hAPP(c_List_Oset(_1672734), _1672738)))), hBOOL(hAPP(hAPP(c_member(_1672734), _1672736), hAPP(c_List_Oset(_1672734), c_List_Osublist(_1672734, _1672738, _1672740))))], (35225 ^ _779327) ^ [_1429788, _1429790, _1429792, _1429794] : [hBOOL(hAPP(hAPP(c_member(_1429788), _1429790), _1429792)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429788, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1429788), _1429790), _1429794)), _1429792) = hAPP(hAPP(c_Set_Oinsert(_1429788), _1429790), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429788, tc_HOL_Obool)), _1429794), _1429792)))], (20863 ^ _779327) ^ [] : [-(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))], (51776 ^ _779327) ^ [_1820572, _1820574, _1820576, _1820578] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1820572, tc_fun(_1820574, tc_HOL_Obool)), _1820576), _1820578) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1820574, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1820574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1820572, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1820574, tc_HOL_Obool)), c_HOL_OEx(_1820572)), hAPP(hAPP(c_COMBB(tc_fun(_1820572, tc_HOL_Obool), tc_fun(_1820572, tc_HOL_Obool), tc_fun(_1820574, tc_HOL_Obool)), hAPP(c_COMBS(_1820572, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1820572), c_fconj), hAPP(hAPP(c_COMBC(_1820572, tc_fun(_1820572, tc_HOL_Obool), tc_HOL_Obool), c_member(_1820572)), _1820576)))), hAPP(hAPP(c_COMBC(tc_fun(_1820574, tc_HOL_Obool), tc_fun(_1820572, tc_fun(_1820574, tc_HOL_Obool)), tc_fun(_1820572, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820574, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1820572, tc_fun(_1820574, tc_HOL_Obool)), tc_fun(_1820572, tc_HOL_Obool)), tc_fun(_1820574, tc_HOL_Obool)), c_COMBB(tc_fun(_1820574, tc_HOL_Obool), tc_HOL_Obool, _1820572)), c_fequal)), _1820578))))))], (8702 ^ _779327) ^ [_918867, _918869, _918871] : [8703 ^ _779327 : [(8706 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918869), _918871))], (8704 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918867)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918867), _918869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918867), _918871))))], (10572 ^ _779327) ^ [_950666, _950668, _950670, _950672, _950674, _950676] : [class_Rings_Olinordered__semiring__1__strict(_950666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950666), _950668), _950670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950666), _950672), _950670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950666), c_Groups_Ozero__class_Ozero(_950666)), _950674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950666), c_Groups_Ozero__class_Ozero(_950666)), _950676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950666), _950674), _950676) = c_Groups_Oone__class_Oone(_950666), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950666), _950674), _950668)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950666), _950676), _950672))), _950670)))], (51318 ^ _779327) ^ [_1810398, _1810400, _1810402] : [hBOOL(hAPP(hAPP(c_member(_1810398), _1810400), hAPP(c_List_Oset(_1810398), _1810402))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1810398), _1810402), _1810400)))], (14457 ^ _779327) ^ [_1023161, _1023163] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1023161)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1023163)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023161), _1023163))], (7608 ^ _779327) ^ [_898934] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _898934) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48403 ^ _779327) ^ [_1747279, _1747281, _1747283] : [-(c_List_Oconcat(_1747279, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1747279)), _1747281), _1747283)) = hAPP(hAPP(c_List_Oappend(_1747279), _1747281), c_List_Oconcat(_1747279, _1747283)))], (43816 ^ _779327) ^ [_1637495, _1637497, _1637499, _1637501] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637495, tc_fun(_1637497, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637495, tc_HOL_Obool), _1637499)), _1637501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637495, tc_HOL_Obool), tc_fun(_1637497, tc_HOL_Obool)), _1637499), hAPP(hAPP(c_COMBC(tc_fun(_1637495, tc_HOL_Obool), tc_fun(_1637495, tc_fun(_1637497, tc_HOL_Obool)), tc_fun(_1637497, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637495, tc_fun(_1637497, tc_HOL_Obool))), _1637501)))], (29074 ^ _779327) ^ [_1297331, _1297333, _1297335, _1297337, _1297339] : [-(_1297331 = c_Orderings_Obot__class_Obot(tc_fun(_1297333, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1297335), _1297337), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297333, tc_fun(_1297335, tc_HOL_Obool)), _1297331), _1297339)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297333, tc_fun(_1297335, tc_HOL_Obool)), _1297331), hAPP(hAPP(c_COMBB(tc_fun(_1297335, tc_HOL_Obool), tc_fun(_1297335, tc_HOL_Obool), _1297333), hAPP(c_Set_Oinsert(_1297335), _1297337)), _1297339)))], (16527 ^ _779327) ^ [_1059404, _1059406] : [class_Groups_Oordered__ab__group__add__abs(_1059404), 16530 ^ _779327 : [(16537 ^ _779327) ^ [] : [-(_1059406 = c_Groups_Ozero__class_Ozero(_1059404)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059404), c_Groups_Ozero__class_Ozero(_1059404)), hAPP(c_Groups_Oabs__class_Oabs(_1059404), _1059406))))], (16531 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059404), c_Groups_Ozero__class_Ozero(_1059404)), hAPP(c_Groups_Oabs__class_Oabs(_1059404), _1059406))), _1059406 = c_Groups_Ozero__class_Ozero(_1059404)]]], (12409 ^ _779327) ^ [_985874, _985876] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985874), hAPP(c_Nat_OSuc, _985876)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985874), _985876)))], (51221 ^ _779327) ^ [_1807609, _1807611, _1807613] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807609)), c_List_Oreplicate(_1807609, _1807611, _1807613)) = _1807611)], (27064 ^ _779327) ^ [_1256945, _1256947, _1256949, _1256951, _1256953] : [class_Lattices_Osemilattice__sup(_1256945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256945), _1256947), _1256949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256945), _1256951), _1256953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256945), _1256947), _1256951)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256945), _1256949), _1256953))))], (36209 ^ _779327) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (18352 ^ _779327) ^ [] : [-(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)))))], (50102 ^ _779327) ^ [_1783771, _1783773, _1783775] : [-(hBOOL(hAPP(hAPP(c_member(_1783771), _1783773), hAPP(c_List_Oset(_1783771), _1783775)))), -(c_List_Oinsert(_1783771, _1783773, _1783775) = hAPP(hAPP(c_List_Olist_OCons(_1783771), _1783773), _1783775))], (49709 ^ _779327) ^ [_1775533, _1775535, _1775537] : [c_List_OtakeWhile(_1775533, _1775535, _1775537) = _1775537, 49712 ^ _779327 : [(49713 ^ _779327) ^ [_1775620] : [hBOOL(hAPP(hAPP(c_member(_1775533), _1775620), hAPP(c_List_Oset(_1775533), _1775537))), -(hBOOL(hAPP(_1775535, _1775620)))]]], (38972 ^ _779327) ^ [_1516574, _1516576] : [class_Lattices_Olattice(_1516574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516574), _1516576)), -(c_Big__Operators_Olattice__class_OSup__fin(_1516574, _1516576) = hAPP(c_Finite__Set_Ofold1(_1516574, c_Lattices_Osemilattice__sup__class_Osup(_1516574)), _1516576))], (49125 ^ _779327) ^ [_1763427, _1763429, _1763431, _1763433, _1763435] : [class_Orderings_Olinorder(_1763427), 49128 ^ _779327 : [(49135 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1763427, hAPP(hAPP(c_List_Omap(_1763429, _1763427), _1763431), _1763435)), -(c_List_Olinorder__class_Osorted(_1763427, hAPP(hAPP(c_List_Omap(_1763429, _1763427), _1763431), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1763429, _1763427, _1763431), _1763433), _1763435))))], (49129 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1763427, hAPP(hAPP(c_List_Omap(_1763429, _1763427), _1763431), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1763429, _1763427, _1763431), _1763433), _1763435))), -(c_List_Olinorder__class_Osorted(_1763427, hAPP(hAPP(c_List_Omap(_1763429, _1763427), _1763431), _1763435)))]]], (34593 ^ _779327) ^ [_1416041, _1416043, _1416045, _1416047] : [hBOOL(hAPP(_1416041, _1416043)), hBOOL(hAPP(_1416045, _1416043)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416047, tc_HOL_Obool)), _1416041), _1416045), _1416043)))], (44438 ^ _779327) ^ [_1651751, _1651753] : [-(c_FunDef_Ois__measure(_1651751, _1651753))], (22667 ^ _779327) ^ [_1171731, _1171733] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1171731), _1171733) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1171731, _1171733)))], (22763 ^ _779327) ^ [_1173538, _1173540, _1173542, _1173544] : [class_Orderings_Olinorder(_1173538), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173538), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173538), _1173540), _1173542)), _1173544) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173538), _1173540), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173538), _1173542), _1173544)))], (18528 ^ _779327) ^ [_1094021, _1094023, _1094025] : [class_Rings_Olinordered__idom(_1094021), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094021), c_Groups_Ozero__class_Ozero(_1094021)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094021), hAPP(hAPP(c_Power_Opower__class_Opower(_1094021), _1094023), 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(_1094021), _1094025), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (15213 ^ _779327) ^ [_1035572, _1035574, _1035576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035572), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 15216 ^ _779327 : [(15217 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1035574, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035576), _1035572)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1035576, _1035572))), 15220 ^ _779327 : [(15221 ^ _779327) ^ [_1035782, _1035784] : [-(hBOOL(hAPP(hAPP(_1035574, _1035784), _1035782))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035572), _1035782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035782), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1035576 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035572), _1035784)), _1035782)]]], (15235 ^ _779327) ^ [] : [15238 ^ _779327 : [(15241 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 15237 ^ [_1035572, _1035574, _1035576]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15243 ^ _779327) ^ [] : [-(_1035576 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1035572), 15236 ^ [_1035572, _1035574, _1035576])), 15237 ^ [_1035572, _1035574, _1035576]))], (15245 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1035574, 15236 ^ [_1035572, _1035574, _1035576]), 15237 ^ [_1035572, _1035574, _1035576]))], (15239 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035572), 15237 ^ [_1035572, _1035574, _1035576])))]], -(hBOOL(hAPP(hAPP(_1035574, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035576), _1035572)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1035576, _1035572))))]]], (40406 ^ _779327) ^ [_1556770, _1556772, _1556774, _1556776, _1556778, _1556780, _1556782] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556770, _1556772, _1556774), hAPP(hAPP(c_Relation_Orel__comp(_1556770, _1556776, _1556772), _1556778), _1556780)), _1556782) = hAPP(hAPP(c_Relation_Orel__comp(_1556770, _1556776, _1556774), _1556778), hAPP(hAPP(c_Relation_Orel__comp(_1556776, _1556772, _1556774), _1556780), _1556782)))], (43750 ^ _779327) ^ [_1635817, _1635819, _1635821, _1635823] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635817, tc_HOL_Obool), hAPP(c_Set_Oimage(_1635819, tc_fun(_1635817, tc_HOL_Obool), _1635821), _1635823)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635819, tc_fun(_1635817, tc_HOL_Obool)), _1635823), _1635821))], (25478 ^ _779327) ^ [_1224087, _1224089, _1224091] : [class_Groups_Ocomm__monoid__add(_1224087), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224087), _1224089), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1224091))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224087), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224087), _1224089), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1224091))), hAPP(_1224089, _1224091)))], (27474 ^ _779327) ^ [_1265351, _1265353, _1265355, _1265357] : [class_Orderings_Olinorder(_1265351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265351), _1265353), _1265355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265351), _1265355), _1265357)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265351, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1265351, _1265353, _1265355)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1265351, _1265355, _1265357)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1265351, _1265353, _1265357))], (30789 ^ _779327) ^ [_1335805, _1335807, _1335809, _1335811] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335805), _1335807)), hBOOL(hAPP(hAPP(c_member(_1335805), _1335809), _1335807)), hBOOL(hAPP(hAPP(c_member(_1335805), _1335811), _1335807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1335805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335805, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335805, tc_HOL_Obool)), _1335807), hAPP(hAPP(c_Set_Oinsert(_1335805), _1335809), c_Orderings_Obot__class_Obot(tc_fun(_1335805, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1335805), _1335811), c_Orderings_Obot__class_Obot(tc_fun(_1335805, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1335805), _1335807))))], (24447 ^ _779327) ^ [_1204845, _1204847, _1204849] : [class_Rings_Ocomm__semiring__1(_1204845), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204845), _1204847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204845), _1204849), _1204847))))], (31632 ^ _779327) ^ [_1354088, _1354090] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354088), _1354090)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354090, _1354088) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (26617 ^ _779327) ^ [_1247874] : [-(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)), _1247874)))], (33010 ^ _779327) ^ [_1380233, _1380235, _1380237, _1380239, _1380241, _1380243] : [-(_1380233 = _1380235), -(hAPP(c_Fun_Ofun__upd(_1380237, _1380239, _1380241, _1380235, _1380243), _1380233) = hAPP(_1380241, _1380233))], (47118 ^ _779327) ^ [_1719967] : [class_Groups_Omonoid__add(_1719967), -(c_List_Omonoid__add__class_Olistsum(_1719967) = c_List_Ofoldl(_1719967, _1719967, c_Groups_Oplus__class_Oplus(_1719967), c_Groups_Ozero__class_Ozero(_1719967)))], (33778 ^ _779327) ^ [_1396810, _1396812] : [c_Relation_Oirrefl(_1396810, _1396812), 33781 ^ _779327 : [(33782 ^ _779327) ^ [_1396892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1396810, _1396810)), hAPP(hAPP(c_Product__Type_OPair(_1396810, _1396810), _1396892), _1396892)), _1396812))]]], (45500 ^ _779327) ^ [_1681592, _1681594] : [_1681594 = c_List_Olist_ONil(_1681592), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681592)), _1681594) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7087 ^ _779327) ^ [_890194, _890196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890196)), _890194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890194), _890196))], (22229 ^ _779327) ^ [_1163554, _1163556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163556), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1163554), _1163556) = 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), _1163554), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163556)))))], (40605 ^ _779327) ^ [_1562517, _1562519, _1562521, _1562523] : [c_Wellfounded_Owf(_1562517, _1562519), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562517, _1562517)), hAPP(hAPP(c_Product__Type_OPair(_1562517, _1562517), _1562521), _1562523)), _1562519)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562517, _1562517)), hAPP(hAPP(c_Product__Type_OPair(_1562517, _1562517), _1562523), _1562521)), _1562519))], (48482 ^ _779327) ^ [_1749186, _1749188, _1749190] : [48484 ^ _779327 : [(48487 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1749186), tc_List_Olist(_1749186), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1749186), tc_fun(tc_List_Olist(_1749186), tc_Nat_Onat), tc_fun(tc_List_Olist(_1749186), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1749186), tc_Nat_Onat), tc_fun(tc_List_Olist(_1749186), tc_HOL_Obool)), tc_List_Olist(_1749186)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1749186))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1749186)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1749186))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1749186)))), 48483 ^ [_1749186, _1749188, _1749190]))], (48485 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749186), tc_List_Olist(_1749186))), 48483 ^ [_1749186, _1749188, _1749190]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1749186), tc_List_Olist(_1749186))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1749186), tc_List_Olist(_1749186)), _1749188), _1749190)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1749186))), _1749188) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1749186))), _1749190), 48492 ^ _779327 : [(48499 ^ _779327) ^ [] : [_1749188 = _1749190, -(c_List_Oconcat(_1749186, _1749188) = c_List_Oconcat(_1749186, _1749190))], (48493 ^ _779327) ^ [] : [c_List_Oconcat(_1749186, _1749188) = c_List_Oconcat(_1749186, _1749190), -(_1749188 = _1749190)]]], (51141 ^ _779327) ^ [_1806126, _1806128, _1806130, _1806132, _1806134] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806126, _1806128, _1806130), _1806132), _1806134)), -(hBOOL(hAPP(hAPP(_1806130, _1806134), _1806132)))], (18090 ^ _779327) ^ [_1086487] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1086487)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1086487)))], (29909 ^ _779327) ^ [_1313948, _1313950, _1313952] : [_1313950 = _1313952, -(hAPP(hAPP(c_COMBC(_1313948, tc_fun(_1313948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1313948)), _1313950) = hAPP(hAPP(c_COMBC(_1313948, tc_fun(_1313948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1313948)), _1313952))], (15333 ^ _779327) ^ [_1037913, _1037915, _1037917, _1037919] : [class_Divides_Osemiring__div(_1037913), -(c_Divides_Odiv__class_Omod(_1037913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037913), _1037915), _1037917), _1037919) = c_Divides_Odiv__class_Omod(_1037913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037913), _1037915), c_Divides_Odiv__class_Omod(_1037913, _1037917, _1037919)), _1037919))], (42488 ^ _779327) ^ [_1607249, _1607251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1607249), _1607251)), -(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), _1607249), _1607251)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (25209 ^ _779327) ^ [_1218749, _1218751, _1218753] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218749), _1218751)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218749), _1218753))), -(_1218749 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218751), _1218753)))], (8618 ^ _779327) ^ [_917326, _917328, _917330] : [class_Rings_Olinordered__semidom(_917326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917326), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917326), _917328)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917326), _917330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917328), _917330)))], (10939 ^ _779327) ^ [_957706, _957708, _957710, _957712] : [class_Groups_Ocancel__ab__semigroup__add(_957706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957706), _957708), _957710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957706), _957708), _957712), -(_957710 = _957712)], (27593 ^ _779327) ^ [_1268009, _1268011, _1268013, _1268015, _1268017, _1268019] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268009, tc_fun(_1268011, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268013, tc_fun(_1268009, tc_HOL_Obool)), _1268015), _1268017)), _1268019) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268013, tc_fun(_1268011, tc_HOL_Obool)), _1268015), hAPP(hAPP(c_COMBC(_1268013, tc_fun(_1268009, tc_fun(_1268011, tc_HOL_Obool)), tc_fun(_1268011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268009, tc_HOL_Obool), tc_fun(tc_fun(_1268009, tc_fun(_1268011, tc_HOL_Obool)), tc_fun(_1268011, tc_HOL_Obool)), _1268013), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268009, tc_fun(_1268011, tc_HOL_Obool))), _1268017)), _1268019)))], (36835 ^ _779327) ^ [_1466490, _1466492, _1466494, _1466496] : [c_Fun_Oinj__on(_1466490, _1466492, _1466494, _1466496), 36838 ^ _779327 : [(36839 ^ _779327) ^ [_1466598] : [hBOOL(hAPP(hAPP(c_member(_1466490), _1466598), _1466496)), 36842 ^ _779327 : [(36843 ^ _779327) ^ [_1466700] : [hBOOL(hAPP(hAPP(c_member(_1466490), _1466700), _1466496)), hAPP(_1466494, _1466598) = hAPP(_1466494, _1466700), -(_1466598 = _1466700)]]]]], (17092 ^ _779327) ^ [_1069484, _1069486, _1069488, _1069490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069486), _1069488)), -(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), _1069488), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1069490, _1069484))), _1069486)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069488), _1069484))))], (48951 ^ _779327) ^ [_1760787, _1760789] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1760787, _1760789)))], (52998 ^ _779327) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (49816 ^ _779327) ^ [_1777682, _1777684, _1777686] : [hBOOL(hAPP(c_List_Odistinct(_1777682), _1777684)), hBOOL(hAPP(hAPP(c_member(_1777682), _1777686), hAPP(c_List_Oset(_1777682), _1777684))), -(c_List_OtakeWhile(_1777682, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777682), c_fNot), hAPP(hAPP(c_COMBC(_1777682, _1777682, tc_HOL_Obool), c_fequal), _1777686)), hAPP(c_List_Orev(_1777682), _1777684)) = hAPP(c_List_Orev(_1777682), hAPP(c_List_Otl(_1777682), c_List_OdropWhile(_1777682, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777682), c_fNot), hAPP(hAPP(c_COMBC(_1777682, _1777682, tc_HOL_Obool), c_fequal), _1777686)), _1777684))))], (51165 ^ _779327) ^ [_1806616, _1806618, _1806620, _1806622, _1806624] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806616, _1806618, _1806620), _1806622), _1806624)), -(hBOOL(hAPP(hAPP(_1806620, _1806624), _1806622)))], (9757 ^ _779327) ^ [_937484] : [class_Rings_Ozero__neq__one(_937484), c_Groups_Oone__class_Oone(_937484) = c_Groups_Ozero__class_Ozero(_937484)], (7622 ^ _779327) ^ [_899224, _899226, _899228] : [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, _899224)), _899226)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899224)), _899228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _899226), _899228)))], (7616 ^ _779327) ^ [_899089, _899091, _899093] : [_899091 = _899093, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899089)), _899091) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899089)), _899093))], (10765 ^ _779327) ^ [_954505, _954507, _954509] : [class_Int_Onumber__ring(_954505), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954505), hAPP(c_Int_Onumber__class_Onumber__of(_954505), _954507)), hAPP(c_Int_Onumber__class_Onumber__of(_954505), _954509)) = hAPP(c_Int_Onumber__class_Onumber__of(_954505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _954507), _954509)))], (8822 ^ _779327) ^ [_921185, _921187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _921185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _921187)), -(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), _921187), _921185))))], (40013 ^ _779327) ^ [_1542395, _1542397] : [-(hAPP(c_Set_OPow(_1542395), _1542397) = hAPP(c_Set_OCollect(tc_fun(_1542395, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1542395, tc_HOL_Obool), tc_fun(_1542395, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1542395, tc_HOL_Obool))), _1542397)))], (43822 ^ _779327) ^ [_1637758, _1637760, _1637762] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1637758, tc_HOL_Obool)), _1637760), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637758, tc_HOL_Obool), _1637762)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637758, tc_HOL_Obool), tc_fun(_1637758, tc_HOL_Obool)), _1637762), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1637758, tc_HOL_Obool)), _1637760)))], (18074 ^ _779327) ^ [_1086193, _1086195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086193)), c_Int_OBit0(_1086195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086193), _1086195)))], (26460 ^ _779327) ^ [_1245243, _1245245, _1245247] : [class_Groups_Oordered__ab__group__add(_1245243), -(hAPP(c_Set_Oimage(_1245243, _1245243, c_Groups_Ouminus__class_Ouminus(_1245243)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1245243, _1245245), _1245247)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1245243, hAPP(c_Groups_Ouminus__class_Ouminus(_1245243), _1245247), hAPP(c_Groups_Ouminus__class_Ouminus(_1245243), _1245245)))], (10509 ^ _779327) ^ [_949502, _949504] : [-(hBOOL(hAPP(_949502, hAPP(c_Int_Onat, _949504)))), 10513 ^ _779327 : [(10516 ^ _779327) ^ [] : [hBOOL(hAPP(_949502, 10512 ^ [_949502, _949504]))], (10514 ^ _779327) ^ [] : [-(_949504 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 10512 ^ [_949502, _949504]))]], 10517 ^ _779327 : [(10520 ^ _779327) ^ [] : [hBOOL(hAPP(_949502, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10518 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949504), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (46528 ^ _779327) ^ [_1707177, _1707179] : [hAPP(c_List_Orotate1(_1707177), _1707179) = c_List_Olist_ONil(_1707177), -(_1707179 = c_List_Olist_ONil(_1707177))], (2580 ^ _779327) ^ [_817210, _817212] : [_817212 = _817210, -(c_DSequence_Oempty(_817212) = c_DSequence_Oempty(_817210))], (5538 ^ _779327) ^ [_863815, _863817, _863819, _863821, _863823, _863825] : [-(c_COMBC(_863825, _863821, _863817) = c_COMBC(_863823, _863819, _863815)), _863825 = _863823, _863821 = _863819, _863817 = _863815], (51620 ^ _779327) ^ [_1817054, _1817056] : [c_Relation_Otrans(_1817054, _1817056), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1817054, _1817054), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1817054, _1817054, _1817054), _1817056), _1817056)), _1817056)))], (42605 ^ _779327) ^ [_1610168, _1610170] : [c_Wellfounded_Owf(_1610168, hAPP(c_Relation_Oconverse(_1610168, _1610168), _1610170)), -(c_Wellfounded_Owf(_1610168, hAPP(c_Relation_Oconverse(_1610168, _1610168), c_Transitive__Closure_Otrancl(_1610168, _1610170))))], (9138 ^ _779327) ^ [_927020, _927022, _927024] : [_927020 = _927022, 9141 ^ _779327 : [(9144 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927024, tc_HOL_Obool)), _927022), _927020)))], (9142 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927024, tc_HOL_Obool)), _927020), _927022)))]]], (51159 ^ _779327) ^ [_1806479, _1806481, _1806483, _1806485, _1806487] : [hBOOL(hAPP(hAPP(_1806483, _1806487), _1806485)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806479, _1806481, _1806483), _1806485), _1806487)))], (25293 ^ _779327) ^ [_1220353, _1220355, _1220357] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220353, _1220355) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220357, _1220355), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220353), _1220357))))], (40210 ^ _779327) ^ [_1550322, _1550324, _1550326, _1550328, _1550330, _1550332, _1550334] : [class_Rings_Osemiring__0(_1550322), c_Fun_Oinj__on(tc_prod(_1550324, _1550326), _1550322, hAPP(c_Product__Type_Oprod_Oprod__case(_1550324, _1550326, _1550322), hAPP(hAPP(c_COMBC(_1550324, tc_fun(_1550326, _1550322), tc_fun(_1550326, _1550322)), hAPP(hAPP(c_COMBB(tc_fun(_1550322, _1550322), tc_fun(tc_fun(_1550326, _1550322), tc_fun(_1550326, _1550322)), _1550324), c_COMBB(_1550322, _1550322, _1550326)), hAPP(hAPP(c_COMBB(_1550322, tc_fun(_1550322, _1550322), _1550324), c_Groups_Otimes__class_Otimes(_1550322)), _1550328))), _1550330)), hAPP(hAPP(c_Product__Type_OSigma(_1550324, _1550326), _1550332), hAPP(c_COMBK(tc_fun(_1550326, tc_HOL_Obool), _1550324), _1550334))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1550322), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550324, _1550322), _1550328), _1550332)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550326, _1550322), _1550330), _1550334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550322, _1550322), c_Fun_Oid(_1550322)), hAPP(c_Set_OCollect(_1550322), hAPP(hAPP(c_COMBB(tc_fun(_1550324, tc_HOL_Obool), tc_HOL_Obool, _1550322), c_HOL_OEx(_1550324)), hAPP(hAPP(c_COMBB(tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool)), tc_fun(_1550324, tc_HOL_Obool), _1550322), hAPP(c_COMBB(tc_fun(_1550326, tc_HOL_Obool), tc_HOL_Obool, _1550324), c_HOL_OEx(_1550326))), hAPP(hAPP(c_COMBC(_1550322, tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool)), tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1550324, tc_fun(tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool))), tc_fun(tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool)), tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool))), _1550322), c_COMBS(_1550324, tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1550324, tc_fun(_1550326, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1550324, tc_fun(tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool))), _1550322), hAPP(c_COMBB(tc_fun(_1550326, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool)), _1550324), c_COMBS(_1550326, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool)), tc_fun(_1550324, tc_fun(_1550326, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1550322), hAPP(c_COMBB(tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1550324), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550326), c_fconj))), hAPP(hAPP(c_COMBC(_1550322, tc_fun(_1550324, tc_fun(_1550326, _1550322)), tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550326, _1550322), tc_fun(_1550326, tc_HOL_Obool)), tc_fun(tc_fun(_1550324, tc_fun(_1550326, _1550322)), tc_fun(_1550324, tc_fun(_1550326, tc_HOL_Obool))), _1550322), c_COMBB(tc_fun(_1550326, _1550322), tc_fun(_1550326, tc_HOL_Obool), _1550324)), hAPP(hAPP(c_COMBB(tc_fun(_1550322, tc_HOL_Obool), tc_fun(tc_fun(_1550326, _1550322), tc_fun(_1550326, tc_HOL_Obool)), _1550322), c_COMBB(_1550322, tc_HOL_Obool, _1550326)), c_fequal))), hAPP(hAPP(c_COMBC(_1550324, tc_fun(_1550326, _1550322), tc_fun(_1550326, _1550322)), hAPP(hAPP(c_COMBB(tc_fun(_1550322, _1550322), tc_fun(tc_fun(_1550326, _1550322), tc_fun(_1550326, _1550322)), _1550324), c_COMBB(_1550322, _1550322, _1550326)), hAPP(hAPP(c_COMBB(_1550322, tc_fun(_1550322, _1550322), _1550324), c_Groups_Otimes__class_Otimes(_1550322)), _1550328))), _1550330)))))), hAPP(hAPP(c_COMBC(_1550324, tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1550326, tc_HOL_Obool), tc_fun(_1550326, tc_HOL_Obool)), _1550324), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1550326)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550324), c_fconj), hAPP(hAPP(c_COMBC(_1550324, tc_fun(_1550324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550324)), _1550332)))), hAPP(hAPP(c_COMBC(_1550326, tc_fun(_1550326, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550326)), _1550334))))))))], (51626 ^ _779327) ^ [_1817192, _1817194] : [-(hBOOL(hAPP(_1817194, 51633 ^ [_1817192, _1817194]))), 51627 ^ _779327 : [(51628 ^ _779327) ^ [_1817253] : [hBOOL(hAPP(hAPP(c_member(_1817192), _1817253), c_Orderings_Otop__class_Otop(tc_fun(_1817192, tc_HOL_Obool)))), hBOOL(hAPP(_1817194, _1817253))]]], (35723 ^ _779327) ^ [_1441411, _1441413, _1441415, _1441417, _1441419] : [c_Finite__Set_Ofolding__one(_1441411, _1441413, _1441415), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441411), _1441417)), -(_1441417 = c_Orderings_Obot__class_Obot(tc_fun(_1441411, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441411), _1441419)), -(_1441419 = c_Orderings_Obot__class_Obot(tc_fun(_1441411, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441411, tc_HOL_Obool)), _1441417), _1441419) = c_Orderings_Obot__class_Obot(tc_fun(_1441411, tc_HOL_Obool)), -(hAPP(_1441415, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441411, tc_HOL_Obool)), _1441417), _1441419)) = hAPP(hAPP(_1441413, hAPP(_1441415, _1441417)), hAPP(_1441415, _1441419)))], (34633 ^ _779327) ^ [_1417063, _1417065, _1417067, _1417069, _1417071] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417063, tc_HOL_Obool)), _1417065), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417067, tc_fun(_1417063, tc_HOL_Obool)), _1417069), _1417071)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417067, tc_fun(_1417063, tc_HOL_Obool)), _1417069), hAPP(hAPP(c_COMBB(tc_fun(_1417063, tc_HOL_Obool), tc_fun(_1417063, tc_HOL_Obool), _1417067), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417063, tc_HOL_Obool)), _1417065)), _1417071)))], (21732 ^ _779327) ^ [_1153552, _1153554] : [-(_1153552 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153554, _1153552), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1153554), _1153552)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1153554, _1153552)))))], (10907 ^ _779327) ^ [_957189, _957191] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957189), _957191)), _957191) = _957189)], (21806 ^ _779327) ^ [_1155036, _1155038] : [_1155036 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1155036, _1155038) = 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)))], (41799 ^ _779327) ^ [_1590254, _1590256, _1590258] : [-(c_Hilbert__Choice_OEps(tc_prod(_1590254, _1590256), _1590258) = c_Hilbert__Choice_OEps(tc_prod(_1590254, _1590256), hAPP(c_Product__Type_Oprod_Oprod__case(_1590254, _1590256, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1590256, tc_prod(_1590254, _1590256)), tc_fun(_1590256, tc_HOL_Obool), _1590254), hAPP(c_COMBB(tc_prod(_1590254, _1590256), tc_HOL_Obool, _1590256), _1590258)), c_Product__Type_OPair(_1590254, _1590256)))))], (5514 ^ _779327) ^ [_863445, _863447, _863449, _863451] : [-(c_COMBK(_863451, _863447) = c_COMBK(_863449, _863445)), _863451 = _863449, _863447 = _863445], (5190 ^ _779327) ^ [_858483, _858485, _858487, _858489] : [-(c_Complete__Lattice_OSup__class_OSup(_858489, _858485) = c_Complete__Lattice_OSup__class_OSup(_858487, _858483)), _858489 = _858487, _858485 = _858483], (28731 ^ _779327) ^ [_1291472, _1291474, _1291476, _1291478] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291472, tc_fun(_1291474, tc_HOL_Obool)), _1291476), _1291478) = c_Orderings_Obot__class_Obot(tc_fun(_1291474, tc_HOL_Obool)), 28734 ^ _779327 : [(28735 ^ _779327) ^ [_1291588] : [hBOOL(hAPP(hAPP(c_member(_1291472), _1291588), _1291476)), -(hAPP(_1291478, _1291588) = c_Orderings_Obot__class_Obot(tc_fun(_1291474, tc_HOL_Obool)))]]], (17494 ^ _779327) ^ [_1076273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1076273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1076273))))], (44472 ^ _779327) ^ [_1653211, _1653213, _1653215] : [_1653211 = hAPP(hAPP(c_List_Olist_OCons(_1653213), _1653215), _1653211)], (38952 ^ _779327) ^ [_1516206, _1516208, _1516210, _1516212] : [-(_1516206 = c_Orderings_Obot__class_Obot(tc_fun(_1516208, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1516210, _1516208), _1516210, c_Product__Type_Ofst(_1516210, _1516208)), hAPP(hAPP(c_Product__Type_OSigma(_1516210, _1516208), _1516212), hAPP(c_COMBK(tc_fun(_1516208, tc_HOL_Obool), _1516210), _1516206))) = _1516212)], (544 ^ _779327) ^ [_787673, _787675, _787677, _787679, _787681, _787683, _787685, _787687] : [-(c_Finite__Set_Ofolding__idem(_787685, _787681, _787677, _787673)), c_Finite__Set_Ofolding__idem(_787687, _787683, _787679, _787675), _787687 = _787685, _787683 = _787681, _787679 = _787677, _787675 = _787673], (45514 ^ _779327) ^ [_1681904, _1681906, _1681908] : [-(hAPP(hAPP(c_List_Ozip(_1681904, _1681906), _1681908), c_List_Olist_ONil(_1681906)) = c_List_Olist_ONil(tc_prod(_1681904, _1681906)))], (7192 ^ _779327) ^ [_891925, _891927, _891929, _891931] : [class_Orderings_Oorder(_891925), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891925), hAPP(_891927, 7197 ^ [_891925, _891927, _891929, _891931])), hAPP(_891927, hAPP(c_Nat_OSuc, 7197 ^ [_891925, _891927, _891929, _891931])))), 7200 ^ _779327 : [(7207 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891929), _891931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891925), hAPP(_891927, _891929)), hAPP(_891927, _891931))))], (7201 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891925), hAPP(_891927, _891929)), hAPP(_891927, _891931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891929), _891931)))]]], (45139 ^ _779327) ^ [_1672520, _1672522, _1672524, _1672526, _1672528] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1672520), tc_List_Olist(_1672522), tc_List_Olist(_1672524), hAPP(c_List_Omap(_1672520, _1672522), _1672526)), hAPP(c_List_Omap(_1672524, _1672520), _1672528)) = hAPP(c_List_Omap(_1672524, _1672522), hAPP(c_Fun_Ocomp(_1672520, _1672522, _1672524, _1672526), _1672528)))], (52638 ^ _779327) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (17526 ^ _779327) ^ [_1076824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1076824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1076824)))], (42302 ^ _779327) ^ [_1602913, _1602915] : [-(hAPP(c_Relation_OImage(_1602913, _1602913, c_Relation_OId(_1602913)), _1602915) = _1602915)], (44703 ^ _779327) ^ [_1660358, _1660360, _1660362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1660358, _1660358), tc_HOL_Obool)), _1660360), _1660362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1660358), tc_List_Olist(_1660358)), tc_HOL_Obool)), c_List_Olistrel(_1660358, _1660360)), c_List_Olistrel(_1660358, _1660362))))], (4398 ^ _779327) ^ [_846221, _846223] : [_846223 = _846221, -(c_List_Oreturn__list(_846223) = c_List_Oreturn__list(_846221))], (12918 ^ _779327) ^ [_995208, _995210] : [class_Groups_Olinordered__ab__group__add(_995208), 12921 ^ _779327 : [(12928 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995208), c_Groups_Ozero__class_Ozero(_995208)), _995210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995208), hAPP(c_Groups_Ouminus__class_Ouminus(_995208), _995210)), _995210)))], (12922 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995208), hAPP(c_Groups_Ouminus__class_Ouminus(_995208), _995210)), _995210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995208), c_Groups_Ozero__class_Ozero(_995208)), _995210)))]]], (36458 ^ _779327) ^ [_1459626, _1459628, _1459630, _1459632, _1459634] : [c_Relation_Orefl__on(_1459626, _1459628, _1459630), c_Relation_Orefl__on(_1459626, _1459632, _1459634), -(c_Relation_Orefl__on(_1459626, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459626, tc_HOL_Obool)), _1459628), _1459632), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1459626, _1459626), tc_HOL_Obool)), _1459630), _1459634)))], (9733 ^ _779327) ^ [_937174] : [class_Rings_Osemiring__1(_937174), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_937174), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_937174))], (15758 ^ _779327) ^ [_1045880, _1045882] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045880, _1045882) = 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), _1045880), _1045882) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27520 ^ _779327) ^ [_1266248, _1266250, _1266252, _1266254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266248, _1266250)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266252, _1266254)))), 27521 ^ _779327 : [(27524 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266252), _1266248)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266250), _1266254))], (27522 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266248), _1266250)))]]], (10655 ^ _779327) ^ [_952237, _952239] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952237) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _952239), 10658 ^ _779327 : [(10661 ^ _779327) ^ [] : [-(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), _952239))))], (10659 ^ _779327) ^ [] : [-(_952237 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _952239)))]]], (24529 ^ _779327) ^ [_1206335, _1206337, _1206339] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206335), _1206337)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206335), _1206339)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206337), _1206339))))], (38210 ^ _779327) ^ [_1496886, _1496888, _1496890, _1496892, _1496894] : [-(_1496886 = c_Orderings_Obot__class_Obot(tc_fun(_1496888, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496888, tc_fun(_1496890, tc_HOL_Obool)), _1496886), hAPP(hAPP(c_COMBB(tc_fun(_1496890, tc_HOL_Obool), tc_fun(_1496890, tc_HOL_Obool), _1496888), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1496890, tc_HOL_Obool)), _1496892)), _1496894)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1496890, tc_HOL_Obool)), _1496892), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1496888, tc_fun(_1496890, tc_HOL_Obool)), _1496886), _1496894)))], (52852 ^ _779327) ^ [_1838846, _1838848] : [-(class_Enum_Oenum(tc_sum(_1838846, _1838848))), class_Enum_Oenum(_1838846), class_Enum_Oenum(_1838848)], (50985 ^ _779327) ^ [_1803233, _1803235, _1803237] : [-(c_List_Osplice(_1803233, hAPP(hAPP(c_List_Olist_OCons(_1803233), _1803235), _1803237), c_List_Olist_ONil(_1803233)) = hAPP(hAPP(c_List_Olist_OCons(_1803233), _1803235), _1803237))], (45137 ^ _779327) ^ [_1672449, _1672451, _1672453, _1672455, _1672457] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1672449), tc_List_Olist(_1672451), tc_List_Olist(_1672453), hAPP(c_List_Omap(_1672449, _1672451), _1672455)), hAPP(c_List_Omap(_1672453, _1672449), _1672457)) = hAPP(c_List_Omap(_1672453, _1672451), hAPP(c_Fun_Ocomp(_1672449, _1672451, _1672453, _1672455), _1672457)))], (50660 ^ _779327) ^ [_1796513, _1796515, _1796517] : [c_List_Olist__ex(_1796513, _1796515, hAPP(c_List_Orev(_1796513), _1796517)), -(c_List_Olist__ex(_1796513, _1796515, _1796517))], (10763 ^ _779327) ^ [_954459, _954461] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _954459)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _954461)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _954459), _954461)))], (48141 ^ _779327) ^ [_1741669, _1741671, _1741673, _1741675, _1741677, _1741679] : [c_List_Olist__all2(_1741669, _1741671, _1741673, _1741675, _1741677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741679), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741671)), _1741677))), -(hBOOL(hAPP(hAPP(_1741673, hAPP(hAPP(c_List_Onth(_1741669), _1741675), _1741679)), hAPP(hAPP(c_List_Onth(_1741671), _1741677), _1741679))))], (1418 ^ _779327) ^ [_800040, _800042] : [-(class_Lattices_Obounded__lattice__top(_800040)), _800042 = _800040, class_Lattices_Obounded__lattice__top(_800042)], (35653 ^ _779327) ^ [_1439884, _1439886, _1439888, _1439890, _1439892] : [class_Groups_Ocomm__monoid__add(_1439884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439886), _1439888)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439886, _1439884), _1439890), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439886, tc_HOL_Obool)), _1439888), _1439892)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439886, _1439884), hAPP(hAPP(c_COMBC(_1439886, _1439884, _1439884), hAPP(hAPP(c_COMBS(_1439886, _1439884, tc_fun(_1439884, _1439884)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1439884, tc_fun(_1439884, _1439884)), _1439886), c_If(_1439884)), hAPP(hAPP(c_COMBC(_1439886, tc_fun(_1439886, tc_HOL_Obool), tc_HOL_Obool), c_member(_1439886)), _1439892))), _1439890)), c_Groups_Ozero__class_Ozero(_1439884))), _1439888))], (51991 ^ _779327) ^ [_1825783] : [-(c_Relation_Oantisym(_1825783, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1825783, _1825783), tc_HOL_Obool))))], (29676 ^ _779327) ^ [_1309534, _1309536] : [hBOOL(hAPP(hAPP(c_member(_1309534), _1309536), c_Orderings_Obot__class_Obot(tc_fun(_1309534, tc_HOL_Obool))))], (17800 ^ _779327) ^ [_1081210, _1081212] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081210))), _1081212) = 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)))), _1081210), _1081212))], (43507 ^ _779327) ^ [_1631022] : [class_Groups_Oab__semigroup__mult(_1631022), -(c_Finite__Set_Ofun__left__comm(_1631022, _1631022, c_Groups_Otimes__class_Otimes(_1631022)))], (35291 ^ _779327) ^ [_1431627, _1431629, _1431631] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431627, tc_HOL_Obool)), _1431629), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431627, tc_HOL_Obool)), _1431631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431627, tc_HOL_Obool)), _1431629), _1431631))], (48307 ^ _779327) ^ [_1745393, _1745395] : [c_List_Oremdups(_1745393, _1745395) = _1745395, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745393)), c_List_Oremdups(_1745393, _1745395)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745393)), _1745395))], (39774 ^ _779327) ^ [_1534115, _1534117, _1534119] : [hBOOL(hAPP(_1534119, _1534117)), -(hBOOL(hAPP(hAPP(c_member(_1534115), _1534117), hAPP(c_Set_OCollect(_1534115), _1534119))))], (22781 ^ _779327) ^ [_1173967, _1173969, _1173971, _1173973] : [class_Orderings_Olinorder(_1173967), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173967), _1173969), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173967), _1173971), _1173973)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173967), _1173971), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173967), _1173969), _1173973)))], (46339 ^ _779327) ^ [_1701943, _1701945, _1701947, _1701949, _1701951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701943), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701945)), _1701947))), 46342 ^ _779327 : [(46349 ^ _779327) ^ [] : [-(_1701943 = _1701949), -(hAPP(hAPP(c_List_Onth(_1701945), hAPP(hAPP(c_List_Olist__update(_1701945, _1701947), _1701943), _1701951)), _1701949) = hAPP(hAPP(c_List_Onth(_1701945), _1701947), _1701949))], (46343 ^ _779327) ^ [] : [_1701943 = _1701949, -(hAPP(hAPP(c_List_Onth(_1701945), hAPP(hAPP(c_List_Olist__update(_1701945, _1701947), _1701943), _1701951)), _1701949) = _1701951)]]], (1698 ^ _779327) ^ [_803540, _803542] : [-(class_Groups_Oab__semigroup__add(_803540)), _803542 = _803540, class_Groups_Oab__semigroup__add(_803542)], (2274 ^ _779327) ^ [_812427, _812429, _812431, _812433, _812435, _812437, _812439, _812441, _812443, _812445] : [-(c_Product__Type_Oprod_Oprod__rec(_812445, _812441, _812437, _812433, _812429) = c_Product__Type_Oprod_Oprod__rec(_812443, _812439, _812435, _812431, _812427)), _812445 = _812443, _812441 = _812439, _812437 = _812435, _812433 = _812431, _812429 = _812427], (48074 ^ _779327) ^ [_1739870, _1739872, _1739874, _1739876, _1739878, _1739880, _1739882] : [c_List_Olist__all2(_1739870, _1739872, _1739874, hAPP(hAPP(c_List_Omap(_1739876, _1739870), _1739878), _1739880), _1739882), -(c_List_Olist__all2(_1739876, _1739872, hAPP(hAPP(c_COMBB(_1739870, tc_fun(_1739872, tc_HOL_Obool), _1739876), _1739874), _1739878), _1739880, _1739882))], (7145 ^ _779327) ^ [_891152] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _891152)], (24463 ^ _779327) ^ [_1205131, _1205133, _1205135, _1205137] : [class_Rings_Ocomm__semiring__1(_1205131), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205131), _1205133), _1205135)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205131), _1205133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205131), _1205137), _1205135))))], (9222 ^ _779327) ^ [_928549, _928551, _928553] : [_928549 = _928551, 9225 ^ _779327 : [(9228 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928553, tc_HOL_Obool)), _928551), _928549)))], (9226 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928553, tc_HOL_Obool)), _928549), _928551)))]]], (22799 ^ _779327) ^ [_1174360, _1174362, _1174364] : [class_Orderings_Olinorder(_1174360), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174360), _1174362), _1174364) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174360), _1174364), _1174362))], (20979 ^ _779327) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (16685 ^ _779327) ^ [_1062331, _1062333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062333, _1062331)), _1062331)))], (8890 ^ _779327) ^ [_922316, _922318, _922320] : [class_Rings_Ocomm__semiring__1(_922316), -(hAPP(hAPP(c_Power_Opower__class_Opower(_922316), _922318), hAPP(c_Nat_OSuc, _922320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922316), _922318), hAPP(hAPP(c_Power_Opower__class_Opower(_922316), _922318), _922320)))], (39626 ^ _779327) ^ [_1531038, _1531040, _1531042, _1531044, _1531046] : [c_Finite__Set_Ofun__left__comm__idem(_1531038, _1531040, _1531042), -(c_Finite__Set_Ofun__left__comm__idem(_1531044, _1531040, hAPP(hAPP(c_COMBB(_1531038, tc_fun(_1531040, _1531040), _1531044), _1531042), _1531046)))], (38469 ^ _779327) ^ [_1504021, _1504023, _1504025, _1504027] : [c_Fun_Oinj__on(_1504021, _1504023, _1504025, c_Orderings_Otop__class_Otop(tc_fun(_1504021, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1504021, _1504023, _1504025), hAPP(c_Set_Oimage(_1504021, _1504023, _1504025), _1504027)) = _1504027)], (27677 ^ _779327) ^ [_1270326, _1270328, _1270330, _1270332, _1270334, _1270336] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270326, tc_fun(_1270328, tc_HOL_Obool)), _1270330), hAPP(hAPP(c_COMBB(_1270332, tc_fun(_1270328, tc_HOL_Obool), _1270326), _1270334), _1270336)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270332, tc_fun(_1270328, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1270326, _1270332, _1270336), _1270330)), _1270334))], (26428 ^ _779327) ^ [_1244624, _1244626] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244624), _1244626) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1244624, _1244626))], (43435 ^ _779327) ^ [_1629602, _1629604, _1629606] : [class_Orderings_Olinorder(_1629602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629602), _1629604)), -(hBOOL(hAPP(hAPP(c_member(_1629602), _1629606), _1629604))), -(c_Big__Operators_Olinorder__class_OMax(_1629602, hAPP(hAPP(c_Set_Oinsert(_1629602), _1629606), _1629604)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629602, _1629602, c_Orderings_Oord__class_Omax(_1629602)), _1629606), _1629604))], (46182 ^ _779327) ^ [_1698151, _1698153, _1698155, _1698157, _1698159, _1698161] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1698151, _1698153), hAPP(hAPP(c_List_Ozip(_1698151, _1698153), _1698155), _1698157)), _1698159), _1698161) = hAPP(hAPP(c_List_Ozip(_1698151, _1698153), hAPP(hAPP(c_List_Olist__update(_1698151, _1698155), _1698159), hAPP(c_Product__Type_Ofst(_1698151, _1698153), _1698161))), hAPP(hAPP(c_List_Olist__update(_1698153, _1698157), _1698159), hAPP(c_Product__Type_Osnd(_1698151, _1698153), _1698161))))], (51471 ^ _779327) ^ [_1813939, _1813941, _1813943, _1813945, _1813947, _1813949, _1813951] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1813939, tc_fun(_1813941, tc_fun(_1813943, tc_HOL_Obool))), _1813945), _1813947), _1813949), _1813951)), 51475 ^ _779327 : [(51478 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1813947, 51474 ^ [_1813939, _1813941, _1813943, _1813945, _1813947, _1813949, _1813951]), _1813949), _1813951)))], (51476 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813939), 51474 ^ [_1813939, _1813941, _1813943, _1813945, _1813947, _1813949, _1813951]), _1813945)))]]], (35499 ^ _779327) ^ [_1436135, _1436137, _1436139, _1436141, _1436143] : [class_Orderings_Olinorder(_1436135), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436135, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1436135, _1436137, _1436139)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1436135, _1436141, _1436143)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1436135, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1436135), _1436137), _1436141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1436135), _1436139), _1436143)))], (42514 ^ _779327) ^ [_1607820, _1607822, _1607824, _1607826, _1607828] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607820, _1607820)), hAPP(hAPP(c_Product__Type_OPair(_1607820, _1607820), hAPP(_1607822, hAPP(c_Nat_OSuc, 42515 ^ [_1607820, _1607822, _1607824, _1607826, _1607828]))), hAPP(_1607822, 42515 ^ [_1607820, _1607822, _1607824, _1607826, _1607828]))), c_Transitive__Closure_Ortrancl(_1607820, _1607824))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607820, _1607820)), hAPP(hAPP(c_Product__Type_OPair(_1607820, _1607820), hAPP(_1607822, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1607826), _1607828))), hAPP(_1607822, _1607826))), c_Transitive__Closure_Ortrancl(_1607820, _1607824))))], (48758 ^ _779327) ^ [_1756964, _1756966, _1756968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756964), _1756966)), -(c_List_Oupt(_1756964, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1756966), _1756968)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1756964, _1756966)), c_List_Oupt(_1756966, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1756966), _1756968))))], (51307 ^ _779327) ^ [_1810063, _1810065, _1810067, _1810069, _1810071, _1810073] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1810063, _1810065, _1810067, _1810069, c_Lazy__Sequence_Olazy__sequence_OInsert(_1810065, _1810071, _1810073)) = hAPP(hAPP(_1810069, _1810071), _1810073))], (44626 ^ _779327) ^ [_1657875, _1657877, _1657879, _1657881, _1657883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657875), tc_List_Olist(_1657875))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657875), tc_List_Olist(_1657875)), _1657877), _1657879)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1657875), c_List_Olistrel1(_1657875, _1657881)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657875), tc_List_Olist(_1657875))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657875), tc_List_Olist(_1657875)), hAPP(hAPP(c_List_Olist_OCons(_1657875), _1657883), _1657877)), hAPP(hAPP(c_List_Olist_OCons(_1657875), _1657883), _1657879))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1657875), c_List_Olistrel1(_1657875, _1657881)))))], (46934 ^ _779327) ^ [_1716055, _1716057, _1716059, _1716061] : [hBOOL(hAPP(c_List_Odistinct(_1716055), hAPP(hAPP(c_List_Omap(_1716057, _1716055), _1716059), _1716061))), 46937 ^ _779327 : [(46940 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1716057, _1716055, _1716059, hAPP(c_List_Oset(_1716057), _1716061)))], (46938 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1716057), _1716061)))]]], (42354 ^ _779327) ^ [_1604095, _1604097, _1604099, _1604101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604095, _1604095)), hAPP(hAPP(c_Product__Type_OPair(_1604095, _1604095), _1604097), _1604099)), c_Transitive__Closure_Ortrancl(_1604095, _1604101))), -(_1604097 = _1604099), 42361 ^ _779327 : [(42364 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604095, _1604095)), hAPP(hAPP(c_Product__Type_OPair(_1604095, _1604095), _1604097), _1604099)), c_Transitive__Closure_Otrancl(_1604095, _1604101))))], (42362 ^ _779327) ^ [] : [_1604097 = _1604099]]], (35333 ^ _779327) ^ [_1432697, _1432699, _1432701, _1432703, _1432705] : [-(_1432697 = c_Orderings_Obot__class_Obot(tc_fun(_1432699, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432701, tc_HOL_Obool)), _1432703), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432699, tc_fun(_1432701, tc_HOL_Obool)), _1432697), _1432705)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432699, tc_fun(_1432701, tc_HOL_Obool)), _1432697), hAPP(hAPP(c_COMBB(tc_fun(_1432701, tc_HOL_Obool), tc_fun(_1432701, tc_HOL_Obool), _1432699), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432701, tc_HOL_Obool)), _1432703)), _1432705)))], (23714 ^ _779327) ^ [_1192203, _1192205] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1192203), _1192205) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1192203)), hAPP(c_Code__Numeral_Onat__of, _1192205))))], (21764 ^ _779327) ^ [_1154116, _1154118, _1154120, _1154122] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1154116, _1154118), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1154120), _1154122))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154116), _1154118), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1154122), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154120)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1154122), 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), _1154118), _1154122))))))], (32514 ^ _779327) ^ [_1369925, _1369927] : [class_Orderings_Olinorder(_1369925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369925), _1369927)), -(_1369927 = c_Orderings_Obot__class_Obot(tc_fun(_1369925, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1369925), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369925), 32527 ^ [_1369925, _1369927]), 32528 ^ [_1369925, _1369927])), hAPP(hAPP(c_Set_Oinsert(_1369925), 32527 ^ [_1369925, _1369927]), hAPP(hAPP(c_Set_Oinsert(_1369925), 32528 ^ [_1369925, _1369927]), c_Orderings_Obot__class_Obot(tc_fun(_1369925, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1369925), c_Big__Operators_Olinorder__class_OMin(_1369925, _1369927)), _1369927)))], (3568 ^ _779327) ^ [_833224, _833226] : [_833226 = _833224, -(c_Nat_Ofunpow(_833226) = c_Nat_Ofunpow(_833224))], (16792 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (33969 ^ _779327) ^ [_1400846, _1400848, _1400850, _1400852] : [c_Finite__Set_Ofolding__one__idem(_1400846, _1400848, _1400850), -(hAPP(hAPP(_1400848, _1400852), _1400852) = _1400852)], (37589 ^ _779327) ^ [_1482859, _1482861, _1482863] : [class_Lattices_Obounded__lattice__top(_1482859), 37592 ^ _779327 : [(37601 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1482859), _1482861), _1482863) = c_Orderings_Otop__class_Otop(_1482859)), _1482861 = c_Orderings_Otop__class_Otop(_1482859), _1482863 = c_Orderings_Otop__class_Otop(_1482859)], (37593 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1482859), _1482861), _1482863) = c_Orderings_Otop__class_Otop(_1482859), 37596 ^ _779327 : [(37599 ^ _779327) ^ [] : [-(_1482863 = c_Orderings_Otop__class_Otop(_1482859))], (37597 ^ _779327) ^ [] : [-(_1482861 = c_Orderings_Otop__class_Otop(_1482859))]]]]], (34160 ^ _779327) ^ [_1405244, _1405246, _1405248, _1405250, _1405252] : [-(hAPP(c_Relation_OImage(_1405244, _1405246, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1405244, _1405246), tc_HOL_Obool)), _1405248), _1405250)), _1405252) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405246, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405244, _1405246, _1405248), _1405252)), hAPP(c_Relation_OImage(_1405244, _1405246, _1405250), _1405252)))], (8600 ^ _779327) ^ [_917048, _917050] : [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), _917048), _917050))), 8603 ^ _779327 : [(8606 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _917050)))], (8604 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _917048)))]]], (38401 ^ _779327) ^ [_1502264, _1502266, _1502268, _1502270, _1502272] : [-(hAPP(c_Set_Ovimage(_1502264, _1502266, _1502268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502266, tc_HOL_Obool)), _1502270), _1502272)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502264, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502264, _1502266, _1502268), _1502270)), hAPP(c_Set_Ovimage(_1502264, _1502266, _1502268), _1502272)))], (29246 ^ _779327) ^ [_1300785] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1300785)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300785)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (15776 ^ _779327) ^ [_1046213, _1046215, _1046217] : [-(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), _1046213), _1046215)), _1046215)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046213, _1046215))), _1046217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1046213), _1046217))], (2694 ^ _779327) ^ [_819079, _819081] : [_819081 = _819079, -(c_Code__Numeral_OSuc__code__numeral(_819081) = c_Code__Numeral_OSuc__code__numeral(_819079))], (51303 ^ _779327) ^ [_1809968, _1809970, _1809972, _1809974, _1809976] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1809968, _1809970, _1809972, _1809974, _1809976) = c_Option_Ooption_Ooption__case(_1809968, tc_prod(_1809970, tc_Lazy__Sequence_Olazy__sequence(_1809970)), _1809972, hAPP(c_Product__Type_Oprod_Oprod__case(_1809970, tc_Lazy__Sequence_Olazy__sequence(_1809970), _1809968), _1809974), hAPP(c_Lazy__Sequence_Oyield(_1809970), _1809976)))], (27450 ^ _779327) ^ [_1264887, _1264889, _1264891] : [class_Orderings_Olinorder(_1264887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264887), _1264889), _1264891)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264887, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1264887, _1264889, _1264891)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1264887), _1264891)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1264887), _1264889))], (25105 ^ _779327) ^ [_1216990, _1216992] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216990), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216992))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216990))), _1216992)))], (42844 ^ _779327) ^ [_1615954, _1615956, _1615958, _1615960, _1615962] : [c_Relation_Osingle__valued(_1615954, _1615956, hAPP(c_Relation_Oconverse(_1615956, _1615954), _1615958)), -(hAPP(c_Relation_OImage(_1615956, _1615954, _1615958), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615956, tc_HOL_Obool)), _1615960), _1615962)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615954, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1615956, _1615954, _1615958), _1615960)), hAPP(c_Relation_OImage(_1615956, _1615954, _1615958), _1615962)))], (44460 ^ _779327) ^ [_1652147, _1652149] : [-(c_List_Olenlex(_1652147, _1652149) = 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hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1652147), tc_Nat_Onat), tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool)), tc_List_Olist(_1652147)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1652147))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1652147)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1652147))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1652147)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1652147), tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1652147), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool)), tc_List_Olist(_1652147)), c_COMBS(tc_List_Olist(_1652147), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652147), 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tc_fun(tc_fun(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652147), tc_HOL_Obool)), tc_List_Olist(_1652147)), c_COMBC(tc_List_Olist(_1652147), tc_fun(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1652147), tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147))), tc_fun(tc_List_Olist(_1652147), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1652147)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1652147)), c_member(tc_prod(tc_List_Olist(_1652147), tc_List_Olist(_1652147))))), c_Product__Type_OPair(tc_List_Olist(_1652147), tc_List_Olist(_1652147))))), c_List_Olex(_1652147, _1652149)))))))], (36893 ^ _779327) ^ [_1467731, _1467733, _1467735, _1467737] : [c_Fun_Oinj__on(_1467731, _1467733, _1467735, _1467737), -(hAPP(c_Finite__Set_Ocard(_1467733), hAPP(c_Set_Oimage(_1467731, _1467733, _1467735), _1467737)) = hAPP(c_Finite__Set_Ocard(_1467731), _1467737))], (9166 ^ _779327) ^ [_927482, _927484, _927486] : [9167 ^ _779327 : [(9170 ^ _779327) ^ [] : [_927484 = _927486], (9168 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927482, tc_HOL_Obool)), _927484), _927486))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927482, tc_HOL_Obool)), _927484), _927486)))], (45062 ^ _779327) ^ [_1670612, _1670614, _1670616] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1670612, tc_HOL_Obool)), hAPP(c_List_Oset(_1670612), hAPP(hAPP(c_List_Otake(_1670612), _1670614), _1670616))), hAPP(c_List_Oset(_1670612), _1670616))))], (47768 ^ _779327) ^ [_1733482] : [class_Orderings_Olinorder(_1733482), -(c_Finite__Set_Ofun__left__comm(_1733482, tc_List_Olist(_1733482), c_List_Olinorder__class_Oinsort__key(_1733482, _1733482, c_COMBI(_1733482))))], (49836 ^ _779327) ^ [_1778270, _1778272, _1778274] : [-(hAPP(hAPP(c_List_Oappend(_1778270), c_List_OtakeWhile(_1778270, _1778272, _1778274)), c_List_OdropWhile(_1778270, _1778272, _1778274)) = _1778274)], (40192 ^ _779327) ^ [_1549851, _1549853, _1549855, _1549857] : [-(c_Nitpick_Oprod(_1549851, _1549853, _1549855, _1549857) = hAPP(c_Set_OCollect(tc_prod(_1549851, _1549853)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549851, _1549853, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549851, tc_fun(_1549853, tc_HOL_Obool), tc_fun(_1549853, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549853, tc_HOL_Obool), tc_fun(_1549853, tc_HOL_Obool)), _1549851), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549853)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549851), c_fconj), hAPP(hAPP(c_COMBC(_1549851, tc_fun(_1549851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549851)), _1549855)))), hAPP(hAPP(c_COMBC(_1549853, tc_fun(_1549853, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549853)), _1549857)))))], (13943 ^ _779327) ^ [_1013530, _1013532, _1013534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013530)), _1013530 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1013532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013530), _1013534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1013534), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (13985 ^ _779327) ^ [_1014221, _1014223, _1014225] : [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), _1014221), _1014223)), _1014225)), 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)), _1014225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014223), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24665 ^ _779327) ^ [_1208679, _1208681, _1208683, _1208685] : [class_Divides_Osemiring__div(_1208679), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208679), _1208681), _1208683)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208679), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208679), _1208683), _1208681)), _1208685) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208679), _1208683), _1208685)), _1208681))], (42938 ^ _779327) ^ [_1618421, _1618423, _1618425] : [-(hAPP(hAPP(c_Nat_Ocompow(_1618421, _1618421), hAPP(c_Nat_OSuc, _1618423)), _1618425) = hAPP(c_Fun_Ocomp(_1618421, _1618421, _1618421, _1618425), hAPP(hAPP(c_Nat_Ocompow(_1618421, _1618421), _1618423), _1618425)))], (46166 ^ _779327) ^ [_1697661, _1697663] : [-(hAPP(hAPP(c_List_Oappend(_1697661), c_List_Olist_ONil(_1697661)), _1697663) = _1697663)], (50966 ^ _779327) ^ [_1802804, _1802806, _1802808] : [-(c_List_Olist__ex1(_1802804, _1802806, _1802808)), 50967 ^ _779327 : [(50968 ^ _779327) ^ [_1802898] : [hBOOL(hAPP(hAPP(c_member(_1802804), _1802898), hAPP(c_List_Oset(_1802804), _1802808))), hBOOL(hAPP(_1802806, _1802898)), 50976 ^ _779327 : [(50981 ^ _779327) ^ [] : [50975 ^ [_1802804, _1802806, _1802808, _1802898] = _1802898], (50979 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1802806, 50975 ^ [_1802804, _1802806, _1802808, _1802898])))], (50977 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802804), 50975 ^ [_1802804, _1802806, _1802808, _1802898]), hAPP(c_List_Oset(_1802804), _1802808))))]]]]], (45022 ^ _779327) ^ [_1669493, _1669495, _1669497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669493)), _1669495)), _1669497)), -(hAPP(hAPP(c_List_Otake(_1669493), _1669497), _1669495) = _1669495)], (20 ^ _779327) ^ [_779587, _779589, _779591, _779593, _779595, _779597] : [-(c_Hoare__Mirabelle_Ohoare__valids(_779595, _779591, _779587)), c_Hoare__Mirabelle_Ohoare__valids(_779597, _779593, _779589), _779597 = _779595, _779593 = _779591, _779589 = _779587], (28108 ^ _779327) ^ [_1279196, _1279198, _1279200] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279196), _1279198)), 28111 ^ _779327 : [(28131 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1279196, tc_Nat_Onat), _1279200), _1279198) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 28132 ^ _779327 : [(28133 ^ _779327) ^ [_1279677] : [hBOOL(hAPP(hAPP(c_member(_1279196), _1279677), _1279198)), hAPP(_1279200, _1279677) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28141 ^ _779327 : [(28146 ^ _779327) ^ [] : [hAPP(_1279200, 28140 ^ [_1279196, _1279198, _1279200, _1279677]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28144 ^ _779327) ^ [] : [_1279677 = 28140 ^ [_1279196, _1279198, _1279200, _1279677]], (28142 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1279196), 28140 ^ [_1279196, _1279198, _1279200, _1279677]), _1279198)))]]]]], (28112 ^ _779327) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1279196, tc_Nat_Onat), _1279200), _1279198) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28116 ^ _779327 : [(28121 ^ _779327) ^ [_1279516] : [hBOOL(hAPP(hAPP(c_member(_1279196), _1279516), _1279198)), -(28115 ^ [_1279196, _1279198, _1279200] = _1279516), -(hAPP(_1279200, _1279516) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28119 ^ _779327) ^ [] : [-(hAPP(_1279200, 28115 ^ [_1279196, _1279198, _1279200]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28117 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1279196), 28115 ^ [_1279196, _1279198, _1279200]), _1279198)))]]]]], (37613 ^ _779327) ^ [_1483228, _1483230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483228, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1483228, tc_HOL_Obool))), _1483230) = c_Orderings_Otop__class_Otop(tc_fun(_1483228, tc_HOL_Obool)))], (17278 ^ _779327) ^ [_1072567, _1072569, _1072571] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072567), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072569)), _1072571)) = 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), _1072567), _1072569))), _1072571))], (31740 ^ _779327) ^ [_1356025, _1356027, _1356029] : [class_Lattices_Olattice(_1356025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356025), _1356027)), hBOOL(hAPP(hAPP(c_member(_1356025), _1356029), _1356027)), 31751 ^ _779327 : [(31758 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356025, tc_HOL_Obool)), _1356027), hAPP(hAPP(c_Set_Oinsert(_1356025), _1356029), c_Orderings_Obot__class_Obot(tc_fun(_1356025, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1356025, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1356025, _1356027) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1356025), _1356029), c_Big__Operators_Olattice__class_OSup__fin(_1356025, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356025, tc_HOL_Obool)), _1356027), hAPP(hAPP(c_Set_Oinsert(_1356025), _1356029), c_Orderings_Obot__class_Obot(tc_fun(_1356025, tc_HOL_Obool)))))))], (31752 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356025, tc_HOL_Obool)), _1356027), hAPP(hAPP(c_Set_Oinsert(_1356025), _1356029), c_Orderings_Obot__class_Obot(tc_fun(_1356025, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1356025, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1356025, _1356027) = _1356029)]]], (13532 ^ _779327) ^ [_1005889, _1005891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005889), _1005891)), -(_1005891 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005889), 13535 ^ [_1005889, _1005891])))], (14455 ^ _779327) ^ [_1023118, _1023120] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023118), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1023120)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1023118)), _1023120))], (7081 ^ _779327) ^ [_890149, _890151] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890149), _890151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890151)), _890149)))], (150 ^ _779327) ^ [_781440, _781442, _781444, _781446, _781448, _781450, _781452, _781454] : [-(c_Orderings_Oorder_Ostrict__mono(_781452, _781448, _781444, _781440)), c_Orderings_Oorder_Ostrict__mono(_781454, _781450, _781446, _781442), _781454 = _781452, _781450 = _781448, _781446 = _781444, _781442 = _781440], (39191 ^ _779327) ^ [_1521331, _1521333, _1521335] : [class_Orderings_Olinorder(_1521331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521331), _1521333)), -(_1521333 = c_Orderings_Obot__class_Obot(tc_fun(_1521331, tc_HOL_Obool))), 39202 ^ _779327 : [(39203 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1521331), _1521335), hAPP(c_Finite__Set_Ofold1(_1521331, c_Orderings_Oord__class_Omin(_1521331)), _1521333))), 39206 ^ _779327 : [(39207 ^ _779327) ^ [_1521624] : [hBOOL(hAPP(hAPP(c_member(_1521331), _1521624), _1521333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1521331), _1521335), _1521624)))]]], (39213 ^ _779327) ^ [] : [39215 ^ _779327 : [(39218 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1521331), _1521335), 39214 ^ [_1521331, _1521333, _1521335]))], (39216 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521331), 39214 ^ [_1521331, _1521333, _1521335]), _1521333)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1521331), _1521335), hAPP(c_Finite__Set_Ofold1(_1521331, c_Orderings_Oord__class_Omin(_1521331)), _1521333))))]]], (23488 ^ _779327) ^ [_1187656, _1187658, _1187660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1187656), c_Nitpick_Oplus__frac(_1187656, _1187658, c_Nitpick_Ouminus__frac(_1187656, _1187660)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1187656, _1187658, _1187660))], (47452 ^ _779327) ^ [_1726732] : [-(c_List_Obutlast(_1726732, c_List_Olist_ONil(_1726732)) = c_List_Olist_ONil(_1726732))], (47292 ^ _779327) ^ [_1723809, _1723811, _1723813, _1723815] : [-(_1723809 = c_List_Olist_ONil(_1723811)), -(c_List_Olast(_1723813, hAPP(hAPP(c_List_Omap(_1723811, _1723813), _1723815), _1723809)) = hAPP(_1723815, c_List_Olast(_1723811, _1723809)))], (9549 ^ _779327) ^ [] : [-(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))))], (26860 ^ _779327) ^ [_1252684, _1252686, _1252688, _1252690] : [26861 ^ _779327 : [(26862 ^ _779327) ^ [_1252794] : [hBOOL(hAPP(hAPP(c_member(_1252684), _1252794), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252684, tc_HOL_Obool)), _1252686), _1252688))), hBOOL(hAPP(_1252690, _1252794))]], 26870 ^ _779327 : [(26873 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1252690, 26869 ^ [_1252684, _1252686, _1252688, _1252690])))], (26871 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1252684), 26869 ^ [_1252684, _1252686, _1252688, _1252690]), _1252686)))]], 26875 ^ _779327 : [(26878 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1252690, 26874 ^ [_1252684, _1252686, _1252688, _1252690])))], (26876 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1252684), 26874 ^ [_1252684, _1252686, _1252688, _1252690]), _1252688)))]]], (28828 ^ _779327) ^ [_1293215, _1293217, _1293219, _1293221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1293215, _1293217)), c_Sum__Type_OPlus(_1293215, _1293217, _1293219, _1293221))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1293217), _1293221)))], (172 ^ _779327) ^ [_781793, _781795, _781797, _781799, _781801, _781803, _781805, _781807] : [-(c_Orderings_Oorder_Omono(_781805, _781801, _781797, _781793)), c_Orderings_Oorder_Omono(_781807, _781803, _781799, _781795), _781807 = _781805, _781803 = _781801, _781799 = _781797, _781795 = _781793], (19871 ^ _779327) ^ [_1118247, _1118249, _1118251, _1118253] : [class_Fields_Ofield(_1118247), -(_1118249 = c_Groups_Ozero__class_Ozero(_1118247)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118247), _1118251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118247), _1118253), _1118249)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118247), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118247), _1118249), _1118251)), _1118253)), _1118249))], (28719 ^ _779327) ^ [_1291246, _1291248, _1291250, _1291252] : [_1291246 = c_Orderings_Obot__class_Obot(tc_fun(_1291248, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291248, tc_fun(_1291250, tc_HOL_Obool)), _1291246), hAPP(c_COMBK(tc_fun(_1291250, tc_HOL_Obool), _1291248), _1291252)) = c_Orderings_Obot__class_Obot(tc_fun(_1291250, tc_HOL_Obool)))], (18746 ^ _779327) ^ [_1098287, _1098289, _1098291] : [18748 ^ _779327 : [(18751 ^ _779327) ^ [] : [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(_1098289, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18747 ^ [_1098287, _1098289, _1098291]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1098289, 18747 ^ [_1098287, _1098289, _1098291])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18749 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18747 ^ [_1098287, _1098289, _1098291]), _1098287)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1098289, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1098291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1098291), hAPP(_1098289, _1098287))), 18761 ^ _779327 : [(18764 ^ _779327) ^ [] : [-(hAPP(_1098289, 18760 ^ [_1098287, _1098289, _1098291]) = _1098291)], (18762 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18760 ^ [_1098287, _1098289, _1098291]), _1098287)))]]], (30361 ^ _779327) ^ [_1325362, _1325364] : [c_Nat__Transfer_Onat__set(_1325362), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1325364), _1325362)), -(c_Nat__Transfer_Ois__nat(_1325364))], (28031 ^ _779327) ^ [_1277746, _1277748, _1277750, _1277752] : [class_Groups_Ocomm__monoid__add(_1277746), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277748), _1277750))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1277748, _1277746), _1277752), _1277750) = c_Groups_Ozero__class_Ozero(_1277746))], (1958 ^ _779327) ^ [_806790, _806792] : [-(class_Nat_Osize(_806790)), _806792 = _806790, class_Nat_Osize(_806792)], (4662 ^ _779327) ^ [_850373, _850375, _850377, _850379] : [-(c_Wellfounded_Oaccp(_850379, _850375) = c_Wellfounded_Oaccp(_850377, _850373)), _850379 = _850377, _850375 = _850373], (52938 ^ _779327) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (12588 ^ _779327) ^ [_989285, _989287, _989289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989285), _989287)), _989289)), 12591 ^ _779327 : [(12594 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989287), _989289)))], (12592 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989285), _989289)))]]], (33987 ^ _779327) ^ [_1401213, _1401215, _1401217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401213, tc_HOL_Obool)), _1401215), _1401217)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1401213, tc_HOL_Obool)), _1401215), hAPP(c_Set_OPow(_1401213), _1401217))))], (31806 ^ _779327) ^ [_1357346, _1357348, _1357350] : [class_Rings_Oring__1(_1357346), hBOOL(hAPP(hAPP(c_member(_1357346), _1357348), c_Int_Oring__1__class_OInts(_1357346))), hBOOL(hAPP(hAPP(c_member(_1357346), _1357350), c_Int_Oring__1__class_OInts(_1357346))), -(hBOOL(hAPP(hAPP(c_member(_1357346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357346), _1357348), _1357350)), c_Int_Oring__1__class_OInts(_1357346))))], (9973 ^ _779327) ^ [_940800] : [class_Rings_Olinordered__semidom(_940800), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940800), c_Groups_Ozero__class_Ozero(_940800)), c_Groups_Oone__class_Oone(_940800))))], (36478 ^ _779327) ^ [_1460020, _1460022, _1460024] : [class_Lattices_Olattice(_1460020), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460020), _1460022)), hBOOL(hAPP(hAPP(c_member(_1460020), _1460024), _1460022)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1460020), _1460024), c_Big__Operators_Olattice__class_OInf__fin(_1460020, _1460022)) = _1460024)], (25133 ^ _779327) ^ [_1217507, _1217509] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217507), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217509))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217507), _1217509)))], (860 ^ _779327) ^ [_792483, _792485, _792487, _792489, _792491, _792493] : [-(c_List_Olist__ex1(_792491, _792487, _792483)), c_List_Olist__ex1(_792493, _792489, _792485), _792493 = _792491, _792489 = _792487, _792485 = _792483], (10253 ^ _779327) ^ [_945352, _945354, _945356] : [class_Rings_Olinordered__semidom(_945352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945352), c_Groups_Oone__class_Oone(_945352)), _945354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945352), c_Groups_Oone__class_Oone(_945352)), hAPP(hAPP(c_Power_Opower__class_Opower(_945352), _945354), hAPP(c_Nat_OSuc, _945356)))))], (39832 ^ _779327) ^ [_1535725, _1535727, _1535729] : [-(hBOOL(hAPP(_1535725, _1535727))), -(hAPP(c_Set_OCollect(_1535729), hAPP(hAPP(c_COMBS(_1535729, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535729), c_fconj), hAPP(hAPP(c_COMBC(_1535729, _1535729, tc_HOL_Obool), c_fequal), _1535727))), _1535725)) = c_Orderings_Obot__class_Obot(tc_fun(_1535729, tc_HOL_Obool)))], (26584 ^ _779327) ^ [_1247286, _1247288] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247286), _1247288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247288), _1247286))], (11785 ^ _779327) ^ [_974462, _974464, _974466] : [class_Groups_Oordered__ab__group__add(_974462), 11788 ^ _779327 : [(11795 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974462), _974466), hAPP(c_Groups_Ouminus__class_Ouminus(_974462), _974464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974462), _974464), hAPP(c_Groups_Ouminus__class_Ouminus(_974462), _974466))))], (11789 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974462), _974464), hAPP(c_Groups_Ouminus__class_Ouminus(_974462), _974466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974462), _974466), hAPP(c_Groups_Ouminus__class_Ouminus(_974462), _974464))))]]], (31221 ^ _779327) ^ [_1344864, _1344866] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344864), _1344866)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344864), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344866))))], (15403 ^ _779327) ^ [_1039456, _1039458, _1039460, _1039462] : [class_Divides_Oring__div(_1039456), -(c_Divides_Odiv__class_Omod(_1039456, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039456), _1039458), _1039460), _1039462) = c_Divides_Odiv__class_Omod(_1039456, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039456), c_Divides_Odiv__class_Omod(_1039456, _1039458, _1039462)), _1039460), _1039462))], (10325 ^ _779327) ^ [_946723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _946723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946723)))], (14445 ^ _779327) ^ [_1022938, _1022940, _1022942] : [_1022940 = _1022942, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022938, tc_HOL_Obool)), _1022940) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022938, tc_HOL_Obool)), _1022942))], (36026 ^ _779327) ^ [_1447871, _1447873, _1447875] : [class_Orderings_Olinorder(_1447871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447871), _1447873)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447871), _1447875)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447871, tc_HOL_Obool)), _1447873), _1447875) = c_Orderings_Obot__class_Obot(tc_fun(_1447871, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447871), c_Big__Operators_Olattice_OSup__fin(_1447871, c_Orderings_Oord__class_Omax(_1447871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447871, tc_HOL_Obool)), _1447873), _1447875))), c_Big__Operators_Olattice_OSup__fin(_1447871, c_Orderings_Oord__class_Omax(_1447871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447871, tc_HOL_Obool)), _1447873), _1447875))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447871), c_Big__Operators_Olattice_OSup__fin(_1447871, c_Orderings_Oord__class_Omax(_1447871), _1447873)), c_Big__Operators_Olattice_OSup__fin(_1447871, c_Orderings_Oord__class_Omax(_1447871), _1447875)))], (27202 ^ _779327) ^ [_1259351, _1259353, _1259355] : [class_Lattices_Olattice(_1259351), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259351), _1259353), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259351), _1259353), _1259355))))], (41587 ^ _779327) ^ [_1585554, _1585556, _1585558, _1585560, _1585562, _1585564] : [c_Finite__Set_Ofolding(_1585554, _1585556, _1585558, _1585560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585554), _1585562)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585554), _1585564)), -(hAPP(c_Fun_Ocomp(_1585556, _1585556, _1585556, hAPP(_1585560, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585554, tc_HOL_Obool)), _1585562), _1585564))), hAPP(_1585560, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1585554, tc_HOL_Obool)), _1585562), _1585564))) = hAPP(c_Fun_Ocomp(_1585556, _1585556, _1585556, hAPP(_1585560, _1585562)), hAPP(_1585560, _1585564)))], (23678 ^ _779327) ^ [_1191534] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1191534)) = _1191534)], (27747 ^ _779327) ^ [_1272293, _1272295, _1272297, _1272299] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272293, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272295, tc_fun(_1272293, tc_HOL_Obool)), _1272297), _1272299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1272295, tc_fun(_1272293, tc_HOL_Obool)), _1272297), hAPP(hAPP(c_COMBB(tc_fun(_1272293, tc_HOL_Obool), tc_fun(_1272293, tc_HOL_Obool), _1272295), c_Groups_Ouminus__class_Ouminus(tc_fun(_1272293, tc_HOL_Obool))), _1272299)))], (52812 ^ _779327) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (36312 ^ _779327) ^ [_1455819, _1455821, _1455823, _1455825, _1455827] : [class_Groups_Ocomm__monoid__mult(_1455819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455821), _1455823)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455821), _1455825)), 36326 ^ _779327 : [(36329 ^ _779327) ^ [] : [hAPP(_1455827, 36325 ^ [_1455819, _1455821, _1455823, _1455825, _1455827]) = c_Groups_Oone__class_Oone(_1455819)], (36327 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455821), 36325 ^ [_1455819, _1455821, _1455823, _1455825, _1455827]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455821, tc_HOL_Obool)), _1455823), _1455825))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1455821, _1455819), _1455827), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455821, tc_HOL_Obool)), _1455823), _1455825)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455819), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1455821, _1455819), _1455827), _1455823)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1455821, _1455819), _1455827), _1455825)))], (52574 ^ _779327) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (46000 ^ _779327) ^ [_1694305, _1694307, _1694309, _1694311, _1694313, _1694315] : [hAPP(hAPP(c_List_Olist_OCons(_1694305), _1694307), _1694309) = _1694311, _1694313 = hAPP(hAPP(c_List_Oappend(_1694305), _1694309), _1694315), -(hAPP(hAPP(c_List_Olist_OCons(_1694305), _1694307), _1694313) = hAPP(hAPP(c_List_Oappend(_1694305), _1694311), _1694315))], (12153 ^ _779327) ^ [_981280, _981282, _981284, _981286, _981288] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_981280), 12156 ^ _779327 : [(12157 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981282), _981286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981284), _981288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981282), _981288)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981284), _981286)), -(_981282 = _981284), -(_981286 = _981288)], (12167 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981282), _981286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981284), _981288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981282), _981288)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981280), _981284), _981286))), 12170 ^ _779327 : [(12173 ^ _779327) ^ [] : [_981286 = _981288], (12171 ^ _779327) ^ [] : [_981282 = _981284]]]]], (9112 ^ _779327) ^ [_926511, _926513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _926511), _926513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926513))))], (9080 ^ _779327) ^ [] : [-(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))], (16095 ^ _779327) ^ [_1051825, _1051827, _1051829] : [hBOOL(hAPP(_1051825, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1051827, _1051829))), 16098 ^ _779327 : [(16123 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051829), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 16126 ^ _779327 : [(16127 ^ _779327) ^ [_1052447, _1052449] : [-(hBOOL(hAPP(_1051825, _1052447))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051829), _1052447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052447), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1051827 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051829), _1052449)), _1052447)]]], (16105 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051829)), 16108 ^ _779327 : [(16109 ^ _779327) ^ [_1052155, _1052157] : [-(hBOOL(hAPP(_1051825, _1052155))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052155), _1051829)), _1051827 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051829), _1052157)), _1052155)]]], (16099 ^ _779327) ^ [] : [_1051829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1051825, _1051827)))]]], (42850 ^ _779327) ^ [_1616137, _1616139, _1616141] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616137, _1616137)), _1616139), c_Transitive__Closure_Ortrancl(_1616137, _1616141))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616137, _1616137)), _1616139), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1616137, _1616137), 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(_1616137, _1616137), tc_HOL_Obool), tc_fun(tc_prod(_1616137, _1616137), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1616137, _1616137), tc_HOL_Obool)), _1616141)))))], (34663 ^ _779327) ^ [_1417823, _1417825, _1417827, _1417829] : [class_Lattices_Osemilattice__inf(_1417823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417823), _1417825), _1417827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417823), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417823), _1417825), _1417829)), _1417827)))], (22187 ^ _779327) ^ [_1162841, _1162843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162841), 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)), _1162843)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1162841, _1162843) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1162841, _1162843)))], (29915 ^ _779327) ^ [_1314107, _1314109, _1314111] : [hBOOL(hAPP(hAPP(c_member(_1314107), _1314109), hAPP(c_fequal, _1314111))), -(_1314109 = _1314111)], (37638 ^ _779327) ^ [_1483893, _1483895, _1483897, _1483899] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483893, tc_fun(_1483895, tc_HOL_Obool)), _1483897), _1483899) = c_Orderings_Otop__class_Otop(tc_fun(_1483895, tc_HOL_Obool)), 37641 ^ _779327 : [(37642 ^ _779327) ^ [_1484009] : [hBOOL(hAPP(hAPP(c_member(_1483893), _1484009), _1483897)), -(hAPP(_1483899, _1484009) = c_Orderings_Otop__class_Otop(tc_fun(_1483895, tc_HOL_Obool)))]]], (39517 ^ _779327) ^ [_1528569, _1528571, _1528573] : [-(hAPP(c_Product__Type_Omap__pair(_1528569, _1528569, _1528571, _1528571, c_COMBI(_1528569), c_COMBI(_1528571)), _1528573) = _1528573)], (13812 ^ _779327) ^ [_1011237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011237)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011237), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1011237)], (20975 ^ _779327) ^ [_1138608, _1138610, _1138612, _1138614] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1138608, _1138610, _1138612, c_Code__Numeral_OSuc__code__numeral(_1138614)) = hAPP(_1138612, _1138614))], (25826 ^ _779327) ^ [_1232145, _1232147, _1232149] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232145, tc_Nat_Onat), _1232147), _1232149) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232145, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1232145), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232147)), _1232149)))], (22003 ^ _779327) ^ [_1158890, _1158892, _1158894, _1158896, _1158898, _1158900] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1158890, _1158892, _1158894), _1158896), hAPP(hAPP(c_Product__Type_OPair(_1158890, _1158892), _1158898), _1158900)) = hAPP(hAPP(_1158896, _1158898), _1158900))], (12435 ^ _779327) ^ [_986354, _986356, _986358, _986360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986354), _986356)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986358), _986356) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986354), _986360), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986358), _986360)))], (52718 ^ _779327) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (24545 ^ _779327) ^ [_1206603] : [_1206603 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206603), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (1318 ^ _779327) ^ [_798790, _798792] : [-(class_Int_Oring__char__0(_798790)), _798792 = _798790, class_Int_Oring__char__0(_798792)], (27304 ^ _779327) ^ [_1261881, _1261883, _1261885, _1261887, _1261889] : [class_Lattices_Osemilattice__sup(_1261881), class_Lattices_Osemilattice__sup(_1261883), c_Orderings_Oorder__class_Omono(_1261883, _1261881, _1261885), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261881), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261881), hAPP(_1261885, _1261887)), hAPP(_1261885, _1261889))), hAPP(_1261885, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261883), _1261887), _1261889)))))], (28725 ^ _779327) ^ [_1291383, _1291385, _1291387, _1291389] : [-(_1291383 = c_Orderings_Obot__class_Obot(tc_fun(_1291385, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291385, tc_fun(_1291387, tc_HOL_Obool)), _1291383), hAPP(c_COMBK(tc_fun(_1291387, tc_HOL_Obool), _1291385), _1291389)) = _1291389)], (12455 ^ _779327) ^ [_986726, _986728, _986730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986726), _986728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986726), _986730)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986728), _986730))))], (50672 ^ _779327) ^ [_1796715, _1796717, _1796719] : [c_List_Olist__ex(_1796715, _1796717, _1796719), 50676 ^ _779327 : [(50679 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1796717, 50675 ^ [_1796715, _1796717, _1796719])))], (50677 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796715), 50675 ^ [_1796715, _1796717, _1796719]), hAPP(c_List_Oset(_1796715), _1796719))))]]], (52674 ^ _779327) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (23754 ^ _779327) ^ [_1193015, _1193017, _1193019, _1193021, _1193023, _1193025, _1193027] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1193015, _1193017, _1193019, _1193021), _1193023), _1193025), _1193027) = c_New__DSequence_Opos__bind(_1193015, _1193017, hAPP(hAPP(hAPP(_1193019, _1193023), _1193025), _1193027), hAPP(hAPP(c_COMBC(_1193015, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1193017))), hAPP(hAPP(c_COMBC(_1193015, 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(_1193017)))), hAPP(hAPP(c_COMBC(_1193015, 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(_1193017))))), _1193021), _1193023)), _1193025)), _1193027)))], (4802 ^ _779327) ^ [_852461, _852463] : [_852463 = _852461, -(c_List_Onth(_852463) = c_List_Onth(_852461))], (51833 ^ _779327) ^ [_1823157, _1823159] : [c_Relation_Otrans(_1823157, hAPP(c_Set_OCollect(tc_prod(_1823157, _1823157)), hAPP(c_Product__Type_Oprod_Oprod__case(_1823157, _1823157, tc_HOL_Obool), _1823159))), -(c_Predicate_Otransp(_1823157, _1823159))], (44363 ^ _779327) ^ [_1650102, _1650104, _1650106, _1650108] : [class_Rings_Olinordered__semidom(_1650102), 44369 ^ _779327 : [(44372 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1650102), c_Groups_Ozero__class_Ozero(_1650102)), hAPP(_1650108, 44368 ^ [_1650102, _1650104, _1650106, _1650108])))], (44370 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1650104), 44368 ^ [_1650102, _1650104, _1650106, _1650108]), _1650106)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1650102), c_Groups_Ozero__class_Ozero(_1650102)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1650104, _1650102), _1650108), _1650106))))], (21142 ^ _779327) ^ [_1141975] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1141975) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1141975)))], (10795 ^ _779327) ^ [_955075, _955077, _955079, _955081] : [class_Rings_Ocomm__semiring__1(_955075), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955075), _955077), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955075), _955079), _955081)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955075), _955079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955075), _955077), _955081)))], (42100 ^ _779327) ^ [_1597053, _1597055, _1597057, _1597059, _1597061] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597053, _1597053)), hAPP(hAPP(c_Product__Type_OPair(_1597053, _1597053), _1597055), _1597057)), _1597059)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1597053, _1597053)), hAPP(hAPP(c_Product__Type_OPair(_1597053, _1597053), _1597057), _1597061)), c_Transitive__Closure_Otrancl(_1597053, _1597059))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597053, _1597053)), hAPP(hAPP(c_Product__Type_OPair(_1597053, _1597053), _1597055), _1597061)), c_Transitive__Closure_Otrancl(_1597053, _1597059))))], (12175 ^ _779327) ^ [_981698, _981700, _981702, _981704] : [class_Rings_Ocomm__semiring__1(_981698), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981698), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981698), _981700), _981702)), _981704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981698), _981700), _981704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981698), _981702), _981704)))], (34259 ^ _779327) ^ [_1408134, _1408136, _1408138] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408134), _1408136), _1408138) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408134, tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool)), _1408136), hAPP(hAPP(c_COMBC(_1408134, tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408134, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool)), _1408134), c_Set_Oinsert(tc_fun(_1408134, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1408134, tc_HOL_Obool), tc_fun(_1408134, tc_HOL_Obool), _1408134), c_Relation_OImage(_1408134, _1408134, _1408138)), hAPP(hAPP(c_COMBC(_1408134, tc_fun(_1408134, tc_HOL_Obool), tc_fun(_1408134, tc_HOL_Obool)), c_Set_Oinsert(_1408134)), c_Orderings_Obot__class_Obot(tc_fun(_1408134, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408134, tc_HOL_Obool), tc_HOL_Obool)))))], (23267 ^ _779327) ^ [_1183181, _1183183, _1183185, _1183187, _1183189] : [-(_1183181 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1183183, _1183185, _1183181, _1183187), _1183189) = hAPP(hAPP(c_Product__Type_Oscomp(_1183185, _1183183, _1183185, tc_prod(_1183183, _1183185)), hAPP(_1183187, _1183189)), c_Random_Oiterate(_1183183, _1183185, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1183181), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1183187)))], (6861 ^ _779327) ^ [_886604, _886606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886604), hAPP(c_Nat_OSuc, _886606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886604), _886606)))], (1688 ^ _779327) ^ [_803415, _803417] : [-(class_Groups_Ocomm__monoid__mult(_803415)), _803417 = _803415, class_Groups_Ocomm__monoid__mult(_803417)], (1014 ^ _779327) ^ [_794760, _794762, _794764, _794766, _794768, _794770] : [-(c_Relation_Orefl__on(_794768, _794764, _794760)), c_Relation_Orefl__on(_794770, _794766, _794762), _794770 = _794768, _794766 = _794764, _794762 = _794760], (49513 ^ _779327) ^ [_1771419, _1771421, _1771423, _1771425, _1771427] : [c_List_Olist__all2(_1771419, _1771421, _1771423, _1771425, hAPP(c_List_Orev(_1771421), _1771427)), -(c_List_Olist__all2(_1771419, _1771421, _1771423, hAPP(c_List_Orev(_1771419), _1771425), _1771427))], (20920 ^ _779327) ^ [_1137704, _1137706] : [20921 ^ _779327 : [(20924 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1137706), _1137704))], (20922 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1137704), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1137704, _1137706) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38926 ^ _779327) ^ [_1515706, _1515708, _1515710, _1515712] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1515706, _1515708)), hAPP(hAPP(c_Product__Type_OSigma(_1515706, _1515708), _1515710), hAPP(c_COMBK(tc_fun(_1515708, tc_HOL_Obool), _1515706), _1515712)))), -(_1515712 = c_Orderings_Obot__class_Obot(tc_fun(_1515708, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515706), _1515710)))], (45209 ^ _779327) ^ [_1673946, _1673948, _1673950, _1673952, _1673954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673946), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673948)), _1673950))), -(hAPP(hAPP(c_List_Onth(_1673952), hAPP(hAPP(c_List_Omap(_1673948, _1673952), _1673954), _1673950)), _1673946) = hAPP(_1673954, hAPP(hAPP(c_List_Onth(_1673948), _1673950), _1673946)))], (2202 ^ _779327) ^ [_811293, _811295, _811297, _811299] : [-(c_Divides_Odivmod__int__rel(_811299, _811295) = c_Divides_Odivmod__int__rel(_811297, _811293)), _811299 = _811297, _811295 = _811293], (41695 ^ _779327) ^ [_1588145, _1588147, _1588149, _1588151, _1588153, _1588155] : [c_Finite__Set_Ofolding__idem(_1588145, _1588147, _1588149, _1588151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588145), _1588153)), hBOOL(hAPP(hAPP(c_member(_1588145), _1588155), _1588153)), -(hAPP(c_Fun_Ocomp(_1588147, _1588147, _1588147, hAPP(_1588151, _1588153)), hAPP(_1588149, _1588155)) = hAPP(_1588151, _1588153))], (34015 ^ _779327) ^ [_1402038, _1402040, _1402042] : [hBOOL(hAPP(c_Predicate_OPowp(_1402038, hAPP(hAPP(c_COMBC(_1402038, tc_fun(_1402038, tc_HOL_Obool), tc_HOL_Obool), c_member(_1402038)), _1402040)), _1402042)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1402038, tc_HOL_Obool)), _1402042), hAPP(c_Set_OPow(_1402038), _1402040))))], (6608 ^ _779327) ^ [_882904, _882906, _882908] : [class_Orderings_Oorder(_882904), 6611 ^ _779327 : [(6612 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882904), _882906), _882908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882904), _882906), _882908))), -(_882906 = _882908)], (6622 ^ _779327) ^ [] : [6623 ^ _779327 : [(6626 ^ _779327) ^ [] : [_882906 = _882908], (6624 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882904), _882906), _882908))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882904), _882906), _882908)))]]], (30982 ^ _779327) ^ [_1340241, _1340243] : [c_Nitpick_Orefl_H(_1340241, _1340243), 30985 ^ _779327 : [(30986 ^ _779327) ^ [_1340319] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1340241, _1340241)), hAPP(hAPP(c_Product__Type_OPair(_1340241, _1340241), _1340319), _1340319)), _1340243)))]]], (8728 ^ _779327) ^ [_919397, _919399, _919401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919397), _919399)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919397), _919401))), 8731 ^ _779327 : [(8734 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919399), _919401)))], (8732 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919397)))]]], (19827 ^ _779327) ^ [_1117466, _1117468, _1117470, _1117472] : [class_Fields_Ofield(_1117466), -(_1117468 = c_Groups_Ozero__class_Ozero(_1117466)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117466), _1117470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117466), _1117472), _1117468)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117466), _1117468), _1117470)), _1117472)), _1117468))], (18160 ^ _779327) ^ [_1087630] : [-(c_Int_Osucc(c_Int_OBit0(_1087630)) = c_Int_OBit1(_1087630))], (17260 ^ _779327) ^ [_1072267, _1072269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072267), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072267)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072269)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18250 ^ _779327) ^ [_1089277, _1089279] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1089277)), c_Int_OBit1(_1089279)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1089277), c_Int_Osucc(_1089279))))], (1268 ^ _779327) ^ [_798165, _798167] : [-(class_Rings_Oordered__ring(_798165)), _798167 = _798165, class_Rings_Oordered__ring(_798167)], (51181 ^ _779327) ^ [_1806916, _1806918, _1806920] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806916, _1806916, hAPP(hAPP(c_COMBB(tc_fun(_1806916, tc_HOL_Obool), tc_fun(_1806916, tc_HOL_Obool), _1806916), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1806916), c_fNot)), c_fequal)), _1806918), _1806920)), _1806918 = _1806920], (22175 ^ _779327) ^ [_1162630, _1162632] : [-(c_Divides_Odivmod__nat(_1162630, _1162632) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1162630), _1162632)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1162630, _1162632)))], (674 ^ _779327) ^ [_789648, _789650, _789652, _789654, _789656, _789658, _789660, _789662, _789664, _789666, _789668, _789670] : [-(c_Finite__Set_Ofolding__image__simple__idem(_789668, _789664, _789660, _789656, _789652, _789648)), c_Finite__Set_Ofolding__image__simple__idem(_789670, _789666, _789662, _789658, _789654, _789650), _789670 = _789668, _789666 = _789664, _789662 = _789660, _789658 = _789656, _789654 = _789652, _789650 = _789648], (46020 ^ _779327) ^ [_1694837, _1694839, _1694841, _1694843, _1694845, _1694847, _1694849] : [-(hAPP(hAPP(c_List_Ozip(_1694837, _1694839), hAPP(hAPP(c_List_Olist__update(_1694837, _1694841), _1694843), _1694845)), hAPP(hAPP(c_List_Olist__update(_1694839, _1694847), _1694843), _1694849)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1694837, _1694839), hAPP(hAPP(c_List_Ozip(_1694837, _1694839), _1694841), _1694847)), _1694843), hAPP(hAPP(c_Product__Type_OPair(_1694837, _1694839), _1694845), _1694849)))], (51564 ^ _779327) ^ [_1815882, _1815884, _1815886, _1815888] : [c_Relation_Otrans(_1815882, _1815884), c_Relation_Otrans(_1815886, _1815888), -(c_Relation_Otrans(tc_prod(_1815882, _1815886), c_Wellfounded_Olex__prod(_1815882, _1815886, _1815884, _1815888)))], (16934 ^ _779327) ^ [_1066550, _1066552, _1066554] : [-(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), _1066550), _1066552)), _1066554)), _1066552) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1066554), _1066552))], (5662 ^ _779327) ^ [_868741, _868743, _868745, _868747, _868749] : [-(hAPP(hAPP(c_Power_Opower_Opower(_868741, _868743, _868745), _868747), hAPP(c_Nat_OSuc, _868749)) = hAPP(hAPP(_868745, _868747), hAPP(hAPP(c_Power_Opower_Opower(_868741, _868743, _868745), _868747), _868749)))], (22977 ^ _779327) ^ [_1177433, _1177435, _1177437] : [class_Orderings_Olinorder(_1177433), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177433), _1177435), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177433), _1177435), _1177437))))], (40245 ^ _779327) ^ [_1552087, _1552089] : [-(hAPP(c_Set_Ovimage(_1552087, _1552087, c_Fun_Oid(_1552087)), _1552089) = _1552089)], (28288 ^ _779327) ^ [_1282787, _1282789] : [class_Finite__Set_Ofinite(_1282787), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282787), _1282789)))], (15483 ^ _779327) ^ [_1041059, _1041061, _1041063, _1041065] : [class_Divides_Osemiring__div(_1041059), -(c_Divides_Odiv__class_Omod(_1041059, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041059), _1041061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041059), _1041063), _1041065)), _1041065) = c_Divides_Odiv__class_Omod(_1041059, _1041061, _1041065))], (48752 ^ _779327) ^ [_1756915, _1756917] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756915), _1756917))), -(c_List_Oupt(_1756915, hAPP(c_Nat_OSuc, _1756917)) = c_List_Olist_ONil(tc_Nat_Onat))], (4170 ^ _779327) ^ [_842641, _842643] : [_842643 = _842641, -(c_List_Otranspose__rel(_842643) = c_List_Otranspose__rel(_842641))], (33814 ^ _779327) ^ [_1397545] : [-(hAPP(c_Relation_OField(_1397545), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1397545, _1397545), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1397545, tc_HOL_Obool)))], (31437 ^ _779327) ^ [_1349534, _1349536] : [class_Complete__Lattice_Ocomplete__lattice(_1349534), c_Orderings_Oorder__class_Omono(_1349534, _1349534, _1349536), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1349534, _1349536) = hAPP(_1349536, c_Inductive_Ocomplete__lattice__class_Olfp(_1349534, _1349536)))], (26482 ^ _779327) ^ [_1245733, _1245735, _1245737] : [class_Groups_Ocomm__monoid__add(_1245733), class_Groups_Ocomm__monoid__mult(_1245733), c_Nat__Transfer_Onat__set(_1245735), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1245733), _1245737), _1245735) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245733), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1245733, tc_Nat_Onat), _1245737), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1245735)))], (28624 ^ _779327) ^ [_1289362, _1289364, _1289366] : [-(hAPP(c_Set_Oimage(_1289362, _1289364, _1289366), c_Orderings_Obot__class_Obot(tc_fun(_1289362, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1289364, tc_HOL_Obool)))], (37475 ^ _779327) ^ [_1480315, _1480317, _1480319, _1480321, _1480323, _1480325] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480315, _1480317, _1480319, _1480321, _1480323), _1480325)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1480315), _1480323)))], (46068 ^ _779327) ^ [_1695938, _1695940, _1695942, _1695944] : [hAPP(hAPP(c_List_Olist__update(_1695938, _1695940), _1695942), _1695944) = c_List_Olist_ONil(_1695938), -(_1695940 = c_List_Olist_ONil(_1695938))], (34739 ^ _779327) ^ [_1419447, _1419449, _1419451] : [class_Lattices_Osemilattice__inf(_1419447), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419447), _1419449), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419447), _1419449), _1419451)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419447), _1419449), _1419451))], (35171 ^ _779327) ^ [_1428675, _1428677, _1428679] : [class_Lattices_Oboolean__algebra(_1428675), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1428675), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428675), _1428677), _1428679)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428675), hAPP(c_Groups_Ouminus__class_Ouminus(_1428675), _1428677)), hAPP(c_Groups_Ouminus__class_Ouminus(_1428675), _1428679)))], (9771 ^ _779327) ^ [_937690, _937692] : [class_Rings_Ocomm__semiring__1(_937690), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937690), c_Groups_Oone__class_Oone(_937690)), _937692) = _937692)], (45960 ^ _779327) ^ [_1693403, _1693405, _1693407, _1693409, _1693411] : [-(hAPP(hAPP(c_List_Olist_OCons(_1693403), _1693405), _1693407) = hAPP(hAPP(c_List_Oappend(_1693403), _1693409), _1693411)), 45961 ^ _779327 : [(45968 ^ _779327) ^ [_1693586] : [hAPP(hAPP(c_List_Olist_OCons(_1693403), _1693405), _1693586) = _1693409, _1693407 = hAPP(hAPP(c_List_Oappend(_1693403), _1693586), _1693411)], (45962 ^ _779327) ^ [] : [_1693409 = c_List_Olist_ONil(_1693403), hAPP(hAPP(c_List_Olist_OCons(_1693403), _1693405), _1693407) = _1693411]]], (28618 ^ _779327) ^ [_1289245, _1289247, _1289249, _1289251] : [_1289251 = c_Orderings_Obot__class_Obot(tc_fun(_1289245, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1289245, _1289247, _1289249), _1289251) = c_Orderings_Obot__class_Obot(tc_fun(_1289247, tc_HOL_Obool)))], (23626 ^ _779327) ^ [_1190715] : [-(_1190715 = 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, _1190715)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1190715))))], (6168 ^ _779327) ^ [_876486, _876488, _876490, _876492] : [class_Orderings_Oord(_876486), _876488 = _876490, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876486), _876490), _876492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876486), _876488), _876492)))], (15503 ^ _779327) ^ [_1041411, _1041413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041411), _1041413)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1041411), _1041413) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23650 ^ _779327) ^ [_1191109, _1191111] : [hAPP(c_Code__Numeral_Onat__of, _1191109) = hAPP(c_Code__Numeral_Onat__of, _1191111), -(_1191109 = _1191111)], (52930 ^ _779327) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (29843 ^ _779327) ^ [_1312818, _1312820, _1312822] : [hBOOL(hAPP(_1312822, _1312820)), -(hBOOL(hAPP(hAPP(c_member(_1312818), _1312820), _1312822)))], (8970 ^ _779327) ^ [_923818, _923820] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923818), _923820))), -(_923818 = _923820), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923820), _923818)))], (23590 ^ _779327) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (18316 ^ _779327) ^ [_1090422, _1090424] : [class_Groups_Omonoid__mult(_1090422), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090422), _1090424), 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(_1090422), _1090424), _1090424))], (22527 ^ _779327) ^ [_1169178, _1169180, _1169182, _1169184] : [class_Orderings_Olinorder(_1169178), 22530 ^ _779327 : [(22531 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169178), _1169180), _1169182)), _1169184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), _1169180), _1169184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), _1169182), _1169184)))], (22541 ^ _779327) ^ [] : [22542 ^ _779327 : [(22545 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), _1169182), _1169184))], (22543 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), _1169180), _1169184))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169178), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169178), _1169180), _1169182)), _1169184)))]]], (48193 ^ _779327) ^ [_1742790, _1742792] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1742790))), c_Enum_Osublists(_1742790, _1742792)) = 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(_1742790)), _1742792)))], (23117 ^ _779327) ^ [_1180238, _1180240, _1180242, _1180244, _1180246, _1180248] : [hAPP(c_Product__Type_Oapfst(_1180238, _1180240, _1180242, _1180244), _1180246) = hAPP(c_Product__Type_Oapfst(_1180238, _1180240, _1180242, _1180248), _1180246), -(hAPP(_1180244, hAPP(c_Product__Type_Ofst(_1180238, _1180242), _1180246)) = hAPP(_1180248, hAPP(c_Product__Type_Ofst(_1180238, _1180242), _1180246)))], (9202 ^ _779327) ^ [_928155, _928157, _928159, _928161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928155, tc_HOL_Obool)), _928157), _928159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928155, tc_HOL_Obool)), _928159), _928161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928155, tc_HOL_Obool)), _928157), _928161)))], (42043 ^ _779327) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (45261 ^ _779327) ^ [_1675213, _1675215, _1675217, _1675219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675213), _1675215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675217, tc_HOL_Obool)), hAPP(c_List_Oset(_1675217), hAPP(hAPP(c_List_Otake(_1675217), _1675213), _1675219))), hAPP(c_List_Oset(_1675217), hAPP(hAPP(c_List_Otake(_1675217), _1675215), _1675219)))))], (10771 ^ _779327) ^ [_954640, _954642, _954644] : [class_Int_Onumber(_954640), 10774 ^ _779327 : [(10781 ^ _779327) ^ [] : [_954644 = hAPP(c_Int_Onumber__class_Onumber__of(_954640), _954642), -(hAPP(c_Int_Onumber__class_Onumber__of(_954640), _954642) = _954644)], (10775 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_954640), _954642) = _954644, -(_954644 = hAPP(c_Int_Onumber__class_Onumber__of(_954640), _954642))]]], (21834 ^ _779327) ^ [_1155561, _1155563] : [-(_1155561 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21837 ^ _779327 : [(21844 ^ _779327) ^ [] : [-(_1155563 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1155561, _1155563) = 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, _1155563))), 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, _1155561)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1155563))), c_Divides_Opdivmod(_1155561, _1155563)), 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), _1155563))))), c_Divides_Opdivmod(_1155561, _1155563)))))], (21838 ^ _779327) ^ [] : [_1155563 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1155561, _1155563) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155561))]]], (47114 ^ _779327) ^ [_1719870, _1719872, _1719874] : [-(hAPP(c_List_Orotate(_1719870, _1719872), _1719874) = hAPP(c_List_Orotate(_1719870, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1719872, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719870)), _1719874))), _1719874))], (18676 ^ _779327) ^ [_1097102, _1097104] : [class_Int_Onumber__ring(_1097102), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1097102), hAPP(c_Int_Onumber__class_Onumber__of(_1097102), 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)))), _1097104)) = c_Groups_Oone__class_Oone(_1097102))], (43620 ^ _779327) ^ [_1633203, _1633205, _1633207, _1633209] : [hBOOL(hAPP(hAPP(c_member(_1633203), _1633205), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1633203, tc_HOL_Obool), _1633207))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1633203, tc_HOL_Obool)), _1633209), _1633207)), -(hBOOL(hAPP(hAPP(c_member(_1633203), _1633205), _1633209)))], (38649 ^ _779327) ^ [_1507907, _1507909, _1507911, _1507913] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507907), _1507909)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507907), _1507911)), -(_1507911 = c_Orderings_Obot__class_Obot(tc_fun(_1507907, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1507907, tc_HOL_Obool), tc_fun(_1507907, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1507907, tc_HOL_Obool), tc_fun(_1507907, tc_HOL_Obool)), _1507909), _1507911)), c_Wellfounded_Omax__ext(_1507907, _1507913)))), 38663 ^ _779327 : [(38666 ^ _779327) ^ [_1508312] : [hBOOL(hAPP(hAPP(c_member(_1507907), _1508312), _1507911)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507907, _1507907)), hAPP(hAPP(c_Product__Type_OPair(_1507907, _1507907), 38662 ^ [_1507907, _1507909, _1507911, _1507913]), _1508312)), _1507913))], (38664 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507907), 38662 ^ [_1507907, _1507909, _1507911, _1507913]), _1507909)))]]], (44985 ^ _779327) ^ [_1668292, _1668294, _1668296, _1668298] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668292), tc_List_Olist(_1668292))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668292), tc_List_Olist(_1668292)), _1668294), _1668296)), c_List_Olexord(_1668292, _1668298))), 44990 ^ _779327 : [(44993 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1668292), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668292)), _1668294)), _1668296) = _1668294)], (44991 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668292)), _1668294)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668292)), _1668296))))]], 44995 ^ _779327 : [(45000 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668292, _1668292)), hAPP(hAPP(c_Product__Type_OPair(_1668292, _1668292), hAPP(hAPP(c_List_Onth(_1668292), _1668294), 44994 ^ [_1668292, _1668294, _1668296, _1668298])), hAPP(hAPP(c_List_Onth(_1668292), _1668296), 44994 ^ [_1668292, _1668294, _1668296, _1668298]))), _1668298)))], (44998 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1668292), 44994 ^ [_1668292, _1668294, _1668296, _1668298]), _1668294) = hAPP(hAPP(c_List_Otake(_1668292), 44994 ^ [_1668292, _1668294, _1668296, _1668298]), _1668296))], (44996 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44994 ^ [_1668292, _1668294, _1668296, _1668298]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668292)), _1668294)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668292)), _1668296)))))]]], (52992 ^ _779327) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (13551 ^ _779327) ^ [_1006243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006243), 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)), _1006243)), _1006243)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51305 ^ _779327) ^ [_1810030] : [-(c_Lazy__Sequence_Oyieldn(_1810030) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1810030), _1810030, c_Lazy__Sequence_Oyield(_1810030)))], (2782 ^ _779327) ^ [_820589, _820591] : [_820591 = _820589, -(c_New__DSequence_Opos__empty(_820591) = c_New__DSequence_Opos__empty(_820589))], (13585 ^ _779327) ^ [_1006979, _1006981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006979), _1006981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1006981), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (22463 ^ _779327) ^ [_1168025, _1168027, _1168029] : [class_Orderings_Olinorder(_1168025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168025), _1168027), _1168029)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168025), _1168029), _1168027) = _1168027)], (4200 ^ _779327) ^ [_843096, _843098] : [_843098 = _843096, -(c_Int_Onumber__class_Onumber__of(_843098) = c_Int_Onumber__class_Onumber__of(_843096))], (40867 ^ _779327) ^ [_1568784, _1568786] : [-(hAPP(c_List_Olexn(_1568784, _1568786), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1568784), tc_List_Olist(_1568784)), tc_HOL_Obool)))], (11399 ^ _779327) ^ [_967355, _967357] : [_967355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967355), _967357) = _967357)], (5689 ^ _779327) ^ [_869246, _869248, _869250, _869252, _869254] : [hAPP(_869246, 5690 ^ [_869246, _869248, _869250, _869252, _869254]) = hAPP(c_Nat_Onat_Onat__rec(_869248, _869250, _869252), 5690 ^ [_869246, _869248, _869250, _869252, _869254]), -(hAPP(_869246, hAPP(c_Nat_OSuc, _869254)) = hAPP(hAPP(_869252, _869254), hAPP(_869246, _869254)))], (38806 ^ _779327) ^ [_1512290, _1512292, _1512294, _1512296, _1512298, _1512300] : [class_Groups_Ocomm__monoid__mult(_1512290), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1512292, _1512290), hAPP(hAPP(c_COMBC(_1512292, tc_fun(_1512294, tc_HOL_Obool), _1512290), hAPP(hAPP(c_COMBB(tc_fun(_1512294, _1512290), tc_fun(tc_fun(_1512294, tc_HOL_Obool), _1512290), _1512292), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1512294, _1512290)), _1512296)), _1512298)), _1512300) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1512292, _1512294), _1512290), hAPP(c_Product__Type_Oprod_Oprod__case(_1512292, _1512294, _1512290), _1512296)), hAPP(hAPP(c_Product__Type_OSigma(_1512292, _1512294), _1512300), hAPP(c_COMBK(tc_fun(_1512294, tc_HOL_Obool), _1512292), _1512298))))], (45269 ^ _779327) ^ [_1675432, _1675434, _1675436, _1675438, _1675440] : [hBOOL(hAPP(hAPP(c_member(_1675432), _1675434), hAPP(c_List_Oset(_1675432), _1675436))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675438), hAPP(_1675440, _1675434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675438), c_List_Olist_Olist__size(_1675432, _1675440, _1675436))))], (27877 ^ _779327) ^ [_1274994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1274994)), -(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)), _1274994))))], (45745 ^ _779327) ^ [_1688137, _1688139, _1688141, _1688143, _1688145] : [class_Rings_Osemiring__0(_1688137), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1688137), hAPP(hAPP(c_List_Omap(_1688139, _1688137), hAPP(hAPP(c_COMBB(_1688137, _1688137, _1688139), hAPP(c_Groups_Otimes__class_Otimes(_1688137), _1688141)), _1688143)), _1688145)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1688137), _1688141), hAPP(c_List_Omonoid__add__class_Olistsum(_1688137), hAPP(hAPP(c_List_Omap(_1688139, _1688137), _1688143), _1688145))))], (47151 ^ _779327) ^ [_1720544, _1720546, _1720548] : [-(c_List_Orotate(_1720544, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720546), _1720548)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1720544), tc_List_Olist(_1720544), tc_List_Olist(_1720544), c_List_Orotate(_1720544, _1720546)), c_List_Orotate(_1720544, _1720548)))], (26247 ^ _779327) ^ [_1240769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240769)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240769) = 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, _1240769))))], (27693 ^ _779327) ^ [_1271101, _1271103, _1271105, _1271107, _1271109] : [class_Complete__Lattice_Ocomplete__lattice(_1271101), 27696 ^ _779327 : [(27697 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271101), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271103, _1271101), _1271105), _1271107)), _1271109)), 27700 ^ _779327 : [(27701 ^ _779327) ^ [_1271282] : [hBOOL(hAPP(hAPP(c_member(_1271103), _1271282), _1271105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271101), hAPP(_1271107, _1271282)), _1271109)))]]], (27707 ^ _779327) ^ [] : [27709 ^ _779327 : [(27712 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271101), hAPP(_1271107, 27708 ^ [_1271101, _1271103, _1271105, _1271107, _1271109])), _1271109))], (27710 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1271103), 27708 ^ [_1271101, _1271103, _1271105, _1271107, _1271109]), _1271105)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271101), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271103, _1271101), _1271105), _1271107)), _1271109)))]]], (2096 ^ _779327) ^ [_809632, _809634, _809636, _809638, _809640, _809642] : [-(c_Random_Ominus__shift(_809642, _809638, _809634) = c_Random_Ominus__shift(_809640, _809636, _809632)), _809642 = _809640, _809638 = _809636, _809634 = _809632], (25448 ^ _779327) ^ [_1223195, _1223197, _1223199] : [25449 ^ _779327 : [(25450 ^ _779327) ^ [_1223276, _1223278] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223195), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223197), _1223278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1223199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223197), _1223276))]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223195, _1223197) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223199, _1223197))], (21170 ^ _779327) ^ [_1142634, _1142636] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1142634))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1142636)), hAPP(c_Int_Onat, _1142634)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142636), _1142634)), 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)))], (9751 ^ _779327) ^ [_937402] : [class_Rings_Ozero__neq__one(_937402), c_Groups_Ozero__class_Ozero(_937402) = c_Groups_Oone__class_Oone(_937402)], (46796 ^ _779327) ^ [_1713174, _1713176, _1713178, _1713180] : [hBOOL(hAPP(c_List_Odistinct(_1713174), _1713176)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1713178, _1713174)), hAPP(hAPP(c_List_Ozip(_1713178, _1713174), _1713180), _1713176))))], (35463 ^ _779327) ^ [_1435333, _1435335, _1435337] : [class_Orderings_Oorder(_1435333), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435333, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1435333), _1435335)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435333, _1435335), _1435337)) = c_Orderings_Obot__class_Obot(tc_fun(_1435333, tc_HOL_Obool)))], (2110 ^ _779327) ^ [_809853, _809855, _809857, _809859] : [-(c_Random_Oinc__shift(_809859, _809855) = c_Random_Oinc__shift(_809857, _809853)), _809859 = _809857, _809855 = _809853], (2466 ^ _779327) ^ [_815397, _815399, _815401, _815403] : [-(c_Nitpick_OAbs__Frac(_815403, _815399) = c_Nitpick_OAbs__Frac(_815401, _815397)), _815403 = _815401, _815399 = _815397], (16665 ^ _779327) ^ [_1061998, _1062000, _1062002] : [class_Rings_Olinordered__idom(_1061998), -(hAPP(c_Groups_Oabs__class_Oabs(_1061998), hAPP(hAPP(c_Power_Opower__class_Opower(_1061998), hAPP(c_Groups_Ouminus__class_Ouminus(_1061998), _1062000)), _1062002)) = hAPP(c_Groups_Oabs__class_Oabs(_1061998), hAPP(hAPP(c_Power_Opower__class_Opower(_1061998), _1062000), _1062002)))], (13718 ^ _779327) ^ [_1009438, _1009440, _1009442] : [class_Groups_Oordered__comm__monoid__add(_1009438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009438), _1009440), c_Groups_Ozero__class_Ozero(_1009438))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009438), _1009442), c_Groups_Ozero__class_Ozero(_1009438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009438), _1009440), _1009442)), c_Groups_Ozero__class_Ozero(_1009438))))], (52984 ^ _779327) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52932 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (27855 ^ _779327) ^ [_1274573, _1274575] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1274573, _1274575))))], (47885 ^ _779327) ^ [_1735936, _1735938, _1735940] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1735936)), _1735940), c_List_Olists(_1735936, _1735938))), -(hBOOL(hAPP(c_List_Olistsp(_1735936, hAPP(hAPP(c_COMBC(_1735936, tc_fun(_1735936, tc_HOL_Obool), tc_HOL_Obool), c_member(_1735936)), _1735938)), _1735940)))], (38429 ^ _779327) ^ [_1503101, _1503103, _1503105, _1503107, _1503109] : [hAPP(_1503107, _1503103) = _1503109, -(hBOOL(hAPP(hAPP(c_member(_1503101), _1503103), hAPP(c_Set_Ovimage(_1503101, _1503105, _1503107), hAPP(hAPP(c_Set_Oinsert(_1503105), _1503109), c_Orderings_Obot__class_Obot(tc_fun(_1503105, tc_HOL_Obool)))))))], (19419 ^ _779327) ^ [_1109871, _1109873, _1109875] : [class_Fields_Ofield__inverse__zero(_1109871), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109871), c_Groups_Oone__class_Oone(_1109871)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109871), _1109873), _1109875)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1109871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109871), c_Groups_Oone__class_Oone(_1109871)), _1109873)), _1109875))], (16003 ^ _779327) ^ [_1050181, _1050183] : [class_Int_Onumber__ring(_1050181), -(hAPP(c_Int_Onumber__class_Onumber__of(_1050181), c_Int_Osucc(_1050183)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050181), c_Groups_Oone__class_Oone(_1050181)), hAPP(c_Int_Onumber__class_Onumber__of(_1050181), _1050183)))], (3158 ^ _779327) ^ [_826745, _826747] : [_826747 = _826745, -(c_SetInterval_Oord__class_OgreaterThan(_826747) = c_SetInterval_Oord__class_OgreaterThan(_826745))], (42306 ^ _779327) ^ [_1602986, _1602988, _1602990] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1602986, _1602986, _1602988), c_Relation_OId(_1602986)), _1602990) = _1602990)], (29628 ^ _779327) ^ [_1308588, _1308590, _1308592, _1308594, _1308596, _1308598] : [hBOOL(hAPP(hAPP(c_member(_1308588), _1308590), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1308592, tc_fun(_1308588, tc_HOL_Obool)), _1308594), _1308596))), -(hBOOL(hAPP(hAPP(c_member(_1308588), _1308590), hAPP(_1308596, _1308598)))), hBOOL(hAPP(hAPP(c_member(_1308592), _1308598), _1308594))], (39838 ^ _779327) ^ [_1535819, _1535821, _1535823] : [hBOOL(hAPP(_1535819, _1535821)), -(hAPP(c_Set_OCollect(_1535823), hAPP(hAPP(c_COMBS(_1535823, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535823), c_fconj), hAPP(c_fequal, _1535821))), _1535819)) = hAPP(hAPP(c_Set_Oinsert(_1535823), _1535821), c_Orderings_Obot__class_Obot(tc_fun(_1535823, tc_HOL_Obool))))], (18206 ^ _779327) ^ [_1088519, _1088521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1088519)), c_Int_OBit0(_1088521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088519), _1088521)))], (42573 ^ _779327) ^ [_1609494, _1609496, _1609498] : [c_Relation_Orefl__on(_1609494, _1609496, _1609498), -(c_Relation_Orefl__on(_1609494, _1609496, hAPP(c_Relation_Oconverse(_1609494, _1609494), _1609498)))], (23929 ^ _779327) ^ [_1196322, _1196324, _1196326] : [class_Rings_Ocomm__ring__1(_1196322), 23932 ^ _779327 : [(23939 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196322), _1196324), _1196326)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196322), _1196324), hAPP(c_Groups_Ouminus__class_Ouminus(_1196322), _1196326))))], (23933 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196322), _1196324), hAPP(c_Groups_Ouminus__class_Ouminus(_1196322), _1196326))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196322), _1196324), _1196326)))]]], (40933 ^ _779327) ^ [_1570392, _1570394, _1570396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570392, _1570394)), _1570396)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1570392), hAPP(c_Relation_ODomain(_1570392, _1570394), _1570396))))], (23279 ^ _779327) ^ [_1183485, _1183487, _1183489, _1183491, _1183493, _1183495, _1183497] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1183485, _1183487, _1183489, _1183491), _1183493), _1183495), _1183497) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183487, _1183489, _1183491), _1183495), hAPP(_1183493, _1183497)))], (40263 ^ _779327) ^ [_1552385, _1552387] : [-(c_Product__Type_Omap__pair(_1552385, _1552385, _1552387, _1552387, c_Fun_Oid(_1552385), c_Fun_Oid(_1552387)) = c_Fun_Oid(tc_prod(_1552385, _1552387)))], (34278 ^ _779327) ^ [_1408695, _1408697, _1408699] : [_1408697 = c_Orderings_Obot__class_Obot(tc_fun(_1408695, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408695, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408695), _1408697), _1408699))], (28463 ^ _779327) ^ [_1286090, _1286092, _1286094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1286090), _1286092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1286090, tc_HOL_Obool)), _1286094), _1286092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1286090), _1286094)), hAPP(c_Finite__Set_Ocard(_1286090), _1286092))))], (39638 ^ _779327) ^ [_1531272] : [-(c_Finite__Set_Ofun__left__comm__idem(_1531272, tc_fun(_1531272, tc_HOL_Obool), c_Set_Oinsert(_1531272)))], (23796 ^ _779327) ^ [_1194086, _1194088, _1194090] : [23798 ^ _779327 : [(23801 ^ _779327) ^ [] : [hBOOL(hAPP(_1194088, 23797 ^ [_1194086, _1194088, _1194090]))], (23799 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1194086), 23797 ^ [_1194086, _1194088, _1194090]), _1194090)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1194086, _1194088), _1194090)))], (52764 ^ _779327) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (39712 ^ _779327) ^ [_1532838, _1532840, _1532842] : [-(hAPP(c_Set_OCollect(_1532838), hAPP(hAPP(c_COMBS(_1532838, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532838), c_fdisj), _1532840)), _1532842)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1532838, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1532838), _1532840)), hAPP(c_Set_OCollect(_1532838), _1532842)))], (50781 ^ _779327) ^ [_1799077, _1799079, _1799081] : [c_List_Olist__all(_1799077, _1799079, _1799081), 50784 ^ _779327 : [(50785 ^ _779327) ^ [_1799166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1799166), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799077)), _1799081))), -(hBOOL(hAPP(_1799079, hAPP(hAPP(c_List_Onth(_1799077), _1799081), _1799166))))]]], (13324 ^ _779327) ^ [_1002384, _1002386] : [class_Rings_Ocomm__semiring__1(_1002384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002384), _1002386), _1002386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002384), c_Groups_Oone__class_Oone(_1002384)), c_Groups_Oone__class_Oone(_1002384))), _1002386))], (30405 ^ _779327) ^ [_1326210, _1326212, _1326214, _1326216, _1326218, _1326220] : [hBOOL(hAPP(hAPP(c_member(_1326210), _1326212), _1326214)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326210, tc_fun(_1326216, tc_HOL_Obool)), _1326214), hAPP(hAPP(c_COMBB(tc_fun(_1326216, tc_HOL_Obool), tc_fun(_1326216, tc_HOL_Obool), _1326210), hAPP(c_Set_Oinsert(_1326216), _1326218)), _1326220)) = hAPP(hAPP(c_Set_Oinsert(_1326216), _1326218), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326210, tc_fun(_1326216, tc_HOL_Obool)), _1326214), _1326220)))], (15983 ^ _779327) ^ [_1049783, _1049785, _1049787] : [-(hBOOL(hAPP(_1049783, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049785), _1049787)))), 15984 ^ _779327 : [(15991 ^ _779327) ^ [_1049951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049787), _1049951)), _1049785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049787), hAPP(c_Nat_OSuc, _1049951)))), hBOOL(hAPP(_1049783, _1049951))], (15985 ^ _779327) ^ [] : [_1049787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1049783, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (27302 ^ _779327) ^ [_1261678, _1261680, _1261682, _1261684, _1261686, _1261688, _1261690] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261678, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261680, tc_fun(_1261678, tc_HOL_Obool)), _1261682), _1261684)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261686, tc_fun(_1261678, tc_HOL_Obool)), _1261688), _1261690)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261680, tc_fun(_1261678, tc_HOL_Obool)), _1261682), hAPP(hAPP(c_COMBB(tc_fun(_1261686, tc_fun(_1261678, tc_HOL_Obool)), tc_fun(_1261678, tc_HOL_Obool), _1261680), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261686, tc_fun(_1261678, tc_HOL_Obool)), _1261688)), hAPP(hAPP(c_COMBC(_1261680, tc_fun(_1261686, tc_fun(_1261678, tc_HOL_Obool)), tc_fun(_1261686, tc_fun(_1261678, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1261678, tc_HOL_Obool), tc_fun(_1261678, tc_HOL_Obool)), tc_fun(tc_fun(_1261686, tc_fun(_1261678, tc_HOL_Obool)), tc_fun(_1261686, tc_fun(_1261678, tc_HOL_Obool))), _1261680), c_COMBB(tc_fun(_1261678, tc_HOL_Obool), tc_fun(_1261678, tc_HOL_Obool), _1261686)), hAPP(hAPP(c_COMBB(tc_fun(_1261678, tc_HOL_Obool), tc_fun(tc_fun(_1261678, tc_HOL_Obool), tc_fun(_1261678, tc_HOL_Obool)), _1261680), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261678, tc_HOL_Obool))), _1261684))), _1261690))))], (12694 ^ _779327) ^ [_991478, _991480] : [class_Groups_Osgn__if(_991478), 12697 ^ _779327 : [(12704 ^ _779327) ^ [] : [-(_991480 = c_Groups_Ozero__class_Ozero(_991478)), 12707 ^ _779327 : [(12714 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991478), c_Groups_Ozero__class_Ozero(_991478)), _991480))), -(c_Groups_Osgn__class_Osgn(_991478, _991480) = hAPP(c_Groups_Ouminus__class_Ouminus(_991478), c_Groups_Oone__class_Oone(_991478)))], (12708 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991478), c_Groups_Ozero__class_Ozero(_991478)), _991480)), -(c_Groups_Osgn__class_Osgn(_991478, _991480) = c_Groups_Oone__class_Oone(_991478))]]], (12698 ^ _779327) ^ [] : [_991480 = c_Groups_Ozero__class_Ozero(_991478), -(c_Groups_Osgn__class_Osgn(_991478, _991480) = c_Groups_Ozero__class_Ozero(_991478))]]], (14017 ^ _779327) ^ [_1014809, _1014811, _1014813, _1014815, _1014817, _1014819] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014809), _1014811)), _1014813) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014815), _1014817)), _1014819), 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), _1014815), _1014817)), _1014819))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014819), _1014815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014815), _1014809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014811), _1014817)))], (41742 ^ _779327) ^ [_1589190, _1589192, _1589194, _1589196, _1589198] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1589190), _1589192), _1589194), _1589196), _1589198) = c_New__DSequence_Oneg__single(_1589190, _1589192))], (33784 ^ _779327) ^ [_1396932, _1396934] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396932, _1396932)), hAPP(hAPP(c_Product__Type_OPair(_1396932, _1396932), 33785 ^ [_1396932, _1396934]), 33785 ^ [_1396932, _1396934])), _1396934))), -(c_Relation_Oirrefl(_1396932, _1396934))], (17456 ^ _779327) ^ [_1075694] : [c_Int_OMin = _1075694, -(c_Int_OMin = c_Int_OBit1(_1075694))], (9409 ^ _779327) ^ [_931727, _931729, _931731] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931727), _931729)), _931731) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931729), _931731)))], (13454 ^ _779327) ^ [_1004726, _1004728] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004726), _1004728)), 13455 ^ _779327 : [(13462 ^ _779327) ^ [] : [_1004726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1004728 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13456 ^ _779327) ^ [] : [_1004726 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1004728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51102 ^ _779327) ^ [_1805307, _1805309, _1805311, _1805313] : [51103 ^ _779327 : [(51106 ^ _779327) ^ [] : [_1805309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51104 ^ _779327) ^ [] : [hBOOL(hAPP(_1805313, _1805311))]], 51107 ^ _779327 : [(51108 ^ _779327) ^ [_1805432] : [hBOOL(hAPP(hAPP(c_member(_1805307), _1805432), hAPP(c_List_Oset(_1805307), c_List_Oreplicate(_1805307, _1805309, _1805311)))), -(hBOOL(hAPP(_1805313, _1805432)))]]], (47572 ^ _779327) ^ [_1729046, _1729048, _1729050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729046, tc_HOL_Obool)), hAPP(c_List_Oset(_1729046), c_List_Oremove1(_1729046, _1729048, _1729050))), hAPP(c_List_Oset(_1729046), _1729050))))], (35177 ^ _779327) ^ [_1428814, _1428816, _1428818] : [class_Lattices_Oboolean__algebra(_1428814), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1428814), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428814), _1428816), _1428818)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1428814), hAPP(c_Groups_Ouminus__class_Ouminus(_1428814), _1428816)), hAPP(c_Groups_Ouminus__class_Ouminus(_1428814), _1428818)))], (30731 ^ _779327) ^ [_1334456, _1334458, _1334460, _1334462, _1334464] : [class_Groups_Ocomm__monoid__add(_1334456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334458), _1334460)), hBOOL(hAPP(hAPP(c_member(_1334458), _1334462), _1334460)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334458, _1334456), _1334464), _1334460) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334456), hAPP(_1334464, _1334462)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334458, _1334456), _1334464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334458, tc_HOL_Obool)), _1334460), hAPP(hAPP(c_Set_Oinsert(_1334458), _1334462), c_Orderings_Obot__class_Obot(tc_fun(_1334458, tc_HOL_Obool)))))))], (14305 ^ _779327) ^ [_1020408, _1020410, _1020412] : [class_Lattices_Oboolean__algebra(_1020408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020408), _1020410), _1020412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020408), hAPP(c_Groups_Ouminus__class_Ouminus(_1020408), _1020412)), hAPP(c_Groups_Ouminus__class_Ouminus(_1020408), _1020410))))], (26516 ^ _779327) ^ [_1246281, _1246283] : [c_Nat__Transfer_Onat__set(_1246281), c_Nat__Transfer_Onat__set(_1246283), 26523 ^ _779327 : [(26530 ^ _779327) ^ [] : [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), _1246281)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1246283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1246281), _1246283)))], (26524 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1246281), _1246283)), -(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), _1246281)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1246283))))]]], (49505 ^ _779327) ^ [_1771244, _1771246] : [-(hAPP(c_List_Oset(_1771244), hAPP(c_List_Orev(_1771244), _1771246)) = hAPP(c_List_Oset(_1771244), _1771246))], (2924 ^ _779327) ^ [_823002, _823004, _823006, _823008, _823010, _823012, _823014, _823016] : [-(c_SetInterval_Oord_OatLeastAtMost(_823016, _823012, _823008, _823004) = c_SetInterval_Oord_OatLeastAtMost(_823014, _823010, _823006, _823002)), _823016 = _823014, _823012 = _823010, _823008 = _823006, _823004 = _823002], (29290 ^ _779327) ^ [_1301590, _1301592] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301590), _1301592))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1301590), hAPP(c_Nat_OSuc, _1301592)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (27603 ^ _779327) ^ [_1268480, _1268482, _1268484, _1268486, _1268488] : [27605 ^ _779327 : [(27608 ^ _779327) ^ [] : [hBOOL(hAPP(_1268488, 27604 ^ [_1268480, _1268482, _1268484, _1268486, _1268488]))], (27606 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1268480), 27604 ^ [_1268480, _1268482, _1268484, _1268486, _1268488]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268482, tc_fun(_1268480, tc_HOL_Obool)), _1268484), _1268486))))]], 27609 ^ _779327 : [(27610 ^ _779327) ^ [_1268702] : [hBOOL(hAPP(hAPP(c_member(_1268482), _1268702), _1268484)), 27613 ^ _779327 : [(27614 ^ _779327) ^ [_1268799] : [hBOOL(hAPP(hAPP(c_member(_1268480), _1268799), hAPP(_1268486, _1268702))), -(hBOOL(hAPP(_1268488, _1268799)))]]]]], (12489 ^ _779327) ^ [_987429, _987431, _987433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _987429), _987431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987433), _987429)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987433), _987431))))], (17780 ^ _779327) ^ [_1080792, _1080794] : [class_Int_Onumber__ring(_1080792), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080792), c_Groups_Oone__class_Oone(_1080792)), hAPP(c_Int_Onumber__class_Onumber__of(_1080792), _1080794)) = hAPP(c_Int_Onumber__class_Onumber__of(_1080792), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080794)))], (4796 ^ _779327) ^ [_852376, _852378] : [_852378 = _852376, -(c_Orderings_Oord__class_Omin(_852378) = c_Orderings_Oord__class_Omin(_852376))], (49595 ^ _779327) ^ [_1772996, _1772998] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1772996), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1772996))), c_List_Otranspose(_1772996, _1772998)))))], (37577 ^ _779327) ^ [_1482669, _1482671] : [class_Lattices_Obounded__lattice__top(_1482669), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1482669), c_Orderings_Otop__class_Otop(_1482669)), _1482671) = _1482671)], (34997 ^ _779327) ^ [_1424369, _1424371, _1424373, _1424375, _1424377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424369, tc_HOL_Obool)), _1424371), _1424373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424369, tc_HOL_Obool)), _1424375), _1424377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424369, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424369, tc_HOL_Obool)), _1424371), _1424375)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424369, tc_HOL_Obool)), _1424373), _1424377))))], (45568 ^ _779327) ^ [_1683265, _1683267, _1683269] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683265), tc_List_Olist(_1683265))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683265), tc_List_Olist(_1683265)), c_List_Olist_ONil(_1683265)), _1683267)), c_List_Olistrel1(_1683265, _1683269)))], (39802 ^ _779327) ^ [_1534878, _1534880, _1534882] : [-(hAPP(hAPP(c_Set_Oinsert(_1534878), _1534880), _1534882) = hAPP(c_Set_OCollect(_1534878), hAPP(hAPP(c_COMBS(_1534878, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534878), c_fdisj), hAPP(hAPP(c_COMBC(_1534878, _1534878, tc_HOL_Obool), c_fequal), _1534880))), hAPP(hAPP(c_COMBC(_1534878, tc_fun(_1534878, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534878)), _1534882))))], (38804 ^ _779327) ^ [_1512198, _1512200, _1512202] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1512198, _1512200), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512198, _1512200), _1512202), hAPP(c_COMBK(tc_fun(_1512200, tc_HOL_Obool), _1512198), c_Orderings_Otop__class_Otop(tc_fun(_1512200, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1512198, _1512200), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1512198, tc_HOL_Obool)), _1512202)), hAPP(c_COMBK(tc_fun(_1512200, tc_HOL_Obool), _1512198), c_Orderings_Otop__class_Otop(tc_fun(_1512200, tc_HOL_Obool)))))], (20067 ^ _779327) ^ [_1121475, _1121477, _1121479] : [class_Fields_Olinordered__field(_1121475), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121475), _1121477), _1121479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121475), _1121477), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121475), _1121477), _1121479)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121475), c_Groups_Oone__class_Oone(_1121475)), c_Groups_Oone__class_Oone(_1121475))))))], (16730 ^ _779327) ^ [_1063030, _1063032] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1063030), _1063032)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1063030) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (43269 ^ _779327) ^ [_1626500, _1626502, _1626504] : [class_Lattices_Oab__semigroup__idem__mult(_1626500), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626500), _1626502)), -(hAPP(c_Finite__Set_Ofold1(_1626500, c_Groups_Otimes__class_Otimes(_1626500)), hAPP(hAPP(c_Set_Oinsert(_1626500), _1626504), _1626502)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626500, _1626500, c_Groups_Otimes__class_Otimes(_1626500)), _1626504), _1626502))], (30803 ^ _779327) ^ [_1336160, _1336162, _1336164] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336160), _1336162)), hBOOL(hAPP(hAPP(c_member(_1336160), _1336164), _1336162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1336160), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336160, tc_HOL_Obool)), _1336162), hAPP(hAPP(c_Set_Oinsert(_1336160), _1336164), c_Orderings_Obot__class_Obot(tc_fun(_1336160, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1336160), _1336162))))], (45414 ^ _779327) ^ [_1679858, _1679860] : [_1679860 = c_List_Olist_ONil(_1679858), -(c_Orderings_Obot__class_Obot(tc_fun(_1679858, tc_HOL_Obool)) = hAPP(c_List_Oset(_1679858), _1679860))], (23742 ^ _779327) ^ [_1192790, _1192792] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1192790), _1192792))), -(c_Quickcheck_Obeyond(_1192790, _1192792) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (45929 ^ _779327) ^ [_1692739, _1692741, _1692743, _1692745, _1692747] : [-(hAPP(hAPP(c_List_Oappend(_1692739), _1692741), _1692743) = hAPP(hAPP(c_List_Olist_OCons(_1692739), _1692745), _1692747)), 45930 ^ _779327 : [(45937 ^ _779327) ^ [_1692922] : [_1692741 = hAPP(hAPP(c_List_Olist_OCons(_1692739), _1692745), _1692922), hAPP(hAPP(c_List_Oappend(_1692739), _1692922), _1692743) = _1692747], (45931 ^ _779327) ^ [] : [_1692741 = c_List_Olist_ONil(_1692739), _1692743 = hAPP(hAPP(c_List_Olist_OCons(_1692739), _1692745), _1692747)]]], (21918 ^ _779327) ^ [_1157072, _1157074, _1157076, _1157078] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1157072, _1157074, _1157076), hAPP(hAPP(c_COMBB(tc_fun(_1157074, tc_prod(_1157072, _1157074)), tc_fun(_1157074, _1157076), _1157072), hAPP(c_COMBB(tc_prod(_1157072, _1157074), _1157076, _1157074), _1157078)), c_Product__Type_OPair(_1157072, _1157074))) = _1157078)], (46824 ^ _779327) ^ [_1713673, _1713675] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1713673, _1713675))))], (33636 ^ _779327) ^ [_1392693, _1392695, _1392697, _1392699] : [c_Wellfounded_Omax__extp(_1392693, hAPP(hAPP(c_COMBC(_1392693, tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_fun(_1392693, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392693, tc_fun(tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_fun(_1392693, tc_HOL_Obool)), _1392693), c_COMBC(_1392693, tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1392693, tc_prod(_1392693, _1392693)), tc_fun(_1392693, tc_fun(tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_HOL_Obool)), _1392693), hAPP(c_COMBB(tc_prod(_1392693, _1392693), tc_fun(tc_fun(tc_prod(_1392693, _1392693), tc_HOL_Obool), tc_HOL_Obool), _1392693), c_member(tc_prod(_1392693, _1392693)))), c_Product__Type_OPair(_1392693, _1392693)))), _1392695), _1392697, _1392699), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1392693, tc_HOL_Obool), tc_fun(_1392693, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1392693, tc_HOL_Obool), tc_fun(_1392693, tc_HOL_Obool)), _1392697), _1392699)), c_Wellfounded_Omax__ext(_1392693, _1392695))))], (37571 ^ _779327) ^ [_1482550, _1482552] : [-(hBOOL(hAPP(hAPP(c_member(_1482550), _1482552), c_Orderings_Otop__class_Otop(tc_fun(_1482550, tc_HOL_Obool)))))], (37715 ^ _779327) ^ [_1485476, _1485478] : [-(c_Sum__Type_OPlus(_1485476, _1485478, c_Orderings_Otop__class_Otop(tc_fun(_1485476, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1485478, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1485476, _1485478), tc_HOL_Obool)))], (23500 ^ _779327) ^ [_1187949, _1187951, _1187953, _1187955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1187949), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1187951, _1187953, _1187949, _1187955) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1187951)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1187951)))], (23656 ^ _779327) ^ [_1191194, _1191196] : [_1191194 = _1191196, -(hAPP(c_Code__Numeral_Onat__of, _1191194) = hAPP(c_Code__Numeral_Onat__of, _1191196))], (5314 ^ _779327) ^ [_860423, _860425, _860427, _860429] : [-(c_Transitive__Closure_Ortrancl(_860429, _860425) = c_Transitive__Closure_Ortrancl(_860427, _860423)), _860429 = _860427, _860425 = _860423], (53104 ^ _779327) ^ [_1841777, _1841779] : [hBOOL(hAPP(hAPP(c_fimplies, _1841777), _1841779)), hBOOL(_1841777), -(hBOOL(_1841779))], (42963 ^ _779327) ^ [_1619049, _1619051] : [-(c_Transitive__Closure_Ortrancl(_1619049, _1619051) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1619049, _1619049), 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(_1619049, _1619049), tc_HOL_Obool), tc_fun(tc_prod(_1619049, _1619049), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1619049, _1619049), tc_HOL_Obool)), _1619051)))], (8654 ^ _779327) ^ [_917953, _917955, _917957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917953), _917955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _917957), _917953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _917957), _917955))))], (10991 ^ _779327) ^ [_958570, _958572, _958574, _958576] : [class_Groups_Oab__semigroup__add(_958570), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958570), _958572), _958574)), _958576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958570), _958572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958570), _958574), _958576)))], (18306 ^ _779327) ^ [] : [-(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))))], (13484 ^ _779327) ^ [_1005151, _1005153] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005151), _1005153) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 13485 ^ _779327 : [(13492 ^ _779327) ^ [] : [_1005151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1005153 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13486 ^ _779327) ^ [] : [_1005151 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (42942 ^ _779327) ^ [_1618547, _1618549] : [-(hAPP(hAPP(c_Nat_Ocompow(_1618547, _1618547), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1618549) = c_Fun_Oid(_1618547))], (3942 ^ _779327) ^ [_839117, _839119, _839121, _839123] : [-(c_Big__Operators_Olinorder__class_OMax(_839123, _839119) = c_Big__Operators_Olinorder__class_OMax(_839121, _839117)), _839123 = _839121, _839119 = _839117], (28393 ^ _779327) ^ [_1284724, _1284726, _1284728, _1284730, _1284732] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284724), _1284726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284728, tc_HOL_Obool)), _1284730), hAPP(c_Set_Oimage(_1284724, _1284728, _1284732), _1284726))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284728), _1284730)))], (52254 ^ _779327) ^ [_1830681, _1830683] : [52255 ^ _779327 : [(52256 ^ _779327) ^ [_1830737] : [hBOOL(hAPP(hAPP(_1830681, _1830737), _1830737))]], c_Predicate_Osymp(_1830683, _1830681), c_Predicate_Otransp(_1830683, _1830681), -(c_Equiv__Relations_Opart__equivp(_1830683, _1830681))], (49732 ^ _779327) ^ [_1776065, _1776067, _1776069, _1776071, _1776073] : [-(c_List_OtakeWhile(_1776065, _1776067, hAPP(hAPP(c_List_Omap(_1776069, _1776065), _1776071), _1776073)) = hAPP(hAPP(c_List_Omap(_1776069, _1776065), _1776071), c_List_OtakeWhile(_1776069, hAPP(c_Fun_Ocomp(_1776065, tc_HOL_Obool, _1776069, _1776067), _1776071), _1776073)))], (52776 ^ _779327) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (24675 ^ _779327) ^ [_1208892, _1208894, _1208896, _1208898, _1208900] : [class_Divides_Osemiring__div(_1208892), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208892), _1208894), _1208896)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208892), _1208898), _1208900)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208892), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208892), _1208896), _1208894)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208892), _1208900), _1208898)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208892), _1208896), _1208900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208892), _1208894), _1208898)))], (42940 ^ _779327) ^ [_1618477, _1618479, _1618481, _1618483] : [-(hAPP(hAPP(c_Nat_Ocompow(_1618477, _1618477), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1618479), _1618481)), _1618483) = hAPP(c_Fun_Ocomp(_1618477, _1618477, _1618477, hAPP(hAPP(c_Nat_Ocompow(_1618477, _1618477), _1618479), _1618483)), hAPP(hAPP(c_Nat_Ocompow(_1618477, _1618477), _1618481), _1618483)))], (18360 ^ _779327) ^ [_1091179, _1091181] : [class_Rings_Olinordered__idom(_1091179), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091179), hAPP(c_Groups_Oabs__class_Oabs(_1091179), _1091181)), 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(_1091179), _1091181), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (47225 ^ _779327) ^ [_1722160, _1722162, _1722164, _1722166] : [class_Complete__Lattice_Ocomplete__lattice(_1722160), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722162, _1722160), hAPP(c_List_Oset(_1722162), _1722164)), _1722166) = hAPP(c_List_Ofoldl(_1722160, _1722162, hAPP(c_COMBC(_1722162, _1722160, _1722160), hAPP(hAPP(c_COMBB(_1722160, tc_fun(_1722160, _1722160), _1722162), c_Lattices_Osemilattice__inf__class_Oinf(_1722160)), _1722166)), c_Orderings_Otop__class_Otop(_1722160)), _1722164))], (27861 ^ _779327) ^ [_1274663] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1274663))))], (38818 ^ _779327) ^ [_1512843, _1512845, _1512847, _1512849] : [-(hAPP(c_Set_Oimage(tc_prod(_1512843, _1512845), tc_prod(_1512845, _1512843), hAPP(c_Product__Type_Oprod_Oprod__case(_1512843, _1512845, tc_prod(_1512845, _1512843)), hAPP(c_COMBC(_1512845, _1512843, tc_prod(_1512845, _1512843)), c_Product__Type_OPair(_1512845, _1512843)))), hAPP(hAPP(c_Product__Type_OSigma(_1512843, _1512845), _1512847), hAPP(c_COMBK(tc_fun(_1512845, tc_HOL_Obool), _1512843), _1512849))) = hAPP(hAPP(c_Product__Type_OSigma(_1512845, _1512843), _1512849), hAPP(c_COMBK(tc_fun(_1512843, tc_HOL_Obool), _1512845), _1512847)))], (52994 ^ _779327) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (20959 ^ _779327) ^ [_1138372, _1138374] : [c_Code__Numeral_OSuc__code__numeral(_1138372) = c_Code__Numeral_OSuc__code__numeral(_1138374), -(_1138372 = _1138374)], (18238 ^ _779327) ^ [_1089065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089065), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1089065)), c_Int_OMin)))], (35894 ^ _779327) ^ [_1445354, _1445356, _1445358] : [class_Orderings_Olinorder(_1445354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445354), _1445356)), -(_1445356 = c_Orderings_Obot__class_Obot(tc_fun(_1445354, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445354), _1445358)), -(_1445358 = c_Orderings_Obot__class_Obot(tc_fun(_1445354, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445354, tc_HOL_Obool)), _1445356), _1445358) = c_Orderings_Obot__class_Obot(tc_fun(_1445354, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1445354, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445354, tc_HOL_Obool)), _1445356), _1445358)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1445354), c_Big__Operators_Olinorder__class_OMin(_1445354, _1445356)), c_Big__Operators_Olinorder__class_OMin(_1445354, _1445358)))], (2192 ^ _779327) ^ [_811144, _811146, _811148, _811150] : [-(c_Divides_Opdivmod(_811150, _811146) = c_Divides_Opdivmod(_811148, _811144)), _811150 = _811148, _811146 = _811144], (48872 ^ _779327) ^ [_1758951] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1758951) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1758951)))], (5222 ^ _779327) ^ [_858951, _858953] : [_858953 = _858951, -(c_Orderings_Obot__class_Obot(_858953) = c_Orderings_Obot__class_Obot(_858951))], (52692 ^ _779327) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (50757 ^ _779327) ^ [_1798450, _1798452, _1798454] : [-(hBOOL(hAPP(hAPP(c_member(_1798450), _1798452), hAPP(c_List_Oset(_1798450), _1798454)))), 50758 ^ _779327 : [(50759 ^ _779327) ^ [_1798539, _1798541] : [_1798454 = hAPP(hAPP(c_List_Oappend(_1798450), _1798541), hAPP(hAPP(c_List_Olist_OCons(_1798450), _1798452), _1798539)), -(hBOOL(hAPP(hAPP(c_member(_1798450), _1798452), hAPP(c_List_Oset(_1798450), _1798539))))]]], (23584 ^ _779327) ^ [_1189974, _1189976] : [_1189974 = _1189976, -(hAPP(c_Code__Numeral_Oof__nat, _1189974) = hAPP(c_Code__Numeral_Oof__nat, _1189976))], (44869 ^ _779327) ^ [_1665249, _1665251, _1665253] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665249)), _1665251), c_List_Olists(_1665249, c_Wellfounded_Oacc(_1665249, _1665253)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665249)), _1665251), c_Wellfounded_Oacc(tc_List_Olist(_1665249), c_List_Olistrel1(_1665249, _1665253)))))], (8942 ^ _779327) ^ [_923294, _923296, _923298, _923300] : [class_Rings_Ocomm__semiring__1(_923294), -(hAPP(hAPP(c_Power_Opower__class_Opower(_923294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923294), _923296), _923298)), _923300) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923294), hAPP(hAPP(c_Power_Opower__class_Opower(_923294), _923296), _923300)), hAPP(hAPP(c_Power_Opower__class_Opower(_923294), _923298), _923300)))], (48670 ^ _779327) ^ [_1754001, _1754003, _1754005] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754001)), hAPP(c_List_Ofilter(_1754001, _1754003), _1754005)) = 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(_1754001)), _1754005)))), hAPP(hAPP(c_COMBB(_1754001, tc_HOL_Obool, tc_Nat_Onat), _1754003), hAPP(c_List_Onth(_1754001), _1754005))))))], (49871 ^ _779327) ^ [_1778992, _1778994, _1778996, _1778998] : [hBOOL(hAPP(_1778992, _1778994)), -(c_List_OdropWhile(_1778996, _1778992, hAPP(hAPP(c_List_Olist_OCons(_1778996), _1778994), _1778998)) = c_List_OdropWhile(_1778996, _1778992, _1778998))], (37372 ^ _779327) ^ [_1477985, _1477987, _1477989, _1477991] : [class_Groups_Ocomm__monoid__mult(_1477985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477987), _1477989)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1477987, _1477985), _1477991), _1477989) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1477985, _1477987, c_Groups_Otimes__class_Otimes(_1477985)), _1477991), c_Groups_Oone__class_Oone(_1477985)), _1477989))], (18094 ^ _779327) ^ [_1086563, _1086565] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086563)), c_Int_OBit1(_1086565)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086563), _1086565)))], (31521 ^ _779327) ^ [_1351502, _1351504, _1351506, _1351508] : [c_Orderings_Oorder__class_Omono(tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool), _1351504), hBOOL(hAPP(hAPP(c_member(_1351502), _1351506), _1351508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351502, tc_HOL_Obool)), _1351508), hAPP(_1351504, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1351502, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1351502, tc_HOL_Obool), tc_fun(tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool)), tc_fun(_1351502, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351502, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1351502, tc_HOL_Obool), tc_fun(tc_fun(_1351502, tc_HOL_Obool), tc_fun(_1351502, tc_HOL_Obool)), tc_fun(_1351502, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351502, tc_HOL_Obool))), _1351504)), _1351508))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1351502, tc_HOL_Obool), _1351504)))))), -(hBOOL(hAPP(hAPP(c_member(_1351502), _1351506), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1351502, tc_HOL_Obool), _1351504))))], (23644 ^ _779327) ^ [_1191014, _1191016, _1191018, _1191020, _1191022] : [-(_1191014 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1191016, _1191018, _1191020, _1191022), _1191014) = hAPP(c_Lazy__Sequence_Obind(_1191016, _1191018, hAPP(_1191020, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1191014), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1191016, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1191018)), _1191022), _1191014)))], (38437 ^ _779327) ^ [_1503330, _1503332, _1503334, _1503336] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503330), hAPP(c_Set_Ovimage(_1503330, _1503332, _1503334), _1503336))), hAPP(c_Set_Oimage(_1503330, _1503332, _1503334), c_Orderings_Otop__class_Otop(tc_fun(_1503330, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503332, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1503332), _1503336)))], (23303 ^ _779327) ^ [_1183965, _1183967] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1183965), _1183967) = 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), _1183965)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1183967)))))], (13330 ^ _779327) ^ [_1002515, _1002517, _1002519] : [class_Rings_Ocomm__semiring__1(_1002515), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002515), _1002517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002515), _1002519), _1002517)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002515), _1002519), c_Groups_Oone__class_Oone(_1002515))), _1002517))], (52045 ^ _779327) ^ [_1826975, _1826977] : [c_Wellfounded_Oacyclic(_1826975, _1826977), -(c_Relation_Oantisym(_1826975, c_Transitive__Closure_Ortrancl(_1826975, _1826977)))], (34697 ^ _779327) ^ [_1418452, _1418454, _1418456, _1418458, _1418460] : [class_Lattices_Olattice(_1418452), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418454, _1418452)), _1418456), _1418458), _1418460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418452), hAPP(_1418456, _1418460)), hAPP(_1418458, _1418460)))], (8228 ^ _779327) ^ [_910482, _910484, _910486] : [class_Rings_Olinordered__semidom(_910482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910482), c_Groups_Ozero__class_Ozero(_910482)), _910484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910482), c_Groups_Ozero__class_Ozero(_910482)), hAPP(hAPP(c_Power_Opower__class_Opower(_910482), _910484), _910486))))], (36506 ^ _779327) ^ [_1460484, _1460486, _1460488, _1460490] : [c_Relation_Orefl__on(_1460484, _1460486, _1460488), hBOOL(hAPP(hAPP(c_member(_1460484), _1460490), _1460486)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1460484, _1460484)), hAPP(hAPP(c_Product__Type_OPair(_1460484, _1460484), _1460490), _1460490)), _1460488)))], (16894 ^ _779327) ^ [_1065973] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1065973), hAPP(c_Int_Onumber__class_Onumber__of(_1065973), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1065973)), class_Int_Onumber__ring(_1065973), class_Rings_Olinordered__idom(_1065973)], (42623 ^ _779327) ^ [_1610523, _1610525, _1610527, _1610529] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610523, _1610523)), hAPP(hAPP(c_Product__Type_OPair(_1610523, _1610523), _1610525), _1610527)), c_Transitive__Closure_Ortrancl(_1610523, hAPP(c_Relation_Oconverse(_1610523, _1610523), _1610529)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610523, _1610523)), hAPP(hAPP(c_Product__Type_OPair(_1610523, _1610523), _1610527), _1610525)), c_Transitive__Closure_Ortrancl(_1610523, _1610529))))], (40649 ^ _779327) ^ [_1563347, _1563349] : [hBOOL(hAPP(hAPP(c_member(_1563347), 40650 ^ [_1563347, _1563349]), c_Wellfounded_Oacc(_1563347, _1563349))), -(c_Wellfounded_Owf(_1563347, _1563349))], (6258 ^ _779327) ^ [_877811, _877813, _877815] : [class_Orderings_Oorder(_877811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877811), _877813), _877815)), 6265 ^ _779327 : [(6272 ^ _779327) ^ [] : [_877815 = _877813, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877811), _877815), _877813)))], (6266 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877811), _877815), _877813)), -(_877815 = _877813)]]], (6674 ^ _779327) ^ [_883886, _883888, _883890] : [class_Orderings_Oorder(_883886), 6677 ^ _779327 : [(6686 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883886), _883888), _883890))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883886), _883888), _883890)), -(_883888 = _883890)], (6678 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883886), _883888), _883890)), 6681 ^ _779327 : [(6684 ^ _779327) ^ [] : [_883888 = _883890], (6682 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883886), _883888), _883890)))]]]]], (39856 ^ _779327) ^ [_1536255, _1536257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), hAPP(c_Set_OCollect(_1536255), _1536257))), 39859 ^ _779327 : [(39866 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), c_Orderings_Otop__class_Otop(tc_fun(_1536255, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), hAPP(c_Set_OCollect(_1536255), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536255), c_fNot), _1536257)))))], (39860 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), hAPP(c_Set_OCollect(_1536255), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536255), c_fNot), _1536257)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), c_Orderings_Otop__class_Otop(tc_fun(_1536255, tc_HOL_Obool)))))]]], (10223 ^ _779327) ^ [_944879, _944881, _944883] : [class_Rings_Olinordered__semidom(_944879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944879), c_Groups_Oone__class_Oone(_944879)), _944881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944879), c_Groups_Oone__class_Oone(_944879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944879), _944881), hAPP(hAPP(c_Power_Opower__class_Opower(_944879), _944881), _944883)))))], (29720 ^ _779327) ^ [_1310449, _1310451, _1310453, _1310455] : [hBOOL(hAPP(hAPP(c_member(_1310449), _1310451), _1310453)), -(hBOOL(hAPP(hAPP(c_member(_1310449), _1310451), hAPP(hAPP(c_Set_Oinsert(_1310449), _1310455), _1310453))))], (47165 ^ _779327) ^ [_1720828, _1720830, _1720832, _1720834, _1720836] : [c_Finite__Set_Ofun__left__comm__idem(_1720828, _1720830, _1720832), -(hAPP(hAPP(c_Finite__Set_Ofold(_1720828, _1720830, _1720832), _1720834), hAPP(c_List_Oset(_1720828), _1720836)) = hAPP(c_List_Ofoldl(_1720830, _1720828, hAPP(c_COMBC(_1720828, _1720830, _1720830), _1720832), _1720834), _1720836))], (19857 ^ _779327) ^ [_1118000, _1118002, _1118004, _1118006, _1118008] : [class_Fields_Ofield(_1118000), -(_1118002 = c_Groups_Ozero__class_Ozero(_1118000)), -(_1118004 = c_Groups_Ozero__class_Ozero(_1118000)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118000), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118000), _1118006), _1118002)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118000), _1118008), _1118004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118000), _1118006), _1118004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118000), _1118008), _1118002))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118000), _1118002), _1118004)))], (44694 ^ _779327) ^ [_1660123, _1660125, _1660127] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660123, _1660123)), hAPP(hAPP(c_Product__Type_OPair(_1660123, _1660123), 44695 ^ [_1660123, _1660125, _1660127]), 44695 ^ [_1660123, _1660125, _1660127])), _1660125))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660123), tc_List_Olist(_1660123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660123), tc_List_Olist(_1660123)), _1660127), _1660127)), c_List_Olexord(_1660123, _1660125)))], (13760 ^ _779327) ^ [_1010232, _1010234, _1010236] : [class_Rings_Olinordered__ring__strict(_1010232), 13763 ^ _779327 : [(13764 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010232), c_Groups_Ozero__class_Ozero(_1010232)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010232), _1010234), _1010234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010232), _1010236), _1010236)))), _1010234 = c_Groups_Ozero__class_Ozero(_1010232), _1010236 = c_Groups_Ozero__class_Ozero(_1010232)], (13774 ^ _779327) ^ [] : [13775 ^ _779327 : [(13778 ^ _779327) ^ [] : [-(_1010236 = c_Groups_Ozero__class_Ozero(_1010232))], (13776 ^ _779327) ^ [] : [-(_1010234 = c_Groups_Ozero__class_Ozero(_1010232))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010232), c_Groups_Ozero__class_Ozero(_1010232)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010232), _1010234), _1010234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010232), _1010236), _1010236)))))]]], (29334 ^ _779327) ^ [_1302607, _1302609, _1302611] : [class_Orderings_Olinorder(_1302607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302607), _1302609), _1302611)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302607, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302607, _1302609), _1302611)), hAPP(hAPP(c_Set_Oinsert(_1302607), _1302611), c_Orderings_Obot__class_Obot(tc_fun(_1302607, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1302607, _1302609, _1302611))], (40522 ^ _779327) ^ [_1561049, _1561051] : [c_Wellfounded_Owf(_1561049, _1561051), -(c_Wellfounded_Owf(_1561049, hAPP(hAPP(c_Relation_Orel__comp(_1561049, _1561049, _1561049), _1561051), _1561051)))], (27652 ^ _779327) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (33044 ^ _779327) ^ [_1380778, _1380780, _1380782, _1380784, _1380786, _1380788, _1380790] : [-(_1380778 = _1380780), -(c_Fun_Ofun__upd(_1380782, _1380784, c_Fun_Ofun__upd(_1380782, _1380784, _1380786, _1380778, _1380788), _1380780, _1380790) = c_Fun_Ofun__upd(_1380782, _1380784, c_Fun_Ofun__upd(_1380782, _1380784, _1380786, _1380780, _1380790), _1380778, _1380788))], (42879 ^ _779327) ^ [_1616747, _1616749, _1616751, _1616753] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1616747, _1616749), tc_fun(_1616747, _1616749)), _1616751), c_Fun_Ocomp(_1616749, _1616749, _1616747, _1616753)) = c_Fun_Ocomp(_1616749, _1616749, _1616747, hAPP(hAPP(c_Nat_Ocompow(_1616749, _1616749), _1616751), _1616753)))], (23847 ^ _779327) ^ [_1194935] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1194935), _1194935)))], (26598 ^ _779327) ^ [_1247533] : [26600 ^ _779327 : [(26603 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26599 ^ [_1247533]))], (26601 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26599 ^ [_1247533]), _1247533)))]], -(c_Nat__Transfer_Onat__set(_1247533))], (38127 ^ _779327) ^ [_1494158] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1494158), 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, _1494158)) = _1494158)], (30116 ^ _779327) ^ [_1320588, _1320590, _1320592, _1320594, _1320596] : [hBOOL(hAPP(hAPP(c_member(_1320588), _1320590), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1320592, tc_fun(_1320588, tc_HOL_Obool)), _1320594), _1320596))), 30119 ^ _779327 : [(30120 ^ _779327) ^ [_1320712] : [hBOOL(hAPP(hAPP(c_member(_1320592), _1320712), _1320594)), -(hBOOL(hAPP(hAPP(c_member(_1320588), _1320590), hAPP(_1320596, _1320712))))]]], (2546 ^ _779327) ^ [_816691, _816693, _816695, _816697] : [-(c_Divides_Odivmod__nat(_816697, _816693) = c_Divides_Odivmod__nat(_816695, _816691)), _816697 = _816695, _816693 = _816691], (8718 ^ _779327) ^ [_919196, _919198, _919200] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919196), _919198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919200), _919198)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919196), _919200))], (39733 ^ _779327) ^ [_1533214, _1533216] : [-(hBOOL(hAPP(_1533216, 39734 ^ [_1533214, _1533216]))), -(hAPP(c_Set_OCollect(_1533214), _1533216) = c_Orderings_Obot__class_Obot(tc_fun(_1533214, tc_HOL_Obool)))], (33347 ^ _779327) ^ [_1386789, _1386791, _1386793, _1386795, _1386797] : [class_Groups_Ocomm__monoid__mult(_1386789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386791), _1386793)), -(hBOOL(hAPP(hAPP(c_member(_1386791), _1386795), _1386793))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386791, _1386789), _1386797), hAPP(hAPP(c_Set_Oinsert(_1386791), _1386795), _1386793)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386789), hAPP(_1386797, _1386795)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386791, _1386789), _1386797), _1386793)))], (14237 ^ _779327) ^ [_1019273, _1019275] : [class_Lattices_Oab__semigroup__idem__mult(_1019273), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019273), _1019275), _1019275) = _1019275)], (47298 ^ _779327) ^ [_1723881, _1723883, _1723885] : [_1723881 = c_List_Olist_ONil(_1723883), -(c_List_Olast(_1723883, hAPP(hAPP(c_List_Olist_OCons(_1723883), _1723885), _1723881)) = _1723885)], (29204 ^ _779327) ^ [_1300051, _1300053, _1300055, _1300057, _1300059] : [_1300051 = c_Orderings_Obot__class_Obot(tc_fun(_1300053, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300055, tc_HOL_Obool)), _1300057), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1300053, tc_fun(_1300055, tc_HOL_Obool)), _1300051), _1300059)) = _1300057)], (24551 ^ _779327) ^ [_1206690, _1206692, _1206694, _1206696] : [class_Rings_Oidom(_1206690), 24554 ^ _779327 : [(24555 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1206690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206690), _1206692), _1206694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206690), _1206692), _1206696))), -(_1206692 = c_Groups_Ozero__class_Ozero(_1206690)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1206690), _1206694), _1206696)))], (24565 ^ _779327) ^ [] : [24566 ^ _779327 : [(24569 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1206690), _1206694), _1206696))], (24567 ^ _779327) ^ [] : [_1206692 = c_Groups_Ozero__class_Ozero(_1206690)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1206690), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206690), _1206692), _1206694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206690), _1206692), _1206696))))]]], (14243 ^ _779327) ^ [_1019364, _1019366, _1019368, _1019370, _1019372] : [class_Groups_Ominus(_1019364), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019366, _1019364)), _1019368), _1019370), _1019372) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019364), hAPP(_1019368, _1019372)), hAPP(_1019370, _1019372)))], (3760 ^ _779327) ^ [_836312, _836314] : [_836314 = _836312, -(c_Groups_Oabs__class_Oabs(_836314) = c_Groups_Oabs__class_Oabs(_836312))], (47684 ^ _779327) ^ [_1731697, _1731699, _1731701, _1731703] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1731697)), _1731699), c_List_Olists(_1731697, _1731701))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1731697)), _1731699), c_List_Olists(_1731697, _1731703))), -(hBOOL(hAPP(c_List_Olistsp(_1731697, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1731697, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1731697, tc_fun(_1731697, tc_HOL_Obool), tc_HOL_Obool), c_member(_1731697)), _1731701)), hAPP(hAPP(c_COMBC(_1731697, tc_fun(_1731697, tc_HOL_Obool), tc_HOL_Obool), c_member(_1731697)), _1731703))), _1731699)))], (38309 ^ _779327) ^ [_1500351, _1500353, _1500355, _1500357] : [c_Equiv__Relations_Oequivp(_1500351, _1500353), hBOOL(hAPP(hAPP(_1500353, _1500355), _1500357)), -(hBOOL(hAPP(hAPP(_1500353, _1500357), _1500355)))], (53008 ^ _779327) ^ [_1840487] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1840487)))], (11879 ^ _779327) ^ [_976146, _976148, _976150, _976152] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_976146), 11882 ^ _779327 : [(11889 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976146), _976148), _976152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976146), _976148), _976150)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976146), _976152), _976150))))], (11883 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976146), _976148), _976150)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976146), _976152), _976150))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976146), _976148), _976152)))]]], (37047 ^ _779327) ^ [_1470920, _1470922, _1470924, _1470926, _1470928] : [c_Fun_Oinj__on(_1470920, _1470922, _1470924, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470920, tc_HOL_Obool)), _1470926), _1470928)), 37050 ^ _779327 : [(37055 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470922, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470920, _1470922, _1470924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470920, tc_HOL_Obool)), _1470926), _1470928))), hAPP(c_Set_Oimage(_1470920, _1470922, _1470924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470920, tc_HOL_Obool)), _1470928), _1470926))) = c_Orderings_Obot__class_Obot(tc_fun(_1470922, tc_HOL_Obool)))], (37053 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1470920, _1470922, _1470924, _1470928))], (37051 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1470920, _1470922, _1470924, _1470926))]]], (42466 ^ _779327) ^ [_1606686, _1606688, _1606690, _1606692] : [-(c_Wellfounded_Oacyclic(_1606686, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1606686, _1606686)), hAPP(hAPP(c_Product__Type_OPair(_1606686, _1606686), _1606688), _1606690)), _1606692))), c_Wellfounded_Oacyclic(_1606686, _1606692), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606686, _1606686)), hAPP(hAPP(c_Product__Type_OPair(_1606686, _1606686), _1606690), _1606688)), c_Transitive__Closure_Ortrancl(_1606686, _1606692))))], (46840 ^ _779327) ^ [_1713919, _1713921] : [hBOOL(hAPP(c_List_Odistinct(_1713919), _1713921)), -(hBOOL(hAPP(c_List_Odistinct(_1713919), hAPP(c_List_Orotate1(_1713919), _1713921))))], (39614 ^ _779327) ^ [_1530880] : [class_Lattices_Osemilattice__inf(_1530880), -(c_Finite__Set_Ofun__left__comm__idem(_1530880, _1530880, c_Lattices_Osemilattice__inf__class_Oinf(_1530880)))], (2556 ^ _779327) ^ [_816840, _816842, _816844, _816846] : [-(c_Divides_Odivmod__nat__rel(_816846, _816842) = c_Divides_Odivmod__nat__rel(_816844, _816840)), _816846 = _816844, _816842 = _816840], (45131 ^ _779327) ^ [_1672278] : [-(hAPP(c_List_Omap(_1672278, _1672278), c_COMBI(_1672278)) = c_Fun_Oid(tc_List_Olist(_1672278)))], (44484 ^ _779327) ^ [_1653457, _1653459, _1653461, _1653463, _1653465] : [-(hAPP(hAPP(c_List_Olist_OCons(_1653457), _1653459), _1653461) = hAPP(hAPP(c_List_Olist_OCons(_1653457), _1653463), _1653465)), _1653459 = _1653463, _1653461 = _1653465], (35283 ^ _779327) ^ [_1431348, _1431350] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431348, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431348, tc_HOL_Obool)), _1431350)), _1431350) = c_Orderings_Obot__class_Obot(tc_fun(_1431348, tc_HOL_Obool)))], (28548 ^ _779327) ^ [_1287827] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1287827), c_Orderings_Obot__class_Obot(tc_fun(_1287827, tc_HOL_Obool)))))], (6594 ^ _779327) ^ [_882773, _882775, _882777] : [class_Orderings_Olinorder(_882773), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882773), _882775), _882777))), -(_882775 = _882777), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882773), _882777), _882775)))], (47366 ^ _779327) ^ [_1724829, _1724831, _1724833] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1724829)), _1724831), c_List_Olists(_1724829, _1724833))), -(_1724831 = c_List_Olist_ONil(_1724829)), 47375 ^ _779327 : [(47380 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1724829)), 47374 ^ [_1724829, _1724831, _1724833]), c_List_Olists(_1724829, _1724833))))], (47378 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724829), 47373 ^ [_1724829, _1724831, _1724833]), _1724833)))], (47376 ^ _779327) ^ [] : [-(_1724831 = hAPP(hAPP(c_List_Olist_OCons(_1724829), 47373 ^ [_1724829, _1724831, _1724833]), 47374 ^ [_1724829, _1724831, _1724833]))]]], (31794 ^ _779327) ^ [_1357144, _1357146] : [class_Lattices_Olattice(_1357144), -(c_Big__Operators_Olattice__class_OSup__fin(_1357144, hAPP(hAPP(c_Set_Oinsert(_1357144), _1357146), c_Orderings_Obot__class_Obot(tc_fun(_1357144, tc_HOL_Obool)))) = _1357146)], (52594 ^ _779327) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (44255 ^ _779327) ^ [_1647676, _1647678] : [-(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)))), _1647676)) = 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)))), _1647678))), 44257 ^ _779327 : [(44260 ^ _779327) ^ [] : [44261 ^ _779327 : [(44264 ^ _779327) ^ [] : [hBOOL(hAPP(_1647678, 44256 ^ [_1647676, _1647678]))], (44262 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1647676, 44256 ^ [_1647676, _1647678])))]], 44265 ^ _779327 : [(44268 ^ _779327) ^ [] : [hBOOL(hAPP(_1647676, 44256 ^ [_1647676, _1647678]))], (44266 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1647678, 44256 ^ [_1647676, _1647678])))]]], (44258 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 44256 ^ [_1647676, _1647678])))]]], (36899 ^ _779327) ^ [_1467850, _1467852, _1467854, _1467856, _1467858] : [c_Fun_Oinj__on(_1467850, _1467852, _1467854, _1467856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1467850, tc_HOL_Obool)), _1467858), _1467856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1467852, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467850, _1467852, _1467854), _1467858)), hAPP(c_Set_Oimage(_1467850, _1467852, _1467854), _1467856))))], (25263 ^ _779327) ^ [_1219777, _1219779] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219777), _1219779)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219777)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219779))))], (12359 ^ _779327) ^ [_984998] : [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)), _984998)), _984998) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (16543 ^ _779327) ^ [_1059619, _1059621] : [class_Groups_Oordered__ab__group__add__abs(_1059619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059619), c_Groups_Ozero__class_Ozero(_1059619)), _1059621)), -(hAPP(c_Groups_Oabs__class_Oabs(_1059619), _1059621) = _1059621)], (9018 ^ _779327) ^ [_924512, _924514] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924512)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924514)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _924512), _924514)))], (30567 ^ _779327) ^ [_1330915, _1330917, _1330919, _1330921, _1330923] : [class_Groups_Ocomm__monoid__add(_1330915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330917), _1330919)), -(hBOOL(hAPP(hAPP(c_member(_1330917), _1330921), _1330919))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330917, _1330915), _1330923), hAPP(hAPP(c_Set_Oinsert(_1330917), _1330921), _1330919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330915), hAPP(_1330923, _1330921)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330917, _1330915), _1330923), _1330919)))], (9701 ^ _779327) ^ [_936678, _936680, _936682] : [class_Rings_Olinordered__semidom(_936678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936678), c_Groups_Ozero__class_Ozero(_936678)), _936680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936678), _936680), c_Groups_Oone__class_Oone(_936678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936678), hAPP(hAPP(c_Power_Opower__class_Opower(_936678), _936680), hAPP(c_Nat_OSuc, _936682))), c_Groups_Oone__class_Oone(_936678))))], (15828 ^ _779327) ^ [_1046988] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046988), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1046988))], (45560 ^ _779327) ^ [_1682765, _1682767, _1682769, _1682771, _1682773, _1682775, _1682777, _1682779] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1682765, _1682767), _1682769), _1682771), hAPP(hAPP(c_List_Ozip(_1682765, _1682767), hAPP(hAPP(c_List_Omap(_1682773, _1682765), _1682775), _1682777)), _1682779)) = hAPP(hAPP(c_List_Omap(tc_prod(_1682773, _1682767), _1682769), hAPP(c_Product__Type_Oprod_Oprod__case(_1682773, _1682767, _1682769), hAPP(hAPP(c_COMBB(tc_fun(_1682767, tc_prod(_1682765, _1682767)), tc_fun(_1682767, _1682769), _1682773), hAPP(c_COMBB(tc_prod(_1682765, _1682767), _1682769, _1682767), _1682771)), hAPP(hAPP(c_COMBB(_1682765, tc_fun(_1682767, tc_prod(_1682765, _1682767)), _1682773), c_Product__Type_OPair(_1682765, _1682767)), _1682775)))), hAPP(hAPP(c_List_Ozip(_1682773, _1682767), _1682777), _1682779)))], (43080 ^ _779327) ^ [_1622602, _1622604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622602, _1622602)), _1622604), c_Relation_OId(_1622602))), -(_1622604 = hAPP(hAPP(c_Product__Type_OPair(_1622602, _1622602), 43083 ^ [_1622602, _1622604]), 43083 ^ [_1622602, _1622604]))], (43309 ^ _779327) ^ [_1627250, _1627252, _1627254] : [class_Orderings_Olinorder(_1627250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627250), _1627252)), -(c_Big__Operators_Olinorder__class_OMax(_1627250, hAPP(hAPP(c_Set_Oinsert(_1627250), _1627254), _1627252)) = hAPP(hAPP(c_Finite__Set_Ofold(_1627250, _1627250, c_Orderings_Oord__class_Omax(_1627250)), _1627254), _1627252))], (22629 ^ _779327) ^ [_1170987, _1170989] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170987)), hAPP(c_Nat_OSuc, _1170989)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1170987), _1170989)))], (21266 ^ _779327) ^ [_1144766, _1144768] : [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(_1144766))), 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)), _1144768)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144766)), hAPP(c_Nat_OSuc, _1144768))))], (40251 ^ _779327) ^ [_1552181, _1552183] : [-(c_Product__Type_Oapfst(_1552181, _1552181, _1552183, c_Fun_Oid(_1552181)) = c_Fun_Oid(tc_prod(_1552181, _1552183)))], (41843 ^ _779327) ^ [_1591490, _1591492, _1591494, _1591496] : [class_Groups_Ocomm__monoid__mult(_1591490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591492), _1591494)), 41853 ^ _779327 : [(41856 ^ _779327) ^ [] : [hAPP(_1591496, 41852 ^ [_1591490, _1591492, _1591494, _1591496]) = c_Groups_Oone__class_Oone(_1591490)], (41854 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591492), 41852 ^ [_1591490, _1591492, _1591494, _1591496]), _1591494)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1591490, _1591492, c_Groups_Otimes__class_Otimes(_1591490)), _1591496), c_Groups_Oone__class_Oone(_1591490)), _1591494) = c_Groups_Oone__class_Oone(_1591490))], (26040 ^ _779327) ^ [_1236297, _1236299, _1236301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1236297, 26041 ^ [_1236297, _1236299, _1236301])), hAPP(_1236299, 26041 ^ [_1236297, _1236299, _1236301]))), -(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), _1236299), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1236301))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1236297), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1236301))) = 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)), _1236299)), _1236297)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1236301)))], (16383 ^ _779327) ^ [_1056936] : [class_Groups_Oordered__ab__group__add__abs(_1056936), -(hAPP(c_Groups_Oabs__class_Oabs(_1056936), c_Groups_Ozero__class_Ozero(_1056936)) = c_Groups_Ozero__class_Ozero(_1056936))], (740 ^ _779327) ^ [_790739, _790741] : [-(c_Nat__Transfer_Onat__set(_790739)), _790741 = _790739, c_Nat__Transfer_Onat__set(_790741)], (15918 ^ _779327) ^ [_1048632, _1048634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1048632), _1048634)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1048632, _1048634) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1048632), _1048634))], (38303 ^ _779327) ^ [_1500262, _1500264, _1500266] : [c_Equiv__Relations_Oequivp(_1500262, _1500264), -(hBOOL(hAPP(hAPP(_1500264, _1500266), _1500266)))], (6112 ^ _779327) ^ [_875596, _875598, _875600, _875602] : [class_Orderings_Opreorder(_875596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875596), _875598), _875600)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875596), _875600), _875602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875596), _875598), _875602)))], (6302 ^ _779327) ^ [_878429, _878431, _878433] : [class_Orderings_Oorder(_878429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878429), _878431), _878433)), _878431 = _878433], (17562 ^ _779327) ^ [_1077400] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1077400)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077400))))], (22443 ^ _779327) ^ [_1167685, _1167687, _1167689, _1167691] : [class_Orderings_Olinorder(_1167685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167685), _1167687), _1167689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167685), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167685), _1167691), _1167687)), _1167689)))], (3780 ^ _779327) ^ [_836618, _836620, _836622, _836624] : [-(c_List_Olistset(_836624, _836620) = c_List_Olistset(_836622, _836618)), _836624 = _836622, _836620 = _836618], (23662 ^ _779327) ^ [_1191300, _1191302] : [hAPP(c_Code__Numeral_Onat__of, _1191300) = hAPP(c_Code__Numeral_Onat__of, _1191302), -(_1191300 = _1191302)], (41499 ^ _779327) ^ [_1583679, _1583681, _1583683, _1583685, _1583687, _1583689, _1583691, _1583693] : [c_Finite__Set_Ofolding__image(_1583679, _1583681, _1583683, _1583685, _1583687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583681), _1583689)), -(hAPP(hAPP(_1583687, hAPP(hAPP(c_COMBS(_1583681, _1583679, _1583679), hAPP(hAPP(c_COMBB(_1583679, tc_fun(_1583679, _1583679), _1583681), _1583683), _1583691)), _1583693)), _1583689) = hAPP(hAPP(_1583683, hAPP(hAPP(_1583687, _1583691), _1583689)), hAPP(hAPP(_1583687, _1583693), _1583689)))], (42659 ^ _779327) ^ [_1611683, _1611685, _1611687] : [c_Relation_Orefl__on(_1611683, _1611685, _1611687), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611683, _1611683), tc_HOL_Obool)), _1611687), hAPP(hAPP(c_Relation_Orel__comp(_1611683, _1611683, _1611683), hAPP(c_Relation_Oconverse(_1611683, _1611683), _1611687)), _1611687))))], (16790 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (13518 ^ _779327) ^ [_1005643, _1005645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1005645)), -(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), _1005643), _1005645))))], (45042 ^ _779327) ^ [_1669971, _1669973, _1669975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669971), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669973)), _1669975))), -(hAPP(c_Random_Opick(_1669973, hAPP(hAPP(c_List_Omap(_1669973, tc_prod(tc_Code__Numeral_Ocode__numeral, _1669973)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1669973), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1669975)), hAPP(c_Code__Numeral_Oof__nat, _1669971)) = hAPP(hAPP(c_List_Onth(_1669973), _1669975), _1669971))], (28682 ^ _779327) ^ [_1290466, _1290468] : [class_Orderings_Obot(_1290466), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290466), c_Orderings_Obot__class_Obot(_1290466)), _1290468)))], (52700 ^ _779327) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (39244 ^ _779327) ^ [_1522288, _1522290, _1522292] : [class_Orderings_Olinorder(_1522288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522288), _1522290)), -(_1522290 = c_Orderings_Obot__class_Obot(tc_fun(_1522288, tc_HOL_Obool))), 39255 ^ _779327 : [(39256 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522288), _1522292), hAPP(c_Finite__Set_Ofold1(_1522288, c_Orderings_Oord__class_Omin(_1522288)), _1522290))), 39259 ^ _779327 : [(39260 ^ _779327) ^ [_1522581] : [hBOOL(hAPP(hAPP(c_member(_1522288), _1522581), _1522290)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522288), _1522292), _1522581)))]]], (39266 ^ _779327) ^ [] : [39268 ^ _779327 : [(39271 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522288), _1522292), 39267 ^ [_1522288, _1522290, _1522292]))], (39269 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522288), 39267 ^ [_1522288, _1522290, _1522292]), _1522290)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522288), _1522292), hAPP(c_Finite__Set_Ofold1(_1522288, c_Orderings_Oord__class_Omin(_1522288)), _1522290))))]]], (27751 ^ _779327) ^ [_1272457, _1272459, _1272461, _1272463, _1272465] : [class_Complete__Lattice_Ocomplete__lattice(_1272457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272459, tc_HOL_Obool)), _1272461), _1272463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272457), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272459, _1272457), _1272461), _1272465)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272459, _1272457), _1272463), _1272465))))], (48848 ^ _779327) ^ [_1758521, _1758523, _1758525, _1758527] : [-(c_List_Oupt(_1758521, _1758523) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1758525), _1758527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758521), _1758523)), _1758521 = _1758525, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758521), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1758523) = _1758527], (46952 ^ _779327) ^ [_1716393, _1716395] : [class_Groups_Ocomm__monoid__add(_1716393), hBOOL(hAPP(c_List_Odistinct(_1716393), _1716395)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716393), _1716395) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1716393, _1716393), c_COMBI(_1716393)), hAPP(c_List_Oset(_1716393), _1716395)))], (44831 ^ _779327) ^ [_1664459] : [-(c_List_Olists(_1664459, c_Orderings_Otop__class_Otop(tc_fun(_1664459, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664459), tc_HOL_Obool)))], (3296 ^ _779327) ^ [_828882, _828884, _828886, _828888, _828890, _828892] : [-(c_Predicate_ODomainP(_828892, _828888, _828884) = c_Predicate_ODomainP(_828890, _828886, _828882)), _828892 = _828890, _828888 = _828886, _828884 = _828882], (10881 ^ _779327) ^ [_956682, _956684] : [class_Groups_Oab__group__add(_956682), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956682), hAPP(c_Groups_Ouminus__class_Ouminus(_956682), _956684)), _956684) = c_Groups_Ozero__class_Ozero(_956682))], (11845 ^ _779327) ^ [_975569, _975571, _975573] : [class_Rings_Oring(_975569), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975569), hAPP(c_Groups_Ouminus__class_Ouminus(_975569), _975571)), _975573) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975569), _975571), hAPP(c_Groups_Ouminus__class_Ouminus(_975569), _975573)))], (33961 ^ _779327) ^ [_1400653, _1400655, _1400657] : [hAPP(c_Set_Oimage(_1400655, tc_fun(_1400655, tc_HOL_Obool), _1400653), _1400657) = hAPP(c_Set_OPow(_1400655), _1400657)], (23061 ^ _779327) ^ [_1178974] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1178974) = _1178974)], (48981 ^ _779327) ^ [_1761216, _1761218, _1761220] : [class_Orderings_Olinorder(_1761216), c_List_Olinorder__class_Osorted(_1761216, _1761218), -(c_List_Olinorder__class_Osorted(_1761216, hAPP(hAPP(c_List_Otake(_1761216), _1761220), _1761218)))], (45516 ^ _779327) ^ [_1681947, _1681949] : [-(c_List_Osublist(_1681947, c_List_Olist_ONil(_1681947), _1681949) = c_List_Olist_ONil(_1681947))], (49565 ^ _779327) ^ [_1772400, _1772402, _1772404, _1772406, _1772408] : [-(c_List_Ofoldr(_1772400, _1772402, _1772404, _1772406, _1772408) = hAPP(c_List_Ofoldl(_1772402, _1772400, hAPP(c_COMBC(_1772400, _1772402, _1772402), _1772404), _1772408), hAPP(c_List_Orev(_1772400), _1772406)))], (13030 ^ _779327) ^ [_997075, _997077, _997079] : [class_Groups_Oordered__comm__monoid__add(_997075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997075), c_Groups_Ozero__class_Ozero(_997075)), _997077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997075), c_Groups_Ozero__class_Ozero(_997075)), _997079)), 13041 ^ _779327 : [(13050 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997075), _997077), _997079) = c_Groups_Ozero__class_Ozero(_997075)), _997077 = c_Groups_Ozero__class_Ozero(_997075), _997079 = c_Groups_Ozero__class_Ozero(_997075)], (13042 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997075), _997077), _997079) = c_Groups_Ozero__class_Ozero(_997075), 13045 ^ _779327 : [(13048 ^ _779327) ^ [] : [-(_997079 = c_Groups_Ozero__class_Ozero(_997075))], (13046 ^ _779327) ^ [] : [-(_997077 = c_Groups_Ozero__class_Ozero(_997075))]]]]], (28554 ^ _779327) ^ [_1287993, _1287995, _1287997, _1287999, _1288001] : [hAPP(hAPP(c_Set_Oinsert(_1287993), _1287995), hAPP(hAPP(c_Set_Oinsert(_1287993), _1287997), c_Orderings_Obot__class_Obot(tc_fun(_1287993, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1287993), _1287999), hAPP(hAPP(c_Set_Oinsert(_1287993), _1288001), c_Orderings_Obot__class_Obot(tc_fun(_1287993, tc_HOL_Obool)))), 28559 ^ _779327 : [(28562 ^ _779327) ^ [] : [-(_1287997 = _1288001)], (28560 ^ _779327) ^ [] : [-(_1287995 = _1287999)]], 28563 ^ _779327 : [(28566 ^ _779327) ^ [] : [-(_1287997 = _1287999)], (28564 ^ _779327) ^ [] : [-(_1287995 = _1288001)]]], (23780 ^ _779327) ^ [_1193680, _1193682, _1193684, _1193686] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1193680, _1193682, _1193684), c_Product__Type_Ocurry(_1193680, _1193682, _1193684, _1193686)) = _1193686)], (34603 ^ _779327) ^ [_1416212, _1416214, _1416216, _1416218] : [hBOOL(hAPP(hAPP(c_member(_1416212), _1416214), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416212, tc_HOL_Obool)), _1416216), _1416218))), 34606 ^ _779327 : [(34609 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416212), _1416214), _1416218)))], (34607 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416212), _1416214), _1416216)))]]], (42196 ^ _779327) ^ [_1600277, _1600279] : [-(c_Transitive__Closure_Otrancl(_1600277, _1600279) = hAPP(hAPP(c_Relation_Orel__comp(_1600277, _1600277, _1600277), _1600279), c_Transitive__Closure_Ortrancl(_1600277, _1600279)))], (11197 ^ _779327) ^ [_962782, _962784, _962786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962782), _962784)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962786), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962784), _962782)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962786), _962782)), _962784))], (36375 ^ _779327) ^ [_1457322, _1457324, _1457326] : [c_Relation_Orefl__on(_1457322, _1457324, _1457326), 36378 ^ _779327 : [(36385 ^ _779327) ^ [_1457806] : [hBOOL(hAPP(hAPP(c_member(_1457322), _1457806), _1457324)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457322, _1457322)), hAPP(hAPP(c_Product__Type_OPair(_1457322, _1457322), _1457806), _1457806)), _1457326)))], (36379 ^ _779327) ^ [_1457533] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457322, _1457322)), _1457533), _1457326)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457322, _1457322, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1457322, tc_fun(_1457322, tc_HOL_Obool), tc_fun(_1457322, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1457322, tc_HOL_Obool), tc_fun(_1457322, tc_HOL_Obool)), _1457322), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1457322)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457322), c_fconj), hAPP(hAPP(c_COMBC(_1457322, tc_fun(_1457322, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457322)), _1457324)))), hAPP(hAPP(c_COMBC(_1457322, tc_fun(_1457322, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457322)), _1457324))), _1457533)))]]], (27815 ^ _779327) ^ [_1273745, _1273747, _1273749, _1273751] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1273745), _1273747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273745, tc_HOL_Obool)), _1273747), _1273749)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1273745, tc_Nat_Onat), _1273751), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273745, tc_HOL_Obool)), _1273749), _1273747)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1273745, tc_Nat_Onat), _1273751), _1273749)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1273745, tc_Nat_Onat), _1273751), _1273747)))], (16910 ^ _779327) ^ [_1066229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066229)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1066229 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35007 ^ _779327) ^ [_1424614, _1424616, _1424618, _1424620, _1424622] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424614, tc_fun(_1424616, tc_HOL_Obool)), _1424618), hAPP(hAPP(c_COMBS(_1424614, tc_fun(_1424616, tc_HOL_Obool), tc_fun(_1424616, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1424616, tc_HOL_Obool), tc_fun(tc_fun(_1424616, tc_HOL_Obool), tc_fun(_1424616, tc_HOL_Obool)), _1424614), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424616, tc_HOL_Obool))), _1424620)), _1424622)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424616, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424614, tc_fun(_1424616, tc_HOL_Obool)), _1424618), _1424620)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424614, tc_fun(_1424616, tc_HOL_Obool)), _1424618), _1424622)))], (45820 ^ _779327) ^ [_1690357, _1690359, _1690361] : [-(c_List_Olist_Olist__size(_1690357, _1690359, _1690361) = 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(_1690357, tc_Nat_Onat), _1690359), _1690361))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690357)), _1690361)))], (34809 ^ _779327) ^ [_1420835, _1420837, _1420839, _1420841] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420835, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420835, tc_HOL_Obool)), _1420837), _1420839)), _1420841) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420835, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420835, tc_HOL_Obool)), _1420837), _1420841)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420835, tc_HOL_Obool)), _1420839), _1420841)))], (2764 ^ _779327) ^ [_820288, _820290, _820292, _820294, _820296, _820298, _820300, _820302] : [-(c_New__Random__Sequence_Opos__empty(_820302, _820298, _820294, _820290) = c_New__Random__Sequence_Opos__empty(_820300, _820296, _820292, _820288)), _820302 = _820300, _820298 = _820296, _820294 = _820292, _820290 = _820288], (2960 ^ _779327) ^ [_823604, _823606, _823608, _823610, _823612, _823614] : [-(c_SetInterval_Oord_OlessThan(_823614, _823610, _823606) = c_SetInterval_Oord_OlessThan(_823612, _823608, _823604)), _823614 = _823612, _823610 = _823608, _823606 = _823604], (43133 ^ _779327) ^ [_1623662, _1623664, _1623666, _1623668] : [class_Lattices_Osemilattice__inf(_1623662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623662), _1623664)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1623662, _1623662, c_Lattices_Osemilattice__inf__class_Oinf(_1623662)), _1623666), hAPP(hAPP(c_Set_Oinsert(_1623662), _1623668), _1623664)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1623662), _1623668), hAPP(hAPP(c_Finite__Set_Ofold(_1623662, _1623662, c_Lattices_Osemilattice__inf__class_Oinf(_1623662)), _1623666), _1623664)))], (8710 ^ _779327) ^ [_919047, _919049, _919051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919047), _919049)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _919051), _919049))), 8713 ^ _779327 : [(8716 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919047), _919051)))], (8714 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919049)))]]], (29224 ^ _779327) ^ [_1300409] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1300409, _1300409) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1300409), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (4330 ^ _779327) ^ [_845151, _845153, _845155, _845157, _845159, _845161, _845163, _845165, _845167, _845169] : [-(c_List_Ofoldr(_845169, _845165, _845161, _845157, _845153) = c_List_Ofoldr(_845167, _845163, _845159, _845155, _845151)), _845169 = _845167, _845165 = _845163, _845161 = _845159, _845157 = _845155, _845153 = _845151], (14983 ^ _779327) ^ [_1031418, _1031420, _1031422] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031418)))), 14986 ^ _779327 : [(14993 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031420)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031420)), _1031422)) = 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), _1031418), _1031420))), _1031422))], (14987 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031420))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031420)), _1031422)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031418)), _1031422))]]], (44965 ^ _779327) ^ [_1667896, _1667898, _1667900, _1667902] : [-(_1667896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1667898), hAPP(hAPP(c_List_Olist_OCons(_1667898), _1667900), _1667902)), _1667896) = hAPP(hAPP(c_List_Onth(_1667898), _1667902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1667896), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (19753 ^ _779327) ^ [_1116171, _1116173, _1116175, _1116177] : [class_Fields_Olinordered__field__inverse__zero(_1116171), 19756 ^ _779327 : [(19757 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116171), _1116175), _1116177))), 19760 ^ _779327 : [(19767 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), c_Groups_Ozero__class_Ozero(_1116171)), _1116177))), 19770 ^ _779327 : [(19777 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116177), c_Groups_Ozero__class_Ozero(_1116171)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116173), c_Groups_Ozero__class_Ozero(_1116171))))], (19771 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116177), c_Groups_Ozero__class_Ozero(_1116171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116171), _1116173), _1116177))))]]], (19761 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), c_Groups_Ozero__class_Ozero(_1116171)), _1116177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116171), _1116173), _1116177)), _1116175)))]]], (19783 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116171), _1116175), _1116177)))), 19786 ^ _779327 : [(19789 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116171), _1116173), _1116177)), _1116175))], (19787 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), c_Groups_Ozero__class_Ozero(_1116171)), _1116177)))]], 19790 ^ _779327 : [(19793 ^ _779327) ^ [] : [19794 ^ _779327 : [(19797 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116171), _1116173), _1116177)))], (19795 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116177), c_Groups_Ozero__class_Ozero(_1116171))))]], 19798 ^ _779327 : [(19801 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116173), c_Groups_Ozero__class_Ozero(_1116171)))], (19799 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), _1116177), c_Groups_Ozero__class_Ozero(_1116171)))]]], (19791 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116171), c_Groups_Ozero__class_Ozero(_1116171)), _1116177))]]]]], (51037 ^ _779327) ^ [_1804210, _1804212, _1804214] : [c_List_Oreplicate(_1804210, _1804212, _1804214) = c_List_Olist_ONil(_1804210), -(_1804212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46640 ^ _779327) ^ [_1709790, _1709792, _1709794, _1709796, _1709798] : [-(hAPP(hAPP(c_List_Oappend(_1709790), _1709792), _1709794) = hAPP(hAPP(c_List_Oappend(_1709790), _1709796), _1709798)), 46643 ^ _779327 : [(46646 ^ _779327) ^ [] : [_1709792 = hAPP(hAPP(c_List_Otake(_1709790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709792)), _1709796), _1709794 = hAPP(hAPP(c_List_Oappend(_1709790), hAPP(hAPP(c_List_Odrop(_1709790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709792)), _1709796)), _1709798)], (46644 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709792)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709796))))]], 46651 ^ _779327 : [(46654 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Otake(_1709790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709796)), _1709792) = _1709796, hAPP(hAPP(c_List_Oappend(_1709790), hAPP(hAPP(c_List_Odrop(_1709790), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709796)), _1709792)), _1709794) = _1709798], (46652 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709792)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709790)), _1709796)))]]], (32634 ^ _779327) ^ [_1372648, _1372650, _1372652] : [class_Orderings_Olinorder(_1372648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372648), _1372650)), -(_1372652 = c_Orderings_Obot__class_Obot(tc_fun(_1372648, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372648, tc_HOL_Obool)), _1372652), _1372650)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372648), c_Big__Operators_Olattice_OSup__fin(_1372648, c_Orderings_Oord__class_Omax(_1372648), _1372652)), c_Big__Operators_Olattice_OSup__fin(_1372648, c_Orderings_Oord__class_Omax(_1372648), _1372650)) = c_Big__Operators_Olattice_OSup__fin(_1372648, c_Orderings_Oord__class_Omax(_1372648), _1372650))], (49948 ^ _779327) ^ [_1780629, _1780631] : [class_Orderings_Olinorder(_1780629), 49955 ^ _779327 : [(49960 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1780629), hAPP(hAPP(c_List_Onth(_1780629), _1780631), 49953 ^ [_1780629, _1780631])), hAPP(hAPP(c_List_Onth(_1780629), _1780631), 49954 ^ [_1780629, _1780631])))], (49958 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49954 ^ [_1780629, _1780631]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780629)), _1780631))))], (49956 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49953 ^ [_1780629, _1780631]), 49954 ^ [_1780629, _1780631])))]], -(c_List_Olinorder__class_Osorted(_1780629, _1780631))], (40544 ^ _779327) ^ [_1561390, _1561392] : [c_Wellfounded_Owf(_1561390, _1561392), -(c_Wellfounded_Owf(tc_fun(_1561390, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1561390, _1561392)))], (37763 ^ _779327) ^ [_1486210, _1486212, _1486214, _1486216, _1486218] : [c_Fun_Oinj__on(_1486210, _1486212, _1486214, c_Orderings_Otop__class_Otop(tc_fun(_1486210, tc_HOL_Obool))), 37766 ^ _779327 : [(37773 ^ _779327) ^ [] : [_1486216 = _1486218, -(hAPP(_1486214, _1486216) = hAPP(_1486214, _1486218))], (37767 ^ _779327) ^ [] : [hAPP(_1486214, _1486216) = hAPP(_1486214, _1486218), -(_1486216 = _1486218)]]], (14061 ^ _779327) ^ [_1015663, _1015665, _1015667, _1015669, _1015671, _1015673] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015663), _1015665)), _1015667) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015669), _1015671)), _1015673), 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), _1015669), _1015671)), _1015673)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1015667), _1015663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1015673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1015669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015669), _1015663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1015671), _1015665)))], (34343 ^ _779327) ^ [_1410388, _1410390, _1410392, _1410394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1410388, _1410388)), hAPP(hAPP(c_Product__Type_OPair(_1410388, _1410388), _1410390), _1410392)), c_Relation_OId__on(_1410388, _1410394))), 34346 ^ _779327 : [(34349 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410388), _1410390), _1410394)))], (34347 ^ _779327) ^ [] : [-(_1410390 = _1410392)]]], (10711 ^ _779327) ^ [_953316, _953318, _953320] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953316), _953318)), _953320) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953316), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953318), _953320)))], (12115 ^ _779327) ^ [_980379, _980381, _980383, _980385] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_980379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980379), _980381), _980383)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980379), _980385), _980383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980379), _980381), _980385)))], (7103 ^ _779327) ^ [_890433, _890435] : [7104 ^ _779327 : [(7107 ^ _779327) ^ [] : [_890433 = hAPP(c_Nat_OSuc, _890435)], (7105 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890433), _890435))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890433), hAPP(c_Nat_OSuc, _890435))))], (5228 ^ _779327) ^ [_859036, _859038, _859040, _859042, _859044, _859046, _859048, _859050, _859052, _859054, _859056, _859058] : [-(c_Partial__Function_Ofun__lub(_859058, _859054, _859050, _859046, _859042, _859038) = c_Partial__Function_Ofun__lub(_859056, _859052, _859048, _859044, _859040, _859036)), _859058 = _859056, _859054 = _859052, _859050 = _859048, _859046 = _859044, _859042 = _859040, _859038 = _859036], (45002 ^ _779327) ^ [_1668832, _1668834, _1668836, _1668838] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668832), tc_List_Olist(_1668832))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668832), tc_List_Olist(_1668832)), _1668834), _1668836)), c_List_Olexord(_1668832, _1668838)))), 45003 ^ _779327 : [(45010 ^ _779327) ^ [_1669139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669139), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668832)), _1668834)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668832)), _1668836)))), hAPP(hAPP(c_List_Otake(_1668832), _1669139), _1668834) = hAPP(hAPP(c_List_Otake(_1668832), _1669139), _1668836), hBOOL(hAPP(hAPP(c_member(tc_prod(_1668832, _1668832)), hAPP(hAPP(c_Product__Type_OPair(_1668832, _1668832), hAPP(hAPP(c_List_Onth(_1668832), _1668834), _1669139)), hAPP(hAPP(c_List_Onth(_1668832), _1668836), _1669139))), _1668838))], (45004 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668832)), _1668834)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668832)), _1668836))), hAPP(hAPP(c_List_Otake(_1668832), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668832)), _1668834)), _1668836) = _1668834]]], (34643 ^ _779327) ^ [_1417509, _1417511] : [c_Nat__Transfer_Onat__set(_1417509), c_Nat__Transfer_Onat__set(_1417511), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1417509), _1417511)))], (42440 ^ _779327) ^ [_1606049, _1606051, _1606053, _1606055] : [c_Wellfounded_Owf(_1606049, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1606049, _1606049)), hAPP(hAPP(c_Product__Type_OPair(_1606049, _1606049), _1606051), _1606053)), _1606055)), 42443 ^ _779327 : [(42446 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606049, _1606049)), hAPP(hAPP(c_Product__Type_OPair(_1606049, _1606049), _1606053), _1606051)), c_Transitive__Closure_Ortrancl(_1606049, _1606055)))], (42444 ^ _779327) ^ [] : [-(c_Wellfounded_Owf(_1606049, _1606055))]]], (48621 ^ _779327) ^ [_1752723, _1752725] : [-(c_List_Otranspose(_1752723, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1752723)), c_List_Olist_ONil(_1752723)), _1752725)) = c_List_Otranspose(_1752723, _1752725))], (52750 ^ _779327) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (39766 ^ _779327) ^ [_1533949, _1533951] : [-(hAPP(c_Set_OCollect(_1533949), hAPP(hAPP(c_COMBC(_1533949, tc_fun(_1533949, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533949)), _1533951)) = _1533951)], (7416 ^ _779327) ^ [_895854, _895856, _895858] : [class_Nat_Osemiring__char__0(_895854), 7419 ^ _779327 : [(7426 ^ _779327) ^ [] : [_895856 = _895858, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_895854), _895856) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_895854), _895858))], (7420 ^ _779327) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_895854), _895856) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_895854), _895858), -(_895856 = _895858)]]], (27575 ^ _779327) ^ [_1267515, _1267517, _1267519, _1267521, _1267523] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267515, tc_fun(_1267517, tc_HOL_Obool)), _1267519), _1267521), _1267523))), 27576 ^ _779327 : [(27577 ^ _779327) ^ [_1267587] : [hBOOL(hAPP(hAPP(c_member(_1267515), _1267587), _1267519)), hBOOL(hAPP(hAPP(_1267521, _1267587), _1267523))]]], (30159 ^ _779327) ^ [_1321457, _1321459, _1321461] : [_1321459 = _1321461, -(hBOOL(hAPP(hAPP(c_member(_1321457), _1321459), hAPP(hAPP(c_Set_Oinsert(_1321457), _1321461), c_Orderings_Obot__class_Obot(tc_fun(_1321457, tc_HOL_Obool))))))], (35341 ^ _779327) ^ [_1432882, _1432884, _1432886, _1432888, _1432890] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432882, tc_fun(_1432884, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432882, tc_HOL_Obool)), _1432886), _1432888)), _1432890) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432884, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432882, tc_fun(_1432884, tc_HOL_Obool)), _1432886), _1432890)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432882, tc_fun(_1432884, tc_HOL_Obool)), _1432888), _1432890)))], (42711 ^ _779327) ^ [_1612830, _1612832] : [-(c_Relation_Osingle__valued(_1612830, _1612830, c_Relation_OId__on(_1612830, _1612832)))], (16956 ^ _779327) ^ [_1067070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067070), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21997 ^ _779327) ^ [_1158773, _1158775, _1158777] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158773), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158775)), _1158777)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1158773, _1158775), hAPP(c_Divides_OnegateSnd, _1158777))))], (248 ^ _779327) ^ [_783009, _783011] : [-(class_Fields_Ofield__inverse__zero(_783009)), _783011 = _783009, class_Fields_Ofield__inverse__zero(_783011)], (46542 ^ _779327) ^ [_1707420, _1707422] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707420)), hAPP(c_List_Orotate1(_1707420), _1707422)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707420)), _1707422))], (52413 ^ _779327) ^ [_1833933, _1833935, _1833937] : [hAPP(_1833937, hAPP(c_Hilbert__Choice_Oinv__into(_1833933, _1833935, c_Orderings_Otop__class_Otop(tc_fun(_1833933, tc_HOL_Obool)), _1833937), 52414 ^ [_1833933, _1833935, _1833937])) = 52414 ^ [_1833933, _1833935, _1833937], -(hAPP(c_Set_Oimage(_1833933, _1833935, _1833937), c_Orderings_Otop__class_Otop(tc_fun(_1833933, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1833935, tc_HOL_Obool)))], (45396 ^ _779327) ^ [_1679546, _1679548] : [hAPP(c_List_Oset(_1679546), _1679548) = c_Orderings_Obot__class_Obot(tc_fun(_1679546, tc_HOL_Obool)), -(_1679548 = c_List_Olist_ONil(_1679546))], (41781 ^ _779327) ^ [_1589953, _1589955] : [41782 ^ _779327 : [(41783 ^ _779327) ^ [_1589999] : [hBOOL(hAPP(_1589953, _1589999))]], -(hBOOL(hAPP(_1589953, c_Hilbert__Choice_OEps(_1589955, _1589953))))], (27532 ^ _779327) ^ [_1266480, _1266482, _1266484] : [class_Orderings_Olinorder(_1266480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266480), _1266482), _1266484)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266480, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1266480, _1266482, _1266484)), hAPP(c_SetInterval_Oord__class_OatLeast(_1266480), _1266484)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1266480), _1266482))], (15537 ^ _779327) ^ [_1041943, _1041945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1041943), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1041943), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1041945, _1041943))))], (38345 ^ _779327) ^ [_1501037, _1501039, _1501041, _1501043, _1501045, _1501047] : [hAPP(_1501037, _1501039) = _1501041, hBOOL(hAPP(hAPP(c_member(_1501043), _1501041), _1501045)), -(hBOOL(hAPP(hAPP(c_member(_1501047), _1501039), hAPP(c_Set_Ovimage(_1501047, _1501043, _1501037), _1501045))))], (2490 ^ _779327) ^ [_815767, _815769, _815771, _815773] : [-(c_Nitpick_Ouminus__frac(_815773, _815769) = c_Nitpick_Ouminus__frac(_815771, _815767)), _815773 = _815771, _815769 = _815767], (41892 ^ _779327) ^ [_1592558, _1592560, _1592562, _1592564] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1592558, tc_HOL_Obool), tc_fun(_1592558, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1592558, tc_HOL_Obool), tc_fun(_1592558, tc_HOL_Obool)), _1592560), _1592562)), c_Wellfounded_Omax__ext(_1592558, _1592564)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592558), _1592560)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592558), _1592562)), -(_1592562 = c_Orderings_Obot__class_Obot(tc_fun(_1592558, tc_HOL_Obool))), 41906 ^ _779327 : [(41909 ^ _779327) ^ [_1592963] : [hBOOL(hAPP(hAPP(c_member(_1592558), _1592963), _1592562)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592558, _1592558)), hAPP(hAPP(c_Product__Type_OPair(_1592558, _1592558), 41905 ^ [_1592558, _1592560, _1592562, _1592564]), _1592963)), _1592564))], (41907 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592558), 41905 ^ [_1592558, _1592560, _1592562, _1592564]), _1592560)))]]], (47195 ^ _779327) ^ [_1721461, _1721463, _1721465] : [class_Orderings_Olinorder(_1721461), -(c_Big__Operators_Olinorder__class_OMin(_1721461, hAPP(c_List_Oset(_1721461), hAPP(hAPP(c_List_Olist_OCons(_1721461), _1721463), _1721465))) = hAPP(c_List_Ofoldl(_1721461, _1721461, c_Orderings_Oord__class_Omin(_1721461), _1721463), _1721465))], (52193 ^ _779327) ^ [_1829759, _1829761, _1829763] : [c_Equiv__Relations_Oequiv(_1829759, _1829761, _1829763), 52196 ^ _779327 : [(52201 ^ _779327) ^ [] : [-(c_Relation_Otrans(_1829759, _1829763))], (52199 ^ _779327) ^ [] : [-(c_Relation_Osym(_1829759, _1829763))], (52197 ^ _779327) ^ [] : [-(c_Relation_Orefl__on(_1829759, _1829761, _1829763))]]], (43704 ^ _779327) ^ [_1634838] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1634838, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1634838, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1634838, tc_HOL_Obool)))], (50709 ^ _779327) ^ [_1797362, _1797364, _1797366, _1797368] : [c_List_Olist__ex(_1797362, _1797364, hAPP(hAPP(c_List_Olist_OCons(_1797362), _1797366), _1797368)), -(hBOOL(hAPP(_1797364, _1797366))), -(c_List_Olist__ex(_1797362, _1797364, _1797368))], (10853 ^ _779327) ^ [_956216, _956218] : [class_Groups_Ogroup__add(_956216), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956216), _956218), hAPP(c_Groups_Ouminus__class_Ouminus(_956216), _956218)) = c_Groups_Ozero__class_Ozero(_956216))], (11977 ^ _779327) ^ [_978001, _978003] : [class_Groups_Olinordered__ab__group__add(_978001), 11980 ^ _779327 : [(11987 ^ _779327) ^ [] : [_978003 = c_Groups_Ozero__class_Ozero(_978001), -(c_Groups_Ozero__class_Ozero(_978001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978001), _978003), _978003))], (11981 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_978001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978001), _978003), _978003), -(_978003 = c_Groups_Ozero__class_Ozero(_978001))]]], (5716 ^ _779327) ^ [_869770, _869772, _869774] : [class_Orderings_Oorder(_869770), class_Orderings_Oorder(_869772), c_Orderings_Oorder__class_Ostrict__mono(_869772, _869770, _869774), -(c_Orderings_Oorder__class_Omono(_869772, _869770, _869774))], (50681 ^ _779327) ^ [_1796869, _1796871, _1796873] : [-(c_List_Olist__ex(_1796869, _1796871, _1796873)), 50682 ^ _779327 : [(50683 ^ _779327) ^ [_1796926] : [hBOOL(hAPP(hAPP(c_member(_1796869), _1796926), hAPP(c_List_Oset(_1796869), _1796873))), hBOOL(hAPP(_1796871, _1796926))]]], (38218 ^ _779327) ^ [_1497039, _1497041, _1497043, _1497045, _1497047, _1497049] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497039, tc_fun(_1497041, tc_fun(_1497043, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1497039, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_fun(_1497041, tc_fun(_1497043, tc_HOL_Obool)), _1497039), hAPP(c_COMBC(_1497041, tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_fun(_1497043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497043, tc_fun(tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_fun(_1497043, tc_HOL_Obool)), _1497041), c_COMBC(_1497043, tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497043, tc_prod(_1497041, _1497043)), tc_fun(_1497043, tc_fun(tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_HOL_Obool)), _1497041), hAPP(c_COMBB(tc_prod(_1497041, _1497043), tc_fun(tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool), tc_HOL_Obool), _1497043), c_member(tc_prod(_1497041, _1497043)))), c_Product__Type_OPair(_1497041, _1497043))))), _1497045)), _1497047), _1497049)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497041, _1497043)), hAPP(hAPP(c_Product__Type_OPair(_1497041, _1497043), _1497047), _1497049)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497039, tc_fun(tc_prod(_1497041, _1497043), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1497039, tc_HOL_Obool))), _1497045))))], (11249 ^ _779327) ^ [_963841, _963843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963841), _963843)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963843), _963841)), _963841) = _963843)], (41327 ^ _779327) ^ [_1579897, _1579899, _1579901, _1579903, _1579905, _1579907] : [c_Fun_Oinj__on(_1579897, _1579899, _1579901, _1579903), 41330 ^ _779327 : [(41337 ^ _779327) ^ [] : [c_Fun_Oinj__on(_1579897, _1579905, hAPP(c_Fun_Ocomp(_1579899, _1579905, _1579897, _1579907), _1579901), _1579903), -(c_Fun_Oinj__on(_1579899, _1579905, _1579907, hAPP(c_Set_Oimage(_1579897, _1579899, _1579901), _1579903)))], (41331 ^ _779327) ^ [] : [c_Fun_Oinj__on(_1579899, _1579905, _1579907, hAPP(c_Set_Oimage(_1579897, _1579899, _1579901), _1579903)), -(c_Fun_Oinj__on(_1579897, _1579905, hAPP(c_Fun_Ocomp(_1579899, _1579905, _1579897, _1579907), _1579901), _1579903))]]], (15277 ^ _779327) ^ [_1036729, _1036731, _1036733] : [class_Divides_Osemiring__div(_1036729), -(c_Divides_Odiv__class_Omod(_1036729, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036729), _1036731), _1036733), _1036733) = c_Divides_Odiv__class_Omod(_1036729, _1036731, _1036733))], (38852 ^ _779327) ^ [_1513822, _1513824] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1513822, _1513824), c_Orderings_Otop__class_Otop(tc_fun(_1513822, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1513824, tc_HOL_Obool), _1513822), c_Orderings_Otop__class_Otop(tc_fun(_1513824, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1513822, _1513824), tc_HOL_Obool)))], (41768 ^ _779327) ^ [_1589748, _1589750] : [hBOOL(hAPP(_1589748, c_Hilbert__Choice_OEps(_1589750, _1589748))), -(hBOOL(hAPP(_1589748, 41771 ^ [_1589748, _1589750])))], (22371 ^ _779327) ^ [_1166370, _1166372, _1166374, _1166376] : [class_Orderings_Olinorder(_1166370), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166370), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166370), _1166372), _1166374)), _1166376) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166370), _1166372), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166370), _1166374), _1166376)))], (51309 ^ _779327) ^ [_1810112, _1810114, _1810116, _1810118, _1810120] : [51311 ^ _779327 : [(51314 ^ _779327) ^ [] : [c_Relation_Orefl__on(_1810116, hAPP(_1810118, 51310 ^ [_1810112, _1810114, _1810116, _1810118, _1810120]), hAPP(_1810120, 51310 ^ [_1810112, _1810114, _1810116, _1810118, _1810120]))], (51312 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810112), 51310 ^ [_1810112, _1810114, _1810116, _1810118, _1810120]), _1810114)))]], -(c_Relation_Orefl__on(_1810116, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1810112, tc_fun(_1810116, tc_HOL_Obool)), _1810114), _1810118), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1810112, tc_fun(tc_prod(_1810116, _1810116), tc_HOL_Obool)), _1810114), _1810120)))], (15792 ^ _779327) ^ [_1046473, _1046475] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046473), _1046475) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 15793 ^ _779327 : [(15800 ^ _779327) ^ [] : [_1046473 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1046475 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (15794 ^ _779327) ^ [] : [_1046473 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1046475 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (22145 ^ _779327) ^ [_1162058, _1162060, _1162062] : [-(hAPP(c_Product__Type_Ofst(_1162058, _1162060), _1162062) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1162058, _1162060, _1162058), c_COMBK(_1162058, _1162060)), _1162062))], (51005 ^ _779327) ^ [_1803659, _1803661, _1803663, _1803665] : [hBOOL(hAPP(hAPP(c_member(_1803659), _1803661), hAPP(c_List_Oset(_1803659), c_List_Oreplicate(_1803659, _1803663, _1803665)))), 51008 ^ _779327 : [(51011 ^ _779327) ^ [] : [_1803663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51009 ^ _779327) ^ [] : [-(_1803661 = _1803665)]]], (7778 ^ _779327) ^ [_902056, _902058, _902060, _902062] : [class_Rings_Oordered__semiring(_902056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902056), _902058), _902060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902056), c_Groups_Ozero__class_Ozero(_902056)), _902062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902056), _902058), _902062)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902056), _902060), _902062))))], (40569 ^ _779327) ^ [_1561919, _1561921, _1561923] : [c_Wellfounded_Owf(_1561919, _1561921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561919, _1561919), tc_HOL_Obool)), _1561923), _1561921)), -(c_Wellfounded_Owf(_1561919, _1561923))], (32168 ^ _779327) ^ [_1363333, _1363335, _1363337] : [class_Orderings_Olinorder(_1363333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363333), _1363335)), -(hBOOL(hAPP(hAPP(c_member(_1363333), _1363337), _1363335))), -(_1363335 = c_Orderings_Obot__class_Obot(tc_fun(_1363333, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1363333, hAPP(hAPP(c_Set_Oinsert(_1363333), _1363337), _1363335)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363333), _1363337), c_Big__Operators_Olinorder__class_OMax(_1363333, _1363335)))], (25784 ^ _779327) ^ [_1231095, _1231097, _1231099, _1231101] : [class_Groups_Ocomm__monoid__add(_1231095), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231095), _1231097), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1231099), hAPP(c_Nat_OSuc, _1231101))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231095), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1231095, tc_Nat_Onat), _1231097), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1231099, _1231101)))], (52033 ^ _779327) ^ [_1826759, _1826761] : [c_Relation_Oantisym(_1826759, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1826759, _1826759), tc_HOL_Obool)), _1826761), c_Relation_OId(_1826759))), -(c_Relation_Oantisym(_1826759, _1826761))], (48431 ^ _779327) ^ [_1747842, _1747844, _1747846, _1747848] : [class_Orderings_Olinorder(_1747842), 48434 ^ _779327 : [(48441 ^ _779327) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1747844), _1747848)), -(hBOOL(hAPP(c_List_Odistinct(_1747844), c_List_Olinorder__class_Osort__key(_1747844, _1747842, _1747846, _1747848))))], (48435 ^ _779327) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1747844), c_List_Olinorder__class_Osort__key(_1747844, _1747842, _1747846, _1747848))), -(hBOOL(hAPP(c_List_Odistinct(_1747844), _1747848)))]]], (8842 ^ _779327) ^ [_921497, _921499, _921501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _921497)), 8845 ^ _779327 : [(8852 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921499), _921501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921497), _921499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921497), _921501))))], (8846 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921497), _921499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921497), _921501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921499), _921501)))]]], (42523 ^ _779327) ^ [_1608156] : [-(hAPP(c_Relation_Oconverse(_1608156, _1608156), c_Relation_OId(_1608156)) = c_Relation_OId(_1608156))], (17612 ^ _779327) ^ [_1078222, _1078224] : [class_Int_Onumber__ring(_1078222), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078222), _1078224), hAPP(c_Int_Onumber__class_Onumber__of(_1078222), c_Int_OBit1(c_Int_OPls))) = _1078224)], (44420 ^ _779327) ^ [] : [-(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))))], (52910 ^ _779327) ^ [_1839590, _1839592] : [-(class_Nat_Osize(tc_prod(_1839590, _1839592)))], (3718 ^ _779327) ^ [_835625, _835627, _835629, _835631] : [-(c_Wellfounded_Oacc(_835631, _835627) = c_Wellfounded_Oacc(_835629, _835625)), _835631 = _835629, _835627 = _835625], (35183 ^ _779327) ^ [_1428968, _1428970, _1428972, _1428974] : [hBOOL(hAPP(hAPP(c_member(_1428968), _1428970), _1428972)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428968, tc_HOL_Obool)), _1428972), hAPP(hAPP(c_Set_Oinsert(_1428968), _1428970), _1428974)) = hAPP(hAPP(c_Set_Oinsert(_1428968), _1428970), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428968, tc_HOL_Obool)), _1428972), _1428974)))], (10677 ^ _779327) ^ [_952611, _952613] : [-(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, _952611)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952613))))], (34947 ^ _779327) ^ [_1423384, _1423386, _1423388] : [class_Lattices_Osemilattice__inf(_1423384), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423384), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423384), _1423386), _1423388)), _1423388)))], (9405 ^ _779327) ^ [_931662] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931662), _931662)))], (51537 ^ _779327) ^ [_1815183, _1815185, _1815187] : [51539 ^ _779327 : [(51542 ^ _779327) ^ [] : [hBOOL(hAPP(_1815183, 51538 ^ [_1815183, _1815185, _1815187]))], (51540 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 51538 ^ [_1815183, _1815185, _1815187]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1815185, _1815187))))]], -(c_List_Oall__interval__int(_1815183, _1815185, _1815187))], (52626 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (45036 ^ _779327) ^ [_1669806, _1669808, _1669810, _1669812] : [-(hAPP(hAPP(c_List_Otake(_1669806), hAPP(c_Nat_OSuc, _1669808)), hAPP(hAPP(c_List_Olist_OCons(_1669806), _1669810), _1669812)) = hAPP(hAPP(c_List_Olist_OCons(_1669806), _1669810), hAPP(hAPP(c_List_Otake(_1669806), _1669808), _1669812)))], (12223 ^ _779327) ^ [_982639] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982639) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13000 ^ _779327) ^ [_996537, _996539] : [class_Groups_Olinordered__ab__group__add(_996537), 13003 ^ _779327 : [(13010 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996537), _996539), c_Groups_Ozero__class_Ozero(_996537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996537), _996539), _996539)), c_Groups_Ozero__class_Ozero(_996537))))], (13004 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996537), _996539), _996539)), c_Groups_Ozero__class_Ozero(_996537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996537), _996539), c_Groups_Ozero__class_Ozero(_996537))))]]], (48231 ^ _779327) ^ [_1743705, _1743707, _1743709, _1743711] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1743705)), _1743707), hAPP(c_List_Oset(tc_List_Olist(_1743705)), c_Enum_On__lists(_1743705, _1743709, _1743711)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743705)), _1743707) = _1743709)], (44066 ^ _779327) ^ [_1642999, _1643001, _1643003] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642999, tc_HOL_Obool)), _1643001), _1643003))), 44072 ^ _779327 : [(44076 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642999, tc_HOL_Obool)), 44074 ^ [_1642999, _1643001, _1643003]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1642999, tc_HOL_Obool)), _1643001), _1643003))))], (44078 ^ _779327) ^ [] : [44071 ^ [_1642999, _1643001, _1643003] = 44074 ^ [_1642999, _1643001, _1643003]], (44080 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642999, tc_HOL_Obool)), 44071 ^ [_1642999, _1643001, _1643003]), 44074 ^ [_1642999, _1643001, _1643003]) = c_Orderings_Obot__class_Obot(tc_fun(_1642999, tc_HOL_Obool))], (44073 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642999, tc_HOL_Obool)), 44071 ^ [_1642999, _1643001, _1643003]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1642999, tc_HOL_Obool)), _1643001), _1643003))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642999, tc_HOL_Obool)), _1643001), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642999, tc_HOL_Obool), _1643003)) = c_Orderings_Obot__class_Obot(tc_fun(_1642999, tc_HOL_Obool)))], (49537 ^ _779327) ^ [_1771901, _1771903, _1771905] : [_1771903 = _1771905, -(hAPP(c_List_Orev(_1771901), _1771903) = hAPP(c_List_Orev(_1771901), _1771905))], (21248 ^ _779327) ^ [_1144364, _1144366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144364)), hAPP(c_Nat_OSuc, _1144366))), -(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(_1144364))), 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)), _1144366)))))], (20117 ^ _779327) ^ [_1122348, _1122350] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122348), _1122350), hAPP(c_Int_Onumber__class_Onumber__of(_1122348), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1122348), _1122350)), class_Fields_Ofield__inverse__zero(_1122348), class_Int_Onumber__ring(_1122348)], (18252 ^ _779327) ^ [_1089322, _1089324] : [class_Int_Onumber__ring(_1089322), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089322), c_Groups_Oone__class_Oone(_1089322)), c_Groups_Oone__class_Oone(_1089322))), hAPP(c_Int_Onumber__class_Onumber__of(_1089322), _1089324)) = hAPP(c_Int_Onumber__class_Onumber__of(_1089322), c_Int_OBit0(_1089324)))], (51029 ^ _779327) ^ [_1804098, _1804100, _1804102, _1804104] : [-(hBOOL(hAPP(_1804098, _1804100))), -(hAPP(c_List_Ofilter(_1804102, _1804098), c_List_Oreplicate(_1804102, _1804104, _1804100)) = c_List_Olist_ONil(_1804102))], (33080 ^ _779327) ^ [_1381463, _1381465, _1381467, _1381469] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1381463), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381465, tc_Nat_Onat), _1381467), _1381469)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381465, _1381463), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1381463, _1381465), c_Nat_Osemiring__1__class_Oof__nat(_1381463)), _1381467)), _1381469)), class_Groups_Ocomm__monoid__mult(_1381463), class_Rings_Osemiring__1(_1381463)], (28080 ^ _779327) ^ [_1278713] : [-(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)), _1278713))))], (23730 ^ _779327) ^ [_1192614, _1192616, _1192618, _1192620, _1192622] : [-(_1192614 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1192616, _1192618, _1192620, _1192622), _1192614) = c_Lazy__Sequence_Ohb__bind(_1192616, _1192618, hAPP(_1192620, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1192614), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1192616, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1192618))), _1192622), _1192614)))], (39983 ^ _779327) ^ [_1540841, _1540843, _1540845] : [class_Orderings_Olinorder(_1540841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540841), _1540843)), -(_1540843 = c_Orderings_Obot__class_Obot(tc_fun(_1540841, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540841), _1540845)), -(_1540845 = c_Orderings_Obot__class_Obot(tc_fun(_1540841, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1540841), c_Big__Operators_Olattice_OInf__fin(_1540841, c_Orderings_Oord__class_Omin(_1540841), _1540843)), c_Big__Operators_Olattice_OInf__fin(_1540841, c_Orderings_Oord__class_Omin(_1540841), _1540845)) = c_Big__Operators_Olattice_OInf__fin(_1540841, c_Orderings_Oord__class_Omin(_1540841), hAPP(c_Set_OCollect(_1540841), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_HOL_Obool), tc_HOL_Obool, _1540841), c_HOL_OEx(_1540841)), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool)), tc_fun(_1540841, tc_HOL_Obool), _1540841), hAPP(c_COMBB(tc_fun(_1540841, tc_HOL_Obool), tc_HOL_Obool, _1540841), c_HOL_OEx(_1540841))), hAPP(hAPP(c_COMBC(_1540841, tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool)), tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_fun(tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool))), tc_fun(tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool)), tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool))), _1540841), c_COMBS(_1540841, tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_fun(_1540841, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1540841, tc_fun(tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool))), _1540841), hAPP(c_COMBB(tc_fun(_1540841, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool)), _1540841), c_COMBS(_1540841, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool)), tc_fun(_1540841, tc_fun(_1540841, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1540841), hAPP(c_COMBB(tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1540841), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540841), c_fconj))), hAPP(hAPP(c_COMBC(_1540841, tc_fun(_1540841, tc_fun(_1540841, _1540841)), tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540841, _1540841), tc_fun(_1540841, tc_HOL_Obool)), tc_fun(tc_fun(_1540841, tc_fun(_1540841, _1540841)), tc_fun(_1540841, tc_fun(_1540841, tc_HOL_Obool))), _1540841), c_COMBB(tc_fun(_1540841, _1540841), tc_fun(_1540841, tc_HOL_Obool), _1540841)), hAPP(hAPP(c_COMBB(tc_fun(_1540841, tc_HOL_Obool), tc_fun(tc_fun(_1540841, _1540841), tc_fun(_1540841, tc_HOL_Obool)), _1540841), c_COMBB(_1540841, tc_HOL_Obool, _1540841)), c_fequal))), c_Orderings_Oord__class_Omax(_1540841)))))), hAPP(hAPP(c_COMBC(_1540841, tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540841, tc_HOL_Obool), tc_fun(_1540841, tc_HOL_Obool)), _1540841), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540841)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540841), c_fconj), hAPP(hAPP(c_COMBC(_1540841, tc_fun(_1540841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540841)), _1540843)))), hAPP(hAPP(c_COMBC(_1540841, tc_fun(_1540841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540841)), _1540845))))))))], (44620 ^ _779327) ^ [_1657640, _1657642, _1657644, _1657646, _1657648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657640), tc_List_Olist(_1657640))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657640), tc_List_Olist(_1657640)), _1657642), _1657644)), c_List_Olistrel1(_1657640, _1657646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657640), tc_List_Olist(_1657640))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657640), tc_List_Olist(_1657640)), hAPP(hAPP(c_List_Olist_OCons(_1657640), _1657648), _1657642)), hAPP(hAPP(c_List_Olist_OCons(_1657640), _1657648), _1657644))), c_List_Olistrel1(_1657640, _1657646))))], (44839 ^ _779327) ^ [_1664632, _1664634, _1664636] : [c_Equiv__Relations_Oequiv(_1664632, _1664634, _1664636), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1664632), c_List_Olists(_1664632, _1664634), c_List_Olistrel(_1664632, _1664636)))], (23760 ^ _779327) ^ [_1193249, _1193251, _1193253, _1193255, _1193257] : [hBOOL(hAPP(_1193249, hAPP(hAPP(c_Product__Type_OPair(_1193251, _1193253), _1193255), _1193257))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1193251, _1193253, tc_HOL_Obool, _1193249), _1193255), _1193257)))], (14345 ^ _779327) ^ [_1021178, _1021180] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021178))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021178)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021180)) = 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), _1021180)))], (42130 ^ _779327) ^ [_1597860, _1597862, _1597864, _1597866] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597860, _1597860)), _1597862), c_Transitive__Closure_Otrancl(_1597860, _1597864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597860, _1597860), tc_HOL_Obool)), _1597864), _1597866)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597860, _1597860)), _1597862), c_Transitive__Closure_Otrancl(_1597860, _1597866))))], (22591 ^ _779327) ^ [_1170234, _1170236, _1170238, _1170240] : [class_Orderings_Olinorder(_1170234), 22594 ^ _779327 : [(22603 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170234), _1170238), _1170240)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), _1170238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), _1170240))], (22595 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170234), _1170238), _1170240))), 22598 ^ _779327 : [(22601 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), _1170240)))], (22599 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170234), _1170236), _1170238)))]]]]], (28994 ^ _779327) ^ [_1296015, _1296017] : [_1296017 = c_Orderings_Obot__class_Obot(tc_fun(_1296015, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296015, tc_HOL_Obool)), _1296017), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1296015, tc_HOL_Obool)), _1296017))))], (5750 ^ _779327) ^ [_870289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870289), _870289))], (48537 ^ _779327) ^ [_1750994, _1750996, _1750998] : [48539 ^ _779327 : [(48542 ^ _779327) ^ [] : [hBOOL(hAPP(_1750996, 48538 ^ [_1750994, _1750996, _1750998]))], (48540 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750994), 48538 ^ [_1750994, _1750996, _1750998]), hAPP(c_List_Oset(_1750994), _1750998))))]], -(hAPP(c_List_Ofilter(_1750994, _1750996), _1750998) = _1750998)], (40194 ^ _779327) ^ [_1549979] : [-(c_Int_Oint__ge__less__than(_1549979) = 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), _1549979)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (53014 ^ _779327) ^ [_1840579, _1840581, _1840583, _1840585, _1840587, _1840589] : [-(hAPP(hAPP(hAPP(c_COMBB(_1840579, _1840581, _1840583), _1840585), _1840587), _1840589) = hAPP(_1840585, hAPP(_1840587, _1840589)))], (45733 ^ _779327) ^ [_1687703, _1687705, _1687707, _1687709, _1687711] : [class_Groups_Ocomm__monoid__add(_1687703), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687703), hAPP(hAPP(c_List_Omap(_1687705, _1687703), hAPP(hAPP(c_COMBS(_1687705, _1687703, _1687703), hAPP(hAPP(c_COMBB(_1687703, tc_fun(_1687703, _1687703), _1687705), c_Groups_Oplus__class_Oplus(_1687703)), _1687707)), _1687709)), _1687711)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1687703), hAPP(c_List_Omonoid__add__class_Olistsum(_1687703), hAPP(hAPP(c_List_Omap(_1687705, _1687703), _1687707), _1687711))), hAPP(c_List_Omonoid__add__class_Olistsum(_1687703), hAPP(hAPP(c_List_Omap(_1687705, _1687703), _1687709), _1687711))))], (38447 ^ _779327) ^ [_1503531, _1503533, _1503535, _1503537, _1503539] : [hAPP(c_Set_Oimage(_1503531, _1503533, _1503535), c_Orderings_Otop__class_Otop(tc_fun(_1503531, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1503533, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503531, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1503531, _1503533, _1503535), _1503537)), _1503539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503533, tc_HOL_Obool)), _1503537), hAPP(c_Set_Oimage(_1503531, _1503533, _1503535), _1503539))))], (35279 ^ _779327) ^ [_1431253, _1431255] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1431253), _1431255) = 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)), _1431253)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1431255))))], (37112 ^ _779327) ^ [_1472328, _1472330, _1472332, _1472334] : [c_Fun_Oinj__on(_1472328, tc_fun(tc_fun(_1472328, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1472328, tc_fun(tc_prod(_1472328, _1472328), tc_HOL_Obool), tc_fun(tc_fun(_1472328, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472328, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1472328, _1472328), tc_HOL_Obool), tc_fun(tc_fun(_1472328, tc_HOL_Obool), tc_HOL_Obool)), _1472328), c_Equiv__Relations_Oquotient(_1472328)), hAPP(hAPP(c_COMBC(_1472328, tc_fun(_1472328, tc_HOL_Obool), tc_fun(_1472328, tc_HOL_Obool)), c_Set_Oinsert(_1472328)), c_Orderings_Obot__class_Obot(tc_fun(_1472328, tc_HOL_Obool))))), _1472330), _1472332), hBOOL(hAPP(hAPP(c_member(_1472328), _1472334), _1472332)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472328, tc_HOL_Obool)), _1472332), hAPP(hAPP(c_Set_Oinsert(_1472328), _1472334), c_Orderings_Obot__class_Obot(tc_fun(_1472328, tc_HOL_Obool))))), _1472330) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1472328, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472328), _1472332), _1472330)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472328), hAPP(hAPP(c_Set_Oinsert(_1472328), _1472334), c_Orderings_Obot__class_Obot(tc_fun(_1472328, tc_HOL_Obool)))), _1472330)))], (52510 ^ _779327) ^ [_1835513, _1835515] : [class_Orderings_Oorder(_1835513), -(class_Orderings_Oorder(tc_fun(_1835515, _1835513)))], (34611 ^ _779327) ^ [_1416387, _1416389, _1416391, _1416393] : [hBOOL(hAPP(hAPP(c_member(_1416387), _1416389), _1416391)), hBOOL(hAPP(hAPP(c_member(_1416387), _1416389), _1416393)), -(hBOOL(hAPP(hAPP(c_member(_1416387), _1416389), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416387, tc_HOL_Obool)), _1416391), _1416393))))], (24193 ^ _779327) ^ [_1200703, _1200705, _1200707] : [_1200703 = _1200705, 24204 ^ _779327 : [(24207 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200707), _1200703))], (24205 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200703), _1200707)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200705), _1200707)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200707), _1200705)))], (12413 ^ _779327) ^ [_985946] : [-(hAPP(c_Nat_OSuc, _985946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985946), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10909 ^ _779327) ^ [_957226, _957228, _957230, _957232, _957234] : [class_Groups_Oab__group__add(_957226), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957226), _957228), _957230) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957226), _957232), _957234), 10916 ^ _779327 : [(10923 ^ _779327) ^ [] : [_957232 = _957234, -(_957228 = _957230)], (10917 ^ _779327) ^ [] : [_957228 = _957230, -(_957232 = _957234)]]], (29266 ^ _779327) ^ [_1301163, _1301165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301163), _1301165)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1301165, _1301163) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (41069 ^ _779327) ^ [_1574066, _1574068, _1574070, _1574072] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1574066), _1574068))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574070), hAPP(c_Set_Oimage(_1574066, _1574070, _1574072), _1574068))), 41077 ^ _779327 : [(41080 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1574066), hAPP(c_Set_OCollect(_1574066), hAPP(hAPP(c_COMBS(_1574066, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574066), c_fconj), hAPP(hAPP(c_COMBC(_1574066, tc_fun(_1574066, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574066)), _1574068))), hAPP(hAPP(c_COMBC(_1574066, _1574070, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1574070, tc_fun(_1574070, tc_HOL_Obool), _1574066), c_fequal), _1574072)), hAPP(_1574072, 41076 ^ [_1574066, _1574068, _1574070, _1574072]))))))], (41078 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574066), 41076 ^ [_1574066, _1574068, _1574070, _1574072]), _1574068)))]]], (50144 ^ _779327) ^ [_1784491, _1784493, _1784495, _1784497, _1784499] : [-(c_List_Omaps(_1784491, _1784493, _1784495, hAPP(hAPP(c_List_Olist_OCons(_1784491), _1784497), _1784499)) = hAPP(hAPP(c_List_Oappend(_1784493), hAPP(_1784495, _1784497)), c_List_Omaps(_1784491, _1784493, _1784495, _1784499)))], (42869 ^ _779327) ^ [_1616523, _1616525, _1616527, _1616529] : [-(hAPP(hAPP(c_Nat_Ocompow(_1616523, _1616523), _1616525), hAPP(hAPP(c_Nat_Ocompow(_1616523, _1616523), _1616527), _1616529)) = hAPP(hAPP(c_Nat_Ocompow(_1616523, _1616523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1616527), _1616525)), _1616529))], (45299 ^ _779327) ^ [_1676075, _1676077, _1676079] : [45301 ^ _779327 : [(45304 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1676075), 45300 ^ [_1676075, _1676077, _1676079]), _1676079))], (45302 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676075), 45300 ^ [_1676075, _1676077, _1676079]), hAPP(c_List_Oset(_1676075), _1676077))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676075)), _1676077), c_List_Olists(_1676075, _1676079))))], (13210 ^ _779327) ^ [_1000254, _1000256, _1000258] : [class_Groups_Oordered__comm__monoid__add(_1000254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000254), _1000256), c_Groups_Ozero__class_Ozero(_1000254))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000254), _1000258), c_Groups_Ozero__class_Ozero(_1000254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000254), _1000256), _1000258)), c_Groups_Ozero__class_Ozero(_1000254))))], (37883 ^ _779327) ^ [_1488603, _1488605, _1488607, _1488609, _1488611] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488603), hAPP(c_Set_Oimage(_1488605, _1488603, _1488607), c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488609), hAPP(c_Set_Oimage(_1488605, _1488609, hAPP(hAPP(c_COMBB(_1488603, _1488609, _1488605), _1488611), _1488607)), c_Orderings_Otop__class_Otop(tc_fun(_1488605, tc_HOL_Obool))))))], (50183 ^ _779327) ^ [_1785584, _1785586, _1785588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785584, _1785584)), hAPP(hAPP(c_Product__Type_OPair(_1785584, _1785584), _1785586), _1785588)), c_List_Omeasures(_1785584, c_List_Olist_ONil(tc_fun(_1785584, tc_Nat_Onat)))))], (37146 ^ _779327) ^ [_1473252, _1473254, _1473256, _1473258, _1473260, _1473262, _1473264, _1473266] : [c_Fun_Oinj__on(_1473252, _1473254, _1473256, _1473258), 37152 ^ _779327 : [(37155 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473252, tc_HOL_Obool)), hAPP(_1473264, 37151 ^ [_1473252, _1473254, _1473256, _1473258, _1473260, _1473262, _1473264, _1473266])), _1473258))], (37153 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473260), 37151 ^ [_1473252, _1473254, _1473256, _1473258, _1473260, _1473262, _1473264, _1473266]), _1473262)))]], hBOOL(hAPP(hAPP(c_member(_1473260), _1473266), _1473262)), -(hAPP(c_Set_Oimage(_1473252, _1473254, _1473256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1473260, tc_fun(_1473252, tc_HOL_Obool)), _1473262), _1473264)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1473260, tc_fun(_1473254, tc_HOL_Obool)), _1473262), hAPP(hAPP(c_COMBB(tc_fun(_1473252, tc_HOL_Obool), tc_fun(_1473254, tc_HOL_Obool), _1473260), c_Set_Oimage(_1473252, _1473254, _1473256)), _1473264)))], (14927 ^ _779327) ^ [_1030433] : [-(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, _1030433))))))], (17414 ^ _779327) ^ [_1074968, _1074970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074968), _1074970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1074968)), c_Int_OBit1(_1074970))))], (51729 ^ _779327) ^ [_1819284, _1819286] : [c_Relation_Otrans(_1819284, _1819286), 51732 ^ _779327 : [(51733 ^ _779327) ^ [_1819420, _1819422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1819284, _1819284)), hAPP(hAPP(c_Product__Type_OPair(_1819284, _1819284), _1819422), _1819420)), _1819286)), 51736 ^ _779327 : [(51737 ^ _779327) ^ [_1819563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1819284, _1819284)), hAPP(hAPP(c_Product__Type_OPair(_1819284, _1819284), _1819420), _1819563)), _1819286)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819284, _1819284)), hAPP(hAPP(c_Product__Type_OPair(_1819284, _1819284), _1819422), _1819563)), _1819286)))]]]]], (36391 ^ _779327) ^ [_1457941, _1457943, _1457945] : [-(c_Relation_Orefl__on(_1457941, _1457943, _1457945)), 36395 ^ _779327 : [(36398 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457941, _1457941, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1457941, tc_fun(_1457941, tc_HOL_Obool), tc_fun(_1457941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1457941, tc_HOL_Obool), tc_fun(_1457941, tc_HOL_Obool)), _1457941), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1457941)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457941), c_fconj), hAPP(hAPP(c_COMBC(_1457941, tc_fun(_1457941, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457941)), _1457943)))), hAPP(hAPP(c_COMBC(_1457941, tc_fun(_1457941, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457941)), _1457943))), 36394 ^ [_1457941, _1457943, _1457945]))], (36396 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457941, _1457941)), 36394 ^ [_1457941, _1457943, _1457945]), _1457945)))]], 36400 ^ _779327 : [(36403 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457941, _1457941)), hAPP(hAPP(c_Product__Type_OPair(_1457941, _1457941), 36399 ^ [_1457941, _1457943, _1457945]), 36399 ^ [_1457941, _1457943, _1457945])), _1457945))], (36401 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457941), 36399 ^ [_1457941, _1457943, _1457945]), _1457943)))]]], (13866 ^ _779327) ^ [_1012155, _1012157] : [class_Rings_Olinordered__idom(_1012155), 13869 ^ _779327 : [(13876 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012155), _1012157), c_Groups_Ozero__class_Ozero(_1012155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012155), c_Groups_Osgn__class_Osgn(_1012155, _1012157)), c_Groups_Ozero__class_Ozero(_1012155))))], (13870 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012155), c_Groups_Osgn__class_Osgn(_1012155, _1012157)), c_Groups_Ozero__class_Ozero(_1012155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012155), _1012157), c_Groups_Ozero__class_Ozero(_1012155))))]]], (52806 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (50851 ^ _779327) ^ [_1800444, _1800446, _1800448] : [50853 ^ _779327 : [(50856 ^ _779327) ^ [] : [hBOOL(hAPP(_1800448, 50852 ^ [_1800444, _1800446, _1800448]))], (50854 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800444), 50852 ^ [_1800444, _1800446, _1800448]), hAPP(c_List_Oset(_1800444), _1800446))))]], -(c_List_Olist__all(_1800444, _1800448, _1800446))], (9050 ^ _779327) ^ [_925328, _925330, _925332, _925334] : [class_Rings_Ocomm__semiring__1(_925328), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925328), _925330), _925332)), _925334) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925328), _925330), _925334)), _925332))], (43961 ^ _779327) ^ [_1640897, _1640899] : [class_Complete__Lattice_Ocomplete__lattice(_1640897), -(c_Complete__Lattice_OSup__class_OSup(_1640897, hAPP(hAPP(c_Set_Oinsert(_1640897), _1640899), c_Orderings_Obot__class_Obot(tc_fun(_1640897, tc_HOL_Obool)))) = _1640899)], (17362 ^ _779327) ^ [_1073961, _1073963, _1073965] : [17364 ^ _779327 : [(17367 ^ _779327) ^ [] : [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(_1073963, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17363 ^ [_1073961, _1073963, _1073965]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1073963, 17363 ^ [_1073961, _1073963, _1073965])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17365 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17363 ^ [_1073961, _1073963, _1073965]), _1073961)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1073963, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1073965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1073965), hAPP(_1073963, _1073961))), 17377 ^ _779327 : [(17380 ^ _779327) ^ [] : [-(hAPP(_1073963, 17376 ^ [_1073961, _1073963, _1073965]) = _1073965)], (17378 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17376 ^ [_1073961, _1073963, _1073965]), _1073961)))]]], (45048 ^ _779327) ^ [_1670144, _1670146, _1670148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1670144), _1670146)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1670144)), hAPP(c_Set_OCollect(tc_List_Olist(_1670144)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1670144), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1670144)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670144), tc_fun(_1670144, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1670144, tc_HOL_Obool), tc_fun(tc_fun(_1670144, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1670144)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1670144, tc_HOL_Obool))), c_List_Oset(_1670144))), _1670146))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670144), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1670144)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670144)))), _1670148))))))], (2078 ^ _779327) ^ [_809331, _809333, _809335, _809337, _809339, _809341, _809343, _809345] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809345, _809341, _809337, _809333) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809343, _809339, _809335, _809331)), _809345 = _809343, _809341 = _809339, _809337 = _809335, _809333 = _809331], (23676 ^ _779327) ^ [_1191505] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1191505)) = _1191505)], (7932 ^ _779327) ^ [_904999, _905001] : [class_Rings_Olinordered__ring(_904999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904999), _905001), _905001)), c_Groups_Ozero__class_Ozero(_904999)))], (22569 ^ _779327) ^ [_1169885, _1169887, _1169889, _1169891] : [class_Orderings_Olinorder(_1169885), 22572 ^ _779327 : [(22573 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169885), _1169887), _1169889)), _1169891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), _1169887), _1169891))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), _1169889), _1169891)))], (22583 ^ _779327) ^ [] : [22584 ^ _779327 : [(22587 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), _1169889), _1169891))], (22585 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), _1169887), _1169891))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169885), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169885), _1169887), _1169889)), _1169891)))]]], (42304 ^ _779327) ^ [_1602947, _1602949, _1602951] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1602947, _1602949, _1602949), _1602951), c_Relation_OId(_1602949)) = _1602951)], (34733 ^ _779327) ^ [_1419304, _1419306, _1419308, _1419310] : [class_Lattices_Osemilattice__inf(_1419304), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419304), _1419306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419304), _1419308), _1419310)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419304), _1419308), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419304), _1419306), _1419310)))], (27338 ^ _779327) ^ [_1262585, _1262587, _1262589, _1262591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262585, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262585, tc_HOL_Obool)), _1262587), _1262589)), _1262591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262585, tc_HOL_Obool)), _1262587), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262585, tc_HOL_Obool)), _1262589), _1262591))))], (2422 ^ _779327) ^ [_814721, _814723, _814725, _814727, _814729, _814731] : [-(c_Nitpick_Otimes__frac(_814731, _814727, _814723) = c_Nitpick_Otimes__frac(_814729, _814725, _814721)), _814731 = _814729, _814727 = _814725, _814723 = _814721], (50747 ^ _779327) ^ [_1798195, _1798197, _1798199] : [hBOOL(hAPP(hAPP(c_member(_1798195), _1798197), hAPP(c_List_Oset(_1798195), _1798199))), 50752 ^ _779327 : [(50755 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1798195), _1798197), hAPP(c_List_Oset(_1798195), 50751 ^ [_1798195, _1798197, _1798199])))], (50753 ^ _779327) ^ [] : [-(_1798199 = hAPP(hAPP(c_List_Oappend(_1798195), 50750 ^ [_1798195, _1798197, _1798199]), hAPP(hAPP(c_List_Olist_OCons(_1798195), _1798197), 50751 ^ [_1798195, _1798197, _1798199])))]]], (22139 ^ _779327) ^ [_1161903, _1161905, _1161907, _1161909, _1161911, _1161913] : [hAPP(_1161909, hAPP(c_Product__Type_Osnd(_1161907, _1161903), _1161911)) = hAPP(_1161913, hAPP(c_Product__Type_Osnd(_1161907, _1161903), _1161911)), -(hAPP(c_Product__Type_Oapsnd(_1161903, _1161905, _1161907, _1161909), _1161911) = hAPP(c_Product__Type_Oapsnd(_1161903, _1161905, _1161907, _1161913), _1161911))], (38595 ^ _779327) ^ [_1506796, _1506798, _1506800, _1506802, _1506804, _1506806] : [c_Typedef_Otype__definition(_1506796, _1506798, _1506800, _1506802, _1506804), hBOOL(hAPP(hAPP(c_member(_1506798), _1506806), _1506804)), -(hAPP(_1506800, hAPP(_1506802, _1506806)) = _1506806)], (25063 ^ _779327) ^ [_1216276, _1216278] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1216276)), _1216278)), 25066 ^ _779327 : [(25073 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216276))), -(_1216278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25067 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216276)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216276), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216278))))]]], (13563 ^ _779327) ^ [_1006513, _1006515, _1006517, _1006519] : [class_Rings_Ocomm__semiring__1(_1006513), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006513), hAPP(hAPP(c_Power_Opower__class_Opower(_1006513), _1006515), _1006517)), hAPP(hAPP(c_Power_Opower__class_Opower(_1006513), _1006515), _1006519)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1006513), _1006515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006517), _1006519)))], (23165 ^ _779327) ^ [_1181385, _1181387, _1181389] : [class_Groups_Olinordered__ab__group__add(_1181385), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181385), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181385), _1181387), _1181389)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181385), hAPP(c_Groups_Ouminus__class_Ouminus(_1181385), _1181387)), hAPP(c_Groups_Ouminus__class_Ouminus(_1181385), _1181389)))], (29202 ^ _779327) ^ [_1299995] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1299995), hAPP(c_Nat_OSuc, _1299995)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1299995), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (42713 ^ _779327) ^ [_1612859, _1612861, _1612863, _1612865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1612859, _1612861), tc_HOL_Obool)), _1612863), _1612865)), c_Relation_Osingle__valued(_1612859, _1612861, _1612865), -(c_Relation_Osingle__valued(_1612859, _1612861, _1612863))], (21230 ^ _779327) ^ [_1143983] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143983)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1143983)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143983)), 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)))))], (21334 ^ _779327) ^ [_1146298, _1146300, _1146302] : [class_Int_Onumber__ring(_1146298), 21337 ^ _779327 : [(21344 ^ _779327) ^ [] : [-(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), _1146300)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1146298), hAPP(c_Int_Onumber__class_Onumber__of(_1146298), _1146302)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1146300))) = c_Groups_Oone__class_Oone(_1146298))], (21338 ^ _779327) ^ [] : [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), _1146300))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1146298), hAPP(c_Int_Onumber__class_Onumber__of(_1146298), _1146302)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1146300))) = hAPP(hAPP(c_HOL_OLet(_1146298, _1146298), hAPP(hAPP(c_Power_Opower__class_Opower(_1146298), hAPP(c_Int_Onumber__class_Onumber__of(_1146298), _1146302)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146300))), hAPP(hAPP(c_COMBS(_1146298, _1146298, _1146298), hAPP(hAPP(c_COMBB(_1146298, tc_fun(_1146298, _1146298), _1146298), c_Groups_Otimes__class_Otimes(_1146298)), hAPP(c_Groups_Otimes__class_Otimes(_1146298), hAPP(c_Int_Onumber__class_Onumber__of(_1146298), _1146302)))), c_COMBI(_1146298))))]]], (18626 ^ _779327) ^ [_1096083] : [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, _1096083, 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, _1096083, 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))], (35768 ^ _779327) ^ [_1442684, _1442686, _1442688, _1442690, _1442692] : [class_Groups_Ocomm__monoid__add(_1442684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442686), _1442688)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442686), _1442690)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442686, tc_HOL_Obool)), _1442688), _1442690) = c_Orderings_Obot__class_Obot(tc_fun(_1442686, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442686, _1442684), _1442692), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442686, tc_HOL_Obool)), _1442688), _1442690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1442684), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442686, _1442684), _1442692), _1442688)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442686, _1442684), _1442692), _1442690)))], (466 ^ _779327) ^ [_786524, _786526, _786528, _786530] : [-(c_FunDef_Oreduction__pair(_786528, _786524)), c_FunDef_Oreduction__pair(_786530, _786526), _786530 = _786528, _786526 = _786524], (4584 ^ _779327) ^ [_849114, _849116, _849118, _849120, _849122, _849124, _849126, _849128, _849130, _849132, _849134, _849136] : [-(c_New__Random__Sequence_Opos__union(_849136, _849132, _849128, _849124, _849120, _849116) = c_New__Random__Sequence_Opos__union(_849134, _849130, _849126, _849122, _849118, _849114)), _849136 = _849134, _849132 = _849130, _849128 = _849126, _849124 = _849122, _849120 = _849118, _849116 = _849114], (26611 ^ _779327) ^ [_1247743, _1247745, _1247747] : [class_Groups_Oordered__ab__group__add(_1247743), -(hAPP(c_Set_Oimage(_1247743, _1247743, c_Groups_Ouminus__class_Ouminus(_1247743)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1247743, _1247745, _1247747)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1247743, hAPP(c_Groups_Ouminus__class_Ouminus(_1247743), _1247747), hAPP(c_Groups_Ouminus__class_Ouminus(_1247743), _1247745)))], (46790 ^ _779327) ^ [_1713053, _1713055, _1713057, _1713059] : [hBOOL(hAPP(c_List_Odistinct(_1713053), _1713055)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1713053, _1713057)), hAPP(hAPP(c_List_Ozip(_1713053, _1713057), _1713055), _1713059))))], (29152 ^ _779327) ^ [_1298803, _1298805, _1298807, _1298809, _1298811] : [_1298803 = c_Orderings_Obot__class_Obot(tc_fun(_1298805, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298805, tc_fun(_1298807, tc_HOL_Obool)), _1298803), hAPP(hAPP(c_COMBC(_1298805, tc_fun(_1298807, tc_HOL_Obool), tc_fun(_1298807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298807, tc_HOL_Obool), tc_fun(tc_fun(_1298807, tc_HOL_Obool), tc_fun(_1298807, tc_HOL_Obool)), _1298805), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298807, tc_HOL_Obool))), _1298809)), _1298811)) = c_Orderings_Obot__class_Obot(tc_fun(_1298807, tc_HOL_Obool)))], (18694 ^ _779327) ^ [_1097418] : [-(_1097418 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 18697 ^ _779327 : [(18704 ^ _779327) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1097418, 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, _1097418) = 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), _1097418), 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)))], (18698 ^ _779327) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1097418, 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, _1097418) = 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), _1097418), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (8376 ^ _779327) ^ [_913103, _913105, _913107, _913109, _913111] : [class_Rings_Olinordered__semiring__strict(_913103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913103), _913105), _913107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913103), _913109), _913111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913103), c_Groups_Ozero__class_Ozero(_913103)), _913105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913103), c_Groups_Ozero__class_Ozero(_913103)), _913109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913103), _913105), _913109)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913103), _913107), _913111))))], (50939 ^ _779327) ^ [_1802180, _1802182, _1802184, _1802186, _1802188] : [-(c_List_Osplice(_1802180, hAPP(hAPP(c_List_Olist_OCons(_1802180), _1802182), _1802184), hAPP(hAPP(c_List_Olist_OCons(_1802180), _1802186), _1802188)) = hAPP(hAPP(c_List_Olist_OCons(_1802180), _1802182), hAPP(hAPP(c_List_Olist_OCons(_1802180), _1802186), c_List_Osplice(_1802180, _1802184, _1802188))))], (46317 ^ _779327) ^ [_1701510, _1701512, _1701514, _1701516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701512)), _1701514))), -(hAPP(hAPP(c_List_Onth(_1701512), hAPP(hAPP(c_List_Olist__update(_1701512, _1701514), _1701510), _1701516)), _1701510) = _1701516)], (17356 ^ _779327) ^ [_1073834, _1073836] : [class_Int_Onumber__ring(_1073834), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073834), hAPP(c_Int_Onumber__class_Onumber__of(_1073834), _1073836)), c_Groups_Oone__class_Oone(_1073834)) = hAPP(c_Int_Onumber__class_Onumber__of(_1073834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073836), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (8954 ^ _779327) ^ [_923550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _923550)), -(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), _923550))))], (23674 ^ _779327) ^ [_1191476] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1191476)) = _1191476)], (21324 ^ _779327) ^ [_1146226, _1146228] : [-(c_Divides_OnegDivAlg(_1146226, _1146228) = hAPP(c_Divides_Oadjust(_1146228), c_Divides_OnegDivAlg(_1146226, 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)))), _1146228)))), -(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), _1146226), _1146228)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146228), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (4786 ^ _779327) ^ [_852227, _852229, _852231, _852233] : [-(c_List_Ozip(_852233, _852229) = c_List_Ozip(_852231, _852227)), _852233 = _852231, _852229 = _852227], (15489 ^ _779327) ^ [_1041186, _1041188] : [class_Divides_Osemiring__div(_1041186), -(c_Divides_Odiv__class_Omod(_1041186, _1041188, c_Groups_Oone__class_Oone(_1041186)) = c_Groups_Ozero__class_Ozero(_1041186))], (43814 ^ _779327) ^ [_1637432, _1637434, _1637436] : [-(hAPP(c_Relation_ODomain(_1637432, _1637434), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1637432, _1637434), tc_HOL_Obool), _1637436)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1637432, _1637434), tc_HOL_Obool), tc_fun(_1637432, tc_HOL_Obool)), _1637436), c_Relation_ODomain(_1637432, _1637434)))], (23498 ^ _779327) ^ [_1187853, _1187855, _1187857] : [-(c_HOL_OThe(tc_prod(_1187853, _1187855), hAPP(c_Product__Type_Oprod_Oprod__case(_1187853, _1187855, tc_HOL_Obool), _1187857)) = c_HOL_OThe(tc_prod(_1187853, _1187855), hAPP(hAPP(c_COMBS(tc_prod(_1187853, _1187855), _1187855, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1187853, tc_fun(_1187855, tc_HOL_Obool), tc_prod(_1187853, _1187855)), _1187857), c_Product__Type_Ofst(_1187853, _1187855))), c_Product__Type_Osnd(_1187853, _1187855))))], (23772 ^ _779327) ^ [_1193499, _1193501, _1193503, _1193505, _1193507] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1193499, _1193501, tc_HOL_Obool, _1193503), _1193505), _1193507)), -(hBOOL(hAPP(_1193503, hAPP(hAPP(c_Product__Type_OPair(_1193499, _1193501), _1193505), _1193507))))], (46092 ^ _779327) ^ [_1696382, _1696384, _1696386] : [hAPP(hAPP(c_List_Oappend(_1696382), _1696384), _1696386) = _1696384, -(_1696386 = c_List_Olist_ONil(_1696382))], (26836 ^ _779327) ^ [_1252123, _1252125, _1252127] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252123, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252123, tc_HOL_Obool)), _1252125), _1252127)), _1252127) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252123, tc_HOL_Obool)), _1252125), _1252127))], (42581 ^ _779327) ^ [_1609666, _1609668, _1609670, _1609672] : [-(hAPP(c_Relation_Oconverse(_1609666, _1609666), hAPP(hAPP(c_Relation_Oinv__image(_1609668, _1609666), _1609670), _1609672)) = hAPP(hAPP(c_Relation_Oinv__image(_1609668, _1609666), hAPP(c_Relation_Oconverse(_1609668, _1609668), _1609670)), _1609672))], (39768 ^ _779327) ^ [_1534012, _1534014, _1534016] : [hBOOL(hAPP(hAPP(c_member(_1534012), _1534014), hAPP(c_Set_OCollect(_1534012), _1534016))), -(hBOOL(hAPP(_1534016, _1534014)))], (30073 ^ _779327) ^ [_1319302, _1319304, _1319306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319302, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1319302, tc_fun(_1319302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319302)), _1319304)), hAPP(hAPP(c_COMBC(_1319302, tc_fun(_1319302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319302)), _1319306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319302, tc_HOL_Obool)), _1319304), _1319306)))], (13530 ^ _779327) ^ [_1005835, _1005837] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005835), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005837), _1005835)))))], (43329 ^ _779327) ^ [_1627626, _1627628, _1627630] : [class_Orderings_Olinorder(_1627626), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627626), _1627628)), -(c_Big__Operators_Olattice_OSup__fin(_1627626, c_Orderings_Oord__class_Omax(_1627626), hAPP(hAPP(c_Set_Oinsert(_1627626), _1627630), _1627628)) = hAPP(hAPP(c_Finite__Set_Ofold(_1627626, _1627626, c_Orderings_Oord__class_Omax(_1627626)), _1627630), _1627628))], (43826 ^ _779327) ^ [_1637915, _1637917, _1637919] : [-(hAPP(c_Relation_ORange(_1637915, _1637917), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1637915, _1637917), tc_HOL_Obool), _1637919)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1637915, _1637917), tc_HOL_Obool), tc_fun(_1637917, tc_HOL_Obool)), _1637919), c_Relation_ORange(_1637915, _1637917)))], (19529 ^ _779327) ^ [_1111928, _1111930, _1111932] : [class_Fields_Olinordered__field(_1111928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111928), c_Groups_Ozero__class_Ozero(_1111928)), _1111930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111928), _1111932), c_Groups_Ozero__class_Ozero(_1111928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111928), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111928), _1111930), _1111932)), c_Groups_Ozero__class_Ozero(_1111928))))], (12768 ^ _779327) ^ [_992615, _992617, _992619] : [class_Rings_Olinordered__idom(_992615), -(c_Groups_Osgn__class_Osgn(_992615, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992615), _992617), _992619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_992615), c_Groups_Osgn__class_Osgn(_992615, _992617)), c_Groups_Osgn__class_Osgn(_992615, _992619)))], (48207 ^ _779327) ^ [_1743297, _1743299] : [-(c_Enum_Oenum__the(_1743297, _1743299) = c_HOL_OThe(_1743297, _1743299))], (38700 ^ _779327) ^ [_1509314, _1509316, _1509318, _1509320, _1509322] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1509314, _1509316, hAPP(hAPP(c_Set_Oinsert(_1509314), _1509318), _1509320)), _1509322)), 38705 ^ _779327 : [(38710 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1509314), 38703 ^ [_1509314, _1509316, _1509318, _1509320, _1509322]), 38704 ^ [_1509314, _1509316, _1509318, _1509320, _1509322]))], (38708 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1509314, _1509314, _1509316, 38703 ^ [_1509314, _1509316, _1509318, _1509320, _1509322], 38704 ^ [_1509314, _1509316, _1509318, _1509320, _1509322]), _1509322)))], (38706 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1509314), _1509318), _1509320) = hAPP(hAPP(c_Set_Oinsert(_1509314), 38703 ^ [_1509314, _1509316, _1509318, _1509320, _1509322]), 38704 ^ [_1509314, _1509316, _1509318, _1509320, _1509322]))]]], (49311 ^ _779327) ^ [_1766978, _1766980, _1766982] : [class_Orderings_Olinorder(_1766978), hBOOL(hAPP(hAPP(c_member(_1766978), _1766980), hAPP(c_List_Oset(_1766978), _1766982))), c_List_Olinorder__class_Osorted(_1766978, _1766982), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1766978, _1766978, c_COMBI(_1766978)), _1766980), c_List_Oremove1(_1766978, _1766980, _1766982)) = _1766982)], (47913 ^ _779327) ^ [_1736541, _1736543, _1736545, _1736547, _1736549] : [class_Orderings_Olinorder(_1736541), hBOOL(hAPP(c_List_Odistinct(_1736543), _1736545)), -(hBOOL(hAPP(c_List_Odistinct(_1736543), c_List_Olinorder__class_Oinsort__insert__key(_1736543, _1736541, _1736547, _1736549, _1736545))))], (46098 ^ _779327) ^ [_1696477, _1696479, _1696481] : [_1696481 = c_List_Olist_ONil(_1696477), -(hAPP(hAPP(c_List_Oappend(_1696477), _1696479), _1696481) = _1696479)], (29158 ^ _779327) ^ [_1299010, _1299012, _1299014, _1299016, _1299018] : [-(_1299010 = c_Orderings_Obot__class_Obot(tc_fun(_1299012, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299012, tc_fun(_1299014, tc_HOL_Obool)), _1299010), hAPP(hAPP(c_COMBC(_1299012, tc_fun(_1299014, tc_HOL_Obool), tc_fun(_1299014, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1299014, tc_HOL_Obool), tc_fun(tc_fun(_1299014, tc_HOL_Obool), tc_fun(_1299014, tc_HOL_Obool)), _1299012), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299014, tc_HOL_Obool))), _1299016)), _1299018)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299014, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299012, tc_fun(_1299014, tc_HOL_Obool)), _1299010), _1299016)), _1299018))], (37939 ^ _779327) ^ [] : [-(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)))], (32140 ^ _779327) ^ [_1362910, _1362912] : [class_Int_Oring__char__0(_1362910), hBOOL(hAPP(hAPP(c_member(_1362910), _1362912), c_Int_Oring__1__class_OInts(_1362910))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362910), c_Groups_Oone__class_Oone(_1362910)), _1362912)), _1362912) = c_Groups_Ozero__class_Ozero(_1362910)], (51126 ^ _779327) ^ [_1805822, _1805824, _1805826, _1805828] : [51134 ^ _779327 : [(51137 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1805828, 51133 ^ [_1805822, _1805824, _1805826, _1805828])))], (51135 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805822), 51133 ^ [_1805822, _1805824, _1805826, _1805828]), hAPP(c_List_Oset(_1805822), c_List_Oreplicate(_1805822, _1805824, _1805826)))))]], hBOOL(hAPP(_1805828, _1805826)), -(_1805824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17102 ^ _779327) ^ [_1069689, _1069691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1069689)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069689), _1069691)), _1069689) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20869 ^ _779327) ^ [_1136635, _1136637, _1136639] : [20871 ^ _779327 : [(20876 ^ _779327) ^ [] : [hBOOL(hAPP(_1136637, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 20870 ^ [_1136635, _1136637, _1136639]), _1136635)))], (20874 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1136637, 20870 ^ [_1136635, _1136637, _1136639])))], (20872 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20870 ^ [_1136635, _1136637, _1136639]), _1136635)))]], hBOOL(hAPP(_1136637, _1136639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136639), _1136635)), -(hBOOL(hAPP(_1136637, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45098 ^ _779327) ^ [_1671459, _1671461, _1671463, _1671465, _1671467] : [hAPP(hAPP(c_List_Omap(_1671459, _1671461), _1671463), _1671465) = hAPP(hAPP(c_List_Omap(_1671459, _1671461), _1671463), _1671467), c_Fun_Oinj__on(_1671459, _1671461, _1671463, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1671459, tc_HOL_Obool)), hAPP(c_List_Oset(_1671459), _1671465)), hAPP(c_List_Oset(_1671459), _1671467))), -(_1671465 = _1671467)], (20857 ^ _779327) ^ [_1136514, _1136516] : [-(_1136514 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1136514, _1136516) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1136514), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1136516)))], (22105 ^ _779327) ^ [_1161180, _1161182, _1161184] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1161180, _1161182), _1161184)), -(c_Divides_Odivmod__nat(_1161180, _1161182) = _1161184)], (3790 ^ _779327) ^ [_836767, _836769, _836771, _836773, _836775, _836777, _836779, _836781] : [-(c_Product__Type_Oscomp(_836781, _836777, _836773, _836769) = c_Product__Type_Oscomp(_836779, _836775, _836771, _836767)), _836781 = _836779, _836777 = _836775, _836773 = _836771, _836769 = _836767], (38868 ^ _779327) ^ [_1514249, _1514251, _1514253, _1514255, _1514257, _1514259] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514249, _1514251)), hAPP(hAPP(c_Product__Type_OPair(_1514249, _1514251), _1514253), _1514255)), hAPP(hAPP(c_Product__Type_OSigma(_1514249, _1514251), _1514257), _1514259))), -(hBOOL(hAPP(hAPP(c_member(_1514249), _1514253), _1514257)))], (42037 ^ _779327) ^ [_1595760, _1595762] : [c_Wellfounded_Owf(_1595760, _1595762), -(c_Wellfounded_Owf(_1595760, c_Transitive__Closure_Otrancl(_1595760, _1595762)))], (32546 ^ _779327) ^ [_1370727, _1370729, _1370731, _1370733, _1370735, _1370737, _1370739, _1370741] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1370727, _1370729), tc_prod(_1370727, _1370729))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1370727, _1370729), tc_prod(_1370727, _1370729)), hAPP(hAPP(c_Product__Type_OPair(_1370727, _1370729), _1370731), _1370733)), hAPP(hAPP(c_Product__Type_OPair(_1370727, _1370729), _1370735), _1370737))), c_Wellfounded_Olex__prod(_1370727, _1370729, _1370739, _1370741)))), 32547 ^ _779327 : [(32550 ^ _779327) ^ [] : [_1370731 = _1370735, hBOOL(hAPP(hAPP(c_member(tc_prod(_1370729, _1370729)), hAPP(hAPP(c_Product__Type_OPair(_1370729, _1370729), _1370733), _1370737)), _1370741))], (32548 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1370727, _1370727)), hAPP(hAPP(c_Product__Type_OPair(_1370727, _1370727), _1370731), _1370735)), _1370739))]]], (32756 ^ _779327) ^ [_1375074, _1375076] : [class_Orderings_Olinorder(_1375074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375074), _1375076)), -(_1375076 = c_Orderings_Obot__class_Obot(tc_fun(_1375074, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375074), c_Big__Operators_Olattice_OInf__fin(_1375074, c_Orderings_Oord__class_Omin(_1375074), _1375076)), c_Big__Operators_Olattice_OSup__fin(_1375074, c_Orderings_Oord__class_Omax(_1375074), _1375076))))], (30341 ^ _779327) ^ [_1324940, _1324942, _1324944, _1324946] : [c_Orderings_Oorder__class_Omono(tc_fun(_1324940, tc_HOL_Obool), tc_fun(_1324940, tc_HOL_Obool), _1324942), hBOOL(hAPP(hAPP(c_member(_1324940), _1324944), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1324940, tc_HOL_Obool), _1324942))), -(hBOOL(hAPP(hAPP(c_member(_1324940), _1324944), hAPP(_1324942, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324940, tc_HOL_Obool)), _1324946), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1324940, tc_HOL_Obool), _1324942))))))], (42212 ^ _779327) ^ [_1600691, _1600693] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1600691, _1600691, _1600691), c_Transitive__Closure_Ortrancl(_1600691, _1600693)), c_Transitive__Closure_Ortrancl(_1600691, _1600693)) = c_Transitive__Closure_Ortrancl(_1600691, _1600693))], (44292 ^ _779327) ^ [_1648381, _1648383, _1648385, _1648387, _1648389, _1648391, _1648393, _1648395] : [c_Finite__Set_Ofolding__image__simple__idem(_1648381, _1648383, _1648385, _1648387, _1648389, _1648391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648383), _1648393)), -(hAPP(_1648391, hAPP(hAPP(c_Set_Oinsert(_1648383), _1648395), _1648393)) = hAPP(hAPP(_1648385, hAPP(_1648389, _1648395)), hAPP(_1648391, _1648393)))], (46186 ^ _779327) ^ [_1698329, _1698331, _1698333, _1698335, _1698337] : [hAPP(hAPP(c_List_Oappend(_1698329), _1698331), _1698333) = hAPP(hAPP(c_List_Oappend(_1698329), _1698335), _1698337), 46192 ^ _779327 : [(46195 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1698329), 46189 ^ [_1698329, _1698331, _1698333, _1698335, _1698337]), _1698333) = _1698337)], (46193 ^ _779327) ^ [] : [-(_1698331 = hAPP(hAPP(c_List_Oappend(_1698329), _1698335), 46189 ^ [_1698329, _1698331, _1698333, _1698335, _1698337]))]], 46196 ^ _779327 : [(46199 ^ _779327) ^ [] : [-(_1698333 = hAPP(hAPP(c_List_Oappend(_1698329), 46189 ^ [_1698329, _1698331, _1698333, _1698335, _1698337]), _1698337))], (46197 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1698329), _1698331), 46189 ^ [_1698329, _1698331, _1698333, _1698335, _1698337]) = _1698335)]]], (48874 ^ _779327) ^ [_1758983, _1758985, _1758987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758983), _1758985)), _1758987)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1758983, _1758987)), _1758985) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758983), _1758985))], (35087 ^ _779327) ^ [_1426667, _1426669, _1426671, _1426673] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426667, tc_HOL_Obool)), _1426669), _1426671)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426667, tc_HOL_Obool)), _1426671), _1426673))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426667, tc_HOL_Obool)), _1426673), _1426669)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426667, tc_HOL_Obool)), _1426669), _1426671)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426667, tc_HOL_Obool)), _1426671), _1426673))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426667, tc_HOL_Obool)), _1426673), _1426669)))], (39952 ^ _779327) ^ [_1539653, _1539655, _1539657, _1539659, _1539661, _1539663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539653), _1539655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539657), _1539659)), 39962 ^ _779327 : [(39965 ^ _779327) ^ [] : [hAPP(c_Finite__Set_Ocard(_1539653), hAPP(c_Set_OCollect(_1539653), hAPP(hAPP(c_COMBS(_1539653, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539653), c_fconj), hAPP(hAPP(c_COMBC(_1539653, tc_fun(_1539653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539653)), _1539655))), hAPP(hAPP(c_COMBC(_1539653, _1539657, tc_HOL_Obool), _1539661), 39961 ^ [_1539653, _1539655, _1539657, _1539659, _1539661, _1539663])))) = _1539663], (39963 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539657), 39961 ^ [_1539653, _1539655, _1539657, _1539659, _1539661, _1539663]), _1539659)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539653, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1539657, tc_HOL_Obool), tc_Nat_Onat, _1539653), c_Finite__Set_Ocard(_1539657)), hAPP(hAPP(c_COMBB(tc_fun(_1539657, tc_HOL_Obool), tc_fun(_1539657, tc_HOL_Obool), _1539653), c_Set_OCollect(_1539657)), hAPP(hAPP(c_COMBB(tc_fun(_1539657, tc_HOL_Obool), tc_fun(_1539657, tc_HOL_Obool), _1539653), hAPP(c_COMBS(_1539657, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539657), c_fconj), hAPP(hAPP(c_COMBC(_1539657, tc_fun(_1539657, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539657)), _1539659)))), _1539661)))), _1539655) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1539663), hAPP(c_Finite__Set_Ocard(_1539657), _1539659)))], (35599 ^ _779327) ^ [_1438453, _1438455, _1438457, _1438459, _1438461] : [class_Groups_Ocomm__monoid__mult(_1438453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438455), _1438457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438455), _1438459)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438453), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438455, _1438453), _1438461), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1438455, tc_HOL_Obool)), _1438457), _1438459))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438455, _1438453), _1438461), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1438455, tc_HOL_Obool)), _1438457), _1438459))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438453), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438455, _1438453), _1438461), _1438457)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1438455, _1438453), _1438461), _1438459)))], (8918 ^ _779327) ^ [_922882, _922884, _922886, _922888] : [class_Rings_Ocomm__semiring__1(_922882), -(hAPP(hAPP(c_Power_Opower__class_Opower(_922882), hAPP(hAPP(c_Power_Opower__class_Opower(_922882), _922884), _922886)), _922888) = hAPP(hAPP(c_Power_Opower__class_Opower(_922882), _922884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _922886), _922888)))], (48209 ^ _779327) ^ [_1743328, _1743330, _1743332] : [hBOOL(hAPP(c_List_Odistinct(_1743328), _1743330)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1743328)), c_Enum_On__lists(_1743328, _1743332, _1743330))))], (14795 ^ _779327) ^ [_1028173, _1028175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028173), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14798 ^ _779327 : [(14805 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028175), 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), _1028175), _1028173))))], (14799 ^ _779327) ^ [] : [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), _1028175), _1028173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028175), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (49891 ^ _779327) ^ [_1779302, _1779304, _1779306] : [-(c_List_OdropWhile(_1779302, _1779304, _1779306) = c_List_Olist_ONil(_1779302)), hBOOL(hAPP(_1779304, hAPP(c_List_Ohd(_1779302), c_List_OdropWhile(_1779302, _1779304, _1779306))))], (26564 ^ _779327) ^ [_1247013, _1247015] : [c_Nat__Transfer_Onat__set(_1247013), c_Nat__Transfer_Onat__set(_1247015), 26571 ^ _779327 : [(26578 ^ _779327) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247013) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247015), -(_1247013 = _1247015)], (26572 ^ _779327) ^ [] : [_1247013 = _1247015, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247013) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1247015))]]], (18650 ^ _779327) ^ [_1096581, _1096583, _1096585] : [class_Rings_Olinordered__idom(_1096581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096581), c_Groups_Ozero__class_Ozero(_1096581)), hAPP(hAPP(c_Power_Opower__class_Opower(_1096581), _1096583), 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)))), _1096585))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096581), c_Groups_Ozero__class_Ozero(_1096581)), _1096583)))], (33622 ^ _779327) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (36706 ^ _779327) ^ [_1464098, _1464100, _1464102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1464098), _1464100)), c_Fun_Oinj__on(_1464098, tc_fun(tc_fun(_1464098, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1464098, tc_fun(tc_prod(_1464098, _1464098), tc_HOL_Obool), tc_fun(tc_fun(_1464098, tc_HOL_Obool), 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_1041635))], (26858 ^ _779327) ^ [_1252590, _1252592, _1252594, _1252596] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252590, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252590, tc_HOL_Obool)), _1252592), _1252594)), _1252596) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252590, tc_HOL_Obool)), _1252592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252590, tc_HOL_Obool)), _1252594), _1252596)))], (42308 ^ _779327) ^ [_1603043, _1603045, _1603047] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603043, _1603043)), hAPP(hAPP(c_Product__Type_OPair(_1603043, _1603043), _1603045), _1603047)), c_Relation_OId(_1603043))), -(_1603045 = _1603047)], (7037 ^ _779327) ^ [_889477, _889479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889477), _889479)), -(hAPP(c_Nat_OSuc, _889477) = _889479), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889477)), _889479)))], (44851 ^ 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[-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1753339, tc_HOL_Obool)), hAPP(c_List_Oset(_1753339), _1753341)), hAPP(hAPP(c_Set_Oinsert(_1753339), _1753343), c_Orderings_Obot__class_Obot(tc_fun(_1753339, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1753339), hAPP(c_List_Ofilter(_1753339, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1753339), c_fNot), hAPP(hAPP(c_COMBC(_1753339, _1753339, tc_HOL_Obool), c_fequal), _1753343))), _1753341)))], (44773 ^ _779327) ^ [_1662860, _1662862, _1662864, _1662866, _1662868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662860), tc_List_Olist(_1662860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662860), tc_List_Olist(_1662860)), _1662862), hAPP(hAPP(c_List_Olist_OCons(_1662860), _1662864), _1662866))), c_List_Olistrel(_1662860, _1662868))), 44778 ^ _779327 : [(44783 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662860), tc_List_Olist(_1662860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662860), tc_List_Olist(_1662860)), 44777 ^ [_1662860, _1662862, _1662864, _1662866, _1662868]), _1662866)), c_List_Olistrel(_1662860, _1662868))))], (44781 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662860, _1662860)), hAPP(hAPP(c_Product__Type_OPair(_1662860, _1662860), 44776 ^ [_1662860, _1662862, _1662864, _1662866, _1662868]), _1662864)), _1662868)))], (44779 ^ _779327) ^ [] : [-(_1662862 = hAPP(hAPP(c_List_Olist_OCons(_1662860), 44776 ^ [_1662860, _1662862, _1662864, _1662866, _1662868]), 44777 ^ [_1662860, _1662862, _1662864, _1662866, _1662868]))]]], (11081 ^ _779327) ^ [_960130, _960132, _960134] : [class_Groups_Ogroup__add(_960130), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960130), _960132), _960134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960130), _960132), hAPP(c_Groups_Ouminus__class_Ouminus(_960130), _960134)))], (49754 ^ _779327) ^ [_1776427, _1776429, _1776431] : [-(c_List_OtakeWhile(_1776427, _1776429, _1776431) = hAPP(hAPP(c_List_Otake(_1776427), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776427)), c_List_OtakeWhile(_1776427, _1776429, _1776431))), _1776431))], (42246 ^ _779327) ^ [_1601491, _1601493] : [-(c_Transitive__Closure_Ortrancl(_1601491, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601491, _1601491), tc_HOL_Obool)), _1601493), c_Relation_OId(_1601491))) = c_Transitive__Closure_Ortrancl(_1601491, _1601493))], (18638 ^ _779327) ^ [_1096271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1096271)), -(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), _1096271), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (15283 ^ _779327) ^ [_1036838, _1036840, _1036842] : [class_Divides_Osemiring__div(_1036838), -(c_Divides_Odiv__class_Omod(_1036838, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036838), _1036840), _1036842), _1036840) = c_Divides_Odiv__class_Omod(_1036838, _1036842, _1036840))], (49826 ^ _779327) ^ [_1777973, _1777975, _1777977] : [hBOOL(hAPP(c_List_Odistinct(_1777973), _1777975)), hBOOL(hAPP(hAPP(c_member(_1777973), _1777977), hAPP(c_List_Oset(_1777973), _1777975))), -(c_List_OdropWhile(_1777973, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777973), c_fNot), hAPP(hAPP(c_COMBC(_1777973, _1777973, tc_HOL_Obool), c_fequal), _1777977)), hAPP(c_List_Orev(_1777973), _1777975)) = hAPP(hAPP(c_List_Olist_OCons(_1777973), _1777977), hAPP(c_List_Orev(_1777973), c_List_OtakeWhile(_1777973, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777973), c_fNot), hAPP(hAPP(c_COMBC(_1777973, _1777973, tc_HOL_Obool), c_fequal), _1777977)), _1777975))))], (26536 ^ _779327) ^ [_1246584] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1246584) = 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), _1246584))))], (3164 ^ _779327) ^ [_826830, _826832, _826834, _826836, _826838, _826840] : [-(c_Finite__Set_Ofold1Set(_826840, _826836, _826832) = c_Finite__Set_Ofold1Set(_826838, _826834, _826830)), _826840 = _826838, _826836 = _826834, _826832 = _826830], (8476 ^ _779327) ^ [_915025, _915027, _915029, _915031] : [class_Rings_Olinordered__semiring__strict(_915025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915025), _915027), _915029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915025), _915031), _915029))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915025), c_Groups_Ozero__class_Ozero(_915025)), _915029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915025), _915027), _915031)))], (15592 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (32882 ^ 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094560), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094560), hAPP(hAPP(c_Power_Opower__class_Opower(_1094560), _1094562), 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(_1094560), _1094564), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094560)))], (8006 ^ _779327) ^ [_906321, _906323, _906325, _906327] : [class_Rings_Olinordered__ring__strict(_906321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906321), c_Groups_Ozero__class_Ozero(_906321)), _906323)), 8013 ^ _779327 : [(8020 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906321), _906325), _906327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906321), _906323), _906325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906321), _906323), _906327))))], (8014 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906321), _906323), _906325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906321), _906323), _906327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906321), _906325), _906327)))]]], (16585 ^ _779327) ^ [_1060544, _1060546, _1060548] : [class_Groups_Oordered__ab__group__add__abs(_1060544), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060544), hAPP(c_Groups_Oabs__class_Oabs(_1060544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060544), hAPP(c_Groups_Oabs__class_Oabs(_1060544), _1060546)), hAPP(c_Groups_Oabs__class_Oabs(_1060544), _1060548)))), hAPP(c_Groups_Oabs__class_Oabs(_1060544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060544), _1060546), _1060548)))))], (23636 ^ _779327) ^ [_1190853, _1190855] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1190853), _1190855) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1190853)), hAPP(c_Code__Numeral_Onat__of, _1190855))))], (50993 ^ _779327) ^ [_1803438, _1803440] : [c_Wellfounded_Oacyclic(_1803438, hAPP(c_Set_OCollect(tc_prod(_1803438, _1803438)), hAPP(c_Product__Type_Oprod_Oprod__case(_1803438, _1803438, tc_HOL_Obool), _1803440))), -(c_Wellfounded_Oacyclic(_1803438, hAPP(c_Set_OCollect(tc_prod(_1803438, _1803438)), hAPP(c_Product__Type_Oprod_Oprod__case(_1803438, _1803438, tc_HOL_Obool), c_Predicate_Oconversep(_1803438, _1803438, _1803440)))))], (13372 ^ _779327) ^ [_1003336, _1003338] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003336), _1003338) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003336), _1003338)))], (38 ^ _779327) ^ [_779856, _779858, _779860, _779862] : [-(c_Int_Oiszero(_779860, _779856)), c_Int_Oiszero(_779862, _779858), _779862 = _779860, _779858 = _779856], (38343 ^ _779327) ^ [] : [-(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))))], (11857 ^ _779327) ^ [_975827, _975829, _975831] : [class_Rings_Oidom(_975827), 11860 ^ _779327 : [(11861 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975827), _975829), _975829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975827), _975831), _975831), -(_975829 = _975831), -(_975829 = hAPP(c_Groups_Ouminus__class_Ouminus(_975827), _975831))], (11871 ^ _779327) ^ [] : [11872 ^ _779327 : [(11875 ^ _779327) ^ [] : [_975829 = hAPP(c_Groups_Ouminus__class_Ouminus(_975827), _975831)], (11873 ^ _779327) ^ [] : [_975829 = _975831]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975827), _975829), _975829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975827), _975831), _975831))]]], (40962 ^ _779327) ^ [_1571177, _1571179, _1571181] : [-(hAPP(c_Relation_ODomain(_1571177, _1571179), hAPP(c_Set_OCollect(tc_prod(_1571177, _1571179)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571177, _1571179, tc_HOL_Obool), _1571181))) = hAPP(c_Set_OCollect(_1571177), hAPP(hAPP(c_COMBB(tc_fun(_1571179, tc_HOL_Obool), tc_HOL_Obool, _1571177), c_HOL_OEx(_1571179)), _1571181)))], (33104 ^ _779327) ^ [_1381988, _1381990, _1381992, _1381994] : [class_Rings_Ocomm__semiring__1(_1381988), class_Rings_Ono__zero__divisors(_1381988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381990), _1381992)), 33115 ^ _779327 : [(33125 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381990, _1381988), _1381994), _1381992) = c_Groups_Ozero__class_Ozero(_1381988)), 33126 ^ _779327 : [(33127 ^ _779327) ^ [_1382366] : [hBOOL(hAPP(hAPP(c_member(_1381990), _1382366), _1381992)), hAPP(_1381994, _1382366) = c_Groups_Ozero__class_Ozero(_1381988)]]], (33116 ^ _779327) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381990, _1381988), _1381994), _1381992) = c_Groups_Ozero__class_Ozero(_1381988), 33120 ^ _779327 : [(33123 ^ _779327) ^ [] : [-(hAPP(_1381994, 33119 ^ [_1381988, _1381990, _1381992, _1381994]) = c_Groups_Ozero__class_Ozero(_1381988))], (33121 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381990), 33119 ^ [_1381988, _1381990, _1381992, _1381994]), _1381992)))]]]]], (23668 ^ _779327) ^ [_1191385, _1191387] : [_1191385 = _1191387, -(hAPP(c_Code__Numeral_Onat__of, _1191385) = hAPP(c_Code__Numeral_Onat__of, _1191387))], (53036 ^ _779327) ^ [_1840958] : [hBOOL(hAPP(c_fNot, _1840958)), hBOOL(_1840958)], (48568 ^ _779327) ^ [_1751703, _1751705, _1751707, _1751709, _1751711, _1751713] : [class_Orderings_Olinorder(_1751703), -(hBOOL(hAPP(_1751705, _1751707))), -(hAPP(c_List_Ofilter(_1751709, _1751705), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1751709, _1751703, _1751711), _1751707), _1751713)) = hAPP(c_List_Ofilter(_1751709, _1751705), _1751713))], (17312 ^ _779327) ^ [_1073062, _1073064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1073062)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1073064)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073064), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1073062))))], (33297 ^ _779327) ^ [_1385542, _1385544, _1385546, _1385548, _1385550] : [class_Groups_Ocomm__monoid__mult(_1385542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385544), _1385546)), 33304 ^ _779327 : [(33311 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1385544), _1385548), _1385546))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385544, _1385542), hAPP(hAPP(c_COMBC(_1385544, _1385542, _1385542), hAPP(hAPP(c_COMBS(_1385544, _1385542, tc_fun(_1385542, _1385542)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1385542, tc_fun(_1385542, _1385542)), _1385544), c_If(_1385542)), hAPP(c_fequal, _1385548))), _1385550)), c_Groups_Oone__class_Oone(_1385542))), _1385546) = c_Groups_Oone__class_Oone(_1385542))], (33305 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1385544), _1385548), _1385546)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385544, _1385542), hAPP(hAPP(c_COMBC(_1385544, _1385542, _1385542), hAPP(hAPP(c_COMBS(_1385544, _1385542, tc_fun(_1385542, _1385542)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1385542, tc_fun(_1385542, _1385542)), _1385544), c_If(_1385542)), hAPP(c_fequal, _1385548))), _1385550)), c_Groups_Oone__class_Oone(_1385542))), _1385546) = hAPP(_1385550, _1385548))]]], (51975 ^ _779327) ^ [_1825539, _1825541] : [-(c_Relation_Oantisym(_1825539, c_Relation_OId__on(_1825539, _1825541)))], (31427 ^ _779327) ^ [_1349363, _1349365, _1349367] : [class_Complete__Lattice_Ocomplete__lattice(_1349363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349363), hAPP(_1349365, _1349367)), _1349367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349363), c_Inductive_Ocomplete__lattice__class_Olfp(_1349363, _1349365)), _1349367)))], (48038 ^ _779327) ^ [_1739219, _1739221, _1739223, _1739225] : [_1739225 = c_List_Olist_ONil(_1739219), -(c_List_Olist__all2(_1739219, _1739221, _1739223, _1739225, c_List_Olist_ONil(_1739221)))], (23766 ^ _779327) ^ [_1193374, _1193376, _1193378, _1193380, _1193382] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1193374, _1193376, tc_HOL_Obool, _1193378), _1193380), _1193382)), -(hBOOL(hAPP(_1193378, hAPP(hAPP(c_Product__Type_OPair(_1193374, _1193376), _1193380), _1193382))))], (47116 ^ _779327) ^ [_1719920, _1719922, _1719924] : [-(hAPP(c_List_Orotate(_1719920, hAPP(c_Nat_OSuc, _1719922)), _1719924) = hAPP(c_List_Orotate1(_1719920), hAPP(c_List_Orotate(_1719920, _1719922), _1719924)))], (5030 ^ _779327) ^ [_855973, _855975, _855977, _855979, _855981, _855983, _855985, _855987, _855989, _855991] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855991, _855987, _855983, _855979, _855975) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855989, _855985, _855981, _855977, _855973)), _855991 = _855989, _855987 = _855985, _855983 = _855981, _855979 = _855977, _855975 = _855973], (48728 ^ _779327) ^ [_1756174, _1756176] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1756174))), c_List_Otranspose(_1756174, _1756176)) = c_List_Ofoldr(tc_List_Olist(_1756174), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1756174)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1756174))), _1756176, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27380 ^ _779327) ^ [_1263497, _1263499] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1263497)), _1263499) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1263497, _1263499))], (51229 ^ _779327) ^ [_1807762, _1807764, _1807766, _1807768] : [-(c_List_Oreplicate(_1807762, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1807764), _1807766), _1807768) = hAPP(hAPP(c_List_Oappend(_1807762), c_List_Oreplicate(_1807762, _1807764, _1807768)), c_List_Oreplicate(_1807762, _1807766, _1807768)))], (39878 ^ _779327) ^ [_1536760, _1536762, _1536764, _1536766] : [-(hAPP(c_Set_OCollect(_1536760), hAPP(hAPP(c_COMBB(tc_fun(_1536762, tc_HOL_Obool), tc_HOL_Obool, _1536760), c_HOL_OAll(_1536762)), hAPP(hAPP(c_COMBB(tc_fun(_1536762, tc_HOL_Obool), tc_fun(_1536762, tc_HOL_Obool), _1536760), hAPP(c_COMBS(_1536762, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536762), c_fimplies), hAPP(hAPP(c_COMBC(_1536762, tc_fun(_1536762, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536762)), _1536764)))), _1536766))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1536762, tc_fun(_1536760, tc_HOL_Obool)), _1536764), hAPP(hAPP(c_COMBB(tc_fun(_1536760, tc_HOL_Obool), tc_fun(_1536760, tc_HOL_Obool), _1536762), c_Set_OCollect(_1536760)), hAPP(c_COMBC(_1536760, _1536762, tc_HOL_Obool), _1536766))))], (13150 ^ _779327) ^ [_999180, _999182] : [class_Groups_Olinordered__ab__group__add(_999180), 13153 ^ _779327 : [(13160 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999180), c_Groups_Ozero__class_Ozero(_999180)), _999182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999180), c_Groups_Ozero__class_Ozero(_999180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999180), _999182), _999182))))], (13154 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999180), c_Groups_Ozero__class_Ozero(_999180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999180), _999182), _999182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999180), c_Groups_Ozero__class_Ozero(_999180)), _999182)))]]], (38269 ^ _779327) ^ [_1499597] : [-(c_Equiv__Relations_Oequivp(_1499597, c_fequal))], (50833 ^ _779327) ^ [_1800140, _1800142, _1800144, _1800146] : [c_List_Olist__all(_1800140, _1800142, hAPP(hAPP(c_List_Oappend(_1800140), _1800144), _1800146)), 50836 ^ _779327 : [(50839 ^ _779327) ^ [] : [-(c_List_Olist__all(_1800140, _1800142, _1800146))], (50837 ^ _779327) ^ [] : [-(c_List_Olist__all(_1800140, _1800142, _1800144))]]], (14481 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23305 ^ _779327) ^ [_1184014, _1184016, _1184018] : [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), _1184014), _1184016))), -(hBOOL(hAPP(hAPP(_1184018, _1184014), _1184016))), 23312 ^ _779327 : [(23315 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23311 ^ [_1184014, _1184016, _1184018]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1184018, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23310 ^ [_1184014, _1184016, _1184018])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23311 ^ [_1184014, _1184016, _1184018]))))], (23321 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1184018, 23310 ^ [_1184014, _1184016, _1184018]), 23311 ^ [_1184014, _1184016, _1184018]))], (23313 ^ _779327) ^ [] : [-(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), 23310 ^ [_1184014, _1184016, _1184018]), 23311 ^ [_1184014, _1184016, _1184018]))))]]], (17618 ^ _779327) ^ [_1078323, _1078325] : [class_Int_Onumber__ring(_1078323), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078323), hAPP(c_Int_Onumber__class_Onumber__of(_1078323), c_Int_OBit1(c_Int_OPls))), _1078325) = _1078325)], (39706 ^ _779327) ^ [_1532746] : [-(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)), _1532746)))))], (18793 ^ _779327) ^ [_1099168, _1099170, _1099172, _1099174] : [class_Rings_Odivision__ring(_1099168), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099168), _1099170), _1099172)), _1099174) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099168), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099168), _1099170), _1099174)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099168), _1099172), _1099174)))], (22613 ^ _779327) ^ [_1170614, _1170616, _1170618, _1170620] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1170614), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170614), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170614), _1170616), _1170618)), _1170620) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170614), _1170616), _1170620)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170614), _1170618), _1170620)))], (28041 ^ _779327) ^ [_1277870] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1277870)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1277870), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1277870)))], (15566 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35267 ^ _779327) ^ [_1430890, _1430892, _1430894] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430890, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430890, tc_HOL_Obool)), _1430892), _1430894)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430890, tc_HOL_Obool)), _1430892), _1430894)) = _1430892)], (40198 ^ _779327) ^ [_1550086, _1550088] : [c_Predicate_Oreflp(_1550086, _1550088), -(c_Relation_Orefl__on(_1550086, c_Orderings_Otop__class_Otop(tc_fun(_1550086, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1550086, _1550086)), hAPP(c_Product__Type_Oprod_Oprod__case(_1550086, _1550086, tc_HOL_Obool), _1550088))))], (23277 ^ _779327) ^ [_1183434, _1183436, _1183438, _1183440, _1183442] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1183434, _1183436, _1183434, _1183438), hAPP(c_Product__Type_OPair(_1183436, _1183434), _1183440)), _1183442) = hAPP(_1183442, _1183440))], (38413 ^ _779327) ^ [_1502698, _1502700, _1502702] : [-(hAPP(c_Set_Ovimage(_1502698, _1502700, _1502702), c_Orderings_Otop__class_Otop(tc_fun(_1502700, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1502698, tc_HOL_Obool)))], (43463 ^ _779327) ^ [_1630036, _1630038, _1630040, _1630042, _1630044, _1630046] : [c_Finite__Set_Ofun__left__comm(_1630036, _1630038, _1630040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630036), _1630042)), hBOOL(hAPP(hAPP(c_member(_1630036), _1630044), _1630042)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1630036, _1630038, _1630040), _1630046), _1630042) = hAPP(hAPP(_1630040, _1630044), hAPP(hAPP(c_Finite__Set_Ofold(_1630036, _1630038, _1630040), _1630046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1630036, tc_HOL_Obool)), _1630042), hAPP(hAPP(c_Set_Oinsert(_1630036), _1630044), c_Orderings_Obot__class_Obot(tc_fun(_1630036, tc_HOL_Obool)))))))], (38405 ^ _779327) ^ [_1502382, _1502384, _1502386, _1502388, _1502390] : [-(hAPP(c_Set_Ovimage(_1502382, _1502384, _1502386), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502384, tc_HOL_Obool)), _1502388), _1502390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502382, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502382, _1502384, _1502386), _1502388)), hAPP(c_Set_Ovimage(_1502382, _1502384, _1502386), _1502390)))], (37717 ^ _779327) ^ [_1485524, _1485526, _1485528] : [class_Orderings_Otop(_1485524), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1485526, _1485524)), _1485528) = c_Orderings_Otop__class_Otop(_1485524))], (5482 ^ _779327) ^ [_862977, _862979, _862981, _862983] : [-(tc_Nitpick_Opair__box(_862983, _862979) = tc_Nitpick_Opair__box(_862981, _862977)), _862983 = _862981, _862979 = _862977], (28479 ^ _779327) ^ [_1286445, _1286447, _1286449] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286445), _1286447))), 28482 ^ _779327 : [(28489 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286449), _1286447))), -(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)), _1286445)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1286449), _1286447)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28483 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286449), _1286447)), -(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)), _1286445)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1286449), _1286447)) = 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))))]]], (47550 ^ _779327) ^ [_1728625, _1728627, _1728629] : [hBOOL(hAPP(c_List_Odistinct(_1728625), _1728627)), -(hAPP(c_List_Oset(_1728625), c_List_Oremove1(_1728625, _1728629, _1728627)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1728625, tc_HOL_Obool)), hAPP(c_List_Oset(_1728625), _1728627)), hAPP(hAPP(c_Set_Oinsert(_1728625), _1728629), c_Orderings_Obot__class_Obot(tc_fun(_1728625, tc_HOL_Obool)))))], (8924 ^ _779327) ^ [_923039, _923041, _923043] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _923039), _923041) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _923039), _923043), -(_923039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_923041 = _923043)], (18062 ^ _779327) ^ [_1085970, _1085972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085970)), c_Int_OBit0(_1085972))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085970), _1085972)))], (50648 ^ _779327) ^ [_1796235, _1796237, _1796239] : [-(c_List_Olist__ex(_1796235, _1796237, _1796239)), 50649 ^ _779327 : [(50650 ^ _779327) ^ [_1796300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796300), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796235)), _1796239))), hBOOL(hAPP(_1796237, hAPP(hAPP(c_List_Onth(_1796235), _1796239), _1796300)))]]], (26834 ^ _779327) ^ [_1252039, _1252041, _1252043, _1252045] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252039, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252039, tc_HOL_Obool)), _1252041), _1252043)), _1252045) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252039, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252039, tc_HOL_Obool)), _1252041), _1252045)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252039, tc_HOL_Obool)), _1252043), _1252045)))], (37629 ^ _779327) ^ [_1483642, _1483644, _1483646, _1483648] : [37631 ^ _779327 : [(37634 ^ _779327) ^ [] : [hAPP(_1483648, 37630 ^ [_1483642, _1483644, _1483646, _1483648]) = c_Orderings_Otop__class_Otop(tc_fun(_1483642, tc_HOL_Obool))], (37632 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483644), 37630 ^ [_1483642, _1483644, _1483646, _1483648]), _1483646)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1483642, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483644, tc_fun(_1483642, tc_HOL_Obool)), _1483646), _1483648))], (6352 ^ _779327) ^ [_879176, _879178, _879180] : [class_Orderings_Opreorder(_879176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879176), _879178), _879180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879176), _879178), _879180)))], (24733 ^ _779327) ^ [_1210065, _1210067, _1210069, _1210071, _1210073] : [class_Rings_Ocomm__semiring__1(_1210065), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1210065), hAPP(hAPP(c_Power_Opower__class_Opower(_1210065), _1210067), _1210069)), _1210071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1210073), _1210069)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1210065), hAPP(hAPP(c_Power_Opower__class_Opower(_1210065), _1210067), _1210073)), _1210071)))], (38964 ^ _779327) ^ [_1516456, _1516458, _1516460, _1516462] : [-(_1516456 = c_Orderings_Obot__class_Obot(tc_fun(_1516458, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1516458, _1516460), _1516460, c_Product__Type_Osnd(_1516458, _1516460)), hAPP(hAPP(c_Product__Type_OSigma(_1516458, _1516460), _1516456), hAPP(c_COMBK(tc_fun(_1516460, tc_HOL_Obool), _1516458), _1516462))) = _1516462)], (25401 ^ _779327) ^ [_1222164, _1222166] : [class_Orderings_Oorder(_1222164), 25408 ^ _779327 : [(25413 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222164), hAPP(_1222166, 25406 ^ [_1222164, _1222166])), hAPP(_1222166, 25407 ^ [_1222164, _1222166])))], (25411 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25407 ^ [_1222164, _1222166]), 25406 ^ [_1222164, _1222166]))], (25409 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25406 ^ [_1222164, _1222166]), 25407 ^ [_1222164, _1222166])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1222164, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1222166))], (6126 ^ _779327) ^ [_875829, _875831, _875833, _875835] : [class_Orderings_Oorder(_875829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875829), _875831), _875833)), _875831 = _875835, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875829), _875835), _875833)))], (17138 ^ _779327) ^ [_1070302, _1070304] : [17139 ^ _779327 : [(17142 ^ _779327) ^ [] : [_1070304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17140 ^ _779327) ^ [] : [-(_1070302 = 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), _1070302)), _1070304))))], (27997 ^ _779327) ^ [_1277276, _1277278] : [class_Complete__Lattice_Ocomplete__lattice(_1277276), c_Orderings_Oorder__class_Omono(_1277276, _1277276, _1277278), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1277276, _1277278) = hAPP(_1277278, c_Inductive_Ocomplete__lattice__class_Ogfp(_1277276, _1277278)))], (760 ^ _779327) ^ [_790989, _790991, _790993, _790995, _790997, _790999] : [-(c_Finite__Set_Ofun__left__comm__idem(_790997, _790993, _790989)), c_Finite__Set_Ofun__left__comm__idem(_790999, _790995, _790991), _790999 = _790997, _790995 = _790993, _790991 = _790989], (3966 ^ _779327) ^ [_839487, _839489, _839491, _839493, _839495, _839497] : [-(c_Big__Operators_Olattice_OSup__fin(_839497, _839493, _839489) = c_Big__Operators_Olattice_OSup__fin(_839495, _839491, _839487)), _839497 = _839495, _839493 = _839491, _839489 = _839487], (23027 ^ _779327) ^ [_1178269, _1178271, _1178273, _1178275] : [class_Orderings_Olinorder(_1178269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178269), _1178271), _1178273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178269), _1178271), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178269), _1178273), _1178275))))], (51515 ^ _779327) ^ [_1814846, _1814848, _1814850] : [c_List_Olist__ex(tc_Int_Oint, _1814846, c_List_Oupto(_1814848, _1814850)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1814846), _1814848, _1814850)], (3384 ^ _779327) ^ [_830312, _830314] : [_830314 = _830312, -(c_Nitpick_Onum(_830314) = c_Nitpick_Onum(_830312))], (32726 ^ _779327) ^ [_1374319, _1374321, _1374323, _1374325, _1374327, _1374329, _1374331] : [hBOOL(hAPP(_1374319, _1374321)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1374323, _1374323)), hAPP(hAPP(c_Product__Type_OPair(_1374323, _1374323), _1374325), _1374327)), hAPP(_1374329, _1374321))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1374331, _1374323), tc_prod(_1374331, _1374323))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1374331, _1374323), tc_prod(_1374331, _1374323)), hAPP(hAPP(c_Product__Type_OPair(_1374331, _1374323), _1374321), _1374325)), hAPP(hAPP(c_Product__Type_OPair(_1374331, _1374323), _1374321), _1374327))), c_Recdef_Osame__fst(_1374331, _1374323, _1374319, _1374329))))], (43101 ^ _779327) ^ [_1622964, _1622966, _1622968, _1622970] : [-(hAPP(c_Finite__Set_Ofold__image(_1622964, _1622966, _1622968), _1622970) = c_Finite__Set_Ofold(_1622966, _1622964, hAPP(hAPP(c_COMBB(_1622964, tc_fun(_1622964, _1622964), _1622966), _1622968), _1622970)))], (38457 ^ _779327) ^ [_1503774, _1503776, _1503778, _1503780] : [-(hAPP(c_Set_Oimage(_1503774, _1503776, _1503778), hAPP(c_Set_Ovimage(_1503774, _1503776, _1503778), _1503780)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503776, tc_HOL_Obool)), _1503780), hAPP(c_Set_Oimage(_1503774, _1503776, _1503778), c_Orderings_Otop__class_Otop(tc_fun(_1503774, tc_HOL_Obool)))))], (33666 ^ _779327) ^ [_1393868, _1393870, _1393872, _1393874] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393868), _1393874) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393872), _1393870), -(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), _1393868), _1393870)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1393872), _1393874))), c_Int_Ointrel)))], (15582 ^ _779327) ^ [_1042702] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1042702), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28316 ^ _779327) ^ [_1283277, _1283279, _1283281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283277, tc_HOL_Obool)), _1283279), _1283281)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283277), _1283281)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283277), _1283279)))], (24825 ^ _779327) ^ [_1211686, _1211688, _1211690] : [class_Rings_Odvd(_1211686), class_Rings_Osemiring__0(_1211686), 24832 ^ _779327 : [(24842 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1211688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211686), _1211690), 24849 ^ [_1211686, _1211688, _1211690])))), 24843 ^ _779327 : [(24844 ^ _779327) ^ [_1212015] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1211686), _1211690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211686), _1212015), c_Groups_Ozero__class_Ozero(_1211686)))), hBOOL(hAPP(_1211688, _1212015))]]], (24833 ^ _779327) ^ [] : [24834 ^ _779327 : [(24835 ^ _779327) ^ [_1211878] : [hBOOL(hAPP(_1211688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211686), _1211690), _1211878)))]], 24837 ^ _779327 : [(24840 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1211688, 24836 ^ [_1211686, _1211688, _1211690])))], (24838 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1211686), _1211690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211686), 24836 ^ [_1211686, _1211688, _1211690]), c_Groups_Ozero__class_Ozero(_1211686)))))]]]]], (47720 ^ _779327) ^ [_1732505, _1732507, _1732509, _1732511] : [hBOOL(hAPP(c_List_Olistsp(_1732505, _1732507), hAPP(hAPP(c_List_Olist_OCons(_1732505), _1732509), _1732511))), 47723 ^ _779327 : [(47726 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1732505, _1732507), _1732511)))], (47724 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1732507, _1732509)))]]], (40791 ^ _779327) ^ [_1566768, _1566770, _1566772, _1566774, _1566776] : [-(hAPP(c_Relation_ORange(_1566768, _1566770), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1566768, _1566770)), hAPP(hAPP(c_Product__Type_OPair(_1566768, _1566770), _1566772), _1566774)), _1566776)) = hAPP(hAPP(c_Set_Oinsert(_1566770), _1566774), hAPP(c_Relation_ORange(_1566768, _1566770), _1566776)))], (1578 ^ _779327) ^ [_802040, _802042] : [-(class_Groups_Olinordered__ab__semigroup__add(_802040)), _802042 = _802040, class_Groups_Olinordered__ab__semigroup__add(_802042)], (19221 ^ _779327) ^ [_1106840, _1106842, _1106844, _1106846] : [class_Fields_Ofield__inverse__zero(_1106840), 19224 ^ _779327 : [(19225 ^ _779327) ^ [] : [_1106842 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106840), _1106844), _1106846), 19228 ^ _779327 : [(19235 ^ _779327) ^ [] : [_1106846 = c_Groups_Ozero__class_Ozero(_1106840), -(_1106842 = c_Groups_Ozero__class_Ozero(_1106840))], (19229 ^ _779327) ^ [] : [-(_1106846 = c_Groups_Ozero__class_Ozero(_1106840)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106840), _1106842), _1106846) = _1106844)]]], (19241 ^ _779327) ^ [] : [-(_1106842 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106840), _1106844), _1106846)), 19244 ^ _779327 : [(19247 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106840), _1106842), _1106846) = _1106844], (19245 ^ _779327) ^ [] : [_1106846 = c_Groups_Ozero__class_Ozero(_1106840)]], 19248 ^ _779327 : [(19251 ^ _779327) ^ [] : [_1106842 = c_Groups_Ozero__class_Ozero(_1106840)], (19249 ^ _779327) ^ [] : [-(_1106846 = c_Groups_Ozero__class_Ozero(_1106840))]]]]], (30916 ^ _779327) ^ [_1338558, _1338560, _1338562, _1338564, _1338566, _1338568] : [30917 ^ _779327 : [(30920 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1338564, _1338560), _1338562))], (30918 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1338558, _1338560), _1338562))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338566, tc_fun(_1338568, tc_HOL_Obool))), _1338564), _1338558), _1338560), _1338562)))], (53042 ^ _779327) ^ [_1841034] : [-(hBOOL(_1841034)), -(hBOOL(hAPP(c_fNot, _1841034)))], (9743 ^ _779327) ^ [_937297] : [class_Rings_Oring__1(_937297), -(hAPP(c_Int_Oring__1__class_Oof__int(_937297), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_937297))], (49161 ^ _779327) ^ [_1764104, _1764106, _1764108, _1764110, _1764112] : [class_Orderings_Olinorder(_1764104), c_List_Olinorder__class_Osorted(_1764104, hAPP(hAPP(c_List_Omap(_1764106, _1764104), _1764108), _1764110)), -(c_List_Olinorder__class_Osorted(_1764104, hAPP(hAPP(c_List_Omap(_1764106, _1764104), _1764108), hAPP(c_List_Ofilter(_1764106, _1764112), _1764110))))], (1638 ^ _779327) ^ [_802790, _802792] : [-(class_Rings_Oordered__comm__semiring(_802790)), _802792 = _802790, class_Rings_Oordered__comm__semiring(_802792)], (7139 ^ _779327) ^ [_891040, _891042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _891040)), _891042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _891040), _891042)))], (32500 ^ _779327) ^ [_1369725, _1369727] : [class_Groups_Olinordered__ab__group__add(_1369725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369725), _1369727)), -(_1369727 = c_Orderings_Obot__class_Obot(tc_fun(_1369725, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1369725), c_Big__Operators_Olinorder__class_OMax(_1369725, _1369727)) = c_Big__Operators_Olinorder__class_OMin(_1369725, hAPP(c_Set_Oimage(_1369725, _1369725, c_Groups_Ouminus__class_Ouminus(_1369725)), _1369727)))], (12684 ^ _779327) ^ [_991299, _991301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991301)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _991299), _991301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _991299)), hAPP(c_Int_Onat, _991301)))], (44558 ^ _779327) ^ [_1655792, _1655794, _1655796, _1655798, _1655800, _1655802] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655792), tc_List_Olist(_1655792))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655792), tc_List_Olist(_1655792)), hAPP(hAPP(c_List_Olist_OCons(_1655792), _1655794), _1655796)), hAPP(hAPP(c_List_Olist_OCons(_1655792), _1655798), _1655800))), c_List_Olexord(_1655792, _1655802)))), 44559 ^ _779327 : [(44562 ^ _779327) ^ [] : [_1655794 = _1655798, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655792), tc_List_Olist(_1655792))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655792), tc_List_Olist(_1655792)), _1655796), _1655800)), c_List_Olexord(_1655792, _1655802)))], (44560 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1655792, _1655792)), hAPP(hAPP(c_Product__Type_OPair(_1655792, _1655792), _1655794), _1655798)), _1655802))]]], (2836 ^ _779327) ^ [_821564, _821566, _821568, _821570, _821572, _821574, _821576, _821578] : [-(c_New__DSequence_Opos__bind(_821578, _821574, _821570, _821566) = c_New__DSequence_Opos__bind(_821576, _821572, _821568, _821564)), _821578 = _821576, _821574 = _821572, _821570 = _821568, _821566 = _821564], (7750 ^ _779327) ^ [_901546, _901548, _901550] : [class_Rings_Oordered__cancel__semiring(_901546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901546), _901548), c_Groups_Ozero__class_Ozero(_901546))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901546), c_Groups_Ozero__class_Ozero(_901546)), _901550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_901546), _901548), _901550)), c_Groups_Ozero__class_Ozero(_901546))))], (49589 ^ _779327) ^ [_1772945, _1772947] : [-(_1772945 = c_List_Olist_ONil(_1772947)), -(hAPP(c_List_Ohd(_1772947), hAPP(c_List_Orev(_1772947), _1772945)) = c_List_Olast(_1772947, _1772945))], (9082 ^ _779327) ^ [_926039] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926039) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_926039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15710 ^ _779327) ^ [_1045135, _1045137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1045135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045135), _1045137)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045135, _1045137) = _1045135)], (16691 ^ _779327) ^ [_1062445, _1062447] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062445, _1062447) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1062445 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062447), 16694 ^ [_1062445, _1062447]))], (38216 ^ _779327) ^ [] : [-(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))))], (20938 ^ _779327) ^ [_1137909, _1137911, _1137913] : [class_Divides_Osemiring__div(_1137909), -(_1137911 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137909), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1137909), _1137911), _1137913)), _1137913)), c_Divides_Odiv__class_Omod(_1137909, _1137911, _1137913)))], (46814 ^ _779327) ^ [_1713501, _1713503, _1713505] : [hBOOL(hAPP(c_List_Odistinct(_1713501), _1713503)), -(hBOOL(hAPP(c_List_Odistinct(_1713501), hAPP(hAPP(c_List_Otake(_1713501), _1713505), _1713503))))], (29432 ^ _779327) ^ [_1304669, _1304671, _1304673, _1304675, _1304677] : [c_Finite__Set_Ofolding__one(_1304669, _1304671, _1304673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304669), _1304675)), 29439 ^ _779327 : [(29446 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304669, tc_HOL_Obool)), _1304675), hAPP(hAPP(c_Set_Oinsert(_1304669), _1304677), c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_HOL_Obool))), -(hAPP(_1304673, hAPP(hAPP(c_Set_Oinsert(_1304669), _1304677), _1304675)) = hAPP(hAPP(_1304671, _1304677), hAPP(_1304673, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304669, tc_HOL_Obool)), _1304675), hAPP(hAPP(c_Set_Oinsert(_1304669), _1304677), c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_HOL_Obool)))))))], (29440 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304669, tc_HOL_Obool)), _1304675), hAPP(hAPP(c_Set_Oinsert(_1304669), _1304677), c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1304669, tc_HOL_Obool)), -(hAPP(_1304673, hAPP(hAPP(c_Set_Oinsert(_1304669), _1304677), _1304675)) = _1304677)]]], (51993 ^ _779327) ^ [_1825814, _1825816, _1825818, _1825820] : [c_Relation_Oantisym(_1825814, _1825816), hBOOL(hAPP(hAPP(c_member(tc_prod(_1825814, _1825814)), hAPP(hAPP(c_Product__Type_OPair(_1825814, _1825814), _1825818), _1825820)), _1825816)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1825814, _1825814)), hAPP(hAPP(c_Product__Type_OPair(_1825814, _1825814), _1825820), _1825818)), _1825816)), -(_1825818 = _1825820)], (15818 ^ _779327) ^ [_1046801, _1046803] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046801), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046803), _1046801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046803), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046803, _1046801)))], (14193 ^ _779327) ^ [_1018439, _1018441] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018439), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1018441)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018439), _1018441))], (14451 ^ _779327) ^ [_1023051, _1023053] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1023051, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1023051, tc_HOL_Obool)), _1023053)) = _1023053)], (21164 ^ _779327) ^ [_1142529, _1142531] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1142529)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1142531)), hAPP(c_Int_Onat, _1142529)) = hAPP(c_Int_Onat, _1142531))], (13613 ^ _779327) ^ [_1007511, _1007513] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1007511)), _1007513) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007511), _1007513)))], (2242 ^ _779327) ^ [_811889, _811891, _811893, _811895] : [-(c_Divides_OposDivAlg(_811895, _811891) = c_Divides_OposDivAlg(_811893, _811889)), _811895 = _811893, _811891 = _811889], (26302 ^ _779327) ^ [_1241973, _1241975] : [_1241973 = _1241975, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241973) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241975))], (21528 ^ _779327) ^ [_1149869] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1149869) = 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)))], (17786 ^ _779327) ^ [_1080913, _1080915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1080913)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1080915)), _1080913) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1080915), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1080913), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (19289 ^ _779327) ^ [_1107828, _1107830, _1107832, _1107834] : [class_Fields_Ofield__inverse__zero(_1107828), -(_1107830 = c_Groups_Ozero__class_Ozero(_1107828)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107828), _1107832), _1107830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107828), _1107834), _1107830)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107828), _1107832), _1107834))], (21640 ^ _779327) ^ [_1152307, _1152309] : [-(_1152307 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152309, _1152307), c_Divides_Odivmod__int(_1152309, _1152307))))], (39744 ^ _779327) ^ [_1533395, _1533397, _1533399] : [-(hAPP(c_Set_OCollect(_1533395), hAPP(hAPP(c_COMBS(_1533395, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533395), c_fconj), _1533397)), _1533399)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533395, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1533395), _1533397)), hAPP(c_Set_OCollect(_1533395), _1533399)))], (13591 ^ _779327) ^ [_1007105, _1007107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1007105), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1007107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007105), _1007107)))], (37583 ^ _779327) ^ [_1482764, _1482766] : [class_Lattices_Obounded__lattice__top(_1482764), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1482764), _1482766), c_Orderings_Otop__class_Otop(_1482764)) = _1482766)], (37911 ^ _779327) ^ [_1489457, _1489459, _1489461, _1489463] : [_1489457 = c_Orderings_Obot__class_Obot(tc_fun(_1489459, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489459, tc_fun(_1489461, tc_HOL_Obool)), _1489457), hAPP(c_COMBK(tc_fun(_1489461, tc_HOL_Obool), _1489459), _1489463)) = c_Orderings_Otop__class_Otop(tc_fun(_1489461, tc_HOL_Obool)))], (9881 ^ _779327) ^ [_939342, _939344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _939342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _939344)), 9888 ^ _779327 : [(9895 ^ _779327) ^ [] : [_939342 = _939344, -(hAPP(c_Int_Onat, _939342) = hAPP(c_Int_Onat, _939344))], (9889 ^ _779327) ^ [] : [hAPP(c_Int_Onat, _939342) = hAPP(c_Int_Onat, _939344), -(_939342 = _939344)]]], (16473 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (22487 ^ _779327) ^ [_1168435, _1168437, _1168439, _1168441] : [class_Orderings_Olinorder(_1168435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168435), _1168437), _1168439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168435), _1168437), _1168441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168435), _1168437), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168435), _1168439), _1168441))))], (24417 ^ _779327) ^ [_1204294, _1204296, _1204298, _1204300] : [class_Rings_Ocomm__semiring__1(_1204294), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204294), _1204296), _1204298)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204294), _1204296), _1204300)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204294), _1204296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204294), _1204298), _1204300))))], (15459 ^ _779327) ^ [_1040587, _1040589] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040587), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040589)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040587, _1040589)))], (14453 ^ _779327) ^ [_1023092] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15439 ^ _779327) ^ [_1040193, _1040195, _1040197] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040195), _1040197)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040193), _1040195)), _1040197))], (40705 ^ _779327) ^ [_1564758, _1564760] : [40707 ^ _779327 : [(40708 ^ _779327) ^ [_1564783] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564758, _1564758)), hAPP(hAPP(c_Product__Type_OPair(_1564758, _1564758), hAPP(40706 ^ [_1564758, _1564760], hAPP(c_Nat_OSuc, _1564783))), hAPP(40706 ^ [_1564758, _1564760], _1564783))), _1564760)))]], -(c_Wellfounded_Owf(_1564758, _1564760))], (29416 ^ _779327) ^ [_1304305, _1304307, _1304309] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304305), _1304307)), 29419 ^ _779327 : [(29426 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304305), _1304309), _1304307))), -(hAPP(c_Finite__Set_Ocard(_1304305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304305, tc_HOL_Obool)), _1304307), hAPP(hAPP(c_Set_Oinsert(_1304305), _1304309), c_Orderings_Obot__class_Obot(tc_fun(_1304305, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1304305), _1304307))], (29420 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304305), _1304309), _1304307)), -(hAPP(c_Finite__Set_Ocard(_1304305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304305, tc_HOL_Obool)), _1304307), hAPP(hAPP(c_Set_Oinsert(_1304305), _1304309), c_Orderings_Obot__class_Obot(tc_fun(_1304305, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1304305), _1304307)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (8582 ^ _779327) ^ [_916779, _916781] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _916779), _916781) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8585 ^ _779327 : [(8588 ^ _779327) ^ [] : [-(_916781 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8586 ^ _779327) ^ [] : [-(_916779 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (37573 ^ _779327) ^ [_1482587, _1482589] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482587, tc_HOL_Obool)), _1482589), c_Orderings_Otop__class_Otop(tc_fun(_1482587, tc_HOL_Obool))) = _1482589)], (48098 ^ _779327) ^ [_1740584, _1740586, _1740588, _1740590, _1740592, _1740594] : [c_List_Olist__all2(_1740584, _1740586, _1740588, _1740590, _1740592), -(c_List_Olist__all2(_1740584, _1740586, _1740588, hAPP(hAPP(c_List_Odrop(_1740584), _1740594), _1740590), hAPP(hAPP(c_List_Odrop(_1740586), _1740594), _1740592)))], (46782 ^ _779327) ^ [_1712834, _1712836, _1712838] : [-(hAPP(hAPP(c_List_Odrop(_1712834), _1712836), hAPP(c_List_Otl(_1712834), _1712838)) = hAPP(c_List_Otl(_1712834), hAPP(hAPP(c_List_Odrop(_1712834), _1712836), _1712838)))], (9106 ^ _779327) ^ [_926406, _926408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926406)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _926406), _926408)))], (18226 ^ _779327) ^ [_1088869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1088869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1088869))))], (47674 ^ _779327) ^ [_1731458, _1731460, _1731462] : [class_Orderings_Olinorder(_1731458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1731458), _1731460)), -(c_List_Olinorder__class_Osorted__list__of__set(_1731458, hAPP(hAPP(c_Set_Oinsert(_1731458), _1731462), _1731460)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1731458, _1731458, c_COMBI(_1731458)), _1731462), c_List_Olinorder__class_Osorted__list__of__set(_1731458, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1731458, tc_HOL_Obool)), _1731460), hAPP(hAPP(c_Set_Oinsert(_1731458), _1731462), c_Orderings_Obot__class_Obot(tc_fun(_1731458, tc_HOL_Obool)))))))], (5656 ^ _779327) ^ [_868630, _868632, _868634, _868636] : [class_Rings_Osemiring__1(_868630), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_868630, _868632, hAPP(c_Nat_OSuc, _868634), _868636) = c_Nat_Osemiring__1__class_Oof__nat__aux(_868630, _868632, _868634, hAPP(_868632, _868636)))], (39764 ^ _779327) ^ [_1533910] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1533910, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1533910), hAPP(c_COMBK(tc_HOL_Obool, _1533910), c_fTrue)))], (48205 ^ _779327) ^ [_1743152, _1743154, _1743156] : [-(hAPP(c_List_Oset(tc_List_Olist(_1743152)), c_Enum_On__lists(_1743152, _1743154, _1743156)) = hAPP(c_Set_OCollect(tc_List_Olist(_1743152)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1743152), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1743152)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743152), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1743152)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1743152)))), _1743154))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1743152), tc_fun(_1743152, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1743152, tc_HOL_Obool), tc_fun(tc_fun(_1743152, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1743152)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1743152, tc_HOL_Obool))), c_List_Oset(_1743152))), hAPP(c_List_Oset(_1743152), _1743156)))))], (1288 ^ _779327) ^ [_798415, _798417] : [-(class_Groups_Ogroup__add(_798415)), _798417 = _798415, class_Groups_Ogroup__add(_798417)], (52 ^ _779327) ^ [_780049, _780051] : [-(class_Rings_Odivision__ring__inverse__zero(_780049)), _780051 = _780049, class_Rings_Odivision__ring__inverse__zero(_780051)], (24093 ^ _779327) ^ [_1199082, _1199084, _1199086] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199082), _1199084)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199084), _1199082))), _1199084 = _1199086, 24104 ^ _779327 : [(24107 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199086), _1199082))], (24105 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199082), _1199086)))]]], (43832 ^ _779327) ^ [_1638081, _1638083, _1638085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1638081, tc_HOL_Obool), tc_HOL_Obool)), _1638083), _1638085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638081, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638081, tc_HOL_Obool), _1638083)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638081, tc_HOL_Obool), _1638085))))], (44656 ^ _779327) ^ [_1658963, _1658965, _1658967, _1658969, _1658971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658963, _1658963)), hAPP(hAPP(c_Product__Type_OPair(_1658963, _1658963), _1658965), _1658967)), _1658969)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658963), tc_List_Olist(_1658963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658963), tc_List_Olist(_1658963)), hAPP(hAPP(c_List_Olist_OCons(_1658963), _1658965), _1658971)), hAPP(hAPP(c_List_Olist_OCons(_1658963), _1658967), _1658971))), c_List_Olistrel1(_1658963, _1658969))))], (5744 ^ _779327) ^ [_870187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870187), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33503 ^ _779327) ^ [_1390060, _1390062, _1390064, _1390066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1390060), _1390062)), -(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), _1390060), _1390064)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390062), _1390066))), c_FunDef_Opair__less)))], (26418 ^ _779327) ^ [_1244373, _1244375] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244373), _1244375)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244373)), hAPP(c_Nat_OSuc, _1244375)))], (15257 ^ _779327) ^ [_1036437] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036437, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2660 ^ _779327) ^ [_818544, _818546, _818548, _818550, _818552, _818554, _818556, _818558] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_818558, _818554, _818550, _818546) = c_New__Random__Sequence_Opos__not__random__dseq(_818556, _818552, _818548, _818544)), _818558 = _818556, _818554 = _818552, _818550 = _818548, _818546 = _818544], (47064 ^ _779327) ^ [_1718688, _1718690, _1718692] : [-(hAPP(c_List_Oset(_1718688), hAPP(c_List_Orotate(_1718688, _1718690), _1718692)) = hAPP(c_List_Oset(_1718688), _1718692))], (43477 ^ _779327) ^ [_1630365, _1630367, _1630369, _1630371, _1630373, _1630375] : [c_Finite__Set_Ofun__left__comm(_1630365, _1630367, _1630369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630365), _1630371)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1630365, _1630367, _1630369), _1630373), hAPP(hAPP(c_Set_Oinsert(_1630365), _1630375), _1630371)) = hAPP(hAPP(_1630369, _1630375), hAPP(hAPP(c_Finite__Set_Ofold(_1630365, _1630367, _1630369), _1630373), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1630365, tc_HOL_Obool)), _1630371), hAPP(hAPP(c_Set_Oinsert(_1630365), _1630375), c_Orderings_Obot__class_Obot(tc_fun(_1630365, tc_HOL_Obool)))))))], (25632 ^ _779327) ^ [_1228166, _1228168, _1228170, _1228172, _1228174] : [class_Groups_Ocomm__monoid__add(_1228166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1228170), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228166), _1228172), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228168, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1228170), _1228174))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228166), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228166), _1228172), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228168, _1228170))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228166), _1228172), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1228170), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1228170), _1228174)))))], (45689 ^ _779327) ^ [_1686507, _1686509] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1686507), tc_List_Olist(_1686507), c_List_Olistrel(_1686507, _1686509)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1686507)), c_List_Olist_ONil(_1686507)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1686507), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1686507)), c_List_Olist_ONil(_1686507)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1686507), tc_HOL_Obool))))], (9831 ^ _779327) ^ [_938622, _938624] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938622), _938624)), _938622 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _938624 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (21748 ^ _779327) ^ [_1153762, _1153764] : [-(c_Divides_Odivmod__int(_1153762, _1153764) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1153762), _1153764)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1153762, _1153764)))], (12417 ^ _779327) ^ [_986021, _986023, _986025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986021), _986023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986023), _986025))))], (39073 ^ _779327) ^ [_1518672, _1518674, _1518676, _1518678, _1518680, _1518682, _1518684, _1518686] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1518672, _1518674), tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518672, _1518674), _1518680), hAPP(c_COMBK(tc_fun(_1518674, tc_HOL_Obool), _1518672), _1518682))), hAPP(c_Product__Type_Oprod_Oprod__case(_1518672, _1518674, tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1518672, tc_fun(_1518674, tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool))), tc_fun(_1518674, tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool)), tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool)), tc_fun(tc_fun(_1518674, tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool))), tc_fun(_1518674, tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool))), _1518672), c_COMBB(tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool)), tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool), _1518674)), hAPP(hAPP(c_COMBB(tc_fun(_1518676, tc_HOL_Obool), tc_fun(tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool)), tc_fun(tc_prod(_1518676, _1518678), tc_HOL_Obool)), _1518672), c_Product__Type_OSigma(_1518676, _1518678)), _1518684))), hAPP(hAPP(c_COMBB(tc_fun(_1518678, tc_HOL_Obool), tc_fun(_1518676, tc_fun(_1518678, tc_HOL_Obool)), _1518674), c_COMBK(tc_fun(_1518678, tc_HOL_Obool), _1518676)), _1518686)))) = hAPP(hAPP(c_Product__Type_OSigma(_1518676, _1518678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518672, tc_fun(_1518676, tc_HOL_Obool)), _1518680), _1518684)), hAPP(c_COMBK(tc_fun(_1518678, tc_HOL_Obool), _1518676), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518674, tc_fun(_1518678, tc_HOL_Obool)), _1518682), _1518686))))], (44729 ^ _779327) ^ [_1661109, _1661111, _1661113, _1661115] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661109), tc_List_Olist(_1661109))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661109), tc_List_Olist(_1661109)), _1661111), _1661113)), c_List_Olistrel1(_1661109, _1661115))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661109), tc_List_Olist(_1661109))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661109), tc_List_Olist(_1661109)), _1661111), _1661113)), c_List_Olistrel(_1661109, c_Transitive__Closure_Ortrancl(_1661109, _1661115)))))], (28680 ^ _779327) ^ [_1290426, _1290428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1290426, tc_HOL_Obool)), _1290428), c_Orderings_Obot__class_Obot(tc_fun(_1290426, tc_HOL_Obool))))], (24997 ^ _779327) ^ [_1215103, _1215105, _1215107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215103)), 25000 ^ _779327 : [(25007 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215105), _1215107)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215103), _1215105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215103), _1215107))))], (25001 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215103), _1215105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215103), _1215107))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215105), _1215107)))]]], (2046 ^ _779327) ^ [_808863, _808865] : [_808865 = _808863, -(c_Int_Osucc(_808865) = c_Int_Osucc(_808863))], (47568 ^ _779327) ^ [_1728968, _1728970] : [-(c_List_Oremove1(_1728968, _1728970, c_List_Olist_ONil(_1728968)) = c_List_Olist_ONil(_1728968))], (18326 ^ _779327) ^ [_1090582] : [-(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)))), _1090582) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1090582)))], (46678 ^ _779327) ^ [_1710796, _1710798, _1710800, _1710802] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710796) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1710798), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710796)), hAPP(hAPP(c_List_Olist_OCons(_1710798), _1710800), _1710802)) = hAPP(hAPP(c_List_Odrop(_1710798), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710796)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1710802))], (42697 ^ _779327) ^ [_1612576, _1612578, _1612580] : [c_Relation_Ototal__on(_1612576, _1612578, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1612576, _1612576), tc_HOL_Obool)), _1612580), c_Relation_OId(_1612576))), -(c_Relation_Ototal__on(_1612576, _1612578, _1612580))], (11305 ^ _779327) ^ [_964998, _965000] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _964998)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _965000)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964998), _965000)))], (7628 ^ _779327) ^ [_899355, _899357, _899359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _899357), _899359)), -(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, _899355)), _899357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _899355)), _899359))))], (10165 ^ _779327) ^ [_943806, _943808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943806), hAPP(c_Int_Onat, _943808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943806)), _943808)))], (10055 ^ _779327) ^ [] : [-(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))))], (28650 ^ _779327) ^ [_1289859, _1289861, _1289863] : [class_Orderings_Obot(_1289859), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1289861, _1289859)), _1289863) = c_Orderings_Obot__class_Obot(_1289859))], (48271 ^ _779327) ^ [_1744747, _1744749] : [-(hBOOL(hAPP(c_List_Odistinct(_1744747), c_List_Oremdups(_1744747, _1744749))))], (40333 ^ _779327) ^ [_1553940, _1553942, _1553944, _1553946, _1553948, _1553950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553940, _1553942)), hAPP(hAPP(c_Product__Type_OPair(_1553940, _1553942), _1553944), _1553946)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool), _1553948))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool), tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool), _1553948), 40344 ^ _779327 : [(40347 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1553950, 40342 ^ [_1553940, _1553942, _1553944, _1553946, _1553948, _1553950]), 40343 ^ [_1553940, _1553942, _1553944, _1553946, _1553948, _1553950]))], (40345 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553940, _1553942)), hAPP(hAPP(c_Product__Type_OPair(_1553940, _1553942), 40342 ^ [_1553940, _1553942, _1553944, _1553946, _1553948, _1553950]), 40343 ^ [_1553940, _1553942, _1553944, _1553946, _1553948, _1553950])), hAPP(_1553948, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1553940, _1553942), tc_HOL_Obool), _1553948)), hAPP(c_Set_OCollect(tc_prod(_1553940, _1553942)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553940, _1553942, tc_HOL_Obool), _1553950)))))))]], -(hBOOL(hAPP(hAPP(_1553950, _1553944), _1553946)))], (19399 ^ _779327) ^ [_1109535, _1109537, _1109539, _1109541] : [class_Fields_Ofield(_1109535), -(_1109537 = c_Groups_Ozero__class_Ozero(_1109535)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109535), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109535), _1109539), _1109537)), _1109541) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109535), hAPP(hAPP(c_Power_Opower__class_Opower(_1109535), _1109539), _1109541)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109535), _1109537), _1109541)))], (22121 ^ _779327) ^ [_1161465, _1161467, _1161469, _1161471, _1161473] : [hAPP(c_Product__Type_Osnd(_1161465, _1161467), hAPP(hAPP(c_Product__Type_OPair(_1161465, _1161467), _1161469), _1161471)) = _1161473, -(_1161471 = _1161473)], (22757 ^ _779327) ^ [_1173322, _1173324] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173322)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173324)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1173324))), 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, _1173322))), 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), _1173322)), c_Int_Onat)))))], (43545 ^ _779327) ^ [_1631751, _1631753, _1631755, _1631757, _1631759] : [c_Finite__Set_Ofun__left__comm(_1631751, _1631753, _1631755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631751), _1631757)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1631751, _1631753, _1631755, _1631759, _1631757), hAPP(hAPP(c_Finite__Set_Ofold(_1631751, _1631753, _1631755), _1631759), _1631757))))], (39077 ^ _779327) ^ [_1519226, _1519228, _1519230] : [class_Lattices_Osemilattice__inf(_1519226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519226), _1519228)), hBOOL(hAPP(hAPP(c_member(_1519226), _1519230), _1519228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519226), hAPP(c_Finite__Set_Ofold1(_1519226, c_Lattices_Osemilattice__inf__class_Oinf(_1519226)), _1519228)), _1519230)))], (13704 ^ _779327) ^ [_1009183, _1009185, _1009187] : [class_Groups_Oordered__comm__monoid__add(_1009183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009183), _1009185), c_Groups_Ozero__class_Ozero(_1009183))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009183), _1009187), c_Groups_Ozero__class_Ozero(_1009183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009183), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009183), _1009185), _1009187)), c_Groups_Ozero__class_Ozero(_1009183))))], (10233 ^ _779327) ^ [_945078, _945080] : [class_Power_Opower(_945078), class_Rings_Osemiring__0(_945078), 10240 ^ _779327 : [(10247 ^ _779327) ^ [] : [-(_945080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_945078), c_Groups_Ozero__class_Ozero(_945078)), _945080) = c_Groups_Ozero__class_Ozero(_945078))], (10241 ^ _779327) ^ [] : [_945080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_945078), c_Groups_Ozero__class_Ozero(_945078)), _945080) = c_Groups_Oone__class_Oone(_945078))]]], (45056 ^ _779327) ^ [_1670481, _1670483, _1670485] : [c_Fun_Oinj__on(_1670481, _1670483, _1670485, c_Orderings_Otop__class_Otop(tc_fun(_1670481, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1670481), tc_List_Olist(_1670483), hAPP(c_List_Omap(_1670481, _1670483), _1670485), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670481), tc_HOL_Obool))))], (27761 ^ _779327) ^ [_1272666, _1272668, _1272670] : [class_Orderings_Oorder(_1272666), 27764 ^ _779327 : [(27771 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272666), _1272670), _1272668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1272666), _1272668)), hAPP(c_SetInterval_Oord__class_OatLeast(_1272666), _1272670))))], (27765 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1272666), _1272668)), hAPP(c_SetInterval_Oord__class_OatLeast(_1272666), _1272670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272666), _1272670), _1272668)))]]], (33028 ^ _779327) ^ [_1380515, _1380517, _1380519, _1380521, _1380523, _1380525] : [-(c_Fun_Ofun__upd(_1380515, _1380517, c_Fun_Ofun__upd(_1380515, _1380517, _1380519, _1380521, _1380523), _1380521, _1380525) = c_Fun_Ofun__upd(_1380515, _1380517, _1380519, _1380521, _1380525))], (24403 ^ _779327) ^ [_1204045, _1204047, _1204049, _1204051] : [class_Rings_Ocomm__ring__1(_1204045), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204045), _1204047), _1204049)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204045), _1204047), _1204051)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204045), _1204047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1204045), _1204049), _1204051))))], (9683 ^ _779327) ^ [_936339, _936341, _936343, _936345] : [class_Rings_Olinordered__semidom(_936339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _936341), _936343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936339), c_Groups_Ozero__class_Ozero(_936339)), _936345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936339), _936345), c_Groups_Oone__class_Oone(_936339))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936339), hAPP(hAPP(c_Power_Opower__class_Opower(_936339), _936345), _936343)), hAPP(hAPP(c_Power_Opower__class_Opower(_936339), _936345), _936341))))], (37356 ^ _779327) ^ [_1477713, _1477715, _1477717, _1477719] : [class_Groups_Ocomm__monoid__mult(_1477713), 37359 ^ _779327 : [(37366 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1477715), _1477717))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1477715, _1477713), _1477719), _1477717) = c_Groups_Oone__class_Oone(_1477713))], (37360 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477715), _1477717)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1477715, _1477713), _1477719), _1477717) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1477713, _1477715, c_Groups_Otimes__class_Otimes(_1477713)), _1477719), c_Groups_Oone__class_Oone(_1477713)), _1477717))]]], (22335 ^ _779327) ^ [_1165616, _1165618, _1165620] : [class_Orderings_Olinorder(_1165616), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165616), _1165618), _1165620) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165616), _1165620), _1165618))], (6210 ^ _779327) ^ [_877143, _877145, _877147] : [class_Orderings_Oorder(_877143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877143), _877145), _877147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877143), _877147), _877145))], (46514 ^ _779327) ^ [_1706758, _1706760, _1706762, _1706764, _1706766] : [-(hAPP(hAPP(c_List_Odrop(_1706758), _1706760), hAPP(hAPP(c_List_Omap(_1706762, _1706758), _1706764), _1706766)) = hAPP(hAPP(c_List_Omap(_1706762, _1706758), _1706764), hAPP(hAPP(c_List_Odrop(_1706762), _1706760), _1706766)))], (13358 ^ _779327) ^ [_1003078, _1003080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003080), _1003078)), -(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), _1003078), _1003080))))], (48106 ^ _779327) ^ [_1740776, _1740778, _1740780, _1740782, _1740784] : [c_List_Olist__all2(_1740776, _1740778, _1740780, _1740782, _1740784), 48109 ^ _779327 : [(48112 ^ _779327) ^ [_1740939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740939), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740776)), _1740782))), -(hBOOL(hAPP(hAPP(_1740780, hAPP(hAPP(c_List_Onth(_1740776), _1740782), _1740939)), hAPP(hAPP(c_List_Onth(_1740778), _1740784), _1740939))))], (48110 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740776)), _1740782) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740778)), _1740784))]]], (50108 ^ _779327) ^ [_1783845, _1783847, _1783849] : [hBOOL(hAPP(hAPP(c_member(_1783845), _1783847), hAPP(c_List_Oset(_1783845), _1783849))), -(c_List_Oinsert(_1783845, _1783847, _1783849) = _1783849)], (35469 ^ _779327) ^ [_1435464, _1435466, _1435468, _1435470] : [class_Orderings_Oorder(_1435464), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435464, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1435464, _1435466, _1435468)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1435464, _1435468, _1435470)) = c_Orderings_Obot__class_Obot(tc_fun(_1435464, tc_HOL_Obool)))], (25199 ^ _779327) ^ [_1218595, _1218597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218595), _1218597)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218597), _1218595))], (47460 ^ _779327) ^ [_1726877, _1726879, _1726881] : [-(_1726877 = c_List_Olist_ONil(_1726879)), -(c_List_Obutlast(_1726879, hAPP(hAPP(c_List_Olist_OCons(_1726879), _1726881), _1726877)) = hAPP(hAPP(c_List_Olist_OCons(_1726879), _1726881), c_List_Obutlast(_1726879, _1726877)))], (9389 ^ _779327) ^ [_931423, _931425, _931427, _931429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931423, tc_HOL_Obool)), _931425), _931427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931423, tc_HOL_Obool)), _931427), _931429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931423, tc_HOL_Obool)), _931425), _931429)))], (25762 ^ _779327) ^ [_1230526, _1230528, _1230530, _1230532] : [class_Groups_Ocomm__monoid__add(_1230526), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230526), _1230528), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1230530)), hAPP(c_Nat_OSuc, _1230532))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230526), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1230526, tc_Nat_Onat), _1230528), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1230530), _1230532)))], (22025 ^ _779327) ^ [_1159396, _1159398, _1159400, _1159402, _1159404] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1159396, _1159398), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1159400), _1159402))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159404)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1159396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159398), _1159404)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1159400), _1159404)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159398), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1159400, _1159404))), _1159402)))))], (9631 ^ _779327) ^ [_935360, _935362, _935364, _935366] : [class_Rings_Olinordered__semidom(_935360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935360), c_Groups_Oone__class_Oone(_935360)), _935362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935360), hAPP(hAPP(c_Power_Opower__class_Opower(_935360), _935362), _935364)), hAPP(hAPP(c_Power_Opower__class_Opower(_935360), _935362), _935366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935364), _935366)))], (13545 ^ _779327) ^ [_1006134] : [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)), _1006134)), _1006134)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006134), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27679 ^ _779327) ^ [_1270403, _1270405, _1270407, _1270409, _1270411] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270403, tc_fun(_1270405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270403, tc_HOL_Obool)), _1270407), _1270409)), _1270411) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270405, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270403, tc_fun(_1270405, tc_HOL_Obool)), _1270407), _1270411)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270403, tc_fun(_1270405, tc_HOL_Obool)), _1270409), _1270411)))], (29790 ^ _779327) ^ [_1311741, _1311743] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1311741), _1311743)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1311741)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1311743))))], (1608 ^ _779327) ^ [_802415, _802417] : [-(class_Groups_Oordered__comm__monoid__add(_802415)), _802417 = _802415, class_Groups_Oordered__comm__monoid__add(_802417)], (4770 ^ _779327) ^ [_851993, _851995] : [_851995 = _851993, -(c_List_Odrop(_851995) = c_List_Odrop(_851993))], (42344 ^ _779327) ^ [_1603828, _1603830, _1603832, _1603834, _1603836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603828, _1603828)), hAPP(hAPP(c_Product__Type_OPair(_1603828, _1603828), _1603830), _1603832)), _1603834)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1603828, _1603828)), hAPP(hAPP(c_Product__Type_OPair(_1603828, _1603828), _1603832), _1603836)), c_Transitive__Closure_Ortrancl(_1603828, _1603834))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603828, _1603828)), hAPP(hAPP(c_Product__Type_OPair(_1603828, _1603828), _1603830), _1603836)), c_Transitive__Closure_Otrancl(_1603828, _1603834))))], (51527 ^ _779327) ^ [_1815002, _1815004, _1815006] : [c_List_Oall__interval__int(_1815002, _1815004, _1815006), 51530 ^ _779327 : [(51531 ^ _779327) ^ [_1815080] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1815080), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1815004, _1815006))), -(hBOOL(hAPP(_1815002, _1815080)))]]], (39710 ^ _779327) ^ [_1532808, _1532810] : [-(hAPP(c_Set_OCollect(_1532808), _1532810) = _1532810)], (15746 ^ _779327) ^ [_1045719, _1045721] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045719, _1045721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045719, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1045721)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38487 ^ _779327) ^ [_1504351, _1504353, _1504355, _1504357] : [-(hAPP(c_Set_Ovimage(_1504351, _1504353, _1504355), _1504357) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1504353, tc_fun(_1504351, tc_HOL_Obool)), _1504357), hAPP(hAPP(c_COMBB(tc_fun(_1504353, tc_HOL_Obool), tc_fun(_1504351, tc_HOL_Obool), _1504353), c_Set_Ovimage(_1504351, _1504353, _1504355)), hAPP(hAPP(c_COMBC(_1504353, tc_fun(_1504353, tc_HOL_Obool), tc_fun(_1504353, tc_HOL_Obool)), c_Set_Oinsert(_1504353)), c_Orderings_Obot__class_Obot(tc_fun(_1504353, tc_HOL_Obool))))))], (45402 ^ _779327) ^ [_1679643, _1679645] : [_1679645 = c_List_Olist_ONil(_1679643), -(hAPP(c_List_Oset(_1679643), _1679645) = c_Orderings_Obot__class_Obot(tc_fun(_1679643, tc_HOL_Obool)))], (18220 ^ _779327) ^ [_1088786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1088786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1088786)))], (39908 ^ _779327) ^ [_1538138, _1538140, _1538142, _1538144, _1538146] : [class_Groups_Ocomm__monoid__add(_1538138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538140), _1538142)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538140, _1538138), _1538144), hAPP(c_Set_OCollect(_1538140), hAPP(hAPP(c_COMBS(_1538140, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538140), c_fconj), hAPP(hAPP(c_COMBC(_1538140, tc_fun(_1538140, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538140)), _1538142))), hAPP(hAPP(c_COMBC(_1538140, tc_fun(_1538140, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538140)), _1538146)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538140, _1538138), hAPP(hAPP(c_COMBC(_1538140, _1538138, _1538138), hAPP(hAPP(c_COMBS(_1538140, _1538138, tc_fun(_1538138, _1538138)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1538138, tc_fun(_1538138, _1538138)), _1538140), c_If(_1538138)), hAPP(hAPP(c_COMBC(_1538140, tc_fun(_1538140, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538140)), _1538146))), _1538144)), c_Groups_Ozero__class_Ozero(_1538138))), _1538142))], (37491 ^ _779327) ^ [_1480616, _1480618, _1480620, _1480622, _1480624, _1480626, _1480628] : [-(hBOOL(hAPP(hAPP(c_member(_1480616), _1480618), _1480620))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480616, _1480622, _1480624, _1480626, _1480620), _1480628)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480616, _1480622, _1480624, _1480626, hAPP(hAPP(c_Set_Oinsert(_1480616), _1480618), _1480620)), hAPP(hAPP(_1480624, _1480618), _1480628))))], (46554 ^ _779327) ^ [_1707694, _1707696, _1707698] : [-(hAPP(hAPP(c_List_Oappend(_1707694), hAPP(hAPP(c_List_Otake(_1707694), _1707696), _1707698)), hAPP(hAPP(c_List_Odrop(_1707694), _1707696), _1707698)) = _1707698)], (41184 ^ _779327) ^ [_1576135, _1576137, _1576139] : [c_Wellfounded_OwfP(_1576135, hAPP(_1576137, 41185 ^ [_1576135, _1576137, _1576139])), 41192 ^ _779327 : [(41195 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1576135, tc_HOL_Obool)), c_Predicate_ODomainP(_1576135, _1576135, hAPP(_1576137, 41190 ^ [_1576135, _1576137, _1576139]))), c_Predicate_ORangeP(_1576135, _1576135, hAPP(_1576137, 41191 ^ [_1576135, _1576137, _1576139]))) = c_Orderings_Obot__class_Obot(tc_fun(_1576135, tc_HOL_Obool))], (41193 ^ _779327) ^ [] : [hAPP(_1576137, 41190 ^ [_1576135, _1576137, _1576139]) = hAPP(_1576137, 41191 ^ [_1576135, _1576137, _1576139])]], -(c_Wellfounded_OwfP(_1576135, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1576139, tc_fun(_1576135, tc_fun(_1576135, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1576139, tc_HOL_Obool))), _1576137)))], (14875 ^ _779327) ^ [_1029527, _1029529, _1029531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029527)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029531), _1029527)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029529), _1029531)), _1029527))], (31656 ^ _779327) ^ [_1354526, _1354528] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354526, _1354528) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354526), _1354528)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354528), _1354526)))], (9044 ^ _779327) ^ [_925151, _925153, _925155, _925157, _925159] : [class_Rings_Ocomm__semiring__1(_925151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), _925153), _925155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), _925157), _925159)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), _925153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), _925155), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925151), _925157), _925159))))], (2126 ^ _779327) ^ [_810087, _810089, _810091, _810093, _810095, _810097, _810099, _810101] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810101, _810097, _810093, _810089) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810099, _810095, _810091, _810087)), _810101 = _810099, _810097 = _810095, _810093 = _810091, _810089 = _810087], (27933 ^ _779327) ^ [_1276004, _1276006, _1276008] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276004, tc_HOL_Obool)), _1276006), hAPP(hAPP(c_Set_Oinsert(_1276004), _1276008), _1276006))))], (47672 ^ _779327) ^ [_1731039, _1731041, _1731043, _1731045] : [-(c_List_Opartition(_1731039, _1731041, hAPP(hAPP(c_List_Olist_OCons(_1731039), _1731043), _1731045)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1731039), tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1731039), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1731039), tc_fun(tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), tc_fun(tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), tc_List_Olist(_1731039)), c_COMBS(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_fun(tc_List_Olist(_1731039), tc_fun(tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), tc_List_Olist(_1731039)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_fun(tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_List_Olist(_1731039)), hAPP(c_If(tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), hAPP(_1731041, _1731043)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1731039), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_List_Olist(_1731039)), c_Product__Type_OPair(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), hAPP(c_List_Olist_OCons(_1731039), _1731043))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731039), tc_fun(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039))), tc_fun(tc_fun(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_fun(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), tc_List_Olist(_1731039)), c_COMBB(tc_List_Olist(_1731039), tc_prod(tc_List_Olist(_1731039), tc_List_Olist(_1731039)), tc_List_Olist(_1731039))), c_Product__Type_OPair(tc_List_Olist(_1731039), tc_List_Olist(_1731039)))), hAPP(c_List_Olist_OCons(_1731039), _1731043)))), c_List_Opartition(_1731039, _1731041, _1731045)))], (18340 ^ _779327) ^ [_1090828] : [-(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)))), _1090828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090828), _1090828))], (49575 ^ _779327) ^ [_1772684, _1772686, _1772688, _1772690] : [_1772686 = hAPP(hAPP(c_List_Oappend(_1772684), hAPP(c_List_Orev(_1772684), _1772690)), hAPP(hAPP(c_List_Olist_OCons(_1772684), _1772688), c_List_Olist_ONil(_1772684))), -(hAPP(c_List_Orev(_1772684), _1772686) = hAPP(hAPP(c_List_Olist_OCons(_1772684), _1772688), _1772690))], (21522 ^ _779327) ^ [_1149732, _1149734, _1149736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1149732, tc_fun(_1149732, tc_HOL_Obool))), _1149734), _1149736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1149732, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1149732, _1149736)), c_Wellfounded_Oaccp(_1149732, _1149734))))], (49325 ^ _779327) ^ [_1767219, _1767221] : [class_Orderings_Olinorder(_1767219), 49328 ^ _779327 : [(49329 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1767219, _1767221), 49332 ^ _779327 : [(49333 ^ _779327) ^ [_1767390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1767390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767219)), _1767221))), 49336 ^ _779327 : [(49337 ^ _779327) ^ [_1767507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1767507), _1767390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767219), hAPP(hAPP(c_List_Onth(_1767219), _1767221), _1767507)), hAPP(hAPP(c_List_Onth(_1767219), _1767221), _1767390))))]]]]], (49343 ^ _779327) ^ [] : [49345 ^ _779327 : [(49351 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767219), hAPP(hAPP(c_List_Onth(_1767219), _1767221), 49347 ^ [_1767219, _1767221])), hAPP(hAPP(c_List_Onth(_1767219), _1767221), 49344 ^ [_1767219, _1767221])))], (49349 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49347 ^ [_1767219, _1767221]), 49344 ^ [_1767219, _1767221])))], (49346 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49344 ^ [_1767219, _1767221]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767219)), _1767221))))]], -(c_List_Olinorder__class_Osorted(_1767219, _1767221))]]], (14489 ^ _779327) ^ [_1023659, _1023661] : [class_Rings_Osemiring__1(_1023659), 14492 ^ _779327 : [(14499 ^ _779327) ^ [] : [_1023661 = c_Groups_Ozero__class_Ozero(_1023659), -(c_Int_Oiszero(_1023659, _1023661))], (14493 ^ _779327) ^ [] : [c_Int_Oiszero(_1023659, _1023661), -(_1023661 = c_Groups_Ozero__class_Ozero(_1023659))]]], (40106 ^ _779327) ^ [_1546165, _1546167, _1546169] : [class_Lattices_Odistrib__lattice(_1546165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546165), _1546167)), -(_1546167 = c_Orderings_Obot__class_Obot(tc_fun(_1546165, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1546165), _1546169), c_Big__Operators_Olattice__class_OInf__fin(_1546165, _1546167)) = c_Big__Operators_Olattice__class_OInf__fin(_1546165, hAPP(c_Set_OCollect(_1546165), hAPP(hAPP(c_COMBB(tc_fun(_1546165, tc_HOL_Obool), tc_HOL_Obool, _1546165), c_HOL_OEx(_1546165)), hAPP(hAPP(c_COMBC(_1546165, tc_fun(_1546165, tc_HOL_Obool), tc_fun(_1546165, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546165, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1546165, tc_HOL_Obool), tc_fun(_1546165, tc_HOL_Obool)), _1546165), c_COMBS(_1546165, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546165, tc_HOL_Obool), tc_fun(_1546165, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1546165), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546165), c_fconj)), hAPP(hAPP(c_COMBC(_1546165, tc_fun(_1546165, _1546165), tc_fun(_1546165, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546165, tc_HOL_Obool), tc_fun(tc_fun(_1546165, _1546165), tc_fun(_1546165, tc_HOL_Obool)), _1546165), c_COMBB(_1546165, tc_HOL_Obool, _1546165)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1546165), _1546169))))), hAPP(hAPP(c_COMBC(_1546165, tc_fun(_1546165, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546165)), _1546167))))))], (30013 ^ _779327) ^ [_1315994, _1315996] : [hBOOL(hAPP(hAPP(c_member(_1315994), _1315996), c_Orderings_Obot__class_Obot(tc_fun(_1315994, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1315994, tc_HOL_Obool)), _1315996)))], (47754 ^ _779327) ^ [_1733209, _1733211, _1733213, _1733215, _1733217] : [class_Orderings_Olinorder(_1733209), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733211)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733211, _1733209, _1733213), _1733215), _1733217)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733211)), _1733217)))], (43513 ^ _779327) ^ [_1631101, _1631103, _1631105, _1631107, _1631109, _1631111] : [c_Finite__Set_Ofun__left__comm(_1631101, _1631103, _1631105), -(hAPP(hAPP(_1631105, _1631107), hAPP(hAPP(_1631105, _1631109), _1631111)) = hAPP(hAPP(_1631105, _1631109), hAPP(hAPP(_1631105, _1631107), _1631111)))], (5552 ^ _779327) ^ [_864036, _864038, _864040, _864042, _864044, _864046] : [-(c_COMBS(_864046, _864042, _864038) = c_COMBS(_864044, _864040, _864036)), _864046 = _864044, _864042 = _864040, _864038 = _864036], (40048 ^ _779327) ^ [_1543611] : [-(c_Wellfounded_Ofinite__psubset(_1543611) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1543611, tc_HOL_Obool), tc_fun(_1543611, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1543611, tc_HOL_Obool), tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1543611, tc_HOL_Obool), tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1543611, tc_HOL_Obool)), c_COMBS(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1543611, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1543611, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1543611, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1543611, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1543611)))))], (5595 ^ _779327) ^ [_867382, _867384, _867386] : [c_Hoare__Mirabelle_Otriple__valid(_867382, hAPP(c_Nat_OSuc, _867384), _867386), -(c_Hoare__Mirabelle_Otriple__valid(_867382, _867384, _867386))], (40865 ^ _779327) ^ [_1568734, _1568736] : [-(c_List_Olex(_1568734, _1568736) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1568734), tc_List_Olist(_1568734)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1568734, _1568736)))], (14087 ^ _779327) ^ [_1016168, _1016170] : [-(c_Int_Onat__aux(_1016168, _1016170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1016168)), _1016170))], (35219 ^ _779327) ^ [_1429617, _1429619, _1429621, _1429623] : [hBOOL(hAPP(hAPP(c_member(_1429617), _1429619), _1429621)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429617, tc_HOL_Obool)), _1429621), hAPP(hAPP(c_Set_Oinsert(_1429617), _1429619), _1429623)) = hAPP(hAPP(c_Set_Oinsert(_1429617), _1429619), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429617, tc_HOL_Obool)), _1429621), _1429623)))], (44389 ^ _779327) ^ [_1650694, _1650696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 44390 ^ [_1650694, _1650696]), hAPP(_1650694, 44390 ^ [_1650694, _1650696]))), -(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)), _1650694)), _1650696)))))], (8746 ^ _779327) ^ [_919744, _919746] : [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), _919744), _919746))), 8749 ^ _779327 : [(8752 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919746)))], (8750 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919744)))]]], (38253 ^ _779327) ^ [] : [-(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))], (11485 ^ _779327) ^ [_968994, _968996] : [_968994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968994), _968996) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42478 ^ _779327) ^ [_1606959] : [-(c_Relation_OId(_1606959) = hAPP(c_Set_OCollect(tc_prod(_1606959, _1606959)), hAPP(hAPP(c_COMBB(tc_fun(_1606959, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1606959, _1606959)), c_HOL_OEx(_1606959)), hAPP(hAPP(c_COMBC(tc_prod(_1606959, _1606959), tc_fun(_1606959, tc_prod(_1606959, _1606959)), tc_fun(_1606959, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1606959, _1606959), tc_HOL_Obool), tc_fun(tc_fun(_1606959, tc_prod(_1606959, _1606959)), tc_fun(_1606959, tc_HOL_Obool)), tc_prod(_1606959, _1606959)), c_COMBB(tc_prod(_1606959, _1606959), tc_HOL_Obool, _1606959)), c_fequal)), hAPP(hAPP(c_COMBS(_1606959, _1606959, tc_prod(_1606959, _1606959)), c_Product__Type_OPair(_1606959, _1606959)), c_COMBI(_1606959))))))], (52974 ^ _779327) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (38196 ^ _779327) ^ [] : [-(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))))], (43698 ^ _779327) ^ [_1634689, _1634691, _1634693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1634689, tc_HOL_Obool), tc_HOL_Obool)), _1634691), _1634693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1634689, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1634689, tc_HOL_Obool), _1634693)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1634689, tc_HOL_Obool), _1634691))))], (30233 ^ _779327) ^ [_1323050, _1323052, _1323054, _1323056] : [hBOOL(hAPP(hAPP(c_member(_1323050), _1323052), _1323054)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323050, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1323050), _1323052), _1323056)), _1323054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323050, tc_HOL_Obool)), _1323056), _1323054))], (18799 ^ _779327) ^ [_1099327, _1099329, _1099331, _1099333] : [class_Rings_Odivision__ring(_1099327), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099327), _1099329), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099327), _1099331), _1099333)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099327), _1099329), _1099331)), _1099333))], (49543 ^ _779327) ^ [_1772020, _1772022, _1772024] : [hAPP(c_List_Orev(_1772020), _1772022) = _1772024, -(_1772022 = hAPP(c_List_Orev(_1772020), _1772024))], (36727 ^ _779327) ^ [_1464680, _1464682] : [class_Groups_Oordered__ab__group__add(_1464680), -(c_Fun_Oinj__on(_1464680, _1464680, c_Groups_Ouminus__class_Ouminus(_1464680), _1464682))], (49011 ^ _779327) ^ [_1761649, _1761651, _1761653] : [class_Orderings_Olinorder(_1761649), 49014 ^ _779327 : [(49021 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1761649, _1761653), -(c_List_Olinorder__class_Osorted(_1761649, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1761649, _1761649, c_COMBI(_1761649)), _1761651), _1761653)))], (49015 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1761649, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1761649, _1761649, c_COMBI(_1761649)), _1761651), _1761653)), -(c_List_Olinorder__class_Osorted(_1761649, _1761653))]]], (12407 ^ _779327) ^ [_985831, _985833] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985831)), _985833) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985831), _985833)))], (9717 ^ _779327) ^ [_936957, _936959] : [class_Groups_Oone(_936957), 9720 ^ _779327 : [(9727 ^ _779327) ^ [] : [_936959 = c_Groups_Oone__class_Oone(_936957), -(c_Groups_Oone__class_Oone(_936957) = _936959)], (9721 ^ _779327) ^ [] : [c_Groups_Oone__class_Oone(_936957) = _936959, -(_936959 = c_Groups_Oone__class_Oone(_936957))]]], (38085 ^ _779327) ^ [_1493074, _1493076, _1493078, _1493080, _1493082] : [-(_1493074 = c_Orderings_Obot__class_Obot(tc_fun(_1493076, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493076, tc_fun(_1493078, tc_HOL_Obool)), _1493074), hAPP(hAPP(c_COMBC(_1493076, tc_fun(_1493078, tc_HOL_Obool), tc_fun(_1493078, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493078, tc_HOL_Obool), tc_fun(tc_fun(_1493078, tc_HOL_Obool), tc_fun(_1493078, tc_HOL_Obool)), _1493076), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493078, tc_HOL_Obool))), _1493080)), _1493082)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493078, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493076, tc_fun(_1493078, tc_HOL_Obool)), _1493074), _1493080)), _1493082))], (41563 ^ _779327) ^ [_1585117, _1585119, _1585121, _1585123, _1585125, _1585127, _1585129] : [c_Finite__Set_Ofolding__image(_1585117, _1585119, _1585121, _1585123, _1585125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585119), _1585127)), -(hAPP(hAPP(_1585125, _1585129), _1585127) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1585117, _1585119, _1585121), _1585129), _1585123), _1585127))], (41793 ^ _779327) ^ [_1590161, _1590163, _1590165] : [hBOOL(hAPP(_1590161, _1590163)), -(hBOOL(hAPP(_1590161, c_Hilbert__Choice_OEps(_1590165, _1590161))))], (38802 ^ _779327) ^ [_1512106, _1512108, _1512110] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1512106, _1512108), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512106, _1512108), c_Orderings_Otop__class_Otop(tc_fun(_1512106, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1512108, tc_HOL_Obool), _1512106), _1512110))) = hAPP(hAPP(c_Product__Type_OSigma(_1512106, _1512108), c_Orderings_Otop__class_Otop(tc_fun(_1512106, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1512108, tc_HOL_Obool), _1512106), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1512108, tc_HOL_Obool)), _1512110))))], (52880 ^ _779327) ^ [_1839203, _1839205] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1839203, _1839205))), class_Lazy__Sequence_Osmall__lazy(_1839203), class_Lazy__Sequence_Osmall__lazy(_1839205)], (38686 ^ _779327) ^ [_1508953, _1508955, _1508957, _1508959, _1508961] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1508953, _1508955, hAPP(hAPP(c_Set_Oinsert(_1508953), _1508957), _1508959)), _1508961))), 38687 ^ _779327 : [(38688 ^ _779327) ^ [_1509057, _1509059] : [hAPP(hAPP(c_Set_Oinsert(_1508953), _1508957), _1508959) = hAPP(hAPP(c_Set_Oinsert(_1508953), _1509059), _1509057), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1508953, _1508953, _1508955, _1509059, _1509057), _1508961)), -(hBOOL(hAPP(hAPP(c_member(_1508953), _1509059), _1509057)))]]], (7079 ^ _779327) ^ [_890109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890109)), _890109))], (52914 ^ _779327) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (43379 ^ _779327) ^ [_1628736, _1628738, _1628740] : [class_Groups_Oab__semigroup__mult(_1628736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628736), _1628738)), -(hBOOL(hAPP(hAPP(c_member(_1628736), _1628740), _1628738))), -(hAPP(c_Finite__Set_Ofold1(_1628736, c_Groups_Otimes__class_Otimes(_1628736)), hAPP(hAPP(c_Set_Oinsert(_1628736), _1628740), _1628738)) = hAPP(hAPP(c_Finite__Set_Ofold(_1628736, _1628736, c_Groups_Otimes__class_Otimes(_1628736)), _1628740), _1628738))], (18272 ^ _779327) ^ [_1089717, _1089719] : [class_Int_Onumber__ring(_1089717), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089717), _1089719), hAPP(c_Int_Onumber__class_Onumber__of(_1089717), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089717), _1089719), _1089719))], (29382 ^ _779327) ^ [_1303618, _1303620] : [-(c_Set_Othe__elem(_1303618, hAPP(hAPP(c_Set_Oinsert(_1303618), _1303620), c_Orderings_Obot__class_Obot(tc_fun(_1303618, tc_HOL_Obool)))) = _1303620)], (12355 ^ _779327) ^ [_984934] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984934) = _984934)], (46283 ^ _779327) ^ [_1700528, _1700530, _1700532, _1700534, _1700536, _1700538] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700528), tc_List_Olist(_1700528))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700528), tc_List_Olist(_1700528)), hAPP(hAPP(c_List_Oappend(_1700528), _1700530), _1700536)), hAPP(hAPP(c_List_Oappend(_1700528), _1700532), _1700538))), c_List_Olistrel1(_1700528, _1700534)))), 46284 ^ _779327 : [(46291 ^ _779327) ^ [] : [_1700530 = _1700532, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700528), tc_List_Olist(_1700528))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700528), tc_List_Olist(_1700528)), _1700536), _1700538)), c_List_Olistrel1(_1700528, _1700534)))], (46285 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700528), tc_List_Olist(_1700528))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700528), tc_List_Olist(_1700528)), _1700530), _1700532)), c_List_Olistrel1(_1700528, _1700534))), _1700536 = _1700538]]], (32972 ^ _779327) ^ [_1379274, _1379276, _1379278, _1379280, _1379282, _1379284] : [class_Groups_Ocomm__monoid__mult(_1379274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379276), _1379278)), 32979 ^ _779327 : [(32986 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379276), _1379280), _1379278))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379276, _1379274), hAPP(hAPP(c_COMBC(_1379276, _1379274, _1379274), hAPP(hAPP(c_COMBS(_1379276, _1379274, tc_fun(_1379274, _1379274)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1379274, tc_fun(_1379274, _1379274)), _1379276), c_If(_1379274)), hAPP(hAPP(c_COMBC(_1379276, _1379276, tc_HOL_Obool), c_fequal), _1379280))), _1379282)), _1379284)), _1379278) = hAPP(hAPP(c_Power_Opower__class_Opower(_1379274), _1379284), hAPP(c_Finite__Set_Ocard(_1379276), _1379278)))], (32980 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1379276), _1379280), _1379278)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379276, _1379274), hAPP(hAPP(c_COMBC(_1379276, _1379274, _1379274), hAPP(hAPP(c_COMBS(_1379276, _1379274, tc_fun(_1379274, _1379274)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1379274, tc_fun(_1379274, _1379274)), _1379276), c_If(_1379274)), hAPP(hAPP(c_COMBC(_1379276, _1379276, tc_HOL_Obool), c_fequal), _1379280))), _1379282)), _1379284)), _1379278) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379274), hAPP(_1379282, _1379280)), hAPP(hAPP(c_Power_Opower__class_Opower(_1379274), _1379284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1379276), _1379278)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (7512 ^ _779327) ^ [_897509, _897511, _897513] : [class_Rings_Ono__zero__divisors(_897509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897509), _897511), _897513) = c_Groups_Ozero__class_Ozero(_897509), -(_897511 = c_Groups_Ozero__class_Ozero(_897509)), -(_897513 = c_Groups_Ozero__class_Ozero(_897509))], (7117 ^ _779327) ^ [_890702, _890704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890702), _890704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890702)), hAPP(c_Nat_OSuc, _890704))))], (46620 ^ _779327) ^ [_1709277, _1709279, _1709281, _1709283, _1709285] : [hAPP(hAPP(c_List_Oappend(_1709277), _1709279), _1709281) = hAPP(hAPP(c_List_Oappend(_1709277), _1709283), _1709285), 46623 ^ _779327 : [(46632 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709279)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709283)))), 46635 ^ _779327 : [(46638 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1709277), hAPP(hAPP(c_List_Odrop(_1709277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709283)), _1709279)), _1709281) = _1709285)], (46636 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1709277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709283)), _1709279) = _1709283)]]], (46624 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709279)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709283))), 46627 ^ _779327 : [(46630 ^ _779327) ^ [] : [-(_1709281 = hAPP(hAPP(c_List_Oappend(_1709277), hAPP(hAPP(c_List_Odrop(_1709277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709279)), _1709283)), _1709285))], (46628 ^ _779327) ^ [] : [-(_1709279 = hAPP(hAPP(c_List_Otake(_1709277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709277)), _1709279)), _1709283))]]]]], (53010 ^ _779327) ^ [_1840511, _1840513] : [-(hAPP(c_COMBI(_1840511), _1840513) = _1840513)], (9851 ^ _779327) ^ [_938920, _938922] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938920), _938922) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _938920 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _938922 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (13384 ^ _779327) ^ [_1003532, _1003534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003532), _1003534)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1003534)), _1003532) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003534), _1003532)))], (47738 ^ _779327) ^ [_1732827, _1732829, _1732831, _1732833, _1732835, _1732837] : [class_Orderings_Olinorder(_1732827), 47741 ^ _779327 : [(47748 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732827), hAPP(_1732829, _1732831)), hAPP(_1732829, _1732833)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1732835, _1732827, _1732829), _1732831), hAPP(hAPP(c_List_Olist_OCons(_1732835), _1732833), _1732837)) = hAPP(hAPP(c_List_Olist_OCons(_1732835), _1732833), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1732835, _1732827, _1732829), _1732831), _1732837)))], (47742 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732827), hAPP(_1732829, _1732831)), hAPP(_1732829, _1732833))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1732835, _1732827, _1732829), _1732831), hAPP(hAPP(c_List_Olist_OCons(_1732835), _1732833), _1732837)) = hAPP(hAPP(c_List_Olist_OCons(_1732835), _1732831), hAPP(hAPP(c_List_Olist_OCons(_1732835), _1732833), _1732837)))]]], (52878 ^ _779327) ^ [_1839176, _1839178] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1839176, _1839178)))], (41271 ^ _779327) ^ [_1578558, _1578560, _1578562, _1578564, _1578566, _1578568, _1578570] : [hAPP(c_Fun_Ocomp(_1578558, _1578560, _1578562, _1578564), _1578566) = _1578568, -(hAPP(_1578564, hAPP(_1578566, _1578570)) = hAPP(_1578568, _1578570))], (18120 ^ _779327) ^ [_1086998, _1087000] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1086998))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1087000))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1086998)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087000)))], (41353 ^ _779327) ^ [_1580402, _1580404, _1580406, _1580408, _1580410, _1580412, _1580414, _1580416] : [class_Groups_Ocomm__monoid__mult(_1580402), c_Fun_Oinj__on(_1580404, _1580406, _1580408, _1580410), _1580412 = hAPP(c_Set_Oimage(_1580404, _1580406, _1580408), _1580410), _1580414 = hAPP(c_Fun_Ocomp(_1580406, _1580402, _1580404, _1580416), _1580408), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1580406, _1580402), _1580416), _1580412) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1580404, _1580402), _1580414), _1580410))], (14289 ^ _779327) ^ [_1020108, _1020110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1020108), _1020110)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1020110), _1020108)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1020110)), hAPP(c_Int_Onat, _1020108)))], (53026 ^ _779327) ^ [_1840827, _1840829] : [_1840827 = _1840829, -(hBOOL(hAPP(hAPP(c_fequal, _1840827), _1840829)))], (39727 ^ _779327) ^ [_1533106, _1533108] : [hAPP(c_Set_OCollect(_1533106), _1533108) = c_Orderings_Obot__class_Obot(tc_fun(_1533106, tc_HOL_Obool)), 39730 ^ _779327 : [(39731 ^ _779327) ^ [_1533191] : [hBOOL(hAPP(_1533108, _1533191))]]], (8448 ^ _779327) ^ [_914487, _914489, _914491, _914493] : [class_Rings_Olinordered__semiring(_914487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914487), _914489), _914491)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914487), _914489), _914493))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914487), c_Groups_Ozero__class_Ozero(_914487)), _914489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914487), _914491), _914493)))], (18841 ^ _779327) ^ [_1100288, _1100290, _1100292, _1100294] : [class_Fields_Ofield__inverse__zero(_1100288), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1100288), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100288), _1100290), _1100292)), _1100294) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100288), hAPP(hAPP(c_Power_Opower__class_Opower(_1100288), _1100290), _1100294)), hAPP(hAPP(c_Power_Opower__class_Opower(_1100288), _1100292), _1100294)))], (20433 ^ _779327) ^ [_1128327, _1128329, _1128331, _1128333] : [class_Fields_Olinordered__field__inverse__zero(_1128327), class_Int_Onumber(_1128327), 20440 ^ _779327 : [(20441 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128327), _1128331), _1128333))), 20444 ^ _779327 : [(20451 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), c_Groups_Ozero__class_Ozero(_1128327)), _1128333))), 20454 ^ _779327 : [(20461 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128333), c_Groups_Ozero__class_Ozero(_1128327)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), c_Groups_Ozero__class_Ozero(_1128327))))], (20455 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128333), c_Groups_Ozero__class_Ozero(_1128327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), _1128333))))]]], (20445 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), c_Groups_Ozero__class_Ozero(_1128327)), _1128333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), _1128333)), _1128331)))]]], (20467 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128327), _1128331), _1128333)))), 20470 ^ _779327 : [(20473 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), _1128333)), _1128331))], (20471 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), c_Groups_Ozero__class_Ozero(_1128327)), _1128333)))]], 20474 ^ _779327 : [(20477 ^ _779327) ^ [] : [20478 ^ _779327 : [(20481 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), _1128333)))], (20479 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128333), c_Groups_Ozero__class_Ozero(_1128327))))]], 20482 ^ _779327 : [(20485 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), hAPP(c_Int_Onumber__class_Onumber__of(_1128327), _1128329)), c_Groups_Ozero__class_Ozero(_1128327)))], (20483 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), _1128333), c_Groups_Ozero__class_Ozero(_1128327)))]]], (20475 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128327), c_Groups_Ozero__class_Ozero(_1128327)), _1128333))]]]]], (10843 ^ _779327) ^ [_956056] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _956056)) = _956056)], (258 ^ _779327) ^ [_783134, _783136] : [-(c_Nat__Transfer_Ois__nat(_783134)), _783136 = _783134, c_Nat__Transfer_Ois__nat(_783136)], (38782 ^ _779327) ^ [_1511693, _1511695, _1511697, _1511699] : [hAPP(hAPP(c_Product__Type_OSigma(_1511693, _1511695), _1511697), hAPP(c_COMBK(tc_fun(_1511695, tc_HOL_Obool), _1511693), _1511699)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1511693, _1511695), tc_HOL_Obool)), -(_1511697 = c_Orderings_Obot__class_Obot(tc_fun(_1511693, tc_HOL_Obool))), -(_1511699 = c_Orderings_Obot__class_Obot(tc_fun(_1511695, tc_HOL_Obool)))], (42928 ^ _779327) ^ [_1618108, _1618110, _1618112, _1618114, _1618116, _1618118] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618108, _1618108)), hAPP(hAPP(c_Product__Type_OPair(_1618108, _1618108), _1618110), _1618112)), _1618114)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618108, _1618108)), hAPP(hAPP(c_Product__Type_OPair(_1618108, _1618108), _1618112), _1618116)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1618108, _1618108), tc_HOL_Obool), _1618118), _1618114))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618108, _1618108)), hAPP(hAPP(c_Product__Type_OPair(_1618108, _1618108), _1618110), _1618116)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1618108, _1618108), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1618118)), _1618114))))], (348 ^ _779327) ^ [_784551, _784553, _784555, _784557, _784559, _784561, _784563, _784565, _784567, _784569] : [-(c_Big__Operators_Ocomm__monoid__big(_784567, _784563, _784559, _784555, _784551)), c_Big__Operators_Ocomm__monoid__big(_784569, _784565, _784561, _784557, _784553), _784569 = _784567, _784565 = _784563, _784561 = _784559, _784557 = _784555, _784553 = _784551], (52137 ^ _779327) ^ [_1828679, _1828681] : [c_Relation_Osym(_1828679, _1828681), 52140 ^ _779327 : [(52141 ^ _779327) ^ [_1828785, _1828787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1828679, _1828679)), hAPP(hAPP(c_Product__Type_OPair(_1828679, _1828679), _1828787), _1828785)), _1828681)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828679, _1828679)), hAPP(hAPP(c_Product__Type_OPair(_1828679, _1828679), _1828785), _1828787)), _1828681)))]]], (31358 ^ _779327) ^ [_1347849, _1347851, _1347853, _1347855] : [class_Orderings_Oorder(_1347849), class_Orderings_Oorder(_1347851), c_Orderings_Oorder__class_Omono(_1347851, _1347849, _1347853), -(c_Orderings_Oord__class_OLeast(_1347849, hAPP(hAPP(c_COMBC(_1347849, tc_fun(_1347849, tc_HOL_Obool), tc_HOL_Obool), c_member(_1347849)), hAPP(c_Set_Oimage(_1347851, _1347849, _1347853), _1347855))) = hAPP(_1347853, c_Orderings_Oord__class_OLeast(_1347851, hAPP(hAPP(c_COMBC(_1347851, tc_fun(_1347851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1347851)), _1347855)))), 31371 ^ _779327 : [(31372 ^ _779327) ^ [_1348133] : [hBOOL(hAPP(hAPP(c_member(_1347851), _1348133), _1347855)), 31376 ^ _779327 : [(31379 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347851), _1348133), 31375 ^ [_1347849, _1347851, _1347853, _1347855, _1348133]))], (31377 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347851), 31375 ^ [_1347849, _1347851, _1347853, _1347855, _1348133]), _1347855)))]]]]], (34827 ^ _779327) ^ [_1421299, _1421301, _1421303, _1421305, _1421307] : [class_Lattices_Osemilattice__inf(_1421299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421299), _1421301), _1421303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421299), _1421305), _1421307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421299), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421299), _1421301), _1421305)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421299), _1421303), _1421307))))], (48319 ^ _779327) ^ [_1745647, _1745649] : [c_List_Olist_ONil(_1745647) = c_List_Oremdups(_1745647, _1745649), -(_1745649 = c_List_Olist_ONil(_1745647))], (20987 ^ _779327) ^ [_1138823, _1138825, _1138827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1138823), _1138825))), -(c_Random_Ominus__shift(_1138827, _1138823, _1138825) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1138823), _1138825))], (21214 ^ _779327) ^ [_1143526, _1143528] : [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(_1143528))), 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)), _1143526))))), -(hAPP(c_Nat_OSuc, _1143526) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143528))], (17754 ^ _779327) ^ [_1080360, _1080362] : [class_Int_Onumber__ring(_1080360), class_Rings_Olinordered__idom(_1080360), 17761 ^ _779327 : [(17768 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080360), c_Groups_Oone__class_Oone(_1080360)), hAPP(c_Int_Onumber__class_Onumber__of(_1080360), _1080362))))], (17762 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080360), c_Groups_Oone__class_Oone(_1080360)), hAPP(c_Int_Onumber__class_Onumber__of(_1080360), _1080362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1080362)))]]], (16962 ^ _779327) ^ [_1067175] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067175), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067175), c_Int_OPls)))], (13539 ^ _779327) ^ [_1006002, _1006004] : [13540 ^ _779327 : [(13541 ^ _779327) ^ [_1006055] : [_1006004 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006002), _1006055))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006002), _1006004)))], (51675 ^ _779327) ^ [_1818352, _1818354, _1818356] : [hBOOL(hAPP(hAPP(c_member(_1818354), _1818352), c_Orderings_Obot__class_Obot(tc_fun(_1818354, tc_HOL_Obool)))), hBOOL(hAPP(_1818356, _1818352))], (1588 ^ _779327) ^ [_802165, _802167] : [-(class_Rings_Olinordered__semiring__strict(_802165)), _802167 = _802165, class_Rings_Olinordered__semiring__strict(_802167)], (43019 ^ _779327) ^ [_1620591, _1620593, _1620595, _1620597, _1620599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620591, _1620591)), hAPP(hAPP(c_Product__Type_OPair(_1620591, _1620591), _1620593), _1620595)), c_Transitive__Closure_Ortrancl(_1620591, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620591, _1620591), tc_HOL_Obool)), _1620597), _1620599)))), 43025 ^ _779327 : [(43031 ^ _779327) ^ [] : [43027 ^ [_1620591, _1620593, _1620595, _1620597, _1620599] = 43024 ^ [_1620591, _1620593, _1620595, _1620597, _1620599]], (43029 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620591, _1620591)), hAPP(hAPP(c_Product__Type_OPair(_1620591, _1620591), 43027 ^ [_1620591, _1620593, _1620595, _1620597, _1620599]), 43024 ^ [_1620591, _1620593, _1620595, _1620597, _1620599])), _1620599)))], (43026 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620591, _1620591)), hAPP(hAPP(c_Product__Type_OPair(_1620591, _1620591), 43024 ^ [_1620591, _1620593, _1620595, _1620597, _1620599]), _1620595)), c_Transitive__Closure_Ortrancl(_1620591, _1620597))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620591, _1620591)), hAPP(hAPP(c_Product__Type_OPair(_1620591, _1620591), _1620593), _1620595)), c_Transitive__Closure_Ortrancl(_1620591, _1620597))))], (47213 ^ _779327) ^ [_1721854, _1721856, _1721858] : [class_Orderings_Olinorder(_1721854), -(c_Big__Operators_Olattice_OSup__fin(_1721854, c_Orderings_Oord__class_Omax(_1721854), hAPP(c_List_Oset(_1721854), hAPP(hAPP(c_List_Olist_OCons(_1721854), _1721856), _1721858))) = hAPP(c_List_Ofoldl(_1721854, _1721854, c_Orderings_Oord__class_Omax(_1721854), _1721856), _1721858))], (35115 ^ _779327) ^ [_1427566, _1427568, _1427570] : [35117 ^ _779327 : [(35123 ^ _779327) ^ [] : [-(35116 ^ [_1427566, _1427568, _1427570] = 35119 ^ [_1427566, _1427568, _1427570])], (35121 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427566), 35119 ^ [_1427566, _1427568, _1427570]), _1427570)))], (35118 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427566), 35116 ^ [_1427566, _1427568, _1427570]), _1427568)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427566, tc_HOL_Obool)), _1427568), _1427570) = c_Orderings_Obot__class_Obot(tc_fun(_1427566, tc_HOL_Obool)))], (23283 ^ _779327) ^ [_1183609, _1183611] : [class_Orderings_Olinorder(_1183609), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183609), _1183611), _1183611) = _1183611)], (50802 ^ _779327) ^ [_1799545, _1799547, _1799549] : [c_List_Olist__all(_1799545, _1799547, hAPP(c_List_Orev(_1799545), _1799549)), -(c_List_Olist__all(_1799545, _1799547, _1799549))], (45793 ^ _779327) ^ [_1689699, _1689701, _1689703, _1689705, _1689707] : [-(hAPP(hAPP(c_List_Ozip(_1689699, _1689701), hAPP(hAPP(c_List_Olist_OCons(_1689699), _1689703), _1689705)), _1689707) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1689699, _1689701)), _1689701, c_List_Olist_ONil(tc_prod(_1689699, _1689701)), hAPP(hAPP(c_COMBC(_1689701, tc_fun(tc_List_Olist(_1689701), tc_List_Olist(tc_prod(_1689699, _1689701))), tc_fun(tc_List_Olist(_1689701), tc_List_Olist(tc_prod(_1689699, _1689701)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1689699, _1689701)), tc_List_Olist(tc_prod(_1689699, _1689701))), tc_fun(tc_fun(tc_List_Olist(_1689701), tc_List_Olist(tc_prod(_1689699, _1689701))), tc_fun(tc_List_Olist(_1689701), tc_List_Olist(tc_prod(_1689699, _1689701)))), _1689701), c_COMBB(tc_List_Olist(tc_prod(_1689699, _1689701)), tc_List_Olist(tc_prod(_1689699, _1689701)), tc_List_Olist(_1689701))), hAPP(hAPP(c_COMBB(tc_prod(_1689699, _1689701), tc_fun(tc_List_Olist(tc_prod(_1689699, _1689701)), tc_List_Olist(tc_prod(_1689699, _1689701))), _1689701), c_List_Olist_OCons(tc_prod(_1689699, _1689701))), hAPP(c_Product__Type_OPair(_1689699, _1689701), _1689703)))), hAPP(c_List_Ozip(_1689699, _1689701), _1689705))), _1689707))], (5052 ^ _779327) ^ [_856362, _856364, _856366, _856368, _856370, _856372] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_856372, _856368, _856364) = c_Lazy__Sequence_Olazy__sequence_OInsert(_856370, _856366, _856362)), _856372 = _856370, _856368 = _856366, _856364 = _856362], (34001 ^ _779327) ^ [_1401536, _1401538, _1401540] : [-(hAPP(c_Set_OPow(_1401536), hAPP(hAPP(c_Set_Oinsert(_1401536), _1401538), _1401540)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1401536, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1401536), _1401540)), hAPP(c_Set_Oimage(tc_fun(_1401536, tc_HOL_Obool), tc_fun(_1401536, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1401536), _1401538)), hAPP(c_Set_OPow(_1401536), _1401540))))], (31191 ^ _779327) ^ [_1344225, _1344227, _1344229, _1344231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1344225, _1344225)), hAPP(hAPP(c_Product__Type_OPair(_1344225, _1344225), _1344227), _1344229)), hAPP(c_Wellfounded_Omeasure(_1344225), _1344231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1344231, _1344227)), hAPP(_1344231, _1344229))))], (42190 ^ _779327) ^ [_1600149, _1600151] : [-(c_Transitive__Closure_Ortrancl(_1600149, c_Transitive__Closure_Otrancl(_1600149, _1600151)) = c_Transitive__Closure_Ortrancl(_1600149, _1600151))], (14231 ^ _779327) ^ [_1019182, _1019184] : [class_Lattices_Oab__semigroup__idem__mult(_1019182), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019182), _1019184), _1019184) = _1019184)], (46512 ^ _779327) ^ [_1706703, _1706705, _1706707] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1706703, tc_HOL_Obool)), hAPP(c_List_Oset(_1706703), hAPP(hAPP(c_List_Odrop(_1706703), _1706705), _1706707))), hAPP(c_List_Oset(_1706703), _1706707))))], (46028 ^ _779327) ^ [_1695048, _1695050, _1695052, _1695054, _1695056] : [-(_1695048 = _1695050), -(hAPP(hAPP(c_List_Onth(_1695052), hAPP(hAPP(c_List_Olist__update(_1695052, _1695054), _1695048), _1695056)), _1695050) = hAPP(hAPP(c_List_Onth(_1695052), _1695054), _1695050))], (41225 ^ _779327) ^ [_1577357, _1577359, _1577361, _1577363, _1577365, _1577367, _1577369] : [hAPP(c_Fun_Ocomp(_1577357, _1577359, _1577361, _1577363), _1577365) = hAPP(c_Fun_Ocomp(_1577359, _1577359, _1577361, c_Fun_Oid(_1577359)), _1577367), -(hAPP(_1577363, hAPP(_1577365, _1577369)) = hAPP(_1577367, _1577369))], (29384 ^ _779327) ^ [_1303680, _1303682, _1303684, _1303686] : [c_Sum__Type_OPlus(_1303680, _1303682, _1303684, _1303686) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1303680, _1303682), tc_HOL_Obool)), 29387 ^ _779327 : [(29390 ^ _779327) ^ [] : [-(_1303686 = c_Orderings_Obot__class_Obot(tc_fun(_1303682, tc_HOL_Obool)))], (29388 ^ _779327) ^ [] : [-(_1303684 = c_Orderings_Obot__class_Obot(tc_fun(_1303680, tc_HOL_Obool)))]]], (15944 ^ _779327) ^ [_1049077, _1049079, _1049081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1049077)), 15947 ^ _779327 : [(15948 ^ _779327) ^ [] : [-(_1049079 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049081), _1049077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049077), _1049079)), _1049081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049081), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049077), hAPP(c_Nat_OSuc, _1049079))))], (15958 ^ _779327) ^ [] : [_1049079 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049081), _1049077), 15961 ^ _779327 : [(15964 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049081), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049077), hAPP(c_Nat_OSuc, _1049079)))))], (15962 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049077), _1049079)), _1049081)))]]]]], (34757 ^ _779327) ^ [_1419822, _1419824, _1419826] : [class_Lattices_Osemilattice__inf(_1419822), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419822), _1419824), _1419826) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419822), _1419826), _1419824))], (23095 ^ _779327) ^ [_1179791, _1179793, _1179795] : [class_Orderings_Olinorder(_1179791), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179791), _1179793), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179791), _1179793), _1179795)) = _1179793)], (9950 ^ _779327) ^ [_940430] : [-(hBOOL(hAPP(_940430, 9957 ^ [_940430]))), 9951 ^ _779327 : [(9952 ^ _779327) ^ [_940482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _940482)), hBOOL(hAPP(_940430, hAPP(c_Int_Onat, _940482)))]]], (22155 ^ _779327) ^ [_1162269, _1162271, _1162273, _1162275] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162269, _1162271), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1162273), _1162275))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1162269), _1162271) = _1162273)], (3498 ^ _779327) ^ [_832157, _832159, _832161, _832163, _832165, _832167, _832169, _832171] : [-(c_New__Random__Sequence_Opos__bind(_832171, _832167, _832163, _832159) = c_New__Random__Sequence_Opos__bind(_832169, _832165, _832161, _832157)), _832171 = _832169, _832167 = _832165, _832163 = _832161, _832159 = _832157], (17642 ^ _779327) ^ [_1078705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078705), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1078705)), c_Int_OPls)))], (25506 ^ _779327) ^ [_1224630, _1224632, _1224634] : [class_Groups_Ocomm__monoid__add(_1224630), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224632, _1224630), hAPP(c_COMBK(_1224630, _1224632), c_Groups_Ozero__class_Ozero(_1224630))), _1224634) = c_Groups_Ozero__class_Ozero(_1224630))], (25874 ^ _779327) ^ [_1232974, _1232976, _1232978] : [class_Groups_Ocomm__monoid__add(_1232974), hAPP(_1232976, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1232974), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1232974), _1232976), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1232978)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1232974), _1232976), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232978)))], (16221 ^ _779327) ^ [_1054229, _1054231] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1054229)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054229)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054231)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1054229)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1054231))))], (374 ^ _779327) ^ [_784996, _784998, _785000, _785002, _785004, _785006, _785008, _785010, _785012, _785014] : [-(c_Typedef_Otype__definition(_785012, _785008, _785004, _785000, _784996)), c_Typedef_Otype__definition(_785014, _785010, _785006, _785002, _784998), _785014 = _785012, _785010 = _785008, _785006 = _785004, _785002 = _785000, _784998 = _784996], (42965 ^ _779327) ^ [_1619120] : [-(c_Nat_Ofunpow(_1619120) = c_Nat_Ocompow(_1619120, _1619120))], (28674 ^ _779327) ^ [_1290314, _1290316] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290314, tc_HOL_Obool)), _1290316), c_Orderings_Obot__class_Obot(tc_fun(_1290314, tc_HOL_Obool))) = _1290316)], (8550 ^ _779327) ^ [_916230, _916232] : [8551 ^ _779327 : [(8554 ^ _779327) ^ [] : [_916232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8552 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _916230))]], -(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), _916230), _916232))))], (45574 ^ _779327) ^ [_1683599, _1683601, _1683603, _1683605, _1683607, _1683609] : [-(hAPP(hAPP(c_List_Ozip(_1683599, _1683601), _1683603), hAPP(hAPP(c_List_Omap(_1683605, _1683601), _1683607), _1683609)) = hAPP(hAPP(c_List_Omap(tc_prod(_1683599, _1683605), tc_prod(_1683599, _1683601)), hAPP(c_Product__Type_Oprod_Oprod__case(_1683599, _1683605, tc_prod(_1683599, _1683601)), hAPP(hAPP(c_COMBC(_1683599, tc_fun(_1683605, _1683601), tc_fun(_1683605, tc_prod(_1683599, _1683601))), hAPP(hAPP(c_COMBB(tc_fun(_1683601, tc_prod(_1683599, _1683601)), tc_fun(tc_fun(_1683605, _1683601), tc_fun(_1683605, tc_prod(_1683599, _1683601))), _1683599), c_COMBB(_1683601, tc_prod(_1683599, _1683601), _1683605)), c_Product__Type_OPair(_1683599, _1683601))), _1683607))), hAPP(hAPP(c_List_Ozip(_1683599, _1683605), _1683603), _1683609)))], (40275 ^ _779327) ^ [_1552631, _1552633, _1552635, _1552637] : [class_Groups_Ocomm__monoid__add(_1552631), c_Fun_Oinj__on(_1552633, _1552631, _1552635, _1552637), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552633, _1552631), _1552635), _1552637) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1552631, _1552631), c_Fun_Oid(_1552631)), hAPP(c_Set_Oimage(_1552633, _1552631, _1552635), _1552637)))], (26740 ^ _779327) ^ [_1250184, _1250186, _1250188, _1250190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250184, _1250186)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250188, _1250190))), 26743 ^ _779327 : [(26744 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250184), _1250186)), 26747 ^ _779327 : [(26752 ^ _779327) ^ [] : [26753 ^ _779327 : [(26756 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250184), _1250188))], (26754 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250188), _1250184)))]], 26757 ^ _779327 : [(26760 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250190), _1250186))], (26758 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250186), _1250190)))]]], (26750 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250186), _1250190)))], (26748 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250188), _1250184)))]]], (26762 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250188), _1250190)))]]], (42264 ^ _779327) ^ [_1601963, _1601965, _1601967, _1601969, _1601971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601963, _1601963)), hAPP(hAPP(c_Product__Type_OPair(_1601963, _1601963), _1601965), _1601967)), _1601969)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1601963, _1601963)), hAPP(hAPP(c_Product__Type_OPair(_1601963, _1601963), _1601967), _1601971)), c_Transitive__Closure_Ortrancl(_1601963, _1601969))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601963, _1601963)), hAPP(hAPP(c_Product__Type_OPair(_1601963, _1601963), _1601965), _1601971)), c_Transitive__Closure_Ortrancl(_1601963, _1601969))))], (34763 ^ _779327) ^ [_1419931, _1419933, _1419935] : [class_Lattices_Olattice(_1419931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419931), _1419933), _1419935) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419931), _1419935), _1419933))], (9495 ^ _779327) ^ [_933127, _933129, _933131] : [class_Rings_Olinordered__idom(_933127), 9498 ^ _779327 : [(9505 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933129), _933131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933127), hAPP(c_Int_Oring__1__class_Oof__int(_933127), _933129)), hAPP(c_Int_Oring__1__class_Oof__int(_933127), _933131))))], (9499 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933127), hAPP(c_Int_Oring__1__class_Oof__int(_933127), _933129)), hAPP(c_Int_Oring__1__class_Oof__int(_933127), _933131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _933129), _933131)))]]], (18372 ^ _779327) ^ [_1091395, _1091397] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1091395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1091397))) = 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), _1091395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091397))))], (9146 ^ _779327) ^ [_927161, _927163, _927165] : [-(_927161 = _927163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927165, tc_HOL_Obool)), _927161), _927163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927165, tc_HOL_Obool)), _927163), _927161))], (34219 ^ _779327) ^ [_1406940, _1406942] : [-(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), _1406940), _1406942)), 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), _1406942), _1406940)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (39370 ^ _779327) ^ [_1524691, _1524693, _1524695, _1524697, _1524699, _1524701] : [class_Groups_Ocomm__monoid__mult(_1524691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524693), _1524695)), 39380 ^ _779327 : [(39383 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524697), hAPP(_1524699, 39379 ^ [_1524691, _1524693, _1524695, _1524697, _1524699, _1524701])))], (39381 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524693), 39379 ^ [_1524691, _1524693, _1524695, _1524697, _1524699, _1524701]), _1524695)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1524693, _1524691), hAPP(hAPP(c_COMBS(_1524693, tc_fun(_1524697, tc_HOL_Obool), _1524691), hAPP(hAPP(c_COMBB(tc_fun(_1524697, _1524691), tc_fun(tc_fun(_1524697, tc_HOL_Obool), _1524691), _1524693), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1524697, _1524691)), _1524701)), _1524699)), _1524695) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1524693, _1524697), _1524691), hAPP(c_Product__Type_Oprod_Oprod__case(_1524693, _1524697, _1524691), _1524701)), hAPP(hAPP(c_Product__Type_OSigma(_1524693, _1524697), _1524695), _1524699)))], (40793 ^ _779327) ^ [_1566839, _1566841, _1566843, _1566845] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566839, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1566841, _1566839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1566841, _1566839), tc_HOL_Obool)), _1566843), _1566845))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566839, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1566841, _1566839), _1566843)), hAPP(c_Relation_ORange(_1566841, _1566839), _1566845)))))], (17664 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (48714 ^ _779327) ^ [_1755855, _1755857, _1755859, _1755861, _1755863, _1755865, _1755867] : [-(c_List_Ofoldr(_1755855, _1755857, _1755859, hAPP(hAPP(c_List_Omap(_1755861, _1755855), _1755863), _1755865), _1755867) = c_List_Ofoldr(_1755861, _1755857, hAPP(c_Fun_Ocomp(_1755855, tc_fun(_1755857, _1755857), _1755861, _1755859), _1755863), _1755865, _1755867))], (43915 ^ _779327) ^ [_1639952, _1639954, _1639956] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1639952, tc_HOL_Obool)), _1639954), _1639956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1639952, tc_HOL_Obool)), _1639954), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1639952, tc_HOL_Obool), _1639956))))], (19207 ^ _779327) ^ [_1106610, _1106612, _1106614, _1106616] : [class_Rings_Odivision__ring(_1106610), -(_1106612 = c_Groups_Ozero__class_Ozero(_1106610)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106610), _1106614), _1106612) = _1106616, -(_1106614 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106610), _1106616), _1106612))], (6570 ^ _779327) ^ [_882414, _882416, _882418, _882420, _882422] : [class_Orderings_Oorder(_882414), class_Orderings_Olinorder(_882416), c_Orderings_Oorder__class_Ostrict__mono(_882416, _882414, _882418), 6581 ^ _779327 : [(6588 ^ _779327) ^ [] : [_882420 = _882422, -(hAPP(_882418, _882420) = hAPP(_882418, _882422))], (6582 ^ _779327) ^ [] : [hAPP(_882418, _882420) = hAPP(_882418, _882422), -(_882420 = _882422)]]], (29210 ^ _779327) ^ [_1300184, _1300186, _1300188, _1300190, _1300192] : [-(_1300184 = c_Orderings_Obot__class_Obot(tc_fun(_1300186, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300188, tc_HOL_Obool)), _1300190), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1300186, tc_fun(_1300188, tc_HOL_Obool)), _1300184), _1300192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1300186, tc_fun(_1300188, tc_HOL_Obool)), _1300184), hAPP(hAPP(c_COMBB(tc_fun(_1300188, tc_HOL_Obool), tc_fun(_1300188, tc_HOL_Obool), _1300186), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300188, tc_HOL_Obool)), _1300190)), _1300192)))], (47090 ^ _779327) ^ [_1719368, _1719370, _1719372] : [hAPP(c_List_Orotate(_1719368, _1719370), _1719372) = c_List_Olist_ONil(_1719368), -(_1719372 = c_List_Olist_ONil(_1719368))], (36211 ^ _779327) ^ [_1452522, _1452524, _1452526, _1452528, _1452530, _1452532] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452522, tc_fun(_1452524, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1452522, tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_fun(_1452524, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452524, tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_fun(_1452524, tc_HOL_Obool)), _1452522), c_COMBC(_1452524, tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452524, tc_prod(_1452522, _1452524)), tc_fun(_1452524, tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), _1452522), hAPP(c_COMBB(tc_prod(_1452522, _1452524), tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool), _1452524), c_member(tc_prod(_1452522, _1452524)))), c_Product__Type_OPair(_1452522, _1452524)))), _1452526)), hAPP(hAPP(c_COMBC(_1452522, tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_fun(_1452524, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452524, tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_fun(_1452524, tc_HOL_Obool)), _1452522), c_COMBC(_1452524, tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452524, tc_prod(_1452522, _1452524)), tc_fun(_1452524, tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool)), _1452522), hAPP(c_COMBB(tc_prod(_1452522, _1452524), tc_fun(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool), tc_HOL_Obool), _1452524), c_member(tc_prod(_1452522, _1452524)))), c_Product__Type_OPair(_1452522, _1452524)))), _1452528)), _1452530), _1452532)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452522, _1452524)), hAPP(hAPP(c_Product__Type_OPair(_1452522, _1452524), _1452530), _1452532)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1452522, _1452524), tc_HOL_Obool)), _1452526), _1452528))))], (4368 ^ _779327) ^ [_845774, _845776, _845778, _845780] : [-(c_Product__Type_Osnd(_845780, _845776) = c_Product__Type_Osnd(_845778, _845774)), _845780 = _845778, _845776 = _845774], (19463 ^ _779327) ^ [_1110659, _1110661, _1110663, _1110665, _1110667] : [class_Fields_Olinordered__field(_1110659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110659), c_Groups_Ozero__class_Ozero(_1110659)), _1110661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110659), _1110661), _1110663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110659), c_Groups_Ozero__class_Ozero(_1110659)), _1110665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110659), _1110665), _1110667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110659), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110659), _1110661), _1110667)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110659), _1110663), _1110665))))], (10859 ^ _779327) ^ [_956321, _956323, _956325] : [class_Groups_Ogroup__add(_956321), 10862 ^ _779327 : [(10869 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956321), _956323), _956325) = c_Groups_Ozero__class_Ozero(_956321), -(_956323 = hAPP(c_Groups_Ouminus__class_Ouminus(_956321), _956325))], (10863 ^ _779327) ^ [] : [_956323 = hAPP(c_Groups_Ouminus__class_Ouminus(_956321), _956325), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956321), _956323), _956325) = c_Groups_Ozero__class_Ozero(_956321))]]], (15455 ^ _779327) ^ [_1040493, _1040495, _1040497] : [-(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, _1040493, _1040495)), _1040497), _1040495) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040493), _1040497), _1040495))], (49838 ^ _779327) ^ [_1778313, _1778315, _1778317, _1778319, _1778321] : [-(c_List_OdropWhile(_1778313, _1778315, hAPP(hAPP(c_List_Omap(_1778317, _1778313), _1778319), _1778321)) = hAPP(hAPP(c_List_Omap(_1778317, _1778313), _1778319), c_List_OdropWhile(_1778317, hAPP(c_Fun_Ocomp(_1778313, tc_HOL_Obool, _1778317, _1778315), _1778319), _1778321)))], (48645 ^ _779327) ^ [_1753426, _1753428, _1753430] : [hBOOL(hAPP(c_List_Odistinct(_1753426), _1753428)), -(hAPP(c_List_Ofilter(_1753426, hAPP(hAPP(c_COMBC(_1753426, tc_fun(_1753426, tc_HOL_Obool), tc_HOL_Obool), c_member(_1753426)), hAPP(c_List_Oset(_1753426), c_List_Osublist(_1753426, _1753428, _1753430)))), _1753428) = c_List_Osublist(_1753426, _1753428, _1753430))], (49762 ^ _779327) ^ [_1776580] : [-(c_List_Oreturn__list(_1776580) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1776580))], (25145 ^ _779327) ^ [_1217726, _1217728] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217726)), _1217728)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217726), _1217728)))], (35271 ^ _779327) ^ [_1431034, _1431036, _1431038, _1431040] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431034, tc_HOL_Obool)), _1431036), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431034, tc_HOL_Obool)), _1431038), _1431040)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431034, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431034, tc_HOL_Obool)), _1431036), _1431038)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431034, tc_HOL_Obool)), _1431036), _1431040)))], (30951 ^ _779327) ^ [_1339423, _1339425, _1339427, _1339429, _1339431, _1339433] : [hBOOL(hAPP(hAPP(_1339423, _1339425), _1339427)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339429, tc_fun(_1339431, tc_HOL_Obool))), _1339423), _1339433), _1339425), _1339427)))], (19805 ^ _779327) ^ [_1117136] : [c_Nat__Transfer_Ois__nat(_1117136), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117136)))], (21035 ^ _779327) ^ [_1139530, _1139532, _1139534, _1139536] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1139530, _1139532, _1139534, c_Code__Numeral_OSuc__code__numeral(_1139536)) = hAPP(hAPP(_1139534, _1139536), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1139530, _1139532, _1139534, _1139536)))], (23363 ^ _779327) ^ [_1185021, _1185023, _1185025] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1185021), _1185023), _1185025) = c_Nitpick_OAbs__Frac(_1185021, c_Nitpick_Onorm__frac(_1185023, _1185025)))], (49555 ^ _779327) ^ [_1772216, _1772218] : [-(hAPP(c_List_Orev(_1772216), hAPP(c_List_Orev(_1772216), _1772218)) = _1772218)], (27212 ^ _779327) ^ [_1259572, _1259574, _1259576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259572, tc_HOL_Obool)), _1259574), _1259576)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259572, tc_HOL_Obool)), _1259574), _1259576) = _1259576)], (52798 ^ _779327) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (19085 ^ _779327) ^ [_1104544, _1104546, _1104548] : [class_Fields_Olinordered__field__inverse__zero(_1104544), 19088 ^ _779327 : [(19103 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104544), _1104546), _1104548)), c_Groups_Ozero__class_Ozero(_1104544)))), 19104 ^ _779327 : [(19111 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), _1104546), c_Groups_Ozero__class_Ozero(_1104544))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), c_Groups_Ozero__class_Ozero(_1104544)), _1104548))], (19105 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), c_Groups_Ozero__class_Ozero(_1104544)), _1104546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), _1104548), c_Groups_Ozero__class_Ozero(_1104544)))]]], (19089 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104544), _1104546), _1104548)), c_Groups_Ozero__class_Ozero(_1104544))), 19094 ^ _779327 : [(19097 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), _1104548), c_Groups_Ozero__class_Ozero(_1104544))))], (19095 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), c_Groups_Ozero__class_Ozero(_1104544)), _1104546)))]], 19098 ^ _779327 : [(19101 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), c_Groups_Ozero__class_Ozero(_1104544)), _1104548)))], (19099 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104544), _1104546), c_Groups_Ozero__class_Ozero(_1104544))))]]]]], (52007 ^ _779327) ^ [_1826098, _1826100] : [c_Relation_Oantisym(_1826098, _1826100), 52010 ^ _779327 : [(52011 ^ _779327) ^ [_1826210, _1826212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1826098, _1826098)), hAPP(hAPP(c_Product__Type_OPair(_1826098, _1826098), _1826212), _1826210)), _1826100)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1826098, _1826098)), hAPP(hAPP(c_Product__Type_OPair(_1826098, _1826098), _1826210), _1826212)), _1826100)), -(_1826212 = _1826210)]]], (29979 ^ _779327) ^ [_1315344, _1315346, _1315348, _1315350] : [hBOOL(hAPP(hAPP(c_member(_1315344), _1315346), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315344, tc_HOL_Obool)), _1315348), _1315350))), -(hBOOL(hAPP(hAPP(c_member(_1315344), _1315346), _1315348))), -(hBOOL(hAPP(hAPP(c_member(_1315344), _1315346), _1315350)))], (24473 ^ _779327) ^ [_1205310, _1205312, _1205314, _1205316, _1205318] : [class_Rings_Ocomm__semiring__1(_1205310), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205310), _1205312), _1205314)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205310), _1205316), _1205318)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205310), _1205312), _1205316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205310), _1205314), _1205318))))], (21288 ^ _779327) ^ [_1145480, _1145482, _1145484] : [class_Int_Onumber__ring(_1145480), 21291 ^ _779327 : [(21298 ^ _779327) ^ [] : [-(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), _1145482)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145480), _1145484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1145482))) = c_Groups_Oone__class_Oone(_1145480))], (21292 ^ _779327) ^ [] : [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), _1145482))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1145480), _1145484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1145482))) = hAPP(hAPP(c_HOL_OLet(_1145480, _1145480), hAPP(hAPP(c_Power_Opower__class_Opower(_1145480), _1145484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145482))), hAPP(hAPP(c_COMBS(_1145480, _1145480, _1145480), hAPP(hAPP(c_COMBB(_1145480, tc_fun(_1145480, _1145480), _1145480), c_Groups_Otimes__class_Otimes(_1145480)), hAPP(c_Groups_Otimes__class_Otimes(_1145480), _1145484))), c_COMBI(_1145480))))]]], (44701 ^ _779327) ^ [_1660298, _1660300, _1660302] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660298), tc_List_Olist(_1660298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660298), tc_List_Olist(_1660298)), _1660300), _1660300)), c_List_Olistrel(_1660298, c_Transitive__Closure_Ortrancl(_1660298, _1660302)))))], (4868 ^ _779327) ^ [_853456, _853458, _853460, _853462, _853464, _853466, _853468, _853470, _853472, _853474] : [-(c_Predicate_Opred__comp(_853474, _853470, _853466, _853462, _853458) = c_Predicate_Opred__comp(_853472, _853468, _853464, _853460, _853456)), _853474 = _853472, _853470 = _853468, _853466 = _853464, _853462 = _853460, _853458 = _853456], (3414 ^ _779327) ^ [_830783, _830785, _830787, _830789, _830791, _830793, _830795, _830797] : [-(c_Random__Sequence_Obind(_830797, _830793, _830789, _830785) = c_Random__Sequence_Obind(_830795, _830791, _830787, _830783)), _830797 = _830795, _830793 = _830791, _830789 = _830787, _830785 = _830783], (16804 ^ _779327) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (23604 ^ _779327) ^ [_1190285, _1190287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190285), _1190287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190285)), hAPP(c_Code__Numeral_Oof__nat, _1190287))))], (21150 ^ _779327) ^ [_1142107, _1142109, _1142111] : [class_Int_Onumber__ring(_1142107), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1142107), _1142109), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1142111))) = hAPP(hAPP(c_HOL_OLet(_1142107, _1142107), hAPP(hAPP(c_Power_Opower__class_Opower(_1142107), _1142109), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142111))), hAPP(hAPP(c_COMBS(_1142107, _1142107, _1142107), c_Groups_Otimes__class_Otimes(_1142107)), c_COMBI(_1142107))))], (3662 ^ _779327) ^ [_834693, _834695, _834697, _834699] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_834699, _834695) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_834697, _834693)), _834699 = _834697, _834695 = _834693], (43103 ^ _779327) ^ [_1623017, _1623019, _1623021, _1623023] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1623017, _1623019, _1623021), _1623023), c_Orderings_Obot__class_Obot(tc_fun(_1623017, tc_HOL_Obool))) = _1623023)], (33050 ^ _779327) ^ [_1380844, _1380846, _1380848, _1380850, _1380852, _1380854] : [-(_1380844 = _1380846), -(hAPP(c_Fun_Ofun__upd(_1380848, _1380850, _1380852, _1380846, _1380854), _1380844) = hAPP(_1380852, _1380844))], (44001 ^ _779327) ^ [_1641827, _1641829] : [class_Complete__Lattice_Ocomplete__lattice(_1641827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641827), _1641829)), -(_1641829 = c_Orderings_Obot__class_Obot(tc_fun(_1641827, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1641827, _1641829) = c_Complete__Lattice_OSup__class_OSup(_1641827, _1641829))], (39535 ^ _779327) ^ [_1529165, _1529167, _1529169, _1529171, _1529173, _1529175, _1529177, _1529179] : [c_Fun_Oinj__on(_1529165, _1529167, _1529169, _1529171), c_Fun_Oinj__on(_1529173, _1529175, _1529177, _1529179), -(c_Fun_Oinj__on(tc_prod(_1529165, _1529173), tc_prod(_1529167, _1529175), c_Product__Type_Omap__pair(_1529165, _1529167, _1529173, _1529175, _1529169, _1529177), hAPP(hAPP(c_Product__Type_OSigma(_1529165, _1529173), _1529171), hAPP(c_COMBK(tc_fun(_1529173, tc_HOL_Obool), _1529165), _1529179))))], (18458 ^ _779327) ^ [_1092870, _1092872] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1092870), hAPP(c_Int_Onumber__class_Onumber__of(_1092870), _1092872)), 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(_1092870), hAPP(c_Int_Onumber__class_Onumber__of(_1092870), _1092872)), hAPP(c_Int_Onumber__class_Onumber__of(_1092870), _1092872))), class_Groups_Omonoid__mult(_1092870), class_Int_Onumber(_1092870)], (48415 ^ _779327) ^ [_1747520, _1747522] : [-(c_List_Oconcat(_1747520, _1747522) = hAPP(c_List_Ofoldl(tc_List_Olist(_1747520), tc_List_Olist(_1747520), c_List_Oappend(_1747520), c_List_Olist_ONil(_1747520)), _1747522))], (37231 ^ _779327) ^ [_1475098, _1475100, _1475102, _1475104, _1475106] : [class_Groups_Ocomm__monoid__mult(_1475098), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475100), _1475102)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475100), _1475104)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475100, tc_HOL_Obool)), _1475102), _1475104) = c_Orderings_Obot__class_Obot(tc_fun(_1475100, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1475098, _1475100, c_Groups_Otimes__class_Otimes(_1475098)), _1475106), c_Groups_Oone__class_Oone(_1475098)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475100, tc_HOL_Obool)), _1475102), _1475104)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1475098), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1475098, _1475100, c_Groups_Otimes__class_Otimes(_1475098)), _1475106), c_Groups_Oone__class_Oone(_1475098)), _1475102)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1475098, _1475100, c_Groups_Otimes__class_Otimes(_1475098)), _1475106), c_Groups_Oone__class_Oone(_1475098)), _1475104)))], (47450 ^ _779327) ^ [_1726679, _1726681, _1726683, _1726685] : [-(hAPP(hAPP(c_List_Omap(_1726679, _1726681), _1726683), c_List_Obutlast(_1726679, _1726685)) = c_List_Obutlast(_1726681, hAPP(hAPP(c_List_Omap(_1726679, _1726681), _1726683), _1726685)))], (49687 ^ _779327) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (26726 ^ _779327) ^ [_1249894, _1249896, _1249898, _1249900] : [class_Orderings_Olinorder(_1249894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249894), _1249896), _1249898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249894), _1249898), _1249900)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249894, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1249894, _1249896, _1249898)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1249894, _1249898, _1249900)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1249894, _1249896), _1249900))], (8934 ^ _779327) ^ [_923151, _923153, _923155] : [8935 ^ _779327 : [(8938 ^ _779327) ^ [] : [_923153 = _923155], (8936 ^ _779327) ^ [] : [_923151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _923151), _923153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _923151), _923155))], (24635 ^ _779327) ^ [_1208112, _1208114, _1208116] : [class_Divides_Osemiring__div(_1208112), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208112), _1208114), _1208116)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208112), _1208114), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208112), _1208116), _1208114)) = _1208116)], (25013 ^ _779327) ^ [_1215386, _1215388, _1215390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215386, tc_HOL_Obool)), _1215388), _1215390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1215386, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1215386, _1215388)), c_Predicate_OPowp(_1215386, _1215390))))], (30988 ^ _779327) ^ [_1340361, _1340363] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1340361, _1340361)), hAPP(hAPP(c_Product__Type_OPair(_1340361, _1340361), 30989 ^ [_1340361, _1340363]), 30989 ^ [_1340361, _1340363])), _1340363)), -(c_Nitpick_Orefl_H(_1340361, _1340363))], (35245 ^ _779327) ^ [_1430222, _1430224, _1430226, _1430228, _1430230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430222, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1430224, _1430222, _1430226), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430224, tc_HOL_Obool)), _1430228), _1430230))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430222, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1430224, _1430222, _1430226), _1430228)), hAPP(c_Set_Oimage(_1430224, _1430222, _1430226), _1430230)))))], (51287 ^ _779327) ^ [_1809460, _1809462, _1809464, _1809466, _1809468] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1809460, _1809462, _1809464) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1809460, _1809466, _1809468)), _1809462 = _1809466, _1809464 = _1809468], (12187 ^ _779327) ^ [_982016, _982018, _982020, _982022, _982024] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_982016), 12190 ^ _779327 : [(12191 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982018), _982020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982022), _982024)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982018), _982024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982022), _982020)), -(_982018 = _982022), -(_982020 = _982024)], (12201 ^ _779327) ^ [] : [12202 ^ _779327 : [(12205 ^ _779327) ^ [] : [_982020 = _982024], (12203 ^ _779327) ^ [] : [_982018 = _982022]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982018), _982020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982022), _982024)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982018), _982024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982016), _982022), _982020)))]]], (16968 ^ _779327) ^ [_1067262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067262), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067262))], (43087 ^ _779327) ^ [_1622744, _1622746, _1622748] : [class_Orderings_Olinorder(_1622744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622744), _1622746)), -(hBOOL(hAPP(hAPP(c_member(_1622744), _1622748), _1622746))), -(c_Big__Operators_Olattice_OSup__fin(_1622744, c_Orderings_Oord__class_Omax(_1622744), hAPP(hAPP(c_Set_Oinsert(_1622744), _1622748), _1622746)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622744, _1622744, c_Orderings_Oord__class_Omax(_1622744)), _1622748), _1622746))], (16784 ^ _779327) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (41259 ^ _779327) ^ [_1578212, _1578214, _1578216, _1578218, _1578220, _1578222, _1578224] : [-(hAPP(c_Product__Type_Oapsnd(_1578212, _1578214, _1578216, _1578218), hAPP(c_Product__Type_Oapsnd(_1578220, _1578212, _1578216, _1578222), _1578224)) = hAPP(c_Product__Type_Oapsnd(_1578220, _1578214, _1578216, hAPP(c_Fun_Ocomp(_1578212, _1578214, _1578220, _1578218), _1578222)), _1578224))], (13240 ^ _779327) ^ [_1000792, _1000794, _1000796] : [class_Int_Onumber__ring(_1000792), class_Rings_Olinordered__idom(_1000792), 13247 ^ _779327 : [(13254 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000794), _1000796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000792), hAPP(c_Int_Onumber__class_Onumber__of(_1000792), _1000794)), hAPP(c_Int_Onumber__class_Onumber__of(_1000792), _1000796))))], (13248 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000792), hAPP(c_Int_Onumber__class_Onumber__of(_1000792), _1000794)), hAPP(c_Int_Onumber__class_Onumber__of(_1000792), _1000796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1000794), _1000796)))]]], (24219 ^ _779327) ^ [_1201130, _1201132] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201130), _1201132)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201132), _1201130)), -(_1201130 = _1201132)], (11389 ^ _779327) ^ [_967147, _967149, _967151] : [class_Rings_Oring__1(_967147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967149), _967151)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_967147), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967151), _967149)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967147), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_967147), _967151)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_967147), _967149)))], (6969 ^ _779327) ^ [_888387, _888389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888389), hAPP(c_Nat_OSuc, _888387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888387), _888389))], (37729 ^ _779327) ^ [] : [-(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))], (17482 ^ _779327) ^ [_1076077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076077), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076077)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8068 ^ _779327) ^ [_907467, _907469, _907471] : [class_Rings_Olinordered__semiring__strict(_907467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907467), c_Groups_Ozero__class_Ozero(_907467)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907467), _907469), _907471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907467), c_Groups_Ozero__class_Ozero(_907467)), _907469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907467), c_Groups_Ozero__class_Ozero(_907467)), _907471)))], (5782 ^ _779327) ^ [_870633] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _870633)))], (23855 ^ _779327) ^ [_1195056] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1195056)))], (52756 ^ _779327) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (48325 ^ _779327) ^ [_1745734, _1745736] : [_1745736 = c_List_Olist_ONil(_1745734), -(c_List_Olist_ONil(_1745734) = c_List_Oremdups(_1745734, _1745736))], (14315 ^ _779327) ^ [_1020605, _1020607, _1020609] : [hBOOL(hAPP(_1020605, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1020607), _1020609)))), 14318 ^ _779327 : [(14325 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020607), _1020609)), -(hBOOL(hAPP(_1020605, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14319 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020609), _1020607)), -(hBOOL(hAPP(_1020605, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1020607)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1020609)))))]]], (46168 ^ _779327) ^ [_1697696, _1697698, _1697700, _1697702, _1697704, _1697706] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697696)), _1697698) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697700)), _1697702), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697696)), _1697704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697700)), _1697706), -(hAPP(hAPP(c_List_Ozip(_1697696, _1697700), hAPP(hAPP(c_List_Oappend(_1697696), _1697698), _1697704)), hAPP(hAPP(c_List_Oappend(_1697700), _1697702), _1697706)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1697696, _1697700)), hAPP(hAPP(c_List_Ozip(_1697696, _1697700), _1697698), _1697702)), hAPP(hAPP(c_List_Ozip(_1697696, _1697700), _1697704), _1697706)))], (38459 ^ _779327) ^ [_1503840, _1503842, _1503844, _1503846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503840), _1503842)), c_Fun_Oinj__on(_1503844, _1503840, _1503846, c_Orderings_Otop__class_Otop(tc_fun(_1503844, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1503844), hAPP(c_Set_Ovimage(_1503844, _1503840, _1503846), _1503842))))], (10331 ^ _779327) ^ [_946802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _946802)))], (40243 ^ _779327) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (39275 ^ _779327) ^ [_1522866, _1522868, _1522870] : [class_Orderings_Olinorder(_1522866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522866), _1522868)), -(_1522868 = c_Orderings_Obot__class_Obot(tc_fun(_1522866, tc_HOL_Obool))), 39286 ^ _779327 : [(39296 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522866), hAPP(c_Finite__Set_Ofold1(_1522866, c_Orderings_Oord__class_Omin(_1522866)), _1522868)), _1522870))), 39297 ^ _779327 : [(39298 ^ _779327) ^ [_1523255] : [hBOOL(hAPP(hAPP(c_member(_1522866), _1523255), _1522868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522866), _1523255), _1522870))]]], (39287 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522866), hAPP(c_Finite__Set_Ofold1(_1522866, c_Orderings_Oord__class_Omin(_1522866)), _1522868)), _1522870)), 39291 ^ _779327 : [(39294 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1522866), 39290 ^ [_1522866, _1522868, _1522870]), _1522870)))], (39292 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522866), 39290 ^ [_1522866, _1522868, _1522870]), _1522868)))]]]]], (41976 ^ _779327) ^ [_1594464, _1594466, _1594468] : [class_Orderings_Olinorder(_1594464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594464), _1594466)), 41986 ^ _779327 : [(41989 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1594464), _1594468), 41985 ^ [_1594464, _1594466, _1594468]))], (41987 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1594464), 41985 ^ [_1594464, _1594466, _1594468]), _1594466)))]], hBOOL(hAPP(hAPP(c_member(_1594464), _1594468), _1594466)), -(c_Big__Operators_Olinorder__class_OMin(_1594464, _1594466) = _1594468)], (51521 ^ _779327) ^ [_1814936, _1814938, _1814940] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1814936), _1814938, _1814940)), -(c_List_Olist__ex(tc_Int_Oint, _1814936, c_List_Oupto(_1814938, _1814940)))], (20057 ^ _779327) ^ [_1121260, _1121262, _1121264] : [class_Fields_Olinordered__field(_1121260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121260), _1121262), _1121264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121260), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121260), _1121262), _1121264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121260), c_Groups_Oone__class_Oone(_1121260)), c_Groups_Oone__class_Oone(_1121260)))), _1121264)))], (28068 ^ _779327) ^ [_1278369, _1278371, _1278373, _1278375, _1278377] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278369, tc_fun(_1278371, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1278369), _1278373), _1278375)), _1278377) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278371, tc_HOL_Obool)), hAPP(_1278377, _1278373)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278369, tc_fun(_1278371, tc_HOL_Obool)), _1278375), _1278377)))], (45351 ^ _779327) ^ [_1677673, _1677675, _1677677, _1677679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1677673), tc_List_Olist(_1677673))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677673), tc_List_Olist(_1677673)), _1677675), _1677677)), c_List_Olistrel(_1677673, _1677679))), 45354 ^ _779327 : [(45357 ^ _779327) ^ [_1678009] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1677673, _1677673)), _1678009), hAPP(c_List_Oset(tc_prod(_1677673, _1677673)), hAPP(hAPP(c_List_Ozip(_1677673, _1677673), _1677675), _1677677)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1677673, _1677673, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1677673, tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_fun(_1677673, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1677673, tc_fun(tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_fun(_1677673, tc_HOL_Obool)), _1677673), c_COMBC(_1677673, tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1677673, tc_prod(_1677673, _1677673)), tc_fun(_1677673, tc_fun(tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_HOL_Obool)), _1677673), hAPP(c_COMBB(tc_prod(_1677673, _1677673), tc_fun(tc_fun(tc_prod(_1677673, _1677673), tc_HOL_Obool), tc_HOL_Obool), _1677673), c_member(tc_prod(_1677673, _1677673)))), c_Product__Type_OPair(_1677673, _1677673)))), _1677679)), _1678009)))], (45355 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677673)), _1677675) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677673)), _1677677))]]], (16183 ^ _779327) ^ [_1053568, _1053570] : [-(_1053568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16186 ^ _779327 : [(16193 ^ _779327) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053570, _1053568) = 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), _1053570)), _1053568) = 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), _1053570), _1053568))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16187 ^ _779327) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053570, _1053568) = 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), _1053570)), _1053568) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1053570), _1053568)))]]], (38407 ^ _779327) ^ [_1502456, _1502458, _1502460, _1502462, _1502464] : [-(hAPP(c_Set_Ovimage(_1502456, _1502458, _1502460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1502458, tc_HOL_Obool)), _1502462), _1502464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1502456, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502456, _1502458, _1502460), _1502462)), hAPP(c_Set_Ovimage(_1502456, _1502458, _1502460), _1502464)))], (11053 ^ _779327) ^ [_959651, _959653, _959655] : [class_Groups_Ogroup__add(_959651), 11056 ^ _779327 : [(11063 ^ _779327) ^ [] : [_959655 = hAPP(c_Groups_Ouminus__class_Ouminus(_959651), _959653), -(_959653 = hAPP(c_Groups_Ouminus__class_Ouminus(_959651), _959655))], (11057 ^ _779327) ^ [] : [_959653 = hAPP(c_Groups_Ouminus__class_Ouminus(_959651), _959655), -(_959655 = hAPP(c_Groups_Ouminus__class_Ouminus(_959651), _959653))]]], (1060 ^ _779327) ^ [_795415, _795417, _795419, _795421] : [-(c_Equiv__Relations_Oequivp(_795419, _795415)), c_Equiv__Relations_Oequivp(_795421, _795417), _795421 = _795419, _795417 = _795415], (33583 ^ _779327) ^ [_1391531, _1391533, _1391535, _1391537] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1391531), _1391533)), 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)), _1391535), _1391531)), 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)), _1391537), _1391533)), 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)), _1391535), _1391537)), _1391533)), c_FunDef_Omax__weak)))], (36568 ^ _779327) ^ [_1461587, _1461589, _1461591] : [class_Lattices_Olattice(_1461587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461587), _1461589)), -(_1461589 = c_Orderings_Obot__class_Obot(tc_fun(_1461587, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461587), _1461591)), -(_1461591 = c_Orderings_Obot__class_Obot(tc_fun(_1461587, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1461587, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461587, tc_HOL_Obool)), _1461589), _1461591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461587), c_Big__Operators_Olattice__class_OInf__fin(_1461587, _1461589)), c_Big__Operators_Olattice__class_OInf__fin(_1461587, _1461591)))], (36733 ^ _779327) ^ [_1464763, _1464765, _1464767, _1464769, _1464771] : [c_Fun_Oinj__on(_1464763, _1464765, _1464767, _1464769), c_Fun_Oinj__on(_1464763, _1464765, _1464767, _1464771), -(c_Fun_Oinj__on(_1464763, _1464765, _1464767, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464763, tc_HOL_Obool)), _1464769), _1464771)))], (29861 ^ _779327) ^ [_1313108, _1313110, _1313112, _1313114] : [_1313108 = _1313110, 29864 ^ _779327 : [(29871 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313112), _1313114), _1313110)), -(hBOOL(hAPP(hAPP(c_member(_1313112), _1313114), _1313108)))], (29865 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313112), _1313114), _1313108)), -(hBOOL(hAPP(hAPP(c_member(_1313112), _1313114), _1313110)))]]], (48580 ^ _779327) ^ [_1751918] : [-(c_List_Otranspose(_1751918, c_List_Olist_ONil(tc_List_Olist(_1751918))) = c_List_Olist_ONil(tc_List_Olist(_1751918)))], (29134 ^ _779327) ^ [_1298399, _1298401, _1298403, _1298405, _1298407] : [-(_1298399 = c_Orderings_Obot__class_Obot(tc_fun(_1298401, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298403, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298401, tc_fun(_1298403, tc_HOL_Obool)), _1298399), _1298405)), _1298407) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298401, tc_fun(_1298403, tc_HOL_Obool)), _1298399), hAPP(hAPP(c_COMBC(_1298401, tc_fun(_1298403, tc_HOL_Obool), tc_fun(_1298403, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298403, tc_HOL_Obool), tc_fun(tc_fun(_1298403, tc_HOL_Obool), tc_fun(_1298403, tc_HOL_Obool)), _1298401), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298403, tc_HOL_Obool))), _1298405)), _1298407)))], (21408 ^ _779327) ^ [_1147750, _1147752] : [-(c_Divides_OposDivAlg(_1147750, _1147752) = hAPP(c_Divides_Oadjust(_1147752), c_Divides_OposDivAlg(_1147750, 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)))), _1147752)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147750), _1147752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147752), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20019 ^ _779327) ^ [_1120650, _1120652, _1120654, _1120656] : [class_Fields_Ofield__inverse__zero(_1120650), class_Int_Onumber(_1120650), 20026 ^ _779327 : [(20027 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120650), _1120652), hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654)) = _1120656, 20030 ^ _779327 : [(20037 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654) = c_Groups_Ozero__class_Ozero(_1120650), -(_1120656 = c_Groups_Ozero__class_Ozero(_1120650))], (20031 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654) = c_Groups_Ozero__class_Ozero(_1120650)), -(_1120652 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120650), _1120656), hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654)))]]], (20043 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120650), _1120652), hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654)) = _1120656), 20046 ^ _779327 : [(20049 ^ _779327) ^ [] : [_1120652 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120650), _1120656), hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654))], (20047 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654) = c_Groups_Ozero__class_Ozero(_1120650)]], 20050 ^ _779327 : [(20053 ^ _779327) ^ [] : [_1120656 = c_Groups_Ozero__class_Ozero(_1120650)], (20051 ^ _779327) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1120650), _1120654) = c_Groups_Ozero__class_Ozero(_1120650))]]]]], (47066 ^ _779327) ^ [_1718731, _1718733, _1718735, _1718737, _1718739, _1718741, _1718743] : [-(hAPP(c_List_Ofoldl(_1718731, _1718733, _1718735, _1718737), hAPP(hAPP(c_List_Omap(_1718739, _1718733), _1718741), _1718743)) = hAPP(c_List_Ofoldl(_1718731, _1718739, hAPP(hAPP(c_COMBC(_1718731, tc_fun(_1718739, _1718733), tc_fun(_1718739, _1718731)), hAPP(hAPP(c_COMBB(tc_fun(_1718733, _1718731), tc_fun(tc_fun(_1718739, _1718733), tc_fun(_1718739, _1718731)), _1718731), c_COMBB(_1718733, _1718731, _1718739)), _1718735)), _1718741), _1718737), _1718743))], (31352 ^ _779327) ^ [_1347698, _1347700, _1347702, _1347704, _1347706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1347698, _1347700)), hAPP(_1347698, _1347702))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1347704, _1347704)), hAPP(hAPP(c_Product__Type_OPair(_1347704, _1347704), _1347700), _1347702)), c_Wellfounded_Omlex__prod(_1347704, _1347698, _1347706))))], (51171 ^ _779327) ^ [_1806723, _1806725, _1806727, _1806729, _1806731] : [hBOOL(hAPP(hAPP(_1806727, _1806731), _1806729)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806723, _1806725, _1806727), _1806729), _1806731)))], (40504 ^ _779327) ^ [_1560704, _1560706, _1560708, _1560710] : [c_Wellfounded_Owf(_1560704, _1560706), c_Wellfounded_Owf(_1560708, _1560710), -(c_Wellfounded_Owf(tc_prod(_1560704, _1560708), c_Wellfounded_Olex__prod(_1560704, _1560708, _1560706, _1560710)))], (40690 ^ _779327) ^ [_1564381, _1564383, _1564385] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564381, _1564383)), _1564385)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564383), hAPP(c_Relation_ORange(_1564381, _1564383), _1564385))))], (47110 ^ _779327) ^ [_1719778, _1719780] : [-(c_List_Orotate(_1719778, _1719780) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1719778), tc_List_Olist(_1719778)), _1719780), c_List_Orotate1(_1719778)))], (52157 ^ _779327) ^ [_1829207, _1829209] : [-(c_Relation_Osym(_1829207, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1829207, _1829207), tc_HOL_Obool)), _1829209), hAPP(c_Relation_Oconverse(_1829207, _1829207), _1829209))))], (8858 ^ _779327) ^ [_921780, _921782, _921784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _921780)), 8861 ^ _779327 : [(8868 ^ _779327) ^ [] : [_921782 = _921784, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921780), _921782) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921780), _921784))], (8862 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921780), _921782) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921780), _921784), -(_921782 = _921784)]]], (35445 ^ _779327) ^ [_1434876, _1434878, _1434880, _1434882, _1434884] : [class_Orderings_Olinorder(_1434876), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434876, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1434876, _1434878, _1434880)), c_SetInterval_Oord__class_OatLeastAtMost(_1434876, _1434882, _1434884)) = c_SetInterval_Oord__class_OatLeastAtMost(_1434876, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1434876), _1434878), _1434882), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1434876), _1434880), _1434884)))], (15301 ^ _779327) ^ [_1037217, _1037219, _1037221, _1037223] : [class_Divides_Osemiring__div(_1037217), -(c_Divides_Odiv__class_Omod(_1037217, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037217), _1037219), _1037221), _1037223) = c_Divides_Odiv__class_Omod(_1037217, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037217), c_Divides_Odiv__class_Omod(_1037217, _1037219, _1037223)), c_Divides_Odiv__class_Omod(_1037217, _1037221, _1037223)), _1037223))], (49171 ^ _779327) ^ [_1764291, _1764293, _1764295, _1764297, _1764299] : [class_Orderings_Olinorder(_1764291), -(c_List_Olinorder__class_Osorted(_1764291, hAPP(hAPP(c_List_Omap(_1764293, _1764291), _1764295), hAPP(c_List_Ofilter(_1764293, hAPP(hAPP(c_COMBC(_1764293, _1764291, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1764291, tc_fun(_1764291, tc_HOL_Obool), _1764293), c_fequal), _1764295)), hAPP(_1764297, _1764299))), _1764299))))], (23444 ^ _779327) ^ [_1186661, _1186663, _1186665] : [-(c_Nitpick_Oplus__frac(_1186661, _1186663, _1186665) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1186661), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1186661), _1186663), hAPP(c_Nitpick_Odenom(_1186661), _1186665))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1186661), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1186661), tc_Int_Oint), c_Nitpick_Ofrac(_1186661)), 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(_1186661), _1186663))), 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(_1186661), _1186663))))), 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(_1186661), _1186665))), 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(_1186661), _1186665)))))), c_COMBI(tc_Int_Oint))))], (1808 ^ _779327) ^ [_804915, _804917] : [-(class_Orderings_Olinorder(_804915)), _804917 = _804915, class_Orderings_Olinorder(_804917)], (26649 ^ _779327) ^ [_1248424, _1248426] : [class_Orderings_Olinorder(_1248424), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1248424, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1248424), _1248426)) = hAPP(c_SetInterval_Oord__class_OatMost(_1248424), _1248426))], (42031 ^ _779327) ^ [_1595649, _1595651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1595649), _1595651)), -(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), _1595649), _1595651)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (30106 ^ _779327) ^ [_1320315, _1320317, _1320319, _1320321, _1320323] : [-(hBOOL(hAPP(hAPP(c_member(_1320315), _1320317), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1320319, tc_fun(_1320315, tc_HOL_Obool)), _1320321), _1320323)))), 30107 ^ _779327 : [(30108 ^ _779327) ^ [_1320397] : [hBOOL(hAPP(hAPP(c_member(_1320319), _1320397), _1320321)), hBOOL(hAPP(hAPP(c_member(_1320315), _1320317), hAPP(_1320323, _1320397)))]]], (47696 ^ _779327) ^ [_1732027, _1732029, _1732031, _1732033] : [hBOOL(hAPP(c_List_Olistsp(_1732027, _1732029), hAPP(hAPP(c_List_Oappend(_1732027), _1732031), _1732033))), 47699 ^ _779327 : [(47702 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1732027, _1732029), _1732033)))], (47700 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1732027, _1732029), _1732031)))]]], (9463 ^ _779327) ^ [_932675, _932677] : [class_Int_Oring__char__0(_932675), 9466 ^ _779327 : [(9473 ^ _779327) ^ [] : [_932677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_932675) = hAPP(c_Int_Oring__1__class_Oof__int(_932675), _932677))], (9467 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_932675) = hAPP(c_Int_Oring__1__class_Oof__int(_932675), _932677), -(_932677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (15658 ^ _779327) ^ [_1044212, _1044214, _1044216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1044212)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044212), _1044214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044212), _1044216)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044214), _1044216))], (14133 ^ _779327) ^ [_1017034, _1017036] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017034), _1017036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017036), _1017034))], (5798 ^ _779327) ^ [_870890, _870892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870890), _870892)), 5801 ^ _779327 : [(5804 ^ _779327) ^ [] : [_870890 = _870892], (5802 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _870890), _870892)))]]], (40498 ^ _779327) ^ [_1560605, _1560607, _1560609, _1560611] : [c_Wellfounded_Owf(_1560605, _1560607), -(c_Wellfounded_Owf(_1560609, hAPP(hAPP(c_Relation_Oinv__image(_1560605, _1560609), _1560607), _1560611)))], (39800 ^ _779327) ^ [_1534793, _1534795, _1534797] : [-(hAPP(hAPP(c_Set_Oinsert(_1534793), _1534795), _1534797) = hAPP(c_Set_OCollect(_1534793), hAPP(hAPP(c_COMBS(_1534793, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534793), c_fdisj), hAPP(hAPP(c_COMBC(_1534793, _1534793, tc_HOL_Obool), c_fequal), _1534795))), hAPP(hAPP(c_COMBC(_1534793, tc_fun(_1534793, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534793)), _1534797))))], (48032 ^ _779327) ^ [_1739128, _1739130, _1739132, _1739134] : [c_List_Olist__all2(_1739128, _1739130, _1739132, _1739134, c_List_Olist_ONil(_1739130)), -(_1739134 = c_List_Olist_ONil(_1739128))], (40054 ^ _779327) ^ [_1544053] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1544053) = 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), _1544053), c_Int_Onat)))))], (26556 ^ _779327) ^ [_1246893] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1246893)) = _1246893)], (52748 ^ _779327) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52988 ^ _779327) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (23201 ^ _779327) ^ [_1182162, _1182164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1182164, _1182162) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182164), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182162)))], (5460 ^ _779327) ^ [_862658, _862660] : [_862660 = _862658, -(tc_List_Olist(_862660) = tc_List_Olist(_862658))], (35099 ^ _779327) ^ [_1427188, _1427190] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427188, tc_HOL_Obool)), _1427190), c_Orderings_Obot__class_Obot(tc_fun(_1427188, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1427188, tc_HOL_Obool)))], (52606 ^ _779327) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (29526 ^ _779327) ^ [_1306626, _1306628, _1306630, _1306632, _1306634, _1306636] : [_1306626 = hAPP(_1306628, _1306630), hBOOL(hAPP(hAPP(c_member(_1306632), _1306630), _1306634)), -(hBOOL(hAPP(hAPP(c_member(_1306636), _1306626), hAPP(c_Set_Oimage(_1306632, _1306636, _1306628), _1306634))))], (35541 ^ _779327) ^ [_1437124, _1437126, _1437128] : [class_Orderings_Oorder(_1437124), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437124, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1437124), _1437126)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1437124, _1437126, _1437128)) = c_Orderings_Obot__class_Obot(tc_fun(_1437124, tc_HOL_Obool)))], (42072 ^ _779327) ^ [_1596435] : [-(c_Transitive__Closure_Otrancl(_1596435, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1596435, _1596435), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1596435, _1596435), tc_HOL_Obool)))], (2872 ^ _779327) ^ [_822166, _822168, _822170, _822172, _822174, _822176, _822178, _822180] : [-(c_Product__Type_Ocurry(_822180, _822176, _822172, _822168) = c_Product__Type_Ocurry(_822178, _822174, _822170, _822166)), _822180 = _822178, _822176 = _822174, _822172 = _822170, _822168 = _822166], (12634 ^ _779327) ^ [_990186, _990188, _990190] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _990186), _990188)), _990190) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990186), _990190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990188), _990190)))], (42527 ^ _779327) ^ [_1608258, _1608260, _1608262, _1608264] : [-(hAPP(c_Relation_Oconverse(_1608258, _1608260), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1608258, _1608260), tc_HOL_Obool)), _1608262), _1608264)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1608260, _1608258), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1608258, _1608260), _1608262)), hAPP(c_Relation_Oconverse(_1608258, _1608260), _1608264)))], (4296 ^ _779327) ^ [_844632, _844634, _844636, _844638] : [-(c_List_Orotate(_844638, _844634) = c_List_Orotate(_844636, _844632)), _844638 = _844636, _844634 = _844632], (32770 ^ _779327) ^ [_1375272, _1375274, _1375276] : [class_Orderings_Olinorder(_1375272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375272), _1375274)), hBOOL(hAPP(hAPP(c_member(_1375272), _1375276), _1375274)), 32781 ^ _779327 : [(32788 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375272, tc_HOL_Obool)), _1375274), hAPP(hAPP(c_Set_Oinsert(_1375272), _1375276), c_Orderings_Obot__class_Obot(tc_fun(_1375272, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375272, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1375272, c_Orderings_Oord__class_Omin(_1375272), _1375274) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1375272), _1375276), c_Big__Operators_Olattice_OInf__fin(_1375272, c_Orderings_Oord__class_Omin(_1375272), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375272, tc_HOL_Obool)), _1375274), hAPP(hAPP(c_Set_Oinsert(_1375272), _1375276), c_Orderings_Obot__class_Obot(tc_fun(_1375272, tc_HOL_Obool)))))))], (32782 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375272, tc_HOL_Obool)), _1375274), hAPP(hAPP(c_Set_Oinsert(_1375272), _1375276), c_Orderings_Obot__class_Obot(tc_fun(_1375272, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375272, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1375272, c_Orderings_Oord__class_Omin(_1375272), _1375274) = _1375276)]]], (46156 ^ _779327) ^ [_1697498, _1697500, _1697502] : [-(c_List_Olist_ONil(_1697498) = hAPP(hAPP(c_List_Oappend(_1697498), _1697500), _1697502)), _1697500 = c_List_Olist_ONil(_1697498), _1697502 = c_List_Olist_ONil(_1697498)], (45663 ^ _779327) ^ [_1686133, _1686135, _1686137] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1686133))), -(c_List_Osublist(_1686135, hAPP(hAPP(c_List_Olist_OCons(_1686135), _1686137), c_List_Olist_ONil(_1686135)), _1686133) = c_List_Olist_ONil(_1686135))], (16479 ^ _779327) ^ [_1058668] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1058668) = c_Int_OPls)], (41285 ^ _779327) ^ [_1579020, _1579022, _1579024, _1579026, _1579028] : [hAPP(c_Set_Oimage(_1579020, _1579022, _1579024), c_Orderings_Otop__class_Otop(tc_fun(_1579020, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579022, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1579022, _1579026, _1579028), c_Orderings_Otop__class_Otop(tc_fun(_1579022, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579026, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1579020, _1579026, hAPP(c_Fun_Ocomp(_1579022, _1579026, _1579020, _1579028), _1579024)), c_Orderings_Otop__class_Otop(tc_fun(_1579020, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579026, tc_HOL_Obool)))], (11031 ^ _779327) ^ [_959291, _959293, _959295] : [class_Groups_Ogroup__add(_959291), 11034 ^ _779327 : [(11041 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_959291), _959295) = _959293, -(hAPP(c_Groups_Ouminus__class_Ouminus(_959291), _959293) = _959295)], (11035 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_959291), _959293) = _959295, -(hAPP(c_Groups_Ouminus__class_Ouminus(_959291), _959295) = _959293)]]], (1508 ^ _779327) ^ [_801165, _801167] : [-(class_Groups_Ouminus(_801165)), _801167 = _801165, class_Groups_Ouminus(_801167)], (10837 ^ _779327) ^ [_955945, _955947] : [class_Int_Onumber__ring(_955945), -(hAPP(c_Groups_Ouminus__class_Ouminus(_955945), hAPP(c_Int_Onumber__class_Onumber__of(_955945), _955947)) = hAPP(c_Int_Onumber__class_Onumber__of(_955945), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _955947)))], (42553 ^ _779327) ^ [_1609039, _1609041, _1609043, _1609045, _1609047] : [-(hAPP(c_Relation_Oconverse(_1609039, _1609041), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609043, tc_fun(tc_prod(_1609039, _1609041), tc_HOL_Obool)), _1609045), _1609047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609043, tc_fun(tc_prod(_1609041, _1609039), tc_HOL_Obool)), _1609045), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1609039, _1609041), tc_HOL_Obool), tc_fun(tc_prod(_1609041, _1609039), tc_HOL_Obool), _1609043), c_Relation_Oconverse(_1609039, _1609041)), _1609047)))], (23343 ^ _779327) ^ [_1184738] : [-(c_Nitpick_Oone__frac(_1184738) = c_Nitpick_OAbs__Frac(_1184738, 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))))], (17886 ^ _779327) ^ [_1082945, _1082947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1082945)), c_Int_OBit0(_1082947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1082945), _1082947)))], (18324 ^ _779327) ^ [_1090547] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090547), 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, _1090547)))], (27967 ^ _779327) ^ [_1276717, _1276719, _1276721, _1276723, _1276725] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1276717, tc_fun(_1276719, tc_HOL_Obool)), _1276721), hAPP(hAPP(c_COMBB(tc_fun(_1276719, tc_HOL_Obool), tc_fun(_1276719, tc_HOL_Obool), _1276717), hAPP(c_Set_Oinsert(_1276719), _1276723)), _1276725)) = hAPP(hAPP(c_Set_Oinsert(_1276719), _1276723), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1276717, tc_fun(_1276719, tc_HOL_Obool)), _1276721), _1276725)))], (39575 ^ _779327) ^ [_1530160, _1530162, _1530164] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530160), _1530162)), 39581 ^ _779327 : [(39584 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1530164, 39580 ^ [_1530160, _1530162, _1530164])))], (39582 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530160), 39580 ^ [_1530160, _1530162, _1530164]), _1530162)))]], -(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(_1530160, tc_Nat_Onat), _1530164), _1530162))))], (7834 ^ _779327) ^ [_903132, _903134, _903136, _903138] : [class_Rings_Oordered__ring(_903132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903132), _903134), _903136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903132), _903138), c_Groups_Ozero__class_Ozero(_903132))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903132), _903138), _903136)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903132), _903138), _903134))))], (1678 ^ _779327) ^ [_803290, _803292] : [-(class_Groups_Oab__semigroup__mult(_803290)), _803292 = _803290, class_Groups_Oab__semigroup__mult(_803292)], (12065 ^ _779327) ^ [_979411, _979413, _979415, _979417] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_979411), 12068 ^ _779327 : [(12075 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979411), _979415), _979417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979411), _979413), _979415)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979411), _979413), _979417))))], (12069 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979411), _979413), _979415)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979411), _979413), _979417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979411), _979415), _979417)))]]], (50355 ^ _779327) ^ [_1789766] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1789766) = c_Lazy__Sequence_Osmall__lazy_H(_1789766, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1789766)))], (44530 ^ _779327) ^ [_1654604, _1654606, _1654608] : 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tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1654604, tc_fun(tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool))), tc_List_Olist(_1654604)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654604), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), _1654604), c_COMBS(tc_List_Olist(_1654604), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1654604)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1654604), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1654604)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654604), tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_List_Olist(_1654604))), tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1654604), tc_List_Olist(_1654604)), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), tc_fun(tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_List_Olist(_1654604))), tc_fun(_1654604, tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool))), tc_List_Olist(_1654604)), c_COMBB(tc_fun(tc_List_Olist(_1654604), tc_List_Olist(_1654604)), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), _1654604)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1654604), tc_List_Olist(_1654604)), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), tc_List_Olist(_1654604)), c_COMBB(tc_List_Olist(_1654604), tc_HOL_Obool, tc_List_Olist(_1654604))), c_fequal))), c_List_Olist_OCons(_1654604)))))), hAPP(hAPP(c_COMBC(_1654604, tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool)), _1654604), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1654604))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1654604), c_fconj), hAPP(hAPP(c_COMBC(_1654604, tc_fun(_1654604, tc_HOL_Obool), tc_HOL_Obool), c_member(_1654604)), _1654606)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654604), tc_fun(tc_List_Olist(_1654604), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1654604))), _1654608)))))))], (44278 ^ _779327) ^ [_1648104, _1648106, _1648108, _1648110, _1648112, _1648114, _1648116, _1648118] : [c_Finite__Set_Ofolding__image__simple__idem(_1648104, _1648106, _1648108, _1648110, _1648112, _1648114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648106), _1648116)), hBOOL(hAPP(hAPP(c_member(_1648106), _1648118), _1648116)), -(hAPP(hAPP(_1648108, hAPP(_1648112, _1648118)), hAPP(_1648114, _1648116)) = hAPP(_1648114, _1648116))], (48026 ^ _779327) ^ [_1738990, _1738992, _1738994, _1738996, _1738998] : [c_List_Olist__all2(_1738990, _1738992, _1738994, _1738996, _1738998), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738990)), _1738996) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738992)), _1738998))], (37909 ^ _779327) ^ [_1489393, _1489395, _1489397] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489393, tc_fun(_1489395, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1489393, tc_HOL_Obool))), _1489397) = c_Orderings_Otop__class_Otop(tc_fun(_1489395, tc_HOL_Obool)))], (41283 ^ _779327) ^ [_1578958, _1578960, _1578962, _1578964, _1578966, _1578968] : [-(hAPP(c_Set_Oimage(_1578958, _1578960, hAPP(c_Fun_Ocomp(_1578962, _1578960, _1578958, _1578964), _1578966)), _1578968) = hAPP(c_Set_Oimage(_1578962, _1578960, _1578964), hAPP(c_Set_Oimage(_1578958, _1578962, _1578966), _1578968)))], (30049 ^ _779327) ^ [_1317623, _1317625, _1317627, _1317629, _1317631, _1317633] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317623, tc_fun(_1317625, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1317623, tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_fun(_1317625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317625, tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_fun(_1317625, tc_HOL_Obool)), _1317623), c_COMBC(_1317625, tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317625, tc_prod(_1317623, _1317625)), tc_fun(_1317625, tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), _1317623), hAPP(c_COMBB(tc_prod(_1317623, _1317625), tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool), _1317625), c_member(tc_prod(_1317623, _1317625)))), c_Product__Type_OPair(_1317623, _1317625)))), _1317627)), hAPP(hAPP(c_COMBC(_1317623, tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_fun(_1317625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317625, tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_fun(_1317625, tc_HOL_Obool)), _1317623), c_COMBC(_1317625, tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317625, tc_prod(_1317623, _1317625)), tc_fun(_1317625, tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool)), _1317623), hAPP(c_COMBB(tc_prod(_1317623, _1317625), tc_fun(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool), tc_HOL_Obool), _1317625), c_member(tc_prod(_1317623, _1317625)))), c_Product__Type_OPair(_1317623, _1317625)))), _1317629)), _1317631), _1317633)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1317623, _1317625)), hAPP(hAPP(c_Product__Type_OPair(_1317623, _1317625), _1317631), _1317633)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1317623, _1317625), tc_HOL_Obool)), _1317627), _1317629))))], (44500 ^ _779327) ^ [_1653750, _1653752, _1653754, _1653756, _1653758, _1653760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653750), tc_List_Olist(_1653750))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653750), tc_List_Olist(_1653750)), hAPP(hAPP(c_List_Olist_OCons(_1653750), _1653752), _1653754)), hAPP(hAPP(c_List_Olist_OCons(_1653750), _1653756), _1653758))), c_List_Olex(_1653750, _1653760))), 44505 ^ _779327 : [(44508 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653750)), _1653754) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653750)), _1653758))], (44506 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653750, _1653750)), hAPP(hAPP(c_Product__Type_OPair(_1653750, _1653750), _1653752), _1653756)), _1653760)))]], 44509 ^ _779327 : [(44512 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653750), tc_List_Olist(_1653750))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653750), tc_List_Olist(_1653750)), _1653754), _1653758)), c_List_Olex(_1653750, _1653760))))], (44510 ^ _779327) ^ [] : [-(_1653752 = _1653756)]]], (25894 ^ _779327) ^ [_1233396, _1233398, _1233400, _1233402] : [class_Groups_Ocomm__monoid__add(_1233396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233398), _1233400)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233396), _1233402), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1233398, _1233400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1233396), hAPP(_1233402, _1233398)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233396), _1233402), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1233398), _1233400))))], (44190 ^ _779327) ^ [_1646009, _1646011, _1646013, _1646015] : [class_Lattices_Osemilattice__sup(_1646009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1646009), _1646011)), 44200 ^ _779327 : [(44203 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1646009), 44199 ^ [_1646009, _1646011, _1646013, _1646015]), _1646013))], (44201 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646009), 44199 ^ [_1646009, _1646011, _1646013, _1646015]), _1646011)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1646009), hAPP(hAPP(c_Finite__Set_Ofold(_1646009, _1646009, c_Lattices_Osemilattice__sup__class_Osup(_1646009)), _1646015), _1646011)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1646009), _1646013), _1646015))))], (16736 ^ _779327) ^ [_1063131] : [class_Int_Onumber__ring(_1063131), -(hAPP(c_Int_Onumber__class_Onumber__of(_1063131), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1063131))], (35920 ^ _779327) ^ [_1445831, _1445833, _1445835] : [class_Orderings_Olinorder(_1445831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445831), _1445833)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445831), _1445835)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445831, tc_HOL_Obool)), _1445833), _1445835) = c_Orderings_Obot__class_Obot(tc_fun(_1445831, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1445831), c_Big__Operators_Olinorder__class_OMin(_1445831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445831, tc_HOL_Obool)), _1445833), _1445835))), c_Big__Operators_Olinorder__class_OMin(_1445831, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445831, tc_HOL_Obool)), _1445833), _1445835))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1445831), c_Big__Operators_Olinorder__class_OMin(_1445831, _1445833)), c_Big__Operators_Olinorder__class_OMin(_1445831, _1445835)))], (16573 ^ _779327) ^ [_1060238, _1060240, _1060242] : [class_Groups_Oordered__ab__group__add__abs(_1060238), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060238), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060238), hAPP(c_Groups_Oabs__class_Oabs(_1060238), _1060240)), hAPP(c_Groups_Oabs__class_Oabs(_1060238), _1060242))), hAPP(c_Groups_Oabs__class_Oabs(_1060238), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060238), _1060242), _1060240)))))], (15249 ^ _779327) ^ [_1036305] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036305), c_Int_OMin) = c_Int_Osucc(_1036305))], (40579 ^ _779327) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (9038 ^ _779327) ^ [_924974, _924976, _924978, _924980, _924982] : [class_Rings_Ocomm__semiring__1(_924974), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), _924976), _924978)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), _924980), _924982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), _924980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924974), _924976), _924978)), _924982)))], (40696 ^ _779327) ^ [_1564494, _1564496, _1564498] : [-(hAPP(c_Set_Oimage(tc_prod(_1564494, _1564496), _1564496, c_Product__Type_Osnd(_1564494, _1564496)), _1564498) = hAPP(c_Relation_ORange(_1564494, _1564496), _1564498))], (23538 ^ _779327) ^ [_1189047, _1189049, _1189051, _1189053] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1189047), _1189049), _1189051), _1189053) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1189047)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1189047), _1189049)))], (42953 ^ _779327) ^ [_1618799, _1618801, _1618803] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618799, _1618799)), _1618801), c_Transitive__Closure_Otrancl(_1618799, _1618803)))), 42954 ^ _779327 : [(42955 ^ _779327) ^ [_1618878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1618878)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618799, _1618799)), _1618801), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1618799, _1618799), tc_HOL_Obool), _1618878), _1618803)))]]], (33616 ^ _779327) ^ [] : [-(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)))))], (25790 ^ _779327) ^ [_1231258, _1231260, _1231262, _1231264, _1231266] : [class_Groups_Ocomm__monoid__add(_1231258), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231258), _1231260), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1231262), _1231264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1231266), _1231264))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231258), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1231258, tc_Nat_Onat), _1231260), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1231264))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1231262, _1231266)))], (40438 ^ _779327) ^ [_1557658, _1557660, _1557662, _1557664, _1557666, _1557668, _1557670, _1557672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557658, _1557660), tc_HOL_Obool)), _1557662), hAPP(hAPP(c_Product__Type_OSigma(_1557658, _1557660), _1557664), hAPP(c_COMBK(tc_fun(_1557660, tc_HOL_Obool), _1557658), _1557666)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557660, _1557668), tc_HOL_Obool)), _1557670), hAPP(hAPP(c_Product__Type_OSigma(_1557660, _1557668), _1557666), hAPP(c_COMBK(tc_fun(_1557668, tc_HOL_Obool), _1557660), _1557672)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557658, _1557668), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1557658, _1557660, _1557668), _1557662), _1557670)), hAPP(hAPP(c_Product__Type_OSigma(_1557658, _1557668), _1557664), hAPP(c_COMBK(tc_fun(_1557668, tc_HOL_Obool), _1557658), _1557672)))))], (39882 ^ _779327) ^ [_1536975, _1536977] : [-(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), _1536975)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1536977))))))], (37735 ^ _779327) ^ [] : [-(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)))], (3474 ^ _779327) ^ [_831771, _831773] : [_831773 = _831771, -(c_New__Random__Sequence_Oneg__single(_831773) = c_New__Random__Sequence_Oneg__single(_831771))], (47556 ^ _779327) ^ [_1728803, _1728805, _1728807, _1728809] : [_1728803 = _1728805, -(c_List_Oremove1(_1728807, _1728803, hAPP(hAPP(c_List_Olist_OCons(_1728807), _1728805), _1728809)) = _1728809)], (4646 ^ _779327) ^ [_850139, _850141] : [_850141 = _850139, -(c_Lazy__Sequence_Osingle(_850141) = c_Lazy__Sequence_Osingle(_850139))], (20325 ^ _779327) ^ [_1126260, _1126262, _1126264, _1126266] : [class_Fields_Olinordered__field__inverse__zero(_1126260), 20328 ^ _779327 : [(20329 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126262), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126260), _1126264), _1126266))), 20332 ^ _779327 : [(20339 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), c_Groups_Ozero__class_Ozero(_1126260)), _1126266))), 20342 ^ _779327 : [(20349 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), _1126266), c_Groups_Ozero__class_Ozero(_1126260)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126262), c_Groups_Ozero__class_Ozero(_1126260))))], (20343 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), _1126266), c_Groups_Ozero__class_Ozero(_1126260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126260), _1126262), _1126266))))]]], (20333 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), c_Groups_Ozero__class_Ozero(_1126260)), _1126266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126260), _1126262), _1126266)), _1126264)))]]], (20355 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126262), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126260), _1126264), _1126266)))), 20358 ^ _779327 : [(20361 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126260), _1126262), _1126266)), _1126264))], (20359 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), c_Groups_Ozero__class_Ozero(_1126260)), _1126266)))]], 20362 ^ _779327 : [(20365 ^ _779327) ^ [] : [20366 ^ _779327 : [(20369 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126260), _1126262), _1126266)))], (20367 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), _1126266), c_Groups_Ozero__class_Ozero(_1126260))))]], 20370 ^ _779327 : [(20373 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126260), _1126262), c_Groups_Ozero__class_Ozero(_1126260)))], (20371 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), _1126266), c_Groups_Ozero__class_Ozero(_1126260)))]]], (20363 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1126260), c_Groups_Ozero__class_Ozero(_1126260)), _1126266))]]]]], (22131 ^ _779327) ^ [_1161673, _1161675, _1161677, _1161679, _1161681] : [-(hAPP(c_Product__Type_Osnd(_1161673, _1161675), hAPP(c_Product__Type_Oapsnd(_1161677, _1161675, _1161673, _1161679), _1161681)) = hAPP(_1161679, hAPP(c_Product__Type_Osnd(_1161673, _1161677), _1161681)))], (15808 ^ _779327) ^ [_1046699, _1046701] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046699), _1046701) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1046699 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1046699 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (50800 ^ _779327) ^ [_1799499, _1799501] : [-(c_List_Olist__all(_1799499, _1799501, c_List_Olist_ONil(_1799499)))], (17806 ^ _779327) ^ [_1081355, _1081357] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081355)))), _1081357) = 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)))), _1081355)), _1081357))], (51187 ^ _779327) ^ [_1807054, _1807056, _1807058] : [-(_1807056 = _1807058), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1807054, _1807054, hAPP(hAPP(c_COMBB(tc_fun(_1807054, tc_HOL_Obool), tc_fun(_1807054, tc_HOL_Obool), _1807054), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1807054), c_fNot)), c_fequal)), _1807056), _1807058)))], (42579 ^ _779327) ^ [_1609591, _1609593, _1609595, _1609597] : [-(hAPP(c_Relation_Oconverse(_1609591, _1609593), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1609591, _1609593), tc_HOL_Obool)), _1609595), _1609597)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1609593, _1609591), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1609591, _1609593), _1609595)), hAPP(c_Relation_Oconverse(_1609591, _1609593), _1609597)))], (14881 ^ _779327) ^ [_1029658, _1029660, _1029662, _1029664] : [class_Divides_Osemiring__div(_1029658), -(_1029660 = c_Groups_Ozero__class_Ozero(_1029658)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029658), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029658), _1029662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029658), _1029664), _1029660))), _1029660) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029658), _1029664), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1029658), _1029662), _1029660)))], (17232 ^ _779327) ^ [_1071773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071773)), -(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), _1071773))))], (28150 ^ _779327) ^ [_1280030, _1280032, _1280034] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280030), _1280032)), 28153 ^ _779327 : [(28173 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280030, tc_Nat_Onat), _1280034), _1280032) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 28174 ^ _779327 : [(28175 ^ _779327) ^ [_1280511] : [hBOOL(hAPP(hAPP(c_member(_1280030), _1280511), _1280032)), hAPP(_1280034, _1280511) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 28183 ^ _779327 : [(28188 ^ _779327) ^ [] : [hAPP(_1280034, 28182 ^ [_1280030, _1280032, _1280034, _1280511]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28186 ^ _779327) ^ [] : [_1280511 = 28182 ^ [_1280030, _1280032, _1280034, _1280511]], (28184 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280030), 28182 ^ [_1280030, _1280032, _1280034, _1280511]), _1280032)))]]]]], (28154 ^ _779327) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280030, tc_Nat_Onat), _1280034), _1280032) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 28158 ^ _779327 : [(28163 ^ _779327) ^ [_1280350] : [hBOOL(hAPP(hAPP(c_member(_1280030), _1280350), _1280032)), -(28157 ^ [_1280030, _1280032, _1280034] = _1280350), -(hAPP(_1280034, _1280350) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28161 ^ _779327) ^ [] : [-(hAPP(_1280034, 28157 ^ [_1280030, _1280032, _1280034]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28159 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280030), 28157 ^ [_1280030, _1280032, _1280034]), _1280032)))]]]]], (21512 ^ _779327) ^ [_1149565, _1149567, _1149569, _1149571] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1149565, _1149567), _1149569)), hBOOL(hAPP(hAPP(_1149567, _1149571), _1149569)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1149565, _1149567), _1149571)))], (92 ^ _779327) ^ [_780549, _780551, _780553, _780555, _780557, _780559] : [-(c_Nitpick_Oless__frac(_780557, _780553, _780549)), c_Nitpick_Oless__frac(_780559, _780555, _780551), _780559 = _780557, _780555 = _780553, _780551 = _780549], (34223 ^ _779327) ^ [_1407022] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1407022) = 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), _1407022), 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))))))], (320 ^ _779327) ^ [_784157, _784159] : [-(class_Fields_Ofield(_784157)), _784159 = _784157, class_Fields_Ofield(_784159)], (45570 ^ _779327) ^ [_1683324, _1683326, _1683328, _1683330, _1683332, _1683334, _1683336, _1683338] : [-(hAPP(hAPP(c_List_Ozip(_1683324, _1683326), hAPP(hAPP(c_List_Omap(_1683328, _1683324), _1683330), _1683332)), hAPP(hAPP(c_List_Omap(_1683334, _1683326), _1683336), _1683338)) = hAPP(hAPP(c_List_Omap(tc_prod(_1683328, _1683334), tc_prod(_1683324, _1683326)), hAPP(c_Product__Type_Oprod_Oprod__case(_1683328, _1683334, tc_prod(_1683324, _1683326)), hAPP(hAPP(c_COMBC(_1683328, tc_fun(_1683334, _1683326), tc_fun(_1683334, tc_prod(_1683324, _1683326))), hAPP(hAPP(c_COMBB(tc_fun(_1683326, tc_prod(_1683324, _1683326)), tc_fun(tc_fun(_1683334, _1683326), tc_fun(_1683334, tc_prod(_1683324, _1683326))), _1683328), c_COMBB(_1683326, tc_prod(_1683324, _1683326), _1683334)), hAPP(hAPP(c_COMBB(_1683324, tc_fun(_1683326, tc_prod(_1683324, _1683326)), _1683328), c_Product__Type_OPair(_1683324, _1683326)), _1683330))), _1683336))), hAPP(hAPP(c_List_Ozip(_1683328, _1683334), _1683332), _1683338)))], (16345 ^ _779327) ^ [_1056304, _1056306] : [class_Int_Onumber__ring(_1056304), 16348 ^ _779327 : [(16355 ^ _779327) ^ [] : [c_Int_Oiszero(_1056304, hAPP(c_Int_Onumber__class_Onumber__of(_1056304), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1056306)))), -(c_Groups_Ozero__class_Ozero(_1056304) = hAPP(c_Int_Onumber__class_Onumber__of(_1056304), _1056306))], (16349 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_1056304) = hAPP(c_Int_Onumber__class_Onumber__of(_1056304), _1056306), -(c_Int_Oiszero(_1056304, hAPP(c_Int_Onumber__class_Onumber__of(_1056304), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1056306)))))]]], (20851 ^ _779327) ^ [_1136437, _1136439] : [_1136437 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1136437, _1136439) = _1136439)], (41295 ^ _779327) ^ [_1579279, _1579281, _1579283, _1579285, _1579287, _1579289] : [c_Fun_Oinj__on(_1579279, _1579281, hAPP(c_Fun_Ocomp(_1579283, _1579281, _1579279, _1579285), _1579287), _1579289), -(c_Fun_Oinj__on(_1579279, _1579283, _1579287, _1579289))], (5492 ^ _779327) ^ [_863126, _863128, _863130, _863132] : [-(tc_prod(_863132, _863128) = tc_prod(_863130, _863126)), _863132 = _863130, _863128 = _863126], (28918 ^ _779327) ^ [_1294813, _1294815, _1294817] : [class_Orderings_Oorder(_1294813), 28921 ^ _779327 : [(28928 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294813), _1294815), _1294817))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1294813, _1294815), _1294817) = c_Orderings_Obot__class_Obot(tc_fun(_1294813, tc_HOL_Obool)))], (28922 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1294813, _1294815), _1294817) = c_Orderings_Obot__class_Obot(tc_fun(_1294813, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294813), _1294815), _1294817))]]], (38271 ^ _779327) ^ [_1499635, _1499637] : [c_Equiv__Relations_Oequivp(_1499635, _1499637), 38274 ^ _779327 : [(38281 ^ _779327) ^ [_1499828, _1499830] : [hAPP(_1499637, _1499830) = hAPP(_1499637, _1499828), -(hBOOL(hAPP(hAPP(_1499637, _1499830), _1499828)))], (38275 ^ _779327) ^ [_1499729, _1499731] : [hBOOL(hAPP(hAPP(_1499637, _1499731), _1499729)), -(hAPP(_1499637, _1499731) = hAPP(_1499637, _1499729))]]], (45376 ^ _779327) ^ [_1679136, _1679138] : [-(_1679136 = c_List_Olist_ONil(_1679138)), -(c_Random_Oselect__weight(_1679138, hAPP(hAPP(c_List_Omap(_1679138, tc_prod(tc_Code__Numeral_Ocode__numeral, _1679138)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1679138), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1679136)) = c_Random_Oselect(_1679138, _1679136))], (48582 ^ _779327) ^ [_1751952, _1751954] : [-(hAPP(c_List_Ofilter(_1751952, _1751954), c_List_Olist_ONil(_1751952)) = c_List_Olist_ONil(_1751952))], (14865 ^ _779327) ^ [_1029368, _1029370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1029370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029368), _1029370)), _1029368)))], (11999 ^ _779327) ^ [_978337, _978339] : [class_Groups_Ocomm__monoid__add(_978337), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978337), _978339), c_Groups_Ozero__class_Ozero(_978337)) = _978339)], (8238 ^ _779327) ^ [_910665, _910667, _910669] : [class_Rings_Olinordered__semidom(_910665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910665), c_Groups_Ozero__class_Ozero(_910665)), _910667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910665), c_Groups_Ozero__class_Ozero(_910665)), hAPP(hAPP(c_Power_Opower__class_Opower(_910665), _910667), _910669))))], (26207 ^ _779327) ^ [_1239825, _1239827, _1239829, _1239831] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239825), _1239827)), 26210 ^ _779327 : [(26211 ^ _779327) ^ [_1239983] : [26213 ^ _779327 : [(26219 ^ _779327) ^ [] : [-(_1239983 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26215 ^ [_1239825, _1239827, _1239829, _1239831, _1239983]), 26212 ^ [_1239825, _1239827, _1239829, _1239831, _1239983]))], (26217 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26215 ^ [_1239825, _1239827, _1239829, _1239831, _1239983]), _1239829)))], (26214 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26212 ^ [_1239825, _1239827, _1239829, _1239831, _1239983]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1239827))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239983), _1239831)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1239825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239983), _1239827)), _1239831)))]]], (46822 ^ _779327) ^ [_1713644] : [-(hBOOL(hAPP(c_List_Odistinct(_1713644), c_List_Olist_ONil(_1713644))))], (52580 ^ _779327) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (41764 ^ _779327) ^ [_1589664, _1589666] : [-(c_Hilbert__Choice_OEps(_1589664, hAPP(c_fequal, _1589666)) = _1589666)], (48527 ^ _779327) ^ [_1750794, _1750796, _1750798] : [hAPP(c_List_Ofilter(_1750794, _1750796), _1750798) = _1750798, 48530 ^ _779327 : [(48531 ^ _779327) ^ [_1750885] : [hBOOL(hAPP(hAPP(c_member(_1750794), _1750885), hAPP(c_List_Oset(_1750794), _1750798))), -(hBOOL(hAPP(_1750796, _1750885)))]]], (40954 ^ _779327) ^ [_1570889, _1570891, _1570893, _1570895, _1570897] : [-(hAPP(c_Relation_ODomain(_1570889, _1570891), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1570889, _1570891)), hAPP(hAPP(c_Product__Type_OPair(_1570889, _1570891), _1570893), _1570895)), _1570897)) = hAPP(hAPP(c_Set_Oinsert(_1570889), _1570893), hAPP(c_Relation_ODomain(_1570889, _1570891), _1570897)))], (52588 ^ _779327) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (48365 ^ _779327) ^ [_1746470, _1746472] : [c_List_Olist_ONil(_1746470) = c_List_Oconcat(_1746470, _1746472), 48368 ^ _779327 : [(48369 ^ _779327) ^ [_1746561] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1746470)), _1746561), hAPP(c_List_Oset(tc_List_Olist(_1746470)), _1746472))), -(_1746561 = c_List_Olist_ONil(_1746470))]]], (580 ^ _779327) ^ [_788219, _788221, _788223, _788225, _788227, _788229] : [-(c_Relation_Ototal__on(_788227, _788223, _788219)), c_Relation_Ototal__on(_788229, _788225, _788221), _788229 = _788227, _788225 = _788223, _788221 = _788219], (5450 ^ _779327) ^ [_862509, _862511, _862513, _862515] : [-(tc_fun(_862515, _862511) = tc_fun(_862513, _862509)), _862515 = _862513, _862511 = _862509], (31481 ^ _779327) ^ [_1350191, _1350193] : [class_Complete__Lattice_Ocomplete__lattice(_1350191), c_Orderings_Oorder__class_Omono(_1350191, _1350191, _1350193), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350191), hAPP(_1350193, c_Inductive_Ocomplete__lattice__class_Olfp(_1350191, _1350193))), c_Inductive_Ocomplete__lattice__class_Olfp(_1350191, _1350193))))], (40448 ^ _779327) ^ [_1558017, _1558019, _1558021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1558017, _1558017), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1558017, _1558017, _1558017), _1558019), _1558021)), _1558019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1558017, _1558019)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1558017, _1558021)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1558017, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1558017, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1558017, tc_HOL_Obool), tc_fun(_1558017, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1558017, _1558019))))], (11069 ^ _779327) ^ [_959892, _959894, _959896] : [class_Groups_Ogroup__add(_959892), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959892), _959894), hAPP(c_Groups_Ouminus__class_Ouminus(_959892), _959896)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959892), _959894), _959896))], (43857 ^ _779327) ^ [_1638779, _1638781] : [-(hAPP(c_Relation_OField(_1638779), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1638779, _1638779), tc_HOL_Obool), _1638781)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638779, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1638779, _1638779), tc_HOL_Obool), tc_fun(_1638779, tc_HOL_Obool), c_Relation_OField(_1638779)), _1638781)))], (35153 ^ _779327) ^ [_1428346, _1428348] : [class_Lattices_Oboolean__algebra(_1428346), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428346), hAPP(c_Groups_Ouminus__class_Ouminus(_1428346), _1428348)), _1428348) = c_Orderings_Obot__class_Obot(_1428346))], (26394 ^ _779327) ^ [_1243962, _1243964] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1243962, _1243964)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243964), _1243962)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5844 ^ _779327) ^ [_871487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871487), _871487))], (37617 ^ _779327) ^ [_1483320, _1483322, _1483324, _1483326, _1483328] : [-(hAPP(c_Set_Oimage(_1483320, _1483322, hAPP(hAPP(c_COMBB(_1483324, _1483322, _1483320), _1483326), _1483328)), c_Orderings_Otop__class_Otop(tc_fun(_1483320, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1483324, _1483322, _1483326), hAPP(c_Set_Oimage(_1483320, _1483324, _1483328), c_Orderings_Otop__class_Otop(tc_fun(_1483320, tc_HOL_Obool)))))], (8590 ^ _779327) ^ [_916890, _916892] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _916890), _916892) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _916890 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _916892 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47382 ^ _779327) ^ [_1725112, _1725114, _1725116] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1725112)), _1725114), c_List_Olists(_1725112, _1725116)))), 47383 ^ _779327 : [(47386 ^ _779327) ^ [_1725240, _1725242] : [_1725114 = hAPP(hAPP(c_List_Olist_OCons(_1725112), _1725242), _1725240), hBOOL(hAPP(hAPP(c_member(_1725112), _1725242), _1725116)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1725112)), _1725240), c_List_Olists(_1725112, _1725116)))], (47384 ^ _779327) ^ [] : [_1725114 = c_List_Olist_ONil(_1725112)]]], (38255 ^ _779327) ^ [_1498897, _1498899] : [-(hBOOL(hAPP(hAPP(c_member(_1498897), _1498899), c_Orderings_Otop__class_Otop(tc_fun(_1498897, tc_HOL_Obool)))))], (17828 ^ _779327) ^ [_1081815, _1081817] : [-(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), _1081815)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1081817)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081815))) = 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), _1081817)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081815)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (2346 ^ _779327) ^ [_813585, _813587, _813589, _813591] : [-(c_Nitpick_Onat__lcm(_813591, _813587) = c_Nitpick_Onat__lcm(_813589, _813585)), _813591 = _813589, _813587 = _813585], (39353 ^ _779327) ^ [_1524204, _1524206, _1524208, _1524210] : [-(c_Fun_Oinj__on(_1524204, tc_prod(_1524206, _1524204), 39351 ^ [_1524204, _1524206, _1524208, _1524210], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524206, tc_fun(_1524204, tc_HOL_Obool)), _1524208), _1524210)))], (31598 ^ _779327) ^ [_1353423, _1353425, _1353427, _1353429, _1353431, _1353433] : [-(hBOOL(hAPP(hAPP(c_member(_1353423), _1353425), c_SetInterval_Oord_OatLeastLessThan(_1353423, _1353427, _1353429, _1353431, _1353433)))), hBOOL(hAPP(hAPP(_1353427, _1353431), _1353425)), hBOOL(hAPP(hAPP(_1353429, _1353425), _1353433))], (40631 ^ _779327) ^ [] : [-(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)))))], (10395 ^ _779327) ^ [_947746, _947748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947748)), 10402 ^ _779327 : [(10409 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _947746), _947748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _947746)), hAPP(c_Int_Onat, _947748))))], (10403 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _947746)), hAPP(c_Int_Onat, _947748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _947746), _947748)))]]], (25936 ^ _779327) ^ [_1234302, _1234304] : [25938 ^ _779327 : [(25941 ^ _779327) ^ [] : [hBOOL(hAPP(_1234304, 25937 ^ [_1234302, _1234304]))], (25939 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25937 ^ [_1234302, _1234304]), _1234302)))]], 25942 ^ _779327 : [(25943 ^ _779327) ^ [_1234453] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1234453), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1234302))), -(hBOOL(hAPP(_1234304, _1234453)))]]], (48979 ^ _779327) ^ [_1761188, _1761190] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1761188, _1761190)))], (52268 ^ _779327) ^ [_1830885, _1830887] : [c_Equiv__Relations_Oequivp(_1830885, _1830887), -(c_Equiv__Relations_Opart__equivp(_1830885, _1830887))], (45510 ^ _779327) ^ [_1681824, _1681826, _1681828] : [hAPP(hAPP(c_List_Olist_OCons(_1681824), _1681826), _1681828) = c_List_Olist_ONil(_1681824)], (52720 ^ _779327) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52772 ^ _779327) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (42619 ^ _779327) ^ [_1610433, _1610435, _1610437] : [-(hAPP(c_Relation_ODomain(_1610433, _1610435), hAPP(c_Relation_Oconverse(_1610435, _1610433), _1610437)) = hAPP(c_Relation_ORange(_1610435, _1610433), _1610437))], (21612 ^ _779327) ^ [_1151810, _1151812] : [_1151810 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1151812, _1151810) = 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), _1151812)))], (48708 ^ _779327) ^ [_1755742, _1755744, _1755746] : [class_Groups_Oab__semigroup__add(_1755742), -(c_List_Ofoldr(_1755742, _1755742, c_Groups_Oplus__class_Oplus(_1755742), _1755744, _1755746) = hAPP(c_List_Ofoldl(_1755742, _1755742, c_Groups_Oplus__class_Oplus(_1755742), _1755746), _1755744))], (18308 ^ _779327) ^ [] : [-(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))))], (45508 ^ _779327) ^ [_1681772, _1681774, _1681776] : [c_List_Olist_ONil(_1681772) = hAPP(hAPP(c_List_Olist_OCons(_1681772), _1681774), _1681776)], (2 ^ _779327) ^ [_779354] : [-(_779354 = _779354)], (15265 ^ _779327) ^ [_1036555, _1036557] : [class_Divides_Osemiring__div(_1036555), -(c_Divides_Odiv__class_Omod(_1036555, _1036557, c_Groups_Ozero__class_Ozero(_1036555)) = _1036557)], (50841 ^ _779327) ^ [_1800265, _1800267, _1800269, _1800271] : [-(c_List_Olist__all(_1800265, _1800267, hAPP(hAPP(c_List_Oappend(_1800265), _1800269), _1800271))), c_List_Olist__all(_1800265, _1800267, _1800269), c_List_Olist__all(_1800265, _1800267, _1800271)], (47407 ^ _779327) ^ [_1725728, _1725730, _1725732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725728), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725730)), _1725732))), -(c_List_Obutlast(_1725730, hAPP(hAPP(c_List_Otake(_1725730), _1725728), _1725732)) = hAPP(hAPP(c_List_Otake(_1725730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1725728), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1725732))], (12403 ^ _779327) ^ [_985731, _985733, _985735] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985731), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _985733), _985735)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985731), _985733)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985731), _985735)))], (41683 ^ _779327) ^ [_1587867, _1587869, _1587871, _1587873, _1587875] : [c_Finite__Set_Ofolding__idem(_1587867, _1587869, _1587871, _1587873), -(hAPP(c_Fun_Ocomp(_1587869, _1587869, _1587869, hAPP(_1587871, _1587875)), hAPP(_1587871, _1587875)) = hAPP(_1587871, _1587875))], (30837 ^ _779327) ^ [_1336926, _1336928, _1336930, _1336932, _1336934] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1336926, _1336928, _1336930), _1336932), _1336934)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1336926, _1336928)), hAPP(hAPP(c_Product__Type_OPair(_1336926, _1336928), _1336932), _1336934)), _1336930)))], (22759 ^ _779327) ^ [_1173394, _1173396] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173394)), hAPP(c_Nat_OSuc, _1173396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1173394))), 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, _1173396))), 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)), _1173396)))))], (48672 ^ _779327) ^ [_1754081, _1754083] : [-(c_List_Oconcat(tc_List_Olist(_1754081), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754081), tc_List_Olist(tc_List_Olist(_1754081))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1754081)), _1754081, c_List_Olist_ONil(tc_List_Olist(_1754081)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1754081), tc_List_Olist(tc_List_Olist(_1754081))), _1754081), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754081), tc_List_Olist(tc_List_Olist(_1754081)), tc_List_Olist(tc_List_Olist(_1754081))), c_List_Olist_OCons(tc_List_Olist(_1754081))), c_List_Olist_ONil(tc_List_Olist(_1754081)))))), _1754083)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754081), tc_List_Olist(_1754081)), c_List_Otl(_1754081)), hAPP(c_List_Ofilter(tc_List_Olist(_1754081), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1754081)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754081), tc_List_Olist(_1754081), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1754081)))), _1754083)))], (18879 ^ _779327) ^ [_1100917, _1100919] : [c_Nat__Transfer_Ois__nat(_1100917), c_Nat__Transfer_Ois__nat(_1100919), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1100917, _1100919)))], (53034 ^ _779327) ^ [] : [-(hBOOL(c_fTrue))], (52934 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40404 ^ _779327) ^ [_1556715, _1556717, _1556719, _1556721] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556715, _1556717, _1556719), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1556715, _1556717), tc_HOL_Obool))), _1556721) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1556715, _1556719), tc_HOL_Obool)))], (11519 ^ _779327) ^ [_969731, _969733, _969735, _969737, _969739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969731), _969733)), 11522 ^ _779327 : [(11529 ^ _779327) ^ [] : [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), _969733), _969731)), _969735)), _969737) = _969739, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969733), _969735)), _969737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969731), _969735)), _969739))], (11523 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969733), _969735)), _969737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969731), _969735)), _969739), -(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), _969733), _969731)), _969735)), _969737) = _969739)]]], (5634 ^ _779327) ^ [_868289] : [_868289 = hAPP(c_Nat_OSuc, _868289)], (31075 ^ _779327) ^ [_1342021, _1342023, _1342025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342021)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1342023), _1342025)), 31082 ^ _779327 : [(31083 ^ _779327) ^ [_1342211] : [31085 ^ _779327 : [(31091 ^ _779327) ^ [] : [-(_1342211 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 31087 ^ [_1342021, _1342023, _1342025, _1342211]), 31084 ^ [_1342021, _1342023, _1342025, _1342211]))], (31089 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31087 ^ [_1342021, _1342023, _1342025, _1342211]), _1342025)))], (31086 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31084 ^ [_1342021, _1342023, _1342025, _1342211]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1342021))))]], -(_1342211 = _1342023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1342211), _1342021) = _1342023]]], (11015 ^ _779327) ^ [_959050, _959052, _959054] : [class_Groups_Ogroup__add(_959050), 11018 ^ _779327 : [(11025 ^ _779327) ^ [] : [_959052 = _959054, -(hAPP(c_Groups_Ouminus__class_Ouminus(_959050), _959052) = hAPP(c_Groups_Ouminus__class_Ouminus(_959050), _959054))], (11019 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_959050), _959052) = hAPP(c_Groups_Ouminus__class_Ouminus(_959050), _959054), -(_959052 = _959054)]]], (17808 ^ _779327) ^ [_1081404, _1081406] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081404)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081406)) = 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)))), _1081404)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081406)))], (28632 ^ _779327) ^ [_1289538, _1289540, _1289542, _1289544] : [_1289544 = c_Orderings_Obot__class_Obot(tc_fun(_1289540, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1289538, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1289540, _1289538, _1289542), _1289544))], (49429 ^ _779327) ^ [_1769651, _1769653] : [hBOOL(hAPP(c_List_Odistinct(_1769651), hAPP(c_List_Orev(_1769651), _1769653))), -(hBOOL(hAPP(c_List_Odistinct(_1769651), _1769653)))], (9326 ^ _779327) ^ [_930438] : [-(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), _930438))))], (49883 ^ _779327) ^ [_1779167, _1779169] : [-(c_List_OdropWhile(_1779167, _1779169, c_List_Olist_ONil(_1779167)) = c_List_Olist_ONil(_1779167))], (1198 ^ _779327) ^ [_797290, _797292] : [-(class_Rings_Oring__no__zero__divisors(_797290)), _797292 = _797290, class_Rings_Oring__no__zero__divisors(_797292)], (820 ^ _779327) ^ [_791845, _791847, _791849, _791851, _791853, _791855, _791857, _791859, _791861, _791863] : [-(c_List_Olist__all2(_791861, _791857, _791853, _791849, _791845)), c_List_Olist__all2(_791863, _791859, _791855, _791851, _791847), _791863 = _791861, _791859 = _791857, _791855 = _791853, _791851 = _791849, _791847 = _791845], (7588 ^ _779327) ^ [_898678, _898680] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898678), _898680) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_898678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_898680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9004 ^ _779327) ^ [_924278, _924280] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924278)), _924280) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _924278), _924280)))], (53018 ^ _779327) ^ [_1840683, _1840685, _1840687, _1840689, _1840691, _1840693] : [-(hAPP(hAPP(hAPP(c_COMBS(_1840683, _1840685, _1840687), _1840689), _1840691), _1840693) = hAPP(hAPP(_1840689, _1840693), hAPP(_1840691, _1840693)))], (27749 ^ _779327) ^ [_1272375, _1272377, _1272379, _1272381] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272375, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1272377, tc_fun(_1272375, tc_HOL_Obool)), _1272379), _1272381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272377, tc_fun(_1272375, tc_HOL_Obool)), _1272379), hAPP(hAPP(c_COMBB(tc_fun(_1272375, tc_HOL_Obool), tc_fun(_1272375, tc_HOL_Obool), _1272377), c_Groups_Ouminus__class_Ouminus(tc_fun(_1272375, tc_HOL_Obool))), _1272381)))], (1758 ^ _779327) ^ [_804290, _804292] : [-(class_Divides_Osemiring__div(_804290)), _804292 = _804290, class_Divides_Osemiring__div(_804292)], (47704 ^ _779327) ^ [_1732176, _1732178, _1732180, _1732182] : [-(hBOOL(hAPP(c_List_Olistsp(_1732176, _1732178), hAPP(hAPP(c_List_Oappend(_1732176), _1732180), _1732182)))), hBOOL(hAPP(c_List_Olistsp(_1732176, _1732178), _1732180)), hBOOL(hAPP(c_List_Olistsp(_1732176, _1732178), _1732182))], (35089 ^ _779327) ^ [_1426806, _1426808, _1426810, _1426812] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426806, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426806, tc_HOL_Obool)), _1426808), _1426810)), _1426812) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426806, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426806, tc_HOL_Obool)), _1426808), _1426812)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426806, tc_HOL_Obool)), _1426810), _1426812)))], (41162 ^ _779327) ^ [_1575673, _1575675, _1575677, _1575679] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1575673), _1575675)), 41168 ^ _779327 : [(41171 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1575677), hAPP(_1575679, 41167 ^ [_1575673, _1575675, _1575677, _1575679])))], (41169 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575673), 41167 ^ [_1575673, _1575675, _1575677, _1575679]), _1575675)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1575677), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1575673, tc_fun(_1575677, tc_HOL_Obool)), _1575675), _1575679))))], (40749 ^ _779327) ^ [_1565635] : [class_Orderings_Owellorder(_1565635), -(c_Wellfounded_Owf(_1565635, hAPP(c_Set_OCollect(tc_prod(_1565635, _1565635)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565635, _1565635, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1565635)))))], (52954 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (23273 ^ _779327) ^ [_1183261, _1183263, _1183265, _1183267, _1183269, _1183271, _1183273, _1183275, _1183277] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1183261, _1183263, _1183265, _1183267), hAPP(hAPP(c_Product__Type_Oscomp(_1183261, _1183269, _1183271, tc_prod(_1183263, _1183265)), _1183273), _1183275)), _1183277) = hAPP(hAPP(c_Product__Type_Oscomp(_1183261, _1183269, _1183271, _1183267), _1183273), hAPP(hAPP(c_COMBC(_1183269, tc_fun(_1183263, tc_fun(_1183265, _1183267)), tc_fun(_1183271, _1183267)), hAPP(hAPP(c_COMBB(tc_fun(_1183271, tc_prod(_1183263, _1183265)), tc_fun(tc_fun(_1183263, tc_fun(_1183265, _1183267)), tc_fun(_1183271, _1183267)), _1183269), c_Product__Type_Oscomp(_1183271, _1183263, _1183265, _1183267)), _1183275)), _1183277)))], (46299 ^ _779327) ^ [_1700976, _1700978, _1700980, _1700982, _1700984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1700976, tc_HOL_Obool)), hAPP(c_List_Oset(_1700976), _1700978)), _1700980)), hBOOL(hAPP(hAPP(c_member(_1700976), _1700982), _1700980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1700976, tc_HOL_Obool)), hAPP(c_List_Oset(_1700976), hAPP(hAPP(c_List_Olist__update(_1700976, _1700978), _1700984), _1700982))), _1700980)))], (21712 ^ _779327) ^ [_1153267, _1153269, _1153271, _1153273] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153267, _1153269), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1153271), _1153273))), -(_1153269 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1153267), _1153269) = _1153271)], (7634 ^ _779327) ^ [_899492, _899494] : [class_Rings_Olinordered__ring(_899492), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899492), c_Groups_Ozero__class_Ozero(_899492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899492), _899494), _899494))))], (35571 ^ _779327) ^ [_1437759, _1437761, _1437763, _1437765, _1437767, _1437769, _1437771, _1437773] : [c_Finite__Set_Ofolding__image__simple(_1437759, _1437761, _1437763, _1437765, _1437767, _1437769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437761), _1437771)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1437761), _1437773)), -(hAPP(hAPP(_1437763, hAPP(_1437769, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437761, tc_HOL_Obool)), _1437771), _1437773))), hAPP(_1437769, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437761, tc_HOL_Obool)), _1437771), _1437773))) = hAPP(hAPP(_1437763, hAPP(_1437769, _1437771)), hAPP(_1437769, _1437773)))], (7374 ^ _779327) ^ [_894968, _894970, _894972, _894974] : [class_Orderings_Oord(_894968), 7377 ^ _779327 : [(7386 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_894970, _894968)), _894972), _894974))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894970, _894968)), _894972), _894974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894970, _894968)), _894974), _894972)))], (7378 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_894970, _894968)), _894972), _894974)), 7381 ^ _779327 : [(7384 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894970, _894968)), _894974), _894972))], (7382 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894970, _894968)), _894972), _894974)))]]]]], (718 ^ _779327) ^ [_790386, _790388, _790390, _790392, _790394, _790396, _790398, _790400] : [-(c_List_Olistrelp(_790398, _790394, _790390, _790386)), c_List_Olistrelp(_790400, _790396, _790392, _790388), _790400 = _790398, _790396 = _790394, _790392 = _790390, _790388 = _790386], (29486 ^ _779327) ^ [_1305864, _1305866, _1305868, _1305870, _1305872, _1305874, _1305876, _1305878] : [hBOOL(hAPP(hAPP(c_member(_1305864), _1305866), _1305868)), hBOOL(hAPP(hAPP(hAPP(_1305870, _1305866), _1305872), _1305874)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305864, tc_fun(_1305876, tc_fun(_1305878, tc_HOL_Obool))), _1305868), _1305870), _1305872), _1305874)))], (16511 ^ _779327) ^ [_1059145, _1059147] : [class_Groups_Oordered__ab__group__add__abs(_1059145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059145), c_Groups_Ozero__class_Ozero(_1059145)), _1059147)), -(hAPP(c_Groups_Oabs__class_Oabs(_1059145), _1059147) = _1059147)], (32794 ^ _779327) ^ [_1375796, _1375798, _1375800] : [class_Orderings_Olinorder(_1375796), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375796), _1375798)), hBOOL(hAPP(hAPP(c_member(_1375796), _1375800), _1375798)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1375796), _1375800), c_Big__Operators_Olattice_OInf__fin(_1375796, c_Orderings_Oord__class_Omin(_1375796), _1375798)) = c_Big__Operators_Olattice_OInf__fin(_1375796, c_Orderings_Oord__class_Omin(_1375796), _1375798))], (37897 ^ _779327) ^ [_1488949, _1488951, _1488953, _1488955] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1488949, tc_fun(_1488951, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488949, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1488951, tc_HOL_Obool), tc_fun(_1488951, tc_HOL_Obool), _1488949), hAPP(c_COMBC(_1488951, tc_fun(_1488951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1488951))), _1488953)), _1488955)), -(hBOOL(hAPP(hAPP(c_member(_1488951), _1488955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1488949, tc_fun(_1488951, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488949, tc_HOL_Obool))), _1488953))))], (3808 ^ _779327) ^ [_837068, _837070] : [_837070 = _837068, -(c_Random_Orange(_837070) = c_Random_Orange(_837068))], (21420 ^ _779327) ^ [_1147880, _1147882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147880)), 21423 ^ _779327 : [(21430 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147882), _1147880))), -(c_Divides_OposDivAlg(_1147882, _1147880) = hAPP(c_Divides_Oadjust(_1147880), c_Divides_OposDivAlg(_1147882, 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)))), _1147880))))], (21424 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147882), _1147880)), -(c_Divides_OposDivAlg(_1147882, _1147880) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147882))]]], (37181 ^ _779327) ^ [_1474083, _1474085, _1474087] : [-(c_Fun_Oinj__on(tc_prod(_1474083, _1474085), tc_prod(_1474085, _1474083), hAPP(c_Product__Type_Oprod_Oprod__case(_1474083, _1474085, tc_prod(_1474085, _1474083)), hAPP(c_COMBC(_1474085, _1474083, tc_prod(_1474085, _1474083)), c_Product__Type_OPair(_1474085, _1474083))), _1474087))], (45349 ^ _779327) ^ [_1677508, _1677510, _1677512] : [-(hAPP(c_List_Oset(_1677508), c_List_Osublist(_1677508, _1677510, _1677512)) = hAPP(c_Set_OCollect(_1677508), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1677508), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1677508, 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)), _1677508), 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)), _1677508), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1677508, tc_fun(tc_Nat_Onat, _1677508), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1677508, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1677508), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1677508), c_COMBB(_1677508, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1677508), _1677510))))), 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(_1677508)), _1677510)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1677512))))))], (30963 ^ _779327) ^ [_1339719, _1339721, _1339723, _1339725, _1339727, _1339729, _1339731] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1339719, tc_fun(_1339721, tc_fun(_1339723, tc_HOL_Obool))), _1339725), _1339727), _1339729), _1339731)), 30966 ^ _779327 : [(30967 ^ _779327) ^ [_1339847] : [hBOOL(hAPP(hAPP(c_member(_1339719), _1339847), _1339725)), -(hBOOL(hAPP(hAPP(hAPP(_1339727, _1339847), _1339729), _1339731)))]]], (48068 ^ _779327) ^ [_1739753, _1739755, _1739757] : [c_List_Olist__all2(_1739757, _1739757, c_fequal, _1739753, _1739755), -(_1739753 = _1739755)], (10949 ^ _779327) ^ [_957873, _957875, _957877, _957879] : [class_Groups_Ocancel__semigroup__add(_957873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957873), _957875), _957877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957873), _957875), _957879), -(_957877 = _957879)], (9317 ^ _779327) ^ [_930289] : [9318 ^ _779327 : [(9319 ^ _779327) ^ [_930346] : [hBOOL(hAPP(_930289, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930346)))]], 9321 ^ _779327 : [(9324 ^ _779327) ^ [] : [-(hBOOL(hAPP(_930289, 9320 ^ [_930289])))], (9322 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9320 ^ [_930289])))]]], (2026 ^ _779327) ^ [_808565, _808567, _808569, _808571] : [-(c_SMT_Oz3div(_808571, _808567) = c_SMT_Oz3div(_808569, _808565)), _808571 = _808569, _808567 = _808565], (5834 ^ _779327) ^ [_871425, _871427] : [-(_871425 = _871427), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871425), _871427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871427), _871425)))], (12473 ^ _779327) ^ [_987089, _987091, _987093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987089), _987091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987089), _987093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987091), _987093)))], (34304 ^ _779327) ^ [_1409334, _1409336, _1409338, _1409340, _1409342] : [c_Equiv__Relations_Oequiv(_1409334, _1409336, _1409338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409334, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1409334, _1409334, _1409338), hAPP(hAPP(c_Set_Oinsert(_1409334), _1409340), c_Orderings_Obot__class_Obot(tc_fun(_1409334, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1409334, _1409334, _1409338), hAPP(hAPP(c_Set_Oinsert(_1409334), _1409342), c_Orderings_Obot__class_Obot(tc_fun(_1409334, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1409334), _1409340), _1409336)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1409334, _1409334)), hAPP(hAPP(c_Product__Type_OPair(_1409334, _1409334), _1409342), _1409340)), _1409338)))], (16485 ^ _779327) ^ [] : [c_Int_OPls = c_Int_OMin], (30417 ^ _779327) ^ [_1326562, _1326564, _1326566, _1326568, _1326570] : [hBOOL(hAPP(hAPP(c_member(_1326562), _1326564), _1326566)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326568, tc_HOL_Obool)), hAPP(_1326570, _1326564)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326562, tc_fun(_1326568, tc_HOL_Obool)), _1326566), _1326570)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326562, tc_fun(_1326568, tc_HOL_Obool)), _1326566), _1326570))], (22839 ^ _779327) ^ [_1175018, _1175020, _1175022, _1175024] : [class_Orderings_Olinorder(_1175018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175018), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175018), _1175020), _1175022)), _1175024)), 22846 ^ _779327 : [(22849 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175018), _1175022), _1175024)))], (22847 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175018), _1175020), _1175024)))]]], (4890 ^ _779327) ^ [_853845, _853847] : [_853847 = _853845, -(c_Groups_Oplus__class_Oplus(_853847) = c_Groups_Oplus__class_Oplus(_853845))], (38091 ^ _779327) ^ [_1493219, _1493221, _1493223, _1493225, _1493227] : [_1493219 = c_Orderings_Obot__class_Obot(tc_fun(_1493221, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493221, tc_fun(_1493223, tc_HOL_Obool)), _1493219), hAPP(hAPP(c_COMBB(tc_fun(_1493223, tc_HOL_Obool), tc_fun(_1493223, tc_HOL_Obool), _1493221), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493223, tc_HOL_Obool)), _1493225)), _1493227)) = c_Orderings_Otop__class_Otop(tc_fun(_1493223, tc_HOL_Obool)))], (27889 ^ _779327) ^ [_1275170, _1275172, _1275174, _1275176, _1275178] : [-(hAPP(c_Set_Oimage(_1275170, _1275172, _1275174), hAPP(hAPP(c_Set_Oinsert(_1275170), _1275176), _1275178)) = hAPP(hAPP(c_Set_Oinsert(_1275172), hAPP(_1275174, _1275176)), hAPP(c_Set_Oimage(_1275170, _1275172, _1275174), _1275178)))], (15934 ^ _779327) ^ [_1048892, _1048894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1048892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048892), _1048894)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1048894), _1048892) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048894), _1048892)), _1048892)))], (51231 ^ _779327) ^ [_1807817, _1807819, _1807821, _1807823] : [-(hAPP(hAPP(c_List_Oappend(_1807817), c_List_Oreplicate(_1807817, _1807819, _1807821)), c_List_Oreplicate(_1807817, _1807823, _1807821)) = hAPP(hAPP(c_List_Oappend(_1807817), c_List_Oreplicate(_1807817, _1807823, _1807821)), c_List_Oreplicate(_1807817, _1807819, _1807821)))], (28021 ^ _779327) ^ [_1277622, _1277624, _1277626, _1277628] : [class_Groups_Ocomm__monoid__add(_1277622), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1277624), _1277626))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1277624, _1277622), _1277628), _1277626) = c_Groups_Ozero__class_Ozero(_1277622))], (42597 ^ _779327) ^ [_1610034, _1610036] : [c_Wellfounded_Oacyclic(_1610034, _1610036), -(c_Wellfounded_Oacyclic(_1610034, hAPP(c_Relation_Oconverse(_1610034, _1610034), _1610036)))], (52940 ^ _779327) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (48692 ^ _779327) ^ [_1755194] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1755194)), c_List_Otranspose__rel(_1755194)), c_List_Olist_ONil(tc_List_Olist(_1755194)))), -(c_List_Otranspose(_1755194, c_List_Olist_ONil(tc_List_Olist(_1755194))) = c_List_Olist_ONil(tc_List_Olist(_1755194)))], (41754 ^ _779327) ^ [_1589504, _1589506, _1589508] : [41755 ^ _779327 : [(41756 ^ _779327) ^ [_1589558] : [hBOOL(hAPP(_1589504, _1589558))]], _1589506 = c_Hilbert__Choice_OEps(_1589508, _1589504), -(hBOOL(hAPP(_1589504, _1589506)))], (18200 ^ _779327) ^ [_1088397, _1088399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088397), _1088399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1088397)), c_Int_OBit0(_1088399))))], (46520 ^ _779327) ^ [_1706932, _1706934, _1706936, _1706938] : [-(hAPP(hAPP(c_List_Odrop(_1706932), _1706934), hAPP(hAPP(c_List_Odrop(_1706932), _1706936), _1706938)) = hAPP(hAPP(c_List_Odrop(_1706932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1706934), _1706936)), _1706938))], (28592 ^ _779327) ^ [_1288743, _1288745] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288743, tc_HOL_Obool)), _1288745), c_Orderings_Obot__class_Obot(tc_fun(_1288743, tc_HOL_Obool))) = _1288745)], (48674 ^ _779327) ^ [_1754233, _1754235, _1754237, _1754239] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1754233)), c_List_Otranspose__rel(_1754233)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754233)), hAPP(hAPP(c_List_Olist_OCons(_1754233), _1754235), _1754237)), _1754239))), -(c_List_Otranspose(_1754233, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754233)), hAPP(hAPP(c_List_Olist_OCons(_1754233), _1754235), _1754237)), _1754239)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754233)), hAPP(hAPP(c_List_Olist_OCons(_1754233), _1754235), c_List_Oconcat(_1754233, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754233), tc_List_Olist(_1754233)), c_List_Olist_Olist__case(tc_List_Olist(_1754233), _1754233, c_List_Olist_ONil(_1754233), hAPP(hAPP(c_COMBB(tc_List_Olist(_1754233), tc_fun(tc_List_Olist(_1754233), tc_List_Olist(_1754233)), _1754233), c_COMBK(tc_List_Olist(_1754233), tc_List_Olist(_1754233))), hAPP(hAPP(c_COMBC(_1754233, tc_List_Olist(_1754233), tc_List_Olist(_1754233)), c_List_Olist_OCons(_1754233)), c_List_Olist_ONil(_1754233))))), _1754239)))), c_List_Otranspose(_1754233, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754233)), _1754237), c_List_Oconcat(tc_List_Olist(_1754233), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754233), tc_List_Olist(tc_List_Olist(_1754233))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1754233)), _1754233, c_List_Olist_ONil(tc_List_Olist(_1754233)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1754233), tc_List_Olist(tc_List_Olist(_1754233))), _1754233), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754233), tc_List_Olist(tc_List_Olist(_1754233)), tc_List_Olist(tc_List_Olist(_1754233))), c_List_Olist_OCons(tc_List_Olist(_1754233))), c_List_Olist_ONil(tc_List_Olist(_1754233)))))), _1754239))))))], (42871 ^ _779327) ^ [_1616585, _1616587, _1616589, _1616591] : [-(hAPP(_1616585, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1616587, _1616587), _1616589), _1616585), _1616591)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1616587, _1616587), _1616589), _1616585), hAPP(_1616585, _1616591)))], (52996 ^ _779327) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (16794 ^ _779327) ^ [] : [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)], (23612 ^ _779327) ^ [_1190457, _1190459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190457)), hAPP(c_Code__Numeral_Oof__nat, _1190459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190457), _1190459)))], (27958 ^ _779327) ^ [_1276538] : [27960 ^ _779327 : [(27963 ^ _779327) ^ [_1276648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27959 ^ [_1276538, _1276648]), _1276648))], (27961 ^ _779327) ^ [_1276614] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27959 ^ [_1276538, _1276614]), _1276538)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1276538)))], (16009 ^ _779327) ^ [_1050300, _1050302, _1050304, _1050306] : [_1050300 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050302), _1050304)), _1050306), -(_1050302 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050300, _1050302) = _1050306), 16016 ^ _779327 : [(16019 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050306), _1050302))], (16017 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050302)))]], 16024 ^ _779327 : [(16027 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050302), _1050306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050306), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (16025 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050302))]]], (53002 ^ _779327) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (30411 ^ _779327) ^ [_1326415, _1326417, _1326419, _1326421, _1326423] : [hBOOL(hAPP(hAPP(c_member(_1326415), _1326417), _1326419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326421, tc_HOL_Obool)), hAPP(_1326423, _1326417)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1326415, tc_fun(_1326421, tc_HOL_Obool)), _1326419), _1326423))))], (28741 ^ _779327) ^ [_1291701, _1291703, _1291705, _1291707] : [28743 ^ _779327 : [(28746 ^ _779327) ^ [] : [hAPP(_1291707, 28742 ^ [_1291701, _1291703, _1291705, _1291707]) = c_Orderings_Obot__class_Obot(tc_fun(_1291703, tc_HOL_Obool))], (28744 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291701), 28742 ^ [_1291701, _1291703, _1291705, _1291707]), _1291705)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291701, tc_fun(_1291703, tc_HOL_Obool)), _1291705), _1291707) = c_Orderings_Obot__class_Obot(tc_fun(_1291703, tc_HOL_Obool)))], (37163 ^ _779327) ^ [_1473741, _1473743, _1473745, _1473747, _1473749, _1473751] : [c_Fun_Oinj__on(_1473741, _1473743, _1473745, _1473747), hBOOL(hAPP(hAPP(c_member(_1473743), _1473749), hAPP(c_Set_Oimage(_1473741, _1473743, _1473745), _1473747))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473741, tc_HOL_Obool)), _1473747), _1473751)), -(hBOOL(hAPP(hAPP(c_member(_1473741), hAPP(c_Fun_Othe__inv__into(_1473741, _1473743, _1473747, _1473745), _1473749)), _1473751)))], (23536 ^ _779327) ^ [_1188998, _1189000, _1189002] : [-(c_Random__Sequence_Oempty(_1188998, _1189000, _1189002) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188998)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1188998)))], (11605 ^ _779327) ^ [_971590, _971592, _971594] : [class_Groups_Oab__group__add(_971590), 11608 ^ _779327 : [(11615 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971590), _971592), _971594) = c_Groups_Ozero__class_Ozero(_971590), -(_971592 = _971594)], (11609 ^ _779327) ^ [] : [_971592 = _971594, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971590), _971592), _971594) = c_Groups_Ozero__class_Ozero(_971590))]]], (34775 ^ _779327) ^ [_1420149, _1420151] : [class_Lattices_Osemilattice__inf(_1420149), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420149), _1420151), _1420151) = _1420151)], (2382 ^ _779327) ^ [_814117, _814119, _814121, _814123] : [-(c_Nitpick_Onorm__frac(_814123, _814119) = c_Nitpick_Onorm__frac(_814121, _814117)), _814123 = _814121, _814119 = _814117], (41113 ^ _779327) ^ [_1574971, _1574973] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574971, _1574971)), _1574973)), 41116 ^ _779327 : [(41123 ^ _779327) ^ [] : [c_Wellfounded_Oacyclic(_1574971, _1574973), -(c_Wellfounded_Owf(_1574971, _1574973))], (41117 ^ _779327) ^ [] : [c_Wellfounded_Owf(_1574971, _1574973), -(c_Wellfounded_Oacyclic(_1574971, _1574973))]]], (22129 ^ _779327) ^ [_1161622, _1161624, _1161626, _1161628, _1161630] : [-(hAPP(c_Product__Type_Ofst(_1161622, _1161624), hAPP(c_Product__Type_Oapsnd(_1161626, _1161624, _1161622, _1161628), _1161630)) = hAPP(c_Product__Type_Ofst(_1161622, _1161626), _1161630))], (24523 ^ _779327) ^ [_1206224, _1206226] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206224), _1206226)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206224), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206226), _1206224))))], (13579 ^ _779327) ^ [_1006874, _1006876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1006876), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006874), _1006876)))], (11753 ^ _779327) ^ [_974004, _974006] : [class_Groups_Ogroup__add(_974004), 11756 ^ _779327 : [(11763 ^ _779327) ^ [] : [_974006 = c_Groups_Ozero__class_Ozero(_974004), -(hAPP(c_Groups_Ouminus__class_Ouminus(_974004), _974006) = c_Groups_Ozero__class_Ozero(_974004))], (11757 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_974004), _974006) = c_Groups_Ozero__class_Ozero(_974004), -(_974006 = c_Groups_Ozero__class_Ozero(_974004))]]], (14739 ^ _779327) ^ [_1027286, _1027288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027286)), 14742 ^ _779327 : [(14751 ^ _779327) ^ [] : [-(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), _1027286), _1027288)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027288), _1027286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027288))], (14743 ^ _779327) ^ [] : [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), _1027286), _1027288))), 14746 ^ _779327 : [(14749 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027288)))], (14747 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1027288), _1027286)))]]]]], (1228 ^ _779327) ^ [_797665, _797667] : [-(class_Rings_Oordered__ring__abs(_797665)), _797667 = _797665, class_Rings_Oordered__ring__abs(_797667)], (42090 ^ _779327) ^ [_1596792, _1596794, _1596796, _1596798, _1596800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596792, _1596792)), hAPP(hAPP(c_Product__Type_OPair(_1596792, _1596792), _1596794), _1596796)), _1596798)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1596792, _1596792)), hAPP(hAPP(c_Product__Type_OPair(_1596792, _1596792), _1596796), _1596800)), _1596798)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596792, _1596792)), hAPP(hAPP(c_Product__Type_OPair(_1596792, _1596792), _1596794), _1596800)), c_Transitive__Closure_Otrancl(_1596792, _1596798))))], (38033 ^ _779327) ^ [_1491734, _1491736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491734), c_Orderings_Otop__class_Otop(tc_fun(_1491734, tc_HOL_Obool)))), c_Fun_Oinj__on(_1491734, _1491734, _1491736, c_Orderings_Otop__class_Otop(tc_fun(_1491734, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1491734, _1491734, _1491736), c_Orderings_Otop__class_Otop(tc_fun(_1491734, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1491734, tc_HOL_Obool)))], (14659 ^ _779327) ^ [_1026131] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1026131)), -(hAPP(c_Int_Onat, _1026131) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49699 ^ _779327) ^ [_1775298, _1775300, _1775302] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775298)), c_List_OtakeWhile(_1775298, _1775300, _1775302))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775298)), _1775302))))], (11099 ^ _779327) ^ [_960527, _960529, _960531] : [class_Groups_Oab__group__add(_960527), -(hAPP(c_Groups_Ouminus__class_Ouminus(_960527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960527), _960529), _960531)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960527), _960531), _960529))], (13690 ^ _779327) ^ [_1008930, _1008932, _1008934, _1008936] : [class_Groups_Oordered__comm__monoid__add(_1008930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008930), c_Groups_Ozero__class_Ozero(_1008930)), _1008932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008930), _1008934), _1008936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008930), _1008934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008930), _1008932), _1008936))))], (48215 ^ _779327) ^ [_1743444, _1743446] : [_1743444 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1743446, _1743444, c_List_Olist_ONil(_1743446)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743446)), c_List_Olist_ONil(_1743446)), c_List_Olist_ONil(tc_List_Olist(_1743446))))], (4410 ^ _779327) ^ [_846391, _846393] : [_846393 = _846391, -(c_Nat_Osemiring__1__class_Oof__nat(_846393) = c_Nat_Osemiring__1__class_Oof__nat(_846391))], (36450 ^ _779327) ^ [_1459482, _1459484] : [class_Lattices_Olattice(_1459482), -(c_Big__Operators_Olattice__class_OInf__fin(_1459482, hAPP(hAPP(c_Set_Oinsert(_1459482), _1459484), c_Orderings_Obot__class_Obot(tc_fun(_1459482, tc_HOL_Obool)))) = _1459484)], (27106 ^ _779327) ^ [_1257714, _1257716, _1257718] : [class_Lattices_Osemilattice__sup(_1257714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257714), _1257716), _1257718)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257714), _1257718), _1257716) = _1257718)], (27913 ^ _779327) ^ [_1275663, _1275665, _1275667, _1275669] : [-(hAPP(hAPP(c_Set_Oinsert(_1275663), _1275665), hAPP(hAPP(c_Set_Oinsert(_1275663), _1275667), _1275669)) = hAPP(hAPP(c_Set_Oinsert(_1275663), _1275667), hAPP(hAPP(c_Set_Oinsert(_1275663), _1275665), _1275669)))], (27971 ^ _779327) ^ [_1276885, _1276887, _1276889] : [class_Complete__Lattice_Ocomplete__lattice(_1276885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276885), _1276887), hAPP(_1276889, _1276887))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276885), _1276887), c_Inductive_Ocomplete__lattice__class_Ogfp(_1276885, _1276889))))], (52432 ^ _779327) ^ [_1834443, _1834445, _1834447, _1834449, _1834451] : [hBOOL(hAPP(hAPP(c_member(_1834443), _1834445), hAPP(c_Set_Oimage(_1834447, _1834443, _1834449), _1834451))), -(hAPP(_1834449, hAPP(c_Hilbert__Choice_Oinv__into(_1834447, _1834443, _1834451, _1834449), _1834445)) = _1834445)], (26824 ^ _779327) ^ [_1251810, _1251812, _1251814, _1251816] : [26825 ^ _779327 : [(26828 ^ _779327) ^ [] : [hBOOL(hAPP(_1251814, _1251812))], (26826 ^ _779327) ^ [] : [hBOOL(hAPP(_1251810, _1251812))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251816, tc_HOL_Obool)), _1251814), _1251810), _1251812)))], (47933 ^ _779327) ^ [_1736879, _1736881, _1736883] : [class_Orderings_Olinorder(_1736879), -(hAPP(c_List_Oset(_1736879), c_List_Olinorder__class_Oinsort__insert__key(_1736879, _1736879, c_COMBI(_1736879), _1736881, _1736883)) = hAPP(hAPP(c_Set_Oinsert(_1736879), _1736881), hAPP(c_List_Oset(_1736879), _1736883)))], (22167 ^ _779327) ^ [_1162485, _1162487] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162485, _1162487), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1162485), _1162487)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1162485, _1162487)))))], (6777 ^ _779327) ^ [_885312, _885314, _885316] : [class_Orderings_Olinorder(_885312), 6780 ^ _779327 : [(6787 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885312), _885316), _885314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885312), _885314), _885316))], (6781 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885312), _885314), _885316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885312), _885316), _885314)))]]], (35213 ^ _779327) ^ [_1429540, _1429542, _1429544, _1429546] : [-(hBOOL(hAPP(hAPP(c_member(_1429540), _1429542), _1429544))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429540, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1429540), _1429542), _1429546)), _1429544) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429540, tc_HOL_Obool)), _1429546), _1429544))], (52101 ^ _779327) ^ [_1828071] : [-(c_Relation_Osym(_1828071, c_Relation_OId(_1828071)))], (18002 ^ _779327) ^ [_1084921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084921)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084921), c_Int_OPls)))], (932 ^ _779327) ^ [_793559, _793561, _793563, _793565] : [-(c_Predicate_Oreflp(_793563, _793559)), c_Predicate_Oreflp(_793565, _793561), _793565 = _793563, _793561 = _793559], (10681 ^ _779327) ^ [_952703, _952705, _952707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _952703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _952705), _952707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952703), _952707)), _952705)))], (6042 ^ _779327) ^ [_874459, _874461, _874463, _874465] : [class_Orderings_Oorder(_874459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874459), _874461), _874463)), _874461 = _874465, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874459), _874465), _874463)))], (42863 ^ _779327) ^ [_1616416, _1616418, _1616420] : [c_Relation_Osingle__valued(_1616416, _1616416, _1616418), -(c_Relation_Osingle__valued(_1616416, _1616416, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616416, _1616416), tc_HOL_Obool), _1616420), _1616418)))], (50126 ^ _779327) ^ [_1784117, _1784119, _1784121] : [-(c_List_Oinsert(_1784117, _1784119, c_List_Oremdups(_1784117, _1784121)) = c_List_Oremdups(_1784117, c_List_Oinsert(_1784117, _1784119, _1784121)))], (38850 ^ _779327) ^ [_1513763, _1513765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1513763, _1513763), tc_HOL_Obool)), c_Relation_OId__on(_1513763, _1513765)), hAPP(hAPP(c_Product__Type_OSigma(_1513763, _1513763), _1513765), hAPP(c_COMBK(tc_fun(_1513763, tc_HOL_Obool), _1513763), _1513765)))))], (23129 ^ _779327) ^ [_1180542, _1180544, _1180546, _1180548, _1180550] : [-(hAPP(c_Product__Type_Ofst(_1180542, _1180544), hAPP(c_Product__Type_Oapfst(_1180546, _1180542, _1180544, _1180548), _1180550)) = hAPP(_1180548, hAPP(c_Product__Type_Ofst(_1180546, _1180544), _1180550)))], (45161 ^ _779327) ^ [_1672995, _1672997, _1672999, _1673001] : [hBOOL(hAPP(hAPP(c_member(_1672995), _1672997), hAPP(c_List_Oset(_1672995), hAPP(hAPP(c_List_Olist_OCons(_1672995), _1672999), _1673001)))), -(_1672997 = _1672999), -(hBOOL(hAPP(hAPP(c_member(_1672995), _1672997), hAPP(c_List_Oset(_1672995), _1673001))))], (49479 ^ _779327) ^ [_1770585, _1770587, _1770589] : [hAPP(c_List_Orev(_1770585), _1770587) = hAPP(hAPP(c_List_Olist_OCons(_1770585), _1770589), c_List_Olist_ONil(_1770585)), -(_1770587 = hAPP(hAPP(c_List_Olist_OCons(_1770585), _1770589), c_List_Olist_ONil(_1770585)))], (12790 ^ _779327) ^ [_993025, _993027, _993029] : [class_Groups_Oordered__ab__group__add(_993025), 12793 ^ _779327 : [(12800 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_993025), _993027), _993029)), c_Groups_Ozero__class_Ozero(_993025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993025), _993027), _993029)))], (12794 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993025), _993027), _993029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_993025), _993027), _993029)), c_Groups_Ozero__class_Ozero(_993025))))]]], (40925 ^ _779327) ^ [_1570169, _1570171, _1570173, _1570175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570169, _1570171), tc_HOL_Obool)), _1570173), _1570175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570169, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1570169, _1570171), _1570173)), hAPP(c_Relation_ODomain(_1570169, _1570171), _1570175))))], (15704 ^ _779327) ^ [_1045030, _1045032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045030), 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, _1045032, _1045030)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37408 ^ _779327) ^ [_1478986, _1478988] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478986), _1478988)), -(hAPP(c_Finite__Set_Ocard(_1478986), _1478988) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1478986, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1478986), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1478988))], (46485 ^ _779327) ^ [_1705912, _1705914, _1705916, _1705918, _1705920] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705912), tc_List_Olist(_1705912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705912), tc_List_Olist(_1705912)), hAPP(hAPP(c_List_Oappend(_1705912), _1705914), _1705916)), hAPP(hAPP(c_List_Oappend(_1705912), _1705914), _1705918))), c_List_Olexord(_1705912, _1705920))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1705912, _1705912)), hAPP(hAPP(c_Product__Type_OPair(_1705912, _1705912), 46490 ^ [_1705912, _1705914, _1705916, _1705918, _1705920]), 46490 ^ [_1705912, _1705914, _1705916, _1705918, _1705920])), _1705920))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705912), tc_List_Olist(_1705912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705912), tc_List_Olist(_1705912)), _1705916), _1705918)), c_List_Olexord(_1705912, _1705920))))], (30745 ^ _779327) ^ [_1334781, _1334783, _1334785, _1334787, _1334789] : [class_Rings_Oring(_1334781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334783), _1334785)), hBOOL(hAPP(hAPP(c_member(_1334783), _1334787), _1334785)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334783, _1334781), _1334789), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334783, tc_HOL_Obool)), _1334785), hAPP(hAPP(c_Set_Oinsert(_1334783), _1334787), c_Orderings_Obot__class_Obot(tc_fun(_1334783, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334781), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334783, _1334781), _1334789), _1334785)), hAPP(_1334789, _1334787)))], (49752 ^ _779327) ^ [_1776394, _1776396] : [-(c_List_OtakeWhile(_1776394, _1776396, c_List_Olist_ONil(_1776394)) = c_List_Olist_ONil(_1776394))], (22411 ^ _779327) ^ [_1167126, _1167128, _1167130, _1167132] : [class_Orderings_Olinorder(_1167126), 22414 ^ _779327 : [(22423 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167126), _1167130), _1167132)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), _1167130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), _1167132))], (22415 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167126), _1167130), _1167132))), 22418 ^ _779327 : [(22421 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), _1167132)))], (22419 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167126), _1167128), _1167130)))]]]]], (9256 ^ _779327) ^ [_929193, _929195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929193)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _929193), _929195)))], (1648 ^ _779327) ^ [_802915, _802917] : [-(class_Groups_Ocancel__semigroup__add(_802915)), _802917 = _802915, class_Groups_Ocancel__semigroup__add(_802917)], (50171 ^ _779327) ^ [_1785268, _1785270, _1785272, _1785274, _1785276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1785268, _1785270)), hAPP(_1785268, _1785272))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1785274, _1785274)), hAPP(hAPP(c_Product__Type_OPair(_1785274, _1785274), _1785270), _1785272)), c_List_Omeasures(_1785274, _1785276))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785274, _1785274)), hAPP(hAPP(c_Product__Type_OPair(_1785274, _1785274), _1785270), _1785272)), c_List_Omeasures(_1785274, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1785274, tc_Nat_Onat)), _1785268), _1785276)))))], (16281 ^ _779327) ^ [_1055261] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055261)))), -(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), _1055261)) = 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), _1055261))))], (15728 ^ _779327) ^ [_1045423, _1045425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1045423)), -(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, _1045425, _1045423))))], (38435 ^ _779327) ^ [_1503246, _1503248, _1503250, _1503252, _1503254] : [-(hAPP(c_Set_Ovimage(_1503246, _1503248, _1503250), hAPP(hAPP(c_Set_Oinsert(_1503248), _1503252), _1503254)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503246, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1503246, _1503248, _1503250), hAPP(hAPP(c_Set_Oinsert(_1503248), _1503252), c_Orderings_Obot__class_Obot(tc_fun(_1503248, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1503246, _1503248, _1503250), _1503254)))], (30227 ^ _779327) ^ [_1322963, _1322965, _1322967, _1322969] : [-(hBOOL(hAPP(hAPP(c_member(_1322963), _1322965), _1322967))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322963, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1322963), _1322965), _1322969)), _1322967) = hAPP(hAPP(c_Set_Oinsert(_1322963), _1322965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322963, tc_HOL_Obool)), _1322969), _1322967)))], (2614 ^ _779327) ^ [_817769, _817771, _817773, _817775, _817777, _817779, _817781, _817783, _817785, _817787] : [-(c_Nitpick_Opair__box_Opair__box__rec(_817787, _817783, _817779, _817775, _817771) = c_Nitpick_Opair__box_Opair__box__rec(_817785, _817781, _817777, _817773, _817769)), _817787 = _817785, _817783 = _817781, _817779 = _817777, _817775 = _817773, _817771 = _817769], (14641 ^ _779327) ^ [_1025857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025857)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1025857))], (28082 ^ _779327) ^ [_1278741, _1278743] : [class_Complete__Lattice_Ocomplete__lattice(_1278741), c_Orderings_Oorder__class_Omono(_1278741, _1278741, _1278743), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278741), hAPP(_1278743, c_Inductive_Ocomplete__lattice__class_Ogfp(_1278741, _1278743))), c_Inductive_Ocomplete__lattice__class_Ogfp(_1278741, _1278743))))], (3824 ^ _779327) ^ [_837302, _837304, _837306, _837308, _837310, _837312, _837314, _837316] : [-(c_Nat_Onat_Onat__case(_837316, _837312, _837308, _837304) = c_Nat_Onat_Onat__case(_837314, _837310, _837306, _837302)), _837316 = _837314, _837312 = _837310, _837308 = _837306, _837304 = _837302], (10975 ^ _779327) ^ [_958305, _958307, _958309, _958311] : [class_Groups_Ocancel__semigroup__add(_958305), 10978 ^ _779327 : [(10985 ^ _779327) ^ [] : [_958309 = _958311, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958305), _958307), _958309) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958305), _958307), _958311))], (10979 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958305), _958307), _958309) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958305), _958307), _958311), -(_958309 = _958311)]]], (52740 ^ _779327) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (37382 ^ _779327) ^ [_1478180, _1478182, _1478184, _1478186, _1478188] : [class_Groups_Ocomm__monoid__mult(_1478180), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478182), _1478184)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478182), _1478186)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1478180), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1478180, _1478182, c_Groups_Otimes__class_Otimes(_1478180)), _1478188), c_Groups_Oone__class_Oone(_1478180)), _1478184)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1478180, _1478182, c_Groups_Otimes__class_Otimes(_1478180)), _1478188), c_Groups_Oone__class_Oone(_1478180)), _1478186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1478180), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1478180, _1478182, c_Groups_Otimes__class_Otimes(_1478180)), _1478188), c_Groups_Oone__class_Oone(_1478180)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478182, tc_HOL_Obool)), _1478184), _1478186))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1478180, _1478182, c_Groups_Otimes__class_Otimes(_1478180)), _1478188), c_Groups_Oone__class_Oone(_1478180)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478182, tc_HOL_Obool)), _1478184), _1478186))))], (45343 ^ _779327) ^ [_1677205, _1677207, _1677209] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1677205), _1677207)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1677205)), hAPP(c_Set_OCollect(tc_List_Olist(_1677205)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1677205), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1677205)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677205), tc_fun(_1677205, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1677205, tc_HOL_Obool), tc_fun(tc_fun(_1677205, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1677205)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1677205, tc_HOL_Obool))), c_List_Oset(_1677205))), _1677207))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677205), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1677205)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1677205)))), _1677209))))))], (41243 ^ _779327) ^ [_1577794, _1577796, _1577798, _1577800, _1577802, _1577804] : [-(hAPP(hAPP(c_Fun_Ocomp(_1577794, _1577796, _1577798, _1577800), _1577802), _1577804) = hAPP(_1577800, hAPP(_1577802, _1577804)))], (20957 ^ _779327) ^ [_1138320, _1138322] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1138320), _1138322) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1138320), _1138322))], (18420 ^ _779327) ^ [_1092271, _1092273] : [class_Rings_Olinordered__idom(_1092271), 18423 ^ _779327 : [(18430 ^ _779327) ^ [] : [-(_1092273 = c_Groups_Ozero__class_Ozero(_1092271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092271), c_Groups_Ozero__class_Ozero(_1092271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1092271), _1092273), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (18424 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092271), c_Groups_Ozero__class_Ozero(_1092271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1092271), _1092273), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1092273 = c_Groups_Ozero__class_Ozero(_1092271)]]], (14141 ^ _779327) ^ [_1017236, _1017238, _1017240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017236, tc_HOL_Obool)), _1017240), _1017238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017236, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017236, tc_HOL_Obool)), _1017238)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017236, tc_HOL_Obool)), _1017240))))], (47642 ^ _779327) ^ [_1730347, _1730349, _1730351, _1730353, _1730355] : [c_List_Opartition(_1730347, _1730349, _1730351) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730347), tc_List_Olist(_1730347)), _1730353), _1730355), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1730347, tc_HOL_Obool)), hAPP(c_List_Oset(_1730347), _1730353)), hAPP(c_List_Oset(_1730347), _1730355)) = hAPP(c_List_Oset(_1730347), _1730351))], (51495 ^ _779327) ^ [_1814470, _1814472, _1814474, _1814476] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1814470, _1814472, _1814474, _1814476, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814472)) = _1814474)], (32960 ^ _779327) ^ [_1379004, _1379006, _1379008, _1379010, _1379012, _1379014] : [hBOOL(hAPP(hAPP(c_member(_1379004), _1379006), _1379008)), -(hAPP(c_Set_Oimage(_1379004, _1379010, c_Fun_Ofun__upd(_1379004, _1379010, _1379012, _1379006, _1379014)), _1379008) = hAPP(hAPP(c_Set_Oinsert(_1379010), _1379014), hAPP(c_Set_Oimage(_1379004, _1379010, _1379012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379004, tc_HOL_Obool)), _1379008), hAPP(hAPP(c_Set_Oinsert(_1379004), _1379006), c_Orderings_Obot__class_Obot(tc_fun(_1379004, tc_HOL_Obool)))))))], (47413 ^ _779327) ^ [_1725881, _1725883, _1725885, _1725887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725883)), _1725885))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1725881), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725883)), _1725887))), 47423 ^ _779327 : [(47426 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Onth(_1725883), _1725885), 47422 ^ [_1725881, _1725883, _1725885, _1725887]) = hAPP(hAPP(c_List_Onth(_1725883), _1725887), 47422 ^ [_1725881, _1725883, _1725885, _1725887])], (47424 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47422 ^ [_1725881, _1725883, _1725885, _1725887]), _1725881)))]], -(hAPP(hAPP(c_List_Otake(_1725883), _1725881), _1725885) = hAPP(hAPP(c_List_Otake(_1725883), _1725881), _1725887))], (52972 ^ _779327) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (796 ^ _779327) ^ [_791527, _791529] : [-(c_List_Onat__list(_791527)), _791529 = _791527, c_List_Onat__list(_791529)], (6873 ^ _779327) ^ [_886823, _886825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886823), _886825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886823)), _886825)))], (52786 ^ _779327) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (13500 ^ _779327) ^ [_1005392, _1005394] : [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), _1005392), _1005394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005394)))], (1358 ^ _779327) ^ [_799290, _799292] : [-(class_Rings_Oring__1(_799290)), _799292 = _799290, class_Rings_Oring__1(_799292)], (35081 ^ _779327) ^ [_1426558, _1426560, _1426562] : [class_Lattices_Olattice(_1426558), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426558), _1426560), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426558), _1426560), _1426562)) = _1426560)], (52936 ^ _779327) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (30827 ^ _779327) ^ [_1336673, _1336675, _1336677] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336673), _1336675)), hBOOL(hAPP(hAPP(c_member(_1336673), _1336677), _1336675)), -(hAPP(c_Finite__Set_Ocard(_1336673), _1336675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1336673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336673, tc_HOL_Obool)), _1336675), hAPP(hAPP(c_Set_Oinsert(_1336673), _1336677), c_Orderings_Obot__class_Obot(tc_fun(_1336673, tc_HOL_Obool)))))))], (4902 ^ _779327) ^ [_854015, _854017, _854019, _854021, _854023, _854025, _854027, _854029, _854031, _854033] : [-(c_Option_Ooption_Ooption__case(_854033, _854029, _854025, _854021, _854017) = c_Option_Ooption_Ooption__case(_854031, _854027, _854023, _854019, _854015)), _854033 = _854031, _854029 = _854027, _854025 = _854023, _854021 = _854019, _854017 = _854015], (5644 ^ _779327) ^ [_868450, _868452] : [_868450 = _868452, -(hAPP(c_Nat_OSuc, _868450) = hAPP(c_Nat_OSuc, _868452))], (21286 ^ _779327) ^ [_1145328, _1145330, _1145332, _1145334, _1145336] : [-(hAPP(c_Nat_Onat_Onat__rec(_1145328, _1145330, _1145332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145334)), _1145336)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1145328), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1145334))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1145328, _1145328), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1145328, tc_fun(_1145328, _1145328)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1145328, tc_fun(_1145328, _1145328)), tc_Int_Oint), c_If(_1145328)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1145328, _1145330, _1145332), _1145336))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1145328, _1145328), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1145328, _1145328), tc_Int_Oint), _1145332), 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)), _1145336))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1145328, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1145328, _1145330, _1145332)), 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)), _1145336))))))], (1718 ^ _779327) ^ [_803790, _803792] : [-(class_Rings_Ono__zero__divisors(_803790)), _803792 = _803790, class_Rings_Ono__zero__divisors(_803792)], (25171 ^ _779327) ^ [_1218173, _1218175] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218173), _1218175)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218175), _1218173)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1218173) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1218175))], (25093 ^ _779327) ^ [_1216747, _1216749] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216747)), _1216749)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216747), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216749)))))], (25796 ^ _779327) ^ [_1231441, _1231443, _1231445] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1231441, tc_Nat_Onat), _1231443), _1231445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1231441, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1231441), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1231443)), _1231445))], (40482 ^ _779327) ^ [_1560286, _1560288, _1560290] : [-(hAPP(c_Relation_ORange(_1560286, _1560288), hAPP(c_Set_OCollect(tc_prod(_1560286, _1560288)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560286, _1560288, tc_HOL_Obool), _1560290))) = hAPP(c_Set_OCollect(_1560288), hAPP(hAPP(c_COMBB(tc_fun(_1560286, tc_HOL_Obool), tc_HOL_Obool, _1560288), c_HOL_OEx(_1560286)), hAPP(c_COMBC(_1560286, _1560288, tc_HOL_Obool), _1560290))))], (42396 ^ _779327) ^ [_1605170] : [-(hAPP(c_Relation_ODomain(_1605170, _1605170), c_Relation_OId(_1605170)) = c_Orderings_Otop__class_Otop(tc_fun(_1605170, tc_HOL_Obool)))], (43583 ^ _779327) ^ [_1632442, _1632444, _1632446, _1632448, _1632450, _1632452, _1632454] : [c_Finite__Set_Ofun__left__comm(_1632442, _1632444, _1632446), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1632442, _1632444, _1632446, _1632448, _1632450), _1632452)), hBOOL(hAPP(hAPP(c_member(_1632442), _1632454), _1632450)), 43595 ^ _779327 : [(43598 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1632442, _1632444, _1632446, _1632448, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632442, tc_HOL_Obool)), _1632450), hAPP(hAPP(c_Set_Oinsert(_1632442), _1632454), c_Orderings_Obot__class_Obot(tc_fun(_1632442, tc_HOL_Obool))))), 43594 ^ [_1632442, _1632444, _1632446, _1632448, _1632450, _1632452, _1632454])))], (43596 ^ _779327) ^ [] : [-(_1632452 = hAPP(hAPP(_1632446, _1632454), 43594 ^ [_1632442, _1632444, _1632446, _1632448, _1632450, _1632452, _1632454]))]]], (13903 ^ _779327) ^ [_1012813, _1012815] : [_1012813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1012815), _1012813) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (44302 ^ _779327) ^ [_1648596, _1648598, _1648600, _1648602, _1648604, _1648606, _1648608, _1648610] : [c_Finite__Set_Ofolding__image__simple__idem(_1648596, _1648598, _1648600, _1648602, _1648604, _1648606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1648598), _1648608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648598, tc_HOL_Obool)), _1648610), _1648608)), -(hAPP(hAPP(_1648600, hAPP(_1648606, _1648610)), hAPP(_1648606, _1648608)) = hAPP(_1648606, _1648608))], (47526 ^ _779327) ^ [_1728126, _1728128, _1728130, _1728132] : [-(hAPP(hAPP(c_List_Oappend(_1728126), _1728128), hAPP(hAPP(c_List_Olist_OCons(_1728126), _1728130), c_List_Olist_ONil(_1728126))) = _1728132), -(_1728132 = c_List_Olist_ONil(_1728126)), c_List_Obutlast(_1728126, _1728132) = _1728128, c_List_Olast(_1728126, _1728132) = _1728130], (46784 ^ _779327) ^ [_1712887, _1712889, _1712891] : [-(hAPP(c_List_Otl(_1712887), hAPP(hAPP(c_List_Odrop(_1712887), _1712889), _1712891)) = hAPP(hAPP(c_List_Odrop(_1712887), _1712889), hAPP(c_List_Otl(_1712887), _1712891)))], (22119 ^ _779327) ^ [_1161421, _1161423, _1161425, _1161427] : [-(hAPP(c_Product__Type_Ofst(_1161421, _1161423), hAPP(hAPP(c_Product__Type_OPair(_1161421, _1161423), _1161425), _1161427)) = _1161425)], (9186 ^ _779327) ^ [_927839, _927841, _927843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927839, tc_HOL_Obool)), _927841), _927843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927839, tc_HOL_Obool)), _927841), _927843)))], (46014 ^ _779327) ^ [_1694643, _1694645, _1694647, _1694649] : [-(hAPP(hAPP(c_List_Olist__update(_1694643, hAPP(hAPP(c_List_Olist_OCons(_1694643), _1694645), _1694647)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1694649) = hAPP(hAPP(c_List_Olist_OCons(_1694643), _1694649), _1694647))], (15123 ^ _779327) ^ [_1034060, _1034062] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1034060))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034060)), _1034062)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1034062))], (52534 ^ _779327) ^ [_1835829, _1835831] : [class_Groups_Ouminus(_1835829), -(class_Groups_Ouminus(tc_fun(_1835831, _1835829)))], (23394 ^ _779327) ^ [_1185692, _1185694, _1185696, _1185698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1185692, tc_HOL_Obool)), _1185694), _1185696)), hBOOL(hAPP(_1185694, _1185698)), -(hBOOL(hAPP(_1185696, _1185698)))], (47540 ^ _779327) ^ [_1728376, _1728378, _1728380, _1728382, _1728384] : [class_Groups_Ocomm__monoid__add(_1728376), hBOOL(hAPP(hAPP(c_member(_1728378), _1728380), hAPP(c_List_Oset(_1728378), _1728382))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1728376), hAPP(hAPP(c_List_Omap(_1728378, _1728376), _1728384), _1728382)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1728376), hAPP(_1728384, _1728380)), hAPP(c_List_Omonoid__add__class_Olistsum(_1728376), hAPP(hAPP(c_List_Omap(_1728378, _1728376), _1728384), c_List_Oremove1(_1728378, _1728380, _1728382)))))], (44825 ^ _779327) ^ [_1664214, _1664216, _1664218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1664214, _1664214), tc_HOL_Obool)), _1664216), hAPP(hAPP(c_Product__Type_OSigma(_1664214, _1664214), _1664218), hAPP(c_COMBK(tc_fun(_1664214, tc_HOL_Obool), _1664214), _1664218)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1664214), tc_List_Olist(_1664214)), tc_HOL_Obool)), c_List_Olistrel(_1664214, _1664216)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1664214), tc_List_Olist(_1664214)), c_List_Olists(_1664214, _1664218)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1664214), tc_HOL_Obool), tc_List_Olist(_1664214)), c_List_Olists(_1664214, _1664218))))))], (47245 ^ _779327) ^ [_1722733, _1722735, _1722737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1722733), tc_List_Olist(_1722733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722733), tc_List_Olist(_1722733)), c_List_Olist_ONil(_1722733)), _1722735)), c_List_Olexord(_1722733, _1722737))), -(_1722735 = hAPP(hAPP(c_List_Olist_OCons(_1722733), 47248 ^ [_1722733, _1722735, _1722737]), 47249 ^ [_1722733, _1722735, _1722737]))], (28409 ^ _779327) ^ [_1285089, _1285091, _1285093, _1285095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285089, tc_HOL_Obool)), _1285091), _1285095))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285089, tc_HOL_Obool)), _1285091), hAPP(hAPP(c_Set_Oinsert(_1285089), _1285093), _1285095)))))], (32308 ^ _779327) ^ [_1366371, _1366373, _1366375, _1366377, _1366379, _1366381, _1366383] : [-(c_Nitpick_Ofold__graph_H(_1366371, _1366373, _1366375, _1366377, _1366379, hAPP(hAPP(_1366375, _1366381), _1366383))), 32309 ^ _779327 : [(32316 ^ _779327) ^ [_1366600, _1366602] : [hAPP(hAPP(_1366375, _1366381), _1366383) = hAPP(hAPP(_1366375, _1366602), _1366600), hBOOL(hAPP(hAPP(c_member(_1366371), _1366602), _1366379)), c_Nitpick_Ofold__graph_H(_1366371, _1366373, _1366375, _1366377, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1366371, tc_HOL_Obool)), _1366379), hAPP(hAPP(c_Set_Oinsert(_1366371), _1366602), c_Orderings_Obot__class_Obot(tc_fun(_1366371, tc_HOL_Obool)))), _1366600)], (32310 ^ _779327) ^ [] : [_1366379 = c_Orderings_Obot__class_Obot(tc_fun(_1366371, tc_HOL_Obool)), hAPP(hAPP(_1366375, _1366381), _1366383) = _1366377]]], (50090 ^ _779327) ^ [_1783505, _1783507, _1783509] : [hBOOL(hAPP(c_List_Odistinct(_1783505), _1783507)), -(c_List_Oremove1(_1783505, _1783509, _1783507) = hAPP(c_List_OremoveAll(_1783505, _1783509), _1783507))], (37249 ^ _779327) ^ [_1475541, _1475543, _1475545] : [class_Lattices_Olattice(_1475541), hAPP(_1475543, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1475541), 37254 ^ [_1475541, _1475543, _1475545]), 37255 ^ [_1475541, _1475543, _1475545])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1475541), hAPP(_1475543, 37254 ^ [_1475541, _1475543, _1475545])), hAPP(_1475543, 37255 ^ [_1475541, _1475543, _1475545])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475541), _1475545)), -(_1475545 = c_Orderings_Obot__class_Obot(tc_fun(_1475541, tc_HOL_Obool))), -(hAPP(_1475543, c_Big__Operators_Olattice__class_OInf__fin(_1475541, _1475545)) = c_Big__Operators_Olattice__class_OInf__fin(_1475541, hAPP(c_Set_Oimage(_1475541, _1475541, _1475543), _1475545)))], (32600 ^ _779327) ^ [_1372068, _1372070, _1372072] : [class_Orderings_Olinorder(_1372068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372068), _1372070)), hBOOL(hAPP(hAPP(c_member(_1372068), _1372072), _1372070)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372068), _1372072), c_Big__Operators_Olattice_OSup__fin(_1372068, c_Orderings_Oord__class_Omax(_1372068), _1372070)) = c_Big__Operators_Olattice_OSup__fin(_1372068, c_Orderings_Oord__class_Omax(_1372068), _1372070))], (3536 ^ _779327) ^ [_832756, _832758] : [_832758 = _832756, -(c_New__Random__Sequence_Opos__single(_832758) = c_New__Random__Sequence_Opos__single(_832756))], (33793 ^ _779327) ^ [_1397094, _1397096, _1397098, _1397100, _1397102] : [class_Groups_Ocomm__monoid__mult(_1397094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397096), _1397098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397096, tc_HOL_Obool)), _1397100), _1397098)), 33807 ^ _779327 : [(33810 ^ _779327) ^ [] : [hAPP(_1397102, 33806 ^ [_1397094, _1397096, _1397098, _1397100, _1397102]) = c_Groups_Oone__class_Oone(_1397094)], (33808 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397096), 33806 ^ [_1397094, _1397096, _1397098, _1397100, _1397102]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1397096, tc_HOL_Obool)), _1397098), _1397100))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397096, _1397094), _1397102), _1397100) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397096, _1397094), _1397102), _1397098))], (26322 ^ _779327) ^ [_1242451, _1242453, _1242455] : [class_Groups_Oordered__ab__group__add(_1242451), -(hAPP(c_Set_Oimage(_1242451, _1242451, c_Groups_Ouminus__class_Ouminus(_1242451)), c_SetInterval_Oord__class_OatLeastAtMost(_1242451, _1242453, _1242455)) = c_SetInterval_Oord__class_OatLeastAtMost(_1242451, hAPP(c_Groups_Ouminus__class_Ouminus(_1242451), _1242455), hAPP(c_Groups_Ouminus__class_Ouminus(_1242451), _1242453)))], (40859 ^ _779327) ^ [_1568639, _1568641, _1568643] : [c_Wellfounded_Owf(_1568639, _1568641), -(c_Wellfounded_Owf(tc_List_Olist(_1568639), hAPP(c_List_Olexn(_1568639, _1568641), _1568643)))], (14199 ^ _779327) ^ [_1018543, _1018545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018543), _1018545)), -(c_Nat__Transfer_Otsub(_1018545, _1018543) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018545), _1018543))], (48459 ^ _779327) ^ [_1748398, _1748400] : [class_Orderings_Olinorder(_1748398), -(c_List_Olinorder__class_Osort__key(_1748398, _1748398, c_COMBI(_1748398), _1748400) = hAPP(c_List_Ofoldl(tc_List_Olist(_1748398), _1748398, hAPP(c_COMBC(_1748398, tc_List_Olist(_1748398), tc_List_Olist(_1748398)), c_List_Olinorder__class_Oinsort__key(_1748398, _1748398, c_COMBI(_1748398))), c_List_Olist_ONil(_1748398)), _1748400))], (25828 ^ _779327) ^ [_1232203, _1232205, _1232207, _1232209, _1232211] : [class_Orderings_Oorder(_1232203), 25831 ^ _779327 : [(25852 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1232203, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1232203, _1232205, _1232207)), c_SetInterval_Oord__class_OatLeastAtMost(_1232203, _1232209, _1232211)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232209), _1232211)), 25855 ^ _779327 : [(25858 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232209), _1232205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232207), _1232211)), 25865 ^ _779327 : [(25868 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232203), _1232207), _1232211))], (25866 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232203), _1232209), _1232205))]]], (25856 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232205), _1232207)))]]], (25832 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1232203, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1232203, _1232205, _1232207)), c_SetInterval_Oord__class_OatLeastAtMost(_1232203, _1232209, _1232211))), 25835 ^ _779327 : [(25836 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232205), _1232207)), 25839 ^ _779327 : [(25844 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232203), _1232209), _1232205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232203), _1232207), _1232211)))], (25842 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232207), _1232211)))], (25840 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232209), _1232205)))]]], (25850 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232203), _1232209), _1232211)))]]]]], (52071 ^ _779327) ^ [_1827602, _1827604] : [c_Relation_Osym(_1827602, _1827604), -(c_Relation_Osym(tc_List_Olist(_1827602), c_List_Olistrel(_1827602, _1827604)))], (45739 ^ _779327) ^ [_1687934, _1687936, _1687938, _1687940, _1687942] : [class_Rings_Osemiring__0(_1687934), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687934), hAPP(hAPP(c_List_Omap(_1687936, _1687934), hAPP(hAPP(c_COMBC(_1687936, _1687934, _1687934), hAPP(hAPP(c_COMBB(_1687934, tc_fun(_1687934, _1687934), _1687936), c_Groups_Otimes__class_Otimes(_1687934)), _1687938)), _1687940)), _1687942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1687934), hAPP(c_List_Omonoid__add__class_Olistsum(_1687934), hAPP(hAPP(c_List_Omap(_1687936, _1687934), _1687938), _1687942))), _1687940))], (16411 ^ _779327) ^ [_1057418, _1057420, _1057422] : [class_Rings_Olinordered__idom(_1057418), -(hAPP(c_Groups_Oabs__class_Oabs(_1057418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057418), _1057420), _1057422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057418), hAPP(c_Groups_Oabs__class_Oabs(_1057418), _1057420)), hAPP(c_Groups_Oabs__class_Oabs(_1057418), _1057422)))], (5576 ^ _779327) ^ [_864406, _864408] : [_864408 = _864406, -(c_member(_864408) = c_member(_864406))], (9407 ^ _779327) ^ [_931690, _931692] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931690), _931692) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _931692), _931690))], (18044 ^ _779327) ^ [_1085670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085670), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085670)), c_Int_OPls)))], (51193 ^ _779327) ^ [_1807150, _1807152, _1807154, _1807156, _1807158] : [c_List_Oreplicate(_1807150, _1807152, _1807154) = c_List_Oreplicate(_1807150, _1807156, _1807158), 51196 ^ _779327 : [(51199 ^ _779327) ^ [] : [-(_1807152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1807154 = _1807158)], (51197 ^ _779327) ^ [] : [-(_1807152 = _1807156)]]], (32426 ^ _779327) ^ [_1368469, _1368471, _1368473] : [class_Orderings_Olinorder(_1368469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368469), _1368471)), -(_1368471 = c_Orderings_Obot__class_Obot(tc_fun(_1368469, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368469), _1368473)), -(_1368473 = c_Orderings_Obot__class_Obot(tc_fun(_1368469, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1368469, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1368469, tc_HOL_Obool)), _1368471), _1368473)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368469), c_Big__Operators_Olinorder__class_OMin(_1368469, _1368471)), c_Big__Operators_Olinorder__class_OMin(_1368469, _1368473)))], (4306 ^ _779327) ^ [_844781, _844783, _844785, _844787, _844789, _844791] : [-(c_Divides_Odiv__class_Omod(_844791, _844787, _844783) = c_Divides_Odiv__class_Omod(_844789, _844785, _844781)), _844791 = _844789, _844787 = _844785, _844783 = _844781], (52240 ^ _779327) ^ [_1830475, _1830477] : [-(c_Equiv__Relations_Opart__equivp(_1830475, _1830477)), 52243 ^ _779327 : [(52244 ^ _779327) ^ [_1830552] : [hBOOL(hAPP(hAPP(_1830477, _1830552), _1830552))]], c_Predicate_Osymp(_1830475, _1830477), c_Predicate_Otransp(_1830475, _1830477)], (49549 ^ _779327) ^ [_1772115, _1772117, _1772119] : [_1772117 = hAPP(c_List_Orev(_1772115), _1772119), -(hAPP(c_List_Orev(_1772115), _1772117) = _1772119)], (7892 ^ _779327) ^ [_904247, _904249, _904251] : [class_Rings_Oordered__ring(_904247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904247), c_Groups_Ozero__class_Ozero(_904247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904247), _904249), _904251)))), 7897 ^ _779327 : [(7904 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904247), _904249), c_Groups_Ozero__class_Ozero(_904247))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904247), _904251), c_Groups_Ozero__class_Ozero(_904247)))], (7898 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904247), c_Groups_Ozero__class_Ozero(_904247)), _904249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904247), c_Groups_Ozero__class_Ozero(_904247)), _904251))]]], (52516 ^ _779327) ^ [_1835592, _1835594] : [class_Orderings_Otop(_1835592), -(class_Orderings_Otop(tc_fun(_1835594, _1835592)))], (82 ^ _779327) ^ [_780424, _780426] : [-(class_Rings_Oinverse(_780424)), _780426 = _780424, class_Rings_Oinverse(_780426)], (18670 ^ _779327) ^ [_1096971, _1096973] : [class_Rings_Oring__1(_1096971), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096971), hAPP(c_Groups_Ouminus__class_Ouminus(_1096971), c_Groups_Oone__class_Oone(_1096971))), 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)))), _1096973))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1096971), c_Groups_Oone__class_Oone(_1096971)))], (11427 ^ _779327) ^ [_967799, _967801, _967803] : [-(hBOOL(hAPP(_967799, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967801), _967803)))), 11430 ^ _779327 : [(11433 ^ _779327) ^ [] : [hBOOL(hAPP(_967799, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11431 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967801), _967803)))]], 11435 ^ _779327 : [(11438 ^ _779327) ^ [] : [hBOOL(hAPP(_967799, 11434 ^ [_967799, _967801, _967803]))], (11436 ^ _779327) ^ [] : [-(_967801 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967803), 11434 ^ [_967799, _967801, _967803]))]]], (21384 ^ _779327) ^ [_1147340] : [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), _1147340))), 21387 ^ _779327 : [(21394 ^ _779327) ^ [] : [-(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), _1147340)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147340)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147340)), 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), _1147340)))))], (21388 ^ _779327) ^ [] : [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), _1147340))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1147340)) = 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)))]]], (33997 ^ _779327) ^ [_1401434, _1401436] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1401434, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1401434, tc_HOL_Obool))), hAPP(c_Set_OPow(_1401434), _1401436))))], (3040 ^ _779327) ^ [_824858, _824860, _824862, _824864, _824866, _824868, _824870, _824872, _824874, _824876] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_824876, _824872, _824868, _824864, _824860) = c_SetInterval_Oord_OgreaterThanAtMost(_824874, _824870, _824866, _824862, _824858)), _824876 = _824874, _824872 = _824870, _824868 = _824866, _824864 = _824862, _824860 = _824858], (20993 ^ _779327) ^ [_1138887, _1138889] : [_1138887 = _1138889, -(c_Random_Oinc__shift(_1138887, _1138889) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (45912 ^ _779327) ^ [_1692335, _1692337, _1692339, _1692341] : [-(c_List_Osublist(_1692335, hAPP(hAPP(c_List_Olist_OCons(_1692335), _1692337), _1692339), _1692341) = hAPP(hAPP(c_List_Oappend(_1692335), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1692335)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1692341)), hAPP(hAPP(c_List_Olist_OCons(_1692335), _1692337), c_List_Olist_ONil(_1692335))), c_List_Olist_ONil(_1692335))), c_List_Osublist(_1692335, _1692339, 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)), _1692341)))))], (16453 ^ _779327) ^ [_1058243, _1058245] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1058243), _1058245) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058243, _1058245)), _1058245))], (17692 ^ _779327) ^ [] : [-(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)))))], (37525 ^ _779327) ^ [_1481198, _1481200, _1481202, _1481204, _1481206, _1481208, _1481210] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481198, _1481200, _1481202, _1481204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1481198, tc_HOL_Obool)), _1481206), hAPP(hAPP(c_Set_Oinsert(_1481198), _1481208), c_Orderings_Obot__class_Obot(tc_fun(_1481198, tc_HOL_Obool))))), _1481210)), hBOOL(hAPP(hAPP(c_member(_1481198), _1481208), _1481206)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481198, _1481200, _1481202, _1481204, _1481206), hAPP(hAPP(_1481202, _1481208), _1481210))))], (34047 ^ _779327) ^ [_1402778, _1402780, _1402782, _1402784, _1402786] : [c_Finite__Set_Ofolding__one__idem(_1402778, _1402780, _1402782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402778), _1402784)), -(_1402784 = c_Orderings_Obot__class_Obot(tc_fun(_1402778, tc_HOL_Obool))), -(hAPP(_1402782, hAPP(hAPP(c_Set_Oinsert(_1402778), _1402786), _1402784)) = hAPP(hAPP(_1402780, _1402786), hAPP(_1402782, _1402784)))], (4634 ^ _779327) ^ [_849969, _849971] : [_849971 = _849969, -(c_Groups_Ouminus__class_Ouminus(_849971) = c_Groups_Ouminus__class_Ouminus(_849969))], (42248 ^ _779327) ^ [_1601538, _1601540, _1601542] : [-(c_Transitive__Closure_Ortrancl(_1601538, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601538, _1601538), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1601538, _1601540)), c_Transitive__Closure_Ortrancl(_1601538, _1601542))) = c_Transitive__Closure_Ortrancl(_1601538, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601538, _1601538), tc_HOL_Obool)), _1601540), _1601542)))], (39160 ^ _779327) ^ [_1520781, _1520783, _1520785] : [class_Orderings_Olinorder(_1520781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520781), _1520783)), -(_1520783 = c_Orderings_Obot__class_Obot(tc_fun(_1520781, tc_HOL_Obool))), 39171 ^ _779327 : [(39181 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520781), hAPP(c_Finite__Set_Ofold1(_1520781, c_Orderings_Oord__class_Omin(_1520781)), _1520783)), _1520785))), 39182 ^ _779327 : [(39183 ^ _779327) ^ [_1521170] : [hBOOL(hAPP(hAPP(c_member(_1520781), _1521170), _1520783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520781), _1521170), _1520785))]]], (39172 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520781), hAPP(c_Finite__Set_Ofold1(_1520781, c_Orderings_Oord__class_Omin(_1520781)), _1520783)), _1520785)), 39176 ^ _779327 : [(39179 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520781), 39175 ^ [_1520781, _1520783, _1520785]), _1520785)))], (39177 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1520781), 39175 ^ [_1520781, _1520783, _1520785]), _1520783)))]]]]], (20273 ^ _779327) ^ [_1125307, _1125309, _1125311, _1125313] : [class_Fields_Olinordered__field__inverse__zero(_1125307), 20276 ^ _779327 : [(20277 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125307), _1125309), _1125311)), _1125313)), 20280 ^ _779327 : [(20287 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125311))), 20290 ^ _779327 : [(20297 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), _1125311), c_Groups_Ozero__class_Ozero(_1125307)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125313)))], (20291 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), _1125311), c_Groups_Ozero__class_Ozero(_1125307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125307), _1125313), _1125311)), _1125309)))]]], (20281 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), _1125309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125307), _1125313), _1125311))))]]], (20303 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125307), _1125309), _1125311)), _1125313))), 20306 ^ _779327 : [(20309 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), _1125309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125307), _1125313), _1125311)))], (20307 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125311)))]], 20310 ^ _779327 : [(20313 ^ _779327) ^ [] : [20314 ^ _779327 : [(20317 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125307), _1125313), _1125311)), _1125309))], (20315 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), _1125311), c_Groups_Ozero__class_Ozero(_1125307))))]], 20318 ^ _779327 : [(20321 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125313))], (20319 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), _1125311), c_Groups_Ozero__class_Ozero(_1125307)))]]], (20311 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125307), c_Groups_Ozero__class_Ozero(_1125307)), _1125311))]]]]], (32828 ^ _779327) ^ [_1376376, _1376378, _1376380] : [class_Orderings_Olinorder(_1376376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376376), _1376378)), -(_1376380 = c_Orderings_Obot__class_Obot(tc_fun(_1376376, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376376, tc_HOL_Obool)), _1376380), _1376378)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376376), c_Big__Operators_Olattice_OInf__fin(_1376376, c_Orderings_Oord__class_Omin(_1376376), _1376380)), c_Big__Operators_Olattice_OInf__fin(_1376376, c_Orderings_Oord__class_Omin(_1376376), _1376378)) = c_Big__Operators_Olattice_OInf__fin(_1376376, c_Orderings_Oord__class_Omin(_1376376), _1376378))], (23456 ^ _779327) ^ [_1186992, _1186994, _1186996] : [-(c_Nitpick_Oof__frac(_1186994, _1186992, _1186996) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186992), hAPP(c_Int_Oring__1__class_Oof__int(_1186992), hAPP(c_Nitpick_Onum(_1186994), _1186996))), hAPP(c_Int_Oring__1__class_Oof__int(_1186992), hAPP(c_Nitpick_Odenom(_1186994), _1186996)))), class_Rings_Oinverse(_1186992), class_Rings_Oring__1(_1186992)], (25311 ^ _779327) ^ [_1220684] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1220684) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220684), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19333 ^ _779327) ^ [_1108601, _1108603, _1108605] : [class_Rings_Odivision__ring(_1108601), -(_1108603 = c_Groups_Ozero__class_Ozero(_1108601)), 19340 ^ _779327 : [(19347 ^ _779327) ^ [] : [_1108605 = _1108603, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108601), _1108605), _1108603) = c_Groups_Oone__class_Oone(_1108601))], (19341 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1108601), _1108605), _1108603) = c_Groups_Oone__class_Oone(_1108601), -(_1108605 = _1108603)]]], (1748 ^ _779327) ^ [_804165, _804167] : [-(class_Groups_Osemigroup__add(_804165)), _804167 = _804165, class_Groups_Osemigroup__add(_804167)], (42228 ^ _779327) ^ [_1601062, _1601064, _1601066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601062, _1601062), tc_HOL_Obool)), _1601064), _1601066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601062, _1601062), tc_HOL_Obool)), _1601066), c_Transitive__Closure_Ortrancl(_1601062, _1601064))), -(c_Transitive__Closure_Ortrancl(_1601062, _1601066) = c_Transitive__Closure_Ortrancl(_1601062, _1601064))], (48273 ^ _779327) ^ [_1744779, _1744781] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744779)), c_List_Oremdups(_1744779, _1744781))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744779)), _1744781))))], (25355 ^ _779327) ^ [_1221444, _1221446] : [-(_1221444 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1221446), _1221444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1221446)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1221444))))], (25798 ^ _779327) ^ [_1231499, _1231501, _1231503, _1231505, _1231507] : [class_Groups_Ocomm__monoid__add(_1231499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231501), _1231503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231503), _1231505)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231499), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231499), _1231507), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231501), _1231503))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231499), _1231507), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231503), _1231505))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231499), _1231507), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231501), _1231505)))], (16778 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10041 ^ _779327) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1708 ^ _779327) ^ [_803665, _803667] : [-(class_Rings_Oordered__semiring(_803665)), _803667 = _803665, class_Rings_Oordered__semiring(_803667)], (52710 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (43153 ^ _779327) ^ [_1624108, _1624110, _1624112, _1624114] : [class_Orderings_Olinorder(_1624108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624108), _1624110)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1624108, _1624108, c_Orderings_Oord__class_Omax(_1624108)), _1624112), hAPP(hAPP(c_Set_Oinsert(_1624108), _1624114), _1624110)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1624108), _1624114), hAPP(hAPP(c_Finite__Set_Ofold(_1624108, _1624108, c_Orderings_Oord__class_Omax(_1624108)), _1624112), _1624110)))], (3480 ^ _779327) ^ [_831856, _831858, _831860, _831862, _831864, _831866, _831868, _831870] : [-(c_New__Random__Sequence_Opos__map(_831870, _831866, _831862, _831858) = c_New__Random__Sequence_Opos__map(_831868, _831864, _831860, _831856)), _831870 = _831868, _831866 = _831864, _831862 = _831860, _831858 = _831856], (27801 ^ _779327) ^ [_1273461, _1273463] : [class_Groups_Oordered__ab__group__add(_1273461), -(hAPP(c_Set_Oimage(_1273461, _1273461, c_Groups_Ouminus__class_Ouminus(_1273461)), hAPP(c_SetInterval_Oord__class_OatMost(_1273461), _1273463)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1273461), hAPP(c_Groups_Ouminus__class_Ouminus(_1273461), _1273463)))], (2540 ^ _779327) ^ [_816606, _816608] : [_816608 = _816606, -(c_DSequence_Ounion(_816608) = c_DSequence_Ounion(_816606))], (46524 ^ _779327) ^ [_1707058, _1707060, _1707062, _1707064] : [-(hAPP(hAPP(c_List_Odrop(_1707058), _1707060), hAPP(hAPP(c_List_Otake(_1707058), _1707062), _1707064)) = hAPP(hAPP(c_List_Otake(_1707058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1707062), _1707060)), hAPP(hAPP(c_List_Odrop(_1707058), _1707060), _1707064)))], (42521 ^ _779327) ^ [_1608113, _1608115] : [-(c_Transitive__Closure_Ortrancl(_1608113, hAPP(c_Relation_Oconverse(_1608113, _1608113), _1608115)) = hAPP(c_Relation_Oconverse(_1608113, _1608113), c_Transitive__Closure_Ortrancl(_1608113, _1608115)))], (23414 ^ _779327) ^ [_1186048, _1186050, _1186052, _1186054, _1186056, _1186058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1186048, tc_fun(_1186050, tc_HOL_Obool))), _1186052), _1186054)), hBOOL(hAPP(hAPP(_1186052, _1186056), _1186058)), -(hBOOL(hAPP(hAPP(_1186054, _1186056), _1186058)))], (21260 ^ _779327) ^ [_1144639, _1144641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144639)), hAPP(c_Nat_OSuc, _1144641))), -(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(_1144639))), 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)), _1144641)))))], (23053 ^ _779327) ^ [_1178786, _1178788, _1178790, _1178792] : [class_Groups_Oordered__ab__group__add(_1178786), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178786), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178786), _1178788), _1178790)), _1178792) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178786), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178786), _1178788), _1178792)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178786), _1178790), _1178792)))], (21662 ^ _779327) ^ [_1152670, _1152672, _1152674, _1152676, _1152678, _1152680] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152670, _1152672), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152674), _1152676))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152670, _1152672), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152678), _1152680))), -(_1152672 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1152674 = _1152678)], (30924 ^ _779327) ^ [_1338759, _1338761, _1338763, _1338765] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1338759, tc_fun(_1338761, tc_HOL_Obool))), _1338763), _1338765))], (16976 ^ _779327) ^ [_1067388, _1067390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067390))), 16979 ^ _779327 : [(16980 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067388), _1067390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1067390)))], (16986 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067388), _1067390)))]]], (11689 ^ _779327) ^ [_972993, _972995, _972997] : [class_Groups_Oordered__ab__group__add(_972993), 11692 ^ _779327 : [(11699 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), _972997), _972995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), hAPP(c_Groups_Ouminus__class_Ouminus(_972993), _972995)), hAPP(c_Groups_Ouminus__class_Ouminus(_972993), _972997))))], (11693 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), hAPP(c_Groups_Ouminus__class_Ouminus(_972993), _972995)), hAPP(c_Groups_Ouminus__class_Ouminus(_972993), _972997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972993), _972997), _972995)))]]], (50945 ^ _779327) ^ [_1802322, _1802324] : [-(c_List_Osplice(_1802322, c_List_Olist_ONil(_1802322), _1802324) = _1802324)], (49840 ^ _779327) ^ [_1778378, _1778380, _1778382] : [class_Orderings_Olinorder(_1778378), c_List_Olinorder__class_Osorted(_1778378, _1778380), -(c_List_Olinorder__class_Osorted(_1778378, c_List_OdropWhile(_1778378, _1778382, _1778380)))], (52810 ^ _779327) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52660 ^ _779327) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (33999 ^ _779327) ^ [_1401479] : [-(hAPP(c_Set_OPow(_1401479), c_Orderings_Obot__class_Obot(tc_fun(_1401479, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1401479, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1401479, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1401479, tc_HOL_Obool), tc_HOL_Obool))))], (43359 ^ _779327) ^ [_1628306, _1628308, _1628310, _1628312] : [class_Complete__Lattice_Ocomplete__lattice(_1628306), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628308), _1628310)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1628308, _1628306), _1628310), _1628312) = hAPP(hAPP(c_Finite__Set_Ofold(_1628308, _1628306, hAPP(hAPP(c_COMBB(_1628306, tc_fun(_1628306, _1628306), _1628308), c_Lattices_Osemilattice__sup__class_Osup(_1628306)), _1628312)), c_Orderings_Obot__class_Obot(_1628306)), _1628310))], (26316 ^ _779327) ^ [_1242213, _1242215, _1242217, _1242219, _1242221, _1242223] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1242213, tc_fun(_1242215, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1242217, _1242213, _1242219), _1242221)), _1242223) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1242217, tc_fun(_1242215, tc_HOL_Obool)), _1242221), hAPP(hAPP(c_COMBB(_1242213, tc_fun(_1242215, tc_HOL_Obool), _1242217), _1242223), _1242219)))], (4446 ^ _779327) ^ [_846931, _846933, _846935, _846937] : [-(c_List_Oremdups(_846937, _846933) = c_List_Oremdups(_846935, _846931)), _846937 = _846935, _846933 = _846931], (51955 ^ _779327) ^ [_1825219, _1825221] : [c_Relation_Otrans(_1825219, _1825221), c_Relation_Oantisym(_1825219, _1825221), -(c_Relation_Otrans(_1825219, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1825219, _1825219), tc_HOL_Obool)), _1825221), c_Relation_OId(_1825219))))], (29296 ^ _779327) ^ [_1301642, _1301644] : [class_Orderings_Olinorder(_1301642), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301642, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1301642), _1301644), c_Orderings_Obot__class_Obot(tc_fun(_1301642, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1301642), _1301644)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1301642), _1301644))], (29669 ^ _779327) ^ [_1309465, _1309467] : [-(_1309467 = c_Orderings_Obot__class_Obot(tc_fun(_1309465, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1309465), 29672 ^ [_1309465, _1309467]), _1309467)))], (6230 ^ _779327) ^ [_877463, _877465, _877467] : [class_Orderings_Oorder(_877463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877463), _877465), _877467)), -(_877467 = _877465), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_877463), _877465), _877467)))], (12616 ^ _779327) ^ [_989889, _989891] : [class_Int_Onumber__ring(_989889), 12619 ^ _779327 : [(12626 ^ _779327) ^ [] : [-(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), _989891)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_989889), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _989891)) = c_Groups_Ozero__class_Ozero(_989889))], (12620 ^ _779327) ^ [] : [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), _989891))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_989889), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _989891)) = hAPP(c_Int_Onumber__class_Onumber__of(_989889), _989891))]]], (51085 ^ _779327) ^ [_1804951, _1804953, _1804955] : [-(c_List_Oreplicate(_1804951, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1804951)), hAPP(c_List_Ofilter(_1804951, hAPP(c_fequal, _1804953)), _1804955)), _1804953) = hAPP(c_List_Ofilter(_1804951, hAPP(c_fequal, _1804953)), _1804955))], (40204 ^ _779327) ^ [_1550201, _1550203] : [c_Relation_Orefl__on(_1550201, c_Orderings_Otop__class_Otop(tc_fun(_1550201, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1550201, _1550201)), hAPP(c_Product__Type_Oprod_Oprod__case(_1550201, _1550201, tc_HOL_Obool), _1550203))), -(c_Predicate_Oreflp(_1550201, _1550203))], (33135 ^ _779327) ^ [_1382521, _1382523, _1382525, _1382527] : [class_Rings_Ocomm__semiring__1(_1382521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382523), _1382525)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382523, _1382521), _1382527), _1382525) = c_Groups_Ozero__class_Ozero(_1382521)), 33144 ^ _779327 : [(33145 ^ _779327) ^ [_1382702] : [hBOOL(hAPP(hAPP(c_member(_1382523), _1382702), _1382525)), hAPP(_1382527, _1382702) = c_Groups_Ozero__class_Ozero(_1382521)]]], (44038 ^ _779327) ^ [_1642428, _1642430, _1642432] : [44040 ^ _779327 : [(44043 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1642428, tc_HOL_Obool)), 44039 ^ [_1642428, _1642430, _1642432]), _1642432))], (44041 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1642428, tc_HOL_Obool)), 44039 ^ [_1642428, _1642430, _1642432]), _1642430)))]], -(_1642430 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1642428, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1642428, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1642428, tc_HOL_Obool), _1642430)), _1642432)))], (21850 ^ _779327) ^ [_1155882, _1155884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155882)), 21853 ^ _779327 : [(21860 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155884))), 21863 ^ _779327 : [(21870 ^ _779327) ^ [] : [-(_1155882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1155882, _1155884) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1155882), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1155884))))], (21864 ^ _779327) ^ [] : [_1155882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1155882, _1155884) = 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)))]]], (21854 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1155884)), -(c_Divides_Odivmod__int(_1155882, _1155884) = c_Divides_OposDivAlg(_1155882, _1155884))]]], (26496 ^ _779327) ^ [_1245978, _1245980] : [c_Nat__Transfer_Onat__set(_1245978), c_Nat__Transfer_Onat__set(_1245980), 26503 ^ _779327 : [(26510 ^ _779327) ^ [] : [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), _1245978)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1245980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1245978), _1245980)))], (26504 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1245978), _1245980)), -(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), _1245978)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1245980))))]]], (42400 ^ _779327) ^ [_1605242] : [-(c_Relation_Orefl__on(_1605242, c_Orderings_Otop__class_Otop(tc_fun(_1605242, tc_HOL_Obool)), c_Relation_OId(_1605242)))], (52217 ^ _779327) ^ [_1830096, _1830098] : [c_Predicate_Osymp(_1830096, _1830098), -(c_Relation_Osym(_1830096, hAPP(c_Set_OCollect(tc_prod(_1830096, _1830096)), hAPP(c_Product__Type_Oprod_Oprod__case(_1830096, _1830096, tc_HOL_Obool), _1830098))))], (19633 ^ _779327) ^ [_1113918, _1113920, _1113922, _1113924] : [class_Fields_Olinordered__field(_1113918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113918), c_Groups_Ozero__class_Ozero(_1113918)), _1113920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113918), _1113922), _1113920)), _1113924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113918), _1113922), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113918), _1113924), _1113920))))], (46243 ^ _779327) ^ [_1699592, _1699594, _1699596, _1699598, _1699600, _1699602] : [-(_1699592 = _1699594), -(hAPP(hAPP(c_List_Olist__update(_1699596, hAPP(hAPP(c_List_Olist__update(_1699596, _1699598), _1699592), _1699600)), _1699594), _1699602) = hAPP(hAPP(c_List_Olist__update(_1699596, hAPP(hAPP(c_List_Olist__update(_1699596, _1699598), _1699594), _1699602)), _1699592), _1699600))], (8874 ^ _779327) ^ [_922033, _922035, _922037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _922033)), 8877 ^ _779327 : [(8884 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922035), _922037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _922033), _922035)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _922033), _922037))))], (8878 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _922033), _922035)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _922033), _922037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922035), _922037)))]]], (16950 ^ _779327) ^ [_1066983] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1066983) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1066983), c_Int_OPls)))], (45289 ^ _779327) ^ [_1675848, _1675850, _1675852] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1675848)), _1675850), c_List_Olists(_1675848, _1675852))), 45292 ^ _779327 : [(45293 ^ _779327) ^ [_1675956] : [hBOOL(hAPP(hAPP(c_member(_1675848), _1675956), hAPP(c_List_Oset(_1675848), _1675850))), -(hBOOL(hAPP(hAPP(c_member(_1675848), _1675956), _1675852)))]]], (22257 ^ _779327) ^ [_1164060, _1164062] : [-(c_Divides_Odivmod__nat(_1164062, _1164060) = 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), _1164062), _1164060), _1164060))), -(_1164060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1164062), _1164060)))], (1848 ^ _779327) ^ [_805415, _805417] : [-(class_Rings_Osemiring__0(_805415)), _805417 = _805415, class_Rings_Osemiring__0(_805417)], (52986 ^ _779327) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (3202 ^ _779327) ^ [_827437, _827439, _827441, _827443] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_827443, _827439) = c_Inductive_Ocomplete__lattice__class_Ogfp(_827441, _827437)), _827443 = _827441, _827439 = _827437], (45339 ^ _779327) ^ [_1677001, _1677003] : [-(c_List_Olists(_1677001, _1677003) = hAPP(c_Set_OCollect(tc_List_Olist(_1677001)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677001), tc_fun(_1677001, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1677001, tc_HOL_Obool), tc_fun(tc_fun(_1677001, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1677001)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1677001, tc_HOL_Obool))), c_List_Oset(_1677001))), _1677003)))], (9449 ^ _779327) ^ [_932431] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _932431)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _932431))], (26586 ^ _779327) ^ [_1247326, _1247328] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1247326, _1247328)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247328), _1247326))], (47024 ^ _779327) ^ [_1717950, _1717952] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1717950), _1717952)), -(c_Nitpick_Ocard_H(_1717950, _1717952) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717950)), c_Hilbert__Choice_OEps(tc_List_Olist(_1717950), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717950), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1717950)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717950), tc_fun(_1717950, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1717950, tc_HOL_Obool), tc_fun(tc_fun(_1717950, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1717950)), c_fequal), c_List_Oset(_1717950))), _1717952))), c_List_Odistinct(_1717950)))))], (29692 ^ _779327) ^ [_1309871, _1309873, _1309875, _1309877] : [-(hBOOL(hAPP(hAPP(c_member(_1309871), _1309873), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309871, tc_HOL_Obool)), _1309875), _1309877)))), hBOOL(hAPP(hAPP(c_member(_1309871), _1309873), _1309875)), -(hBOOL(hAPP(hAPP(c_member(_1309871), _1309873), _1309877)))], (26049 ^ _779327) ^ [_1236571, _1236573, _1236575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236571)), 26052 ^ _779327 : [(26053 ^ _779327) ^ [_1236705] : [26055 ^ _779327 : [(26061 ^ _779327) ^ [] : [-(_1236705 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26057 ^ [_1236571, _1236573, _1236575, _1236705]), 26054 ^ [_1236571, _1236573, _1236575, _1236705]))], (26059 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26057 ^ [_1236571, _1236573, _1236575, _1236705]), _1236573)))], (26056 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26054 ^ [_1236571, _1236573, _1236575, _1236705]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1236571))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236575), _1236705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236575), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236705), _1236571))))]]], (12576 ^ _779327) ^ [_989063, _989065, _989067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989063), _989065)), _989067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989065), _989067)))], (23454 ^ _779327) ^ [_1186921, _1186923, _1186925] : [-(c_Nitpick_Otimes__frac(_1186921, _1186923, _1186925) = hAPP(hAPP(c_Nitpick_Ofrac(_1186921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1186921), _1186923)), hAPP(c_Nitpick_Onum(_1186921), _1186925))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1186921), _1186923)), hAPP(c_Nitpick_Odenom(_1186921), _1186925))))], (17624 ^ _779327) ^ [_1078424] : [class_Int_Onumber__ring(_1078424), -(hAPP(c_Int_Onumber__class_Onumber__of(_1078424), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1078424))], (46534 ^ _779327) ^ [_1707268, _1707270] : [_1707270 = c_List_Olist_ONil(_1707268), -(hAPP(c_List_Orotate1(_1707268), _1707270) = c_List_Olist_ONil(_1707268))], (50226 ^ _779327) ^ [_1786901, _1786903, _1786905, _1786907] : [class_Orderings_Oorder(_1786901), class_Enum_Oenum(_1786903), 50233 ^ _779327 : [(50242 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1786903, _1786901)), _1786905), _1786907))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1786903, _1786901)), _1786905), _1786907)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1786903), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1786903), c_fNot), hAPP(hAPP(c_COMBS(_1786903, _1786901, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1786901, tc_fun(_1786901, tc_HOL_Obool), _1786903), c_fequal), _1786905)), _1786907))))], (50234 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1786903, _1786901)), _1786905), _1786907)), 50237 ^ _779327 : [(50240 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1786903), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1786903), c_fNot), hAPP(hAPP(c_COMBS(_1786903, _1786901, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1786901, tc_fun(_1786901, tc_HOL_Obool), _1786903), c_fequal), _1786905)), _1786907)))))], (50238 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1786903, _1786901)), _1786905), _1786907)))]]]]], (29062 ^ _779327) ^ [_1297087, _1297089, _1297091, _1297093] : [-(_1297087 = c_Orderings_Obot__class_Obot(tc_fun(_1297089, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1297089, _1297091, hAPP(c_COMBK(_1297091, _1297089), _1297093)), _1297087) = hAPP(hAPP(c_Set_Oinsert(_1297091), _1297093), c_Orderings_Obot__class_Obot(tc_fun(_1297091, tc_HOL_Obool))))], (5864 ^ _779327) ^ [_871779, _871781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871779), _871781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871779), _871781)))], (35095 ^ _779327) ^ [_1427058, _1427060, _1427062, _1427064] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427058, tc_HOL_Obool)), _1427060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427058, tc_HOL_Obool)), _1427062), _1427064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427058, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427058, tc_HOL_Obool)), _1427060), _1427062)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427058, tc_HOL_Obool)), _1427060), _1427064)))], (44570 ^ _779327) ^ [_1656186, _1656188, _1656190, _1656192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656186), tc_List_Olist(_1656186))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656186), tc_List_Olist(_1656186)), _1656188), _1656190)), c_List_Olex(_1656186, _1656192))), 44573 ^ _779327 : [(44576 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656186)), _1656188) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656186)), _1656190))], (44574 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656186), tc_List_Olist(_1656186))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656186), tc_List_Olist(_1656186)), _1656188), _1656190)), c_List_Olexord(_1656186, _1656192))))]]], (43525 ^ _779327) ^ [_1631349, _1631351, _1631353, _1631355, _1631357, _1631359] : [c_Finite__Set_Ofun__left__comm(_1631349, _1631351, _1631353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631349), _1631355)), -(hAPP(hAPP(_1631353, _1631357), hAPP(hAPP(c_Finite__Set_Ofold(_1631349, _1631351, _1631353), _1631359), _1631355)) = hAPP(hAPP(c_Finite__Set_Ofold(_1631349, _1631351, _1631353), hAPP(hAPP(_1631353, _1631357), _1631359)), _1631355))], (14609 ^ _779327) ^ [_1025397, _1025399, _1025401, _1025403] : [class_Divides_Osemiring__div(_1025397), 14612 ^ _779327 : [(14619 ^ _779327) ^ [] : [-(_1025399 = c_Groups_Ozero__class_Ozero(_1025397)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025397), _1025399), _1025401)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025397), _1025399), _1025403)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025397), _1025401), _1025403))], (14613 ^ _779327) ^ [] : [_1025399 = c_Groups_Ozero__class_Ozero(_1025397), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025397), _1025399), _1025401)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025397), _1025399), _1025403)) = c_Groups_Ozero__class_Ozero(_1025397))]]], (42386 ^ _779327) ^ [_1604897, _1604899, _1604901, _1604903, _1604905] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604897, _1604897)), hAPP(hAPP(c_Product__Type_OPair(_1604897, _1604897), _1604899), _1604901)), c_Transitive__Closure_Ortrancl(_1604897, _1604903))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604897, _1604897)), hAPP(hAPP(c_Product__Type_OPair(_1604897, _1604897), _1604901), _1604905)), c_Transitive__Closure_Otrancl(_1604897, _1604903))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604897, _1604897)), hAPP(hAPP(c_Product__Type_OPair(_1604897, _1604897), _1604899), _1604905)), c_Transitive__Closure_Otrancl(_1604897, _1604903))))], (41653 ^ _779327) ^ [_1587244, _1587246, _1587248, _1587250] : [-(c_Random__Sequence_Omap(_1587244, _1587246, _1587248, _1587250) = c_Random__Sequence_Obind(_1587244, _1587246, _1587250, hAPP(c_Fun_Ocomp(_1587246, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1587246)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1587244, c_Random__Sequence_Osingle(_1587246)), _1587248)))], (51219 ^ _779327) ^ [_1807540, _1807542, _1807544, _1807546] : [-(c_Predicate_Oconversep(_1807540, _1807542, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807540, tc_fun(_1807542, tc_HOL_Obool))), _1807544), _1807546)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807542, tc_fun(_1807540, tc_HOL_Obool))), c_Predicate_Oconversep(_1807540, _1807542, _1807544)), c_Predicate_Oconversep(_1807540, _1807542, _1807546)))], (13196 ^ _779327) ^ [_1000001, _1000003, _1000005, _1000007] : [class_Rings_Olinordered__semidom(_1000001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000001), c_Groups_Ozero__class_Ozero(_1000001)), _1000003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000001), _1000005), _1000007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000001), _1000005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000001), _1000003), _1000007))))], (44751 ^ _779327) ^ [_1661744, _1661746, _1661748, _1661750, _1661752, _1661754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661744, _1661744)), hAPP(hAPP(c_Product__Type_OPair(_1661744, _1661744), _1661746), _1661748)), _1661750)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661744), tc_List_Olist(_1661744))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661744), tc_List_Olist(_1661744)), _1661752), _1661754)), c_List_Olistrel(_1661744, _1661750))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661744), tc_List_Olist(_1661744))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661744), tc_List_Olist(_1661744)), hAPP(hAPP(c_List_Olist_OCons(_1661744), _1661746), _1661752)), hAPP(hAPP(c_List_Olist_OCons(_1661744), _1661748), _1661754))), c_List_Olistrel(_1661744, _1661750))))], (41039 ^ _779327) ^ [_1573118, _1573120, _1573122, _1573124] : [41040 ^ _779327 : [(41041 ^ _779327) ^ [_1573172] : [hBOOL(hAPP(hAPP(_1573122, _1573124), _1573172))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1573118, _1573120, _1573122), _1573124)))], (35285 ^ _779327) ^ [_1431397, _1431399, _1431401, _1431403, _1431405] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431397, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1431399, _1431397, _1431401), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431399, tc_HOL_Obool)), _1431403), _1431405))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431397, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1431399, _1431397, _1431401), _1431403)), hAPP(c_Relation_OImage(_1431399, _1431397, _1431401), _1431405)))))], (14811 ^ _779327) ^ [_1028429, _1028431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028429), 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)), _1028431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028429), _1028431)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46281 ^ _779327) ^ [_1700446, _1700448, _1700450, _1700452] : [-(hAPP(hAPP(c_List_Otake(_1700446), _1700448), hAPP(hAPP(c_List_Oappend(_1700446), _1700450), _1700452)) = hAPP(hAPP(c_List_Oappend(_1700446), hAPP(hAPP(c_List_Otake(_1700446), _1700448), _1700450)), hAPP(hAPP(c_List_Otake(_1700446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1700448), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700446)), _1700450))), _1700452)))], (3258 ^ _779327) ^ [_828275, _828277] : [_828277 = _828275, -(c_Int_Oint__ge__less__than(_828277) = c_Int_Oint__ge__less__than(_828275))], (16579 ^ _779327) ^ [_1060391, _1060393, _1060395] : [class_Groups_Oordered__ab__group__add__abs(_1060391), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060391), hAPP(c_Groups_Oabs__class_Oabs(_1060391), _1060393)), hAPP(c_Groups_Oabs__class_Oabs(_1060391), _1060395))), hAPP(c_Groups_Oabs__class_Oabs(_1060391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1060391), _1060393), _1060395)))))], (40056 ^ _779327) ^ [_1544094, _1544096, _1544098] : [class_Groups_Olinordered__ab__semigroup__add(_1544094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544094), _1544096)), -(_1544096 = c_Orderings_Obot__class_Obot(tc_fun(_1544094, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1544094), _1544098), c_Big__Operators_Olinorder__class_OMax(_1544094, _1544096)) = c_Big__Operators_Olinorder__class_OMax(_1544094, hAPP(c_Set_OCollect(_1544094), hAPP(hAPP(c_COMBB(tc_fun(_1544094, tc_HOL_Obool), tc_HOL_Obool, _1544094), c_HOL_OEx(_1544094)), hAPP(hAPP(c_COMBC(_1544094, tc_fun(_1544094, tc_HOL_Obool), tc_fun(_1544094, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544094, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1544094, tc_HOL_Obool), tc_fun(_1544094, tc_HOL_Obool)), _1544094), c_COMBS(_1544094, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544094, tc_HOL_Obool), tc_fun(_1544094, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1544094), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544094), c_fconj)), hAPP(hAPP(c_COMBC(_1544094, tc_fun(_1544094, _1544094), tc_fun(_1544094, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544094, tc_HOL_Obool), tc_fun(tc_fun(_1544094, _1544094), tc_fun(_1544094, tc_HOL_Obool)), _1544094), c_COMBB(_1544094, tc_HOL_Obool, _1544094)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1544094), _1544098))))), hAPP(hAPP(c_COMBC(_1544094, tc_fun(_1544094, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544094)), _1544096))))))], (14707 ^ _779327) ^ [_1026795, _1026797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026795)), 14710 ^ _779327 : [(14717 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026797)), -(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), _1026797), _1026795))))], (14711 ^ _779327) ^ [] : [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), _1026797), _1026795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026797)))]]], (39620 ^ _779327) ^ [_1530959] : [class_Lattices_Oab__semigroup__idem__mult(_1530959), -(c_Finite__Set_Ofun__left__comm__idem(_1530959, _1530959, c_Groups_Otimes__class_Otimes(_1530959)))], (35687 ^ _779327) ^ [_1440666, _1440668, _1440670, _1440672, _1440674, _1440676, _1440678, _1440680] : [c_Finite__Set_Ofolding__image__simple(_1440666, _1440668, _1440670, _1440672, _1440674, _1440676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440668), _1440678)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440668), _1440680)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440668, tc_HOL_Obool)), _1440678), _1440680) = c_Orderings_Obot__class_Obot(tc_fun(_1440668, tc_HOL_Obool)), -(hAPP(_1440676, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440668, tc_HOL_Obool)), _1440678), _1440680)) = hAPP(hAPP(_1440670, hAPP(_1440676, _1440678)), hAPP(_1440676, _1440680)))], (17968 ^ _779327) ^ [_1084332, _1084334] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1084332)), _1084334) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1084332), _1084334)))], (9118 ^ _779327) ^ [_926622, _926624] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926622, tc_HOL_Obool)), _926624), _926624)))], (5362 ^ _779327) ^ [_861125, _861127, _861129, _861131, _861133, _861135] : [-(c_Product__Type_Oprod_Oprod__case(_861135, _861131, _861127) = c_Product__Type_Oprod_Oprod__case(_861133, _861129, _861125)), _861135 = _861133, _861131 = _861129, _861127 = _861125], (51839 ^ _779327) ^ [_1823266, _1823268, _1823270, _1823272, _1823274] : [c_Predicate_Otransp(_1823266, _1823268), hBOOL(hAPP(hAPP(_1823268, _1823270), _1823272)), hBOOL(hAPP(hAPP(_1823268, _1823272), _1823274)), -(hBOOL(hAPP(hAPP(_1823268, _1823270), _1823274)))], (1568 ^ _779327) ^ [_801915, _801917] : [-(class_Rings_Olinordered__comm__semiring__strict(_801915)), _801917 = _801915, class_Rings_Olinordered__comm__semiring__strict(_801917)], (1628 ^ _779327) ^ [_802665, _802667] : [-(class_Rings_Oordered__cancel__semiring(_802665)), _802667 = _802665, class_Rings_Oordered__cancel__semiring(_802667)], (48044 ^ _779327) ^ [_1739337, _1739339, _1739341, _1739343] : [c_List_Olist__all2(_1739337, _1739339, _1739341, c_List_Olist_ONil(_1739337), _1739343), -(_1739343 = c_List_Olist_ONil(_1739339))], (22923 ^ _779327) ^ [_1176511, _1176513, _1176515, _1176517] : [class_Orderings_Olinorder(_1176511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176511), _1176513), _1176515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176511), _1176513), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176511), _1176515), _1176517))))], (9533 ^ _779327) ^ [_933758, _933760] : [class_Rings_Olinordered__idom(_933758), 9536 ^ _779327 : [(9543 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _933760), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933758), hAPP(c_Int_Oring__1__class_Oof__int(_933758), _933760)), c_Groups_Ozero__class_Ozero(_933758))))], (9537 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933758), hAPP(c_Int_Oring__1__class_Oof__int(_933758), _933760)), c_Groups_Ozero__class_Ozero(_933758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _933760), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4098 ^ _779327) ^ [_841515, _841517, _841519, _841521, _841523, _841525] : [-(c_Enum_On__lists(_841525, _841521, _841517) = c_Enum_On__lists(_841523, _841519, _841515)), _841525 = _841523, _841521 = _841519, _841517 = _841515], (50496 ^ _779327) ^ [_1793066, _1793068, _1793070, _1793072, _1793074] : [hAPP(c_List_Ofilter(_1793066, _1793068), _1793070) = hAPP(hAPP(c_List_Olist_OCons(_1793066), _1793072), _1793074), 50501 ^ _779327 : [(50510 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1793068, _1793072)))], (50512 ^ _779327) ^ [] : [-(_1793074 = hAPP(c_List_Ofilter(_1793066, _1793068), 50500 ^ [_1793066, _1793068, _1793070, _1793072, _1793074]))], (50504 ^ _779327) ^ [_1793380] : [hBOOL(hAPP(hAPP(c_member(_1793066), _1793380), hAPP(c_List_Oset(_1793066), 50499 ^ [_1793066, _1793068, _1793070, _1793072, _1793074]))), hBOOL(hAPP(_1793068, _1793380))], (50502 ^ _779327) ^ [] : [-(_1793070 = hAPP(hAPP(c_List_Oappend(_1793066), 50499 ^ [_1793066, _1793068, _1793070, _1793072, _1793074]), hAPP(hAPP(c_List_Olist_OCons(_1793066), _1793072), 50500 ^ [_1793066, _1793068, _1793070, _1793072, _1793074])))]]], (41003 ^ _779327) ^ [_1572524, _1572526] : [c_Wellfounded_OwfP(_1572524, _1572526), 41006 ^ _779327 : [(41007 ^ _779327) ^ [_1572588] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1572524, _1572526), _1572588)))]]], (44803 ^ _779327) ^ [_1663628, _1663630, _1663632, _1663634, _1663636, _1663638] : [-(c_List_Olistrelp(_1663628, _1663630, hAPP(hAPP(c_List_Olist_OCons(_1663628), _1663632), _1663634), hAPP(hAPP(c_List_Olist_OCons(_1663628), _1663636), _1663638))), hBOOL(hAPP(hAPP(_1663630, _1663632), _1663636)), c_List_Olistrelp(_1663628, _1663630, _1663634, _1663638)], (12487 ^ _779327) ^ [_987393, _987395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987393), _987395)), _987393))], (45566 ^ _779327) ^ [_1683191, _1683193, _1683195] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683191), tc_List_Olist(_1683191))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683191), tc_List_Olist(_1683191)), _1683193), c_List_Olist_ONil(_1683191))), c_List_Olistrel1(_1683191, _1683195)))], (9843 ^ _779327) ^ [_938809, _938811] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _938809), _938811) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 9846 ^ _779327 : [(9849 ^ _779327) ^ [] : [-(_938811 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9847 ^ _779327) ^ [] : [-(_938809 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (28904 ^ _779327) ^ [_1294546, _1294548, _1294550] : [-(hAPP(hAPP(c_Set_Oinsert(_1294546), _1294548), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294546, tc_HOL_Obool)), _1294550), hAPP(hAPP(c_Set_Oinsert(_1294546), _1294548), c_Orderings_Obot__class_Obot(tc_fun(_1294546, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1294546), _1294548), _1294550))], (36516 ^ _779327) ^ [_1460675, _1460677, _1460679, _1460681, _1460683] : [c_Relation_Orefl__on(_1460675, _1460677, _1460679), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460675, _1460675)), hAPP(hAPP(c_Product__Type_OPair(_1460675, _1460675), _1460681), _1460683)), _1460679)), -(hBOOL(hAPP(hAPP(c_member(_1460675), _1460681), _1460677)))], (45195 ^ _779327) ^ [_1673649, _1673651, _1673653, _1673655, _1673657] : [hAPP(hAPP(c_List_Omap(_1673649, _1673651), _1673653), _1673655) = hAPP(hAPP(c_List_Omap(_1673649, _1673651), _1673653), _1673657), c_Fun_Oinj__on(_1673649, _1673651, _1673653, c_Orderings_Otop__class_Otop(tc_fun(_1673649, tc_HOL_Obool))), -(_1673655 = _1673657)], (32808 ^ _779327) ^ [_1376043, _1376045] : [class_Orderings_Olinorder(_1376043), -(c_Big__Operators_Olattice_OInf__fin(_1376043, c_Orderings_Oord__class_Omin(_1376043), hAPP(hAPP(c_Set_Oinsert(_1376043), _1376045), c_Orderings_Obot__class_Obot(tc_fun(_1376043, tc_HOL_Obool)))) = _1376045)], (33758 ^ _779327) ^ [_1396392, _1396394, _1396396] : [class_Lattices_Olattice(_1396392), hAPP(_1396394, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396392), 33763 ^ [_1396392, _1396394, _1396396]), 33764 ^ [_1396392, _1396394, _1396396])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1396392), hAPP(_1396394, 33763 ^ [_1396392, _1396394, _1396396])), hAPP(_1396394, 33764 ^ [_1396392, _1396394, _1396396])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396392), _1396396)), -(_1396396 = c_Orderings_Obot__class_Obot(tc_fun(_1396392, tc_HOL_Obool))), -(hAPP(_1396394, c_Big__Operators_Olattice__class_OSup__fin(_1396392, _1396396)) = c_Big__Operators_Olattice__class_OSup__fin(_1396392, hAPP(c_Set_Oimage(_1396392, _1396392, _1396394), _1396396)))], (48299 ^ _779327) ^ [_1745227, _1745229] : [-(hAPP(c_List_Oset(_1745227), c_List_Oremdups(_1745227, _1745229)) = hAPP(c_List_Oset(_1745227), _1745229))], (15129 ^ _779327) ^ [_1034171, _1034173] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1034171)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034171)), _1034173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1034171))), _1034173))], (24259 ^ _779327) ^ [_1201734, _1201736] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201734), _1201736)), -(_1201734 = _1201736), 24266 ^ _779327 : [(24269 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201736), _1201734))], (24267 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201734), _1201736)))]]], (16475 ^ _779327) ^ [_1058613] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058613), c_Int_OPls) = _1058613)], (10901 ^ _779327) ^ [_957050, _957052, _957054] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957050), _957052)), _957054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957050), _957054)), _957052))], (50435 ^ _779327) ^ [_1791421, _1791423, _1791425, _1791427] : [50437 ^ _779327 : [(50440 ^ _779327) ^ [] : [hBOOL(hAPP(_1791425, 50436 ^ [_1791421, _1791423, _1791425, _1791427]))], (50438 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791421), 50436 ^ [_1791421, _1791423, _1791425, _1791427]), hAPP(c_List_Oset(_1791421), _1791423))))]], -(c_List_OtakeWhile(_1791421, _1791425, hAPP(hAPP(c_List_Oappend(_1791421), _1791423), _1791427)) = hAPP(hAPP(c_List_Oappend(_1791421), _1791423), c_List_OtakeWhile(_1791421, _1791425, _1791427)))], (51681 ^ _779327) ^ [_1818473, _1818475] : [c_Relation_Otrans(_1818473, hAPP(c_Relation_Oconverse(_1818473, _1818473), _1818475)), -(c_Relation_Otrans(_1818473, _1818475))], (22207 ^ _779327) ^ [_1163165, _1163167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163165)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163167)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1163165, _1163167) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1163165, _1163167)))], (23005 ^ _779327) ^ [_1177889, _1177891, _1177893, _1177895] : [class_Orderings_Olinorder(_1177889), 23008 ^ _779327 : [(23017 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177889), _1177891), _1177893)), _1177895))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), _1177891), _1177895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), _1177893), _1177895))], (23009 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177889), _1177891), _1177893)), _1177895)), 23012 ^ _779327 : [(23015 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), _1177893), _1177895)))], (23013 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177889), _1177891), _1177895)))]]]]], (21892 ^ _779327) ^ [_1156480, _1156482, _1156484] : [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), _1156480), _1156482))), -(hBOOL(hAPP(hAPP(_1156484, _1156480), _1156482))), 21899 ^ _779327 : [(21902 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1156484, 21897 ^ [_1156480, _1156482, _1156484]), 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)))), 21898 ^ [_1156480, _1156482, _1156484])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 21897 ^ [_1156480, _1156482, _1156484]), 21898 ^ [_1156480, _1156482, _1156484]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 21898 ^ [_1156480, _1156482, _1156484]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21912 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1156484, 21897 ^ [_1156480, _1156482, _1156484]), 21898 ^ [_1156480, _1156482, _1156484]))], (21900 ^ _779327) ^ [] : [-(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), 21897 ^ [_1156480, _1156482, _1156484]), 21898 ^ [_1156480, _1156482, _1156484]))))]]], (50737 ^ _779327) ^ [_1797894, _1797896, _1797898] : [-(hBOOL(hAPP(hAPP(c_member(_1797894), _1797896), hAPP(c_List_Oset(_1797894), _1797898)))), 50738 ^ _779327 : [(50739 ^ _779327) ^ [_1797983] : [50740 ^ _779327 : [(50741 ^ _779327) ^ [_1798056] : [_1797898 = hAPP(hAPP(c_List_Oappend(_1797894), _1797983), hAPP(hAPP(c_List_Olist_OCons(_1797894), _1797896), _1798056))]], -(hBOOL(hAPP(hAPP(c_member(_1797894), _1797896), hAPP(c_List_Oset(_1797894), _1797983))))]]], (42110 ^ _779327) ^ [_1597320, _1597322, _1597324, _1597326, _1597328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597320, _1597320)), hAPP(hAPP(c_Product__Type_OPair(_1597320, _1597320), _1597322), _1597324)), c_Transitive__Closure_Otrancl(_1597320, _1597326))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1597320, _1597320)), hAPP(hAPP(c_Product__Type_OPair(_1597320, _1597320), _1597324), _1597328)), _1597326)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597320, _1597320)), hAPP(hAPP(c_Product__Type_OPair(_1597320, _1597320), _1597322), _1597328)), c_Transitive__Closure_Otrancl(_1597320, _1597326))))], (43123 ^ _779327) ^ [_1623439, _1623441, _1623443, _1623445] : [class_Lattices_Osemilattice__sup(_1623439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623439), _1623441)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1623439, _1623439, c_Lattices_Osemilattice__sup__class_Osup(_1623439)), _1623443), hAPP(hAPP(c_Set_Oinsert(_1623439), _1623445), _1623441)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1623439), _1623445), hAPP(hAPP(c_Finite__Set_Ofold(_1623439, _1623439, c_Lattices_Osemilattice__sup__class_Osup(_1623439)), _1623443), _1623441)))], (47201 ^ _779327) ^ [_1721590, _1721592, _1721594] : [class_Orderings_Olinorder(_1721590), -(c_Big__Operators_Olinorder__class_OMax(_1721590, hAPP(c_List_Oset(_1721590), hAPP(hAPP(c_List_Olist_OCons(_1721590), _1721592), _1721594))) = hAPP(c_List_Ofoldl(_1721590, _1721590, c_Orderings_Oord__class_Omax(_1721590), _1721592), _1721594))], (47084 ^ _779327) ^ [_1719235, _1719237, _1719239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719235), _1719237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719235), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1719237), _1719239))))], (47670 ^ _779327) ^ [_1730991, _1730993] : [-(c_List_Opartition(_1730991, _1730993, c_List_Olist_ONil(_1730991)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730991), tc_List_Olist(_1730991)), c_List_Olist_ONil(_1730991)), c_List_Olist_ONil(_1730991)))], (51669 ^ _779327) ^ [_1818265, _1818267] : [c_Relation_Otrans(_1818265, _1818267), -(c_Relation_Otrans(tc_List_Olist(_1818265), c_List_Olistrel(_1818265, _1818267)))], (2914 ^ _779327) ^ [_822853, _822855, _822857, _822859] : [-(c_Set_Othe__elem(_822859, _822855) = c_Set_Othe__elem(_822857, _822853)), _822859 = _822857, _822855 = _822853], (10311 ^ _779327) ^ [_946446, _946448, _946450, _946452] : [class_Rings_Olinordered__semidom(_946446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946448), _946450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946446), c_Groups_Oone__class_Oone(_946446)), _946452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946446), hAPP(hAPP(c_Power_Opower__class_Opower(_946446), _946452), _946448)), hAPP(hAPP(c_Power_Opower__class_Opower(_946446), _946452), _946450))))], (38361 ^ _779327) ^ [_1501361, _1501363, _1501365, _1501367, _1501369] : [hBOOL(hAPP(_1501367, hAPP(_1501365, _1501369))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1501361, _1501363, _1501365), _1501367), _1501369)))], (25431 ^ _779327) ^ [_1222798, _1222800, _1222802] : [-(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), _1222798)), 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))), _1222800))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1222802))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222798), 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), _1222802), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1222800)))))], (13818 ^ _779327) ^ [_1011334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011334)), -(_1011334 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1011334), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10283 ^ _779327) ^ [_945916, _945918, _945920, _945922] : [class_Rings_Olinordered__semidom(_945916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945916), c_Groups_Oone__class_Oone(_945916)), _945918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945916), hAPP(hAPP(c_Power_Opower__class_Opower(_945916), _945918), _945920)), hAPP(hAPP(c_Power_Opower__class_Opower(_945916), _945918), _945922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945920), _945922)))], (12495 ^ _779327) ^ [_987552, _987554, _987556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _987552), _987554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987552), _987556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _987554), _987556))))], (7764 ^ _779327) ^ [_901801, _901803, _901805] : [class_Rings_Oordered__ring(_901801), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901801), _901803), c_Groups_Ozero__class_Ozero(_901801))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901801), _901805), c_Groups_Ozero__class_Ozero(_901801))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901801), c_Groups_Ozero__class_Ozero(_901801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_901801), _901803), _901805))))], (48596 ^ _779327) ^ [_1752201, _1752203, _1752205, _1752207] : [-(hAPP(c_List_Ofilter(_1752201, _1752203), hAPP(hAPP(c_List_Oappend(_1752201), _1752205), _1752207)) = hAPP(hAPP(c_List_Oappend(_1752201), hAPP(c_List_Ofilter(_1752201, _1752203), _1752205)), hAPP(c_List_Ofilter(_1752201, _1752203), _1752207)))], (22303 ^ _779327) ^ [_1164931, _1164933, _1164935, _1164937, _1164939, _1164941] : [hBOOL(hAPP(_1164931, _1164933)), hBOOL(hAPP(_1164935, _1164937)), 22310 ^ _779327 : [(22313 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1164935, hAPP(c_Product__Type_Osnd(_1164939, _1164941), hAPP(hAPP(c_Product__Type_OPair(_1164939, _1164941), _1164933), _1164937)))))], (22311 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1164931, hAPP(c_Product__Type_Ofst(_1164939, _1164941), hAPP(hAPP(c_Product__Type_OPair(_1164939, _1164941), _1164933), _1164937)))))]]], (13850 ^ _779327) ^ [_1011887, _1011889] : [class_Rings_Olinordered__idom(_1011887), 13853 ^ _779327 : [(13860 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011887), c_Groups_Ozero__class_Ozero(_1011887)), _1011889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011887), c_Groups_Ozero__class_Ozero(_1011887)), c_Groups_Osgn__class_Osgn(_1011887, _1011889))))], (13854 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011887), c_Groups_Ozero__class_Ozero(_1011887)), c_Groups_Osgn__class_Osgn(_1011887, _1011889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011887), c_Groups_Ozero__class_Ozero(_1011887)), _1011889)))]]], (5288 ^ _779327) ^ [_860040, _860042] : [_860042 = _860040, -(c_Relation_OId(_860042) = c_Relation_OId(_860040))], (5588 ^ _779327) ^ [_867256, _867258] : [hAPP(_867256, 5589 ^ [_867256, _867258]) = hAPP(_867258, 5589 ^ [_867256, _867258]), -(_867256 = _867258)], (46016 ^ _779327) ^ [_1694697, _1694699, _1694701, _1694703, _1694705] : [-(hAPP(hAPP(c_List_Olist__update(_1694697, hAPP(hAPP(c_List_Oappend(_1694697), _1694699), hAPP(hAPP(c_List_Olist_OCons(_1694697), _1694701), _1694703))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694697)), _1694699)), _1694705) = hAPP(hAPP(c_List_Oappend(_1694697), _1694699), hAPP(hAPP(c_List_Olist_OCons(_1694697), _1694705), _1694703)))], (17922 ^ _779327) ^ [_1083614, _1083616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083614)), c_Int_OBit0(_1083616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083614), _1083616)))], (21208 ^ _779327) ^ [_1143403, _1143405] : [hAPP(c_Nat_OSuc, _1143403) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143405), -(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(_1143405))), 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)), _1143403))))))], (5702 ^ _779327) ^ [_869525, _869527, _869529, _869531] : [-(hAPP(hAPP(c_Power_Opower_Opower(_869525, _869527, _869529), _869531), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _869527)], (27875 ^ _779327) ^ [_1274915, _1274917, _1274919, _1274921] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274915, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1274915), _1274917), _1274919)), _1274921) = hAPP(hAPP(c_Set_Oinsert(_1274915), _1274917), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274915, tc_HOL_Obool)), _1274919), _1274921)))], (15832 ^ _779327) ^ [_1047051, _1047053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1047051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047053), _1047051))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047053), _1047051) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047053), _1047051)), _1047051)))], (3594 ^ _779327) ^ [_833615, _833617, _833619, _833621] : [-(c_Relation_ODomain(_833621, _833617) = c_Relation_ODomain(_833619, _833615)), _833621 = _833619, _833617 = _833615], (38814 ^ _779327) ^ [_1512618, _1512620, _1512622, _1512624, _1512626] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512618, _1512620), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512618, tc_HOL_Obool)), _1512622), _1512624)), hAPP(c_COMBK(tc_fun(_1512620, tc_HOL_Obool), _1512618), _1512626)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512618, _1512620), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512618, _1512620), _1512622), hAPP(c_COMBK(tc_fun(_1512620, tc_HOL_Obool), _1512618), _1512626))), hAPP(hAPP(c_Product__Type_OSigma(_1512618, _1512620), _1512624), hAPP(c_COMBK(tc_fun(_1512620, tc_HOL_Obool), _1512618), _1512626))))], (18328 ^ _779327) ^ [_1090614] : [class_Rings_Osemiring__1(_1090614), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090614), c_Groups_Oone__class_Oone(_1090614)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1090614))], (18847 ^ _779327) ^ [_1100447, _1100449, _1100451] : [class_Fields_Olinordered__field__inverse__zero(_1100447), -(hAPP(c_Groups_Oabs__class_Oabs(_1100447), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100447), _1100449), _1100451)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100447), hAPP(c_Groups_Oabs__class_Oabs(_1100447), _1100449)), hAPP(c_Groups_Oabs__class_Oabs(_1100447), _1100451)))], (39101 ^ _779327) ^ [_1519696, _1519698, _1519700] : [class_Lattices_Osemilattice__inf(_1519696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519696), _1519698)), -(_1519698 = c_Orderings_Obot__class_Obot(tc_fun(_1519696, tc_HOL_Obool))), 39112 ^ _779327 : [(39113 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519696), _1519700), hAPP(c_Finite__Set_Ofold1(_1519696, c_Lattices_Osemilattice__inf__class_Oinf(_1519696)), _1519698))), 39116 ^ _779327 : [(39117 ^ _779327) ^ [_1519989] : [hBOOL(hAPP(hAPP(c_member(_1519696), _1519989), _1519698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519696), _1519700), _1519989)))]]], (39123 ^ _779327) ^ [] : [39125 ^ _779327 : [(39128 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519696), _1519700), 39124 ^ [_1519696, _1519698, _1519700]))], (39126 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519696), 39124 ^ [_1519696, _1519698, _1519700]), _1519698)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519696), _1519700), hAPP(c_Finite__Set_Ofold1(_1519696, c_Lattices_Osemilattice__inf__class_Oinf(_1519696)), _1519698))))]]], (1658 ^ _779327) ^ [_803040, _803042] : [-(class_Rings_Olinordered__semiring(_803040)), _803042 = _803040, class_Rings_Olinordered__semiring(_803042)], (45038 ^ _779327) ^ [_1669870, _1669872, _1669874, _1669876] : [-(hAPP(hAPP(c_List_Otake(_1669870), _1669872), hAPP(hAPP(c_List_Otake(_1669870), _1669874), _1669876)) = hAPP(hAPP(c_List_Otake(_1669870), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1669872), _1669874)), _1669876))], (40656 ^ _779327) ^ [_1563480, _1563482] : [hAPP(hAPP(c_Relation_Orel__comp(_1563480, _1563480, _1563480), _1563482), _1563482) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563480, _1563480), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1563480, _1563482))], (30447 ^ _779327) ^ [_1328312, _1328314, _1328316] : [-(hBOOL(hAPP(hAPP(c_member(_1328312), _1328314), _1328316))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328312, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328312), _1328314), _1328316)), hAPP(hAPP(c_Set_Oinsert(_1328312), _1328314), c_Orderings_Obot__class_Obot(tc_fun(_1328312, tc_HOL_Obool)))) = _1328316)], (51766 ^ _779327) ^ [_1820307] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1820307, tc_HOL_Obool) = c_Set_OBex(_1820307))], (22793 ^ _779327) ^ [_1174235, _1174237, _1174239] : [class_Orderings_Olinorder(_1174235), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174235), _1174237), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174235), _1174237), _1174239)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174235), _1174237), _1174239))], (5666 ^ _779327) ^ [_868841, _868843, _868845, _868847] : [-(hAPP(c_Nat_Onat_Onat__rec(_868841, _868843, _868845), hAPP(c_Nat_OSuc, _868847)) = hAPP(hAPP(_868845, _868847), hAPP(c_Nat_Onat_Onat__rec(_868841, _868843, _868845), _868847)))], (39595 ^ _779327) ^ [_1530526, _1530528] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1530526), c_Int_OInteg)), hBOOL(hAPP(_1530528, hAPP(c_Int_ORep__Integ, 39600 ^ [_1530526, _1530528]))), -(hBOOL(hAPP(_1530528, _1530526)))], (17822 ^ _779327) ^ [_1081668, _1081670] : [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), _1081668))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1081670)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081668))) = 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), _1081670), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081668)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5664 ^ _779327) ^ [_868801, _868803, _868805, _868807] : [-(c_Nat_Onat_Onat__case(_868801, _868803, _868805, hAPP(c_Nat_OSuc, _868807)) = hAPP(_868805, _868807))], (43828 ^ _779327) ^ [_1637978, _1637980, _1637982, _1637984] : [-(hAPP(c_Set_Ovimage(_1637978, _1637980, _1637982), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637980, tc_HOL_Obool), _1637984)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637980, tc_HOL_Obool), tc_fun(_1637978, tc_HOL_Obool)), _1637984), c_Set_Ovimage(_1637978, _1637980, _1637982)))], (46375 ^ _779327) ^ [_1702736, _1702738, _1702740, _1702742] : [-(c_List_Osublist(_1702736, hAPP(hAPP(c_List_Oappend(_1702736), _1702738), _1702740), _1702742) = hAPP(hAPP(c_List_Oappend(_1702736), c_List_Osublist(_1702736, _1702738, _1702742)), c_List_Osublist(_1702736, _1702740, 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(_1702736)), _1702738)))), _1702742)))))], (48050 ^ _779327) ^ [_1739428, _1739430, _1739432, _1739434] : [_1739434 = c_List_Olist_ONil(_1739430), -(c_List_Olist__all2(_1739428, _1739430, _1739432, c_List_Olist_ONil(_1739428), _1739434))], (36431 ^ _779327) ^ [_1459088, _1459090, _1459092, _1459094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459088), _1459090)), c_Equiv__Relations_Oequiv(_1459088, _1459090, _1459092), 36441 ^ _779327 : [(36444 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1459094), hAPP(c_Finite__Set_Ocard(_1459088), 36440 ^ [_1459088, _1459090, _1459092, _1459094])))], (36442 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1459088, tc_HOL_Obool)), 36440 ^ [_1459088, _1459090, _1459092, _1459094]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1459088), _1459090), _1459092))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1459094), hAPP(c_Finite__Set_Ocard(_1459088), _1459090))))], (45858 ^ _779327) ^ [_1691266, _1691268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1691266), _1691268)), -(c_List_Oupto(_1691268, _1691266) = c_List_Olist_ONil(tc_Int_Oint))], (51083 ^ _779327) ^ [_1804900, _1804902, _1804904, _1804906] : [-(hAPP(hAPP(c_List_Odrop(_1804900), _1804902), c_List_Oreplicate(_1804900, _1804904, _1804906)) = c_List_Oreplicate(_1804900, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1804904), _1804902), _1804906))], (48888 ^ _779327) ^ [_1759277, _1759279, _1759281, _1759283] : [class_Groups_Ocomm__monoid__add(_1759277), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1759277), _1759279), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1759281, _1759283))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1759277), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1759277), _1759279), c_List_Oupt(_1759281, _1759283))))], (9741 ^ _779327) ^ [] : [-(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)))], (31021 ^ _779327) ^ [_1341020, _1341022] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1341020), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1341022)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1341020), _1341022)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1341022), _1341020)))], (14477 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (45562 ^ _779327) ^ [_1682908, _1682910, _1682912, _1682914, _1682916, _1682918, _1682920, _1682922] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1682908, _1682910), _1682912), _1682914), hAPP(hAPP(c_List_Ozip(_1682908, _1682910), _1682916), hAPP(hAPP(c_List_Omap(_1682918, _1682910), _1682920), _1682922))) = hAPP(hAPP(c_List_Omap(tc_prod(_1682908, _1682918), _1682912), hAPP(c_Product__Type_Oprod_Oprod__case(_1682908, _1682918, _1682912), hAPP(hAPP(c_COMBB(tc_fun(_1682918, tc_prod(_1682908, _1682910)), tc_fun(_1682918, _1682912), _1682908), hAPP(c_COMBB(tc_prod(_1682908, _1682910), _1682912, _1682918), _1682914)), hAPP(hAPP(c_COMBC(_1682908, tc_fun(_1682918, _1682910), tc_fun(_1682918, tc_prod(_1682908, _1682910))), hAPP(hAPP(c_COMBB(tc_fun(_1682910, tc_prod(_1682908, _1682910)), tc_fun(tc_fun(_1682918, _1682910), tc_fun(_1682918, tc_prod(_1682908, _1682910))), _1682908), c_COMBB(_1682910, tc_prod(_1682908, _1682910), _1682918)), c_Product__Type_OPair(_1682908, _1682910))), _1682920)))), hAPP(hAPP(c_List_Ozip(_1682908, _1682918), _1682916), _1682922)))], (34477 ^ _779327) ^ [_1413276, _1413278, _1413280, _1413282, _1413284] : [c_Equiv__Relations_Oequiv(_1413276, _1413278, _1413280), 34480 ^ _779327 : [(34491 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1413276, _1413276)), hAPP(hAPP(c_Product__Type_OPair(_1413276, _1413276), _1413282), _1413284)), _1413280))), hAPP(c_Relation_OImage(_1413276, _1413276, _1413280), hAPP(hAPP(c_Set_Oinsert(_1413276), _1413282), c_Orderings_Obot__class_Obot(tc_fun(_1413276, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1413276, _1413276, _1413280), hAPP(hAPP(c_Set_Oinsert(_1413276), _1413284), c_Orderings_Obot__class_Obot(tc_fun(_1413276, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1413276), _1413282), _1413278)), hBOOL(hAPP(hAPP(c_member(_1413276), _1413284), _1413278))], (34481 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1413276, _1413276)), hAPP(hAPP(c_Product__Type_OPair(_1413276, _1413276), _1413282), _1413284)), _1413280)), 34484 ^ _779327 : [(34489 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413276), _1413284), _1413278)))], (34487 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413276), _1413282), _1413278)))], (34485 ^ _779327) ^ [] : [-(hAPP(c_Relation_OImage(_1413276, _1413276, _1413280), hAPP(hAPP(c_Set_Oinsert(_1413276), _1413282), c_Orderings_Obot__class_Obot(tc_fun(_1413276, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1413276, _1413276, _1413280), hAPP(hAPP(c_Set_Oinsert(_1413276), _1413284), c_Orderings_Obot__class_Obot(tc_fun(_1413276, tc_HOL_Obool)))))]]]]], (42587 ^ _779327) ^ [_1609805, _1609807] : [-(hAPP(c_Relation_Oconverse(_1609805, _1609805), c_Relation_OId__on(_1609805, _1609807)) = c_Relation_OId__on(_1609805, _1609807))], (38244 ^ _779327) ^ [_1498621, _1498623, _1498625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498621, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498621, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38245 ^ [_1498621, _1498623, _1498625])), _1498623)), _1498625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498621, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498621, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1498623)), _1498625)))], (11673 ^ _779327) ^ [_972710, _972712, _972714] : [class_Groups_Oordered__ab__group__add(_972710), 11676 ^ _779327 : [(11683 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972710), hAPP(c_Groups_Ouminus__class_Ouminus(_972710), _972714)), _972712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972710), hAPP(c_Groups_Ouminus__class_Ouminus(_972710), _972712)), _972714)))], (11677 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972710), hAPP(c_Groups_Ouminus__class_Ouminus(_972710), _972712)), _972714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972710), hAPP(c_Groups_Ouminus__class_Ouminus(_972710), _972714)), _972712)))]]], (34272 ^ _779327) ^ [_1408578, _1408580, _1408582] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408578, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408578), _1408580), _1408582), -(_1408580 = c_Orderings_Obot__class_Obot(tc_fun(_1408578, tc_HOL_Obool)))], (6910 ^ _779327) ^ [_887456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887456), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_887456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5618 ^ _779327) ^ [_867879, _867881, _867883] : [-(c_Hoare__Mirabelle_Ohoare__valids(_867879, _867881, _867883)), 5620 ^ _779327 : [(5621 ^ _779327) ^ [_868025] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_867879)), _868025), _867881)), -(c_Hoare__Mirabelle_Otriple__valid(_867879, 5619 ^ [_867879, _867881, _867883], _868025))], (5630 ^ _779327) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_867879, 5619 ^ [_867879, _867881, _867883], 5626 ^ [_867879, _867881, _867883])], (5628 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_867879)), 5626 ^ [_867879, _867881, _867883]), _867883)))]]], (50070 ^ _779327) ^ [_1783178, _1783180, _1783182, _1783184] : [_1783178 = _1783180, -(hAPP(c_List_OremoveAll(_1783182, _1783178), hAPP(hAPP(c_List_Olist_OCons(_1783182), _1783180), _1783184)) = hAPP(c_List_OremoveAll(_1783182, _1783178), _1783184))], (30239 ^ _779327) ^ [_1323205, _1323207, _1323209] : [class_Orderings_Oord(_1323205), 30242 ^ _779327 : [(30249 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323205), _1323207), _1323209)), -(hBOOL(hAPP(hAPP(c_member(_1323205), _1323207), hAPP(c_SetInterval_Oord__class_OlessThan(_1323205), _1323209))))], (30243 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1323205), _1323207), hAPP(c_SetInterval_Oord__class_OlessThan(_1323205), _1323209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323205), _1323207), _1323209)))]]], (14135 ^ _779327) ^ [_1017089, _1017091, _1017093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017089, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017089, tc_HOL_Obool)), _1017091)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017089, tc_HOL_Obool)), _1017093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017089, tc_HOL_Obool)), _1017093), _1017091)))], (33660 ^ _779327) ^ [_1393721, _1393723, _1393725, _1393727] : [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), _1393721), _1393723)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1393725), _1393727))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393721), _1393727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393725), _1393723))], (42741 ^ _779327) ^ [_1613333, _1613335, _1613337] : [c_Relation_Ototal__on(_1613333, _1613335, _1613337), -(c_Relation_Ototal__on(_1613333, _1613335, hAPP(c_Relation_Oconverse(_1613333, _1613333), _1613337)))], (53032 ^ _779327) ^ [] : [hBOOL(c_fFalse)], (8558 ^ _779327) ^ [_916367, _916369] : [class_Rings_Olinordered__semidom(_916367), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916367), c_Groups_Ozero__class_Ozero(_916367)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_916367), _916369))))], (46670 ^ _779327) ^ [_1710584, _1710586, _1710588, _1710590] : [-(hAPP(c_List_Orotate1(_1710586), hAPP(hAPP(c_List_Olist_OCons(_1710586), _1710588), _1710590)) = hAPP(hAPP(c_List_Oappend(_1710586), _1710590), hAPP(hAPP(c_List_Olist_OCons(_1710586), _1710588), c_List_Olist_ONil(_1710586))))], (36492 ^ _779327) ^ [_1460249, _1460251, _1460253] : [class_Lattices_Olattice(_1460249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460249), _1460251)), hBOOL(hAPP(hAPP(c_member(_1460249), _1460253), _1460251)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1460249), _1460253), c_Big__Operators_Olattice__class_OInf__fin(_1460249, _1460251)) = c_Big__Operators_Olattice__class_OInf__fin(_1460249, _1460251))], (12005 ^ _779327) ^ [_978432, _978434] : [class_Rings_Ocomm__semiring__1(_978432), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978432), c_Groups_Ozero__class_Ozero(_978432)), _978434) = _978434)], (16465 ^ _779327) ^ [_1058447, _1058449, _1058451] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058447), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058449, _1058451)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058447), _1058449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058447), _1058451)))], (52446 ^ _779327) ^ [_1834673, _1834675] : [class_Complete__Lattice_Ocomplete__lattice(_1834673), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1834675, _1834673)))], (28007 ^ _779327) ^ [_1277423, _1277425, _1277427] : [class_Complete__Lattice_Ocomplete__lattice(_1277423), _1277425 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1277423, _1277427), c_Orderings_Oorder__class_Omono(_1277423, _1277423, _1277427), -(_1277425 = hAPP(_1277427, _1277425))], (38224 ^ _779327) ^ [_1497522, _1497524, _1497526, _1497528, _1497530, _1497532] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497524, _1497526)), hAPP(hAPP(c_Product__Type_OPair(_1497524, _1497526), _1497530), _1497532)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497522, tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1497522, tc_HOL_Obool))), _1497528))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497522, tc_fun(_1497524, tc_fun(_1497526, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1497522, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_fun(_1497524, tc_fun(_1497526, tc_HOL_Obool)), _1497522), hAPP(c_COMBC(_1497524, tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_fun(_1497526, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497526, tc_fun(tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_fun(_1497526, tc_HOL_Obool)), _1497524), c_COMBC(_1497526, tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497526, tc_prod(_1497524, _1497526)), tc_fun(_1497526, tc_fun(tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_HOL_Obool)), _1497524), hAPP(c_COMBB(tc_prod(_1497524, _1497526), tc_fun(tc_fun(tc_prod(_1497524, _1497526), tc_HOL_Obool), tc_HOL_Obool), _1497526), c_member(tc_prod(_1497524, _1497526)))), c_Product__Type_OPair(_1497524, _1497526))))), _1497528)), _1497530), _1497532)))], (21964 ^ _779327) ^ [_1158079, _1158081, _1158083, _1158085, _1158087, _1158089] : [-(hAPP(hAPP(c_Product__Type_OPair(_1158079, _1158081), _1158083), _1158085) = hAPP(hAPP(c_Product__Type_OPair(_1158079, _1158081), _1158087), _1158089)), _1158083 = _1158087, _1158085 = _1158089], (45082 ^ _779327) ^ [_1671134, _1671136, _1671138, _1671140, _1671142] : [c_Fun_Oinj__on(_1671134, _1671136, _1671138, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1671134, tc_HOL_Obool)), hAPP(c_List_Oset(_1671134), _1671140)), hAPP(c_List_Oset(_1671134), _1671142))), 45085 ^ _779327 : [(45092 ^ _779327) ^ [] : [_1671140 = _1671142, -(hAPP(hAPP(c_List_Omap(_1671134, _1671136), _1671138), _1671140) = hAPP(hAPP(c_List_Omap(_1671134, _1671136), _1671138), _1671142))], (45086 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Omap(_1671134, _1671136), _1671138), _1671140) = hAPP(hAPP(c_List_Omap(_1671134, _1671136), _1671138), _1671142), -(_1671140 = _1671142)]]], (12870 ^ _779327) ^ [_994392, _994394] : [class_Groups_Oordered__ab__group__add(_994392), 12873 ^ _779327 : [(12880 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994392), _994394), c_Groups_Ozero__class_Ozero(_994392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994392), c_Groups_Ozero__class_Ozero(_994392)), hAPP(c_Groups_Ouminus__class_Ouminus(_994392), _994394))))], (12874 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994392), c_Groups_Ozero__class_Ozero(_994392)), hAPP(c_Groups_Ouminus__class_Ouminus(_994392), _994394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994392), _994394), c_Groups_Ozero__class_Ozero(_994392))))]]], (20916 ^ _779327) ^ [_1137623] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1137623)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1137623)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2654 ^ _779327) ^ [_818459, _818461] : [_818461 = _818459, -(c_Lazy__Sequence_Ohb__not__seq(_818461) = c_Lazy__Sequence_Ohb__not__seq(_818459))], (15445 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (47322 ^ _779327) ^ [_1724191, _1724193, _1724195] : [_1724191 = c_List_Olist_ONil(_1724193), -(c_List_Olast(_1724193, hAPP(hAPP(c_List_Oappend(_1724193), _1724195), _1724191)) = c_List_Olast(_1724193, _1724195))], (43888 ^ _779327) ^ [_1639338, _1639340, _1639342, _1639344] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1639338, tc_HOL_Obool), tc_fun(_1639340, tc_HOL_Obool)), _1639342), hAPP(hAPP(c_COMBC(tc_fun(_1639338, tc_HOL_Obool), tc_fun(_1639338, tc_fun(_1639340, tc_HOL_Obool)), tc_fun(_1639340, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639338, tc_fun(_1639340, tc_HOL_Obool))), _1639344)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639338, tc_fun(_1639340, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1639338, tc_HOL_Obool), _1639342)), _1639344))], (48690 ^ _779327) ^ [_1755131, _1755133] : [-(c_Random_Oselect__weight(_1755131, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755131), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1755131, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1755131, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1755131)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1755133)) = c_Random_Oselect__weight(_1755131, _1755133))], (47030 ^ _779327) ^ [_1718187, _1718189] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1718187), _1718189))), -(c_Nitpick_Ocard_H(_1718187, _1718189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36987 ^ _779327) ^ [_1469626, _1469628, _1469630, _1469632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1469626), hAPP(c_Set_Oimage(_1469628, _1469626, _1469630), _1469632))), hAPP(c_Finite__Set_Ocard(_1469628), _1469632))), c_Fun_Oinj__on(_1469628, _1469626, _1469630, _1469632)], (50719 ^ _779327) ^ [_1797476, _1797478, _1797480, _1797482] : [50720 ^ _779327 : [(50723 ^ _779327) ^ [] : [c_List_Olist__ex(_1797476, _1797478, _1797482)], (50721 ^ _779327) ^ [] : [hBOOL(hAPP(_1797478, _1797480))]], -(c_List_Olist__ex(_1797476, _1797478, hAPP(hAPP(c_List_Olist_OCons(_1797476), _1797480), _1797482)))], (16039 ^ _779327) ^ [_1050765, _1050767, _1050769, _1050771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1050765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050767), _1050769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050769), 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), _1050767), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050771, _1050765))), _1050769)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44600 ^ _779327) ^ [_1657145, _1657147, _1657149, _1657151] : [hBOOL(hAPP(hAPP(c_member(_1657145), _1657147), c_Wellfounded_Oacc(_1657145, _1657149))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657145)), _1657151), c_Wellfounded_Oacc(tc_List_Olist(_1657145), c_List_Olistrel1(_1657145, _1657149)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657145)), hAPP(hAPP(c_List_Olist_OCons(_1657145), _1657147), _1657151)), c_Wellfounded_Oacc(tc_List_Olist(_1657145), c_List_Olistrel1(_1657145, _1657149)))))], (7213 ^ _779327) ^ [_892343, _892345, _892347, _892349] : [class_Orderings_Oorder(_892343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892343), hAPP(_892345, 7218 ^ [_892343, _892345, _892347, _892349])), hAPP(_892345, hAPP(c_Nat_OSuc, 7218 ^ [_892343, _892345, _892347, _892349])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _892347), _892349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892343), hAPP(_892345, _892347)), hAPP(_892345, _892349))))], (23327 ^ _779327) ^ [_1184533] : [-(c_Nitpick_Ozero__frac(_1184533) = c_Nitpick_OAbs__Frac(_1184533, 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))))], (9012 ^ _779327) ^ [_924421, _924423] : [_924421 = _924423, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924421) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924423))], (10699 ^ _779327) ^ [_952996, _952998, _953000, _953002, _953004] : [class_Rings_Ocomm__semiring__1(_952996), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), _952998), _953000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), _953002), _953004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), _952998), _953002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952996), _953000), _953004)))], (40813 ^ _779327) ^ [_1567566, _1567568, _1567570, _1567572] : [hBOOL(hAPP(hAPP(c_member(_1567568), _1567572), hAPP(c_Relation_ORange(_1567566, _1567568), _1567570))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1567566, _1567568, hAPP(hAPP(c_COMBC(_1567566, tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_fun(_1567568, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567568, tc_fun(tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_fun(_1567568, tc_HOL_Obool)), _1567566), c_COMBC(_1567568, tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567568, tc_prod(_1567566, _1567568)), tc_fun(_1567568, tc_fun(tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_HOL_Obool)), _1567566), hAPP(c_COMBB(tc_prod(_1567566, _1567568), tc_fun(tc_fun(tc_prod(_1567566, _1567568), tc_HOL_Obool), tc_HOL_Obool), _1567568), c_member(tc_prod(_1567566, _1567568)))), c_Product__Type_OPair(_1567566, _1567568)))), _1567570)), _1567572)))], (18122 ^ _779327) ^ [_1087063] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1087063)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087063))))], (29248 ^ _779327) ^ [_1300847, _1300849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1300847), _1300849))), 29251 ^ _779327 : [(29254 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1300847), _1300849)))], (29252 ^ _779327) ^ [] : [_1300849 = c_Orderings_Obot__class_Obot(tc_fun(_1300847, tc_HOL_Obool))]]], (13915 ^ _779327) ^ [_1012958, _1012960, _1012962, _1012964, _1012966, _1012968] : [class_Rings_Olinordered__semiring__1(_1012958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012958), _1012960), _1012962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012958), _1012964), _1012962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012958), c_Groups_Ozero__class_Ozero(_1012958)), _1012966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012958), c_Groups_Ozero__class_Ozero(_1012958)), _1012968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012958), _1012966), _1012968) = c_Groups_Oone__class_Oone(_1012958), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012958), _1012966), _1012960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012958), _1012968), _1012964))), _1012962)))], (40559 ^ _779327) ^ [_1561699, _1561701, _1561703, _1561705, _1561707, _1561709, _1561711] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1561699, _1561701, _1561703, _1561705, _1561707), _1561709), _1561711))), 40560 ^ _779327 : [(40561 ^ _779327) ^ [_1561770] : [hBOOL(hAPP(hAPP(_1561705, _1561709), _1561770)), hBOOL(hAPP(hAPP(_1561707, _1561770), _1561711))]]], (23981 ^ _779327) ^ [_1197199, _1197201, _1197203, _1197205] : [class_Divides_Osemiring__div(_1197199), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197199), _1197201), _1197203)), -(c_Divides_Odiv__class_Omod(_1197199, c_Divides_Odiv__class_Omod(_1197199, _1197205, _1197203), _1197201) = c_Divides_Odiv__class_Omod(_1197199, _1197205, _1197201))], (52760 ^ _779327) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (5972 ^ _779327) ^ [_873334, _873336, _873338] : [class_Orderings_Oorder(_873334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873334), _873336), _873338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873334), _873338), _873336)), -(_873338 = _873336)], (30957 ^ _779327) ^ [_1339556, _1339558, _1339560, _1339562, _1339564, _1339566] : [hBOOL(hAPP(hAPP(_1339556, _1339558), _1339560)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339562, tc_fun(_1339564, tc_HOL_Obool))), _1339566), _1339556), _1339558), _1339560)))], (41241 ^ _779327) ^ [_1577727, _1577729, _1577731, _1577733, _1577735, _1577737, _1577739] : [-(hAPP(c_Fun_Ocomp(_1577727, _1577729, _1577731, _1577733), hAPP(c_Fun_Ocomp(_1577735, _1577727, _1577731, _1577737), _1577739)) = hAPP(c_Fun_Ocomp(_1577735, _1577729, _1577731, hAPP(c_Fun_Ocomp(_1577727, _1577729, _1577735, _1577733), _1577737)), _1577739))], (27675 ^ _779327) ^ [_1270242, _1270244, _1270246, _1270248, _1270250, _1270252] : [-(hAPP(c_Set_Oimage(_1270242, _1270244, _1270246), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270248, tc_fun(_1270242, tc_HOL_Obool)), _1270250), _1270252)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270248, tc_fun(_1270244, tc_HOL_Obool)), _1270250), hAPP(hAPP(c_COMBB(tc_fun(_1270242, tc_HOL_Obool), tc_fun(_1270244, tc_HOL_Obool), _1270248), c_Set_Oimage(_1270242, _1270244, _1270246)), _1270252)))], (51612 ^ _779327) ^ [_1816771, _1816773, _1816775, _1816777] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1816771, tc_fun(_1816773, tc_HOL_Obool)), _1816775), _1816777) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1816773, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1816773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816771, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1816773, tc_HOL_Obool)), c_HOL_OEx(_1816771)), hAPP(hAPP(c_COMBB(tc_fun(_1816771, tc_HOL_Obool), tc_fun(_1816771, tc_HOL_Obool), tc_fun(_1816773, tc_HOL_Obool)), hAPP(c_COMBS(_1816771, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1816771), c_fconj), hAPP(hAPP(c_COMBC(_1816771, tc_fun(_1816771, tc_HOL_Obool), tc_HOL_Obool), c_member(_1816771)), _1816775)))), hAPP(hAPP(c_COMBC(tc_fun(_1816773, tc_HOL_Obool), tc_fun(_1816771, tc_fun(_1816773, tc_HOL_Obool)), tc_fun(_1816771, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1816773, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1816771, tc_fun(_1816773, tc_HOL_Obool)), tc_fun(_1816771, tc_HOL_Obool)), tc_fun(_1816773, tc_HOL_Obool)), c_COMBB(tc_fun(_1816773, tc_HOL_Obool), tc_HOL_Obool, _1816771)), c_fequal)), _1816777))))))], (16671 ^ _779327) ^ [_1062137] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062137, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51324 ^ _779327) ^ [_1810511, _1810513, _1810515] : [hBOOL(hAPP(hAPP(c_List_Omember(_1810511), _1810515), _1810513)), -(hBOOL(hAPP(hAPP(c_member(_1810511), _1810513), hAPP(c_List_Oset(_1810511), _1810515))))], (27911 ^ _779327) ^ [_1275612, _1275614, _1275616] : [-(hAPP(hAPP(c_Set_Oinsert(_1275612), _1275614), hAPP(hAPP(c_Set_Oinsert(_1275612), _1275614), _1275616)) = hAPP(hAPP(c_Set_Oinsert(_1275612), _1275614), _1275616))], (3252 ^ _779327) ^ [_828190, _828192] : [_828192 = _828190, -(c_Int_Oint__ge__less__than2(_828192) = c_Int_Oint__ge__less__than2(_828190))], (12401 ^ _779327) ^ [_985674, _985676, _985678] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _985674), _985676)), _985678) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985674), _985678)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985676), _985678)))], (6382 ^ _779327) ^ [_879640, _879642, _879644] : [class_Orderings_Opreorder(_879640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879640), _879642), _879644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879640), _879644), _879642))], (48237 ^ _779327) ^ [_1743840, _1743842, _1743844, _1743846, _1743848] : [48239 ^ _779327 : [(48242 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1743840, _1743842, tc_HOL_Obool), _1743848), 48238 ^ [_1743840, _1743842, _1743844, _1743846, _1743848]))], (48240 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743840, _1743842)), 48238 ^ [_1743840, _1743842, _1743844, _1743846, _1743848]), hAPP(c_List_Oset(tc_prod(_1743840, _1743842)), hAPP(hAPP(c_List_Ozip(_1743840, _1743842), _1743844), _1743846)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743840)), _1743844) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743842)), _1743846), -(c_List_Olist__all2(_1743840, _1743842, _1743848, _1743844, _1743846))], (15858 ^ _779327) ^ [_1047471, _1047473, _1047475] : [hBOOL(hAPP(_1047471, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047473), _1047475))), 15861 ^ _779327 : [(15868 ^ _779327) ^ [] : [-(_1047475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15871 ^ _779327 : [(15872 ^ _779327) ^ [_1047723, _1047725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047723), _1047475)), _1047473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047475), _1047725)), _1047723), -(hBOOL(hAPP(_1047471, _1047725)))]]], (15862 ^ _779327) ^ [] : [_1047475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1047471, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (27294 ^ _779327) ^ [_1261280, _1261282, _1261284, _1261286, _1261288] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261280, tc_fun(_1261282, tc_HOL_Obool)), _1261284), hAPP(hAPP(c_COMBC(_1261280, tc_fun(_1261282, tc_HOL_Obool), tc_fun(_1261282, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261282, tc_HOL_Obool), tc_fun(tc_fun(_1261282, tc_HOL_Obool), tc_fun(_1261282, tc_HOL_Obool)), _1261280), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261282, tc_HOL_Obool))), _1261286)), _1261288)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261282, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261280, tc_fun(_1261282, tc_HOL_Obool)), _1261284), _1261286)), _1261288))], (52372 ^ _779327) ^ [_1832772, _1832774] : [c_Equiv__Relations_Opart__equivp(_1832772, _1832774), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1832772, tc_HOL_Obool)), 52375 ^ [_1832772, _1832774]), hAPP(hAPP(c_COMBB(tc_fun(_1832772, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1832772, tc_HOL_Obool)), c_HOL_OEx(_1832772)), hAPP(hAPP(c_COMBB(tc_fun(_1832772, tc_HOL_Obool), tc_fun(_1832772, tc_HOL_Obool), tc_fun(_1832772, tc_HOL_Obool)), hAPP(c_COMBS(_1832772, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1832772), c_fconj), hAPP(hAPP(c_COMBS(_1832772, _1832772, tc_HOL_Obool), _1832774), c_COMBI(_1832772))))), hAPP(hAPP(c_COMBC(tc_fun(_1832772, tc_HOL_Obool), tc_fun(_1832772, tc_fun(_1832772, tc_HOL_Obool)), tc_fun(_1832772, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1832772, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1832772, tc_fun(_1832772, tc_HOL_Obool)), tc_fun(_1832772, tc_HOL_Obool)), tc_fun(_1832772, tc_HOL_Obool)), c_COMBB(tc_fun(_1832772, tc_HOL_Obool), tc_HOL_Obool, _1832772)), c_fequal)), _1832774))))))], (35481 ^ _779327) ^ [_1435718, _1435720, _1435722, _1435724] : [class_Orderings_Oorder(_1435718), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435718, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1435718, _1435720, _1435722)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1435718, _1435722, _1435724)) = c_Orderings_Obot__class_Obot(tc_fun(_1435718, tc_HOL_Obool)))], (50941 ^ _779327) ^ [_1802251, _1802253] : [-(c_List_Osplice(_1802251, _1802253, c_List_Olist_ONil(_1802251)) = _1802253)], (25275 ^ _779327) ^ [_1220008, _1220010] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220008)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220010))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220008), _1220010)))], (46988 ^ _779327) ^ [_1717172, _1717174] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717172)), hAPP(c_List_Otl(_1717172), _1717174)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717172)), _1717174)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12674 ^ _779327) ^ [_991120, _991122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991122)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _991120)), hAPP(c_Int_Onat, _991122)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _991120), _991122)))], (40312 ^ _779327) ^ [_1553400, _1553402, _1553404, _1553406, _1553408] : [_1553400 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1553402, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1553402, tc_HOL_Obool), tc_fun(_1553402, tc_HOL_Obool), tc_fun(_1553402, tc_HOL_Obool)), c_Set_OCollect(_1553402)), _1553404)), c_Orderings_Oorder__class_Omono(tc_fun(_1553402, tc_HOL_Obool), tc_fun(_1553402, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1553402, tc_HOL_Obool), tc_fun(_1553402, tc_HOL_Obool), tc_fun(_1553402, tc_HOL_Obool)), c_Set_OCollect(_1553402)), _1553404)), hBOOL(hAPP(hAPP(c_member(_1553402), _1553406), _1553408)), 40326 ^ _779327 : [(40329 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1553404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1553402, tc_HOL_Obool)), _1553408), _1553400)), 40325 ^ [_1553400, _1553402, _1553404, _1553406, _1553408]))], (40327 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553402), 40325 ^ [_1553400, _1553402, _1553404, _1553406, _1553408]), _1553408)))]], -(hBOOL(hAPP(hAPP(c_member(_1553402), _1553406), _1553400)))], (48375 ^ _779327) ^ [_1746676, _1746678] : [48377 ^ _779327 : [(48380 ^ _779327) ^ [] : [48376 ^ [_1746676, _1746678] = c_List_Olist_ONil(_1746676)], (48378 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1746676)), 48376 ^ [_1746676, _1746678]), hAPP(c_List_Oset(tc_List_Olist(_1746676)), _1746678))))]], -(c_List_Olist_ONil(_1746676) = c_List_Oconcat(_1746676, _1746678))], (28612 ^ _779327) ^ [_1289134, _1289136, _1289138, _1289140] : [hAPP(c_Set_Oimage(_1289134, _1289136, _1289138), _1289140) = c_Orderings_Obot__class_Obot(tc_fun(_1289136, tc_HOL_Obool)), -(_1289140 = c_Orderings_Obot__class_Obot(tc_fun(_1289134, tc_HOL_Obool)))], (21186 ^ _779327) ^ [_1142879] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1142879) = 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), _1142879), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19811 ^ _779327) ^ [_1117209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117209)), -(c_Nat__Transfer_Ois__nat(_1117209))], (15720 ^ _779327) ^ [_1045286, _1045288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1045286)), 15723 ^ _779327 : [(15726 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045288, _1045286)), _1045286)))], (15724 ^ _779327) ^ [] : [-(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, _1045288, _1045286))))]]], (37733 ^ _779327) ^ [] : [-(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))], (47068 ^ _779327) ^ [_1718833, _1718835, _1718837, _1718839, _1718841] : [-(hAPP(c_List_Orotate(_1718833, _1718835), hAPP(hAPP(c_List_Omap(_1718837, _1718833), _1718839), _1718841)) = hAPP(hAPP(c_List_Omap(_1718837, _1718833), _1718839), hAPP(c_List_Orotate(_1718837, _1718835), _1718841)))], (41223 ^ _779327) ^ [_1577320, _1577322, _1577324] : [-(hAPP(c_Fun_Ocomp(_1577320, _1577322, _1577320, _1577324), c_Fun_Oid(_1577320)) = _1577324)], (52596 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (41141 ^ _779327) ^ [_1575327, _1575329] : [-(c_Nitpick_Owf_H(_1575327, _1575329)), c_Wellfounded_Oacyclic(_1575327, _1575329), 41146 ^ _779327 : [(41149 ^ _779327) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (41147 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575327, _1575327)), _1575329))]]], (45171 ^ _779327) ^ [_1673153, _1673155, _1673157, _1673159, _1673161, _1673163, _1673165] : [hAPP(hAPP(c_List_Omap(_1673153, _1673155), _1673157), _1673159) = hAPP(hAPP(c_List_Omap(_1673161, _1673155), _1673163), _1673165), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673153)), _1673159) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673161)), _1673165))], (48558 ^ _779327) ^ [_1751533, _1751535, _1751537, _1751539] : [-(hAPP(c_List_Ofilter(_1751533, _1751535), hAPP(c_List_Ofilter(_1751533, _1751537), _1751539)) = hAPP(c_List_Ofilter(_1751533, hAPP(hAPP(c_COMBS(_1751533, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1751533), c_fconj), _1751537)), _1751535)), _1751539))], (35261 ^ _779327) ^ [_1430699, _1430701, _1430703, _1430705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430699, tc_HOL_Obool)), _1430705), _1430701)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430699, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430699, tc_HOL_Obool)), _1430701), _1430703)), _1430705) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430699, tc_HOL_Obool)), _1430701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430699, tc_HOL_Obool)), _1430703), _1430705)))], (28664 ^ _779327) ^ [_1290127, _1290129, _1290131] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290127, tc_HOL_Obool)), _1290129), _1290131) = c_Orderings_Obot__class_Obot(tc_fun(_1290127, tc_HOL_Obool))), _1290129 = c_Orderings_Obot__class_Obot(tc_fun(_1290127, tc_HOL_Obool)), _1290131 = c_Orderings_Obot__class_Obot(tc_fun(_1290127, tc_HOL_Obool))], (34909 ^ _779327) ^ [_1422748, _1422750, _1422752, _1422754] : [class_Lattices_Osemilattice__inf(_1422748), 34912 ^ _779327 : [(34921 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422748), _1422752), _1422754)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), _1422752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), _1422754))], (34913 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422748), _1422752), _1422754))), 34916 ^ _779327 : [(34919 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), _1422754)))], (34917 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422748), _1422750), _1422752)))]]]]], (23452 ^ _779327) ^ [_1186863, _1186865, _1186867, _1186869, _1186871, _1186873] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1186863, _1186865, _1186867), _1186869), hAPP(hAPP(c_Product__Type_OPair(_1186863, _1186865), _1186871), _1186873)) = hAPP(hAPP(_1186869, _1186871), _1186873))], (51273 ^ _779327) ^ [_1809182, _1809184] : [-(c_Predicate_Opred__comp(_1809182, _1809182, _1809182, c_fequal, c_Predicate_Opred__comp(_1809182, _1809182, _1809182, _1809184, c_fequal)) = _1809184)], (43421 ^ _779327) ^ [_1629388, _1629390, _1629392] : [class_Orderings_Olinorder(_1629388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629388), _1629390)), -(hBOOL(hAPP(hAPP(c_member(_1629388), _1629392), _1629390))), -(c_Big__Operators_Olinorder__class_OMin(_1629388, hAPP(hAPP(c_Set_Oinsert(_1629388), _1629392), _1629390)) = hAPP(hAPP(c_Finite__Set_Ofold(_1629388, _1629388, c_Orderings_Oord__class_Omin(_1629388)), _1629392), _1629390))], (16591 ^ _779327) ^ [_1060707, _1060709, _1060711] : [class_Groups_Oordered__ab__group__add__abs(_1060707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060707), hAPP(c_Groups_Oabs__class_Oabs(_1060707), _1060709)), _1060711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060707), hAPP(c_Groups_Ouminus__class_Ouminus(_1060707), _1060709)), _1060711)))], (23618 ^ _779327) ^ [_1190562, _1190564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190562), _1190564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190562)), hAPP(c_Code__Numeral_Oof__nat, _1190564))))], (43945 ^ _779327) ^ [_1640639, _1640641, _1640643] : [class_Complete__Lattice_Ocomplete__lattice(_1640639), hBOOL(hAPP(hAPP(c_member(_1640639), _1640641), _1640643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1640639), _1640641), c_Complete__Lattice_OSup__class_OSup(_1640639, _1640643))))], (37965 ^ _779327) ^ [_1490387, _1490389] : [class_Lattices_Oboolean__algebra(_1490387), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1490387), _1490389), hAPP(c_Groups_Ouminus__class_Ouminus(_1490387), _1490389)) = c_Orderings_Otop__class_Otop(_1490387))], (29598 ^ _779327) ^ [_1307973, _1307975, _1307977, _1307979, _1307981, _1307983] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1307973, tc_fun(_1307975, tc_HOL_Obool)), _1307977), _1307979), _1307981)), hBOOL(hAPP(hAPP(c_member(_1307973), _1307983), _1307977)), -(hBOOL(hAPP(hAPP(_1307979, _1307983), _1307981)))], (40698 ^ _779327) ^ [_1564555, _1564557] : [c_Wellfounded_Owf(_1564555, _1564557), 40702 ^ _779327 : [(40703 ^ _779327) ^ [_1564691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564555, _1564555)), hAPP(hAPP(c_Product__Type_OPair(_1564555, _1564555), hAPP(_1564691, hAPP(c_Nat_OSuc, 40701 ^ [_1564555, _1564557, _1564691]))), hAPP(_1564691, 40701 ^ [_1564555, _1564557, _1564691]))), _1564557))]]], (38403 ^ _779327) ^ [_1502338, _1502340, _1502342] : [-(hAPP(c_Set_Ovimage(_1502338, _1502340, _1502342), c_Orderings_Obot__class_Obot(tc_fun(_1502340, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1502338, tc_HOL_Obool)))], (31057 ^ _779327) ^ [_1341661, _1341663, _1341665, _1341667] : [hBOOL(hAPP(hAPP(_1341665, _1341663), _1341667)), -(hBOOL(hAPP(hAPP(c_member(_1341661), _1341663), c_SetInterval_Oord_OlessThan(_1341661, _1341665, _1341667))))], (43345 ^ _779327) ^ [_1628084, _1628086, _1628088, _1628090, _1628092] : [c_Finite__Set_Ofolding__one(_1628084, _1628086, _1628088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628084), _1628090)), -(hBOOL(hAPP(hAPP(c_member(_1628084), _1628092), _1628090))), -(hAPP(_1628088, hAPP(hAPP(c_Set_Oinsert(_1628084), _1628092), _1628090)) = hAPP(hAPP(c_Finite__Set_Ofold(_1628084, _1628084, _1628086), _1628092), _1628090))], (10171 ^ _779327) ^ [_943911, _943913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943911)), _943913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943911), hAPP(c_Int_Onat, _943913))))], (14977 ^ _779327) ^ [_1031280, _1031282, _1031284] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031280))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031280)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031282)), _1031284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031282)), _1031284))], (13882 ^ _779327) ^ [_1012423] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1012423))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11307 ^ _779327) ^ [_965044, _965046] : [class_Rings_Oring__1(_965044), -(hAPP(c_Int_Oring__1__class_Oof__int(_965044), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _965046)) = hAPP(c_Groups_Ouminus__class_Ouminus(_965044), hAPP(c_Int_Oring__1__class_Oof__int(_965044), _965046)))], (29997 ^ _779327) ^ [_1315683, _1315685, _1315687, _1315689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1315683, tc_HOL_Obool)), _1315685), _1315687)), hBOOL(hAPP(hAPP(c_member(_1315683), _1315689), _1315685)), -(hBOOL(hAPP(hAPP(c_member(_1315683), _1315689), _1315687)))], (1138 ^ _779327) ^ [_796540, _796542] : [-(class_Lattices_Obounded__lattice(_796540)), _796542 = _796540, class_Lattices_Obounded__lattice(_796542)], (10815 ^ _779327) ^ [_955483, _955485, _955487] : [class_Int_Onumber__ring(_955483), -(hAPP(c_Int_Onumber__class_Onumber__of(_955483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _955485), _955487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955483), hAPP(c_Int_Onumber__class_Onumber__of(_955483), _955485)), hAPP(c_Int_Onumber__class_Onumber__of(_955483), _955487)))], (37829 ^ _779327) ^ [_1487416, _1487418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487416), _1487418)), 37832 ^ _779327 : [(37839 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487416), c_Orderings_Otop__class_Otop(tc_fun(_1487416, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487416), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487416, tc_HOL_Obool)), _1487418))))], (37833 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487416), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487416, tc_HOL_Obool)), _1487418))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487416), c_Orderings_Otop__class_Otop(tc_fun(_1487416, tc_HOL_Obool)))))]]], (25235 ^ _779327) ^ [_1219163, _1219165, _1219167, _1219169, _1219171] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219163), _1219165)), 25238 ^ _779327 : [(25245 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219171), _1219165))), _1219169))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219167), _1219169))))], (25239 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219167), _1219169))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219171), _1219165))), _1219169))))]]], (29837 ^ _779327) ^ [_1312725, _1312727, _1312729] : [hBOOL(hAPP(hAPP(c_member(_1312725), _1312727), _1312729)), -(hBOOL(hAPP(_1312729, _1312727)))], (14775 ^ _779327) ^ [_1027853, _1027855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1027853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1027855), 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), _1027853), _1027855)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21920 ^ _779327) ^ [_1157140, _1157142, _1157144, _1157146, _1157148] : [hBOOL(hAPP(hAPP(_1157140, _1157142), _1157144)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1157146, _1157148, tc_HOL_Obool), _1157140), hAPP(hAPP(c_Product__Type_OPair(_1157146, _1157148), _1157142), _1157144))))], (43730 ^ _779327) ^ [_1635453] : [class_Complete__Lattice_Ocomplete__lattice(_1635453), -(c_Complete__Lattice_OInf__class_OInf(_1635453, c_Orderings_Obot__class_Obot(tc_fun(_1635453, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1635453))], (29272 ^ _779327) ^ [_1301252, _1301254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301252), _1301254))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1301254, _1301252) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1301254), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1301254), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1301252)))], (52620 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (4862 ^ _779327) ^ [_853371, _853373] : [_853373 = _853371, -(c_Set_Oinsert(_853373) = c_Set_Oinsert(_853371))], (11177 ^ _779327) ^ [_962296, _962298, _962300, _962302] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962296), hAPP(c_Int_Onumber__class_Onumber__of(_962296), _962298)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_962296), _962300), _962302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_962296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962296), hAPP(c_Int_Onumber__class_Onumber__of(_962296), _962298)), _962300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962296), hAPP(c_Int_Onumber__class_Onumber__of(_962296), _962298)), _962302))), class_Int_Onumber(_962296), class_Rings_Oring(_962296)], (23450 ^ _779327) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9286 ^ _779327) ^ [_929759] : [9288 ^ _779327 : [(9291 ^ _779327) ^ [] : [hBOOL(hAPP(_929759, 9287 ^ [_929759]))], (9289 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9287 ^ [_929759])))]], 9292 ^ _779327 : [(9293 ^ _779327) ^ [_929886] : [-(hBOOL(hAPP(_929759, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929886))))]]], (2052 ^ _779327) ^ [_808948, _808950, _808952, _808954] : [-(c_Nat__Transfer_Otsub(_808954, _808950) = c_Nat__Transfer_Otsub(_808952, _808948)), _808954 = _808952, _808950 = _808948], (34227 ^ _779327) ^ [_1407167, _1407169] : [-(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), _1407167), _1407169)), 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), _1407167), _1407169))], (400 ^ _779327) ^ [_785441, _785443, _785445, _785447, _785449, _785451] : [-(c_Big__Operators_Osemilattice__big(_785449, _785445, _785441)), c_Big__Operators_Osemilattice__big(_785451, _785447, _785443), _785451 = _785449, _785447 = _785445, _785443 = _785441], (1538 ^ _779327) ^ [_801540, _801542] : [-(class_Enum_Oenum(_801540)), _801542 = _801540, class_Enum_Oenum(_801542)], (15928 ^ _779327) ^ [_1048807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048807)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1048807) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35457 ^ _779327) ^ [_1435206, _1435208, _1435210] : [class_Orderings_Oorder(_1435206), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435206, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1435206), _1435208)), c_SetInterval_Oord__class_OatLeastAtMost(_1435206, _1435208, _1435210)) = c_Orderings_Obot__class_Obot(tc_fun(_1435206, tc_HOL_Obool)))], (7408 ^ _779327) ^ [_895662, _895664, _895666] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _895662), _895664)), _895666) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _895662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _895664), _895666)))], (10431 ^ _779327) ^ [_948268, _948270] : [-(_948268 = hAPP(c_Int_Onat, _948270)), 10434 ^ _779327 : [(10437 ^ _779327) ^ [] : [_948270 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948268)], (10435 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948270)))]], 10438 ^ _779327 : [(10441 ^ _779327) ^ [] : [_948268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10439 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948270))]]], (8116 ^ _779327) ^ [_908358, _908360, _908362] : [class_Rings_Olinordered__semiring__strict(_908358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908358), _908360), c_Groups_Ozero__class_Ozero(_908358))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908358), c_Groups_Ozero__class_Ozero(_908358)), _908362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908358), _908360), _908362)), c_Groups_Ozero__class_Ozero(_908358))))], (33519 ^ _779327) ^ [_1390400, _1390402, _1390404, _1390406] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1390400), _1390402)), 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)), _1390404), _1390400)), 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)), _1390406), _1390402)), 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)), _1390404), _1390406)), _1390402)), c_FunDef_Omax__strict)))], (41051 ^ _779327) ^ [_1573336, _1573338] : [c_Wellfounded_OwfP(_1573336, hAPP(hAPP(c_COMBC(_1573336, tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_fun(_1573336, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573336, tc_fun(tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_fun(_1573336, tc_HOL_Obool)), _1573336), c_COMBC(_1573336, tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573336, tc_prod(_1573336, _1573336)), tc_fun(_1573336, tc_fun(tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_HOL_Obool)), _1573336), hAPP(c_COMBB(tc_prod(_1573336, _1573336), tc_fun(tc_fun(tc_prod(_1573336, _1573336), tc_HOL_Obool), tc_HOL_Obool), _1573336), c_member(tc_prod(_1573336, _1573336)))), c_Product__Type_OPair(_1573336, _1573336)))), _1573338)), -(c_Wellfounded_Owf(_1573336, _1573338))], (43487 ^ _779327) ^ [_1630636, _1630638, _1630640, _1630642, _1630644] : [c_Finite__Set_Ofun__left__comm(_1630636, _1630638, _1630640), -(hAPP(c_Fun_Ocomp(_1630638, _1630638, _1630638, hAPP(_1630640, _1630642)), hAPP(_1630640, _1630644)) = hAPP(c_Fun_Ocomp(_1630638, _1630638, _1630638, hAPP(_1630640, _1630644)), hAPP(_1630640, _1630642)))], (45207 ^ _779327) ^ [_1673891, _1673893, _1673895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673891, tc_HOL_Obool)), hAPP(c_List_Oset(_1673891), _1673893)), hAPP(c_List_Oset(_1673891), hAPP(hAPP(c_List_Olist_OCons(_1673891), _1673895), _1673893)))))], (23805 ^ _779327) ^ [_1194266, _1194268, _1194270] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1194266), _1194268)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1194266), _1194270))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1194266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1194268), _1194270)))], (47820 ^ _779327) ^ [_1734608, _1734610, _1734612] : [hBOOL(hAPP(c_List_Olistsp(_1734608, _1734610), _1734612)), 47823 ^ _779327 : [(47824 ^ _779327) ^ [_1734697] : [hBOOL(hAPP(hAPP(c_member(_1734608), _1734697), hAPP(c_List_Oset(_1734608), _1734612))), -(hBOOL(hAPP(_1734610, _1734697)))]]], (41045 ^ _779327) ^ [_1573236, _1573238] : [c_Wellfounded_Owf(_1573236, _1573238), -(c_Wellfounded_OwfP(_1573236, c_FunDef_Oin__rel(_1573236, _1573236, _1573238)))], (41775 ^ _779327) ^ [_1589847, _1589849] : [41776 ^ _779327 : [(41777 ^ _779327) ^ [_1589893] : [hBOOL(hAPP(_1589847, _1589893))]], -(hBOOL(hAPP(_1589847, c_Hilbert__Choice_OEps(_1589849, _1589847))))], (41543 ^ _779327) ^ [_1584687, _1584689, _1584691, _1584693, _1584695, _1584697, _1584699, _1584701] : [c_Finite__Set_Ofolding(_1584687, _1584689, _1584691, _1584693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584687), _1584695)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1584687), _1584697)), -(hAPP(c_Fun_Ocomp(_1584689, _1584689, _1584699, hAPP(_1584693, _1584697)), hAPP(c_Fun_Ocomp(_1584689, _1584689, _1584699, hAPP(_1584693, _1584695)), _1584701)) = hAPP(c_Fun_Ocomp(_1584689, _1584689, _1584699, hAPP(_1584693, _1584695)), hAPP(c_Fun_Ocomp(_1584689, _1584689, _1584699, hAPP(_1584693, _1584697)), _1584701)))], (45699 ^ _779327) ^ [_1686797, _1686799, _1686801, _1686803] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1686799), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686797)), hAPP(hAPP(c_List_Olist_OCons(_1686799), _1686801), _1686803)) = hAPP(hAPP(c_List_Olist_OCons(_1686799), _1686801), hAPP(hAPP(c_List_Otake(_1686799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686797)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1686803)))], (3628 ^ _779327) ^ [_834134, _834136] : [_834136 = _834134, -(c_Relation_OField(_834136) = c_Relation_OField(_834134))], (28858 ^ _779327) ^ [_1293779, _1293781, _1293783] : [class_Orderings_Oorder(_1293779), 28861 ^ _779327 : [(28868 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293779), _1293781), _1293783))), -(c_Orderings_Obot__class_Obot(tc_fun(_1293779, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293779, _1293781, _1293783))], (28862 ^ _779327) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1293779, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293779, _1293781, _1293783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293779), _1293781), _1293783))]]], (26338 ^ _779327) ^ [_1242773, _1242775] : [c_Nat__Transfer_Ois__nat(_1242773), c_Nat__Transfer_Ois__nat(_1242775), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1242773, _1242775) = 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, _1242773), hAPP(c_Int_Onat, _1242775))))], (1838 ^ _779327) ^ [_805290, _805292] : [-(class_Rings_Osemiring__1(_805290)), _805292 = _805290, class_Rings_Osemiring__1(_805292)], (15313 ^ _779327) ^ [_1037495, _1037497, _1037499, _1037501] : [class_Divides_Osemiring__div(_1037495), -(c_Divides_Odiv__class_Omod(_1037495, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037495), c_Divides_Odiv__class_Omod(_1037495, _1037497, _1037499)), _1037501), _1037499) = c_Divides_Odiv__class_Omod(_1037495, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037495), _1037497), _1037501), _1037499))], (13557 ^ _779327) ^ [_1006358, _1006360, _1006362, _1006364] : [class_Groups_Omonoid__mult(_1006358), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1006358), _1006360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006362), _1006364)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006358), hAPP(hAPP(c_Power_Opower__class_Opower(_1006358), _1006360), _1006362)), hAPP(hAPP(c_Power_Opower__class_Opower(_1006358), _1006360), _1006364)))], (39022 ^ _779327) ^ [_1517365, _1517367] : [class_Orderings_Olinorder(_1517365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517365), _1517367)), -(c_Big__Operators_Olattice_OSup__fin(_1517365, c_Orderings_Oord__class_Omax(_1517365), _1517367) = hAPP(c_Finite__Set_Ofold1(_1517365, c_Orderings_Oord__class_Omax(_1517365)), _1517367))], (10713 ^ _779327) ^ [_953367, _953369, _953371, _953373] : [class_Rings_Ocomm__semiring__1(_953367), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953367), _953369), _953371)), _953373) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953367), _953369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953367), _953371), _953373)))], (44610 ^ _779327) ^ [_1657386, _1657388] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1657386), tc_List_Olist(_1657386)), tc_HOL_Obool)), c_List_Olistrel1(_1657386, c_Transitive__Closure_Ortrancl(_1657386, _1657388))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1657386), c_List_Olistrel1(_1657386, _1657388)))))], (44614 ^ _779327) ^ [_1657489, _1657491, _1657493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1657489, _1657489), tc_HOL_Obool)), _1657491), _1657493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1657489), tc_List_Olist(_1657489)), tc_HOL_Obool)), c_List_Olistrel1(_1657489, _1657491)), c_List_Olistrel1(_1657489, _1657493))))], (42885 ^ _779327) ^ [_1616936, _1616938, _1616940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616936, _1616936)), _1616938), c_Transitive__Closure_Ortrancl(_1616936, _1616940))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616936, _1616936)), _1616938), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616936, _1616936), tc_HOL_Obool), 42888 ^ [_1616936, _1616938, _1616940]), _1616940))))], (43183 ^ _779327) ^ [_1624777, _1624779, _1624781, _1624783, _1624785] : [class_Complete__Lattice_Ocomplete__lattice(_1624777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624779), _1624781)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1624777), _1624783), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1624779, _1624777), _1624781), _1624785)) = hAPP(hAPP(c_Finite__Set_Ofold(_1624779, _1624777, hAPP(hAPP(c_COMBB(_1624777, tc_fun(_1624777, _1624777), _1624779), c_Lattices_Osemilattice__sup__class_Osup(_1624777)), _1624785)), _1624783), _1624781))], (21452 ^ _779327) ^ [_1148438, _1148440] : [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), _1148438), _1148440))), 21455 ^ _779327 : [(21464 ^ _779327) ^ [] : [-(c_Divides_OnegDivAlg(_1148438, _1148440) = hAPP(c_Divides_Oadjust(_1148440), c_Divides_OnegDivAlg(_1148438, 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)))), _1148440)))), -(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), _1148438), _1148440)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148440), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21456 ^ _779327) ^ [] : [21457 ^ _779327 : [(21460 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1148440), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21458 ^ _779327) ^ [] : [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), _1148438), _1148440)))]], -(c_Divides_OnegDivAlg(_1148438, _1148440) = 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), _1148438), _1148440)))]]], (50120 ^ _779327) ^ [_1784014, _1784016, _1784018] : [hBOOL(hAPP(c_List_Odistinct(_1784014), _1784016)), -(hBOOL(hAPP(c_List_Odistinct(_1784014), c_List_Oinsert(_1784014, _1784018, _1784016))))], (2182 ^ _779327) ^ [_810995, _810997, _810999, _811001] : [-(c_Groups_Osgn__class_Osgn(_811001, _810997) = c_Groups_Osgn__class_Osgn(_810999, _810995)), _811001 = _810999, _810997 = _810995], (29128 ^ _779327) ^ [_1298266, _1298268, _1298270, _1298272, _1298274] : [_1298266 = c_Orderings_Obot__class_Obot(tc_fun(_1298268, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298270, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298268, tc_fun(_1298270, tc_HOL_Obool)), _1298266), _1298272)), _1298274) = _1298274)], (42910 ^ _779327) ^ [_1617594, _1617596, _1617598, _1617600] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617594, _1617594)), hAPP(hAPP(c_Product__Type_OPair(_1617594, _1617594), _1617596), _1617598)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617594, _1617594), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1617600))), -(_1617596 = _1617598)], (47516 ^ _779327) ^ [_1727937, _1727939, _1727941, _1727943] : [hAPP(hAPP(c_List_Oappend(_1727937), _1727939), hAPP(hAPP(c_List_Olist_OCons(_1727937), _1727941), c_List_Olist_ONil(_1727937))) = _1727943, 47519 ^ _779327 : [(47524 ^ _779327) ^ [] : [-(c_List_Olast(_1727937, _1727943) = _1727941)], (47522 ^ _779327) ^ [] : [-(c_List_Obutlast(_1727937, _1727943) = _1727939)], (47520 ^ _779327) ^ [] : [_1727943 = c_List_Olist_ONil(_1727937)]]], (5846 ^ _779327) ^ [_871515, _871517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871515), _871517)), _871517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48465 ^ _779327) ^ [_1748545, _1748547, _1748549] : [c_List_Oconcat(_1748545, _1748547) = c_List_Oconcat(_1748545, _1748549), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748545))), _1748547) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748545))), _1748549), 48475 ^ _779327 : [(48478 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1748545), tc_List_Olist(_1748545), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1748545), tc_fun(tc_List_Olist(_1748545), tc_Nat_Onat), tc_fun(tc_List_Olist(_1748545), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1748545), tc_Nat_Onat), tc_fun(tc_List_Olist(_1748545), tc_HOL_Obool)), tc_List_Olist(_1748545)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1748545))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1748545)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1748545))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1748545)))), 48474 ^ [_1748545, _1748547, _1748549]))], (48476 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748545), tc_List_Olist(_1748545))), 48474 ^ [_1748545, _1748547, _1748549]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1748545), tc_List_Olist(_1748545))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1748545), tc_List_Olist(_1748545)), _1748547), _1748549)))))]], -(_1748547 = _1748549)], (45054 ^ _779327) ^ [_1670447, _1670449] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1670447), hAPP(c_List_Oset(_1670447), _1670449))))], (15289 ^ _779327) ^ [_1036947, _1036949, _1036951, _1036953] : [class_Divides_Osemiring__div(_1036947), -(c_Divides_Odiv__class_Omod(_1036947, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036947), _1036949), _1036951), _1036953) = c_Divides_Odiv__class_Omod(_1036947, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036947), _1036949), c_Divides_Odiv__class_Omod(_1036947, _1036951, _1036953)), _1036953))], (26268 ^ _779327) ^ [_1241251, _1241253, _1241255, _1241257, _1241259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241251, tc_HOL_Obool)), _1241253), hAPP(c_Set_Oimage(_1241255, _1241251, _1241257), _1241259)))), 26269 ^ _779327 : [(26270 ^ _779327) ^ [_1241331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241255, tc_HOL_Obool)), _1241331), _1241259)), _1241253 = hAPP(c_Set_Oimage(_1241255, _1241251, _1241257), _1241331)]]], (27004 ^ _779327) ^ [_1255706, _1255708, _1255710, _1255712] : [class_Lattices_Osemilattice__sup(_1255706), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255706), _1255708), _1255710)), _1255712) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255706), _1255708), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255706), _1255710), _1255712)))], (39884 ^ _779327) ^ [_1537017, _1537019, _1537021, _1537023, _1537025, _1537027, _1537029] : [class_Groups_Ocomm__monoid__add(_1537017), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537019), _1537021)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537023), _1537025)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537019, _1537017), hAPP(hAPP(c_COMBS(_1537019, tc_fun(_1537023, tc_HOL_Obool), _1537017), hAPP(hAPP(c_COMBB(tc_fun(_1537023, _1537017), tc_fun(tc_fun(_1537023, tc_HOL_Obool), _1537017), _1537019), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537023, _1537017)), _1537027)), hAPP(hAPP(c_COMBB(tc_fun(_1537023, tc_HOL_Obool), tc_fun(_1537023, tc_HOL_Obool), _1537019), c_Set_OCollect(_1537023)), hAPP(hAPP(c_COMBB(tc_fun(_1537023, tc_HOL_Obool), tc_fun(_1537023, tc_HOL_Obool), _1537019), hAPP(c_COMBS(_1537023, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537023), c_fconj), hAPP(hAPP(c_COMBC(_1537023, tc_fun(_1537023, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537023)), _1537025)))), _1537029)))), _1537021) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537023, _1537017), hAPP(hAPP(c_COMBS(_1537023, tc_fun(_1537019, tc_HOL_Obool), _1537017), hAPP(hAPP(c_COMBB(tc_fun(_1537019, _1537017), tc_fun(tc_fun(_1537019, tc_HOL_Obool), _1537017), _1537023), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537019, _1537017)), hAPP(c_COMBC(_1537019, _1537023, _1537017), _1537027))), hAPP(hAPP(c_COMBB(tc_fun(_1537019, tc_HOL_Obool), tc_fun(_1537019, tc_HOL_Obool), _1537023), c_Set_OCollect(_1537019)), hAPP(hAPP(c_COMBB(tc_fun(_1537019, tc_HOL_Obool), tc_fun(_1537019, tc_HOL_Obool), _1537023), hAPP(c_COMBS(_1537019, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537019), c_fconj), hAPP(hAPP(c_COMBC(_1537019, tc_fun(_1537019, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537019)), _1537021)))), hAPP(c_COMBC(_1537019, _1537023, tc_HOL_Obool), _1537029))))), _1537025))], (43722 ^ _779327) ^ [_1635276, _1635278, _1635280] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635276, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1635276, tc_HOL_Obool), tc_HOL_Obool)), _1635278), _1635280)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635276, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635276, tc_HOL_Obool), _1635278)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635276, tc_HOL_Obool), _1635280)))], (38882 ^ _779327) ^ [_1514628, _1514630, _1514632, _1514634, _1514636, _1514638] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514628, _1514630)), hAPP(hAPP(c_Product__Type_OPair(_1514628, _1514630), _1514632), _1514634)), hAPP(hAPP(c_Product__Type_OSigma(_1514628, _1514630), _1514636), _1514638)))), hBOOL(hAPP(hAPP(c_member(_1514628), _1514632), _1514636)), hBOOL(hAPP(hAPP(c_member(_1514630), _1514634), hAPP(_1514638, _1514632)))], (31197 ^ _779327) ^ [_1344372, _1344374, _1344376, _1344378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1344378, _1344374)), hAPP(_1344378, _1344376))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1344372, _1344372)), hAPP(hAPP(c_Product__Type_OPair(_1344372, _1344372), _1344374), _1344376)), hAPP(c_Wellfounded_Omeasure(_1344372), _1344378))))], (2392 ^ _779327) ^ [_814266, _814268, _814270, _814272] : [-(c_Nitpick_Oint__lcm(_814272, _814268) = c_Nitpick_Oint__lcm(_814270, _814266)), _814272 = _814270, _814268 = _814266], (47614 ^ _779327) ^ [_1729835, _1729837, _1729839, _1729841] : [-(hBOOL(hAPP(hAPP(c_member(_1729835), _1729837), hAPP(c_List_Oset(_1729835), _1729839)))), -(c_List_Oremove1(_1729835, _1729837, hAPP(hAPP(c_List_Oappend(_1729835), _1729839), _1729841)) = hAPP(hAPP(c_List_Oappend(_1729835), _1729839), c_List_Oremove1(_1729835, _1729837, _1729841)))], (16846 ^ _779327) ^ [_1065169, _1065171] : [class_Groups_Oordered__ab__group__add__abs(_1065169), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065169), hAPP(c_Groups_Ouminus__class_Ouminus(_1065169), hAPP(c_Groups_Oabs__class_Oabs(_1065169), _1065171))), c_Groups_Ozero__class_Ozero(_1065169))))], (17598 ^ _779327) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (47939 ^ _779327) ^ [_1737008, _1737010, _1737012, _1737014, _1737016] : [class_Orderings_Olinorder(_1737008), hBOOL(hAPP(hAPP(c_member(_1737008), hAPP(_1737010, _1737012)), hAPP(c_Set_Oimage(_1737014, _1737008, _1737010), hAPP(c_List_Oset(_1737014), _1737016)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1737014, _1737008, _1737010, _1737012, _1737016) = _1737016)], (44578 ^ _779327) ^ [_1656437, _1656439, _1656441, _1656443] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656437), tc_List_Olist(_1656437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656437), tc_List_Olist(_1656437)), _1656439), _1656441)), c_List_Olex(_1656437, _1656443)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656437), tc_List_Olist(_1656437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656437), tc_List_Olist(_1656437)), _1656439), _1656441)), c_List_Olexord(_1656437, _1656443))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656437)), _1656439) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656437)), _1656441)], (40909 ^ _779327) ^ [_1569841, _1569843] : [-(hAPP(c_Relation_ODomain(_1569841, _1569841), c_Relation_OId__on(_1569841, _1569843)) = _1569843)], (43742 ^ _779327) ^ [_1635639, _1635641, _1635643] : [class_Complete__Lattice_Ocomplete__lattice(_1635639), -(c_Complete__Lattice_OInf__class_OInf(_1635639, hAPP(hAPP(c_Set_Oinsert(_1635639), _1635641), _1635643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1635639), _1635641), c_Complete__Lattice_OInf__class_OInf(_1635639, _1635643)))], (45789 ^ _779327) ^ [_1689388, _1689390] : [-(c_Random_Oselect__weight(_1689388, _1689390) = 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(_1689388, 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, _1689388), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1689388)), _1689390)))), hAPP(hAPP(c_COMBB(_1689388, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1689388, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1689388, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1689388, _1689390))))], (48165 ^ _779327) ^ [_1742185, _1742187, _1742189, _1742191, _1742193, _1742195, _1742197, _1742199] : [c_List_Olist__all2(_1742185, _1742187, _1742189, _1742191, _1742193), hBOOL(hAPP(hAPP(_1742189, _1742195), _1742197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742187)), _1742193))), -(c_List_Olist__all2(_1742185, _1742187, _1742189, hAPP(hAPP(c_List_Olist__update(_1742185, _1742191), _1742199), _1742195), hAPP(hAPP(c_List_Olist__update(_1742187, _1742193), _1742199), _1742197)))], (43943 ^ _779327) ^ [_1640582, _1640584, _1640586, _1640588] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640582, tc_HOL_Obool), hAPP(c_Set_Oimage(_1640584, tc_fun(_1640582, tc_HOL_Obool), _1640586), _1640588)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640584, tc_fun(_1640582, tc_HOL_Obool)), _1640588), _1640586))], (11271 ^ _779327) ^ [_964211, _964213, _964215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964211), _964213)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964215), _964213)), _964211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964213), _964211)))], (23778 ^ _779327) ^ [_1193624, _1193626, _1193628, _1193630, _1193632, _1193634] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1193624, _1193626, _1193628, _1193630), _1193632), _1193634) = hAPP(_1193630, hAPP(hAPP(c_Product__Type_OPair(_1193624, _1193626), _1193632), _1193634)))], (33022 ^ _779327) ^ [_1380412, _1380414, _1380416, _1380418, _1380420] : [hAPP(_1380416, _1380418) = _1380420, -(c_Fun_Ofun__upd(_1380412, _1380414, _1380416, _1380418, _1380420) = _1380416)], (52568 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (3842 ^ _779327) ^ [_837603, _837605, _837607, _837609, _837611, _837613, _837615, _837617] : [-(c_Nitpick_Osetsum_H(_837617, _837613, _837609, _837605) = c_Nitpick_Osetsum_H(_837615, _837611, _837607, _837603)), _837617 = _837615, _837613 = _837611, _837609 = _837607, _837605 = _837603], (47762 ^ _779327) ^ [_1733376, _1733378, _1733380, _1733382, _1733384] : [class_Orderings_Olinorder(_1733376), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733378, _1733376, _1733380), _1733382), _1733384) = c_List_Olist_ONil(_1733378)], (17468 ^ _779327) ^ [_1075862] : [_1075862 = c_Int_OMin, -(c_Int_OBit1(_1075862) = c_Int_OMin)], (52642 ^ _779327) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (15307 ^ _779327) ^ [_1037360, _1037362, _1037364, _1037366] : [class_Divides_Osemiring__div(_1037360), -(c_Divides_Odiv__class_Omod(_1037360, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037360), _1037362), c_Divides_Odiv__class_Omod(_1037360, _1037364, _1037366)), _1037366) = c_Divides_Odiv__class_Omod(_1037360, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037360), _1037362), _1037364), _1037366))], (42508 ^ _779327) ^ [_1607634, _1607636, _1607638] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1607634, _1607634), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1607634, _1607634), _1607636)), c_Transitive__Closure_Ortrancl(_1607634, _1607636)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1607634, _1607634), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1607634, _1607634)), hAPP(hAPP(c_Product__Type_OPair(_1607634, _1607634), _1607638), _1607638)), c_Transitive__Closure_Otrancl(_1607634, _1607636)))], (50076 ^ _779327) ^ [_1783293, _1783295, _1783297, _1783299] : [-(_1783293 = _1783295), -(hAPP(c_List_OremoveAll(_1783297, _1783293), hAPP(hAPP(c_List_Olist_OCons(_1783297), _1783295), _1783299)) = hAPP(hAPP(c_List_Olist_OCons(_1783297), _1783295), hAPP(c_List_OremoveAll(_1783297, _1783293), _1783299)))], (4538 ^ _779327) ^ [_848371, _848373, _848375, _848377, _848379, _848381] : [-(c_Lazy__Sequence_Obind(_848381, _848377, _848373) = c_Lazy__Sequence_Obind(_848379, _848375, _848371)), _848381 = _848379, _848377 = _848375, _848373 = _848371], (27689 ^ _779327) ^ [_1270950, _1270952, _1270954, _1270956, _1270958, _1270960] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270950, tc_fun(_1270952, tc_HOL_Obool)), _1270954), hAPP(hAPP(c_COMBC(_1270950, tc_fun(_1270956, tc_fun(_1270952, tc_HOL_Obool)), tc_fun(_1270952, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270956, tc_HOL_Obool), tc_fun(tc_fun(_1270956, tc_fun(_1270952, tc_HOL_Obool)), tc_fun(_1270952, tc_HOL_Obool)), _1270950), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270956, tc_fun(_1270952, tc_HOL_Obool))), _1270958)), _1270960)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270956, tc_fun(_1270952, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270950, tc_fun(_1270956, tc_HOL_Obool)), _1270954), _1270958)), _1270960))], (40466 ^ _779327) ^ [_1559424, _1559426, _1559428, _1559430, _1559432, _1559434, _1559436] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559424, _1559428)), hAPP(hAPP(c_Product__Type_OPair(_1559424, _1559428), _1559434), _1559436)), hAPP(hAPP(c_Relation_Orel__comp(_1559424, _1559426, _1559428), _1559430), _1559432))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1559424, _1559426, _1559428, hAPP(hAPP(c_COMBC(_1559424, tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_fun(_1559426, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559426, tc_fun(tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_fun(_1559426, tc_HOL_Obool)), _1559424), c_COMBC(_1559426, tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559426, tc_prod(_1559424, _1559426)), tc_fun(_1559426, tc_fun(tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_HOL_Obool)), _1559424), hAPP(c_COMBB(tc_prod(_1559424, _1559426), tc_fun(tc_fun(tc_prod(_1559424, _1559426), tc_HOL_Obool), tc_HOL_Obool), _1559426), c_member(tc_prod(_1559424, _1559426)))), c_Product__Type_OPair(_1559424, _1559426)))), _1559430), hAPP(hAPP(c_COMBC(_1559426, tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_fun(_1559428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559428, tc_fun(tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_fun(_1559428, tc_HOL_Obool)), _1559426), c_COMBC(_1559428, tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559428, tc_prod(_1559426, _1559428)), tc_fun(_1559428, tc_fun(tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_HOL_Obool)), _1559426), hAPP(c_COMBB(tc_prod(_1559426, _1559428), tc_fun(tc_fun(tc_prod(_1559426, _1559428), tc_HOL_Obool), tc_HOL_Obool), _1559428), c_member(tc_prod(_1559426, _1559428)))), c_Product__Type_OPair(_1559426, _1559428)))), _1559432)), _1559434), _1559436)))], (29044 ^ _779327) ^ [_1296770, _1296772, _1296774] : [class_Orderings_Oorder(_1296770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296770), _1296772), _1296774)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1296770, _1296774, _1296772) = c_Orderings_Obot__class_Obot(tc_fun(_1296770, tc_HOL_Obool)))], (38417 ^ _779327) ^ [_1502795, _1502797, _1502799, _1502801] : [hAPP(c_Set_Oimage(_1502795, _1502797, _1502799), c_Orderings_Otop__class_Otop(tc_fun(_1502795, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1502797, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1502795, _1502797, _1502799), hAPP(c_Set_Ovimage(_1502795, _1502797, _1502799), _1502801)) = _1502801)], (47810 ^ _779327) ^ [_1734401, _1734403, _1734405, _1734407] : [hBOOL(hAPP(c_List_Olistsp(_1734401, _1734403), _1734405)), hBOOL(hAPP(c_List_Olistsp(_1734401, _1734407), _1734405)), -(hBOOL(hAPP(c_List_Olistsp(_1734401, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1734401, tc_HOL_Obool)), _1734403), _1734407)), _1734405)))], (22377 ^ _779327) ^ [_1166513, _1166515, _1166517, _1166519] : [class_Orderings_Olinorder(_1166513), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166513), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166513), _1166515), _1166517)), _1166519) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166513), _1166515), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166513), _1166517), _1166519)))], (42635 ^ _779327) ^ [_1610885, _1610887, _1610889, _1610891] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1610885, _1610885)), hAPP(hAPP(c_Product__Type_OPair(_1610885, _1610885), _1610887), _1610889)), c_Transitive__Closure_Otrancl(_1610885, hAPP(c_Relation_Oconverse(_1610885, _1610885), _1610891)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610885, _1610885)), hAPP(hAPP(c_Product__Type_OPair(_1610885, _1610885), _1610887), _1610889)), hAPP(c_Relation_Oconverse(_1610885, _1610885), c_Transitive__Closure_Otrancl(_1610885, _1610891)))))], (34879 ^ _779327) ^ [_1422229, _1422231, _1422233] : [class_Lattices_Osemilattice__inf(_1422229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422229), _1422231), _1422233)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422229), _1422231), _1422233) = _1422231)], (9006 ^ _779327) ^ [_924336, _924338] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924336) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924338), -(_924336 = _924338)], (15431 ^ _779327) ^ [_1040034, _1040036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040034), _1040036)), _1040034)))], (52796 ^ _779327) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (6154 ^ _779327) ^ [_876267, _876269, _876271, _876273] : [class_Orderings_Oorder(_876267), _876269 = _876271, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876267), _876273), _876271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876267), _876273), _876269)))], (27230 ^ _779327) ^ [_1259933, _1259935, _1259937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259933, tc_HOL_Obool)), _1259935), _1259937)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259933, tc_HOL_Obool)), _1259937), _1259935) = _1259937)], (12411 ^ _779327) ^ [_985917] : [-(hAPP(c_Nat_OSuc, _985917) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _985917))], (3880 ^ _779327) ^ [_838202, _838204, _838206, _838208] : [-(c_Finite__Set_Ofold1(_838208, _838204) = c_Finite__Set_Ofold1(_838206, _838202)), _838208 = _838206, _838204 = _838202], (52361 ^ _779327) ^ [_1832612, _1832614] : [c_Equiv__Relations_Opart__equivp(_1832612, _1832614), 52365 ^ _779327 : [(52370 ^ _779327) ^ [] : [-(c_Predicate_Otransp(_1832612, _1832614))], (52368 ^ _779327) ^ [] : [-(c_Predicate_Osymp(_1832612, _1832614))], (52366 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1832614, 52364 ^ [_1832612, _1832614]), 52364 ^ [_1832612, _1832614])))]]], (18889 ^ _779327) ^ [_1101048, _1101050] : [c_Nat__Transfer_Ois__nat(_1101048), c_Nat__Transfer_Ois__nat(_1101050), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1101048), _1101050)))], (1398 ^ _779327) ^ [_799790, _799792] : [-(class_Orderings_Owellorder(_799790)), _799792 = _799790, class_Orderings_Owellorder(_799792)], (12485 ^ _779327) ^ [_987345, _987347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987345), _987347)), _987347))], (50870 ^ _779327) ^ [_1800837, _1800839, _1800841, _1800843] : [c_List_Olist__all(_1800837, _1800839, hAPP(hAPP(c_List_Olist_OCons(_1800837), _1800841), _1800843)), 50873 ^ _779327 : [(50876 ^ _779327) ^ [] : [-(c_List_Olist__all(_1800837, _1800839, _1800843))], (50874 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1800839, _1800841)))]]], (37340 ^ _779327) ^ [_1477441, _1477443, _1477445, _1477447] : [class_Groups_Ocomm__monoid__add(_1477441), 37343 ^ _779327 : [(37350 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1477443), _1477445))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477443, _1477441), _1477447), _1477445) = c_Groups_Ozero__class_Ozero(_1477441))], (37344 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477443), _1477445)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477443, _1477441), _1477447), _1477445) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1477441, _1477443, c_Groups_Oplus__class_Oplus(_1477441)), _1477447), c_Groups_Ozero__class_Ozero(_1477441)), _1477445))]]], (52614 ^ _779327) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (35505 ^ _779327) ^ [_1436294, _1436296, _1436298, _1436300] : [class_Orderings_Olinorder(_1436294), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436294, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1436294), _1436296)), c_SetInterval_Oord__class_OatLeastAtMost(_1436294, _1436298, _1436300)) = c_SetInterval_Oord__class_OatLeastAtMost(_1436294, _1436298, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1436294), _1436296), _1436300)))], (31296 ^ _779327) ^ [_1346523, _1346525, _1346527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346523, tc_HOL_Obool)), _1346525), hAPP(hAPP(c_Set_Oinsert(_1346523), _1346527), c_Orderings_Obot__class_Obot(tc_fun(_1346523, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1346523, _1346527, _1346525) = _1346527)], (27034 ^ _779327) ^ [_1256409, _1256411] : [class_Lattices_Olattice(_1256409), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256409), _1256411), _1256411) = _1256411)], (23133 ^ _779327) ^ [_1180647, _1180649, _1180651] : [class_Int_Onumber(_1180647), class_Orderings_Oord(_1180647), 23140 ^ _779327 : [(23147 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180647), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180649)), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180651)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1180647), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180649)), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180651)) = hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180649))], (23141 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180647), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180649)), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180651))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1180647), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180649)), hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180651)) = hAPP(c_Int_Onumber__class_Onumber__of(_1180647), _1180651))]]], (34148 ^ _779327) ^ [_1404961, _1404963, _1404965] : [-(hAPP(c_Relation_OImage(_1404961, _1404963, _1404965), c_Orderings_Obot__class_Obot(tc_fun(_1404961, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1404963, tc_HOL_Obool)))], (22009 ^ _779327) ^ [_1159050, _1159052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1159050), _1159052)), -(c_Divides_Odivmod__nat(_1159052, _1159050) = 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), _1159052), _1159050)), _1159050))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1159052), _1159050), _1159050)))], (39665 ^ _779327) ^ [_1531750, _1531752, _1531754, _1531756, _1531758, _1531760, _1531762, _1531764] : [c_Finite__Set_Ofolding__image__simple(_1531750, _1531752, _1531754, _1531756, _1531758, _1531760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531752), _1531762)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531752), _1531764)), 39679 ^ _779327 : [(39682 ^ _779327) ^ [] : [hAPP(_1531758, 39678 ^ [_1531750, _1531752, _1531754, _1531756, _1531758, _1531760, _1531762, _1531764]) = _1531756], (39680 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531752), 39678 ^ [_1531750, _1531752, _1531754, _1531756, _1531758, _1531760, _1531762, _1531764]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531752, tc_HOL_Obool)), _1531762), _1531764))))]], -(hAPP(_1531760, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1531752, tc_HOL_Obool)), _1531762), _1531764)) = hAPP(hAPP(_1531754, hAPP(_1531760, _1531762)), hAPP(_1531760, _1531764)))], (6652 ^ _779327) ^ [_883529, _883531, _883533] : [class_Orderings_Opreorder(_883529), 6655 ^ _779327 : [(6664 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883529), _883531), _883533))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883529), _883531), _883533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883529), _883533), _883531)))], (6656 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883529), _883531), _883533)), 6659 ^ _779327 : [(6662 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883529), _883533), _883531))], (6660 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883529), _883531), _883533)))]]]]], (49635 ^ _779327) ^ [_1774015, _1774017, _1774019] : [class_Orderings_Olinorder(_1774015), c_List_Olinorder__class_Osorted(_1774015, hAPP(c_List_Orev(_1774015), _1774017)), 49642 ^ _779327 : [(49649 ^ _779327) ^ [] : [-(_1774017 = c_List_Olist_ONil(_1774015)), -(c_List_Ofoldr(_1774015, _1774015, c_Orderings_Oord__class_Omax(_1774015), _1774017, _1774019) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1774015), hAPP(hAPP(c_List_Onth(_1774015), _1774017), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1774019))], (49643 ^ _779327) ^ [] : [_1774017 = c_List_Olist_ONil(_1774015), -(c_List_Ofoldr(_1774015, _1774015, c_Orderings_Oord__class_Omax(_1774015), _1774017, _1774019) = _1774019)]]], (25920 ^ _779327) ^ [_1233951, _1233953, _1233955, _1233957] : [class_Groups_Ocomm__monoid__add(_1233951), 25923 ^ _779327 : [(25930 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233953)), _1233955))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233951), _1233957), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1233955, hAPP(c_Nat_OSuc, _1233953))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1233951), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233951), _1233957), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1233955, _1233953))), hAPP(_1233957, hAPP(c_Nat_OSuc, _1233953))))], (25924 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233953)), _1233955)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233951), _1233957), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1233955, hAPP(c_Nat_OSuc, _1233953))) = c_Groups_Ozero__class_Ozero(_1233951))]]], (21196 ^ _779327) ^ [_1143136, _1143138] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143136) = hAPP(c_Nat_OSuc, _1143138), -(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(_1143136))), 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)), _1143138))))))], (9815 ^ _779327) ^ [_938379, _938381] : [class_Groups_Omonoid__mult(_938379), -(hAPP(hAPP(c_Power_Opower__class_Opower(_938379), _938381), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _938381)], (35749 ^ _779327) ^ [_1441933, _1441935, _1441937, _1441939] : [c_Equiv__Relations_Ocongruent(_1441933, _1441935, _1441937, _1441939), 35752 ^ _779327 : [(35753 ^ _779327) ^ [_1442078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1441933, _1441933)), _1442078), _1441937)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441933, _1441933, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1441933, tc_fun(_1441933, _1441935), tc_fun(_1441933, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441935, tc_HOL_Obool), tc_fun(tc_fun(_1441933, _1441935), tc_fun(_1441933, tc_HOL_Obool)), _1441933), c_COMBB(_1441935, tc_HOL_Obool, _1441933)), hAPP(hAPP(c_COMBB(_1441935, tc_fun(_1441935, tc_HOL_Obool), _1441933), c_fequal), _1441939))), _1441939)), _1442078)))]]], (21974 ^ _779327) ^ [_1158280, _1158282, _1158284] : [hBOOL(hAPP(_1158280, 21975 ^ [_1158280, _1158282, _1158284])), 21978 ^ _779327 : [(21979 ^ _779327) ^ [_1158391, _1158393] : [-(hBOOL(hAPP(_1158280, hAPP(hAPP(c_Product__Type_OPair(_1158282, _1158284), _1158393), _1158391))))]]], (8172 ^ _779327) ^ [_909406, _909408, _909410, _909412] : [class_Rings_Olinordered__comm__semiring__strict(_909406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909406), _909408), _909410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909406), c_Groups_Ozero__class_Ozero(_909406)), _909412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909406), _909412), _909408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909406), _909412), _909410))))], (26677 ^ _779327) ^ [_1248925, _1248927, _1248929] : [class_Groups_Ocomm__monoid__add(_1248925), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248925), _1248927), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1248929))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248925), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248925), _1248927), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1248929))), hAPP(_1248927, hAPP(c_Nat_OSuc, _1248929))))], (43193 ^ _779327) ^ [_1625008, _1625010, _1625012, _1625014, _1625016] : [class_Complete__Lattice_Ocomplete__lattice(_1625008), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625010), _1625012)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1625008), _1625014), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625010, _1625008), _1625012), _1625016)) = hAPP(hAPP(c_Finite__Set_Ofold(_1625010, _1625008, hAPP(hAPP(c_COMBB(_1625008, tc_fun(_1625008, _1625008), _1625010), c_Lattices_Osemilattice__inf__class_Oinf(_1625008)), _1625016)), _1625014), _1625012))], (29100 ^ _779327) ^ [_1297883, _1297885] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297883), _1297885))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297883, _1297885))], (40983 ^ _779327) ^ [_1572154, _1572156] : [c_Wellfounded_OwfP(_1572154, _1572156), -(c_Wellfounded_Owf(_1572154, hAPP(c_Set_OCollect(tc_prod(_1572154, _1572154)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572154, _1572154, tc_HOL_Obool), _1572156))))], (30932 ^ _779327) ^ [_1338952, _1338954, _1338956, _1338958, _1338960, _1338962, _1338964] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1338952, tc_fun(_1338954, tc_fun(_1338956, tc_HOL_Obool))), _1338958), _1338960), _1338962), _1338964)), 30936 ^ _779327 : [(30939 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1338960, 30935 ^ [_1338952, _1338954, _1338956, _1338958, _1338960, _1338962, _1338964]), _1338962), _1338964)))], (30937 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338952), 30935 ^ [_1338952, _1338954, _1338956, _1338958, _1338960, _1338962, _1338964]), _1338958)))]]], (45572 ^ _779327) ^ [_1683495, _1683497, _1683499, _1683501, _1683503, _1683505] : [-(hAPP(hAPP(c_List_Ozip(_1683495, _1683497), hAPP(hAPP(c_List_Omap(_1683499, _1683495), _1683501), _1683503)), _1683505) = hAPP(hAPP(c_List_Omap(tc_prod(_1683499, _1683497), tc_prod(_1683495, _1683497)), hAPP(c_Product__Type_Oprod_Oprod__case(_1683499, _1683497, tc_prod(_1683495, _1683497)), hAPP(hAPP(c_COMBB(_1683495, tc_fun(_1683497, tc_prod(_1683495, _1683497)), _1683499), c_Product__Type_OPair(_1683495, _1683497)), _1683501))), hAPP(hAPP(c_List_Ozip(_1683499, _1683497), _1683503), _1683505)))], (1448 ^ _779327) ^ [_800415, _800417] : [-(class_Lattices_Osemilattice__inf(_800415)), _800417 = _800415, class_Lattices_Osemilattice__inf(_800417)], (40384 ^ _779327) ^ [_1555955, _1555957, _1555959, _1555961, _1555963, _1555965, _1555967, _1555969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555955, _1555957)), hAPP(hAPP(c_Product__Type_OPair(_1555955, _1555957), _1555959), _1555961)), _1555963)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1555957, _1555965)), hAPP(hAPP(c_Product__Type_OPair(_1555957, _1555965), _1555961), _1555967)), _1555969)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555955, _1555965)), hAPP(hAPP(c_Product__Type_OPair(_1555955, _1555965), _1555959), _1555967)), hAPP(hAPP(c_Relation_Orel__comp(_1555955, _1555957, _1555965), _1555963), _1555969))))], (32064 ^ _779327) ^ [_1361690, _1361692, _1361694] : [class_Orderings_Olinorder(_1361690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361690), _1361692)), -(_1361692 = c_Orderings_Obot__class_Obot(tc_fun(_1361690, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1361690, hAPP(hAPP(c_Set_Oinsert(_1361690), _1361694), _1361692)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361690), _1361694), c_Big__Operators_Olinorder__class_OMax(_1361690, _1361692)))], (35091 ^ _779327) ^ [_1426890, _1426892, _1426894, _1426896] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426890, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426890, tc_HOL_Obool)), _1426892), _1426894)), _1426896) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426890, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426890, tc_HOL_Obool)), _1426892), _1426896)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426890, tc_HOL_Obool)), _1426894), _1426896)))], (17962 ^ _779327) ^ [_1084229, _1084231] : [c_Int_OBit0(_1084229) = c_Int_OBit1(_1084231)], (45492 ^ _779327) ^ [_1681454] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681454)), c_List_Olist_ONil(_1681454)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36156 ^ _779327) ^ [_1450964, _1450966, _1450968, _1450970, _1450972, _1450974, _1450976, _1450978, _1450980, _1450982, _1450984] : [c_Equiv__Relations_Oequiv(_1450964, _1450966, _1450968), c_Equiv__Relations_Oequiv(_1450970, _1450972, _1450974), c_Equiv__Relations_Ocongruent2(_1450964, _1450970, tc_fun(_1450976, tc_HOL_Obool), _1450968, _1450974, _1450978), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450964, tc_HOL_Obool)), _1450980), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450964), _1450966), _1450968))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450970, tc_HOL_Obool)), _1450982), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450970), _1450972), _1450974))), 36178 ^ _779327 : [(36184 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1450976, tc_HOL_Obool)), hAPP(hAPP(_1450978, 36177 ^ [_1450964, _1450966, _1450968, _1450970, _1450972, _1450974, _1450976, _1450978, _1450980, _1450982, _1450984]), 36180 ^ [_1450964, _1450966, _1450968, _1450970, _1450972, _1450974, _1450976, _1450978, _1450980, _1450982, _1450984])), _1450984))], (36182 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450970), 36180 ^ [_1450964, _1450966, _1450968, _1450970, _1450972, _1450974, _1450976, _1450978, _1450980, _1450982, _1450984]), _1450972)))], (36179 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450964), 36177 ^ [_1450964, _1450966, _1450968, _1450970, _1450972, _1450974, _1450976, _1450978, _1450980, _1450982, _1450984]), _1450966)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1450976, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450964, tc_fun(_1450976, tc_HOL_Obool)), _1450980), hAPP(hAPP(c_COMBB(tc_fun(_1450970, tc_fun(_1450976, tc_HOL_Obool)), tc_fun(_1450976, tc_HOL_Obool), _1450964), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450970, tc_fun(_1450976, tc_HOL_Obool)), _1450982)), _1450978))), _1450984)))], (15624 ^ _779327) ^ [_1043487, _1043489, _1043491, _1043493] : [class_Divides_Osemiring__div(_1043487), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043487), _1043489), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1043487), _1043491), _1043489))), c_Divides_Odiv__class_Omod(_1043487, _1043491, _1043489))), _1043493) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043487), _1043491), _1043493))], (24005 ^ _779327) ^ [_1197613, _1197615, _1197617, _1197619] : [class_Divides_Osemiring__div(_1197613), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197613), _1197615), c_Divides_Odiv__class_Omod(_1197613, _1197617, _1197619))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197613), _1197615), _1197619)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197613), _1197615), _1197617)))], (46776 ^ _779327) ^ [_1712723, _1712725, _1712727] : [hBOOL(hAPP(c_List_Odistinct(_1712723), _1712725)), -(hBOOL(hAPP(c_List_Odistinct(_1712723), hAPP(hAPP(c_List_Odrop(_1712723), _1712727), _1712725))))], (43800 ^ _779327) ^ [_1637123, _1637125, _1637127, _1637129] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1637123, tc_HOL_Obool)), _1637125), _1637127)), hBOOL(hAPP(hAPP(c_member(_1637123), _1637129), _1637125)), -(hBOOL(hAPP(hAPP(c_member(_1637123), _1637129), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637123, tc_HOL_Obool), _1637127))))], (46848 ^ _779327) ^ [_1714093, _1714095, _1714097] : [hBOOL(hAPP(c_List_Odistinct(_1714093), hAPP(hAPP(c_List_Olist_OCons(_1714093), _1714095), _1714097))), 46851 ^ _779327 : [(46854 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1714093), _1714097)))], (46852 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1714093), _1714095), hAPP(c_List_Oset(_1714093), _1714097)))]]], (778 ^ _779327) ^ [_791258, _791260, _791262, _791264, _791266, _791268] : [-(c_Finite__Set_Ofun__left__comm(_791266, _791262, _791258)), c_Finite__Set_Ofun__left__comm(_791268, _791264, _791260), _791268 = _791266, _791264 = _791262, _791260 = _791258], (28264 ^ _779327) ^ [_1282365, _1282367, _1282369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282365), _1282367)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282365), hAPP(hAPP(c_Set_Oinsert(_1282365), _1282369), _1282367))))], (45582 ^ _779327) ^ [_1683963, _1683965, _1683967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683963), tc_List_Olist(_1683963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683963), tc_List_Olist(_1683963)), c_List_Olist_ONil(_1683963)), _1683965)), c_List_Olex(_1683963, _1683967)))], (9567 ^ _779327) ^ [_934303, _934305] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934303) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _934305), -(_934303 = _934305)], (25433 ^ _779327) ^ [_1222885, _1222887, _1222889] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222885, _1222887) = _1222889, -(_1222885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1222889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), 25436 ^ [_1222885, _1222887, _1222889]), _1222887)))], (46018 ^ _779327) ^ [_1694776, _1694778, _1694780] : [-(hAPP(c_List_Oset(_1694776), hAPP(hAPP(c_List_Oappend(_1694776), _1694778), _1694780)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1694776, tc_HOL_Obool)), hAPP(c_List_Oset(_1694776), _1694778)), hAPP(c_List_Oset(_1694776), _1694780)))], (22111 ^ _779327) ^ [_1161275, _1161277] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1161275, _1161277), c_Divides_Odivmod__nat(_1161275, _1161277))))], (9272 ^ _779327) ^ [_929470, _929472] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929470)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929472)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _929470), _929472)))], (49774 ^ _779327) ^ [_1776766, _1776768, _1776770, _1776772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776766), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776768)), c_List_OtakeWhile(_1776768, _1776770, _1776772)))), -(hAPP(hAPP(c_List_Onth(_1776768), c_List_OtakeWhile(_1776768, _1776770, _1776772)), _1776766) = hAPP(hAPP(c_List_Onth(_1776768), _1776772), _1776766))], (40269 ^ _779327) ^ [_1552502, _1552504, _1552506, _1552508] : [-(c_Product__Type_Oapfst(_1552502, _1552504, _1552506, _1552508) = c_Product__Type_Omap__pair(_1552502, _1552504, _1552506, _1552506, _1552508, c_Fun_Oid(_1552506)))], (24153 ^ _779327) ^ [_1200046, _1200048] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200046), _1200048)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200048), _1200046))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200048), _1200046)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200046), _1200048)))], (13364 ^ _779327) ^ [_1003183, _1003185] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003183), _1003185)), hAPP(c_Nat_OSuc, _1003183))))], (34138 ^ _779327) ^ [_1404666, _1404668] : [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)), _1404666), _1404668)), 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)), _1404666), 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)), _1404668), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (46786 ^ _779327) ^ [_1712940, _1712942, _1712944] : [-(hAPP(hAPP(c_List_Otake(_1712940), _1712942), hAPP(c_List_Otl(_1712940), _1712944)) = hAPP(c_List_Otl(_1712940), hAPP(hAPP(c_List_Otake(_1712940), hAPP(c_Nat_OSuc, _1712942)), _1712944)))], (1218 ^ _779327) ^ [_797540, _797542] : [-(class_Groups_Oordered__ab__group__add(_797540)), _797542 = _797540, class_Groups_Oordered__ab__group__add(_797542)], (51035 ^ _779327) ^ [_1804154, _1804156] : [-(c_List_Oconcat(_1804154, c_List_Oreplicate(tc_List_Olist(_1804154), _1804156, c_List_Olist_ONil(_1804154))) = c_List_Olist_ONil(_1804154))], (5888 ^ _779327) ^ [_872119] : [-(_872119 = 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)), _872119)))], (48702 ^ _779327) ^ [_1755587, _1755589, _1755591, _1755593] : [-(c_List_Ofoldr(_1755587, _1755589, _1755591, c_List_Olist_ONil(_1755587), _1755593) = _1755593)], (22095 ^ _779327) ^ [_1161023, _1161025, _1161027, _1161029] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1161023, _1161025), _1161027)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1161023, _1161025), _1161029)), -(_1161027 = _1161029)], (5340 ^ _779327) ^ [_860806, _860808, _860810, _860812] : [-(c_Relation_Oconverse(_860812, _860808) = c_Relation_Oconverse(_860810, _860806)), _860812 = _860810, _860808 = _860806], (13824 ^ _779327) ^ [_1011431, _1011433] : [class_Rings_Osemiring__1(_1011431), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1011431), hAPP(c_Nat_OSuc, _1011433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011431), c_Groups_Oone__class_Oone(_1011431)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1011431), _1011433)))], (40241 ^ _779327) ^ [_1552040, _1552042] : [-(c_Fun_Oinj__on(_1552040, _1552040, c_Fun_Oid(_1552040), _1552042))], (10057 ^ _779327) ^ [_942126] : [hAPP(c_Int_Onat, _942126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _942126), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16840 ^ _779327) ^ [_1065016, _1065018, _1065020] : [class_Groups_Oordered__ab__group__add__abs(_1065016), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065016), hAPP(c_Groups_Oabs__class_Oabs(_1065016), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065016), _1065018), _1065020))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065016), hAPP(c_Groups_Oabs__class_Oabs(_1065016), _1065018)), hAPP(c_Groups_Oabs__class_Oabs(_1065016), _1065020)))))], (29702 ^ _779327) ^ [_1310077, _1310079, _1310081, _1310083] : [hBOOL(hAPP(hAPP(c_member(_1310077), _1310079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310077, tc_HOL_Obool)), _1310081), _1310083))), -(hBOOL(hAPP(hAPP(c_member(_1310077), _1310079), _1310081)))], (46496 ^ _779327) ^ [_1706231, _1706233] : [-(hAPP(c_List_Orotate1(_1706231), _1706233) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1706231), _1706231, c_List_Olist_ONil(_1706231), hAPP(hAPP(c_COMBB(tc_List_Olist(_1706231), tc_fun(tc_List_Olist(_1706231), tc_List_Olist(_1706231)), _1706231), hAPP(c_COMBC(tc_List_Olist(_1706231), tc_List_Olist(_1706231), tc_List_Olist(_1706231)), c_List_Oappend(_1706231))), hAPP(hAPP(c_COMBC(_1706231, tc_List_Olist(_1706231), tc_List_Olist(_1706231)), c_List_Olist_OCons(_1706231)), c_List_Olist_ONil(_1706231)))), _1706233))], (18194 ^ _779327) ^ [_1088296, _1088298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1088296)), c_Int_OBit0(_1088298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088296), _1088298)))], (16287 ^ _779327) ^ [_1055328, _1055330] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055328))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055328), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055330)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15543 ^ _779327) ^ [_1042048, _1042050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042050, _1042048)), _1042048)))], (43967 ^ _779327) ^ [_1641004, _1641006, _1641008] : [class_Complete__Lattice_Ocomplete__lattice(_1641004), -(c_Complete__Lattice_OSup__class_OSup(_1641004, hAPP(hAPP(c_Set_Oinsert(_1641004), _1641006), _1641008)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1641004), _1641006), c_Complete__Lattice_OSup__class_OSup(_1641004, _1641008)))], (46826 ^ _779327) ^ [_1713703, _1713705, _1713707] : [-(hAPP(c_List_Otl(_1713703), hAPP(hAPP(c_List_Olist_OCons(_1713703), _1713705), _1713707)) = _1713707)], (40261 ^ _779327) ^ [_1552344, _1552346] : [-(c_Product__Type_Omap__pair(_1552344, _1552344, _1552346, _1552346, c_COMBI(_1552344), c_COMBI(_1552346)) = c_Fun_Oid(tc_prod(_1552344, _1552346)))], (19389 ^ _779327) ^ [_1109387, _1109389, _1109391] : [class_Rings_Odivision__ring(_1109387), -(_1109389 = c_Groups_Ozero__class_Ozero(_1109387)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1109387), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109387), _1109391), _1109389)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109387), _1109391), hAPP(c_Groups_Ouminus__class_Ouminus(_1109387), _1109389)))], (44926 ^ _779327) ^ [_1666964] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1666964)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1666964), tc_HOL_Obool))))], (42284 ^ _779327) ^ [_1602497, _1602499, _1602501, _1602503, _1602505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602497, _1602497)), hAPP(hAPP(c_Product__Type_OPair(_1602497, _1602497), _1602499), _1602501)), c_Transitive__Closure_Ortrancl(_1602497, _1602503))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602497, _1602497)), hAPP(hAPP(c_Product__Type_OPair(_1602497, _1602497), _1602501), _1602505)), c_Transitive__Closure_Ortrancl(_1602497, _1602503))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602497, _1602497)), hAPP(hAPP(c_Product__Type_OPair(_1602497, _1602497), _1602499), _1602505)), c_Transitive__Closure_Ortrancl(_1602497, _1602503))))], (25161 ^ _779327) ^ [_1218002, _1218004, _1218006] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218002), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1218004, _1218006))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218002), _1218006)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218002), _1218004)))], (7256 ^ _779327) ^ [_893133, _893135, _893137] : [class_Rings_Olinordered__idom(_893133), -(_893135 = _893137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893133), _893135), _893137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893133), _893137), _893135)))], (52870 ^ _779327) ^ [_1839077] : [class_Enum_Oenum(_1839077), -(class_Enum_Oenum(tc_Option_Ooption(_1839077)))], (17668 ^ _779327) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (46128 ^ _779327) ^ [_1697001, _1697003, _1697005] : [_1697005 = c_List_Olist_ONil(_1697003), -(_1697001 = hAPP(hAPP(c_List_Oappend(_1697003), _1697005), _1697001))], (11151 ^ _779327) ^ [_961665, _961667, _961669, _961671] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961665), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961665), _961667), _961669)), hAPP(c_Int_Onumber__class_Onumber__of(_961665), _961671)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961665), _961667), hAPP(c_Int_Onumber__class_Onumber__of(_961665), _961671))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961665), _961669), hAPP(c_Int_Onumber__class_Onumber__of(_961665), _961671)))), class_Int_Onumber(_961665), class_Rings_Oring(_961665)], (47159 ^ _779327) ^ [_1720713, _1720715, _1720717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720713)), _1720715)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1720713, _1720717), _1720715) = _1720715)], (40156 ^ _779327) ^ [_1548236, _1548238, _1548240] : [class_Orderings_Olinorder(_1548236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548236), _1548238)), -(_1548238 = c_Orderings_Obot__class_Obot(tc_fun(_1548236, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1548236), _1548240)), -(_1548240 = c_Orderings_Obot__class_Obot(tc_fun(_1548236, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1548236), c_Big__Operators_Olattice_OSup__fin(_1548236, c_Orderings_Oord__class_Omax(_1548236), _1548238)), c_Big__Operators_Olattice_OSup__fin(_1548236, c_Orderings_Oord__class_Omax(_1548236), _1548240)) = c_Big__Operators_Olattice_OSup__fin(_1548236, c_Orderings_Oord__class_Omax(_1548236), hAPP(c_Set_OCollect(_1548236), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_HOL_Obool), tc_HOL_Obool, _1548236), c_HOL_OEx(_1548236)), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool)), tc_fun(_1548236, tc_HOL_Obool), _1548236), hAPP(c_COMBB(tc_fun(_1548236, tc_HOL_Obool), tc_HOL_Obool, _1548236), c_HOL_OEx(_1548236))), hAPP(hAPP(c_COMBC(_1548236, tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool)), tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_fun(tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool))), tc_fun(tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool)), tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool))), _1548236), c_COMBS(_1548236, tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_fun(_1548236, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1548236, tc_fun(tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool))), _1548236), hAPP(c_COMBB(tc_fun(_1548236, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool)), _1548236), c_COMBS(_1548236, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool)), tc_fun(_1548236, tc_fun(_1548236, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1548236), hAPP(c_COMBB(tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1548236), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548236), c_fconj))), hAPP(hAPP(c_COMBC(_1548236, tc_fun(_1548236, tc_fun(_1548236, _1548236)), tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1548236, _1548236), tc_fun(_1548236, tc_HOL_Obool)), tc_fun(tc_fun(_1548236, tc_fun(_1548236, _1548236)), tc_fun(_1548236, tc_fun(_1548236, tc_HOL_Obool))), _1548236), c_COMBB(tc_fun(_1548236, _1548236), tc_fun(_1548236, tc_HOL_Obool), _1548236)), hAPP(hAPP(c_COMBB(tc_fun(_1548236, tc_HOL_Obool), tc_fun(tc_fun(_1548236, _1548236), tc_fun(_1548236, tc_HOL_Obool)), _1548236), c_COMBB(_1548236, tc_HOL_Obool, _1548236)), c_fequal))), c_Orderings_Oord__class_Omin(_1548236)))))), hAPP(hAPP(c_COMBC(_1548236, tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1548236, tc_HOL_Obool), tc_fun(_1548236, tc_HOL_Obool)), _1548236), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1548236)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548236), c_fconj), hAPP(hAPP(c_COMBC(_1548236, tc_fun(_1548236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548236)), _1548238)))), hAPP(hAPP(c_COMBC(_1548236, tc_fun(_1548236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548236)), _1548240))))))))], (15339 ^ _779327) ^ [_1038048, _1038050, _1038052, _1038054] : [class_Divides_Osemiring__div(_1038048), -(c_Divides_Odiv__class_Omod(_1038048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038048), _1038050), _1038052), _1038054) = c_Divides_Odiv__class_Omod(_1038048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038048), c_Divides_Odiv__class_Omod(_1038048, _1038050, _1038054)), _1038052), _1038054))], (22341 ^ _779327) ^ [_1165725, _1165727, _1165729] : [class_Orderings_Olinorder(_1165725), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165725), _1165727), _1165729) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165725), _1165729), _1165727))], (38383 ^ _779327) ^ [_1501849, _1501851, _1501853, _1501855, _1501857] : [hBOOL(hAPP(hAPP(c_member(_1501849), _1501851), hAPP(c_Set_Ovimage(_1501849, _1501853, _1501855), _1501857))), -(hBOOL(hAPP(hAPP(c_member(_1501853), hAPP(_1501855, _1501851)), _1501857)))], (30711 ^ _779327) ^ [_1334040, _1334042, _1334044, _1334046] : [-(hBOOL(hAPP(hAPP(c_member(_1334040), _1334042), _1334044))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334040, tc_Nat_Onat), _1334046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334040, tc_HOL_Obool)), _1334044), hAPP(hAPP(c_Set_Oinsert(_1334040), _1334042), c_Orderings_Obot__class_Obot(tc_fun(_1334040, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334040, tc_Nat_Onat), _1334046), _1334044))], (29957 ^ _779327) ^ [_1314858, _1314860, _1314862, _1314864] : [hBOOL(hAPP(hAPP(c_member(_1314858), _1314860), _1314862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314858, tc_HOL_Obool)), _1314862), hAPP(_1314864, _1314862))), -(hBOOL(hAPP(hAPP(c_member(_1314858), _1314860), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1314858, tc_HOL_Obool), _1314864))))], (49435 ^ _779327) ^ [_1769750, _1769752] : [hBOOL(hAPP(c_List_Odistinct(_1769750), _1769752)), -(hBOOL(hAPP(c_List_Odistinct(_1769750), hAPP(c_List_Orev(_1769750), _1769752))))], (6028 ^ _779327) ^ [_874226, _874228, _874230, _874232] : [class_Orderings_Opreorder(_874226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874226), _874228), _874230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874226), _874230), _874232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_874226), _874228), _874232)))], (41825 ^ _779327) ^ [_1591025, _1591027, _1591029] : [-(hBOOL(hAPP(hAPP(c_member(_1591025), _1591027), c_Wellfounded_Oacc(_1591025, _1591029)))), 41829 ^ _779327 : [(41832 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1591025), 41828 ^ [_1591025, _1591027, _1591029]), c_Wellfounded_Oacc(_1591025, _1591029)))], (41830 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591025, _1591025)), hAPP(hAPP(c_Product__Type_OPair(_1591025, _1591025), 41828 ^ [_1591025, _1591027, _1591029]), _1591027)), _1591029)))]]], (40408 ^ _779327) ^ [_1556845, _1556847, _1556849, _1556851, _1556853, _1556855, _1556857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556845, _1556847), tc_HOL_Obool)), _1556849), _1556851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556847, _1556853), tc_HOL_Obool)), _1556855), _1556857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556845, _1556853), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1556845, _1556847, _1556853), _1556849), _1556855)), hAPP(hAPP(c_Relation_Orel__comp(_1556845, _1556847, _1556853), _1556851), _1556857))))], (22065 ^ _779327) ^ [_1160431, _1160433, _1160435] : [-(hAPP(hAPP(c_Product__Type_OPair(_1160431, _1160433), hAPP(c_Product__Type_Ofst(_1160431, _1160433), _1160435)), hAPP(c_Product__Type_Osnd(_1160431, _1160433), _1160435)) = _1160435)], (31447 ^ _779327) ^ [_1349681, _1349683, _1349685] : [class_Complete__Lattice_Ocomplete__lattice(_1349681), _1349683 = c_Inductive_Ocomplete__lattice__class_Olfp(_1349681, _1349685), c_Orderings_Oorder__class_Omono(_1349681, _1349681, _1349685), -(_1349683 = hAPP(_1349685, _1349683))], (22743 ^ _779327) ^ [_1173074, _1173076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1173074)), -(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(_1173074), _1173076))), _1173074)))], (41016 ^ _779327) ^ [_1572734, _1572736, _1572738] : [c_Wellfounded_OwfP(_1572734, _1572736), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1572734, _1572736), _1572738)))], (43610 ^ _779327) ^ [_1632995, _1632997] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1632995), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1632995, tc_HOL_Obool), _1632997)))), 43611 ^ _779327 : [(43612 ^ _779327) ^ [_1633059] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1632995, tc_HOL_Obool)), _1633059), _1632997)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632995), _1633059))]]], (40743 ^ _779327) ^ [_1565475, _1565477, _1565479, _1565481] : [40744 ^ _779327 : [(40745 ^ _779327) ^ [_1565550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565479, _1565475)), hAPP(hAPP(c_Product__Type_OPair(_1565479, _1565475), _1565550), _1565477)), _1565481))]], -(hBOOL(hAPP(hAPP(c_member(_1565475), _1565477), hAPP(c_Relation_ORange(_1565479, _1565475), _1565481))))], (29344 ^ _779327) ^ [_1302820, _1302822, _1302824] : [class_Orderings_Olinorder(_1302820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302820), _1302822), _1302824)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302820, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1302820), _1302822), c_Orderings_Obot__class_Obot(tc_fun(_1302820, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1302820, _1302822, _1302824)) = c_SetInterval_Oord__class_OatLeastAtMost(_1302820, _1302822, _1302824))], (48092 ^ _779327) ^ [_1740381, _1740383, _1740385, _1740387, _1740389, _1740391, _1740393] : [c_List_Olist__all2(_1740381, _1740389, hAPP(hAPP(c_COMBC(_1740381, tc_fun(_1740389, _1740383), tc_fun(_1740389, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1740383, tc_HOL_Obool), tc_fun(tc_fun(_1740389, _1740383), tc_fun(_1740389, tc_HOL_Obool)), _1740381), c_COMBB(_1740383, tc_HOL_Obool, _1740389)), _1740385)), _1740391), _1740387, _1740393), -(c_List_Olist__all2(_1740381, _1740383, _1740385, _1740387, hAPP(hAPP(c_List_Omap(_1740389, _1740383), _1740391), _1740393)))], (10793 ^ _779327) ^ [_955024, _955026, _955028] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955024), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955026), _955028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955024), _955028)))], (28206 ^ _779327) ^ [_1281181, _1281183, _1281185, _1281187] : [class_Complete__Lattice_Ocomplete__lattice(_1281181), _1281183 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1281181, _1281185), c_Orderings_Oorder__class_Omono(_1281181, _1281181, _1281185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281181), _1281187), hAPP(_1281185, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281181), _1281187), _1281183)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281181), _1281187), _1281183)))], (36827 ^ _779327) ^ [_1466327, _1466329, _1466331, _1466333, _1466335] : [c_Fun_Oinj__on(_1466327, _1466329, _1466331, _1466333), -(c_Fun_Oinj__on(_1466327, _1466329, _1466331, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1466327, tc_HOL_Obool)), _1466333), _1466335)))], (30553 ^ _779327) ^ [_1330665, _1330667, _1330669, _1330671, _1330673] : [class_Groups_Ocomm__monoid__add(_1330665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330667), _1330669)), -(hBOOL(hAPP(hAPP(c_member(_1330667), _1330671), _1330669))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330667, _1330665), _1330673), hAPP(hAPP(c_Set_Oinsert(_1330667), _1330671), _1330669)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330665), hAPP(_1330673, _1330671)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330667, _1330665), _1330673), _1330669)))], (42366 ^ _779327) ^ [_1604357, _1604359, _1604361, _1604363, _1604365] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604357, _1604357)), hAPP(hAPP(c_Product__Type_OPair(_1604357, _1604357), _1604359), _1604361)), c_Transitive__Closure_Ortrancl(_1604357, _1604363))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604357, _1604357)), hAPP(hAPP(c_Product__Type_OPair(_1604357, _1604357), _1604361), _1604365)), _1604363)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604357, _1604357)), hAPP(hAPP(c_Product__Type_OPair(_1604357, _1604357), _1604359), _1604365)), c_Transitive__Closure_Otrancl(_1604357, _1604363))))], (13788 ^ _779327) ^ [_1010751, _1010753, _1010755] : [class_Rings_Oring__1(_1010751), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1010751), hAPP(c_Groups_Ouminus__class_Ouminus(_1010751), _1010753)), _1010755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010751), hAPP(hAPP(c_Power_Opower__class_Opower(_1010751), hAPP(c_Groups_Ouminus__class_Ouminus(_1010751), c_Groups_Oone__class_Oone(_1010751))), _1010755)), hAPP(hAPP(c_Power_Opower__class_Opower(_1010751), _1010753), _1010755)))], (25460 ^ _779327) ^ [_1223526, _1223528, _1223530, _1223532] : [class_Groups_Oordered__ab__group__add__abs(_1223526), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223526), c_Groups_Ozero__class_Ozero(_1223526)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223528, _1223526), hAPP(hAPP(c_COMBB(_1223526, _1223526, _1223528), c_Groups_Oabs__class_Oabs(_1223526)), _1223530)), _1223532))))], (2586 ^ _779327) ^ [_817295, _817297] : [_817297 = _817295, -(c_DSequence_Osingle(_817297) = c_DSequence_Osingle(_817295))], (39132 ^ _779327) ^ [_1520274, _1520276, _1520278] : [class_Orderings_Olinorder(_1520274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520274), _1520276)), hBOOL(hAPP(hAPP(c_member(_1520274), _1520278), _1520276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1520274), hAPP(c_Finite__Set_Ofold1(_1520274, c_Orderings_Oord__class_Omin(_1520274)), _1520276)), _1520278)))], (9128 ^ _779327) ^ [_926824, _926826, _926828] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926824, tc_HOL_Obool)), _926826), _926828))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926824, tc_HOL_Obool)), _926826), _926828)), -(_926826 = _926828)], (18102 ^ _779327) ^ [_1086713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086713), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1086713)), c_Int_OMin)))], (14357 ^ _779327) ^ [_1021374, _1021376] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021374))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021374)), _1021376) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021376))], (13754 ^ _779327) ^ [_1010089, _1010091, _1010093] : [class_Rings_Olinordered__ring(_1010089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010089), c_Groups_Ozero__class_Ozero(_1010089)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010089), _1010091), _1010091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010089), _1010093), _1010093)))))], (52792 ^ _779327) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (22631 ^ _779327) ^ [_1171033, _1171035, _1171037] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171033), _1171035)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171037), _1171035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1171033), _1171037)), _1171035))], (2636 ^ _779327) ^ [_818158, _818160, _818162, _818164, _818166, _818168, _818170, _818172] : [-(c_Nitpick_Opair__box_OPairBox(_818172, _818168, _818164, _818160) = c_Nitpick_Opair__box_OPairBox(_818170, _818166, _818162, _818158)), _818172 = _818170, _818168 = _818166, _818164 = _818162, _818160 = _818158], (22633 ^ _779327) ^ [_1171090, _1171092, _1171094, _1171096, _1171098] : [class_Orderings_Olinorder(_1171090), class_Orderings_Olinorder(_1171092), c_Orderings_Oorder__class_Omono(_1171092, _1171090, _1171094), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171090), hAPP(_1171094, _1171096)), hAPP(_1171094, _1171098)) = hAPP(_1171094, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171092), _1171096), _1171098)))], (35413 ^ _779327) ^ [_1434322, _1434324, _1434326] : [class_Complete__Lattice_Ocomplete__lattice(_1434322), c_Orderings_Oorder__class_Omono(_1434322, _1434322, _1434324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434322), hAPP(_1434324, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1434322), c_Inductive_Ocomplete__lattice__class_Olfp(_1434322, _1434324)), _1434326))), _1434326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434322), c_Inductive_Ocomplete__lattice__class_Olfp(_1434322, _1434324)), _1434326)))], (44434 ^ _779327) ^ [_1651701, _1651703] : [-(c_FunDef_Ois__measure(_1651701, _1651703))], (49597 ^ _779327) ^ [_1773042, _1773044] : [-(hAPP(c_List_Orev(_1773042), _1773044) = hAPP(c_List_Ofoldl(tc_List_Olist(_1773042), _1773042, hAPP(c_COMBC(_1773042, tc_List_Olist(_1773042), tc_List_Olist(_1773042)), c_List_Olist_OCons(_1773042)), c_List_Olist_ONil(_1773042)), _1773044))], (35027 ^ _779327) ^ [_1425291, _1425293, _1425295, _1425297] : [hBOOL(hAPP(hAPP(c_member(_1425291), _1425293), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425291, tc_HOL_Obool)), _1425295), _1425297))), -(hBOOL(hAPP(hAPP(c_member(_1425291), _1425293), _1425295)))], (27685 ^ _779327) ^ [_1270722, _1270724, _1270726, _1270728, _1270730] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270722, tc_fun(_1270724, tc_HOL_Obool)), _1270726), hAPP(hAPP(c_COMBC(_1270722, tc_fun(_1270724, tc_HOL_Obool), tc_fun(_1270724, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270724, tc_HOL_Obool), tc_fun(tc_fun(_1270724, tc_HOL_Obool), tc_fun(_1270724, tc_HOL_Obool)), _1270722), c_Groups_Ominus__class_Ominus(tc_fun(_1270724, tc_HOL_Obool))), _1270728)), _1270730)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270724, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270722, tc_fun(_1270724, tc_HOL_Obool)), _1270726), _1270728)), _1270730))], (26980 ^ _779327) ^ [_1255152, _1255154, _1255156] : [class_Lattices_Osemilattice__sup(_1255152), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255152), _1255154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255152), _1255154), _1255156)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255152), _1255154), _1255156))], (48590 ^ _779327) ^ [_1752137, _1752139, _1752141, _1752143] : [-(hBOOL(hAPP(_1752137, _1752139))), -(hAPP(c_List_Ofilter(_1752141, _1752137), hAPP(hAPP(c_List_Olist_OCons(_1752141), _1752139), _1752143)) = hAPP(c_List_Ofilter(_1752141, _1752137), _1752143))], (43535 ^ _779327) ^ [_1631568, _1631570, _1631572, _1631574, _1631576, _1631578] : [c_Finite__Set_Ofun__left__comm(_1631568, _1631570, _1631572), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1631568, _1631570, _1631572, _1631574, _1631576), _1631578)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1631568, _1631570, _1631572), _1631574), _1631576) = _1631578)], (8516 ^ _779327) ^ [_915702, _915704] : [8517 ^ _779327 : [(8520 ^ _779327) ^ [] : [_915702 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8518 ^ _779327) ^ [] : [_915704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _915702), _915704) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (28270 ^ _779327) ^ [_1282476, _1282478, _1282480, _1282482] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282476), _1282478)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282480), hAPP(c_Set_Oimage(_1282476, _1282480, _1282482), _1282478))))], (35253 ^ _779327) ^ [_1430439, _1430441, _1430443] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430439, tc_HOL_Obool)), _1430441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430439, tc_HOL_Obool)), _1430443), _1430441)) = c_Orderings_Obot__class_Obot(tc_fun(_1430439, tc_HOL_Obool)))], (34745 ^ _779327) ^ [_1419572, _1419574, _1419576] : [class_Lattices_Olattice(_1419572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419572), _1419574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419572), _1419574), _1419576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419572), _1419574), _1419576))], (20107 ^ _779327) ^ [_1122197, _1122199] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122197), _1122199), hAPP(c_Int_Onumber__class_Onumber__of(_1122197), c_Int_OBit1(c_Int_OPls))) = _1122199), class_Fields_Ofield(_1122197), class_Int_Onumber__ring(_1122197)], (52528 ^ _779327) ^ [_1835750, _1835752] : [class_Orderings_Obot(_1835750), -(class_Orderings_Obot(tc_fun(_1835752, _1835750)))], (29708 ^ _779327) ^ [_1310208, _1310210, _1310212, _1310214] : [hBOOL(hAPP(hAPP(c_member(_1310208), _1310210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310208, tc_HOL_Obool)), _1310212), _1310214))), hBOOL(hAPP(hAPP(c_member(_1310208), _1310210), _1310214))], (47808 ^ _779327) ^ [_1734341, _1734343, _1734345] : [-(c_List_Olistsp(_1734341, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1734341, tc_HOL_Obool)), _1734343), _1734345)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1734341), tc_HOL_Obool)), c_List_Olistsp(_1734341, _1734343)), c_List_Olistsp(_1734341, _1734345)))], (17444 ^ _779327) ^ [_1075530] : [c_Int_OPls = c_Int_OBit1(_1075530)], (34797 ^ _779327) ^ [_1420622] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1420622) = c_Orderings_Oord__class_Omin(_1420622)), class_Lattices_Osemilattice__inf(_1420622), class_Orderings_Olinorder(_1420622)], (31788 ^ _779327) ^ [_1357037, _1357039] : [class_Orderings_Olinorder(_1357037), -(c_Big__Operators_Olinorder__class_OMax(_1357037, hAPP(hAPP(c_Set_Oinsert(_1357037), _1357039), c_Orderings_Obot__class_Obot(tc_fun(_1357037, tc_HOL_Obool)))) = _1357039)], (46034 ^ _779327) ^ [_1695115, _1695117, _1695119] : [-(hAPP(hAPP(c_List_Olist__update(_1695115, _1695117), _1695119), hAPP(hAPP(c_List_Onth(_1695115), _1695117), _1695119)) = _1695117)], (5638 ^ _779327) ^ [_868365, _868367] : [hAPP(c_Nat_OSuc, _868365) = hAPP(c_Nat_OSuc, _868367), -(_868365 = _868367)], (29657 ^ _779327) ^ [_1309225, _1309227] : [_1309227 = c_Orderings_Obot__class_Obot(tc_fun(_1309225, tc_HOL_Obool)), 29660 ^ _779327 : [(29661 ^ _779327) ^ [_1309305] : [hBOOL(hAPP(hAPP(c_member(_1309225), _1309305), _1309227))]]], (46122 ^ _779327) ^ [_1696906, _1696908, _1696910] : [_1696906 = hAPP(hAPP(c_List_Oappend(_1696908), _1696910), _1696906), -(_1696910 = c_List_Olist_ONil(_1696908))], (38836 ^ _779327) ^ [_1513266, _1513268, _1513270] : [-(hAPP(c_Finite__Set_Ofold1(_1513266, _1513268), hAPP(hAPP(c_Set_Oinsert(_1513266), _1513270), c_Orderings_Obot__class_Obot(tc_fun(_1513266, tc_HOL_Obool)))) = _1513270)], (51449 ^ _779327) ^ [_1813420, _1813422, _1813424] : [-(c_FunDef_OTHE__default(_1813422, _1813424, _1813420) = _1813424), 51451 ^ _779327 : [(51454 ^ _779327) ^ [_1813542] : [hBOOL(hAPP(_1813420, _1813542)), -(_1813542 = 51450 ^ [_1813420, _1813422, _1813424])], (51452 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1813420, 51450 ^ [_1813420, _1813422, _1813424])))]]], (7792 ^ _779327) ^ [_902325, _902327, _902329, _902331] : [class_Rings_Oordered__semiring(_902325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902325), _902327), _902329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902325), c_Groups_Ozero__class_Ozero(_902325)), _902331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902325), _902331), _902327)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902325), _902331), _902329))))], (23207 ^ _779327) ^ [_1182268, _1182270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182268), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23210 ^ _779327 : [(23219 ^ _779327) ^ [] : [-(c_Nitpick_Onorm__frac(_1182270, _1182268) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1182270), _1182268)), 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), _1182270))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182268)))), -(_1182270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1182268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23211 ^ _779327) ^ [] : [23212 ^ _779327 : [(23215 ^ _779327) ^ [] : [_1182268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23213 ^ _779327) ^ [] : [_1182270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1182270, _1182268) = 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)))]]], (47153 ^ _779327) ^ [_1720600, _1720602, _1720604] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1720600, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720602)), _1720604)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1720602, _1720600), _1720604) = _1720604)], (23857 ^ _779327) ^ [_1195081, _1195083, _1195085] : [class_Rings_Olinordered__idom(_1195081), 23860 ^ _779327 : [(23867 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195081), _1195083), _1195085)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195081), _1195083), hAPP(c_Groups_Oabs__class_Oabs(_1195081), _1195085))))], (23861 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195081), _1195083), hAPP(c_Groups_Oabs__class_Oabs(_1195081), _1195085))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195081), _1195083), _1195085)))]]], (23752 ^ _779327) ^ [_1192898, _1192900, _1192902, _1192904, _1192906, _1192908, _1192910] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1192898, _1192900, _1192902, _1192904, _1192906, _1192908, _1192910) = c_New__DSequence_Oneg__decr__bind(_1192898, _1192900, hAPP(hAPP(hAPP(_1192902, _1192906), _1192908), _1192910), hAPP(hAPP(c_COMBC(_1192898, 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(_1192900)))), hAPP(hAPP(c_COMBC(_1192898, 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(_1192900))))), hAPP(hAPP(c_COMBC(_1192898, 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(_1192900)))))), _1192904), _1192906)), _1192908)), _1192910)))], (3228 ^ _779327) ^ [_827820, _827822, _827824, _827826, _827828, _827830] : [-(c_Wellfounded_Omlex__prod(_827830, _827826, _827822) = c_Wellfounded_Omlex__prod(_827828, _827824, _827820)), _827830 = _827828, _827826 = _827824, _827822 = _827820], (50134 ^ _779327) ^ [_1784269, _1784271, _1784273] : [-(hAPP(c_List_Oset(_1784269), c_List_Oinsert(_1784269, _1784271, _1784273)) = hAPP(hAPP(c_Set_Oinsert(_1784269), _1784271), hAPP(c_List_Oset(_1784269), _1784273)))], (51863 ^ _779327) ^ [_1823633, _1823635] : [-(c_Equiv__Relations_Oequivp(_1823633, _1823635)), c_Predicate_Oreflp(_1823633, _1823635), c_Predicate_Osymp(_1823633, _1823635), c_Predicate_Otransp(_1823633, _1823635)], (7606 ^ _779327) ^ [_898905] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898905), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32206 ^ _779327) ^ [_1364040, _1364042, _1364044] : [class_Orderings_Olinorder(_1364040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364040), _1364042)), 32213 ^ _779327 : [(32220 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364040, tc_HOL_Obool)), _1364042), hAPP(hAPP(c_Set_Oinsert(_1364040), _1364044), c_Orderings_Obot__class_Obot(tc_fun(_1364040, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364040, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1364040, hAPP(hAPP(c_Set_Oinsert(_1364040), _1364044), _1364042)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364040), _1364044), c_Big__Operators_Olinorder__class_OMax(_1364040, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364040, tc_HOL_Obool)), _1364042), hAPP(hAPP(c_Set_Oinsert(_1364040), _1364044), c_Orderings_Obot__class_Obot(tc_fun(_1364040, tc_HOL_Obool)))))))], (32214 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364040, tc_HOL_Obool)), _1364042), hAPP(hAPP(c_Set_Oinsert(_1364040), _1364044), c_Orderings_Obot__class_Obot(tc_fun(_1364040, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364040, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1364040, hAPP(hAPP(c_Set_Oinsert(_1364040), _1364044), _1364042)) = _1364044)]]], (6755 ^ _779327) ^ [_885058, _885060, _885062] : [class_Orderings_Olinorder(_885058), 6758 ^ _779327 : [(6759 ^ _779327) ^ [] : [-(_885060 = _885062), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885058), _885060), _885062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885058), _885062), _885060)))], (6769 ^ _779327) ^ [] : [6770 ^ _779327 : [(6773 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885058), _885062), _885060))], (6771 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885058), _885060), _885062))]], _885060 = _885062]]], (11119 ^ _779327) ^ [_960871, _960873, _960875, _960877, _960879, _960881] : [class_Rings_Oring(_960871), 11122 ^ _779327 : [(11129 ^ _779327) ^ [] : [_960877 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960871), _960879), _960873)), _960875)), _960881), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), _960873), _960875)), _960877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), _960879), _960875)), _960881))], (11123 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), _960873), _960875)), _960877) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), _960879), _960875)), _960881), -(_960877 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960871), _960879), _960873)), _960875)), _960881))]]], (16704 ^ _779327) ^ [_1062671, _1062673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062671), _1062673)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062671, _1062673) = _1062671)], (35269 ^ _779327) ^ [_1430950, _1430952, _1430954, _1430956] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430950, tc_HOL_Obool)), _1430952), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430950, tc_HOL_Obool)), _1430954), _1430956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430950, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430950, tc_HOL_Obool)), _1430952), _1430954)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430950, tc_HOL_Obool)), _1430952), _1430956)))], (480 ^ _779327) ^ [_786717, _786719, _786721, _786723] : [-(c_Nitpick_Owf_H(_786721, _786717)), c_Nitpick_Owf_H(_786723, _786719), _786723 = _786721, _786719 = _786717], (30637 ^ _779327) ^ [_1332431, _1332433, _1332435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332431), _1332433)), -(hBOOL(hAPP(hAPP(c_member(_1332431), _1332435), _1332433))), -(hAPP(c_Finite__Set_Ocard(_1332431), hAPP(hAPP(c_Set_Oinsert(_1332431), _1332435), _1332433)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1332431), _1332433)))], (41257 ^ _779327) ^ [_1578145, _1578147, _1578149, _1578151, _1578153, _1578155, _1578157] : [-(hAPP(c_Product__Type_Oapfst(_1578145, _1578147, _1578149, _1578151), hAPP(c_Product__Type_Oapfst(_1578153, _1578145, _1578149, _1578155), _1578157)) = hAPP(c_Product__Type_Oapfst(_1578153, _1578147, _1578149, hAPP(c_Fun_Ocomp(_1578145, _1578147, _1578153, _1578151), _1578155)), _1578157))], (49413 ^ _779327) ^ [_1769180, _1769182, _1769184, _1769186] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1769180), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1769180))), _1769182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1769180))), c_List_Otranspose(_1769180, _1769182)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769186), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1769180))), hAPP(c_List_Ofilter(tc_List_Olist(_1769180), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1769180)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769184)), c_Nat_Osize__class_Osize(tc_List_Olist(_1769180)))), _1769182)))), -(hAPP(hAPP(c_List_Onth(_1769180), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1769180)), c_List_Otranspose(_1769180, _1769182)), _1769184)), _1769186) = hAPP(hAPP(c_List_Onth(_1769180), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1769180)), _1769182), _1769186)), _1769184))], (49877 ^ _779327) ^ [_1779103, _1779105, _1779107, _1779109] : [-(hBOOL(hAPP(_1779103, _1779105))), -(c_List_OdropWhile(_1779107, _1779103, hAPP(hAPP(c_List_Olist_OCons(_1779107), _1779105), _1779109)) = hAPP(hAPP(c_List_Olist_OCons(_1779107), _1779105), _1779109))], (41812 ^ _779327) ^ [_1590635, _1590637, _1590639, _1590641, _1590643, _1590645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590635, tc_HOL_Obool)), _1590637), _1590639)), 41818 ^ _779327 : [(41821 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590641, tc_HOL_Obool)), hAPP(_1590643, 41817 ^ [_1590635, _1590637, _1590639, _1590641, _1590643, _1590645])), hAPP(_1590645, 41817 ^ [_1590635, _1590637, _1590639, _1590641, _1590643, _1590645])))], (41819 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590635), 41817 ^ [_1590635, _1590637, _1590639, _1590641, _1590643, _1590645]), _1590637)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590635, _1590641), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1590635, _1590641), _1590637), _1590643)), hAPP(hAPP(c_Product__Type_OSigma(_1590635, _1590641), _1590639), _1590645))))], (34284 ^ _779327) ^ [_1408836, _1408838, _1408840] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408836), _1408838), _1408840) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408836, tc_HOL_Obool), tc_HOL_Obool)), -(_1408838 = c_Orderings_Obot__class_Obot(tc_fun(_1408836, tc_HOL_Obool)))], (26448 ^ _779327) ^ [_1244981, _1244983, _1244985, _1244987] : [class_Rings_Osemiring__1(_1244981), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244983, _1244981), hAPP(c_COMBK(_1244981, _1244983), _1244985)), _1244987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244981), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244981), hAPP(c_Finite__Set_Ocard(_1244983), _1244987))), _1244985))], (35535 ^ _779327) ^ [_1436981, _1436983, _1436985, _1436987] : [class_Orderings_Olinorder(_1436981), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436981, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1436981, _1436983, _1436985)), hAPP(c_SetInterval_Oord__class_OatLeast(_1436981), _1436987)) = c_SetInterval_Oord__class_OatLeastAtMost(_1436981, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1436981), _1436983), _1436987), _1436985))], (40178 ^ _779327) ^ [_1549353, _1549355, _1549357] : [class_Orderings_Olinorder(_1549353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549353), _1549355)), -(_1549355 = c_Orderings_Obot__class_Obot(tc_fun(_1549353, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1549353), _1549357), c_Big__Operators_Olattice_OSup__fin(_1549353, c_Orderings_Oord__class_Omax(_1549353), _1549355)) = c_Big__Operators_Olattice_OSup__fin(_1549353, c_Orderings_Oord__class_Omax(_1549353), hAPP(c_Set_OCollect(_1549353), hAPP(hAPP(c_COMBB(tc_fun(_1549353, tc_HOL_Obool), tc_HOL_Obool, _1549353), c_HOL_OEx(_1549353)), hAPP(hAPP(c_COMBC(_1549353, tc_fun(_1549353, tc_HOL_Obool), tc_fun(_1549353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549353, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1549353, tc_HOL_Obool), tc_fun(_1549353, tc_HOL_Obool)), _1549353), c_COMBS(_1549353, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549353, tc_HOL_Obool), tc_fun(_1549353, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1549353), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549353), c_fconj)), hAPP(hAPP(c_COMBC(_1549353, tc_fun(_1549353, _1549353), tc_fun(_1549353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549353, tc_HOL_Obool), tc_fun(tc_fun(_1549353, _1549353), tc_fun(_1549353, tc_HOL_Obool)), _1549353), c_COMBB(_1549353, tc_HOL_Obool, _1549353)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1549353), _1549357))))), hAPP(hAPP(c_COMBC(_1549353, tc_fun(_1549353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549353)), _1549355))))))], (44340 ^ _779327) ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649471, _1649473)), _1649475), hAPP(hAPP(c_Relation_Orel__comp(_1649471, _1649477, _1649473), _1649479), _1649481))), 44346 ^ _779327 : [(44351 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649477, _1649473)), hAPP(hAPP(c_Product__Type_OPair(_1649477, _1649473), 44344 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481]), 44345 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481])), _1649481)))], (44349 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649471, _1649477)), hAPP(hAPP(c_Product__Type_OPair(_1649471, _1649477), 44343 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481]), 44344 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481])), _1649479)))], (44347 ^ _779327) ^ [] : [-(_1649475 = hAPP(hAPP(c_Product__Type_OPair(_1649471, _1649473), 44343 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481]), 44345 ^ [_1649471, _1649473, _1649475, _1649477, _1649479, _1649481]))]]], (16748 ^ _779327) ^ [_1063305, _1063307] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063305), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063307)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1063305, _1063307)))], (18829 ^ _779327) ^ [_1100030, _1100032, _1100034] : [class_Fields_Ofield__inverse__zero(_1100030), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100030), hAPP(c_Groups_Ouminus__class_Ouminus(_1100030), _1100032)), hAPP(c_Groups_Ouminus__class_Ouminus(_1100030), _1100034)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100030), _1100032), _1100034))], (22559 ^ _779327) ^ [_1169706, _1169708, _1169710, _1169712] : [class_Orderings_Olinorder(_1169706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169706), _1169708), _1169710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169706), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169706), _1169708), _1169712)), _1169710)))], (5080 ^ _779327) ^ [_856804, _856806] : [_856806 = _856804, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_856806) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_856804))], (3708 ^ _779327) ^ [_835476, _835478, _835480, _835482] : [-(c_List_Olexn(_835482, _835478) = c_List_Olexn(_835480, _835476)), _835482 = _835480, _835478 = _835476], (26089 ^ _779327) ^ [_1237387, _1237389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237387)), 26098 ^ _779327 : [(26101 ^ _779327) ^ [] : [hBOOL(hAPP(_1237389, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26094 ^ [_1237387, _1237389]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26095 ^ [_1237387, _1237389]), _1237387))))], (26099 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1237389, 26094 ^ [_1237387, _1237389])))]], 26102 ^ _779327 : [(26105 ^ _779327) ^ [] : [hBOOL(hAPP(_1237389, 26094 ^ [_1237387, _1237389]))], (26103 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1237389, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26094 ^ [_1237387, _1237389]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26095 ^ [_1237387, _1237389]), _1237387)))))]], 26106 ^ _779327 : [(26116 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1237389, 26123 ^ [_1237387, _1237389]))), 26117 ^ _779327 : [(26118 ^ _779327) ^ [_1237934] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1237934), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1237387))), hBOOL(hAPP(_1237389, _1237934))]]], (26107 ^ _779327) ^ [] : [26108 ^ _779327 : [(26109 ^ _779327) ^ [_1237819] : [hBOOL(hAPP(_1237389, _1237819))]], 26111 ^ _779327 : [(26114 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1237389, 26110 ^ [_1237387, _1237389])))], (26112 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26110 ^ [_1237387, _1237389]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1237387))))]]]]], (32688 ^ _779327) ^ [_1373582, _1373584, _1373586] : [class_Orderings_Olinorder(_1373582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373582), _1373584)), -(hBOOL(hAPP(hAPP(c_member(_1373582), _1373586), _1373584))), -(_1373584 = c_Orderings_Obot__class_Obot(tc_fun(_1373582, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1373582, c_Orderings_Oord__class_Omax(_1373582), hAPP(hAPP(c_Set_Oinsert(_1373582), _1373586), _1373584)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373582), _1373586), c_Big__Operators_Olattice_OSup__fin(_1373582, c_Orderings_Oord__class_Omax(_1373582), _1373584)))], (45727 ^ _779327) ^ [_1687578, _1687580, _1687582] : [class_Groups_Omonoid__add(_1687578), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687578), hAPP(hAPP(c_List_Omap(_1687580, _1687578), hAPP(c_COMBK(_1687578, _1687580), c_Groups_Ozero__class_Ozero(_1687578))), _1687582)) = c_Groups_Ozero__class_Ozero(_1687578))], (27863 ^ _779327) ^ [_1274691, _1274693] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1274691), _1274693))))], (38337 ^ _779327) ^ [_1500786, _1500788, _1500790, _1500792] : [c_Fun_Oinj__on(_1500786, _1500788, _1500790, c_Orderings_Otop__class_Otop(tc_fun(_1500786, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500786, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1500786, _1500788, _1500790), hAPP(hAPP(c_Set_Oinsert(_1500788), _1500792), c_Orderings_Obot__class_Obot(tc_fun(_1500788, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1500786), c_HOL_OThe(_1500786, hAPP(hAPP(c_COMBC(_1500786, _1500788, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1500788, tc_fun(_1500788, tc_HOL_Obool), _1500786), c_fequal), _1500790)), _1500792))), c_Orderings_Obot__class_Obot(tc_fun(_1500786, tc_HOL_Obool))))))], (25536 ^ _779327) ^ [_1225631, _1225633, _1225635, _1225637, _1225639] : [class_Groups_Oab__group__add(_1225631), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225633, _1225631), hAPP(hAPP(c_COMBS(_1225633, _1225631, _1225631), hAPP(hAPP(c_COMBB(_1225631, tc_fun(_1225631, _1225631), _1225633), c_Groups_Ominus__class_Ominus(_1225631)), _1225635)), _1225637)), _1225639) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1225631), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225633, _1225631), _1225635), _1225639)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225633, _1225631), _1225637), _1225639)))], (25385 ^ _779327) ^ [_1221917, _1221919] : [-(_1221917 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25388 ^ _779327 : [(25395 ^ _779327) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1221919) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221917), _1221919)), _1221917)))], (25389 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221917), _1221919)), _1221917)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1221919) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (45522 ^ _779327) ^ [_1682111, _1682113, _1682115] : [hAPP(hAPP(c_List_Otake(_1682111), _1682113), _1682115) = c_List_Olist_ONil(_1682111), -(_1682113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1682115 = c_List_Olist_ONil(_1682111))], (13884 ^ _779327) ^ [_1012455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012455)), -(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)), _1012455))))], (27184 ^ _779327) ^ [_1259030, _1259032, _1259034] : [class_Lattices_Osemilattice__sup(_1259030), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259030), _1259032), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259030), _1259034), _1259032))))], (3282 ^ _779327) ^ [_828661, _828663, _828665, _828667, _828669, _828671] : [-(c_FunDef_Oin__rel(_828671, _828667, _828663) = c_FunDef_Oin__rel(_828669, _828665, _828661)), _828671 = _828669, _828667 = _828665, _828663 = _828661], (31854 ^ _779327) ^ [_1358214] : [class_Rings_Oring__1(_1358214), -(hBOOL(hAPP(hAPP(c_member(_1358214), c_Groups_Oone__class_Oone(_1358214)), c_Int_Oring__1__class_OInts(_1358214))))], (15383 ^ _779327) ^ [_1039030, _1039032, _1039034, _1039036, _1039038, _1039040] : [class_Divides_Oring__div(_1039030), c_Divides_Odiv__class_Omod(_1039030, _1039032, _1039034) = c_Divides_Odiv__class_Omod(_1039030, _1039036, _1039034), c_Divides_Odiv__class_Omod(_1039030, _1039038, _1039034) = c_Divides_Odiv__class_Omod(_1039030, _1039040, _1039034), -(c_Divides_Odiv__class_Omod(_1039030, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039030), _1039032), _1039038), _1039034) = c_Divides_Odiv__class_Omod(_1039030, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039030), _1039036), _1039040), _1039034))], (10725 ^ _779327) ^ [_953679, _953681, _953683, _953685] : [class_Int_Onumber__ring(_953679), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953679), hAPP(c_Int_Onumber__class_Onumber__of(_953679), _953681)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953679), hAPP(c_Int_Onumber__class_Onumber__of(_953679), _953683)), _953685)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953679), hAPP(c_Int_Onumber__class_Onumber__of(_953679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953681), _953683))), _953685))], (28538 ^ _779327) ^ [_1287578, _1287580, _1287582] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1287578), _1287580)), -(hAPP(c_Finite__Set_Ocard(_1287578), hAPP(hAPP(c_Set_Oinsert(_1287578), _1287582), _1287580)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1287578), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1287578, tc_HOL_Obool)), _1287580), hAPP(hAPP(c_Set_Oinsert(_1287578), _1287582), c_Orderings_Obot__class_Obot(tc_fun(_1287578, tc_HOL_Obool)))))))], (24747 ^ _779327) ^ [_1210332, _1210334, _1210336, _1210338] : [class_Divides_Osemiring__div(_1210332), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1210332), _1210334), _1210336)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210332), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210332), _1210336), _1210334)), _1210338) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210332), hAPP(hAPP(c_Power_Opower__class_Opower(_1210332), _1210336), _1210338)), hAPP(hAPP(c_Power_Opower__class_Opower(_1210332), _1210334), _1210338)))], (3574 ^ _779327) ^ [_833309, _833311, _833313, _833315, _833317, _833319] : [-(c_Finite__Set_Ofold__image(_833319, _833315, _833311) = c_Finite__Set_Ofold__image(_833317, _833313, _833309)), _833319 = _833317, _833315 = _833313, _833311 = _833309], (17868 ^ _779327) ^ [_1082640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082640)), -(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), _1082640), 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)))))))], (33614 ^ _779327) ^ [] : [-(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)))))], (38023 ^ _779327) ^ [_1491539, _1491541] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491539), c_Orderings_Otop__class_Otop(tc_fun(_1491539, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1491539, _1491539, _1491541), c_Orderings_Otop__class_Otop(tc_fun(_1491539, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1491539, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1491539, _1491539, _1491541, c_Orderings_Otop__class_Otop(tc_fun(_1491539, tc_HOL_Obool))))], (18164 ^ _779327) ^ [_1087690, _1087692] : [class_Int_Onumber__ring(_1087690), -(hAPP(c_Int_Onumber__class_Onumber__of(_1087690), c_Int_OBit0(_1087692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087690), c_Groups_Ozero__class_Ozero(_1087690)), hAPP(c_Int_Onumber__class_Onumber__of(_1087690), _1087692))), hAPP(c_Int_Onumber__class_Onumber__of(_1087690), _1087692)))], (36008 ^ _779327) ^ [_1447499, _1447501, _1447503] : [class_Orderings_Olinorder(_1447499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447499), _1447501)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447499), _1447503)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447499, tc_HOL_Obool)), _1447501), _1447503) = c_Orderings_Obot__class_Obot(tc_fun(_1447499, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1447499), c_Big__Operators_Olattice_OInf__fin(_1447499, c_Orderings_Oord__class_Omin(_1447499), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447499, tc_HOL_Obool)), _1447501), _1447503))), c_Big__Operators_Olattice_OInf__fin(_1447499, c_Orderings_Oord__class_Omin(_1447499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447499, tc_HOL_Obool)), _1447501), _1447503))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1447499), c_Big__Operators_Olattice_OInf__fin(_1447499, c_Orderings_Oord__class_Omin(_1447499), _1447501)), c_Big__Operators_Olattice_OInf__fin(_1447499, c_Orderings_Oord__class_Omin(_1447499), _1447503)))], (11599 ^ _779327) ^ [_971495, _971497] : [class_Groups_Ogroup__add(_971495), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971495), _971497), _971497) = c_Groups_Ozero__class_Ozero(_971495))], (47504 ^ _779327) ^ [_1727779, _1727781, _1727783, _1727785] : [-(_1727779 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727781)), _1727783)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1727781, hAPP(hAPP(c_List_Olist__update(_1727781, _1727783), _1727779), _1727785)) = hAPP(hAPP(c_List_Olist__update(_1727781, c_List_Obutlast(_1727781, _1727783)), _1727779), _1727785))], (36761 ^ _779327) ^ [_1465251, _1465253, _1465255, _1465257, _1465259, _1465261] : [c_Fun_Oinj__on(_1465251, _1465253, _1465255, _1465257), hBOOL(hAPP(hAPP(c_member(_1465251), _1465259), _1465257)), hBOOL(hAPP(hAPP(c_member(_1465251), _1465261), _1465257)), 36772 ^ _779327 : [(36779 ^ _779327) ^ [] : [_1465259 = _1465261, -(hAPP(_1465255, _1465259) = hAPP(_1465255, _1465261))], (36773 ^ _779327) ^ [] : [hAPP(_1465255, _1465259) = hAPP(_1465255, _1465261), -(_1465259 = _1465261)]]], (30469 ^ _779327) ^ [_1328687, _1328689, _1328691, _1328693, _1328695] : [class_Groups_Ocomm__monoid__add(_1328687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328689), _1328691)), 30476 ^ _779327 : [(30483 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328689), _1328693), _1328691))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328689, _1328687), hAPP(hAPP(c_COMBC(_1328689, _1328687, _1328687), hAPP(hAPP(c_COMBS(_1328689, _1328687, tc_fun(_1328687, _1328687)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1328687, tc_fun(_1328687, _1328687)), _1328689), c_If(_1328687)), hAPP(c_fequal, _1328693))), _1328695)), c_Groups_Ozero__class_Ozero(_1328687))), _1328691) = c_Groups_Ozero__class_Ozero(_1328687))], (30477 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1328689), _1328693), _1328691)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1328689, _1328687), hAPP(hAPP(c_COMBC(_1328689, _1328687, _1328687), hAPP(hAPP(c_COMBS(_1328689, _1328687, tc_fun(_1328687, _1328687)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1328687, tc_fun(_1328687, _1328687)), _1328689), c_If(_1328687)), hAPP(c_fequal, _1328693))), _1328695)), c_Groups_Ozero__class_Ozero(_1328687))), _1328691) = hAPP(_1328695, _1328693))]]], (43708 ^ _779327) ^ [_1635008, _1635010, _1635012] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635008, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1635008, tc_HOL_Obool)), _1635010), _1635012)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635008, tc_HOL_Obool)), _1635010), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635008, tc_HOL_Obool), _1635012)))], (29164 ^ _779327) ^ [_1299155, _1299157, _1299159, _1299161, _1299163] : [_1299155 = c_Orderings_Obot__class_Obot(tc_fun(_1299157, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299157, tc_fun(_1299159, tc_HOL_Obool)), _1299155), hAPP(hAPP(c_COMBB(tc_fun(_1299159, tc_HOL_Obool), tc_fun(_1299159, tc_HOL_Obool), _1299157), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299159, tc_HOL_Obool)), _1299161)), _1299163)) = c_Orderings_Obot__class_Obot(tc_fun(_1299159, tc_HOL_Obool)))], (41447 ^ _779327) ^ [_1582475, _1582477, _1582479, _1582481, _1582483, _1582485, _1582487] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582475, _1582477, _1582479), hAPP(c_Fun_Ocomp(_1582481, tc_fun(_1582477, _1582479), _1582475, _1582483), _1582485)), _1582487) = hAPP(hAPP(_1582483, hAPP(_1582485, hAPP(c_Product__Type_Ofst(_1582475, _1582477), _1582487))), hAPP(c_Product__Type_Osnd(_1582475, _1582477), _1582487)))], (9979 ^ _779327) ^ [_940895] : [class_Rings_Olinordered__semidom(_940895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940895), c_Groups_Oone__class_Oone(_940895)), c_Groups_Ozero__class_Ozero(_940895)))], (15912 ^ _779327) ^ [_1048509, _1048511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048509)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1048509), _1048511)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1048509)), hAPP(c_Int_Onat, _1048511)))], (52762 ^ _779327) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (31265 ^ _779327) ^ [_1345786, _1345788, _1345790, _1345792, _1345794, _1345796, _1345798] : [hBOOL(hAPP(hAPP(c_member(_1345786), _1345788), _1345790)), c_Nitpick_Ofold__graph_H(_1345786, _1345792, _1345794, _1345796, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1345786, tc_HOL_Obool)), _1345790), hAPP(hAPP(c_Set_Oinsert(_1345786), _1345788), c_Orderings_Obot__class_Obot(tc_fun(_1345786, tc_HOL_Obool)))), _1345798), -(c_Nitpick_Ofold__graph_H(_1345786, _1345792, _1345794, _1345796, _1345790, hAPP(hAPP(_1345794, _1345788), _1345798)))], (18244 ^ _779327) ^ [_1089166] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1089166)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1089166)))], (16177 ^ _779327) ^ [_1053414, _1053416, _1053418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053414)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053416, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053418), _1053414)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1053418), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1053416), _1053418), _1053414))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053416, _1053418)))], (51153 ^ _779327) ^ [_1806372, _1806374, _1806376, _1806378, _1806380] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806372, _1806374, _1806376), _1806378), _1806380)), -(hBOOL(hAPP(hAPP(_1806376, _1806380), _1806378)))], (29082 ^ _779327) ^ [_1297511, _1297513, _1297515, _1297517, _1297519] : [_1297511 = c_Orderings_Obot__class_Obot(tc_fun(_1297513, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297513, tc_fun(_1297515, tc_HOL_Obool)), _1297511), hAPP(hAPP(c_COMBB(tc_fun(_1297515, tc_HOL_Obool), tc_fun(_1297515, tc_HOL_Obool), _1297513), hAPP(c_Set_Oinsert(_1297515), _1297517)), _1297519)) = c_Orderings_Obot__class_Obot(tc_fun(_1297515, tc_HOL_Obool)))], (16750 ^ _779327) ^ [_1063347, _1063349] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1063347, _1063349)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063347), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1063349)))], (23686 ^ _779327) ^ [_1191683, _1191685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1191683)), hAPP(c_Code__Numeral_Onat__of, _1191685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1191683), _1191685)))], (48706 ^ _779327) ^ [_1755683, _1755685, _1755687, _1755689, _1755691, _1755693] : [-(c_List_Ofoldr(_1755683, _1755685, _1755687, hAPP(hAPP(c_List_Oappend(_1755683), _1755689), _1755691), _1755693) = c_List_Ofoldr(_1755683, _1755685, _1755687, _1755689, c_List_Ofoldr(_1755683, _1755685, _1755687, _1755691, _1755693)))], (5210 ^ _779327) ^ [_858781, _858783] : [_858783 = _858781, -(c_Finite__Set_Ofinite(_858783) = c_Finite__Set_Ofinite(_858781))], (37711 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (27332 ^ _779327) ^ [_1262421, _1262423, _1262425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262421, tc_HOL_Obool)), _1262423), _1262425)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262421, tc_HOL_Obool)), _1262423), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262421, tc_HOL_Obool)), _1262425), _1262423)) = _1262425)], (23171 ^ _779327) ^ [_1181524, _1181526, _1181528] : [class_Groups_Olinordered__ab__group__add(_1181524), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181524), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181524), _1181526), _1181528)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181524), hAPP(c_Groups_Ouminus__class_Ouminus(_1181524), _1181526)), hAPP(c_Groups_Ouminus__class_Ouminus(_1181524), _1181528)))], (29406 ^ _779327) ^ [_1304070, _1304072, _1304074] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1304070), _1304072)), hBOOL(hAPP(hAPP(c_member(_1304070), _1304074), _1304072)), -(hAPP(c_Finite__Set_Ocard(_1304070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304070, tc_HOL_Obool)), _1304072), hAPP(hAPP(c_Set_Oinsert(_1304070), _1304074), c_Orderings_Obot__class_Obot(tc_fun(_1304070, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1304070), _1304072)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18853 ^ _779327) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18020 ^ _779327) ^ [_1085233, _1085235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085233), _1085235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085233)), c_Int_OBit1(_1085235))))], (208 ^ _779327) ^ [_782339, _782341, _782343, _782345, _782347, _782349, _782351, _782353, _782355, _782357, _782359, _782361] : [-(c_Nitpick_Ofold__graph_H(_782359, _782355, _782351, _782347, _782343, _782339)), c_Nitpick_Ofold__graph_H(_782361, _782357, _782353, _782349, _782345, _782341), _782361 = _782359, _782357 = _782355, _782353 = _782351, _782349 = _782347, _782345 = _782343, _782341 = _782339], (9250 ^ _779327) ^ [_929079, _929081] : [class_Rings_Ocomm__semiring__1(_929079), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929079), c_Groups_Ozero__class_Ozero(_929079)), _929081) = c_Groups_Ozero__class_Ozero(_929079))], (19681 ^ _779327) ^ [_1114837, _1114839, _1114841, _1114843] : [class_Fields_Olinordered__field(_1114837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114837), c_Groups_Ozero__class_Ozero(_1114837)), _1114839)), 19688 ^ _779327 : [(19695 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114837), _1114841), _1114839)), _1114843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114837), _1114841), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114837), _1114843), _1114839))))], (19689 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114837), _1114841), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114837), _1114843), _1114839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114837), _1114841), _1114839)), _1114843)))]]], (4758 ^ _779327) ^ [_851823, _851825] : [_851825 = _851823, -(c_List_Otake(_851825) = c_List_Otake(_851823))], (36686 ^ _779327) ^ [_1463654, _1463656] : [class_Lattices_Olattice(_1463654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463654), _1463656)), -(_1463656 = c_Orderings_Obot__class_Obot(tc_fun(_1463654, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1463654), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463654), 36699 ^ [_1463654, _1463656]), 36700 ^ [_1463654, _1463656])), hAPP(hAPP(c_Set_Oinsert(_1463654), 36699 ^ [_1463654, _1463656]), hAPP(hAPP(c_Set_Oinsert(_1463654), 36700 ^ [_1463654, _1463656]), c_Orderings_Obot__class_Obot(tc_fun(_1463654, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1463654), c_Big__Operators_Olattice__class_OInf__fin(_1463654, _1463656)), _1463656)))], (20865 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25592 ^ _779327) ^ [_1226921, _1226923, _1226925, _1226927] : [class_Rings_Ocomm__semiring__1(_1226921), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226921), c_Groups_Oone__class_Oone(_1226921)), c_Groups_Oone__class_Oone(_1226921))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1226921), hAPP(hAPP(c_COMBB(_1226921, _1226921, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1226921), _1226923)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1226921, _1226921), hAPP(hAPP(c_COMBB(_1226921, tc_fun(_1226921, _1226921), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1226921)), c_Nat_Osemiring__1__class_Oof__nat(_1226921))), _1226925))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1226927))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226921), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1226921), _1226927)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226921), _1226923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226921), _1226923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226921), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1226921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1226927), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1226925)))))], (39606 ^ _779327) ^ [_1530708] : [-(c_Finite__Set_Ofun__left__comm__idem(_1530708, tc_fun(_1530708, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1530708, tc_HOL_Obool), tc_fun(tc_fun(_1530708, tc_HOL_Obool), tc_fun(_1530708, tc_HOL_Obool)), _1530708), hAPP(c_COMBC(tc_fun(_1530708, tc_HOL_Obool), tc_fun(_1530708, tc_HOL_Obool), tc_fun(_1530708, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1530708, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1530708, tc_fun(_1530708, tc_HOL_Obool), tc_fun(_1530708, tc_HOL_Obool)), c_Set_Oinsert(_1530708)), c_Orderings_Obot__class_Obot(tc_fun(_1530708, tc_HOL_Obool))))))], (34787 ^ _779327) ^ [_1420331, _1420333, _1420335, _1420337] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420331, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420331, tc_HOL_Obool)), _1420333), _1420335)), _1420337) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420331, tc_HOL_Obool)), _1420333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420331, tc_HOL_Obool)), _1420335), _1420337)))], (45506 ^ _779327) ^ [_1681689, _1681691, _1681693, _1681695] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1681689, _1681691))), hAPP(hAPP(c_List_Ozip(_1681689, _1681691), _1681693), _1681695)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681689)), _1681693)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681691)), _1681695)))], (45542 ^ _779327) ^ [_1682401, _1682403, _1682405, _1682407] : [-(hAPP(hAPP(c_List_Otake(_1682401), _1682403), hAPP(hAPP(c_List_Olist_OCons(_1682401), _1682405), _1682407)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1682401), c_List_Olist_ONil(_1682401), hAPP(hAPP(c_COMBB(tc_List_Olist(_1682401), tc_List_Olist(_1682401), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1682401), _1682405)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1682401), tc_List_Olist(_1682401)), c_List_Otake(_1682401)), _1682407)), _1682403))], (30085 ^ _779327) ^ [_1319679, _1319681, _1319683, _1319685] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319679, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1319679, tc_fun(_1319679, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319679)), _1319681)), hAPP(hAPP(c_COMBC(_1319679, tc_fun(_1319679, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319679)), _1319683)), _1319685)), -(hBOOL(hAPP(hAPP(c_member(_1319679), _1319685), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319679, tc_HOL_Obool)), _1319681), _1319683))))], (47444 ^ _779327) ^ [_1726546, _1726548, _1726550] : [hBOOL(hAPP(hAPP(c_member(_1726546), _1726548), hAPP(c_List_Oset(_1726546), c_List_Obutlast(_1726546, _1726550)))), -(hBOOL(hAPP(hAPP(c_member(_1726546), _1726548), hAPP(c_List_Oset(_1726546), _1726550))))], (48633 ^ _779327) ^ [_1753165, _1753167, _1753169, _1753171] : [hBOOL(hAPP(hAPP(c_member(_1753165), _1753167), hAPP(c_List_Oset(_1753165), _1753169))), -(hBOOL(hAPP(_1753171, _1753167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753165)), hAPP(c_List_Ofilter(_1753165, _1753171), _1753169))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753165)), _1753169))))], (9212 ^ _779327) ^ [_928352, _928354, _928356, _928358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928352, tc_HOL_Obool)), _928354), _928356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928352, tc_HOL_Obool)), _928356), _928358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928352, tc_HOL_Obool)), _928354), _928358)))], (9901 ^ _779327) ^ [_939627, _939629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _939627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _939629)), 9908 ^ _779327 : [(9915 ^ _779327) ^ [] : [_939627 = _939629, -(hAPP(c_Int_Onat, _939627) = hAPP(c_Int_Onat, _939629))], (9909 ^ _779327) ^ [] : [hAPP(c_Int_Onat, _939627) = hAPP(c_Int_Onat, _939629), -(_939627 = _939629)]]], (16722 ^ _779327) ^ [_1062868, _1062870, _1062872] : [-(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), _1062868), _1062870)), _1062872), _1062870) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062872, _1062870))], (24487 ^ _779327) ^ [_1205581, _1205583, _1205585, _1205587] : [class_Rings_Odvd(_1205581), _1205583 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205581), _1205585), _1205587), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205581), _1205585), _1205583)))], (17880 ^ _779327) ^ [_1082843, _1082845] : [_1082843 = _1082845, -(c_Int_OBit0(_1082843) = c_Int_OBit0(_1082845))], (40538 ^ _779327) ^ [_1561303, _1561305, _1561307] : [c_Wellfounded_Owf(_1561303, _1561305), -(c_Wellfounded_Owf(_1561303, c_Wellfounded_Omlex__prod(_1561303, _1561307, _1561305)))], (34639 ^ _779327) ^ [_1417352, _1417354, _1417356, _1417358, _1417360] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417352, tc_fun(_1417354, tc_HOL_Obool)), _1417356), hAPP(hAPP(c_COMBB(tc_fun(_1417354, tc_HOL_Obool), tc_fun(_1417354, tc_HOL_Obool), _1417352), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417354, tc_HOL_Obool)), _1417358)), _1417360)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417354, tc_HOL_Obool)), _1417358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417352, tc_fun(_1417354, tc_HOL_Obool)), _1417356), _1417360)))], (30381 ^ _779327) ^ [_1325688, _1325690, _1325692, _1325694, _1325696] : [c_Finite__Set_Ofolding__one(_1325688, _1325690, _1325692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325688), _1325694)), hBOOL(hAPP(hAPP(c_member(_1325688), _1325696), _1325694)), 30392 ^ _779327 : [(30399 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325688, tc_HOL_Obool)), _1325694), hAPP(hAPP(c_Set_Oinsert(_1325688), _1325696), c_Orderings_Obot__class_Obot(tc_fun(_1325688, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1325688, tc_HOL_Obool))), -(hAPP(_1325692, _1325694) = hAPP(hAPP(_1325690, _1325696), hAPP(_1325692, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325688, tc_HOL_Obool)), _1325694), hAPP(hAPP(c_Set_Oinsert(_1325688), _1325696), c_Orderings_Obot__class_Obot(tc_fun(_1325688, tc_HOL_Obool)))))))], (30393 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325688, tc_HOL_Obool)), _1325694), hAPP(hAPP(c_Set_Oinsert(_1325688), _1325696), c_Orderings_Obot__class_Obot(tc_fun(_1325688, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1325688, tc_HOL_Obool)), -(hAPP(_1325692, _1325694) = _1325696)]]], (35127 ^ _779327) ^ [_1427727, _1427729] : [class_Lattices_Obounded__lattice__bot(_1427727), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427727), c_Orderings_Obot__class_Obot(_1427727)), _1427729) = c_Orderings_Obot__class_Obot(_1427727))], (30126 ^ _779327) ^ [_1320831, _1320833, _1320835, _1320837, _1320839] : [30128 ^ _779327 : [(30131 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1320831), _1320833), hAPP(_1320839, 30127 ^ [_1320831, _1320833, _1320835, _1320837, _1320839])))], (30129 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320835), 30127 ^ [_1320831, _1320833, _1320835, _1320837, _1320839]), _1320837)))]], -(hBOOL(hAPP(hAPP(c_member(_1320831), _1320833), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1320835, tc_fun(_1320831, tc_HOL_Obool)), _1320837), _1320839))))], (9517 ^ _779327) ^ [_933505, _933507] : [class_Rings_Olinordered__idom(_933505), 9520 ^ _779327 : [(9527 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _933507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933505), c_Groups_Ozero__class_Ozero(_933505)), hAPP(c_Int_Oring__1__class_Oof__int(_933505), _933507))))], (9521 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933505), c_Groups_Ozero__class_Ozero(_933505)), hAPP(c_Int_Oring__1__class_Oof__int(_933505), _933507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _933507)))]]], (34215 ^ _779327) ^ [_1406786, _1406788, _1406790, _1406792] : [-(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), _1406786), _1406788)), 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), _1406790), _1406792)), 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), _1406786), _1406790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1406788), _1406792))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1406786), _1406792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1406788), _1406790)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (48548 ^ _779327) ^ [_1751239, _1751241, _1751243] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751239)), hAPP(c_List_Ofilter(_1751239, _1751241), _1751243))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751239)), hAPP(c_List_Ofilter(_1751239, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1751239), c_fNot), _1751241)), _1751243))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751239)), _1751243))], (51087 ^ _779327) ^ [_1805007, _1805009, _1805011, _1805013, _1805015, _1805017] : [-(hAPP(hAPP(c_List_Ozip(_1805007, _1805009), c_List_Oreplicate(_1805007, _1805011, _1805013)), c_List_Oreplicate(_1805009, _1805015, _1805017)) = c_List_Oreplicate(tc_prod(_1805007, _1805009), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1805011), _1805015), hAPP(hAPP(c_Product__Type_OPair(_1805007, _1805009), _1805013), _1805017)))], (31848 ^ _779327) ^ [_1358111, _1358113] : [class_Int_Onumber__ring(_1358111), -(hBOOL(hAPP(hAPP(c_member(_1358111), hAPP(c_Int_Onumber__class_Onumber__of(_1358111), _1358113)), c_Int_Oring__1__class_OInts(_1358111))))], (28370 ^ _779327) ^ [_1284249, _1284251, _1284253, _1284255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284249), _1284251)), 28373 ^ _779327 : [(28374 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284253), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1284249, tc_fun(_1284253, tc_HOL_Obool)), _1284251), _1284255))), 28377 ^ _779327 : [(28378 ^ _779327) ^ [_1284433] : [hBOOL(hAPP(hAPP(c_member(_1284249), _1284433), _1284251)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284253), hAPP(_1284255, _1284433))))]]], (28384 ^ _779327) ^ [] : [28386 ^ _779327 : [(28389 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284253), hAPP(_1284255, 28385 ^ [_1284249, _1284251, _1284253, _1284255])))], (28387 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1284249), 28385 ^ [_1284249, _1284251, _1284253, _1284255]), _1284251)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1284253), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1284249, tc_fun(_1284253, tc_HOL_Obool)), _1284251), _1284255))))]]], (1798 ^ _779327) ^ [_804790, _804792] : [-(class_Orderings_Opreorder(_804790)), _804792 = _804790, class_Orderings_Opreorder(_804792)], (26968 ^ _779327) ^ [_1254902, _1254904, _1254906] : [class_Lattices_Osemilattice__sup(_1254902), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254902), _1254904), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254902), _1254904), _1254906)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254902), _1254904), _1254906))], (17972 ^ _779327) ^ [_1084416] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1084416)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1084416)))], (15409 ^ _779327) ^ [_1039591, _1039593, _1039595, _1039597] : [class_Divides_Oring__div(_1039591), -(c_Divides_Odiv__class_Omod(_1039591, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039591), _1039593), _1039595), _1039597) = c_Divides_Odiv__class_Omod(_1039591, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039591), _1039593), c_Divides_Odiv__class_Omod(_1039591, _1039595, _1039597)), _1039597))], (6342 ^ _779327) ^ [_879016, _879018, _879020] : [class_Orderings_Opreorder(_879016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879016), _879018), _879020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879016), _879020), _879018))], (52630 ^ _779327) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (4212 ^ _779327) ^ [_843266, _843268, _843270, _843272, _843274, _843276] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_843276, _843272, _843268) = c_SetInterval_Oord__class_OgreaterThanAtMost(_843274, _843270, _843266)), _843276 = _843274, _843272 = _843270, _843268 = _843266], (23289 ^ _779327) ^ [_1183700, _1183702] : [class_Orderings_Olinorder(_1183700), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1183700), _1183702), _1183702) = _1183702)], (27654 ^ _779327) ^ [_1269644, _1269646, _1269648, _1269650, _1269652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269644, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1269646, tc_fun(_1269644, tc_HOL_Obool)), _1269648), _1269650)), _1269652)), 27657 ^ _779327 : [(27658 ^ _779327) ^ [_1269777] : [hBOOL(hAPP(hAPP(c_member(_1269646), _1269777), _1269648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269644, tc_HOL_Obool)), hAPP(_1269650, _1269777)), _1269652)))]]], (49583 ^ _779327) ^ [_1772898, _1772900] : [-(_1772898 = c_List_Olist_ONil(_1772900)), -(c_List_Olast(_1772900, hAPP(c_List_Orev(_1772900), _1772898)) = hAPP(c_List_Ohd(_1772900), _1772898))], (45805 ^ _779327) ^ [_1690080] : [45807 ^ _779327 : [(45810 ^ _779327) ^ [] : [45806 ^ [_1690080] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45808 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45806 ^ [_1690080]), hAPP(c_List_Oset(tc_Nat_Onat), _1690080))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1690080) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15674 ^ _779327) ^ [_1044502, _1044504] : [class_Int_Onumber__ring(_1044502), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044502), _1044504), hAPP(c_Int_Onumber__class_Onumber__of(_1044502), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1044502), _1044504))], (3116 ^ _779327) ^ [_826104, _826106] : [_826106 = _826104, -(c_Rings_Oinverse__class_Odivide(_826106) = c_Rings_Oinverse__class_Odivide(_826104))], (52746 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (46377 ^ _779327) ^ [_1702815, _1702817, _1702819, _1702821, _1702823, _1702825, _1702827, _1702829] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1702815, _1702815)), hAPP(hAPP(c_Product__Type_OPair(_1702815, _1702815), _1702817), _1702819)), _1702821)), _1702823 = hAPP(hAPP(c_List_Oappend(_1702815), _1702825), hAPP(hAPP(c_List_Olist_OCons(_1702815), _1702817), _1702827)), _1702829 = hAPP(hAPP(c_List_Oappend(_1702815), _1702825), hAPP(hAPP(c_List_Olist_OCons(_1702815), _1702819), _1702827)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702815), tc_List_Olist(_1702815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702815), tc_List_Olist(_1702815)), _1702823), _1702829)), c_List_Olistrel1(_1702815, _1702821))))], (18584 ^ _779327) ^ [_1095079, _1095081, _1095083] : [class_Int_Onumber__ring(_1095079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095079), _1095081), _1095083)), 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(_1095079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095079), hAPP(hAPP(c_Power_Opower__class_Opower(_1095079), _1095081), 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(_1095079), _1095083), 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(_1095079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095079), hAPP(c_Int_Onumber__class_Onumber__of(_1095079), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1095081)), _1095083)))], (11715 ^ _779327) ^ [_973455] : [class_Groups_Ogroup__add(_973455), -(hAPP(c_Groups_Ouminus__class_Ouminus(_973455), c_Groups_Ozero__class_Ozero(_973455)) = c_Groups_Ozero__class_Ozero(_973455))], (34899 ^ _779327) ^ [_1422569, _1422571, _1422573, _1422575] : [class_Lattices_Osemilattice__inf(_1422569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422569), _1422571), _1422573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422569), _1422571), _1422575)), _1422573)))], (48838 ^ _779327) ^ [_1758348, _1758350, _1758352, _1758354] : [c_List_Oupt(_1758348, _1758350) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1758352), _1758354), 48841 ^ _779327 : [(48846 ^ _779327) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758348), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1758350) = _1758354)], (48844 ^ _779327) ^ [] : [-(_1758348 = _1758352)], (48842 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758348), _1758350)))]]], (2908 ^ _779327) ^ [_822768, _822770] : [_822770 = _822768, -(c_Divides_Odiv__class_Odiv(_822770) = c_Divides_Odiv__class_Odiv(_822768))], (43227 ^ _779327) ^ [_1625699, _1625701, _1625703, _1625705] : [class_Lattices_Osemilattice__inf(_1625699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625699), _1625701)), hBOOL(hAPP(hAPP(c_member(_1625699), _1625703), _1625701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625699), hAPP(hAPP(c_Finite__Set_Ofold(_1625699, _1625699, c_Lattices_Osemilattice__inf__class_Oinf(_1625699)), _1625705), _1625701)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1625699), _1625703), _1625705))))], (47328 ^ _779327) ^ [_1724298, _1724300, _1724302] : [-(_1724298 = c_List_Olist_ONil(_1724300)), -(c_List_Olast(_1724300, hAPP(hAPP(c_List_Oappend(_1724300), _1724302), _1724298)) = c_List_Olast(_1724300, _1724298))], (23961 ^ _779327) ^ [_1196858, _1196860, _1196862, _1196864] : [class_Divides_Osemiring__div(_1196858), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196858), _1196860), _1196862)), 23968 ^ _779327 : [(23975 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196858), _1196860), _1196864)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196858), _1196860), c_Divides_Odiv__class_Omod(_1196858, _1196864, _1196862))))], (23969 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196858), _1196860), c_Divides_Odiv__class_Omod(_1196858, _1196864, _1196862))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196858), _1196860), _1196864)))]]], (11295 ^ _779327) ^ [_964757, _964759, _964761] : [class_Rings_Oring__1(_964757), -(hAPP(c_Int_Oring__1__class_Oof__int(_964757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _964759), _964761)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_964757), hAPP(c_Int_Oring__1__class_Oof__int(_964757), _964759)), hAPP(c_Int_Oring__1__class_Oof__int(_964757), _964761)))], (27595 ^ _779327) ^ [_1268128, _1268130, _1268132, _1268134, _1268136, _1268138] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268128, tc_fun(_1268130, tc_HOL_Obool)), _1268132), hAPP(hAPP(c_COMBC(_1268128, tc_fun(_1268134, tc_fun(_1268130, tc_HOL_Obool)), tc_fun(_1268130, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268134, tc_HOL_Obool), tc_fun(tc_fun(_1268134, tc_fun(_1268130, tc_HOL_Obool)), tc_fun(_1268130, tc_HOL_Obool)), _1268128), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268134, tc_fun(_1268130, tc_HOL_Obool))), _1268136)), _1268138)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268134, tc_fun(_1268130, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268128, tc_fun(_1268134, tc_HOL_Obool)), _1268132), _1268136)), _1268138))], (5406 ^ _779327) ^ [_861817, _861819] : [_861819 = _861817, -(c_Orderings_Oord__class_Oless__eq(_861819) = c_Orderings_Oord__class_Oless__eq(_861817))], (34807 ^ _779327) ^ [_1420751, _1420753, _1420755, _1420757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420751, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420751, tc_HOL_Obool)), _1420753), _1420755)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420751, tc_HOL_Obool)), _1420757), _1420755)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420751, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420751, tc_HOL_Obool)), _1420753), _1420755)), _1420757))], (5786 ^ _779327) ^ [_870707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _870707), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_870707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23123 ^ _779327) ^ [_1180387, _1180389, _1180391, _1180393, _1180395, _1180397] : [hAPP(_1180393, hAPP(c_Product__Type_Ofst(_1180387, _1180391), _1180395)) = hAPP(_1180397, hAPP(c_Product__Type_Ofst(_1180387, _1180391), _1180395)), -(hAPP(c_Product__Type_Oapfst(_1180387, _1180389, _1180391, _1180393), _1180395) = hAPP(c_Product__Type_Oapfst(_1180387, _1180389, _1180391, _1180397), _1180395))], (32994 ^ _779327) ^ [_1379924, _1379926, _1379928] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1379924), _1379926), _1379928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1379924), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1379924, tc_Int_Oint), _1379926), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1379928))), class_Groups_Ocomm__monoid__add(_1379924), class_Groups_Ocomm__monoid__mult(_1379924)], (29796 ^ _779327) ^ [_1311846, _1311848] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1311846)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1311848))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1311846), _1311848)))], (52728 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (27947 ^ _779327) ^ [_1276351] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1276351)), 27951 ^ _779327 : [(27952 ^ _779327) ^ [_1276431] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1276431), _1276351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1276431), 27950 ^ [_1276351])))]]], (49083 ^ _779327) ^ [_1762804, _1762806] : [class_Orderings_Olinorder(_1762804), c_List_Olinorder__class_Osorted(_1762804, _1762806), -(c_List_Olinorder__class_Osorted(_1762804, c_List_Oremdups(_1762804, _1762806)))], (52722 ^ _779327) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (43213 ^ _779327) ^ [_1625432, _1625434, _1625436, _1625438] : [class_Lattices_Osemilattice__sup(_1625432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625432), _1625434)), hBOOL(hAPP(hAPP(c_member(_1625432), _1625436), _1625434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625432), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1625432), _1625436), _1625438)), hAPP(hAPP(c_Finite__Set_Ofold(_1625432, _1625432, c_Lattices_Osemilattice__sup__class_Osup(_1625432)), _1625438), _1625434))))], (28544 ^ _779327) ^ [_1287755] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1287755), c_Orderings_Obot__class_Obot(tc_fun(_1287755, tc_HOL_Obool)))))], (13440 ^ _779327) ^ [_1004542, _1004544] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004542), _1004544), 13445 ^ _779327 : [(13448 ^ _779327) ^ [] : [-(_1004544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13446 ^ _779327) ^ [] : [-(_1004542 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13449 ^ _779327 : [(13452 ^ _779327) ^ [] : [-(_1004544 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13450 ^ _779327) ^ [] : [-(_1004542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22177 ^ _779327) ^ [_1162674, _1162676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162674), 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)), _1162676)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1162674), _1162676) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1162674, _1162676)))], (28192 ^ _779327) ^ [_1280864, _1280866, _1280868, _1280870, _1280872] : [class_Groups_Oab__group__add(_1280864), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280866), _1280868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280866, tc_HOL_Obool)), _1280870), _1280868)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280866, _1280864), _1280872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1280866, tc_HOL_Obool)), _1280868), _1280870)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280864), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280866, _1280864), _1280872), _1280868)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1280866, _1280864), _1280872), _1280870)))], (10929 ^ _779327) ^ [_957539, _957541, _957543, _957545] : [class_Groups_Ocancel__semigroup__add(_957539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957539), _957541), _957543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957539), _957545), _957543), -(_957541 = _957545)], (9579 ^ _779327) ^ [_934479, _934481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_934479, _934481))))], (51462 ^ _779327) ^ [_1813681, _1813683, _1813685, _1813687, _1813689, _1813691, _1813693] : [51464 ^ _779327 : [(51467 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1813685, 51463 ^ [_1813681, _1813683, _1813685, _1813687, _1813689, _1813691, _1813693]), _1813687), _1813689))], (51465 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813681), 51463 ^ [_1813681, _1813683, _1813685, _1813687, _1813689, _1813691, _1813693]), _1813683)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1813681, tc_fun(_1813691, tc_fun(_1813693, tc_HOL_Obool))), _1813683), _1813685), _1813687), _1813689)))], (43859 ^ _779327) ^ [_1638842, _1638844] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638842, tc_HOL_Obool), hAPP(c_Set_OPow(_1638842), _1638844)) = _1638844)], (51330 ^ _779327) ^ [_1810642, _1810644] : [hBOOL(hAPP(hAPP(c_List_Omember(_1810642), c_List_Olist_ONil(_1810642)), _1810644))], (27683 ^ _779327) ^ [_1270613, _1270615, _1270617, _1270619, _1270621] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270613, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270615, tc_fun(_1270613, tc_HOL_Obool)), _1270617), _1270619)), _1270621) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270615, tc_fun(_1270613, tc_HOL_Obool)), _1270617), hAPP(hAPP(c_COMBC(_1270615, tc_fun(_1270613, tc_HOL_Obool), tc_fun(_1270613, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270613, tc_HOL_Obool), tc_fun(tc_fun(_1270613, tc_HOL_Obool), tc_fun(_1270613, tc_HOL_Obool)), _1270615), c_Groups_Ominus__class_Ominus(tc_fun(_1270613, tc_HOL_Obool))), _1270619)), _1270621)))], (51503 ^ _779327) ^ [_1814652, _1814654, _1814656] : [c_List_Olist__all(tc_Int_Oint, _1814652, c_List_Oupto(_1814654, _1814656)), -(c_List_Oall__interval__int(_1814652, _1814654, _1814656))], (22055 ^ _779327) ^ [_1160105, _1160107, _1160109, _1160111, _1160113] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1160105, _1160107, _1160109), _1160111), _1160113) = hAPP(hAPP(_1160111, hAPP(c_Product__Type_Ofst(_1160105, _1160107), _1160113)), hAPP(c_Product__Type_Osnd(_1160105, _1160107), _1160113)))], (27902 ^ _779327) ^ [_1275433] : [27904 ^ _779327 : [(27907 ^ _779327) ^ [_1275543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27903 ^ [_1275433, _1275543]), _1275543))], (27905 ^ _779327) ^ [_1275509] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27903 ^ [_1275433, _1275509]), _1275433)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1275433)))], (34174 ^ _779327) ^ [_1405664, _1405666, _1405668, _1405670, _1405672] : [hBOOL(hAPP(hAPP(c_member(_1405664), _1405666), hAPP(c_Relation_OImage(_1405668, _1405664, _1405670), _1405672))), 34178 ^ _779327 : [(34181 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1405668, _1405664)), hAPP(hAPP(c_Product__Type_OPair(_1405668, _1405664), 34177 ^ [_1405664, _1405666, _1405668, _1405670, _1405672]), _1405666)), _1405670)))], (34179 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405668), 34177 ^ [_1405664, _1405666, _1405668, _1405670, _1405672]), _1405672)))]]], (31800 ^ _779327) ^ [_1357251] : [class_Rings_Oring__1(_1357251), -(hBOOL(hAPP(hAPP(c_member(_1357251), c_Groups_Ozero__class_Ozero(_1357251)), c_Int_Oring__1__class_OInts(_1357251))))], (2120 ^ _779327) ^ [_810002, _810004] : [_810004 = _810002, -(c_Nat_Onat_Onat__size(_810004) = c_Nat_Onat_Onat__size(_810002))], (40970 ^ _779327) ^ [_1571617, _1571619, _1571621, _1571623] : [hBOOL(hAPP(hAPP(c_member(_1571617), _1571623), hAPP(c_Relation_ODomain(_1571617, _1571619), _1571621))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1571617, _1571619, hAPP(hAPP(c_COMBC(_1571617, tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_fun(_1571619, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571619, tc_fun(tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_fun(_1571619, tc_HOL_Obool)), _1571617), c_COMBC(_1571619, tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571619, tc_prod(_1571617, _1571619)), tc_fun(_1571619, tc_fun(tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_HOL_Obool)), _1571617), hAPP(c_COMBB(tc_prod(_1571617, _1571619), tc_fun(tc_fun(tc_prod(_1571617, _1571619), tc_HOL_Obool), tc_HOL_Obool), _1571619), c_member(tc_prod(_1571617, _1571619)))), c_Product__Type_OPair(_1571617, _1571619)))), _1571621)), _1571623)))], (52586 ^ _779327) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11215 ^ _779327) ^ [_963181, _963183, _963185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963181), _963183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963185), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963183), _963185)), _963181))))], (26253 ^ _779327) ^ [_1240872, _1240874, _1240876, _1240878, _1240880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240872, tc_HOL_Obool)), _1240874), _1240876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240878, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1240872, _1240878, _1240880), _1240874)), hAPP(c_Set_Oimage(_1240872, _1240878, _1240880), _1240876))))], (23229 ^ _779327) ^ [_1182566, _1182568] : [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), _1182566), _1182568))), 23232 ^ _779327 : [(23239 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182568), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23242 ^ _779327 : [(23251 ^ _779327) ^ [] : [-(c_Nitpick_Onorm__frac(_1182566, _1182568) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1182566), _1182568)), 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), _1182566))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182568)))), -(_1182566 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1182568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23243 ^ _779327) ^ [] : [23244 ^ _779327 : [(23247 ^ _779327) ^ [] : [_1182568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23245 ^ _779327) ^ [] : [_1182566 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1182566, _1182568) = 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)))]]], (23233 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182568), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1182566, _1182568) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182566), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182568)))]]], (35339 ^ _779327) ^ [_1432805, _1432807, _1432809, _1432811, _1432813] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432805, tc_fun(_1432807, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1432805), _1432809), _1432811)), _1432813) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432807, tc_HOL_Obool)), hAPP(_1432813, _1432809)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432805, tc_fun(_1432807, tc_HOL_Obool)), _1432811), _1432813)))], (15764 ^ _779327) ^ [_1045973, _1045975] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045973, _1045975) = 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), _1045973), _1045975) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1045975), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045973, _1045975)))], (52736 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (18232 ^ _779327) ^ [_1088970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088970)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088970), c_Int_OMin)))], (35207 ^ _779327) ^ [_1429467, _1429469, _1429471, _1429473] : [-(hBOOL(hAPP(hAPP(c_member(_1429467), _1429469), _1429471))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429467, tc_HOL_Obool)), _1429471), hAPP(hAPP(c_Set_Oinsert(_1429467), _1429469), _1429473)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429467, tc_HOL_Obool)), _1429471), _1429473))], (23572 ^ _779327) ^ [_1189792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1189792)), _1189792 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16974 ^ _779327) ^ [] : [-(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))))], (28606 ^ _779327) ^ [_1288994, _1288996] : [_1288996 = c_Orderings_Obot__class_Obot(tc_fun(_1288994, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288994, tc_HOL_Obool)), _1288996), c_Orderings_Obot__class_Obot(tc_fun(_1288994, tc_HOL_Obool)))))], (50332 ^ _779327) ^ [_1789328, _1789330, _1789332, _1789334] : [50334 ^ _779327 : [(50337 ^ _779327) ^ [] : [hBOOL(hAPP(_1789332, 50333 ^ [_1789328, _1789330, _1789332, _1789334]))], (50335 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789328), 50333 ^ [_1789328, _1789330, _1789332, _1789334]), hAPP(c_List_Oset(_1789328), _1789330))))]], -(c_List_OdropWhile(_1789328, _1789332, hAPP(hAPP(c_List_Oappend(_1789328), _1789330), _1789334)) = c_List_OdropWhile(_1789328, _1789332, _1789334))], (17408 ^ _779327) ^ [_1074867, _1074869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1074867)), c_Int_OBit1(_1074869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074867), _1074869)))], (43824 ^ _779327) ^ [_1637825, _1637827, _1637829, _1637831] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1637825, _1637827), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637825, tc_HOL_Obool), _1637829)), _1637831) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637825, tc_HOL_Obool), tc_fun(tc_prod(_1637825, _1637827), tc_HOL_Obool)), _1637829), hAPP(hAPP(c_COMBC(tc_fun(_1637825, tc_HOL_Obool), tc_fun(_1637825, tc_fun(_1637827, tc_HOL_Obool)), tc_fun(tc_prod(_1637825, _1637827), tc_HOL_Obool)), c_Product__Type_OSigma(_1637825, _1637827)), _1637831)))], (17384 ^ _779327) ^ [_1074461, _1074463] : [c_Int_OBit1(_1074461) = c_Int_OBit1(_1074463), -(_1074461 = _1074463)], (45382 ^ _779327) ^ [_1679198, _1679200] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1679198)), c_List_Olist_ONil(_1679198)), c_List_Olists(_1679198, _1679200))))], (25049 ^ _779327) ^ [_1216030, _1216032, _1216034, _1216036] : [class_Orderings_Oorder(_1216030), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1216030, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216032), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216034), _1216036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216030), hAPP(_1216032, _1216034)), hAPP(_1216032, _1216036))))], (34505 ^ _779327) ^ [_1413876, _1413878, _1413880, _1413882, _1413884] : [c_Equiv__Relations_Oequiv(_1413876, _1413878, _1413880), hBOOL(hAPP(hAPP(c_member(tc_prod(_1413876, _1413876)), hAPP(hAPP(c_Product__Type_OPair(_1413876, _1413876), _1413882), _1413884)), _1413880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413876, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1413876, _1413876, _1413880), hAPP(hAPP(c_Set_Oinsert(_1413876), _1413882), c_Orderings_Obot__class_Obot(tc_fun(_1413876, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1413876, _1413876, _1413880), hAPP(hAPP(c_Set_Oinsert(_1413876), _1413884), c_Orderings_Obot__class_Obot(tc_fun(_1413876, tc_HOL_Obool)))))))], (33175 ^ _779327) ^ [_1383193, _1383195, _1383197, _1383199] : [class_Groups_Ocomm__monoid__mult(_1383193), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1383195), _1383197))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383195, _1383193), _1383199), _1383197) = c_Groups_Oone__class_Oone(_1383193))], (27300 ^ _779327) ^ [_1261569, _1261571, _1261573, _1261575, _1261577] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261571, tc_fun(_1261569, tc_HOL_Obool)), _1261573), _1261575)), _1261577) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261571, tc_fun(_1261569, tc_HOL_Obool)), _1261573), hAPP(hAPP(c_COMBC(_1261571, tc_fun(_1261569, tc_HOL_Obool), tc_fun(_1261569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1261569, tc_HOL_Obool), tc_fun(tc_fun(_1261569, tc_HOL_Obool), tc_fun(_1261569, tc_HOL_Obool)), _1261571), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261569, tc_HOL_Obool))), _1261575)), _1261577)))], (4320 ^ _779327) ^ [_845002, _845004, _845006, _845008] : [-(c_List_Olist__update(_845008, _845004) = c_List_Olist__update(_845006, _845002)), _845008 = _845006, _845004 = _845002], (44906 ^ _779327) ^ [_1666408, _1666410, _1666412, _1666414] : [44909 ^ _779327 : [(44914 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1666408, _1666408)), hAPP(hAPP(c_Product__Type_OPair(_1666408, _1666408), 44908 ^ [_1666408, _1666410, _1666412, _1666414]), 44907 ^ [_1666408, _1666410, _1666412, _1666414])), _1666410))], (44912 ^ _779327) ^ [] : [44907 ^ [_1666408, _1666410, _1666412, _1666414] = 44908 ^ [_1666408, _1666410, _1666412, _1666414]], (44910 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1666408, _1666408)), hAPP(hAPP(c_Product__Type_OPair(_1666408, _1666408), 44907 ^ [_1666408, _1666410, _1666412, _1666414]), 44908 ^ [_1666408, _1666410, _1666412, _1666414])), _1666410))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666408), tc_List_Olist(_1666408))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666408), tc_List_Olist(_1666408)), _1666412), _1666414)), c_List_Olexord(_1666408, _1666410)))), -(_1666412 = _1666414), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666408), tc_List_Olist(_1666408))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666408), tc_List_Olist(_1666408)), _1666414), _1666412)), c_List_Olexord(_1666408, _1666410))))], (11473 ^ _779327) ^ [_968687, _968689, _968691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968687), _968689)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968689), _968687))), _968691) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _968689)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968687), _968691)))], (4838 ^ _779327) ^ [_853001, _853003, _853005, _853007] : [-(c_List_Oupt(_853007, _853003) = c_List_Oupt(_853005, _853001)), _853007 = _853005, _853003 = _853001], (48417 ^ _779327) ^ [_1747564, _1747566, _1747568] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1747564), tc_List_Olist(_1747564), c_List_Oappend(_1747564), _1747566), _1747568) = hAPP(hAPP(c_List_Oappend(_1747564), _1747566), c_List_Oconcat(_1747564, _1747568)))], (38776 ^ _779327) ^ [_1511427, _1511429, _1511431, _1511433, _1511435, _1511437] : [class_Groups_Ocomm__monoid__add(_1511427), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511429, _1511427), hAPP(hAPP(c_COMBC(_1511429, tc_fun(_1511431, tc_HOL_Obool), _1511427), hAPP(hAPP(c_COMBB(tc_fun(_1511431, _1511427), tc_fun(tc_fun(_1511431, tc_HOL_Obool), _1511427), _1511429), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511431, _1511427)), _1511433)), _1511435)), _1511437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1511429, _1511431), _1511427), hAPP(c_Product__Type_Oprod_Oprod__case(_1511429, _1511431, _1511427), _1511433)), hAPP(hAPP(c_Product__Type_OSigma(_1511429, _1511431), _1511437), hAPP(c_COMBK(tc_fun(_1511431, tc_HOL_Obool), _1511429), _1511435))))], (46574 ^ _779327) ^ [_1708170, _1708172, _1708174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708170)), _1708172)), _1708174)), -(hAPP(hAPP(c_List_Odrop(_1708170), _1708174), _1708172) = c_List_Olist_ONil(_1708170))], (50054 ^ _779327) ^ [_1782948, _1782950, _1782952, _1782954] : [-(hAPP(c_List_OremoveAll(_1782948, _1782950), hAPP(hAPP(c_List_Oappend(_1782948), _1782952), _1782954)) = hAPP(hAPP(c_List_Oappend(_1782948), hAPP(c_List_OremoveAll(_1782948, _1782950), _1782952)), hAPP(c_List_OremoveAll(_1782948, _1782950), _1782954)))], (37098 ^ _779327) ^ [_1472053, _1472055, _1472057, _1472059, _1472061] : [c_Fun_Oinj__on(_1472053, _1472055, _1472057, _1472059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472055, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472053, _1472055, _1472057), _1472059)), _1472061)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472055), _1472061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1472053), _1472059)), hAPP(c_Finite__Set_Ocard(_1472055), _1472061))))], (22903 ^ _779327) ^ [_1176171, _1176173, _1176175] : [class_Orderings_Olinorder(_1176171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176171), _1176173), _1176175)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176171), _1176173), _1176175) = _1176175)], (48554 ^ _779327) ^ [_1751422, _1751424, _1751426] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1751422), tc_List_Olist(_1751422)), c_List_Opartition(_1751422, _1751424, _1751426)) = hAPP(c_List_Ofilter(_1751422, _1751424), _1751426))], (11593 ^ _779327) ^ [_971400, _971402] : [class_Groups_Ogroup__add(_971400), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971400), _971402), c_Groups_Ozero__class_Ozero(_971400)) = _971402)], (24709 ^ _779327) ^ [_1209607, _1209609, _1209611, _1209613] : [class_Rings_Ocomm__semiring__1(_1209607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209609), _1209611)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209607), hAPP(hAPP(c_Power_Opower__class_Opower(_1209607), _1209613), _1209609)), hAPP(hAPP(c_Power_Opower__class_Opower(_1209607), _1209613), _1209611))))], (29684 ^ _779327) ^ [_1309696, _1309698, _1309700, _1309702] : [hBOOL(hAPP(hAPP(c_member(_1309696), _1309698), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309696, tc_HOL_Obool)), _1309700), _1309702))), 29687 ^ _779327 : [(29690 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1309696), _1309698), _1309702))], (29688 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1309696), _1309698), _1309700)))]]], (34631 ^ _779327) ^ [_1416954, _1416956, _1416958, _1416960, _1416962] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416954, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416956, tc_fun(_1416954, tc_HOL_Obool)), _1416958), _1416960)), _1416962) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416956, tc_fun(_1416954, tc_HOL_Obool)), _1416958), hAPP(hAPP(c_COMBC(_1416956, tc_fun(_1416954, tc_HOL_Obool), tc_fun(_1416954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1416954, tc_HOL_Obool), tc_fun(tc_fun(_1416954, tc_HOL_Obool), tc_fun(_1416954, tc_HOL_Obool)), _1416956), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1416954, tc_HOL_Obool))), _1416960)), _1416962)))], (45384 ^ _779327) ^ [_1679237, _1679239, _1679241] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679237), tc_List_Olist(_1679237))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679237), tc_List_Olist(_1679237)), _1679239), c_List_Olist_ONil(_1679237))), c_List_Olistrel(_1679237, _1679241))), -(_1679239 = c_List_Olist_ONil(_1679237))], (26850 ^ _779327) ^ [_1252372, _1252374] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252372, tc_HOL_Obool)), _1252374), _1252374) = _1252374)], (52790 ^ _779327) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (14665 ^ _779327) ^ [_1026212] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1026212))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1026212)) = _1026212)], (26974 ^ _779327) ^ [_1255027, _1255029, _1255031] : [class_Lattices_Olattice(_1255027), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255027), _1255029), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255027), _1255029), _1255031)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255027), _1255029), _1255031))], (36217 ^ _779327) ^ [_1453179, _1453181, _1453183, _1453185, _1453187, _1453189] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453179, _1453181)), hAPP(hAPP(c_Product__Type_OPair(_1453179, _1453181), _1453187), _1453189)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool)), _1453183), _1453185))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453179, tc_fun(_1453181, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1453179, tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_fun(_1453181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453181, tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_fun(_1453181, tc_HOL_Obool)), _1453179), c_COMBC(_1453181, tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453181, tc_prod(_1453179, _1453181)), tc_fun(_1453181, tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), _1453179), hAPP(c_COMBB(tc_prod(_1453179, _1453181), tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool), _1453181), c_member(tc_prod(_1453179, _1453181)))), c_Product__Type_OPair(_1453179, _1453181)))), _1453183)), hAPP(hAPP(c_COMBC(_1453179, tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_fun(_1453181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453181, tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_fun(_1453181, tc_HOL_Obool)), _1453179), c_COMBC(_1453181, tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453181, tc_prod(_1453179, _1453181)), tc_fun(_1453181, tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool)), _1453179), hAPP(c_COMBB(tc_prod(_1453179, _1453181), tc_fun(tc_fun(tc_prod(_1453179, _1453181), tc_HOL_Obool), tc_HOL_Obool), _1453181), c_member(tc_prod(_1453179, _1453181)))), c_Product__Type_OPair(_1453179, _1453181)))), _1453185)), _1453187), _1453189)))], (19363 ^ _779327) ^ [_1109017, _1109019] : [class_Rings_Odivision__ring__inverse__zero(_1109017), 19366 ^ _779327 : [(19373 ^ _779327) ^ [] : [-(_1109019 = c_Groups_Ozero__class_Ozero(_1109017)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109017), _1109019), _1109019) = c_Groups_Oone__class_Oone(_1109017))], (19367 ^ _779327) ^ [] : [_1109019 = c_Groups_Ozero__class_Ozero(_1109017), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109017), _1109019), _1109019) = c_Groups_Ozero__class_Ozero(_1109017))]]], (45994 ^ _779327) ^ [_1694166, _1694168, _1694170] : [class_Groups_Omonoid__add(_1694166), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1694166), hAPP(hAPP(c_List_Oappend(_1694166), _1694168), _1694170)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1694166), hAPP(c_List_Omonoid__add__class_Olistsum(_1694166), _1694168)), hAPP(c_List_Omonoid__add__class_Olistsum(_1694166), _1694170)))], (6879 ^ _779327) ^ [_886922, _886924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886922)), _886924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886922), _886924)))], (38712 ^ _779327) ^ [_1509707, _1509709, _1509711, _1509713, _1509715, _1509717] : [-(hAPP(c_Set_Oimage(_1509707, tc_prod(_1509709, _1509711), hAPP(hAPP(c_COMBS(_1509707, _1509711, tc_prod(_1509709, _1509711)), hAPP(hAPP(c_COMBB(_1509709, tc_fun(_1509711, tc_prod(_1509709, _1509711)), _1509707), c_Product__Type_OPair(_1509709, _1509711)), _1509713)), _1509715)), _1509717) = hAPP(hAPP(c_Product__Type_OSigma(_1509709, _1509711), hAPP(c_Set_Oimage(_1509707, _1509709, _1509713), _1509717)), hAPP(hAPP(c_COMBB(tc_fun(_1509707, tc_HOL_Obool), tc_fun(_1509711, tc_HOL_Obool), _1509709), c_Set_Oimage(_1509707, _1509711, _1509715)), hAPP(hAPP(c_COMBC(_1509709, tc_fun(_1509707, tc_HOL_Obool), tc_fun(_1509707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509707, tc_HOL_Obool), tc_fun(tc_fun(_1509707, tc_HOL_Obool), tc_fun(_1509707, tc_HOL_Obool)), _1509709), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509707, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1509709, tc_HOL_Obool), tc_fun(_1509707, tc_HOL_Obool), _1509709), c_Set_Ovimage(_1509707, _1509709, _1509713)), hAPP(hAPP(c_COMBC(_1509709, tc_fun(_1509709, tc_HOL_Obool), tc_fun(_1509709, tc_HOL_Obool)), c_Set_Oinsert(_1509709)), c_Orderings_Obot__class_Obot(tc_fun(_1509709, tc_HOL_Obool)))))), _1509717))))], (13428 ^ _779327) ^ [_1004327, _1004329] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004327)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004329)), _1004327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1004329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47949 ^ _779327) ^ [_1737203, _1737205, _1737207, _1737209, _1737211] : [-(c_Enum_Oproduct(_1737203, _1737205, hAPP(hAPP(c_List_Olist_OCons(_1737203), _1737207), _1737209), _1737211) = hAPP(hAPP(c_List_Oappend(tc_prod(_1737203, _1737205)), hAPP(hAPP(c_List_Omap(_1737205, tc_prod(_1737203, _1737205)), hAPP(c_Product__Type_OPair(_1737203, _1737205), _1737207)), _1737211)), c_Enum_Oproduct(_1737203, _1737205, _1737209, _1737211)))], (47058 ^ _779327) ^ [_1718579, _1718581, _1718583] : [hBOOL(hAPP(c_List_Odistinct(_1718579), _1718583)), -(hBOOL(hAPP(c_List_Odistinct(_1718579), hAPP(c_List_Orotate(_1718579, _1718581), _1718583))))], (40402 ^ _779327) ^ [_1556660, _1556662, _1556664, _1556666] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556660, _1556662, _1556664), _1556666), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1556662, _1556664), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1556660, _1556664), tc_HOL_Obool)))], (27789 ^ _779327) ^ [_1273180, _1273182, _1273184, _1273186] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1273180, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1273182)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1273180, tc_HOL_Obool), tc_Nat_Onat), _1273184), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1273186))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1273180, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1273186, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1273182), _1273186))), _1273184))], (45721 ^ _779327) ^ [_1687449, _1687451, _1687453] : [class_Groups_Omonoid__add(_1687449), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1687449), hAPP(hAPP(c_List_Olist_OCons(_1687449), _1687451), _1687453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1687449), _1687451), hAPP(c_List_Omonoid__add__class_Olistsum(_1687449), _1687453)))], (12423 ^ _779327) ^ [_986132, _986134, _986136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986132), _986134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986136), _986134))))], (14111 ^ _779327) ^ [_1016605, _1016607, _1016609] : [_1016605 = _1016609, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016605), _1016607) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016609), _1016607))], (47334 ^ _779327) ^ [_1724364, _1724366, _1724368] : [_1724364 = c_List_Olist_ONil(_1724366), -(c_List_Olast(_1724366, hAPP(hAPP(c_List_Oappend(_1724366), _1724368), _1724364)) = c_List_Olast(_1724366, _1724368))], (5948 ^ _779327) ^ [_872941, _872943, _872945] : [class_Orderings_Opreorder(_872941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_872941), _872943), _872945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_872941), _872945), _872943))], (15259 ^ _779327) ^ [_1036464, _1036466] : [class_Divides_Osemiring__div(_1036464), -(c_Divides_Odiv__class_Omod(_1036464, c_Groups_Ozero__class_Ozero(_1036464), _1036466) = c_Groups_Ozero__class_Ozero(_1036464))], (40956 ^ _779327) ^ [_1570960, _1570962, _1570964, _1570966] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1570960, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1570960, _1570962), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1570960, _1570962), tc_HOL_Obool)), _1570964), _1570966))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1570960, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1570960, _1570962), _1570964)), hAPP(c_Relation_ODomain(_1570960, _1570962), _1570966)))))], (40688 ^ _779327) ^ [_1564309, _1564311, _1564313, _1564315] : [-(hAPP(c_Relation_ORange(_1564309, _1564311), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564309, _1564311), tc_HOL_Obool)), _1564313), _1564315)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564311, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1564309, _1564311), _1564313)), hAPP(c_Relation_ORange(_1564309, _1564311), _1564315)))], (18660 ^ _779327) ^ [_1096776, _1096778, _1096780] : [class_Rings_Olinordered__idom(_1096776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096776), _1096778), c_Groups_Ozero__class_Ozero(_1096776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096776), hAPP(hAPP(c_Power_Opower__class_Opower(_1096776), _1096778), 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)))), _1096780)))), c_Groups_Ozero__class_Ozero(_1096776))))], (16948 ^ _779327) ^ [_1066924, _1066926] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066924, _1066926) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1066924), _1066926)), _1066926)))], (44494 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51237 ^ _779327) ^ [_1807993, _1807995, _1807997] : [-(hAPP(hAPP(c_List_Oappend(_1807993), c_List_Oreplicate(_1807993, _1807995, _1807997)), hAPP(hAPP(c_List_Olist_OCons(_1807993), _1807997), c_List_Olist_ONil(_1807993))) = hAPP(hAPP(c_List_Olist_OCons(_1807993), _1807997), c_List_Oreplicate(_1807993, _1807995, _1807997)))], (26227 ^ _779327) ^ [_1240297, _1240299, _1240301, _1240303] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240297), _1240299)), 26230 ^ _779327 : [(26231 ^ _779327) ^ [_1240455] : [26233 ^ _779327 : [(26239 ^ _779327) ^ [] : [-(_1240455 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26235 ^ [_1240297, _1240299, _1240301, _1240303, _1240455]), 26232 ^ [_1240297, _1240299, _1240301, _1240303, _1240455]))], (26237 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26235 ^ [_1240297, _1240299, _1240301, _1240303, _1240455]), _1240301)))], (26234 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26232 ^ [_1240297, _1240299, _1240301, _1240303, _1240455]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1240299))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240455), _1240303)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240455), _1240299)), _1240303)))]]], (33726 ^ _779327) ^ [_1395609, _1395611, _1395613, _1395615, _1395617, _1395619] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395609, _1395609)), hAPP(hAPP(c_Product__Type_OPair(_1395609, _1395609), _1395611), _1395613)), hAPP(hAPP(c_Relation_Oinv__image(_1395615, _1395609), _1395617), _1395619))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395615, _1395615)), hAPP(hAPP(c_Product__Type_OPair(_1395615, _1395615), hAPP(_1395619, _1395611)), hAPP(_1395619, _1395613))), _1395617)))], (49933 ^ _779327) ^ [_1780238, _1780240, _1780242, _1780244, _1780246] : [class_Groups_Omonoid__add(_1780238), 49939 ^ _779327 : [(49944 ^ _779327) ^ [] : [hAPP(_1780246, 49938 ^ [_1780238, _1780240, _1780242, _1780244, _1780246]) = c_Groups_Ozero__class_Ozero(_1780238)], (49942 ^ _779327) ^ [] : [hBOOL(hAPP(_1780244, 49938 ^ [_1780238, _1780240, _1780242, _1780244, _1780246]))], (49940 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780240), 49938 ^ [_1780238, _1780240, _1780242, _1780244, _1780246]), hAPP(c_List_Oset(_1780240), _1780242))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1780238), hAPP(hAPP(c_List_Omap(_1780240, _1780238), _1780246), hAPP(c_List_Ofilter(_1780240, _1780244), _1780242))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1780238), hAPP(hAPP(c_List_Omap(_1780240, _1780238), _1780246), _1780242)))], (46279 ^ _779327) ^ [_1700380, _1700382, _1700384, _1700386] : [-(hAPP(hAPP(c_List_Onth(_1700380), hAPP(hAPP(c_List_Oappend(_1700380), _1700382), _1700384)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700380)), _1700382)), _1700386)) = hAPP(hAPP(c_List_Onth(_1700380), _1700384), _1700386))], (29778 ^ _779327) ^ [_1311546, _1311548, _1311550] : [hBOOL(hAPP(hAPP(c_member(_1311546), _1311548), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311546, tc_HOL_Obool)), _1311550))), hBOOL(hAPP(hAPP(c_member(_1311546), _1311548), _1311550))], (10461 ^ _779327) ^ [_948699, _948701] : [-(hAPP(c_Int_Onat, _948699) = _948701), 10464 ^ _779327 : [(10467 ^ _779327) ^ [] : [_948699 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948701)], (10465 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948699)))]], 10468 ^ _779327 : [(10471 ^ _779327) ^ [] : [_948701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10469 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948699))]]], (10159 ^ _779327) ^ [_943747] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943747))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _943747)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48080 ^ _779327) ^ [_1740009, _1740011, _1740013, _1740015, _1740017, _1740019, _1740021] : [c_List_Olist__all2(_1740015, _1740011, hAPP(hAPP(c_COMBB(_1740009, tc_fun(_1740011, tc_HOL_Obool), _1740015), _1740013), _1740017), _1740019, _1740021), -(c_List_Olist__all2(_1740009, _1740011, _1740013, hAPP(hAPP(c_List_Omap(_1740015, _1740009), _1740017), _1740019), _1740021))], (27092 ^ _779327) ^ [_1257465, _1257467, _1257469, _1257471] : [class_Lattices_Osemilattice__sup(_1257465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257465), _1257467), _1257469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257465), _1257471), _1257469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257465), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257465), _1257467), _1257471)), _1257469)))], (22627 ^ _779327) ^ [_1170958] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1170958), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45707 ^ _779327) ^ [_1687111] : [-(c_List_Olistset(_1687111, c_List_Olist_ONil(tc_fun(_1687111, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1687111)), c_List_Olist_ONil(_1687111)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1687111), tc_HOL_Obool))))], (27981 ^ _779327) ^ [_1277056] : [c_Nat__Transfer_Onat__set(_1277056), 27984 ^ _779327 : [(27991 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1277056))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1277056)))], (27985 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1277056)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1277056))))]]], (16770 ^ _779327) ^ [_1063698, _1063700] : [class_Rings_Olinordered__idom(_1063698), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063698), c_Groups_Osgn__class_Osgn(_1063698, _1063700)), hAPP(c_Groups_Oabs__class_Oabs(_1063698), _1063700)) = _1063700)], (12429 ^ _779327) ^ [_986243, _986245, _986247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986243), _986245)), _986247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986243), _986247)))], (28473 ^ _779327) ^ [_1286293, _1286295, _1286297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1286293), _1286295)), -(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)), _1286293)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1286297), _1286295)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286297), _1286293)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1286295), _1286293)))], (17244 ^ _779327) ^ [_1071985, _1071987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071985), c_Int_OPls))), 17247 ^ _779327 : [(17254 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071987), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071985)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071987)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071985), _1071987)))], (17248 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071987), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071985)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071987)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071985))]]], (11325 ^ _779327) ^ [_965391, _965393, _965395, _965397, _965399, _965401] : [class_Rings_Oordered__ring(_965391), 11328 ^ _779327 : [(11335 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965391), _965393), _965399)), _965395)), _965397)), _965401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), _965393), _965395)), _965397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), _965399), _965395)), _965401))))], (11329 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), _965393), _965395)), _965397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), _965399), _965395)), _965401))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965391), _965393), _965399)), _965395)), _965397)), _965401)))]]], (44767 ^ _779327) ^ [_1662477, _1662479, _1662481, _1662483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662477), tc_List_Olist(_1662477))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662477), tc_List_Olist(_1662477)), _1662481), _1662483)), c_List_Olistrel(_1662477, _1662479))), -(c_List_Olistrelp(_1662477, hAPP(hAPP(c_COMBC(_1662477, tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_fun(_1662477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662477, tc_fun(tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_fun(_1662477, tc_HOL_Obool)), _1662477), c_COMBC(_1662477, tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662477, tc_prod(_1662477, _1662477)), tc_fun(_1662477, tc_fun(tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_HOL_Obool)), _1662477), hAPP(c_COMBB(tc_prod(_1662477, _1662477), tc_fun(tc_fun(tc_prod(_1662477, _1662477), tc_HOL_Obool), tc_HOL_Obool), _1662477), c_member(tc_prod(_1662477, _1662477)))), c_Product__Type_OPair(_1662477, _1662477)))), _1662479), _1662481, _1662483))], (8158 ^ _779327) ^ [_909137, _909139, _909141, _909143] : [class_Rings_Olinordered__semiring__strict(_909137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909137), _909139), _909141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909137), c_Groups_Ozero__class_Ozero(_909137)), _909143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909137), _909143), _909139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909137), _909143), _909141))))], (12017 ^ _779327) ^ [_978622, _978624, _978626] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_978622), 12020 ^ _779327 : [(12027 ^ _779327) ^ [] : [_978626 = c_Groups_Ozero__class_Ozero(_978622), -(_978624 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978622), _978624), _978626))], (12021 ^ _779327) ^ [] : [_978624 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978622), _978624), _978626), -(_978626 = c_Groups_Ozero__class_Ozero(_978622))]]], (27246 ^ _779327) ^ [_1260273, _1260275, _1260277, _1260279, _1260281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260273, tc_HOL_Obool)), _1260275), _1260277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260273, tc_HOL_Obool)), _1260279), _1260281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260273, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260273, tc_HOL_Obool)), _1260275), _1260279)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260273, tc_HOL_Obool)), _1260277), _1260281))))], (33547 ^ _779327) ^ [_1390962, _1390964, _1390966, _1390968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1390962), _1390964)), -(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), _1390962), _1390966)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390964), _1390968))), c_FunDef_Opair__leq)))], (21995 ^ _779327) ^ [_1158730, _1158732] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1158730), _1158732)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1158730), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158732)))], (38770 ^ _779327) ^ [_1511131, _1511133, _1511135, _1511137, _1511139] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1511131, _1511133), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511131, tc_HOL_Obool)), _1511135), _1511137)), hAPP(c_COMBK(tc_fun(_1511133, tc_HOL_Obool), _1511131), _1511139)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1511131, _1511133), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1511131, _1511133), _1511135), hAPP(c_COMBK(tc_fun(_1511133, tc_HOL_Obool), _1511131), _1511139))), hAPP(hAPP(c_Product__Type_OSigma(_1511131, _1511133), _1511137), hAPP(c_COMBK(tc_fun(_1511133, tc_HOL_Obool), _1511131), _1511139))))], (38920 ^ _779327) ^ [_1515525, _1515527, _1515529, _1515531, _1515533, _1515535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515525, _1515527), tc_HOL_Obool)), _1515529), hAPP(hAPP(c_Product__Type_OSigma(_1515525, _1515527), _1515531), hAPP(c_COMBK(tc_fun(_1515527, tc_HOL_Obool), _1515525), _1515533)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515527, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1515525, _1515527, _1515529), _1515535)), _1515533)))], (52990 ^ _779327) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (43053 ^ _779327) ^ [_1621770, _1621772, _1621774, _1621776, _1621778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621770, _1621770)), hAPP(hAPP(c_Product__Type_OPair(_1621770, _1621770), _1621772), _1621774)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621770, _1621770), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1621776)), _1621778))), 43057 ^ _779327 : [(43060 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621770, _1621770)), hAPP(hAPP(c_Product__Type_OPair(_1621770, _1621770), 43056 ^ [_1621770, _1621772, _1621774, _1621776, _1621778]), _1621774)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621770, _1621770), tc_HOL_Obool), _1621776), _1621778))))], (43058 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621770, _1621770)), hAPP(hAPP(c_Product__Type_OPair(_1621770, _1621770), _1621772), 43056 ^ [_1621770, _1621772, _1621774, _1621776, _1621778])), _1621778)))]]], (26367 ^ _779327) ^ [_1243333, _1243335, _1243337, _1243339, _1243341, _1243343, _1243345, _1243347] : [class_Groups_Ocomm__monoid__add(_1243333), class_Orderings_Oord(_1243335), _1243337 = _1243339, _1243341 = _1243343, 26385 ^ _779327 : [(26390 ^ _779327) ^ [] : [hAPP(_1243345, 26384 ^ [_1243333, _1243335, _1243337, _1243339, _1243341, _1243343, _1243345, _1243347]) = hAPP(_1243347, 26384 ^ [_1243333, _1243335, _1243337, _1243339, _1243341, _1243343, _1243345, _1243347])], (26388 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243335), 26384 ^ [_1243333, _1243335, _1243337, _1243339, _1243341, _1243343, _1243345, _1243347]), _1243343)))], (26386 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243335), _1243339), 26384 ^ [_1243333, _1243335, _1243337, _1243339, _1243341, _1243343, _1243345, _1243347])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1243335, _1243333), _1243345), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243335, _1243337), _1243341)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1243335, _1243333), _1243347), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243335, _1243339), _1243343)))], (16988 ^ _779327) ^ [_1067591, _1067593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067591)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1067593)))), 16991 ^ _779327 : [(16994 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1067593))], (16992 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067591), _1067593)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067591), _1067593))], (40273 ^ _779327) ^ [_1552588, _1552590] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1552588, _1552590, tc_prod(_1552588, _1552590)), c_Product__Type_OPair(_1552588, _1552590)) = c_Fun_Oid(tc_prod(_1552588, _1552590)))], (50349 ^ _779327) ^ [_1789704, _1789706] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789704), _1789706))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789704, _1789706) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789706), c_Lazy__Sequence_Osmall__lazy_H(_1789704, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789706), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48598 ^ _779327) ^ [_1752282, _1752284, _1752286] : [hAPP(c_List_Ofilter(_1752282, _1752284), _1752286) = c_List_Olist_ONil(_1752282), 48601 ^ _779327 : [(48602 ^ _779327) ^ [_1752379] : [hBOOL(hAPP(hAPP(c_member(_1752282), _1752379), hAPP(c_List_Oset(_1752282), _1752286))), hBOOL(hAPP(_1752284, _1752379))]]], (42332 ^ _779327) ^ [_1603562, _1603564, _1603566, _1603568] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603562, _1603562)), hAPP(hAPP(c_Product__Type_OPair(_1603562, _1603562), _1603564), _1603566)), c_Transitive__Closure_Ortrancl(_1603562, _1603568)))), 42333 ^ _779327 : [(42336 ^ _779327) ^ [] : [-(_1603564 = _1603566), hBOOL(hAPP(hAPP(c_member(tc_prod(_1603562, _1603562)), hAPP(hAPP(c_Product__Type_OPair(_1603562, _1603562), _1603564), _1603566)), c_Transitive__Closure_Otrancl(_1603562, _1603568)))], (42334 ^ _779327) ^ [] : [_1603564 = _1603566]]], (49001 ^ _779327) ^ [_1761510, _1761512, _1761514] : [class_Orderings_Olinorder(_1761510), c_List_Olinorder__class_Osorted(_1761510, _1761512), -(c_List_Olinorder__class_Osorted(_1761510, c_List_Oremove1(_1761510, _1761514, _1761512)))], (40851 ^ _779327) ^ [] : [-(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))))], (42482 ^ _779327) ^ [_1607144, _1607146] : [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), _1607144), _1607146)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1607144), _1607146)))], (46504 ^ _779327) ^ [_1706518, _1706520] : [-(hAPP(c_List_Oset(_1706518), hAPP(c_List_Orotate1(_1706518), _1706520)) = hAPP(c_List_Oset(_1706518), _1706520))], (48118 ^ _779327) ^ [_1741092, _1741094, _1741096, _1741098, _1741100] : [-(c_List_Olist__all2(_1741092, _1741094, _1741096, _1741098, _1741100)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741092)), _1741098) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741094)), _1741100), 48124 ^ _779327 : [(48127 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1741096, hAPP(hAPP(c_List_Onth(_1741092), _1741098), 48123 ^ [_1741092, _1741094, _1741096, _1741098, _1741100])), hAPP(hAPP(c_List_Onth(_1741094), _1741100), 48123 ^ [_1741092, _1741094, _1741096, _1741098, _1741100])))], (48125 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48123 ^ [_1741092, _1741094, _1741096, _1741098, _1741100]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741092)), _1741098))))]]], (16389 ^ _779327) ^ [_1057027, _1057029] : [class_Groups_Oordered__ab__group__add__abs(_1057027), 16392 ^ _779327 : [(16399 ^ _779327) ^ [] : [_1057029 = c_Groups_Ozero__class_Ozero(_1057027), -(hAPP(c_Groups_Oabs__class_Oabs(_1057027), _1057029) = c_Groups_Ozero__class_Ozero(_1057027))], (16393 ^ _779327) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1057027), _1057029) = c_Groups_Ozero__class_Ozero(_1057027), -(_1057029 = c_Groups_Ozero__class_Ozero(_1057027))]]], (13528 ^ _779327) ^ [_1005796, _1005798] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005796), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005796), _1005798)))))], (45133 ^ _779327) ^ [_1672313, _1672315, _1672317, _1672319, _1672321, _1672323] : [-(hAPP(hAPP(c_List_Omap(_1672313, _1672315), _1672317), hAPP(hAPP(c_List_Omap(_1672319, _1672313), _1672321), _1672323)) = hAPP(hAPP(c_List_Omap(_1672319, _1672315), hAPP(c_Fun_Ocomp(_1672313, _1672315, _1672319, _1672317), _1672321)), _1672323))], (51277 ^ _779327) ^ [_1809270, _1809272, _1809274, _1809276] : [-(c_Lazy__Sequence_Oappend(_1809270, c_Lazy__Sequence_Olazy__sequence_OInsert(_1809270, _1809272, _1809274), _1809276) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1809270, _1809272, c_Lazy__Sequence_Oappend(_1809270, _1809274, _1809276)))], (8506 ^ _779327) ^ [_915604, _915606] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _915604), _915606) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_915606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_915604 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14785 ^ _779327) ^ [_1028018, _1028020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028018), _1028020)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028018), _1028020) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10530 ^ _779327) ^ [_949888, _949890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _949888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _949890)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _949888)), hAPP(c_Int_Onat, _949890)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _949888), _949890)))], (7820 ^ _779327) ^ [_902863, _902865, _902867, _902869] : [class_Rings_Oordered__ring(_902863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902863), _902865), _902867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902863), _902869), c_Groups_Ozero__class_Ozero(_902863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902863), _902867), _902869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902863), _902865), _902869))))], (7047 ^ _779327) ^ [_889601, _889603, _889605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889601), _889603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889603), _889605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889601)), _889605)))], (9002 ^ _779327) ^ [_924235, _924237] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _924235), _924237)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924235)), _924237))], (25349 ^ _779327) ^ [_1221324, _1221326] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221326), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221324)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221324)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1221326))))], (18162 ^ _779327) ^ [_1087659] : [-(c_Int_Osucc(c_Int_OBit1(_1087659)) = c_Int_OBit0(c_Int_Osucc(_1087659)))], (27745 ^ _779327) ^ [_1272203, _1272205, _1272207, _1272209, _1272211] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272203, tc_HOL_Obool)), _1272205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1272207, tc_fun(_1272203, tc_HOL_Obool)), _1272209), _1272211)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272207, tc_fun(_1272203, tc_HOL_Obool)), _1272209), hAPP(hAPP(c_COMBB(tc_fun(_1272203, tc_HOL_Obool), tc_fun(_1272203, tc_HOL_Obool), _1272207), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272203, tc_HOL_Obool)), _1272205)), _1272211)))], (2372 ^ _779327) ^ [_813968, _813970, _813972, _813974] : [-(c_Nitpick_Onat__gcd(_813974, _813970) = c_Nitpick_Onat__gcd(_813972, _813968)), _813974 = _813972, _813970 = _813968], (17448 ^ _779327) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (44745 ^ _779327) ^ [_1661533, _1661535, _1661537, _1661539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661533), tc_List_Olist(_1661533))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661533), tc_List_Olist(_1661533)), _1661535), _1661537)), c_List_Olistrel(_1661533, _1661539))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661533), tc_List_Olist(_1661533))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661533), tc_List_Olist(_1661533)), _1661535), _1661537)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1661533), c_List_Olistrel1(_1661533, _1661539)))))], (37667 ^ _779327) ^ [_1484547, _1484549] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1484547, _1484549)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1484547, _1484549), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1484549), c_Orderings_Otop__class_Otop(tc_fun(_1484549, tc_HOL_Obool)))))], (48608 ^ _779327) ^ [_1752487, _1752489, _1752491] : [48610 ^ _779327 : [(48613 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1752489, 48609 ^ [_1752487, _1752489, _1752491])))], (48611 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752487), 48609 ^ [_1752487, _1752489, _1752491]), hAPP(c_List_Oset(_1752487), _1752491))))]], -(hAPP(c_List_Ofilter(_1752487, _1752489), _1752491) = c_List_Olist_ONil(_1752487))], (37414 ^ _779327) ^ [_1479113, _1479115] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1479113), _1479115))), -(hAPP(c_Finite__Set_Ocard(_1479113), _1479115) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4 ^ _779327) ^ [_779377, _779379] : [_779379 = _779377, -(_779377 = _779379)], (29256 ^ _779327) ^ [_1300988, _1300990] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1300988), _1300990)))), -(_1300990 = c_Orderings_Obot__class_Obot(tc_fun(_1300988, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300988), _1300990))], (6372 ^ _779327) ^ [_879480, _879482, _879484] : [class_Orderings_Olinorder(_879480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879480), _879482), _879484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879480), _879484), _879482))], (17226 ^ _779327) ^ [_1071688] : [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), _1071688))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071688)))], (23736 ^ _779327) ^ [_1192703, _1192705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1192703), _1192705)), -(c_Quickcheck_Obeyond(_1192703, _1192705) = _1192705)], (35367 ^ _779327) ^ [_1433389, _1433391, _1433393] : [class_Lattices_Olattice(_1433389), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433389), _1433391)), hBOOL(hAPP(hAPP(c_member(_1433389), _1433393), _1433391)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1433389), _1433393), c_Big__Operators_Olattice__class_OSup__fin(_1433389, _1433391)) = _1433393)], (878 ^ _779327) ^ [_792752, _792754, _792756, _792758, _792760, _792762] : [-(c_List_Olist__all(_792760, _792756, _792752)), c_List_Olist__all(_792762, _792758, _792754), _792762 = _792760, _792758 = _792756, _792754 = _792752], (7354 ^ _779327) ^ [_894628, _894630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894628), _894630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894630), _894628)), -(_894628 = _894630)], (17802 ^ _779327) ^ [_1081255, _1081257] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081255))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081257)) = 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)))), _1081255), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081257)))], (11657 ^ _779327) ^ [_972427, _972429, _972431] : [class_Groups_Oordered__ab__group__add(_972427), 11660 ^ _779327 : [(11667 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972427), _972431), hAPP(c_Groups_Ouminus__class_Ouminus(_972427), _972429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972427), _972429), hAPP(c_Groups_Ouminus__class_Ouminus(_972427), _972431))))], (11661 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972427), _972429), hAPP(c_Groups_Ouminus__class_Ouminus(_972427), _972431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972427), _972431), hAPP(c_Groups_Ouminus__class_Ouminus(_972427), _972429))))]]], (38178 ^ _779327) ^ [_1495417, _1495419, _1495421, _1495423, _1495425, _1495427] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495417, tc_fun(_1495419, tc_fun(_1495421, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1495417, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_fun(_1495419, tc_fun(_1495421, tc_HOL_Obool)), _1495417), hAPP(c_COMBC(_1495419, tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_fun(_1495421, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495421, tc_fun(tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_fun(_1495421, tc_HOL_Obool)), _1495419), c_COMBC(_1495421, tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495421, tc_prod(_1495419, _1495421)), tc_fun(_1495421, tc_fun(tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_HOL_Obool)), _1495419), hAPP(c_COMBB(tc_prod(_1495419, _1495421), tc_fun(tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool), tc_HOL_Obool), _1495421), c_member(tc_prod(_1495419, _1495421)))), c_Product__Type_OPair(_1495419, _1495421))))), _1495423)), _1495425), _1495427)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495419, _1495421)), hAPP(hAPP(c_Product__Type_OPair(_1495419, _1495421), _1495425), _1495427)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1495417, tc_fun(tc_prod(_1495419, _1495421), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1495417, tc_HOL_Obool))), _1495423))))], (29772 ^ _779327) ^ [_1311404, _1311406, _1311408] : [hBOOL(hAPP(hAPP(c_member(_1311404), _1311406), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311404, tc_HOL_Obool)), _1311408))), hBOOL(hAPP(hAPP(c_member(_1311404), _1311406), _1311408))], (14105 ^ _779327) ^ [_1016506, _1016508, _1016510] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016506), _1016508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016510), _1016508), -(_1016506 = _1016510)], (3766 ^ _779327) ^ [_836397, _836399, _836401, _836403, _836405, _836407] : [-(c_List_Oset__Cons(_836407, _836403, _836399) = c_List_Oset__Cons(_836405, _836401, _836397)), _836407 = _836405, _836403 = _836401, _836399 = _836397], (17974 ^ _779327) ^ [_1084458] : [c_Int_OBit0(_1084458) = c_Int_OMin], (41395 ^ _779327) ^ [_1581239, _1581241, _1581243, _1581245, _1581247] : [class_Groups_Ocomm__monoid__mult(_1581239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581241), _1581243)), c_Fun_Oinj__on(_1581241, _1581241, _1581245, _1581243), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581241, _1581239), _1581247), hAPP(c_Set_Oimage(_1581241, _1581241, _1581245), _1581243)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1581241, _1581239), hAPP(c_Fun_Ocomp(_1581241, _1581239, _1581241, _1581247), _1581245)), _1581243))], (18436 ^ _779327) ^ [_1092495, _1092497, _1092499] : [class_Rings_Olinordered__idom(_1092495), 18439 ^ _779327 : [(18448 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092495), hAPP(hAPP(c_Power_Opower__class_Opower(_1092495), _1092497), 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(_1092495), _1092499), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1092495)), _1092497 = c_Groups_Ozero__class_Ozero(_1092495), _1092499 = c_Groups_Ozero__class_Ozero(_1092495)], (18440 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092495), hAPP(hAPP(c_Power_Opower__class_Opower(_1092495), _1092497), 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(_1092495), _1092499), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1092495), 18443 ^ _779327 : [(18446 ^ _779327) ^ [] : [-(_1092499 = c_Groups_Ozero__class_Ozero(_1092495))], (18444 ^ _779327) ^ [] : [-(_1092497 = c_Groups_Ozero__class_Ozero(_1092495))]]]]], (30621 ^ _779327) ^ [_1332137, _1332139, _1332141] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332137), _1332139)), 30624 ^ _779327 : [(30631 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332137), _1332141), _1332139))), -(hAPP(c_Finite__Set_Ocard(_1332137), hAPP(hAPP(c_Set_Oinsert(_1332137), _1332141), _1332139)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1332137), _1332139)))], (30625 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332137), _1332141), _1332139)), -(hAPP(c_Finite__Set_Ocard(_1332137), hAPP(hAPP(c_Set_Oinsert(_1332137), _1332141), _1332139)) = hAPP(c_Finite__Set_Ocard(_1332137), _1332139))]]], (41153 ^ _779327) ^ [_1575504, _1575506] : [41155 ^ _779327 : [(41158 ^ _779327) ^ [] : [hBOOL(hAPP(_1575504, hAPP(c_Int_OAbs__Integ, 41154 ^ [_1575504, _1575506])))], (41156 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 41154 ^ [_1575504, _1575506]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1575504, _1575506)))], (7270 ^ _779327) ^ [_893268, _893270] : [class_Groups_Ozero(_893268), 7273 ^ _779327 : [(7280 ^ _779327) ^ [] : [_893270 = c_Groups_Ozero__class_Ozero(_893268), -(c_Groups_Ozero__class_Ozero(_893268) = _893270)], (7274 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(_893268) = _893270, -(_893270 = c_Groups_Ozero__class_Ozero(_893268))]]], (18726 ^ _779327) ^ [_1097937, _1097939] : [class_Fields_Olinordered__field__inverse__zero(_1097937), class_Int_Onumber__ring(_1097937), 18733 ^ _779327 : [(18740 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097937), c_Groups_Ozero__class_Ozero(_1097937)), _1097939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097937), c_Groups_Ozero__class_Ozero(_1097937)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097937), _1097939), hAPP(c_Int_Onumber__class_Onumber__of(_1097937), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (18734 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097937), c_Groups_Ozero__class_Ozero(_1097937)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097937), _1097939), hAPP(c_Int_Onumber__class_Onumber__of(_1097937), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097937), c_Groups_Ozero__class_Ozero(_1097937)), _1097939)))]]], (49497 ^ _779327) ^ [_1771014, _1771016, _1771018] : [-(hAPP(c_List_Orev(_1771014), hAPP(c_List_Ofilter(_1771014, _1771016), _1771018)) = hAPP(c_List_Ofilter(_1771014, _1771016), hAPP(c_List_Orev(_1771014), _1771018)))], (19193 ^ _779327) ^ [_1106380, _1106382, _1106384, _1106386] : [class_Rings_Odivision__ring(_1106380), -(_1106382 = c_Groups_Ozero__class_Ozero(_1106380)), _1106384 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106380), _1106386), _1106382), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106380), _1106384), _1106382) = _1106386)], (42078 ^ _779327) ^ [_1596572, _1596574] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596572, _1596572)), c_Transitive__Closure_Otrancl(_1596572, _1596574))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596572, _1596572)), _1596574)))], (31013 ^ _779327) ^ [_1340875, _1340877] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1340875), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1340877))), 31016 ^ _779327 : [(31019 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340877), _1340875))], (31017 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340875), _1340877)))]]], (49728 ^ _779327) ^ [_1775917, _1775919, _1775921, _1775923, _1775925] : [-(hAPP(hAPP(c_List_Ozip(_1775917, _1775919), _1775921), c_List_OtakeWhile(_1775919, _1775923, _1775925)) = c_List_OtakeWhile(tc_prod(_1775917, _1775919), hAPP(c_Fun_Ocomp(_1775919, tc_HOL_Obool, tc_prod(_1775917, _1775919), _1775923), c_Product__Type_Osnd(_1775917, _1775919)), hAPP(hAPP(c_List_Ozip(_1775917, _1775919), _1775921), _1775925)))], (37483 ^ _779327) ^ [_1480466, _1480468, _1480470, _1480472] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480466, _1480468, _1480470, _1480472, c_Orderings_Obot__class_Obot(tc_fun(_1480466, tc_HOL_Obool))), _1480472)))], (13318 ^ _779327) ^ [_1002215, _1002217, _1002219, _1002221] : [class_Int_Onumber__ring(_1002215), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002215), hAPP(c_Int_Onumber__class_Onumber__of(_1002215), _1002217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002215), hAPP(c_Int_Onumber__class_Onumber__of(_1002215), _1002219)), _1002221)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002215), hAPP(c_Int_Onumber__class_Onumber__of(_1002215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002217), _1002219))), _1002221))], (38071 ^ _779327) ^ [_1492636, _1492638, _1492640, _1492642] : [hAPP(c_Set_Oimage(_1492636, _1492638, _1492640), c_Orderings_Otop__class_Otop(tc_fun(_1492636, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1492638, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492638, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492638, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492636, _1492638, _1492640), _1492642))), hAPP(c_Set_Oimage(_1492636, _1492638, _1492640), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492636, tc_HOL_Obool)), _1492642)))))], (52564 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (18644 ^ _779327) ^ [_1096366, _1096368, _1096370] : [class_Int_Onumber__ring(_1096366), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096366), _1096368), _1096370)), 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(_1096366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096366), hAPP(hAPP(c_Power_Opower__class_Opower(_1096366), _1096368), 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(_1096366), _1096370), 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(_1096366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096366), hAPP(c_Int_Onumber__class_Onumber__of(_1096366), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1096368)), _1096370)))], (13136 ^ _779327) ^ [_998909, _998911, _998913, _998915, _998917] : [class_Groups_Oordered__cancel__ab__semigroup__add(_998909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998909), _998911), _998913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998909), _998915), _998917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998909), _998911), _998915)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998909), _998913), _998917))))], (23680 ^ _779327) ^ [_1191578, _1191580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1191578), _1191580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1191578)), hAPP(c_Code__Numeral_Onat__of, _1191580))))], (8292 ^ _779327) ^ [_911495, _911497, _911499, _911501] : [class_Rings_Olinordered__ring__strict(_911495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911495), c_Groups_Ozero__class_Ozero(_911495)), _911497)), 8299 ^ _779327 : [(8306 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911495), _911499), _911501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911495), _911497), _911499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911495), _911497), _911501))))], (8300 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911495), _911497), _911499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911495), _911497), _911501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911495), _911499), _911501)))]]], (26558 ^ _779327) ^ [_1246922] : [c_Nat__Transfer_Onat__set(_1246922), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1246922) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1246922)))], (15397 ^ _779327) ^ [_1039313, _1039315, _1039317, _1039319] : [class_Divides_Oring__div(_1039313), -(c_Divides_Odiv__class_Omod(_1039313, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039313), _1039315), _1039317), _1039319) = c_Divides_Odiv__class_Omod(_1039313, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039313), c_Divides_Odiv__class_Omod(_1039313, _1039315, _1039319)), c_Divides_Odiv__class_Omod(_1039313, _1039317, _1039319)), _1039319))], (41601 ^ _779327) ^ [_1585879, _1585881, _1585883, _1585885, _1585887, _1585889] : [c_Finite__Set_Ofolding(_1585879, _1585881, _1585883, _1585885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585879), _1585887)), -(hAPP(_1585885, hAPP(hAPP(c_Set_Oinsert(_1585879), _1585889), _1585887)) = hAPP(c_Fun_Ocomp(_1585881, _1585881, _1585881, hAPP(_1585885, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1585879, tc_HOL_Obool)), _1585887), hAPP(hAPP(c_Set_Oinsert(_1585879), _1585889), c_Orderings_Obot__class_Obot(tc_fun(_1585879, tc_HOL_Obool)))))), hAPP(_1585883, _1585889)))], (20253 ^ _779327) ^ [_1124926, _1124928, _1124930, _1124932] : [class_Fields_Olinordered__field(_1124926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124926), c_Groups_Ozero__class_Ozero(_1124926)), _1124928)), 20260 ^ _779327 : [(20267 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124926), _1124930), _1124928)), _1124932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124926), _1124930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124926), _1124932), _1124928))))], (20261 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124926), _1124930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124926), _1124932), _1124928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124926), _1124930), _1124928)), _1124932)))]]], (42621 ^ _779327) ^ [_1610478, _1610480, _1610482] : [-(hAPP(c_Relation_ORange(_1610478, _1610480), hAPP(c_Relation_Oconverse(_1610480, _1610478), _1610482)) = hAPP(c_Relation_ODomain(_1610480, _1610478), _1610482))], (16227 ^ _779327) ^ [_1054299, _1054301, _1054303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054299)), 16230 ^ _779327 : [(16231 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1054301, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1054303), _1054299)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1054303, _1054299))), 16234 ^ _779327 : [(16235 ^ _779327) ^ [_1054500, _1054502] : [-(hBOOL(hAPP(hAPP(_1054301, _1054502), _1054500))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054500), _1054299)), _1054303 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1054299), _1054502)), _1054500)]]], (16249 ^ _779327) ^ [] : [16252 ^ _779327 : [(16255 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 16251 ^ [_1054299, _1054301, _1054303]), _1054299)))], (16257 ^ _779327) ^ [] : [-(_1054303 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1054299), 16250 ^ [_1054299, _1054301, _1054303])), 16251 ^ [_1054299, _1054301, _1054303]))], (16259 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1054301, 16250 ^ [_1054299, _1054301, _1054303]), 16251 ^ [_1054299, _1054301, _1054303]))], (16253 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16251 ^ [_1054299, _1054301, _1054303])))]], -(hBOOL(hAPP(hAPP(_1054301, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1054303), _1054299)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1054303, _1054299))))]]], (29746 ^ _779327) ^ [_1310939, _1310941, _1310943, _1310945] : [hBOOL(hAPP(hAPP(c_member(_1310939), _1310941), hAPP(hAPP(c_Set_Oinsert(_1310939), _1310943), _1310945))), -(_1310941 = _1310943), -(hBOOL(hAPP(hAPP(c_member(_1310939), _1310941), _1310945)))], (50898 ^ _779327) ^ [_1801335, _1801337, _1801339] : [50900 ^ _779327 : [(50903 ^ _779327) ^ [] : [hBOOL(hAPP(_1801337, 50899 ^ [_1801335, _1801337, _1801339]))], (50901 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801335), 50899 ^ [_1801335, _1801337, _1801339]), hAPP(c_List_Oset(_1801335), _1801339))))]], -(c_List_Olist__all(_1801335, _1801337, _1801339))], (40428 ^ _779327) ^ [_1557385, _1557387, _1557389, _1557391] : [hAPP(hAPP(c_Relation_Orel__comp(_1557385, _1557385, _1557385), _1557387), _1557389) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557385, _1557385), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1557385, _1557385, _1557385), _1557391), _1557389) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557385, _1557385), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1557385, _1557385, _1557385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1557385, _1557385), tc_HOL_Obool)), _1557387), _1557391)), _1557389) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557385, _1557385), tc_HOL_Obool)))], (43892 ^ _779327) ^ [_1639518, _1639520, _1639522] : [class_Complete__Lattice_Ocomplete__lattice(_1639518), 43895 ^ _779327 : [(43896 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1639518), c_Complete__Lattice_OSup__class_OSup(_1639518, _1639520)), _1639522)), 43899 ^ _779327 : [(43900 ^ _779327) ^ [_1639676] : [hBOOL(hAPP(hAPP(c_member(_1639518), _1639676), _1639520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1639518), _1639676), _1639522)))]]], (43906 ^ _779327) ^ [] : [43908 ^ _779327 : [(43911 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1639518), 43907 ^ [_1639518, _1639520, _1639522]), _1639522))], (43909 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1639518), 43907 ^ [_1639518, _1639520, _1639522]), _1639520)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1639518), c_Complete__Lattice_OSup__class_OSup(_1639518, _1639520)), _1639522)))]]], (33317 ^ _779327) ^ [_1386052, _1386054, _1386056, _1386058, _1386060] : [class_Groups_Ocomm__monoid__mult(_1386052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386054), _1386056)), 33324 ^ _779327 : [(33331 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386054), _1386058), _1386056))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386054, _1386052), hAPP(hAPP(c_COMBC(_1386054, _1386052, _1386052), hAPP(hAPP(c_COMBS(_1386054, _1386052, tc_fun(_1386052, _1386052)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1386052, tc_fun(_1386052, _1386052)), _1386054), c_If(_1386052)), hAPP(hAPP(c_COMBC(_1386054, _1386054, tc_HOL_Obool), c_fequal), _1386058))), _1386060)), c_Groups_Oone__class_Oone(_1386052))), _1386056) = c_Groups_Oone__class_Oone(_1386052))], (33325 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1386054), _1386058), _1386056)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386054, _1386052), hAPP(hAPP(c_COMBC(_1386054, _1386052, _1386052), hAPP(hAPP(c_COMBS(_1386054, _1386052, tc_fun(_1386052, _1386052)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1386052, tc_fun(_1386052, _1386052)), _1386054), c_If(_1386052)), hAPP(hAPP(c_COMBC(_1386054, _1386054, tc_HOL_Obool), c_fequal), _1386058))), _1386060)), c_Groups_Oone__class_Oone(_1386052))), _1386056) = hAPP(_1386060, _1386058))]]], (45532 ^ _779327) ^ [_1682223, _1682225, _1682227] : [45533 ^ _779327 : [(45536 ^ _779327) ^ [] : [_1682227 = c_List_Olist_ONil(_1682223)], (45534 ^ _779327) ^ [] : [_1682225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1682223), _1682225), _1682227) = c_List_Olist_ONil(_1682223))], (504 ^ _779327) ^ [_787035, _787037, _787039, _787041] : [-(c_Wellfounded_OwfP(_787039, _787035)), c_Wellfounded_OwfP(_787041, _787037), _787041 = _787039, _787037 = _787035], (50052 ^ _779327) ^ [_1782881, _1782883, _1782885] : [-(hAPP(c_List_Oset(_1782881), hAPP(c_List_OremoveAll(_1782881, _1782883), _1782885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1782881, tc_HOL_Obool)), hAPP(c_List_Oset(_1782881), _1782885)), hAPP(hAPP(c_Set_Oinsert(_1782881), _1782883), c_Orderings_Obot__class_Obot(tc_fun(_1782881, tc_HOL_Obool)))))], (20489 ^ _779327) ^ [_1129396, _1129398, _1129400, _1129402] : [class_Fields_Olinordered__field__inverse__zero(_1129396), class_Int_Onumber(_1129396), 20496 ^ _779327 : [(20497 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129396), _1129398), _1129400)), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402))), 20500 ^ _779327 : [(20507 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), _1129400))), 20510 ^ _779327 : [(20517 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129400), c_Groups_Ozero__class_Ozero(_1129396)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402))))], (20511 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129400), c_Groups_Ozero__class_Ozero(_1129396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129396), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)), _1129400)), _1129398)))]]], (20501 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), _1129400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129396), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)), _1129400))))]]], (20523 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129396), _1129398), _1129400)), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)))), 20526 ^ _779327 : [(20529 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129396), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)), _1129400)))], (20527 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), _1129400)))]], 20530 ^ _779327 : [(20533 ^ _779327) ^ [] : [20534 ^ _779327 : [(20537 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129396), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)), _1129400)), _1129398))], (20535 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129400), c_Groups_Ozero__class_Ozero(_1129396))))]], 20538 ^ _779327 : [(20541 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), hAPP(c_Int_Onumber__class_Onumber__of(_1129396), _1129402)))], (20539 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), _1129400), c_Groups_Ozero__class_Ozero(_1129396)))]]], (20531 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129396), c_Groups_Ozero__class_Ozero(_1129396)), _1129400))]]]]], (18396 ^ _779327) ^ [_1091854, _1091856, _1091858] : [class_Rings_Olinordered__semidom(_1091854), hAPP(hAPP(c_Power_Opower__class_Opower(_1091854), _1091856), 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(_1091854), _1091858), 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(_1091854), c_Groups_Ozero__class_Ozero(_1091854)), _1091856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091854), c_Groups_Ozero__class_Ozero(_1091854)), _1091858)), -(_1091856 = _1091858)], (37743 ^ _779327) ^ [_1485908, _1485910] : [class_Lattices_Obounded__lattice__top(_1485908), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1485908), c_Orderings_Otop__class_Otop(_1485908)), _1485910) = c_Orderings_Otop__class_Otop(_1485908))], (9230 ^ _779327) ^ [_928713, _928715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _928713)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _928715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928713), _928715)))], (24977 ^ _779327) ^ [_1214769, _1214771] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1214769), _1214771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1214771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1214769), _1214771)))], (21692 ^ _779327) ^ [_1153025, _1153027, _1153029] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153025, _1153025), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1153027), _1153029))), -(_1153025 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1153027 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40635 ^ _779327) ^ [_1563106] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1563106)))], (21316 ^ _779327) ^ [_1146067, _1146069] : [21317 ^ _779327 : [(21320 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1146069), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21318 ^ _779327) ^ [] : [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), _1146067), _1146069)))]], -(c_Divides_OnegDivAlg(_1146067, _1146069) = 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), _1146067), _1146069)))], (17648 ^ _779327) ^ [_1078818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1078818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1078818)))], (28300 ^ _779327) ^ [_1282995, _1282997, _1282999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282995), _1282999)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282995), hAPP(hAPP(c_Set_Oinsert(_1282995), _1282997), _1282999))))], (48870 ^ _779327) ^ [_1758913, _1758915] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1758913, _1758915) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1758913, hAPP(c_Nat_OSuc, _1758915))))], (36094 ^ _779327) ^ [_1449368, _1449370, _1449372, _1449374, _1449376, _1449378] : [c_Equiv__Relations_Ocongruent(_1449368, _1449370, _1449372, _1449374), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449368, _1449368)), hAPP(hAPP(c_Product__Type_OPair(_1449368, _1449368), _1449376), _1449378)), _1449372)), -(hAPP(_1449374, _1449376) = hAPP(_1449374, _1449378))], (9921 ^ _779327) ^ [_939924] : [hBOOL(hAPP(_939924, 9922 ^ [_939924])), 9925 ^ _779327 : [(9926 ^ _779327) ^ [_940018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _940018)), -(hBOOL(hAPP(_939924, hAPP(c_Int_Onat, _940018))))]]], (8434 ^ _779327) ^ [_914218, _914220, _914222, _914224] : [class_Rings_Olinordered__semiring__strict(_914218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914218), _914220), _914222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914218), _914224), _914222))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914218), c_Groups_Ozero__class_Ozero(_914218)), _914222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914218), _914220), _914224)))], (42687 ^ _779327) ^ [_1612332, _1612334, _1612336, _1612338, _1612340, _1612342] : [c_Relation_Osingle__valued(_1612332, _1612334, hAPP(c_Relation_Oconverse(_1612334, _1612332), _1612336)), -(_1612338 = c_Orderings_Obot__class_Obot(tc_fun(_1612340, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1612334, _1612332, _1612336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612340, tc_fun(_1612334, tc_HOL_Obool)), _1612338), _1612342)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612340, tc_fun(_1612332, tc_HOL_Obool)), _1612338), hAPP(hAPP(c_COMBB(tc_fun(_1612334, tc_HOL_Obool), tc_fun(_1612332, tc_HOL_Obool), _1612340), c_Relation_OImage(_1612334, _1612332, _1612336)), _1612342)))], (23466 ^ _779327) ^ [_1187185, _1187187] : [-(c_Nitpick_Oinverse__frac(_1187185, _1187187) = hAPP(hAPP(c_Nitpick_Ofrac(_1187185), hAPP(c_Nitpick_Odenom(_1187185), _1187187)), hAPP(c_Nitpick_Onum(_1187185), _1187187)))], (17072 ^ _779327) ^ [_1069075, _1069077, _1069079] : [-(hBOOL(hAPP(_1069075, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1069077, _1069079)))), 17075 ^ _779327 : [(17078 ^ _779327) ^ [] : [hBOOL(hAPP(_1069075, _1069077))], (17076 ^ _779327) ^ [] : [-(_1069079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 17079 ^ _779327 : [(17084 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17082 ^ [_1069075, _1069077, _1069079]), _1069079)))], (17086 ^ _779327) ^ [] : [-(_1069077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069079), 17081 ^ [_1069075, _1069077, _1069079])), 17082 ^ [_1069075, _1069077, _1069079]))], (17088 ^ _779327) ^ [] : [hBOOL(hAPP(_1069075, 17082 ^ [_1069075, _1069077, _1069079]))], (17080 ^ _779327) ^ [] : [_1069079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (10679 ^ _779327) ^ [_952653] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _952653)), _952653) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15509 ^ _779327) ^ [_1041522, _1041524, _1041526] : [_1041522 = 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), _1041522), _1041524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1041522), _1041526)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18835 ^ _779327) ^ [_1100159, _1100161, _1100163] : [class_Fields_Ofield__inverse__zero(_1100159), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1100159), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100159), _1100161), _1100163)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1100159), _1100161), hAPP(c_Groups_Ouminus__class_Ouminus(_1100159), _1100163)))], (40196 ^ _779327) ^ [_1550025] : [-(c_Int_Oint__ge__less__than2(_1550025) = 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), _1550025)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (31552 ^ _779327) ^ [_1352403, _1352405, _1352407] : [hAPP(c_Finite__Set_Ocard(_1352403), _1352405) = hAPP(c_Nat_OSuc, _1352407), 31557 ^ _779327 : [(31560 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1352403), 31555 ^ [_1352403, _1352405, _1352407]), 31556 ^ [_1352403, _1352405, _1352407]))], (31562 ^ _779327) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1352403), 31556 ^ [_1352403, _1352405, _1352407]) = _1352407)], (31564 ^ _779327) ^ [] : [_1352407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(31556 ^ [_1352403, _1352405, _1352407] = c_Orderings_Obot__class_Obot(tc_fun(_1352403, tc_HOL_Obool)))], (31558 ^ _779327) ^ [] : [-(_1352405 = hAPP(hAPP(c_Set_Oinsert(_1352403), 31555 ^ [_1352403, _1352405, _1352407]), 31556 ^ [_1352403, _1352405, _1352407]))]]], (26402 ^ _779327) ^ [_1244132, _1244134, _1244136] : [class_Orderings_Olinorder(_1244132), 26405 ^ _779327 : [(26412 ^ _779327) ^ [] : [_1244134 = _1244136, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244132), _1244134) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244132), _1244136))], (26406 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244132), _1244134) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244132), _1244136), -(_1244134 = _1244136)]]], (13611 ^ _779327) ^ [_1007465, _1007467] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007465), hAPP(c_Nat_OSuc, _1007467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1007465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1007465), _1007467)))], (1908 ^ _779327) ^ [_806165, _806167] : [-(class_Power_Opower(_806165)), _806167 = _806165, class_Power_Opower(_806167)], (39646 ^ _779327) ^ [_1531380] : [class_Orderings_Olinorder(_1531380), -(c_Finite__Set_Ofun__left__comm__idem(_1531380, _1531380, c_Orderings_Oord__class_Omax(_1531380)))], (27891 ^ _779327) ^ [_1275246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1275246)), 27895 ^ _779327 : [(27896 ^ _779327) ^ [_1275326] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1275326), _1275246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1275326), 27894 ^ [_1275246])))]]], (38355 ^ _779327) ^ [_1501254, _1501256, _1501258, _1501260, _1501262] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1501254, _1501256, _1501258), _1501260), _1501262)), -(hBOOL(hAPP(_1501260, hAPP(_1501258, _1501262))))], (8490 ^ _779327) ^ [_915294, _915296, _915298, _915300] : [class_Rings_Olinordered__semiring__strict(_915294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915294), _915296), _915298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_915294), _915296), _915300))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915294), c_Groups_Ozero__class_Ozero(_915294)), _915296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915294), _915298), _915300)))], (39487 ^ _779327) ^ [_1527703, _1527705, _1527707, _1527709, _1527711] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527703, _1527705)), _1527707), hAPP(hAPP(c_Product__Type_OSigma(_1527703, _1527705), _1527709), _1527711))), 39491 ^ _779327 : [(39497 ^ _779327) ^ [] : [-(_1527707 = hAPP(hAPP(c_Product__Type_OPair(_1527703, _1527705), 39490 ^ [_1527703, _1527705, _1527707, _1527709, _1527711]), 39493 ^ [_1527703, _1527705, _1527707, _1527709, _1527711]))], (39495 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527705), 39493 ^ [_1527703, _1527705, _1527707, _1527709, _1527711]), hAPP(_1527711, 39490 ^ [_1527703, _1527705, _1527707, _1527709, _1527711]))))], (39492 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527703), 39490 ^ [_1527703, _1527705, _1527707, _1527709, _1527711]), _1527709)))]]], (42198 ^ _779327) ^ [_1600318, _1600320] : [-(c_Transitive__Closure_Otrancl(_1600318, _1600320) = hAPP(hAPP(c_Relation_Orel__comp(_1600318, _1600318, _1600318), c_Transitive__Closure_Ortrancl(_1600318, _1600320)), _1600320))], (52788 ^ _779327) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (40662 ^ _779327) ^ [_1563611, _1563613, _1563615] : [c_Wellfounded_Owf(_1563611, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563611, _1563611), tc_HOL_Obool)), _1563613), _1563615)), -(c_Wellfounded_Owf(_1563611, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563611, _1563611), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563611, _1563611), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563611, _1563611, _1563611), _1563613), _1563613)), hAPP(hAPP(c_Relation_Orel__comp(_1563611, _1563611, _1563611), _1563615), _1563613))), _1563615)))], (49852 ^ _779327) ^ [_1778585, _1778587, _1778589] : [c_List_OdropWhile(_1778585, _1778587, _1778589) = c_List_Olist_ONil(_1778585), 49855 ^ _779327 : [(49856 ^ _779327) ^ [_1778676] : [hBOOL(hAPP(hAPP(c_member(_1778585), _1778676), hAPP(c_List_Oset(_1778585), _1778589))), -(hBOOL(hAPP(_1778587, _1778676)))]]], (45783 ^ _779327) ^ [_1689197, _1689199, _1689201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1689197), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1689199), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1689199)), _1689201)))), -(hBOOL(hAPP(hAPP(c_member(_1689199), hAPP(c_Random_Opick(_1689199, _1689201), _1689197)), hAPP(c_List_Oset(_1689199), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1689199), _1689199), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1689199)), _1689201)))))], (35015 ^ _779327) ^ [_1424955, _1424957, _1424959, _1424961] : [hBOOL(hAPP(hAPP(c_member(_1424955), _1424961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424955, tc_HOL_Obool)), _1424957), _1424959))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424955, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1424955, tc_fun(_1424955, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424955)), _1424957)), hAPP(hAPP(c_COMBC(_1424955, tc_fun(_1424955, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424955)), _1424959)), _1424961)))], (34789 ^ _779327) ^ [_1420404, _1420406, _1420408, _1420410] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420404, tc_HOL_Obool)), _1420406), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420404, tc_HOL_Obool)), _1420408), _1420410)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420404, tc_HOL_Obool)), _1420408), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420404, tc_HOL_Obool)), _1420406), _1420410)))], (41955 ^ _779327) ^ [_1594092, _1594094, _1594096] : [class_Orderings_Olinorder(_1594092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594092), _1594094)), 41965 ^ _779327 : [(41968 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1594092), 41964 ^ [_1594092, _1594094, _1594096]), _1594096))], (41966 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1594092), 41964 ^ [_1594092, _1594094, _1594096]), _1594094)))]], hBOOL(hAPP(hAPP(c_member(_1594092), _1594096), _1594094)), -(c_Big__Operators_Olinorder__class_OMax(_1594092, _1594094) = _1594096)], (32576 ^ _779327) ^ [_1371544, _1371546, _1371548] : [class_Orderings_Olinorder(_1371544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371544), _1371546)), hBOOL(hAPP(hAPP(c_member(_1371544), _1371548), _1371546)), 32587 ^ _779327 : [(32594 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371544, tc_HOL_Obool)), _1371546), hAPP(hAPP(c_Set_Oinsert(_1371544), _1371548), c_Orderings_Obot__class_Obot(tc_fun(_1371544, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371544, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1371544, c_Orderings_Oord__class_Omax(_1371544), _1371546) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1371544), _1371548), c_Big__Operators_Olattice_OSup__fin(_1371544, c_Orderings_Oord__class_Omax(_1371544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371544, tc_HOL_Obool)), _1371546), hAPP(hAPP(c_Set_Oinsert(_1371544), _1371548), c_Orderings_Obot__class_Obot(tc_fun(_1371544, tc_HOL_Obool)))))))], (32588 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371544, tc_HOL_Obool)), _1371546), hAPP(hAPP(c_Set_Oinsert(_1371544), _1371548), c_Orderings_Obot__class_Obot(tc_fun(_1371544, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371544, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1371544, c_Orderings_Oord__class_Omax(_1371544), _1371546) = _1371548)]]], (31934 ^ _779327) ^ [_1359513, _1359515, _1359517] : [class_Orderings_Olinorder(_1359513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359513), _1359515)), hBOOL(hAPP(hAPP(c_member(_1359513), _1359517), _1359515)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359513), _1359517), c_Big__Operators_Olinorder__class_OMax(_1359513, _1359515)) = c_Big__Operators_Olinorder__class_OMax(_1359513, _1359515))], (10731 ^ _779327) ^ [_953848, _953850, _953852, _953854] : [class_Int_Onumber__ring(_953848), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953848), hAPP(c_Int_Onumber__class_Onumber__of(_953848), _953850)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953848), _953852), hAPP(c_Int_Onumber__class_Onumber__of(_953848), _953854))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953848), hAPP(c_Int_Onumber__class_Onumber__of(_953848), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953850), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _953854)))), _953852))], (22383 ^ _779327) ^ [_1166656, _1166658, _1166660] : [class_Orderings_Olinorder(_1166656), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166656), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166656), _1166658), _1166660)), _1166658)))], (5826 ^ _779327) ^ [_871292, _871294] : [5827 ^ _779327 : [(5830 ^ _779327) ^ [] : [_871292 = _871294], (5828 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871292), _871294))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871292), _871294)))], (1328 ^ _779327) ^ [_798915, _798917] : [-(class_Int_Onumber__ring(_798915)), _798917 = _798915, class_Int_Onumber__ring(_798917)], (29766 ^ _779327) ^ [_1311280, _1311282, _1311284] : [hBOOL(hAPP(hAPP(c_member(_1311280), _1311282), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311280, tc_HOL_Obool)), _1311284))), hBOOL(hAPP(hAPP(c_member(_1311280), _1311282), _1311284))], (46086 ^ _779327) ^ [_1696263, _1696265, _1696267] : [_1696265 = c_List_Olist_ONil(_1696263), -(hAPP(hAPP(c_List_Oappend(_1696263), _1696265), _1696267) = _1696267)], (42254 ^ _779327) ^ [_1601691, _1601693, _1601695, _1601697] : [42255 ^ _779327 : [(42258 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601691, _1601691)), _1601693), c_Transitive__Closure_Ortrancl(_1601691, _1601697)))], (42256 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601691, _1601691)), _1601693), c_Transitive__Closure_Ortrancl(_1601691, _1601695)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601691, _1601691)), _1601693), c_Transitive__Closure_Ortrancl(_1601691, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601691, _1601691), tc_HOL_Obool)), _1601695), _1601697)))))], (12389 ^ _779327) ^ [_985458, _985460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _985458)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _985460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985458), _985460)))], (48449 ^ _779327) ^ [_1748151, _1748153] : [-(hAPP(c_List_Oset(_1748151), c_List_Oconcat(_1748151, _1748153)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1748151), tc_fun(_1748151, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1748151)), _1748153)), c_List_Oset(_1748151)))], (27488 ^ _779327) ^ [_1265616, _1265618, _1265620] : [class_Orderings_Olinorder(_1265616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265616), _1265618), _1265620)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265616, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1265616), _1265618)), c_SetInterval_Oord__class_OatLeastAtMost(_1265616, _1265618, _1265620)) = hAPP(c_SetInterval_Oord__class_OatMost(_1265616), _1265620))], (39740 ^ _779327) ^ [_1533271] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1533271, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1533271), hAPP(c_COMBK(tc_HOL_Obool, _1533271), c_fFalse)))], (25472 ^ _779327) ^ [_1223814, _1223816, _1223818, _1223820, _1223822, _1223824] : [class_Groups_Ocomm__monoid__add(_1223814), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223816, _1223814), hAPP(hAPP(c_COMBC(_1223816, tc_fun(_1223818, tc_HOL_Obool), _1223814), hAPP(hAPP(c_COMBB(tc_fun(_1223818, _1223814), tc_fun(tc_fun(_1223818, tc_HOL_Obool), _1223814), _1223816), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223818, _1223814)), _1223820)), _1223822)), _1223824) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223818, _1223814), hAPP(hAPP(c_COMBC(_1223818, tc_fun(_1223816, tc_HOL_Obool), _1223814), hAPP(hAPP(c_COMBB(tc_fun(_1223816, _1223814), tc_fun(tc_fun(_1223816, tc_HOL_Obool), _1223814), _1223818), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223816, _1223814)), hAPP(c_COMBC(_1223816, _1223818, _1223814), _1223820))), _1223824)), _1223822))], (43646 ^ _779327) ^ [_1633728, _1633730, _1633732] : [class_Complete__Lattice_Ocomplete__lattice(_1633728), 43649 ^ _779327 : [(43650 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633728), _1633730), c_Complete__Lattice_OInf__class_OInf(_1633728, _1633732))), 43653 ^ _779327 : [(43654 ^ _779327) ^ [_1633886] : [hBOOL(hAPP(hAPP(c_member(_1633728), _1633886), _1633732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633728), _1633730), _1633886)))]]], (43660 ^ _779327) ^ [] : [43662 ^ _779327 : [(43665 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633728), _1633730), 43661 ^ [_1633728, _1633730, _1633732]))], (43663 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633728), 43661 ^ [_1633728, _1633730, _1633732]), _1633732)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1633728), _1633730), c_Complete__Lattice_OInf__class_OInf(_1633728, _1633732))))]]], (32348 ^ _779327) ^ [_1367226, _1367228] : [class_Orderings_Olinorder(_1367226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367226), _1367228)), -(_1367228 = c_Orderings_Obot__class_Obot(tc_fun(_1367226, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1367226), c_Big__Operators_Olinorder__class_OMin(_1367226, _1367228)), _1367228)))], (45420 ^ _779327) ^ [_1679961] : [-(hAPP(c_List_Oset(_1679961), c_List_Olist_ONil(_1679961)) = c_Orderings_Obot__class_Obot(tc_fun(_1679961, tc_HOL_Obool)))], (20999 ^ _779327) ^ [_1138964, _1138966] : [-(_1138964 = _1138966), -(c_Random_Oinc__shift(_1138964, _1138966) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1138966), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (28590 ^ _779327) ^ [_1288702, _1288704] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288702, tc_HOL_Obool)), _1288704), _1288704) = c_Orderings_Obot__class_Obot(tc_fun(_1288702, tc_HOL_Obool)))], (21310 ^ _779327) ^ [_1146004, _1146006] : [-(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), _1146004)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1146006), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1146004))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23179 ^ _779327) ^ [_1181706, _1181708, _1181710, _1181712, _1181714, _1181716, _1181718] : [-(hAPP(c_Product__Type_Oapsnd(_1181706, _1181708, _1181710, _1181712), hAPP(c_Product__Type_Oapfst(_1181714, _1181710, _1181706, _1181716), _1181718)) = hAPP(c_Product__Type_Oapfst(_1181714, _1181710, _1181708, _1181716), hAPP(c_Product__Type_Oapsnd(_1181706, _1181708, _1181714, _1181712), _1181718)))], (20888 ^ _779327) ^ [_1136997, _1136999, _1137001, _1137003] : [20890 ^ _779327 : [(20895 ^ _779327) ^ [] : [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(_1137001, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 20889 ^ [_1136997, _1136999, _1137001, _1137003]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1137001, 20889 ^ [_1136997, _1136999, _1137001, _1137003])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20893 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20889 ^ [_1136997, _1136999, _1137001, _1137003]), _1136999)))], (20891 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1136997), 20889 ^ [_1136997, _1136999, _1137001, _1137003])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136997), _1136999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1137001, _1136997)), _1137003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137003), hAPP(_1137001, _1136999))), 20909 ^ _779327 : [(20914 ^ _779327) ^ [] : [-(hAPP(_1137001, 20908 ^ [_1136997, _1136999, _1137001, _1137003]) = _1137003)], (20912 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20908 ^ [_1136997, _1136999, _1137001, _1137003]), _1136999)))], (20910 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1136997), 20908 ^ [_1136997, _1136999, _1137001, _1137003])))]]], (43848 ^ _779327) ^ [_1638516, _1638518, _1638520] : [43850 ^ _779327 : [(43853 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638516, tc_HOL_Obool)), 43849 ^ [_1638516, _1638518, _1638520]), _1638520) = c_Orderings_Obot__class_Obot(tc_fun(_1638516, tc_HOL_Obool))], (43851 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1638516, tc_HOL_Obool)), 43849 ^ [_1638516, _1638518, _1638520]), _1638518)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638516, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638516, tc_HOL_Obool), _1638518)), _1638520) = c_Orderings_Obot__class_Obot(tc_fun(_1638516, tc_HOL_Obool)))], (42160 ^ _779327) ^ [_1598878, _1598880, _1598882, _1598884] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1598878, tc_fun(_1598878, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1598878, tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_fun(_1598878, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598878, tc_fun(tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_fun(_1598878, tc_HOL_Obool)), _1598878), c_COMBC(_1598878, tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598878, tc_prod(_1598878, _1598878)), tc_fun(_1598878, tc_fun(tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_HOL_Obool)), _1598878), hAPP(c_COMBB(tc_prod(_1598878, _1598878), tc_fun(tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool), tc_HOL_Obool), _1598878), c_member(tc_prod(_1598878, _1598878)))), c_Product__Type_OPair(_1598878, _1598878)))), _1598880)), c_fequal), _1598882), _1598884)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598878, _1598878)), hAPP(hAPP(c_Product__Type_OPair(_1598878, _1598878), _1598882), _1598884)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1598878, _1598878), tc_HOL_Obool)), _1598880), c_Relation_OId(_1598878)))))], (6922 ^ _779327) ^ [_887636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887636)), -(_887636 = hAPP(c_Nat_OSuc, 6925 ^ [_887636]))], (2408 ^ _779327) ^ [_814500, _814502, _814504, _814506, _814508, _814510] : [-(c_Product__Type_Ointernal__split(_814510, _814506, _814502) = c_Product__Type_Ointernal__split(_814508, _814504, _814500)), _814510 = _814508, _814506 = _814504, _814502 = _814500], (10675 ^ _779327) ^ [_952572, _952574] : [-(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), _952572))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952574))))], (48822 ^ _779327) ^ [_1758040, _1758042] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1758040), _1758042)) = c_List_Oupt(_1758040, _1758042))], (49119 ^ _779327) ^ [_1763320, _1763322, _1763324, _1763326] : [class_Orderings_Olinorder(_1763320), -(c_List_Olinorder__class_Osorted(_1763320, hAPP(hAPP(c_List_Omap(_1763322, _1763320), _1763324), c_List_Olinorder__class_Osort__key(_1763322, _1763320, _1763324, _1763326))))], (45578 ^ _779327) ^ [_1683815, _1683817, _1683819] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683815), tc_List_Olist(_1683815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683815), tc_List_Olist(_1683815)), _1683817), c_List_Olist_ONil(_1683815))), c_List_Olexord(_1683815, _1683819)))], (30591 ^ _779327) ^ [_1331441, _1331443, _1331445, _1331447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331441, tc_HOL_Obool)), _1331443), hAPP(hAPP(c_Set_Oinsert(_1331441), _1331445), _1331447))), 30594 ^ _779327 : [(30601 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331441), _1331445), _1331443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331441, tc_HOL_Obool)), _1331443), _1331447)))], (30595 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1331441), _1331445), _1331443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331441, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331441, tc_HOL_Obool)), _1331443), hAPP(hAPP(c_Set_Oinsert(_1331441), _1331445), c_Orderings_Obot__class_Obot(tc_fun(_1331441, tc_HOL_Obool))))), _1331447)))]]], (37402 ^ _779327) ^ [_1478844, _1478846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478844), _1478846)), -(hAPP(c_Finite__Set_Ocard(_1478844), _1478846) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1478844, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1478844), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1478846))], (36526 ^ _779327) ^ [_1460870, _1460872, _1460874, _1460876, _1460878] : [c_Relation_Orefl__on(_1460870, _1460872, _1460874), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460870, _1460870)), hAPP(hAPP(c_Product__Type_OPair(_1460870, _1460870), _1460876), _1460878)), _1460874)), -(hBOOL(hAPP(hAPP(c_member(_1460870), _1460878), _1460872)))], (31590 ^ _779327) ^ [_1353270, _1353272, _1353274, _1353276, _1353278, _1353280] : [hBOOL(hAPP(hAPP(c_member(_1353270), _1353272), c_SetInterval_Oord_OatLeastLessThan(_1353270, _1353274, _1353276, _1353278, _1353280))), 31593 ^ _779327 : [(31596 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1353276, _1353272), _1353280)))], (31594 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1353274, _1353278), _1353272)))]]], (42904 ^ _779327) ^ [_1617410, _1617412, _1617414] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617410, _1617410), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1617412)), _1617414) = hAPP(hAPP(c_Relation_Orel__comp(_1617410, _1617410, _1617410), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617410, _1617410), tc_HOL_Obool), _1617412), _1617414)), _1617414))], (28906 ^ _779327) ^ [_1294613, _1294615, _1294617] : [class_Orderings_Oorder(_1294613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294613), _1294615), _1294617)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1294613, _1294617), _1294615) = c_Orderings_Obot__class_Obot(tc_fun(_1294613, tc_HOL_Obool)))], (45683 ^ _779327) ^ [_1686443, _1686445, _1686447] : [-(_1686443 = c_List_Olist_ONil(_1686445)), -(hBOOL(hAPP(hAPP(c_member(_1686445), hAPP(c_Product__Type_Ofst(_1686445, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1686445, _1686443), _1686447))), hAPP(c_List_Oset(_1686445), _1686443))))], (40486 ^ _779327) ^ [_1560379, _1560381, _1560383, _1560385, _1560387, _1560389, _1560391, _1560393] : [hBOOL(hAPP(hAPP(_1560379, _1560381), _1560383)), hBOOL(hAPP(hAPP(_1560385, _1560383), _1560387)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1560389, _1560391, _1560393, _1560379, _1560385), _1560381), _1560387)))], (40021 ^ _779327) ^ [_1542815, _1542817, _1542819, _1542821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542815), hAPP(c_Set_OCollect(_1542815), _1542817))), 40024 ^ _779327 : [(40025 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542819), hAPP(c_Set_OCollect(_1542819), hAPP(hAPP(c_COMBB(tc_fun(_1542815, tc_HOL_Obool), tc_HOL_Obool, _1542819), c_HOL_OEx(_1542815)), hAPP(hAPP(c_COMBB(tc_fun(_1542815, tc_HOL_Obool), tc_fun(_1542815, tc_HOL_Obool), _1542819), hAPP(c_COMBS(_1542815, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542815), c_fconj), _1542817))), _1542821))))), 40028 ^ _779327 : [(40029 ^ _779327) ^ [_1543098] : [hBOOL(hAPP(_1542817, _1543098)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542819), hAPP(c_Set_OCollect(_1542819), hAPP(hAPP(c_COMBC(_1542819, _1542815, tc_HOL_Obool), _1542821), _1543098)))))]]], (40035 ^ _779327) ^ [] : [40037 ^ _779327 : [(40040 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542819), hAPP(c_Set_OCollect(_1542819), hAPP(hAPP(c_COMBC(_1542819, _1542815, tc_HOL_Obool), _1542821), 40036 ^ [_1542815, _1542817, _1542819, _1542821]))))], (40038 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1542817, 40036 ^ [_1542815, _1542817, _1542819, _1542821])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542819), hAPP(c_Set_OCollect(_1542819), hAPP(hAPP(c_COMBB(tc_fun(_1542815, tc_HOL_Obool), tc_HOL_Obool, _1542819), c_HOL_OEx(_1542815)), hAPP(hAPP(c_COMBB(tc_fun(_1542815, tc_HOL_Obool), tc_fun(_1542815, tc_HOL_Obool), _1542819), hAPP(c_COMBS(_1542815, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542815), c_fconj), _1542817))), _1542821))))))]]], (10663 ^ _779327) ^ [_952370, _952372] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _952370) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _952372)), _952370 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _952372)), 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), _952372)))], (16788 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (48513 ^ _779327) ^ [_1750489, _1750491, _1750493] : [-(hAPP(c_List_Ofilter(_1750489, _1750491), c_List_Oconcat(_1750489, _1750493)) = c_List_Oconcat(_1750489, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750489), tc_List_Olist(_1750489)), c_List_Ofilter(_1750489, _1750491)), _1750493)))], (40976 ^ _779327) ^ [_1571974, _1571976, _1571978, _1571980] : [hBOOL(hAPP(hAPP(c_member(_1571974), _1571976), hAPP(c_Relation_ODomain(_1571974, _1571978), _1571980))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571974, _1571978)), hAPP(hAPP(c_Product__Type_OPair(_1571974, _1571978), _1571976), 40979 ^ [_1571974, _1571976, _1571978, _1571980])), _1571980)))], (25317 ^ _779327) ^ [_1220777, _1220779] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220777), _1220779)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220779), _1220777)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1220779)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1220777)))], (25299 ^ _779327) ^ [_1220466, _1220468, _1220470] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220466), _1220470))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220466, _1220468) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220470, _1220468))], (10845 ^ _779327) ^ [_956085] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _956085) = _956085)], (12385 ^ _779327) ^ [_985388] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985388), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _985388)], (4388 ^ _779327) ^ [_846072, _846074, _846076, _846078] : [-(c_List_Obutlast(_846078, _846074) = c_List_Obutlast(_846076, _846072)), _846078 = _846076, _846074 = _846072], (35315 ^ _779327) ^ [_1432286, _1432288, _1432290, _1432292, _1432294] : [_1432286 = c_Orderings_Obot__class_Obot(tc_fun(_1432288, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432290, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432288, tc_fun(_1432290, tc_HOL_Obool)), _1432286), _1432292)), _1432294) = _1432294)], (49611 ^ _779327) ^ [_1773479, _1773481, _1773483, _1773485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773481)), _1773483))), -(hAPP(c_List_Orev(_1773481), hAPP(hAPP(c_List_Olist__update(_1773481, _1773483), _1773479), _1773485)) = hAPP(hAPP(c_List_Olist__update(_1773481, hAPP(c_List_Orev(_1773481), _1773483)), 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(_1773481)), _1773483)), _1773479)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1773485))], (52656 ^ _779327) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (32118 ^ _779327) ^ [_1362561, _1362563, _1362565] : [class_Orderings_Olinorder(_1362561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362561), _1362563)), -(_1362563 = c_Orderings_Obot__class_Obot(tc_fun(_1362561, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362561), _1362565)), -(_1362565 = c_Orderings_Obot__class_Obot(tc_fun(_1362561, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1362561, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362561, tc_HOL_Obool)), _1362563), _1362565)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362561), c_Big__Operators_Olinorder__class_OMax(_1362561, _1362563)), c_Big__Operators_Olinorder__class_OMax(_1362561, _1362565)))], (8570 ^ _779327) ^ [_916573, _916575] : [class_Rings_Olinordered__semidom(_916573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916573), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_916573), _916575)), c_Groups_Ozero__class_Ozero(_916573)))], (32534 ^ _779327) ^ [_1370402, _1370404, _1370406, _1370408, _1370410, _1370412, _1370414, _1370416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1370402, _1370404), tc_prod(_1370402, _1370404))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1370402, _1370404), tc_prod(_1370402, _1370404)), hAPP(hAPP(c_Product__Type_OPair(_1370402, _1370404), _1370406), _1370408)), hAPP(hAPP(c_Product__Type_OPair(_1370402, _1370404), _1370410), _1370412))), c_Wellfounded_Olex__prod(_1370402, _1370404, _1370414, _1370416))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1370402, _1370402)), hAPP(hAPP(c_Product__Type_OPair(_1370402, _1370402), _1370406), _1370410)), _1370414))), 32541 ^ _779327 : [(32544 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1370404, _1370404)), hAPP(hAPP(c_Product__Type_OPair(_1370404, _1370404), _1370408), _1370412)), _1370416)))], (32542 ^ _779327) ^ [] : [-(_1370406 = _1370410)]]], (30255 ^ _779327) ^ [_1323497, _1323499, _1323501, _1323503, _1323505] : [hBOOL(hAPP(hAPP(c_member(_1323497), _1323499), c_SetInterval_Oord_OgreaterThanLessThan(_1323497, _1323501, _1323503, _1323505))), 30258 ^ _779327 : [(30261 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1323501, _1323499), _1323505)))], (30259 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1323501, _1323503), _1323499)))]]], (26712 ^ _779327) ^ [_1249629, _1249631, _1249633, _1249635] : [class_Orderings_Olinorder(_1249629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249629), _1249631), _1249633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249629), _1249633), _1249635)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1249629, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1249629, _1249631, _1249633)), c_SetInterval_Oord__class_OatLeastAtMost(_1249629, _1249633, _1249635)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1249629, _1249631, _1249635))], (4764 ^ _779327) ^ [_851908, _851910] : [_851910 = _851908, -(c_List_Ohd(_851910) = c_List_Ohd(_851908))], (22249 ^ _779327) ^ [_1163929, _1163931] : [22250 ^ _779327 : [(22253 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163931), _1163929))], (22251 ^ _779327) ^ [] : [_1163929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1163931, _1163929) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163931))], (26456 ^ _779327) ^ [_1245158, _1245160] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1245158), _1245160)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1245160), _1245158)))], (9457 ^ _779327) ^ [_932588] : [class_Rings_Oring__1(_932588), -(hAPP(c_Int_Oring__1__class_Oof__int(_932588), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_932588))], (40682 ^ _779327) ^ [_1564190, _1564192, _1564194] : [_1564194 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564190, _1564192), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1564190, _1564192), _1564194) = c_Orderings_Obot__class_Obot(tc_fun(_1564192, tc_HOL_Obool)))], (13470 ^ _779327) ^ [_1004967, _1004969] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004967), _1004969) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13475 ^ _779327 : [(13478 ^ _779327) ^ [] : [-(_1004969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13476 ^ _779327) ^ [] : [-(_1004967 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 13479 ^ _779327 : [(13482 ^ _779327) ^ [] : [-(_1004969 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13480 ^ _779327) ^ [] : [-(_1004967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46369 ^ _779327) ^ [_1702589, _1702591, _1702593, _1702595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702589), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702591)), _1702593))), -(hBOOL(hAPP(hAPP(c_member(_1702591), _1702595), hAPP(c_List_Oset(_1702591), hAPP(hAPP(c_List_Olist__update(_1702591, _1702593), _1702589), _1702595)))))], (34207 ^ _779327) ^ [_1406609, _1406611, _1406613] : [class_Rings_Oring__1(_1406609), -(hAPP(c_Int_Oring__1__class_Oof__int(_1406609), 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), _1406611), _1406613)), 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(_1406609), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1406609), _1406611)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1406609), _1406613)))], (52744 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (44934 ^ _779327) ^ [_1667172, _1667174, _1667176] : [_1667172 = _1667174, 44937 ^ _779327 : [(44940 ^ _779327) ^ [_1667320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1667320), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667176)), _1667172))), -(hAPP(hAPP(c_List_Onth(_1667176), _1667172), _1667320) = hAPP(hAPP(c_List_Onth(_1667176), _1667174), _1667320))], (44938 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667176)), _1667172) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667176)), _1667174))]]], (48457 ^ _779327) ^ [_1748344, _1748346, _1748348] : [-(c_List_Oconcat(_1748344, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1748344)), _1748346), _1748348)) = hAPP(hAPP(c_List_Oappend(_1748344), c_List_Oconcat(_1748344, _1748346)), c_List_Oconcat(_1748344, _1748348)))], (44845 ^ _779327) ^ [_1664731, _1664733, _1664735] : [c_Relation_Orefl__on(_1664731, _1664733, _1664735), -(c_Relation_Orefl__on(tc_List_Olist(_1664731), c_List_Olists(_1664731, _1664733), c_List_Olistrel(_1664731, _1664735)))], (48229 ^ _779327) ^ [_1743652, _1743654, _1743656] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1743652))), c_Enum_On__lists(_1743652, _1743654, _1743656)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743652)), _1743656)), _1743654))], (41343 ^ _779327) ^ [_1580189, _1580191, _1580193, _1580195, _1580197, _1580199] : [class_Groups_Ocomm__monoid__add(_1580189), c_Fun_Oinj__on(_1580191, _1580193, _1580195, _1580197), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580193, _1580189), _1580199), hAPP(c_Set_Oimage(_1580191, _1580193, _1580195), _1580197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580191, _1580189), hAPP(c_Fun_Ocomp(_1580193, _1580189, _1580191, _1580199), _1580195)), _1580197))], (24507 ^ _779327) ^ [_1205925, _1205927, _1205929, _1205931] : [class_Rings_Ocomm__semiring__1(_1205925), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205925), _1205927), _1205929)), _1205931)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1205925), _1205929), _1205931)))], (28433 ^ _779327) ^ [_1285521, _1285523, _1285525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285521), _1285523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285521, tc_HOL_Obool)), _1285525), _1285523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1285521), _1285523)), hAPP(c_Finite__Set_Ocard(_1285521), _1285525))), -(_1285525 = _1285523)], (33949 ^ _779327) ^ [_1400421, _1400423] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1400421, tc_HOL_Obool)), hAPP(c_Set_OPow(_1400421), _1400423))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1400421), _1400423)))], (13260 ^ _779327) ^ [_1001123, _1001125, _1001127] : [class_Rings_Olinordered__ring__strict(_1001123), 13263 ^ _779327 : [(13272 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001123), _1001125), _1001125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001123), _1001127), _1001127)) = c_Groups_Ozero__class_Ozero(_1001123)), _1001125 = c_Groups_Ozero__class_Ozero(_1001123), _1001127 = c_Groups_Ozero__class_Ozero(_1001123)], (13264 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001123), _1001125), _1001125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001123), _1001127), _1001127)) = c_Groups_Ozero__class_Ozero(_1001123), 13267 ^ _779327 : [(13270 ^ _779327) ^ [] : [-(_1001127 = c_Groups_Ozero__class_Ozero(_1001123))], (13268 ^ _779327) ^ [] : [-(_1001125 = c_Groups_Ozero__class_Ozero(_1001123))]]]]], (52582 ^ _779327) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (30135 ^ _779327) ^ [_1321079, _1321081, _1321083, _1321085, _1321087] : [c_Finite__Set_Ofolding__one(_1321079, _1321081, _1321083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321079), _1321085)), -(hBOOL(hAPP(hAPP(c_member(_1321079), _1321087), _1321085))), -(_1321085 = c_Orderings_Obot__class_Obot(tc_fun(_1321079, tc_HOL_Obool))), -(hAPP(_1321083, hAPP(hAPP(c_Set_Oinsert(_1321079), _1321087), _1321085)) = hAPP(hAPP(_1321081, _1321087), hAPP(_1321083, _1321085)))], (48578 ^ _779327) ^ [_1751849, _1751851, _1751853, _1751855, _1751857] : [-(hAPP(c_List_Ofilter(_1751849, _1751851), hAPP(hAPP(c_List_Omap(_1751853, _1751849), _1751855), _1751857)) = hAPP(hAPP(c_List_Omap(_1751853, _1751849), _1751855), hAPP(c_List_Ofilter(_1751853, hAPP(c_Fun_Ocomp(_1751849, tc_HOL_Obool, _1751853, _1751851), _1751855)), _1751857)))], (11442 ^ _779327) ^ [_968102, _968104, _968106] : [hBOOL(hAPP(_968102, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968104), _968106))), 11445 ^ _779327 : [(11452 ^ _779327) ^ [_968293] : [_968104 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968106), _968293), -(hBOOL(hAPP(_968102, _968293)))], (11446 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968104), _968106)), -(hBOOL(hAPP(_968102, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (15161 ^ _779327) ^ [_1034581, _1034583, _1034585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034581)), 15167 ^ _779327 : [(15170 ^ _779327) ^ [] : [hBOOL(hAPP(_1034583, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 15166 ^ [_1034581, _1034583, _1034585]), _1034581)))], (15168 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1034583, 15166 ^ [_1034581, _1034583, _1034585])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034585)), 15175 ^ _779327 : [(15176 ^ _779327) ^ [_1034870] : [hBOOL(hAPP(_1034583, _1034870)), -(hBOOL(hAPP(_1034583, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1034870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1034585), _1034581)))))]]], (29216 ^ _779327) ^ [] : [-(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))))], (44544 ^ _779327) ^ [_1655385, _1655387, _1655389] : [-(c_Random_Oselect__weight(_1655385, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1655385)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1655385), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1655387)), _1655389)) = c_Random_Oselect__weight(_1655385, _1655389))], (34013 ^ _779327) ^ [_1401925, _1401927, _1401929, _1401931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1401925, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401927, tc_fun(tc_fun(_1401925, tc_HOL_Obool), tc_HOL_Obool)), _1401929), hAPP(hAPP(c_COMBB(tc_fun(_1401925, tc_HOL_Obool), tc_fun(tc_fun(_1401925, tc_HOL_Obool), tc_HOL_Obool), _1401927), c_Set_OPow(_1401925)), _1401931))), hAPP(c_Set_OPow(_1401925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401927, tc_fun(_1401925, tc_HOL_Obool)), _1401929), _1401931)))))], (25718 ^ _779327) ^ [_1229742, _1229744, _1229746, _1229748, _1229750] : [class_Orderings_Oorder(_1229742), 25721 ^ _779327 : [(25734 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229742, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1229742, _1229744, _1229746)), c_SetInterval_Oord__class_OatLeastAtMost(_1229742, _1229748, _1229750)))), 25735 ^ _779327 : [(25738 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229748), _1229744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229746), _1229750))], (25736 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229744), _1229746)))]]], (25722 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229742, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1229742, _1229744, _1229746)), c_SetInterval_Oord__class_OatLeastAtMost(_1229742, _1229748, _1229750))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229744), _1229746)), 25729 ^ _779327 : [(25732 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229746), _1229750)))], (25730 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229742), _1229748), _1229744)))]]]]], (9295 ^ _779327) ^ [_929916] : [hBOOL(hAPP(_929916, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9296 ^ [_929916]))), 9299 ^ _779327 : [(9300 ^ _779327) ^ [_930016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930016)), -(hBOOL(hAPP(_929916, _930016)))]]], (39044 ^ _779327) ^ [_1517863, _1517865, _1517867] : [-(c_Relation_Orefl__on(_1517863, _1517865, _1517867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517863, _1517863), tc_HOL_Obool)), _1517867), hAPP(hAPP(c_Product__Type_OSigma(_1517863, _1517863), _1517865), hAPP(c_COMBK(tc_fun(_1517863, tc_HOL_Obool), _1517863), _1517865)))), 39050 ^ _779327 : [(39053 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517863, _1517863)), hAPP(hAPP(c_Product__Type_OPair(_1517863, _1517863), 39049 ^ [_1517863, _1517865, _1517867]), 39049 ^ [_1517863, _1517865, _1517867])), _1517867))], (39051 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517863), 39049 ^ [_1517863, _1517865, _1517867]), _1517865)))]]], (42747 ^ _779327) ^ [_1613430, _1613432, _1613434, _1613436, _1613438, _1613440] : [c_Relation_Osingle__valued(_1613430, _1613432, _1613434), hBOOL(hAPP(hAPP(c_member(tc_prod(_1613430, _1613432)), hAPP(hAPP(c_Product__Type_OPair(_1613430, _1613432), _1613436), _1613438)), _1613434)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1613430, _1613432)), hAPP(hAPP(c_Product__Type_OPair(_1613430, _1613432), _1613436), _1613440)), _1613434)), -(_1613438 = _1613440)], (33032 ^ _779327) ^ [_1380627, _1380629, _1380631, _1380633, _1380635, _1380637] : [_1380627 = _1380629, -(hAPP(c_Fun_Ofun__upd(_1380631, _1380633, _1380635, _1380629, _1380637), _1380627) = _1380637)], (1438 ^ _779327) ^ [_800290, _800292] : [-(class_Lattices_Osemilattice__sup(_800290)), _800292 = _800290, class_Lattices_Osemilattice__sup(_800292)], (53058 ^ _779327) ^ [_1841208, _1841210] : [hBOOL(hAPP(hAPP(c_fconj, _1841208), _1841210)), -(hBOOL(_1841208))], (5476 ^ _779327) ^ [_862892, _862894] : [_862894 = _862892, -(tc_Option_Ooption(_862894) = tc_Option_Ooption(_862892))], (8214 ^ _779327) ^ [_910213, _910215, _910217, _910219] : [class_Rings_Olinordered__semidom(_910213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910213), _910215), _910217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910213), c_Groups_Ozero__class_Ozero(_910213)), _910215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910213), hAPP(hAPP(c_Power_Opower__class_Opower(_910213), _910215), _910219)), hAPP(hAPP(c_Power_Opower__class_Opower(_910213), _910217), _910219))))], (14911 ^ _779327) ^ [_1030178, _1030180, _1030182] : [class_Divides_Osemiring__div(_1030178), -(_1030180 = c_Groups_Ozero__class_Ozero(_1030178)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030178), _1030182), _1030180)), _1030180) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030178), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030178), _1030182), _1030180)), c_Groups_Oone__class_Oone(_1030178)))], (21624 ^ _779327) ^ [_1151949, _1151951] : [-(c_Divides_Opdivmod(_1151949, _1151951) = 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), _1151949)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151951))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151949), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1151951))))], (52578 ^ _779327) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (30509 ^ _779327) ^ [_1329735, _1329737, _1329739, _1329741] : [c_Orderings_Oorder__class_Omono(tc_fun(_1329735, tc_HOL_Obool), tc_fun(_1329735, tc_HOL_Obool), _1329737), hBOOL(hAPP(hAPP(c_member(_1329735), _1329739), _1329741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329735, tc_HOL_Obool)), _1329741), hAPP(_1329737, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329735, tc_HOL_Obool)), _1329741), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1329735, tc_HOL_Obool), _1329737))))), -(hBOOL(hAPP(hAPP(c_member(_1329735), _1329739), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1329735, tc_HOL_Obool), _1329737))))], (9999 ^ _779327) ^ [_941246, _941248, _941250] : [class_Rings_Olinordered__semidom(_941246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941246), c_Groups_Oone__class_Oone(_941246)), _941248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941246), c_Groups_Oone__class_Oone(_941246)), hAPP(hAPP(c_Power_Opower__class_Opower(_941246), _941248), _941250))))], (37673 ^ _779327) ^ [_1484687, _1484689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1484687, _1484689)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1484687, _1484689), tc_HOL_Obool)))), 37676 ^ _779327 : [(37679 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1484689), c_Orderings_Otop__class_Otop(tc_fun(_1484689, tc_HOL_Obool)))))], (37677 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1484687), c_Orderings_Otop__class_Otop(tc_fun(_1484687, tc_HOL_Obool)))))]]], (3396 ^ _779327) ^ [_830482, _830484, _830486, _830488, _830490, _830492, _830494, _830496] : [-(c_Random__Sequence_Omap(_830496, _830492, _830488, _830484) = c_Random__Sequence_Omap(_830494, _830490, _830486, _830482)), _830496 = _830494, _830492 = _830490, _830488 = _830486, _830484 = _830482], (16429 ^ _779327) ^ [_1057813] : [class_Rings_Olinordered__idom(_1057813), -(hAPP(c_Groups_Oabs__class_Oabs(_1057813), c_Groups_Oone__class_Oone(_1057813)) = c_Groups_Oone__class_Oone(_1057813))], (27969 ^ _779327) ^ [_1276801, _1276803, _1276805, _1276807, _1276809] : [-(hAPP(hAPP(c_Set_Oinsert(_1276801), _1276803), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1276805, tc_fun(_1276801, tc_HOL_Obool)), _1276807), _1276809)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1276805, tc_fun(_1276801, tc_HOL_Obool)), _1276807), hAPP(hAPP(c_COMBB(tc_fun(_1276801, tc_HOL_Obool), tc_fun(_1276801, tc_HOL_Obool), _1276805), hAPP(c_Set_Oinsert(_1276801), _1276803)), _1276809)))], (48680 ^ _779327) ^ [_1754766, _1754768] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1754766)), c_List_Otranspose__rel(_1754766)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754766)), c_List_Olist_ONil(_1754766)), _1754768))), -(c_List_Otranspose(_1754766, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1754766)), c_List_Olist_ONil(_1754766)), _1754768)) = c_List_Otranspose(_1754766, _1754768))], (35247 ^ _779327) ^ [_1430306, _1430308, _1430310] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430306, tc_HOL_Obool)), _1430308), _1430310) = c_Orderings_Obot__class_Obot(tc_fun(_1430306, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430306, tc_HOL_Obool)), _1430308), _1430310) = _1430308)], (40941 ^ _779327) ^ [_1570572, _1570574, _1570576, _1570578] : [hBOOL(hAPP(hAPP(c_member(_1570572), _1570574), hAPP(c_Relation_ODomain(_1570572, _1570576), _1570578))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570572, _1570576)), hAPP(hAPP(c_Product__Type_OPair(_1570572, _1570576), _1570574), 40944 ^ [_1570572, _1570574, _1570576, _1570578])), _1570578)))], (32046 ^ _779327) ^ [_1361376, _1361378, _1361380] : [class_Lattices_Olattice(_1361376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361376), _1361378)), -(_1361380 = c_Orderings_Obot__class_Obot(tc_fun(_1361376, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1361376, tc_HOL_Obool)), _1361380), _1361378)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1361376), c_Big__Operators_Olattice__class_OSup__fin(_1361376, _1361380)), c_Big__Operators_Olattice__class_OSup__fin(_1361376, _1361378)) = c_Big__Operators_Olattice__class_OSup__fin(_1361376, _1361378))], (17654 ^ _779327) ^ [_1078901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1078901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1078901))))], (41063 ^ _779327) ^ [_1573960, _1573962] : [c_Wellfounded_OwfP(_1573960, _1573962), -(c_Wellfounded_Oacyclic(_1573960, hAPP(c_Set_OCollect(tc_prod(_1573960, _1573960)), hAPP(c_Product__Type_Oprod_Oprod__case(_1573960, _1573960, tc_HOL_Obool), _1573962))))], (25622 ^ _779327) ^ [_1227964, _1227966, _1227968] : [class_Fields_Ofield(_1227964), -(_1227966 = c_Groups_Oone__class_Oone(_1227964)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227964), hAPP(c_Power_Opower__class_Opower(_1227964), _1227966)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227968)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1227964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227964), hAPP(hAPP(c_Power_Opower__class_Opower(_1227964), _1227966), _1227968)), c_Groups_Oone__class_Oone(_1227964))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227964), _1227966), c_Groups_Oone__class_Oone(_1227964))))], (10875 ^ _779327) ^ [_956577, _956579] : [class_Groups_Ogroup__add(_956577), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956577), hAPP(c_Groups_Ouminus__class_Ouminus(_956577), _956579)), _956579) = c_Groups_Ozero__class_Ozero(_956577))], (48507 ^ _779327) ^ [_1750000, _1750002, _1750004] : [-(c_Enum_On__lists(_1750000, hAPP(c_Nat_OSuc, _1750002), _1750004) = c_List_Oconcat(tc_List_Olist(_1750000), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750000), tc_List_Olist(tc_List_Olist(_1750000))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1750000), tc_List_Olist(_1750000), tc_List_Olist(tc_List_Olist(_1750000))), hAPP(hAPP(c_COMBB(tc_fun(_1750000, tc_List_Olist(_1750000)), tc_fun(tc_List_Olist(_1750000), tc_List_Olist(tc_List_Olist(_1750000))), tc_List_Olist(_1750000)), c_List_Omap(_1750000, tc_List_Olist(_1750000))), hAPP(c_COMBC(_1750000, tc_List_Olist(_1750000), tc_List_Olist(_1750000)), c_List_Olist_OCons(_1750000)))), _1750004)), c_Enum_On__lists(_1750000, _1750002, _1750004))))], (45775 ^ _779327) ^ [_1689016, _1689018, _1689020] : [-(c_List_Olistset(_1689016, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1689016, tc_HOL_Obool)), _1689018), _1689020)) = c_List_Oset__Cons(_1689016, _1689018, c_List_Olistset(_1689016, _1689020)))], (52808 ^ _779327) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (47498 ^ _779327) ^ [_1727648, _1727650, _1727652, _1727654] : [_1727648 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727650)), _1727652)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1727650, hAPP(hAPP(c_List_Olist__update(_1727650, _1727652), _1727648), _1727654)) = c_List_Obutlast(_1727650, _1727652))], (16559 ^ _779327) ^ [_1059927, _1059929, _1059931, _1059933, _1059935] : [class_Rings_Olinordered__idom(_1059927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059927), hAPP(c_Groups_Oabs__class_Oabs(_1059927), _1059929)), _1059931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059927), hAPP(c_Groups_Oabs__class_Oabs(_1059927), _1059933)), _1059935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059927), hAPP(c_Groups_Oabs__class_Oabs(_1059927), _1059929)), hAPP(c_Groups_Oabs__class_Oabs(_1059927), _1059933))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059927), _1059931), _1059935))))], (34257 ^ _779327) ^ [_1408083] : [-(_1408083 = 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), 34254 ^ [_1408083]), 34255 ^ [_1408083])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (22549 ^ _779327) ^ [_1169527, _1169529, _1169531, _1169533] : [class_Orderings_Olinorder(_1169527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169527), _1169529), _1169531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169527), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169527), _1169533), _1169529)), _1169531)))], (47648 ^ _779327) ^ [_1730516] : [class_Orderings_Olinorder(_1730516), -(c_List_Olinorder__class_Osorted__list__of__set(_1730516, c_Orderings_Obot__class_Obot(tc_fun(_1730516, tc_HOL_Obool))) = c_List_Olist_ONil(_1730516))], (29106 ^ _779327) ^ [_1297946, _1297948] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297946, _1297948) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1297946), _1297948))], (24699 ^ _779327) ^ [_1209410, _1209412, _1209414] : [class_Divides_Oring__div(_1209410), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209410), _1209412), _1209414)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209410), hAPP(c_Groups_Ouminus__class_Ouminus(_1209410), _1209414)), _1209412) = hAPP(c_Groups_Ouminus__class_Ouminus(_1209410), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209410), _1209414), _1209412)))], (22893 ^ _779327) ^ [_1176010, _1176012, _1176014] : [class_Orderings_Olinorder(_1176010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176010), _1176012), _1176014)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176010), _1176014), _1176012) = _1176014)], (52816 ^ _779327) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (24209 ^ _779327) ^ [_1200967, _1200969, _1200971] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200967), _1200969)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200969), _1200971)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200967), _1200971)))], (11801 ^ _779327) ^ [_974745, _974747, _974749] : [class_Groups_Oordered__ab__group__add(_974745), 11804 ^ _779327 : [(11811 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974745), hAPP(c_Groups_Ouminus__class_Ouminus(_974745), _974749)), _974747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974745), hAPP(c_Groups_Ouminus__class_Ouminus(_974745), _974747)), _974749)))], (11805 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974745), hAPP(c_Groups_Ouminus__class_Ouminus(_974745), _974747)), _974749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974745), hAPP(c_Groups_Ouminus__class_Ouminus(_974745), _974749)), _974747)))]]], (43173 ^ _779327) ^ [_1624554, _1624556, _1624558, _1624560, _1624562, _1624564] : [c_Finite__Set_Ofun__left__comm__idem(_1624554, _1624556, _1624558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624554), _1624560)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1624554, _1624556, _1624558), _1624562), hAPP(hAPP(c_Set_Oinsert(_1624554), _1624564), _1624560)) = hAPP(hAPP(_1624558, _1624564), hAPP(hAPP(c_Finite__Set_Ofold(_1624554, _1624556, _1624558), _1624562), _1624560)))], (31209 ^ _779327) ^ [_1344641, _1344643] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344643), _1344641)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344641), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344643))))], (23193 ^ _779327) ^ [_1182048] : [class_Orderings_Oord(_1182048), -(c_Orderings_Oord__class_Omax(_1182048) = c_Orderings_Oord_Omax(_1182048, c_Orderings_Oord__class_Oless__eq(_1182048)))], (2016 ^ _779327) ^ [_808416, _808418, _808420, _808422] : [-(c_Int_Onat__aux(_808422, _808418) = c_Int_Onat__aux(_808420, _808416)), _808422 = _808420, _808418 = _808416], (45118 ^ _779327) ^ [_1671950, _1671952, _1671954, _1671956, _1671958] : [45120 ^ _779327 : [(45123 ^ _779327) ^ [] : [hAPP(_1671954, 45119 ^ [_1671950, _1671952, _1671954, _1671956, _1671958]) = hAPP(_1671958, 45119 ^ [_1671950, _1671952, _1671954, _1671956, _1671958])], (45121 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671950), 45119 ^ [_1671950, _1671952, _1671954, _1671956, _1671958]), hAPP(c_List_Oset(_1671950), _1671956))))]], -(hAPP(hAPP(c_List_Omap(_1671950, _1671952), _1671954), _1671956) = hAPP(hAPP(c_List_Omap(_1671950, _1671952), _1671958), _1671956))], (49601 ^ _779327) ^ [_1773163, _1773165, _1773167] : [-(hAPP(c_List_Orev(_1773163), hAPP(hAPP(c_List_Otake(_1773163), _1773165), _1773167)) = hAPP(hAPP(c_List_Odrop(_1773163), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773163)), _1773167)), _1773165)), hAPP(c_List_Orev(_1773163), _1773167)))], (18310 ^ _779327) ^ [_1090315, _1090317] : [class_Rings_Ocomm__semiring__1(_1090315), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090315), _1090317), _1090317) = hAPP(hAPP(c_Power_Opower__class_Opower(_1090315), _1090317), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (996 ^ _779327) ^ [_794491, _794493, _794495, _794497, _794499, _794501] : [-(c_Equiv__Relations_Oequiv(_794499, _794495, _794491)), c_Equiv__Relations_Oequiv(_794501, _794497, _794493), _794501 = _794499, _794497 = _794495, _794493 = _794491], (4226 ^ _779327) ^ [_843487, _843489, _843491, _843493, _843495, _843497] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_843497, _843493, _843489) = c_SetInterval_Oord__class_OgreaterThanLessThan(_843495, _843491, _843487)), _843497 = _843495, _843493 = _843491, _843489 = _843487], (34237 ^ _779327) ^ [_1407471, _1407473, _1407475, _1407477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407471), _1407477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407475), _1407473))), -(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), _1407471), _1407473)), 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), _1407475), _1407477)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (43981 ^ _779327) ^ [_1641292, _1641294, _1641296, _1641298, _1641300] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1641292, tc_fun(_1641294, tc_HOL_Obool)), _1641296), hAPP(hAPP(c_COMBS(_1641292, tc_fun(_1641294, tc_HOL_Obool), tc_fun(_1641294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1641294, tc_HOL_Obool), tc_fun(tc_fun(_1641294, tc_HOL_Obool), tc_fun(_1641294, tc_HOL_Obool)), _1641292), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1641294, tc_HOL_Obool))), _1641298)), _1641300)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1641294, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641294, tc_HOL_Obool), hAPP(c_Set_Oimage(_1641292, tc_fun(_1641294, tc_HOL_Obool), _1641298), _1641296))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641294, tc_HOL_Obool), hAPP(c_Set_Oimage(_1641292, tc_fun(_1641294, tc_HOL_Obool), _1641300), _1641296))))], (23347 ^ _779327) ^ [_1184803, _1184805] : [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), _1184803), _1184805))), 23350 ^ _779327 : [(23357 ^ _779327) ^ [] : [-(_1184805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1184803, _1184805) = c_Nitpick_Onat__gcd(_1184805, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1184803, _1184805)))], (23351 ^ _779327) ^ [] : [_1184805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1184803, _1184805) = _1184803)]]], (16469 ^ _779327) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46990 ^ _779327) ^ [_1717222, _1717224, _1717226, _1717228] : [class_Groups_Ocomm__monoid__add(_1717222), hBOOL(hAPP(c_List_Odistinct(_1717224), _1717226)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717222), hAPP(hAPP(c_List_Omap(_1717224, _1717222), _1717228), _1717226)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1717224, _1717222), _1717228), hAPP(c_List_Oset(_1717224), _1717226)))], (49734 ^ _779327) ^ [_1776126, _1776128, _1776130, _1776132, _1776134] : [-(hBOOL(hAPP(_1776126, _1776128))), -(c_List_OtakeWhile(_1776130, _1776126, hAPP(hAPP(c_List_Oappend(_1776130), _1776132), hAPP(hAPP(c_List_Olist_OCons(_1776130), _1776128), _1776134))) = c_List_OtakeWhile(_1776130, _1776126, _1776132))], (31332 ^ _779327) ^ [_1347188, _1347190, _1347192, _1347194, _1347196, _1347198, _1347200, _1347202] : [c_Finite__Set_Ofolding__image__simple(_1347188, _1347190, _1347192, _1347194, _1347196, _1347198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347190), _1347200)), -(hAPP(_1347198, hAPP(hAPP(c_Set_Oinsert(_1347190), _1347202), _1347200)) = hAPP(hAPP(_1347192, hAPP(_1347196, _1347202)), hAPP(_1347198, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347190, tc_HOL_Obool)), _1347200), hAPP(hAPP(c_Set_Oinsert(_1347190), _1347202), c_Orderings_Obot__class_Obot(tc_fun(_1347190, tc_HOL_Obool)))))))], (30429 ^ _779327) ^ [_1326940, _1326942, _1326944, _1326946, _1326948] : [hBOOL(hAPP(hAPP(c_member(_1326940), _1326942), _1326944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326946, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1326940, tc_fun(_1326946, tc_HOL_Obool)), _1326944), _1326948)), hAPP(_1326948, _1326942))))], (13282 ^ _779327) ^ [_1001498, _1001500, _1001502, _1001504, _1001506, _1001508] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1001498), -(_1001500 = c_Groups_Ozero__class_Ozero(_1001498)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001498), _1001502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001498), _1001500), _1001506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001498), _1001504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001498), _1001500), _1001508)), _1001502 = _1001504, -(_1001506 = _1001508)], (51756 ^ _779327) ^ [_1820146, _1820148, _1820150] : [c_Relation_Otrans(_1820146, _1820148), c_Relation_Otrans(_1820146, _1820150), -(c_Relation_Otrans(_1820146, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1820146, _1820146), tc_HOL_Obool)), _1820148), _1820150)))], (37485 ^ _779327) ^ [_1480508, _1480510, _1480512, _1480514, _1480516] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480508, _1480510, _1480512, _1480514, c_Orderings_Obot__class_Obot(tc_fun(_1480508, tc_HOL_Obool))), _1480516)), -(_1480516 = _1480514)], (48199 ^ _779327) ^ [_1743015, _1743017] : [hBOOL(hAPP(c_List_Odistinct(_1743015), _1743017)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1743015, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1743015), tc_fun(_1743015, tc_HOL_Obool)), c_List_Oset(_1743015)), c_Enum_Osublists(_1743015, _1743017)))))], (5324 ^ _779327) ^ [_860572, _860574, _860576, _860578] : [-(c_Product__Type_OPair(_860578, _860574) = c_Product__Type_OPair(_860576, _860572)), _860578 = _860576, _860574 = _860572], (28916 ^ _779327) ^ [_1294780] : [-(hAPP(c_Finite__Set_Ocard(_1294780), c_Orderings_Obot__class_Obot(tc_fun(_1294780, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27022 ^ _779327) ^ [_1256135, _1256137, _1256139, _1256141, _1256143] : [class_Lattices_Olattice(_1256135), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256137, _1256135)), _1256139), _1256141), _1256143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256135), hAPP(_1256139, _1256143)), hAPP(_1256141, _1256143)))], (38537 ^ _779327) ^ [_1505795, _1505797, _1505799, _1505801, _1505803] : [c_Typedef_Otype__definition(_1505795, _1505797, _1505799, _1505801, _1505803), -(hAPP(c_Set_Oimage(_1505797, _1505795, _1505801), _1505803) = c_Orderings_Otop__class_Otop(tc_fun(_1505795, tc_HOL_Obool)))], (46706 ^ _779327) ^ [_1711600, _1711602, _1711604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711600), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711602)), _1711604))), -(hAPP(hAPP(c_List_Oappend(_1711602), hAPP(hAPP(c_List_Otake(_1711602), _1711600), _1711604)), hAPP(hAPP(c_List_Olist_OCons(_1711602), hAPP(c_List_Ohd(_1711602), hAPP(hAPP(c_List_Odrop(_1711602), _1711600), _1711604))), c_List_Olist_ONil(_1711602))) = hAPP(hAPP(c_List_Otake(_1711602), hAPP(c_Nat_OSuc, _1711600)), _1711604))], (47398 ^ _779327) ^ [_1725478, _1725480, _1725482, _1725484] : [47400 ^ _779327 : [(47403 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1725482, 47399 ^ [_1725478, _1725480, _1725482, _1725484])), hAPP(_1725484, 47399 ^ [_1725478, _1725480, _1725482, _1725484])))], (47401 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725478), 47399 ^ [_1725478, _1725480, _1725482, _1725484]), hAPP(c_List_Oset(_1725478), _1725480))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1725478, _1725482, _1725480)), c_List_Olist_Olist__size(_1725478, _1725484, _1725480))))], (4470 ^ _779327) ^ [_847301, _847303, _847305, _847307, _847309, _847311, _847313, _847315] : [-(c_List_Omaps(_847315, _847311, _847307, _847303) = c_List_Omaps(_847313, _847309, _847305, _847301)), _847315 = _847313, _847311 = _847309, _847307 = _847305, _847303 = _847301], (7320 ^ _779327) ^ [_894086, _894088] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894086), _894088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894088), _894086)))], (35850 ^ _779327) ^ [_1444529, _1444531, _1444533] : [class_Lattices_Olattice(_1444529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444529), _1444531)), -(_1444531 = c_Orderings_Obot__class_Obot(tc_fun(_1444529, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444529), _1444533)), -(_1444533 = c_Orderings_Obot__class_Obot(tc_fun(_1444529, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444529, tc_HOL_Obool)), _1444531), _1444533) = c_Orderings_Obot__class_Obot(tc_fun(_1444529, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1444529, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444529, tc_HOL_Obool)), _1444531), _1444533)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1444529), c_Big__Operators_Olattice__class_OSup__fin(_1444529, _1444531)), c_Big__Operators_Olattice__class_OSup__fin(_1444529, _1444533)))], (21148 ^ _779327) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26001 ^ _779327) ^ [_1235563, _1235565] : [26003 ^ _779327 : [(26006 ^ _779327) ^ [] : [hBOOL(hAPP(_1235565, 26002 ^ [_1235563, _1235565]))], (26004 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26002 ^ [_1235563, _1235565]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235563))))]], 26007 ^ _779327 : [(26008 ^ _779327) ^ [_1235716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235716), _1235563)), -(hBOOL(hAPP(_1235565, _1235716)))]]], (18366 ^ _779327) ^ [] : [-(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))))], (21946 ^ _779327) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (1074 ^ _779327) ^ [_795608, _795610, _795612, _795614] : [-(c_Predicate_Osymp(_795612, _795608)), c_Predicate_Osymp(_795614, _795610), _795614 = _795612, _795610 = _795608], (23708 ^ _779327) ^ [_1192086, _1192088] : [-(c_Code__Numeral_Onat__of__aux(_1192086, _1192088) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1192086)), _1192088))], (14459 ^ _779327) ^ [_1023204, _1023206] : [class_Divides_Osemiring__div(_1023204), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1023204), c_Groups_Ozero__class_Ozero(_1023204)), _1023206) = c_Groups_Ozero__class_Ozero(_1023204))], (52203 ^ _779327) ^ [_1829888, _1829890, _1829892] : [-(c_Equiv__Relations_Oequiv(_1829888, _1829890, _1829892)), c_Relation_Orefl__on(_1829888, _1829890, _1829892), c_Relation_Osym(_1829888, _1829892), c_Relation_Otrans(_1829888, _1829892)], (25333 ^ _779327) ^ [_1221041, _1221043] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1221041), _1221043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221041), _1221043)))], (42148 ^ _779327) ^ [_1598339, _1598341, _1598343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598339, _1598339), tc_HOL_Obool)), _1598341), _1598343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598339, _1598339), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1598339, _1598339, _1598339), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1598339, _1598339), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1598339, _1598341)), _1598343)), _1598341)), _1598343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598339, _1598339), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1598339, _1598341)), _1598343)))], (50947 ^ _779327) ^ [_1802371, _1802373, _1802375] : [c_List_Olist__ex1(_1802371, _1802373, _1802375), 50951 ^ _779327 : [(50956 ^ _779327) ^ [_1802617] : [-(_1802617 = 50950 ^ [_1802371, _1802373, _1802375]), hBOOL(hAPP(hAPP(c_member(_1802371), _1802617), hAPP(c_List_Oset(_1802371), _1802375))), hBOOL(hAPP(_1802373, _1802617))], (50954 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1802373, 50950 ^ [_1802371, _1802373, _1802375])))], (50952 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802371), 50950 ^ [_1802371, _1802373, _1802375]), hAPP(c_List_Oset(_1802371), _1802375))))]]], (32620 ^ _779327) ^ [_1372428, _1372430, _1372432] : [class_Orderings_Olinorder(_1372428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372428), _1372430)), -(_1372430 = c_Orderings_Obot__class_Obot(tc_fun(_1372428, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1372428, c_Orderings_Oord__class_Omax(_1372428), hAPP(hAPP(c_Set_Oinsert(_1372428), _1372432), _1372430)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372428), _1372432), c_Big__Operators_Olattice_OSup__fin(_1372428, c_Orderings_Oord__class_Omax(_1372428), _1372430)))], (45945 ^ _779327) ^ [_1693110, _1693112, _1693114, _1693116, _1693118] : [hAPP(hAPP(c_List_Olist_OCons(_1693110), _1693112), _1693114) = hAPP(hAPP(c_List_Oappend(_1693110), _1693116), _1693118), 45950 ^ _779327 : [(45953 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1693110), _1693112), _1693114) = _1693118)], (45951 ^ _779327) ^ [] : [-(_1693116 = c_List_Olist_ONil(_1693110))]], 45955 ^ _779327 : [(45958 ^ _779327) ^ [] : [-(_1693114 = hAPP(hAPP(c_List_Oappend(_1693110), 45954 ^ [_1693110, _1693112, _1693114, _1693116, _1693118]), _1693118))], (45956 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1693110), _1693112), 45954 ^ [_1693110, _1693112, _1693114, _1693116, _1693118]) = _1693116)]]], (43062 ^ _779327) ^ [_1622082, _1622084, _1622086, _1622088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622082, _1622082)), hAPP(hAPP(c_Product__Type_OPair(_1622082, _1622082), _1622084), _1622086)), c_Transitive__Closure_Otrancl(_1622082, _1622088))), 43066 ^ _779327 : [(43069 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622082, _1622082)), hAPP(hAPP(c_Product__Type_OPair(_1622082, _1622082), 43065 ^ [_1622082, _1622084, _1622086, _1622088]), _1622086)), c_Transitive__Closure_Ortrancl(_1622082, _1622088))))], (43067 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622082, _1622082)), hAPP(hAPP(c_Product__Type_OPair(_1622082, _1622082), _1622084), 43065 ^ [_1622082, _1622084, _1622086, _1622088])), _1622088)))]]], (51499 ^ _779327) ^ [_1814570, _1814572, _1814574] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1814570, _1814572, _1814574) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814570)], (35395 ^ _779327) ^ [_1433899, _1433901, _1433903] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433899, tc_HOL_Obool)), _1433901), _1433903) = c_Orderings_Obot__class_Obot(tc_fun(_1433899, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433899, tc_HOL_Obool)), _1433901), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1433899, tc_HOL_Obool)), _1433903))))], (26027 ^ _779327) ^ [_1236060, _1236062] : [26035 ^ _779327 : [(26038 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1236062, 26034 ^ [_1236060, _1236062])))], (26036 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26034 ^ [_1236060, _1236062]), _1236060)))]], 26028 ^ _779327 : [(26029 ^ _779327) ^ [_1236128] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1236128), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1236060))), hBOOL(hAPP(_1236062, _1236128))]]], (2592 ^ _779327) ^ [_817380, _817382, _817384, _817386, _817388, _817390, _817392, _817394, _817396, _817398] : [-(c_Nitpick_Opair__box_Opair__box__case(_817398, _817394, _817390, _817386, _817382) = c_Nitpick_Opair__box_Opair__box__case(_817396, _817392, _817388, _817384, _817380)), _817398 = _817396, _817394 = _817392, _817390 = _817388, _817386 = _817384, _817382 = _817380], (47951 ^ _779327) ^ [_1737305, _1737307, _1737309, _1737311, _1737313] : [c_List_Olist__all2(_1737305, _1737307, _1737309, _1737311, _1737313), 47954 ^ _779327 : [(47957 ^ _779327) ^ [_1737471] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1737305, _1737307)), _1737471), hAPP(c_List_Oset(tc_prod(_1737305, _1737307)), hAPP(hAPP(c_List_Ozip(_1737305, _1737307), _1737311), _1737313)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1737305, _1737307, tc_HOL_Obool), _1737309), _1737471)))], (47955 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737305)), _1737311) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737307)), _1737313))]]], (35139 ^ _779327) ^ [_1427925, _1427927, _1427929, _1427931] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427925, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1427925), _1427927), _1427929)), hAPP(hAPP(c_Set_Oinsert(_1427925), _1427927), _1427931)) = hAPP(hAPP(c_Set_Oinsert(_1427925), _1427927), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427925, tc_HOL_Obool)), _1427929), _1427931)))], (28092 ^ _779327) ^ [_1278902, _1278904] : [class_Complete__Lattice_Ocomplete__lattice(_1278902), c_Orderings_Oorder__class_Omono(_1278902, _1278902, _1278904), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278902), c_Inductive_Ocomplete__lattice__class_Ogfp(_1278902, _1278904)), hAPP(_1278904, c_Inductive_Ocomplete__lattice__class_Ogfp(_1278902, _1278904)))))], (48197 ^ _779327) ^ [_1742881, _1742883, _1742885] : [-(c_Enum_Osublists(_1742881, hAPP(hAPP(c_List_Olist_OCons(_1742881), _1742883), _1742885)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1742881)), tc_List_Olist(tc_List_Olist(_1742881))), c_Enum_Osublists(_1742881, _1742885)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1742881)), tc_List_Olist(tc_List_Olist(_1742881)), tc_List_Olist(tc_List_Olist(_1742881))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1742881)), tc_fun(tc_List_Olist(tc_List_Olist(_1742881)), tc_List_Olist(tc_List_Olist(_1742881))), tc_List_Olist(tc_List_Olist(_1742881))), c_List_Oappend(tc_List_Olist(_1742881))), hAPP(c_List_Omap(tc_List_Olist(_1742881), tc_List_Olist(_1742881)), hAPP(c_List_Olist_OCons(_1742881), _1742883)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1742881))))))], (48425 ^ _779327) ^ [_1747733, _1747735, _1747737, _1747739] : [class_Orderings_Olinorder(_1747733), -(hAPP(c_List_Oset(_1747735), c_List_Olinorder__class_Osort__key(_1747735, _1747733, _1747737, _1747739)) = hAPP(c_List_Oset(_1747735), _1747739))], (656 ^ _779327) ^ [_789379, _789381, _789383, _789385, _789387, _789389] : [-(c_Finite__Set_Ofolding__one(_789387, _789383, _789379)), c_Finite__Set_Ofolding__one(_789389, _789385, _789381), _789389 = _789387, _789385 = _789383, _789381 = _789379], (43724 ^ _779327) ^ [_1635346, _1635348] : [class_Complete__Lattice_Ocomplete__lattice(_1635346), -(c_Complete__Lattice_OInf__class_OInf(_1635346, hAPP(hAPP(c_Set_Oinsert(_1635346), _1635348), c_Orderings_Obot__class_Obot(tc_fun(_1635346, tc_HOL_Obool)))) = _1635348)], (50187 ^ _779327) ^ [_1785735, _1785737, _1785739, _1785741, _1785743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1785735, _1785737)), hAPP(_1785735, _1785739))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785741, _1785741)), hAPP(hAPP(c_Product__Type_OPair(_1785741, _1785741), _1785737), _1785739)), c_List_Omeasures(_1785741, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1785741, tc_Nat_Onat)), _1785735), _1785743)))))], (8628 ^ _779327) ^ [_917501, _917503, _917505] : [class_Rings_Olinordered__semidom(_917501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917503), _917505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917501), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917501), _917503)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917501), _917505))))], (22749 ^ _779327) ^ [_1173181] : [class_Orderings_Oord(_1173181), -(c_Orderings_Oord__class_Omin(_1173181) = c_Orderings_Oord_Omin(_1173181, c_Orderings_Oord__class_Oless__eq(_1173181)))], (46690 ^ _779327) ^ [_1711086, _1711088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711086)), _1711088)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1711086), _1711088) = _1711088)], (10829 ^ _779327) ^ [_955799, _955801] : [class_Int_Onumber__ring(_955799), -(hAPP(c_Int_Onumber__class_Onumber__of(_955799), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _955801)) = hAPP(c_Groups_Ouminus__class_Ouminus(_955799), hAPP(c_Int_Onumber__class_Onumber__of(_955799), _955801)))], (17476 ^ _779327) ^ [_1075982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075982)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075982), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50269 ^ _779327) ^ [_1787664, _1787666] : [class_Enum_Oenum(_1787664), 50272 ^ _779327 : [(50279 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787664), _1787666)), -(hBOOL(hAPP(_1787666, 50282 ^ [_1787664, _1787666])))], (50273 ^ _779327) ^ [] : [50274 ^ _779327 : [(50275 ^ _779327) ^ [_1787766] : [hBOOL(hAPP(_1787666, _1787766))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787664), _1787666)))]]], (33680 ^ _779327) ^ [_1394138, _1394140, _1394142] : [-(c_Wellfounded_Omlex__prod(_1394138, _1394140, _1394142) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1394138), _1394138), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1394138, c_Wellfounded_Oless__than, _1394142)), hAPP(hAPP(c_COMBS(_1394138, _1394138, tc_prod(tc_Nat_Onat, _1394138)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1394138, tc_prod(tc_Nat_Onat, _1394138)), _1394138), c_Product__Type_OPair(tc_Nat_Onat, _1394138)), _1394140)), c_COMBI(_1394138))))], (45876 ^ _779327) ^ [_1691654, _1691656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1691654), _1691656)), -(c_List_Oupto(_1691654, _1691656) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1691654), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1691654), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1691656)))], (34217 ^ _779327) ^ [_1406911] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1406911)) = _1406911)], (23183 ^ _779327) ^ [_1181821, _1181823] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1181821), hAPP(c_Nat_OSuc, _1181823)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1181823), 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)), _1181823)), _1181821))], (38958 ^ _779327) ^ [_1516299, _1516301, _1516303, _1516305] : [_1516299 = c_Orderings_Obot__class_Obot(tc_fun(_1516301, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1516301, _1516303), _1516303, c_Product__Type_Osnd(_1516301, _1516303)), hAPP(hAPP(c_Product__Type_OSigma(_1516301, _1516303), _1516299), hAPP(c_COMBK(tc_fun(_1516303, tc_HOL_Obool), _1516301), _1516305))) = c_Orderings_Obot__class_Obot(tc_fun(_1516303, tc_HOL_Obool)))], (42788 ^ _779327) ^ [_1614493, _1614495, _1614497] : [c_Relation_Ototal__on(_1614493, _1614495, _1614497), 42791 ^ _779327 : [(42792 ^ _779327) ^ [_1614637] : [hBOOL(hAPP(hAPP(c_member(_1614493), _1614637), _1614495)), 42795 ^ _779327 : [(42796 ^ _779327) ^ [_1614777] : [hBOOL(hAPP(hAPP(c_member(_1614493), _1614777), _1614495)), -(_1614637 = _1614777), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614493, _1614493)), hAPP(hAPP(c_Product__Type_OPair(_1614493, _1614493), _1614637), _1614777)), _1614497))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614493, _1614493)), hAPP(hAPP(c_Product__Type_OPair(_1614493, _1614493), _1614777), _1614637)), _1614497)))]]]]], (21005 ^ _779327) ^ [_1139011] : [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), _1139011))), 21008 ^ _779327 : [(21015 ^ _779327) ^ [] : [-(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), _1139011))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1139011)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1139011)), 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), _1139011)))))], (21009 ^ _779327) ^ [] : [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), _1139011)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1139011)) = 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), _1139011))))]]], (17714 ^ _779327) ^ [_1079741, _1079743] : [class_Int_Onumber__ring(_1079741), class_Rings_Olinordered__idom(_1079741), 17721 ^ _779327 : [(17728 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1079743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079741), c_Groups_Oone__class_Oone(_1079741)), hAPP(c_Int_Onumber__class_Onumber__of(_1079741), _1079743))))], (17722 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079741), c_Groups_Oone__class_Oone(_1079741)), hAPP(c_Int_Onumber__class_Onumber__of(_1079741), _1079743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1079743)))]]], (13597 ^ _779327) ^ [_1007210, _1007212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007210), _1007212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1007210), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1007212)))], (6855 ^ _779327) ^ [_886484, _886486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886484), _886486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886484)), _886486)))], (31239 ^ _779327) ^ [_1345237, _1345239, _1345241, _1345243] : [hBOOL(hAPP(hAPP(c_member(_1345237), _1345239), c_SetInterval_Oord_OatLeast(_1345237, _1345241, _1345243))), -(hBOOL(hAPP(hAPP(_1345241, _1345243), _1345239)))], (4624 ^ _779327) ^ [_849820, _849822, _849824, _849826] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_849826, _849822) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_849824, _849820)), _849826 = _849824, _849822 = _849820], (21926 ^ _779327) ^ [_1157269, _1157271, _1157273, _1157275, _1157277] : [hBOOL(hAPP(hAPP(_1157269, _1157271), _1157273)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1157275, _1157277, tc_HOL_Obool), _1157269), hAPP(hAPP(c_Product__Type_OPair(_1157275, _1157277), _1157271), _1157273))))], (12542 ^ _779327) ^ [_988402, _988404, _988406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988404), _988406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988402), _988404)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988402), _988406))))], (15584 ^ _779327) ^ [_1042728] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042728, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1042728)], (45890 ^ _779327) ^ [_1691860, _1691862] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1691860, _1691862) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1691860), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1691862)))], (30858 ^ _779327) ^ [_1337432, _1337434, _1337436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337432)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337434), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1337436)), 30865 ^ _779327 : [(30866 ^ _779327) ^ [_1337640] : [30868 ^ _779327 : [(30874 ^ _779327) ^ [] : [-(_1337640 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30870 ^ [_1337432, _1337434, _1337436, _1337640]), 30867 ^ [_1337432, _1337434, _1337436, _1337640]))], (30872 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30870 ^ [_1337432, _1337434, _1337436, _1337640]), _1337436)))], (30869 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30867 ^ [_1337432, _1337434, _1337436, _1337640]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1337432))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337434), _1337640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337434), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337640), _1337432))))]]], (41437 ^ _779327) ^ [_1582188] : [-(c_Nitpick_Odenom(_1582188) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1582188, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1582188)))], (1788 ^ _779327) ^ [_804665, _804667] : [-(class_Rings_Ozero__neq__one(_804665)), _804667 = _804665, class_Rings_Ozero__neq__one(_804667)], (31147 ^ _779327) ^ [_1343393, _1343395, _1343397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343393)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1343395), _1343397)), 31154 ^ _779327 : [(31155 ^ _779327) ^ [_1343589] : [31157 ^ _779327 : [(31163 ^ _779327) ^ [] : [-(_1343589 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 31159 ^ [_1343393, _1343395, _1343397, _1343589]), 31156 ^ [_1343393, _1343395, _1343397, _1343589]))], (31161 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31159 ^ [_1343393, _1343395, _1343397, _1343589]), _1343397)))], (31158 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31156 ^ [_1343393, _1343395, _1343397, _1343589]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1343393))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343589), _1343395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343589), _1343393)), _1343395)))]]], (9605 ^ _779327) ^ [_934885, _934887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934885)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _934885), _934887)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _934885)), _934887))], (7286 ^ _779327) ^ [_893485, _893487, _893489] : [class_Orderings_Oorder(_893485), class_Orderings_Oorder(_893487), 7297 ^ _779327 : [(7300 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893485), hAPP(_893489, 7295 ^ [_893485, _893487, _893489])), hAPP(_893489, 7296 ^ [_893485, _893487, _893489])))], (7298 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893487), 7295 ^ [_893485, _893487, _893489]), 7296 ^ [_893485, _893487, _893489])))]], -(c_Orderings_Oorder__class_Ostrict__mono(_893487, _893485, _893489))], (13648 ^ _779327) ^ [_1008167, _1008169, _1008171] : [class_Groups_Oordered__comm__monoid__add(_1008167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008167), c_Groups_Ozero__class_Ozero(_1008167)), _1008169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008167), c_Groups_Ozero__class_Ozero(_1008167)), _1008171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008167), c_Groups_Ozero__class_Ozero(_1008167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008167), _1008169), _1008171))))], (24383 ^ _779327) ^ [_1203723, _1203725, _1203727, _1203729] : [class_Rings_Ocomm__semiring__1(_1203723), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203723), _1203725), _1203727)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203723), _1203727), _1203729)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203723), _1203725), _1203729)))], (28334 ^ _779327) ^ [_1283611, _1283613, _1283615] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283611), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283611, tc_HOL_Obool)), _1283613), _1283615)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283611), _1283613)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283611), _1283615))], (50306 ^ _779327) ^ [_1788346, _1788348, _1788350, _1788352, _1788354] : [50307 ^ _779327 : [(50310 ^ _779327) ^ [] : [hBOOL(hAPP(_1788354, hAPP(hAPP(c_List_Ozip(_1788346, _1788350), hAPP(hAPP(c_List_Otake(_1788346), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788346)), _1788348)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788350)), _1788352))), _1788348)), hAPP(hAPP(c_List_Otake(_1788350), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788346)), _1788348)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788350)), _1788352))), _1788352))))], (50308 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788346)), hAPP(hAPP(c_List_Otake(_1788346), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788346)), _1788348)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788350)), _1788352))), _1788348)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788350)), hAPP(hAPP(c_List_Otake(_1788350), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788346)), _1788348)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788350)), _1788352))), _1788352)))]], -(hBOOL(hAPP(_1788354, hAPP(hAPP(c_List_Ozip(_1788346, _1788350), _1788348), _1788352))))], (42589 ^ _779327) ^ [_1609842, _1609844, _1609846, _1609848, _1609850] : [-(hAPP(c_Relation_Oconverse(_1609842, _1609844), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609846, tc_fun(tc_prod(_1609842, _1609844), tc_HOL_Obool)), _1609848), _1609850)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1609846, tc_fun(tc_prod(_1609844, _1609842), tc_HOL_Obool)), _1609848), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1609842, _1609844), tc_HOL_Obool), tc_fun(tc_prod(_1609844, _1609842), tc_HOL_Obool), _1609846), c_Relation_Oconverse(_1609842, _1609844)), _1609850)))], (12293 ^ _779327) ^ [_983826, _983828, _983830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983826), _983828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983826), _983830)), 12300 ^ _779327 : [(12307 ^ _779327) ^ [] : [_983828 = _983830, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983828), _983826) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983830), _983826))], (12301 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983828), _983826) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983830), _983826), -(_983828 = _983830)]]], (12636 ^ _779327) ^ [_990243, _990245] : [class_Int_Onumber__ring(_990243), -(hAPP(c_Int_Onumber__class_Onumber__of(_990243), _990245) = hAPP(c_Int_Oring__1__class_Oof__int(_990243), _990245))], (40376 ^ _779327) ^ [_1555371, _1555373] : [40377 ^ _779327 : [(40378 ^ _779327) ^ [_1555435, _1555437] : [_1555373 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1555371, _1555435), 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)), _1555437)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555371), _1555373)))], (22165 ^ _779327) ^ [_1162450, _1162452] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1162450, _1162452) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1162450, _1162452)))], (4978 ^ _779327) ^ [_855199, _855201, _855203, _855205] : [-(c_HOL_OThe(_855205, _855201) = c_HOL_OThe(_855203, _855199)), _855205 = _855203, _855201 = _855199], (24539 ^ _779327) ^ [_1206522] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206522), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1206522 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52127 ^ _779327) ^ [_1828451, _1828453, _1828455, _1828457] : [c_Relation_Osym(_1828451, _1828453), hBOOL(hAPP(hAPP(c_member(tc_prod(_1828451, _1828451)), hAPP(hAPP(c_Product__Type_OPair(_1828451, _1828451), _1828455), _1828457)), _1828453)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828451, _1828451)), hAPP(hAPP(c_Product__Type_OPair(_1828451, _1828451), _1828457), _1828455)), _1828453)))], (41443 ^ _779327) ^ [_1582329, _1582331, _1582333, _1582335, _1582337, _1582339] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1582329, _1582331), _1582331, tc_prod(_1582333, _1582335), c_Product__Type_Osnd(_1582329, _1582331)), c_Product__Type_Omap__pair(_1582333, _1582329, _1582335, _1582331, _1582337, _1582339)) = hAPP(c_Fun_Ocomp(_1582335, _1582331, tc_prod(_1582333, _1582335), _1582339), c_Product__Type_Osnd(_1582333, _1582335)))], (17568 ^ _779327) ^ [_1077495] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077495))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1077495)))))], (268 ^ _779327) ^ [_783259, _783261, _783263, _783265, _783267, _783269, _783271, _783273, _783275, _783277, _783279, _783281] : [-(c_Equiv__Relations_Ocongruent2(_783279, _783275, _783271, _783267, _783263, _783259)), c_Equiv__Relations_Ocongruent2(_783281, _783277, _783273, _783269, _783265, _783261), _783281 = _783279, _783277 = _783275, _783273 = _783271, _783269 = _783267, _783265 = _783263, _783261 = _783259], (2252 ^ _779327) ^ [_812038, _812040, _812042, _812044, _812046, _812048, _812050, _812052, _812054, _812056] : [-(c_Product__Type_Oprod_Oprod__size(_812056, _812052, _812048, _812044, _812040) = c_Product__Type_Oprod_Oprod__size(_812054, _812050, _812046, _812042, _812038)), _812056 = _812054, _812052 = _812050, _812048 = _812046, _812044 = _812042, _812040 = _812038], (4190 ^ _779327) ^ [_842947, _842949, _842951, _842953] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_842953, _842949) = c_SetInterval_Oord__class_OatLeastLessThan(_842951, _842947)), _842953 = _842951, _842949 = _842947], (34381 ^ _779327) ^ [_1411214, _1411216, _1411218, _1411220, _1411222, _1411224, _1411226] : [c_Equiv__Relations_Oequiv(_1411214, _1411216, _1411218), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411214, tc_HOL_Obool)), _1411220), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411214), _1411216), _1411218))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411214, tc_HOL_Obool)), _1411222), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411214), _1411216), _1411218))), hBOOL(hAPP(hAPP(c_member(_1411214), _1411224), _1411220)), hBOOL(hAPP(hAPP(c_member(_1411214), _1411226), _1411222)), 34400 ^ _779327 : [(34407 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1411214, _1411214)), hAPP(hAPP(c_Product__Type_OPair(_1411214, _1411214), _1411224), _1411226)), _1411218)), -(_1411220 = _1411222)], (34401 ^ _779327) ^ [] : [_1411220 = _1411222, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1411214, _1411214)), hAPP(hAPP(c_Product__Type_OPair(_1411214, _1411214), _1411224), _1411226)), _1411218)))]]], (46802 ^ _779327) ^ [_1713295, _1713297, _1713299] : [hBOOL(hAPP(c_List_Odistinct(_1713295), _1713297)), -(hBOOL(hAPP(c_List_Odistinct(_1713295), c_List_Osublist(_1713295, _1713297, _1713299))))], (44446 ^ _779327) ^ [_1651867, _1651869, _1651871, _1651873, _1651875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651867), tc_List_Olist(_1651867))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651867), tc_List_Olist(_1651867)), _1651869), _1651871)), hAPP(c_List_Olexn(_1651867, _1651873), _1651875))), 44449 ^ _779327 : [(44452 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651867)), _1651871) = _1651875)], (44450 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651867)), _1651869) = _1651875)]]], (22805 ^ _779327) ^ [_1174469, _1174471, _1174473] : [class_Orderings_Olinorder(_1174469), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174469), _1174471), _1174473) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174469), _1174473), _1174471))], (11277 ^ _779327) ^ [_964348, _964350, _964352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964348), _964350)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964350), _964348)), _964352) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964350), _964352)), _964348))], (26794 ^ _779327) ^ [_1251189, _1251191, _1251193] : [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), _1251189), _1251191))), -(hBOOL(hAPP(hAPP(_1251193, _1251189), _1251191))), 26801 ^ _779327 : [(26804 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 26799 ^ [_1251189, _1251191, _1251193]), 26800 ^ [_1251189, _1251191, _1251193])), -(hBOOL(hAPP(hAPP(_1251193, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26799 ^ [_1251189, _1251191, _1251193]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 26800 ^ [_1251189, _1251191, _1251193])))], (26810 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1251193, 26799 ^ [_1251189, _1251191, _1251193]), 26800 ^ [_1251189, _1251191, _1251193]))], (26802 ^ _779327) ^ [] : [-(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), 26799 ^ [_1251189, _1251191, _1251193]), 26800 ^ [_1251189, _1251191, _1251193]))))]]], (29452 ^ _779327) ^ [_1305151, _1305153, _1305155, _1305157] : [_1305151 = _1305153, 29457 ^ _779327 : [(29460 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305155), _1305157), _1305153)))], (29458 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305155), _1305157), _1305151)))]], 29461 ^ _779327 : [(29464 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1305155), _1305157), _1305153))], (29462 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1305155), _1305157), _1305151))]]], (6815 ^ _779327) ^ [_885820, _885822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _885820)), _885822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885820), _885822)))], (29921 ^ _779327) ^ [_1314202, _1314204, _1314206] : [_1314204 = _1314206, -(hBOOL(hAPP(hAPP(c_member(_1314202), _1314204), hAPP(c_fequal, _1314206))))], (49093 ^ _779327) ^ [_1762937, _1762939, _1762941] : [class_Orderings_Olinorder(_1762937), c_List_Olinorder__class_Osorted(_1762937, _1762939), hBOOL(hAPP(c_List_Odistinct(_1762937), _1762939)), c_List_Olinorder__class_Osorted(_1762937, _1762941), hBOOL(hAPP(c_List_Odistinct(_1762937), _1762941)), hAPP(c_List_Oset(_1762937), _1762939) = hAPP(c_List_Oset(_1762937), _1762941), -(_1762939 = _1762941)], (40351 ^ _779327) ^ [_1554515, _1554517, _1554519, _1554521, _1554523, _1554525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554515), _1554517)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554519), _1554521)), 40361 ^ _779327 : [(40364 ^ _779327) ^ [] : [hAPP(c_Finite__Set_Ocard(_1554515), hAPP(c_Set_OCollect(_1554515), hAPP(hAPP(c_COMBS(_1554515, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554515), c_fconj), hAPP(hAPP(c_COMBC(_1554515, tc_fun(_1554515, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554515)), _1554517))), hAPP(hAPP(c_COMBC(_1554515, _1554519, tc_HOL_Obool), _1554523), 40360 ^ [_1554515, _1554517, _1554519, _1554521, _1554523, _1554525])))) = hAPP(_1554525, 40360 ^ [_1554515, _1554517, _1554519, _1554521, _1554523, _1554525])], (40362 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554519), 40360 ^ [_1554515, _1554517, _1554519, _1554521, _1554523, _1554525]), _1554521)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554515, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1554519, tc_HOL_Obool), tc_Nat_Onat, _1554515), c_Finite__Set_Ocard(_1554519)), hAPP(hAPP(c_COMBB(tc_fun(_1554519, tc_HOL_Obool), tc_fun(_1554519, tc_HOL_Obool), _1554515), c_Set_OCollect(_1554519)), hAPP(hAPP(c_COMBB(tc_fun(_1554519, tc_HOL_Obool), tc_fun(_1554519, tc_HOL_Obool), _1554515), hAPP(c_COMBS(_1554519, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554519), c_fconj), hAPP(hAPP(c_COMBC(_1554519, tc_fun(_1554519, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554519)), _1554521)))), _1554523)))), _1554517) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554519, tc_Nat_Onat), _1554525), _1554521))], (1818 ^ _779327) ^ [_805040, _805042] : [-(class_Groups_Omonoid__mult(_805040)), _805042 = _805040, class_Groups_Omonoid__mult(_805042)], (18212 ^ _779327) ^ [_1088620, _1088622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088620), _1088622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1088620)), c_Int_OBit0(_1088622))))], (16463 ^ _779327) ^ [_1058415] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1058415)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1058415))], (11491 ^ _779327) ^ [_969077, _969079] : [-(_969077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969077), _969079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969077), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _969079)))], (52960 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (11209 ^ _779327) ^ [_963056, _963058, _963060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963060), _963058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963056), _963058)), _963060)))], (34201 ^ _779327) ^ [_1406432, _1406434, _1406436, _1406438, _1406440] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1406436, _1406432)), hAPP(hAPP(c_Product__Type_OPair(_1406436, _1406432), _1406440), _1406434)), _1406438)), -(hBOOL(hAPP(hAPP(c_member(_1406432), _1406434), hAPP(c_Relation_OImage(_1406436, _1406432, _1406438), hAPP(hAPP(c_Set_Oinsert(_1406436), _1406440), c_Orderings_Obot__class_Obot(tc_fun(_1406436, tc_HOL_Obool)))))))], (3152 ^ _779327) ^ [_826660, _826662] : [_826662 = _826660, -(c_Int_OBit1(_826662) = c_Int_OBit1(_826660))], (38389 ^ _779327) ^ [_1502004, _1502006, _1502008, _1502010, _1502012] : [hBOOL(hAPP(hAPP(c_member(_1502004), _1502006), hAPP(c_Set_Ovimage(_1502004, _1502008, _1502010), _1502012))), -(hBOOL(hAPP(hAPP(c_member(_1502008), hAPP(_1502010, _1502006)), _1502012)))], (26657 ^ _779327) ^ [_1248567, _1248569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1248567), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1248569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248569), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1248567))))), -(_1248567 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1248569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248569), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1248567))))], (51965 ^ _779327) ^ [_1825380, _1825382, _1825384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1825380, _1825380), tc_HOL_Obool)), _1825382), _1825384)), c_Relation_Oantisym(_1825380, _1825384), -(c_Relation_Oantisym(_1825380, _1825382))], (43973 ^ _779327) ^ [_1641125] : [class_Complete__Lattice_Ocomplete__lattice(_1641125), -(c_Complete__Lattice_OSup__class_OSup(_1641125, c_Orderings_Otop__class_Otop(tc_fun(_1641125, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1641125))], (17964 ^ _779327) ^ [_1084258, _1084260] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1084258)), c_Int_OBit0(_1084260)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1084258), _1084260)))], (3870 ^ _779327) ^ [_838053, _838055, _838057, _838059] : [-(c_Nitpick_Ocard_H(_838059, _838055) = c_Nitpick_Ocard_H(_838057, _838053)), _838059 = _838057, _838055 = _838053], (2700 ^ _779327) ^ [_819164, _819166, _819168, _819170, _819172, _819174, _819176, _819178, _819180, _819182, _819184, _819186, _819188, _819190] : [-(c_New__Random__Sequence_Opos__decr__bind(_819190, _819186, _819182, _819178, _819174, _819170, _819166) = c_New__Random__Sequence_Opos__decr__bind(_819188, _819184, _819180, _819176, _819172, _819168, _819164)), _819190 = _819188, _819186 = _819184, _819182 = _819180, _819178 = _819176, _819174 = _819172, _819170 = _819168, _819166 = _819164], (7674 ^ _779327) ^ [_900191, _900193, _900195] : [class_Rings_Olinordered__ring__strict(_900191), 7677 ^ _779327 : [(7692 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900191), _900193), _900195)), c_Groups_Ozero__class_Ozero(_900191)))), 7693 ^ _779327 : [(7700 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), _900193), c_Groups_Ozero__class_Ozero(_900191))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), c_Groups_Ozero__class_Ozero(_900191)), _900195))], (7694 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), c_Groups_Ozero__class_Ozero(_900191)), _900193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), _900195), c_Groups_Ozero__class_Ozero(_900191)))]]], (7678 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900191), _900193), _900195)), c_Groups_Ozero__class_Ozero(_900191))), 7683 ^ _779327 : [(7686 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), _900195), c_Groups_Ozero__class_Ozero(_900191))))], (7684 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), c_Groups_Ozero__class_Ozero(_900191)), _900193)))]], 7687 ^ _779327 : [(7690 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), c_Groups_Ozero__class_Ozero(_900191)), _900195)))], (7688 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900191), _900193), c_Groups_Ozero__class_Ozero(_900191))))]]]]], (42761 ^ _779327) ^ [_1613731, _1613733, _1613735] : [c_Relation_Osingle__valued(_1613731, _1613733, _1613735), 42764 ^ _779327 : [(42765 ^ _779327) ^ [_1613852, _1613854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613731, _1613733)), hAPP(hAPP(c_Product__Type_OPair(_1613731, _1613733), _1613854), _1613852)), _1613735)), 42768 ^ _779327 : [(42769 ^ _779327) ^ [_1613978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613731, _1613733)), hAPP(hAPP(c_Product__Type_OPair(_1613731, _1613733), _1613854), _1613978)), _1613735)), -(_1613852 = _1613978)]]]]], (43991 ^ _779327) ^ [_1641642, _1641644, _1641646] : [class_Complete__Lattice_Ocomplete__lattice(_1641642), hBOOL(hAPP(c_Finite__Set_Ofinite(_1641642), _1641644)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1641642), _1641646), c_Complete__Lattice_OSup__class_OSup(_1641642, _1641644)) = hAPP(hAPP(c_Finite__Set_Ofold(_1641642, _1641642, c_Lattices_Osemilattice__sup__class_Osup(_1641642)), _1641646), _1641644))], (31417 ^ _779327) ^ [_1349218, _1349220, _1349222] : [class_Orderings_Owellorder(_1349218), hBOOL(hAPP(_1349220, _1349222)), -(hBOOL(hAPP(_1349220, c_Orderings_Oord__class_OLeast(_1349218, _1349220))))], (2788 ^ _779327) ^ [_820674, _820676, _820678, _820680, _820682, _820684, _820686, _820688, _820690, _820692, _820694, _820696, _820698, _820700] : [-(c_New__Random__Sequence_Oneg__decr__bind(_820700, _820696, _820692, _820688, _820684, _820680, _820676) = c_New__Random__Sequence_Oneg__decr__bind(_820698, _820694, _820690, _820686, _820682, _820678, _820674)), _820700 = _820698, _820696 = _820694, _820692 = _820690, _820688 = _820686, _820684 = _820682, _820680 = _820678, _820676 = _820674], (23261 ^ _779327) ^ [_1183076, _1183078, _1183080, _1183082, _1183084] : [_1183076 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1183078, _1183080, _1183076, _1183082), _1183084) = hAPP(c_Product__Type_OPair(_1183078, _1183080), _1183084))], (45751 ^ _779327) ^ [_1688320, _1688322, _1688324, _1688326, _1688328] : [class_Groups_Oab__group__add(_1688320), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1688320), hAPP(hAPP(c_List_Omap(_1688322, _1688320), hAPP(hAPP(c_COMBS(_1688322, _1688320, _1688320), hAPP(hAPP(c_COMBB(_1688320, tc_fun(_1688320, _1688320), _1688322), c_Groups_Ominus__class_Ominus(_1688320)), _1688324)), _1688326)), _1688328)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1688320), hAPP(c_List_Omonoid__add__class_Olistsum(_1688320), hAPP(hAPP(c_List_Omap(_1688322, _1688320), _1688324), _1688328))), hAPP(c_List_Omonoid__add__class_Olistsum(_1688320), hAPP(hAPP(c_List_Omap(_1688322, _1688320), _1688326), _1688328))))], (47360 ^ _779327) ^ [_1724749, _1724751] : [-(_1724749 = c_List_Olist_ONil(_1724751)), -(c_List_Olast(_1724751, _1724749) = hAPP(hAPP(c_List_Onth(_1724751), _1724749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724751)), _1724749)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9801 ^ _779327) ^ [_938165, _938167] : [class_Groups_Omonoid__mult(_938165), -(hAPP(hAPP(c_Power_Opower__class_Opower(_938165), c_Groups_Oone__class_Oone(_938165)), _938167) = c_Groups_Oone__class_Oone(_938165))], (35293 ^ _779327) ^ [_1431684, _1431686, _1431688] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431684, tc_HOL_Obool)), _1431686), _1431688) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431684, tc_HOL_Obool)), _1431686), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431684, tc_HOL_Obool)), _1431688)))], (3542 ^ _779327) ^ [_832841, _832843, _832845, _832847] : [-(c_New__DSequence_Opos__single(_832847, _832843) = c_New__DSequence_Opos__single(_832845, _832841)), _832847 = _832845, _832843 = _832841], (39844 ^ _779327) ^ [_1535978, _1535980, _1535982] : [-(hBOOL(hAPP(_1535978, _1535980))), -(hAPP(c_Set_OCollect(_1535982), hAPP(hAPP(c_COMBS(_1535982, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535982), c_fconj), hAPP(c_fequal, _1535980))), _1535978)) = c_Orderings_Obot__class_Obot(tc_fun(_1535982, tc_HOL_Obool)))], (17990 ^ _779327) ^ [_1084737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084737)))], (20185 ^ _779327) ^ [_1123626, _1123628, _1123630, _1123632] : [class_Fields_Olinordered__field(_1123626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123626), _1123628), c_Groups_Ozero__class_Ozero(_1123626))), 20192 ^ _779327 : [(20199 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123626), _1123632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123626), _1123630), _1123628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123626), _1123630), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123626), _1123632), _1123628))))], (20193 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123626), _1123630), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123626), _1123632), _1123628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123626), _1123632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123626), _1123630), _1123628))))]]], (39930 ^ _779327) ^ [_1539061, _1539063, _1539065, _1539067, _1539069, _1539071] : [class_Groups_Ocomm__monoid__add(_1539061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539063), _1539065)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539063, _1539061), hAPP(hAPP(c_COMBS(_1539063, _1539061, _1539061), hAPP(hAPP(c_COMBS(_1539063, _1539061, tc_fun(_1539061, _1539061)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1539061, tc_fun(_1539061, _1539061)), _1539063), c_If(_1539061)), _1539067)), _1539069)), _1539071)), _1539065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1539061), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539063, _1539061), _1539069), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539063, tc_HOL_Obool)), _1539065), hAPP(c_Set_OCollect(_1539063), _1539067)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539063, _1539061), _1539071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539063, tc_HOL_Obool)), _1539065), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1539063, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1539063), _1539067))))))], (23873 ^ _779327) ^ [_1195349, _1195351, _1195353] : [class_Rings_Olinordered__idom(_1195349), 23876 ^ _779327 : [(23883 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195349), _1195351), _1195353)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195349), hAPP(c_Groups_Oabs__class_Oabs(_1195349), _1195351)), _1195353)))], (23877 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195349), hAPP(c_Groups_Oabs__class_Oabs(_1195349), _1195351)), _1195353)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195349), _1195351), _1195353)))]]], (12519 ^ _779327) ^ [_987957, _987959] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987959), _987957))))], (12233 ^ _779327) ^ [_982829] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _982829)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _982829)], (25524 ^ _779327) ^ [_1225285, _1225287, _1225289, _1225291, _1225293] : [class_Rings_Osemiring__0(_1225285), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225285), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225287, _1225285), _1225289), _1225291)), _1225293) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225287, _1225285), hAPP(hAPP(c_COMBC(_1225287, _1225285, _1225285), hAPP(hAPP(c_COMBB(_1225285, tc_fun(_1225285, _1225285), _1225287), c_Groups_Otimes__class_Otimes(_1225285)), _1225289)), _1225293)), _1225291))], (13676 ^ _779327) ^ [_1008677, _1008679, _1008681, _1008683] : [class_Groups_Oordered__comm__monoid__add(_1008677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008677), c_Groups_Ozero__class_Ozero(_1008677)), _1008679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008677), _1008681), _1008683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008677), _1008681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008677), _1008679), _1008683))))], (22353 ^ _779327) ^ [_1165959, _1165961, _1165963] : [class_Orderings_Olinorder(_1165959), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165959), _1165961), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165959), _1165961), _1165963)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1165959), _1165961), _1165963))], (35475 ^ _779327) ^ [_1435591, _1435593, _1435595, _1435597] : [class_Orderings_Oorder(_1435591), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435591, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1435591, _1435593, _1435595)), c_SetInterval_Oord__class_OatLeastAtMost(_1435591, _1435595, _1435597)) = c_Orderings_Obot__class_Obot(tc_fun(_1435591, tc_HOL_Obool)))], (2500 ^ _779327) ^ [_815916, _815918, _815920, _815922, _815924, _815926, _815928, _815930, _815932, _815934] : [-(c_Nitpick_Opair__box_Opair__box__size(_815934, _815930, _815926, _815922, _815918) = c_Nitpick_Opair__box_Opair__box__size(_815932, _815928, _815924, _815920, _815916)), _815934 = _815932, _815930 = _815928, _815926 = _815924, _815922 = _815920, _815918 = _815916], (41103 ^ _779327) ^ [_1574828, _1574830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1574828, _1574828)), _1574830)), c_Wellfounded_Oacyclic(_1574828, _1574830), -(c_Wellfounded_Owf(_1574828, _1574830))], (3588 ^ _779327) ^ [_833530, _833532] : [_833532 = _833530, -(c_HOL_OAll(_833532) = c_HOL_OAll(_833530))], (52712 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52950 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (16489 ^ _779327) ^ [_1058789, _1058791] : [class_Groups_Oordered__ab__group__add__abs(_1058789), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058789), c_Groups_Ozero__class_Ozero(_1058789)), hAPP(c_Groups_Oabs__class_Oabs(_1058789), _1058791))))], (52089 ^ _779327) ^ [_1827895, _1827897] : [c_Relation_Osym(_1827895, _1827897), -(hAPP(c_Relation_Oconverse(_1827895, _1827895), _1827897) = _1827897)], (2460 ^ _779327) ^ [_815312, _815314] : [_815314 = _815312, -(c_Nitpick_Ofrac(_815314) = c_Nitpick_Ofrac(_815312))], (22761 ^ _779327) ^ [_1173460, _1173462, _1173464, _1173466, _1173468, _1173470, _1173472] : [-(hAPP(c_Product__Type_Oapsnd(_1173460, _1173462, _1173464, _1173466), hAPP(c_Product__Type_Oapfst(_1173468, _1173464, _1173460, _1173470), _1173472)) = hAPP(hAPP(c_Product__Type_OPair(_1173464, _1173462), hAPP(_1173470, hAPP(c_Product__Type_Ofst(_1173468, _1173460), _1173472))), hAPP(_1173466, hAPP(c_Product__Type_Osnd(_1173468, _1173460), _1173472))))], (8040 ^ _779327) ^ [_906957, _906959, _906961] : [class_Rings_Olinordered__semiring__strict(_906957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906957), c_Groups_Ozero__class_Ozero(_906957)), _906959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906957), _906961), c_Groups_Ozero__class_Ozero(_906957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906957), _906959), _906961)), c_Groups_Ozero__class_Ozero(_906957))))], (42200 ^ _779327) ^ [_1600359, _1600361, _1600363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600359, _1600359), tc_HOL_Obool)), c_Relation_OId(_1600359)), _1600361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600359, _1600359), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1600359, _1600359, _1600359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1600359, _1600359), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1600359, _1600363)), _1600361)), _1600363)), _1600361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600359, _1600359), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1600359, _1600363)), _1600361)))], (10807 ^ _779327) ^ [_955337, _955339] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955337), _955339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955339), _955337))], (30153 ^ _779327) ^ [_1321342, _1321344, _1321346] : [hBOOL(hAPP(hAPP(c_member(_1321342), _1321344), hAPP(hAPP(c_Set_Oinsert(_1321342), _1321346), c_Orderings_Obot__class_Obot(tc_fun(_1321342, tc_HOL_Obool))))), -(_1321344 = _1321346)], (52958 ^ _779327) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (21648 ^ _779327) ^ [_1152466, _1152468, _1152470, _1152472, _1152474, _1152476] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152466, _1152468), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152470), _1152472))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152466, _1152468), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152474), _1152476))), -(_1152468 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1152472 = _1152476)], (23101 ^ _779327) ^ [_1179900, _1179902, _1179904, _1179906, _1179908] : [class_Orderings_Olinorder(_1179900), class_Orderings_Olinorder(_1179902), c_Orderings_Oorder__class_Omono(_1179902, _1179900, _1179904), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179900), hAPP(_1179904, _1179906)), hAPP(_1179904, _1179908)) = hAPP(_1179904, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179902), _1179906), _1179908)))], (45155 ^ _779327) ^ [_1672858, _1672860, _1672862, _1672864] : [hBOOL(hAPP(hAPP(c_member(_1672858), _1672860), hAPP(c_List_Oset(_1672858), c_List_Osublist(_1672858, _1672862, _1672864)))), -(hBOOL(hAPP(hAPP(c_member(_1672858), _1672860), hAPP(c_List_Oset(_1672858), _1672862))))], (52119 ^ _779327) ^ [_1828340, _1828342] : [-(c_Relation_Osym(_1828340, c_Relation_OId__on(_1828340, _1828342)))], (32328 ^ _779327) ^ [_1366892, _1366894] : [class_Orderings_Olinorder(_1366892), -(c_Big__Operators_Olinorder__class_OMin(_1366892, hAPP(hAPP(c_Set_Oinsert(_1366892), _1366894), c_Orderings_Obot__class_Obot(tc_fun(_1366892, tc_HOL_Obool)))) = _1366894)], (17334 ^ _779327) ^ [_1073448, _1073450] : [class_Int_Onumber__ring(_1073448), 17337 ^ _779327 : [(17344 ^ _779327) ^ [] : [c_Int_Oiszero(_1073448, hAPP(c_Int_Onumber__class_Onumber__of(_1073448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073450), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1073448), _1073450) = c_Groups_Oone__class_Oone(_1073448))], (17338 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1073448), _1073450) = c_Groups_Oone__class_Oone(_1073448), -(c_Int_Oiszero(_1073448, hAPP(c_Int_Onumber__class_Onumber__of(_1073448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1073450), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (28594 ^ _779327) ^ [_1288784, _1288786] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288784, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1288784, tc_HOL_Obool))), _1288786) = c_Orderings_Obot__class_Obot(tc_fun(_1288784, tc_HOL_Obool)))], (24373 ^ _779327) ^ [_1203572, _1203574] : [-(_1203572 = _1203574), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203572), _1203574)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203574), _1203572))], (40247 ^ _779327) ^ [_1552121, _1552123] : [-(hAPP(c_Fun_Oid(_1552121), _1552123) = _1552123)], (13615 ^ _779327) ^ [_1007572, _1007574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1007572), _1007574)), -(_1007574 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1007572), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 13618 ^ [_1007572, _1007574])))], (27126 ^ _779327) ^ [_1258036, _1258038, _1258040, _1258042] : [class_Lattices_Osemilattice__sup(_1258036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258036), _1258038), _1258040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258036), _1258038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258036), _1258042), _1258040))))], (41245 ^ _779327) ^ [_1577844, _1577846, _1577848, _1577850, _1577852, _1577854, _1577856, _1577858, _1577860] : [hAPP(c_Fun_Ocomp(_1577844, _1577846, _1577848, _1577850), _1577852) = hAPP(c_Fun_Ocomp(_1577854, _1577846, _1577848, _1577856), _1577858), -(hAPP(_1577850, hAPP(_1577852, _1577860)) = hAPP(_1577856, hAPP(_1577858, _1577860)))], (34371 ^ _779327) ^ [_1410953, _1410955, _1410957, _1410959, _1410961] : [c_Equiv__Relations_Oequiv(_1410953, _1410955, _1410957), hBOOL(hAPP(hAPP(c_member(tc_prod(_1410953, _1410953)), hAPP(hAPP(c_Product__Type_OPair(_1410953, _1410953), _1410959), _1410961)), _1410957)), -(hAPP(c_Relation_OImage(_1410953, _1410953, _1410957), hAPP(hAPP(c_Set_Oinsert(_1410953), _1410959), c_Orderings_Obot__class_Obot(tc_fun(_1410953, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1410953, _1410953, _1410957), hAPP(hAPP(c_Set_Oinsert(_1410953), _1410961), c_Orderings_Obot__class_Obot(tc_fun(_1410953, tc_HOL_Obool)))))], (34164 ^ _779327) ^ [_1405415, _1405417, _1405419, _1405421, _1405423, _1405425] : [hBOOL(hAPP(hAPP(c_member(_1405415), _1405417), _1405419)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1405415, _1405421)), hAPP(hAPP(c_Product__Type_OPair(_1405415, _1405421), _1405417), _1405423)), _1405425)), -(hBOOL(hAPP(hAPP(c_member(_1405421), _1405423), hAPP(c_Relation_OImage(_1405415, _1405421, _1405425), _1405419))))], (14439 ^ _779327) ^ [_1022831, _1022833, _1022835] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022831, tc_HOL_Obool)), _1022833) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022831, tc_HOL_Obool)), _1022835), -(_1022833 = _1022835)], (5601 ^ _779327) ^ [_867489, _867491, _867493] : [c_Hoare__Mirabelle_Ohoare__valids(_867489, _867491, _867493), 5604 ^ _779327 : [(5605 ^ _779327) ^ [_867598] : [5607 ^ _779327 : [(5610 ^ _779327) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_867489, _867598, 5606 ^ [_867489, _867491, _867493, _867598])], (5608 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_867489)), 5606 ^ [_867489, _867491, _867493, _867598]), _867491)))]], 5611 ^ _779327 : [(5612 ^ _779327) ^ [_867770] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_867489)), _867770), _867493)), -(c_Hoare__Mirabelle_Otriple__valid(_867489, _867598, _867770))]]]]], (1378 ^ _779327) ^ [_799540, _799542] : [-(class_Rings_Oidom(_799540)), _799542 = _799540, class_Rings_Oidom(_799542)], (39918 ^ _779327) ^ [_1538547, _1538549, _1538551, _1538553, _1538555, _1538557] : [class_Groups_Ocomm__monoid__add(_1538547), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538549), _1538551)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538549, _1538547), _1538553), _1538551) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538555, _1538547), hAPP(hAPP(c_COMBB(tc_fun(_1538549, tc_HOL_Obool), _1538547, _1538555), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538549, _1538547), _1538553)), hAPP(hAPP(c_COMBB(tc_fun(_1538549, tc_HOL_Obool), tc_fun(_1538549, tc_HOL_Obool), _1538555), c_Set_OCollect(_1538549)), hAPP(hAPP(c_COMBB(tc_fun(_1538549, tc_HOL_Obool), tc_fun(_1538549, tc_HOL_Obool), _1538555), hAPP(c_COMBS(_1538549, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538549), c_fconj), hAPP(hAPP(c_COMBC(_1538549, tc_fun(_1538549, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538549)), _1538551)))), hAPP(c_COMBC(_1538549, _1538555, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1538555, tc_fun(_1538555, tc_HOL_Obool), _1538549), c_fequal), _1538557)))))), hAPP(c_Set_Oimage(_1538549, _1538555, _1538557), _1538551)))], (52770 ^ _779327) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (29302 ^ _779327) ^ [_1301785, _1301787, _1301789, _1301791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1301785), _1301787)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301789), _1301791)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1301785, _1301789)), c_Sum__Type_OPlus(_1301785, _1301789, _1301787, _1301791)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1301785), _1301787)), hAPP(c_Finite__Set_Ocard(_1301789), _1301791)))], (22955 ^ _779327) ^ [_1177070, _1177072, _1177074] : [class_Orderings_Olinorder(_1177070), 22958 ^ _779327 : [(22965 ^ _779327) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177070), _1177072), _1177074) = _1177074, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177070), _1177072), _1177074)))], (22959 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177070), _1177072), _1177074)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177070), _1177072), _1177074) = _1177074)]]], (1238 ^ _779327) ^ [_797790, _797792] : [-(class_Rings_Olinordered__ring(_797790)), _797792 = _797790, class_Rings_Olinordered__ring(_797792)], (45552 ^ _779327) ^ [_1682663, _1682665] : [-(_1682665 = c_List_Olist_ONil(_1682663)), -(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(_1682663)), _1682665))))], (52678 ^ _779327) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (1598 ^ _779327) ^ [_802290, _802292] : [-(class_Groups_Oordered__ab__semigroup__add(_802290)), _802292 = _802290, class_Groups_Oordered__ab__semigroup__add(_802292)], (17630 ^ _779327) ^ [_1078511] : [class_Int_Onumber__ring(_1078511), -(c_Groups_Oone__class_Oone(_1078511) = hAPP(c_Int_Onumber__class_Onumber__of(_1078511), c_Int_OBit1(c_Int_OPls)))], (4126 ^ _779327) ^ [_841957, _841959] : [_841959 = _841957, -(c_Finite__Set_Ocard(_841959) = c_Finite__Set_Ocard(_841957))], (29663 ^ _779327) ^ [_1309356, _1309358] : [29664 ^ _779327 : [(29665 ^ _779327) ^ [_1309409] : [hBOOL(hAPP(hAPP(c_member(_1309356), _1309409), _1309358))]], _1309358 = c_Orderings_Obot__class_Obot(tc_fun(_1309356, tc_HOL_Obool))], (45422 ^ _779327) ^ [_1680017, _1680019, _1680021, _1680023] : [hAPP(hAPP(c_List_Omap(_1680017, _1680019), _1680021), _1680023) = c_List_Olist_ONil(_1680019), -(_1680023 = c_List_Olist_ONil(_1680017))], (49689 ^ _779327) ^ [_1775159, _1775161, _1775163] : [class_Orderings_Olinorder(_1775159), c_List_Olinorder__class_Osorted(_1775159, _1775161), -(c_List_Olinorder__class_Osorted(_1775159, c_List_OtakeWhile(_1775159, _1775163, _1775161)))], (5668 ^ _779327) ^ [_868893] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_868893, tc_HOL_Obool) = c_Set_OBall(_868893))], (38369 ^ _779327) ^ [_1501533, _1501535] : [-(hAPP(c_Set_Ovimage(_1501533, _1501533, c_COMBI(_1501533)), _1501535) = _1501535)], (49069 ^ _779327) ^ [_1762612, _1762614] : [class_Orderings_Olinorder(_1762612), -(_1762614 = c_List_Olist_ONil(_1762612)), c_List_Olinorder__class_Osorted(_1762612, _1762614), -(c_List_Olinorder__class_Osorted(_1762612, c_List_Obutlast(_1762612, _1762614)))], (38065 ^ _779327) ^ [_1492453, _1492455, _1492457, _1492459, _1492461] : [c_Fun_Oinj__on(_1492453, _1492455, _1492457, c_Orderings_Otop__class_Otop(tc_fun(_1492453, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1492453, _1492455, _1492457), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492453, tc_HOL_Obool)), _1492459), _1492461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492455, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492453, _1492455, _1492457), _1492459)), hAPP(c_Set_Oimage(_1492453, _1492455, _1492457), _1492461)))], (23564 ^ _779327) ^ [_1189716, _1189718] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1189716), _1189718) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1189716, 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)))), _1189718))))], (25111 ^ _779327) ^ [_1217101, _1217103] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1217101))), _1217103)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217101), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217103))))], (35956 ^ _779327) ^ [_1446527, _1446529, _1446531] : [class_Orderings_Olinorder(_1446527), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446527), _1446529)), -(_1446529 = c_Orderings_Obot__class_Obot(tc_fun(_1446527, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446527), _1446531)), -(_1446531 = c_Orderings_Obot__class_Obot(tc_fun(_1446527, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446527, tc_HOL_Obool)), _1446529), _1446531) = c_Orderings_Obot__class_Obot(tc_fun(_1446527, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1446527, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446527, tc_HOL_Obool)), _1446529), _1446531)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446527), c_Big__Operators_Olinorder__class_OMax(_1446527, _1446529)), c_Big__Operators_Olinorder__class_OMax(_1446527, _1446531)))], (23899 ^ _779327) ^ [_1195782, _1195784, _1195786, _1195788] : [class_Divides_Osemiring__div(_1195782), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), _1195784), _1195786)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), _1195784), _1195788)), 23910 ^ _779327 : [(23917 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), _1195786), _1195788)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1195782), _1195786), _1195784)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1195782), _1195788), _1195784))))], (23911 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1195782), _1195786), _1195784)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1195782), _1195788), _1195784))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1195782), _1195786), _1195788)))]]], (39969 ^ _779327) ^ [_1540343, _1540345, _1540347] : [class_Orderings_Olinorder(_1540343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540343), _1540345)), -(_1540345 = c_Orderings_Obot__class_Obot(tc_fun(_1540343, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1540343), _1540347), c_Big__Operators_Olattice_OInf__fin(_1540343, c_Orderings_Oord__class_Omin(_1540343), _1540345)) = c_Big__Operators_Olattice_OInf__fin(_1540343, c_Orderings_Oord__class_Omin(_1540343), hAPP(c_Set_OCollect(_1540343), hAPP(hAPP(c_COMBB(tc_fun(_1540343, tc_HOL_Obool), tc_HOL_Obool, _1540343), c_HOL_OEx(_1540343)), hAPP(hAPP(c_COMBC(_1540343, tc_fun(_1540343, tc_HOL_Obool), tc_fun(_1540343, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540343, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1540343, tc_HOL_Obool), tc_fun(_1540343, tc_HOL_Obool)), _1540343), c_COMBS(_1540343, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540343, tc_HOL_Obool), tc_fun(_1540343, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1540343), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540343), c_fconj)), hAPP(hAPP(c_COMBC(_1540343, tc_fun(_1540343, _1540343), tc_fun(_1540343, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540343, tc_HOL_Obool), tc_fun(tc_fun(_1540343, _1540343), tc_fun(_1540343, tc_HOL_Obool)), _1540343), c_COMBB(_1540343, tc_HOL_Obool, _1540343)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1540343), _1540347))))), hAPP(hAPP(c_COMBC(_1540343, tc_fun(_1540343, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540343)), _1540345))))))], (14185 ^ _779327) ^ [_1018288, _1018290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018288), _1018290)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018288), _1018290)))], (3952 ^ _779327) ^ [_839266, _839268, _839270, _839272, _839274, _839276] : [-(c_Big__Operators_Olattice_OInf__fin(_839276, _839272, _839268) = c_Big__Operators_Olattice_OInf__fin(_839274, _839270, _839266)), _839276 = _839274, _839272 = _839270, _839268 = _839266], (1308 ^ _779327) ^ [_798665, _798667] : [-(class_Rings_Ocomm__ring(_798665)), _798667 = _798665, class_Rings_Ocomm__ring(_798667)], (8576 ^ _779327) ^ [_916677] : [class_Rings_Osemiring__1(_916677), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_916677), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_916677))], (39804 ^ _779327) ^ [_1534963, _1534965, _1534967] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534963, tc_HOL_Obool)), _1534965), _1534967) = hAPP(c_Set_OCollect(_1534963), hAPP(hAPP(c_COMBS(_1534963, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534963), c_fdisj), hAPP(hAPP(c_COMBC(_1534963, tc_fun(_1534963, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534963)), _1534965))), hAPP(hAPP(c_COMBC(_1534963, tc_fun(_1534963, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534963)), _1534967))))], (23159 ^ _779327) ^ [_1181212, _1181214, _1181216, _1181218] : [class_Orderings_Olinorder(_1181212), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181212), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181212), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181212), _1181214), _1181216)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181212), _1181214), _1181218))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181212), _1181214), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181212), _1181216), _1181218)))))], (29564 ^ _779327) ^ [_1307324, _1307326, _1307328, _1307330] : [hBOOL(hAPP(hAPP(c_member(_1307324), _1307326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307324, tc_HOL_Obool)), _1307328), _1307330))), 29567 ^ _779327 : [(29570 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1307324), _1307326), _1307330))], (29568 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1307324), _1307326), _1307328)))]]], (47070 ^ _779327) ^ [_1718894, _1718896, _1718898, _1718900] : [-(hAPP(c_List_Orotate(_1718894, _1718896), hAPP(c_List_Orotate(_1718894, _1718898), _1718900)) = hAPP(c_List_Orotate(_1718894, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718896), _1718898)), _1718900))], (35195 ^ _779327) ^ [_1429227, _1429229, _1429231, _1429233] : [hBOOL(hAPP(hAPP(c_member(_1429227), _1429229), _1429231)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429227, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1429227), _1429229), _1429233)), _1429231) = hAPP(hAPP(c_Set_Oinsert(_1429227), _1429229), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429227, tc_HOL_Obool)), _1429233), _1429231)))], (7912 ^ _779327) ^ [_904623, _904625, _904627] : [class_Rings_Oordered__cancel__semiring(_904623), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904623), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_904623), _904625), _904627)), c_Groups_Ozero__class_Ozero(_904623)))), 7917 ^ _779327 : [(7924 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904623), _904625), c_Groups_Ozero__class_Ozero(_904623))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904623), c_Groups_Ozero__class_Ozero(_904623)), _904627))], (7918 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904623), c_Groups_Ozero__class_Ozero(_904623)), _904625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904623), _904627), c_Groups_Ozero__class_Ozero(_904623)))]]], (44588 ^ _779327) ^ [_1656724, _1656726, _1656728, _1656730, _1656732, _1656734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656724, _1656724)), hAPP(hAPP(c_Product__Type_OPair(_1656724, _1656724), _1656726), _1656728)), c_Transitive__Closure_Ortrancl(_1656724, _1656730))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656724), tc_List_Olist(_1656724))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656724), tc_List_Olist(_1656724)), _1656732), _1656734)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1656724), c_List_Olistrel1(_1656724, _1656730)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656724), tc_List_Olist(_1656724))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656724), tc_List_Olist(_1656724)), hAPP(hAPP(c_List_Olist_OCons(_1656724), _1656726), _1656732)), hAPP(hAPP(c_List_Olist_OCons(_1656724), _1656728), _1656734))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1656724), c_List_Olistrel1(_1656724, _1656730)))))], (32846 ^ _779327) ^ [_1376708, _1376710, _1376712] : [class_Orderings_Olinorder(_1376708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376708), _1376710)), hBOOL(hAPP(hAPP(c_member(_1376708), _1376712), _1376710)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376708), _1376712), c_Big__Operators_Olattice_OInf__fin(_1376708, c_Orderings_Oord__class_Omin(_1376708), _1376710)) = _1376712)], (8332 ^ _779327) ^ [_912257, _912259, _912261, _912263, _912265] : [class_Rings_Olinordered__semiring__strict(_912257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912257), _912259), _912261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912257), _912263), _912265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912257), c_Groups_Ozero__class_Ozero(_912257)), _912261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912257), c_Groups_Ozero__class_Ozero(_912257)), _912263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912257), _912259), _912263)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_912257), _912261), _912265))))], (42376 ^ _779327) ^ [_1604624, _1604626, _1604628, _1604630, _1604632] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604624, _1604624)), hAPP(hAPP(c_Product__Type_OPair(_1604624, _1604624), _1604626), _1604628)), c_Transitive__Closure_Otrancl(_1604624, _1604630))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604624, _1604624)), hAPP(hAPP(c_Product__Type_OPair(_1604624, _1604624), _1604628), _1604632)), c_Transitive__Closure_Ortrancl(_1604624, _1604630))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604624, _1604624)), hAPP(hAPP(c_Product__Type_OPair(_1604624, _1604624), _1604626), _1604632)), c_Transitive__Closure_Otrancl(_1604624, _1604630))))], (18026 ^ _779327) ^ [_1085355, _1085357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085355)), c_Int_OBit1(_1085357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085355), _1085357)))], (30717 ^ _779327) ^ [_1334131, _1334133, _1334135, _1334137, _1334139] : [class_Groups_Ocomm__monoid__add(_1334131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334133), _1334135)), hBOOL(hAPP(hAPP(c_member(_1334133), _1334137), _1334135)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334133, _1334131), _1334139), _1334135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334131), hAPP(_1334139, _1334137)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1334133, _1334131), _1334139), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334133, tc_HOL_Obool)), _1334135), hAPP(hAPP(c_Set_Oinsert(_1334133), _1334137), c_Orderings_Obot__class_Obot(tc_fun(_1334133, tc_HOL_Obool)))))))], (30263 ^ _779327) ^ [_1323646, _1323648, _1323650, _1323652, _1323654] : [-(hBOOL(hAPP(hAPP(c_member(_1323646), _1323648), c_SetInterval_Oord_OgreaterThanLessThan(_1323646, _1323650, _1323652, _1323654)))), hBOOL(hAPP(hAPP(_1323650, _1323652), _1323648)), hBOOL(hAPP(hAPP(_1323650, _1323648), _1323654))], (26480 ^ _779327) ^ [_1245686, _1245688] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1245686, _1245688)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1245688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1245686), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (18933 ^ _779327) ^ [_1101806, _1101808, _1101810] : [class_Fields_Olinordered__field__inverse__zero(_1101806), 18936 ^ _779327 : [(18951 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101806), _1101808), _1101810)), c_Groups_Ozero__class_Ozero(_1101806)))), 18952 ^ _779327 : [(18959 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), _1101808), c_Groups_Ozero__class_Ozero(_1101806))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), c_Groups_Ozero__class_Ozero(_1101806)), _1101810))], (18953 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), c_Groups_Ozero__class_Ozero(_1101806)), _1101808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), _1101810), c_Groups_Ozero__class_Ozero(_1101806)))]]], (18937 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101806), _1101808), _1101810)), c_Groups_Ozero__class_Ozero(_1101806))), 18942 ^ _779327 : [(18945 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), _1101810), c_Groups_Ozero__class_Ozero(_1101806))))], (18943 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), c_Groups_Ozero__class_Ozero(_1101806)), _1101808)))]], 18946 ^ _779327 : [(18949 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), c_Groups_Ozero__class_Ozero(_1101806)), _1101810)))], (18947 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101806), _1101808), c_Groups_Ozero__class_Ozero(_1101806))))]]]]], (8776 ^ _779327) ^ [_920308, _920310, _920312, _920314] : [class_Rings_Olinordered__semidom(_920308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920308), hAPP(hAPP(c_Power_Opower__class_Opower(_920308), _920310), _920312)), hAPP(hAPP(c_Power_Opower__class_Opower(_920308), _920314), _920312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920308), c_Groups_Ozero__class_Ozero(_920308)), _920314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920308), _920310), _920314)))], (18134 ^ _779327) ^ [_1087259] : [-(c_Int_Opred(c_Int_OBit0(_1087259)) = c_Int_OBit1(c_Int_Opred(_1087259)))], (44932 ^ _779327) ^ [_1667099, _1667101, _1667103, _1667105] : [-(hAPP(hAPP(c_List_Onth(_1667099), hAPP(hAPP(c_List_Olist_OCons(_1667099), _1667101), _1667103)), _1667105) = c_Nat_Onat_Onat__case(_1667099, _1667101, hAPP(c_List_Onth(_1667099), _1667103), _1667105))], (5432 ^ _779327) ^ [_862208, _862210, _862212, _862214, _862216, _862218, _862220, _862222] : [-(c_Hilbert__Choice_Oinv__into(_862222, _862218, _862214, _862210) = c_Hilbert__Choice_Oinv__into(_862220, _862216, _862212, _862208)), _862222 = _862220, _862218 = _862216, _862214 = _862212, _862210 = _862208], (8398 ^ _779327) ^ [_913526, _913528, _913530, _913532, _913534] : [class_Rings_Olinordered__semiring__strict(_913526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913526), _913528), _913530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913526), _913532), _913534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913526), c_Groups_Ozero__class_Ozero(_913526)), _913528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913526), c_Groups_Ozero__class_Ozero(_913526)), _913532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913526), _913528), _913532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_913526), _913530), _913534))))], (8998 ^ _779327) ^ [_924167] : [-(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), _924167))))], (50691 ^ _779327) ^ [_1797086, _1797088, _1797090, _1797092] : [c_List_Olist__ex(_1797086, _1797088, hAPP(hAPP(c_List_Oappend(_1797086), _1797090), _1797092)), -(c_List_Olist__ex(_1797086, _1797088, _1797090)), -(c_List_Olist__ex(_1797086, _1797088, _1797092))], (4610 ^ _779327) ^ [_849599, _849601, _849603, _849605, _849607, _849609] : [-(c_New__DSequence_Opos__union(_849609, _849605, _849601) = c_New__DSequence_Opos__union(_849607, _849603, _849599)), _849609 = _849607, _849605 = _849603, _849601 = _849599], (23089 ^ _779327) ^ [_1179682, _1179684, _1179686] : [class_Orderings_Olinorder(_1179682), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179682), _1179684), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179682), _1179684), _1179686)) = _1179684)], (7093 ^ _779327) ^ [_890315, _890317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890315), hAPP(c_Nat_OSuc, _890317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890315), _890317))), -(_890315 = hAPP(c_Nat_OSuc, _890317))], (1158 ^ _779327) ^ [_796790, _796792] : [-(class_Groups_Oordered__ab__group__add__abs(_796790)), _796792 = _796790, class_Groups_Oordered__ab__group__add__abs(_796792)], (34691 ^ _779327) ^ [_1418315, _1418317, _1418319, _1418321, _1418323] : [class_Lattices_Olattice(_1418315), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418317, _1418315)), _1418319), _1418321), _1418323) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418315), hAPP(_1418319, _1418323)), hAPP(_1418321, _1418323)))], (49531 ^ _779327) ^ [_1771806, _1771808, _1771810] : [hAPP(c_List_Orev(_1771806), _1771808) = hAPP(c_List_Orev(_1771806), _1771810), -(_1771808 = _1771810)], (42262 ^ _779327) ^ [_1601916, _1601918] : [-(c_Transitive__Closure_Ortrancl(_1601916, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1601916, _1601916), tc_HOL_Obool)), _1601918), c_Relation_OId(_1601916))) = c_Transitive__Closure_Ortrancl(_1601916, _1601918))], (18905 ^ _779327) ^ [_1101268, _1101270, _1101272, _1101274] : [class_Fields_Olinordered__field__inverse__zero(_1101268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101268), _1101270), _1101272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101268), _1101274), c_Groups_Ozero__class_Ozero(_1101268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101268), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101268), _1101272), _1101274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1101268), _1101270), _1101274))))], (10475 ^ _779327) ^ [_948923, _948925] : [10476 ^ _779327 : [(10479 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948925))], (10477 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948923))]], 10480 ^ _779327 : [(10487 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948923), _948925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _948923)), hAPP(c_Int_Onat, _948925))))], (10481 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _948923)), hAPP(c_Int_Onat, _948925))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948923), _948925)))]]], (33830 ^ _779327) ^ [_1397907, _1397909, _1397911, _1397913, _1397915] : [class_Groups_Ocomm__monoid__mult(_1397907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397909), _1397911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397909, tc_HOL_Obool)), _1397913), _1397911)), 33844 ^ _779327 : [(33847 ^ _779327) ^ [] : [hAPP(_1397915, 33843 ^ [_1397907, _1397909, _1397911, _1397913, _1397915]) = c_Groups_Oone__class_Oone(_1397907)], (33845 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397909), 33843 ^ [_1397907, _1397909, _1397911, _1397913, _1397915]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1397909, tc_HOL_Obool)), _1397911), _1397913))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397909, _1397907), _1397915), _1397911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397909, _1397907), _1397915), _1397913))], (34889 ^ _779327) ^ [_1422390, _1422392, _1422394, _1422396] : [class_Lattices_Osemilattice__inf(_1422390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422390), _1422392), _1422394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422390), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422390), _1422396), _1422392)), _1422394)))], (33624 ^ _779327) ^ [_1392261, _1392263, _1392265, _1392267, _1392269, _1392271] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool)), _1392263), _1392265)), c_Wellfounded_Omax__ext(_1392261, _1392267))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool)), _1392269), _1392271)), c_Wellfounded_Omax__ext(_1392261, _1392267))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1392261, tc_HOL_Obool), tc_fun(_1392261, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392261, tc_HOL_Obool)), _1392263), _1392269)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392261, tc_HOL_Obool)), _1392265), _1392271))), c_Wellfounded_Omax__ext(_1392261, _1392267))))], (33921 ^ _779327) ^ [_1399912, _1399914, _1399916, _1399918, _1399920] : [c_Finite__Set_Ofolding__one__idem(_1399912, _1399914, _1399916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399912), _1399918)), -(_1399918 = c_Orderings_Obot__class_Obot(tc_fun(_1399912, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399912), _1399920)), -(_1399920 = c_Orderings_Obot__class_Obot(tc_fun(_1399912, tc_HOL_Obool))), -(hAPP(_1399916, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399912, tc_HOL_Obool)), _1399918), _1399920)) = hAPP(hAPP(_1399914, hAPP(_1399916, _1399918)), hAPP(_1399916, _1399920)))], (41803 ^ _779327) ^ [_1590438, _1590440] : [41805 ^ _779327 : [(41808 ^ _779327) ^ [] : [41804 ^ [_1590438, _1590440] = c_Orderings_Obot__class_Obot(tc_fun(_1590438, tc_HOL_Obool))], (41806 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590438, tc_HOL_Obool)), 41804 ^ [_1590438, _1590440]), hAPP(c_Relation_OImage(_1590438, _1590438, _1590440), 41804 ^ [_1590438, _1590440]))))]], -(c_Wellfounded_Owf(_1590438, _1590440))], (23706 ^ _779327) ^ [_1192057] : [-(hAPP(c_Code__Numeral_Onat__of, _1192057) = c_Code__Numeral_Onat__of__aux(_1192057, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42967 ^ _779327) ^ [_1619148, _1619150, _1619152, _1619154, _1619156] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619148, _1619148)), hAPP(hAPP(c_Product__Type_OPair(_1619148, _1619148), _1619150), _1619152)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1619148, _1619148), tc_HOL_Obool), _1619154), _1619156))), 42972 ^ _779327 : [(42975 ^ _779327) ^ [] : [-(_1619150 = _1619152)], (42973 ^ _779327) ^ [] : [-(_1619154 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 42978 ^ _779327 : [(42983 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619148, _1619148)), hAPP(hAPP(c_Product__Type_OPair(_1619148, _1619148), 42976 ^ [_1619148, _1619150, _1619152, _1619154, _1619156]), _1619152)), _1619156)))], (42981 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619148, _1619148)), hAPP(hAPP(c_Product__Type_OPair(_1619148, _1619148), _1619150), 42976 ^ [_1619148, _1619150, _1619152, _1619154, _1619156])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1619148, _1619148), tc_HOL_Obool), 42977 ^ [_1619148, _1619150, _1619152, _1619154, _1619156]), _1619156))))], (42979 ^ _779327) ^ [] : [-(_1619154 = hAPP(c_Nat_OSuc, 42977 ^ [_1619148, _1619150, _1619152, _1619154, _1619156]))]]], (9443 ^ _779327) ^ [_932296, _932298, _932300] : [class_Rings_Oring__1(_932296), -(hAPP(c_Int_Oring__1__class_Oof__int(_932296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _932298), _932300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932296), hAPP(c_Int_Oring__1__class_Oof__int(_932296), _932298)), hAPP(c_Int_Oring__1__class_Oof__int(_932296), _932300)))], (36604 ^ _779327) ^ [_1462122, _1462124, _1462126] : [class_Lattices_Olattice(_1462122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462122), _1462124)), -(hBOOL(hAPP(hAPP(c_member(_1462122), _1462126), _1462124))), -(_1462124 = c_Orderings_Obot__class_Obot(tc_fun(_1462122, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1462122, hAPP(hAPP(c_Set_Oinsert(_1462122), _1462126), _1462124)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462122), _1462126), c_Big__Operators_Olattice__class_OInf__fin(_1462122, _1462124)))], (52820 ^ _779327) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (48131 ^ _779327) ^ [_1741452, _1741454, _1741456, _1741458, _1741460, _1741462] : [c_List_Olist__all2(_1741452, _1741454, _1741456, _1741458, _1741460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741462), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741452)), _1741458))), -(hBOOL(hAPP(hAPP(_1741456, hAPP(hAPP(c_List_Onth(_1741452), _1741458), _1741462)), hAPP(hAPP(c_List_Onth(_1741454), _1741460), _1741462))))], (32558 ^ _779327) ^ [_1371120, _1371122, _1371124] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1371120, tc_HOL_Obool), tc_fun(_1371120, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1371120, tc_HOL_Obool), tc_fun(_1371120, tc_HOL_Obool)), _1371122), _1371124)), c_Wellfounded_Ofinite__psubset(_1371120))), 32561 ^ _779327 : [(32564 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1371120), _1371124)))], (32562 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1371120, tc_HOL_Obool)), _1371122), _1371124)))]]], (40845 ^ _779327) ^ [_1568416, _1568418, _1568420, _1568422] : [40846 ^ _779327 : [(40847 ^ _779327) ^ [_1568470] : [hBOOL(hAPP(hAPP(_1568420, _1568470), _1568422))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1568416, _1568418, _1568420), _1568422)))], (37183 ^ _779327) ^ [_1474141, _1474143, _1474145, _1474147, _1474149, _1474151] : [c_Fun_Oinj__on(_1474141, _1474143, _1474145, _1474147), hAPP(_1474145, _1474149) = _1474151, hBOOL(hAPP(hAPP(c_member(_1474141), _1474149), _1474147)), -(hAPP(c_Fun_Othe__inv__into(_1474141, _1474143, _1474147, _1474145), _1474151) = _1474149)], (33963 ^ _779327) ^ [_1400695, _1400697, _1400699, _1400701, _1400703] : [hAPP(c_Set_Oimage(_1400695, _1400697, _1400699), _1400701) = _1400703, -(hAPP(c_Set_Oimage(tc_fun(_1400695, tc_HOL_Obool), tc_fun(_1400697, tc_HOL_Obool), c_Set_Oimage(_1400695, _1400697, _1400699)), hAPP(c_Set_OPow(_1400695), _1400701)) = hAPP(c_Set_OPow(_1400697), _1400703))], (34515 ^ _779327) ^ [_1414157, _1414159, _1414161, _1414163, _1414165] : [c_Equiv__Relations_Oequiv(_1414157, _1414159, _1414161), hBOOL(hAPP(hAPP(c_member(_1414157), _1414163), _1414159)), hBOOL(hAPP(hAPP(c_member(_1414157), _1414165), _1414159)), 34526 ^ _779327 : [(34533 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1414157, _1414157)), hAPP(hAPP(c_Product__Type_OPair(_1414157, _1414157), _1414163), _1414165)), _1414161)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414157), hAPP(hAPP(c_Set_Oinsert(_1414157), _1414163), c_Orderings_Obot__class_Obot(tc_fun(_1414157, tc_HOL_Obool)))), _1414161) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414157), hAPP(hAPP(c_Set_Oinsert(_1414157), _1414165), c_Orderings_Obot__class_Obot(tc_fun(_1414157, tc_HOL_Obool)))), _1414161))], (34527 ^ _779327) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414157), hAPP(hAPP(c_Set_Oinsert(_1414157), _1414163), c_Orderings_Obot__class_Obot(tc_fun(_1414157, tc_HOL_Obool)))), _1414161) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414157), hAPP(hAPP(c_Set_Oinsert(_1414157), _1414165), c_Orderings_Obot__class_Obot(tc_fun(_1414157, tc_HOL_Obool)))), _1414161), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1414157, _1414157)), hAPP(hAPP(c_Product__Type_OPair(_1414157, _1414157), _1414163), _1414165)), _1414161)))]]], (23546 ^ _779327) ^ [_1189250, _1189252] : [-(c_HOL_OThe(_1189250, hAPP(hAPP(c_COMBC(_1189250, _1189250, tc_HOL_Obool), c_fequal), _1189252)) = _1189252)], (8312 ^ _779327) ^ [_911876, _911878, _911880, _911882] : [class_Rings_Olinordered__ring__strict(_911876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911876), _911878), c_Groups_Ozero__class_Ozero(_911876))), 8319 ^ _779327 : [(8326 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911876), _911882), _911880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911876), _911878), _911880)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911876), _911878), _911882))))], (8320 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911876), _911878), _911880)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_911876), _911878), _911882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911876), _911882), _911880)))]]], (29973 ^ _779327) ^ [_1315192, _1315194, _1315196, _1315198] : [hBOOL(hAPP(hAPP(c_member(_1315192), _1315194), _1315196)), -(hBOOL(hAPP(hAPP(c_member(_1315192), _1315194), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315192, tc_HOL_Obool)), _1315196), _1315198))))], (12231 ^ _779327) ^ [_982783, _982785] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982783), hAPP(c_Nat_OSuc, _982785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982783), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _982785))], (19173 ^ _779327) ^ [_1106052, _1106054, _1106056, _1106058] : [class_Rings_Odivision__ring(_1106052), -(_1106054 = c_Groups_Ozero__class_Ozero(_1106052)), 19180 ^ _779327 : [(19187 ^ _779327) ^ [] : [_1106056 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106052), _1106058), _1106054), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106052), _1106056), _1106054) = _1106058)], (19181 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1106052), _1106056), _1106054) = _1106058, -(_1106056 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106052), _1106058), _1106054))]]], (21254 ^ _779327) ^ [_1144491, _1144493] : [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(_1144491))), 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)), _1144493)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144491)), hAPP(c_Nat_OSuc, _1144493))))], (17606 ^ _779327) ^ [_1078077, _1078079] : [class_Int_Onumber__ring(_1078077), -(hAPP(c_Int_Onumber__class_Onumber__of(_1078077), c_Int_OBit1(_1078079)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078077), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078077), c_Groups_Oone__class_Oone(_1078077)), hAPP(c_Int_Onumber__class_Onumber__of(_1078077), _1078079))), hAPP(c_Int_Onumber__class_Onumber__of(_1078077), _1078079)))], (14089 ^ _779327) ^ [_1016205, _1016207, _1016209] : [class_Lattices_Oboolean__algebra(_1016205), 14092 ^ _779327 : [(14099 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016205), _1016209), _1016207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016205), hAPP(c_Groups_Ouminus__class_Ouminus(_1016205), _1016207)), hAPP(c_Groups_Ouminus__class_Ouminus(_1016205), _1016209))))], (14093 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016205), hAPP(c_Groups_Ouminus__class_Ouminus(_1016205), _1016207)), hAPP(c_Groups_Ouminus__class_Ouminus(_1016205), _1016209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016205), _1016209), _1016207)))]]], (1938 ^ _779327) ^ [_806540, _806542] : [-(class_Groups_Oone(_806540)), _806542 = _806540, class_Groups_Oone(_806542)], (36550 ^ _779327) ^ [_1461273, _1461275, _1461277] : [class_Lattices_Olattice(_1461273), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461273), _1461275)), -(_1461277 = c_Orderings_Obot__class_Obot(tc_fun(_1461273, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461273, tc_HOL_Obool)), _1461277), _1461275)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461273), c_Big__Operators_Olattice__class_OInf__fin(_1461273, _1461277)), c_Big__Operators_Olattice__class_OInf__fin(_1461273, _1461275)) = c_Big__Operators_Olattice__class_OInf__fin(_1461273, _1461275))], (16447 ^ _779327) ^ [_1058138, _1058140] : [class_Rings_Olinordered__idom(_1058138), -(hAPP(c_Groups_Oabs__class_Oabs(_1058138), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058138), _1058140)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058138), _1058140))], (23365 ^ _779327) ^ [_1185086, _1185088, _1185090, _1185092, _1185094] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1185086, tc_fun(_1185088, tc_HOL_Obool)), _1185090), _1185092), _1185094)), 23368 ^ _779327 : [(23369 ^ _779327) ^ [_1185195] : [hBOOL(hAPP(hAPP(c_member(_1185086), _1185195), _1185090)), -(hBOOL(hAPP(hAPP(_1185092, _1185195), _1185094)))]]], (16862 ^ _779327) ^ [_1065447, _1065449] : [class_Groups_Oabs__if(_1065447), 16865 ^ _779327 : [(16872 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065447), _1065449), c_Groups_Ozero__class_Ozero(_1065447)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1065447), _1065449) = _1065449)], (16866 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065447), _1065449), c_Groups_Ozero__class_Ozero(_1065447))), -(hAPP(c_Groups_Oabs__class_Oabs(_1065447), _1065449) = hAPP(c_Groups_Ouminus__class_Ouminus(_1065447), _1065449))]]], (33678 ^ _779327) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (47124 ^ _779327) ^ [_1720077, _1720079] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720077), _1720079) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 47127 ^ _779327 : [(47130 ^ _779327) ^ [_1720191] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1720191), hAPP(c_List_Oset(tc_Nat_Onat), _1720079))), -(_1720191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47128 ^ _779327) ^ [] : [-(_1720077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42238 ^ _779327) ^ [_1601265, _1601267, _1601269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601265, _1601265), tc_HOL_Obool)), _1601267), c_Transitive__Closure_Ortrancl(_1601265, _1601269))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601265, _1601265), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1601265, _1601267)), c_Transitive__Closure_Ortrancl(_1601265, _1601269))))], (34791 ^ _779327) ^ [_1420477, _1420479, _1420481] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420477, tc_HOL_Obool)), _1420479), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420477, tc_HOL_Obool)), _1420479), _1420481)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420477, tc_HOL_Obool)), _1420479), _1420481))], (43941 ^ _779327) ^ [_1640525, _1640527, _1640529, _1640531] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640525, tc_fun(_1640527, tc_HOL_Obool)), _1640529), _1640531) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640527, tc_HOL_Obool), hAPP(c_Set_Oimage(_1640525, tc_fun(_1640527, tc_HOL_Obool), _1640531), _1640529)))], (20971 ^ _779327) ^ [_1138549] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1138549)], (38489 ^ _779327) ^ [_1504442, _1504444, _1504446, _1504448, _1504450] : [c_Fun_Oinj__on(_1504442, _1504444, _1504446, c_Orderings_Otop__class_Otop(tc_fun(_1504442, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1504444, tc_HOL_Obool)), _1504448), hAPP(c_Set_Oimage(_1504442, _1504444, _1504446), _1504450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1504442, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1504442, _1504444, _1504446), _1504448)), _1504450)))], (51301 ^ _779327) ^ [_1809775, _1809777, _1809779] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1809775, _1809777), _1809779) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1809775, tc_Lazy__Sequence_Olazy__sequence(_1809775)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1809775, tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1809775, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat)), _1809775), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1809775), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1809775)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1809775, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1809775), tc_Nat_Onat)), _1809775), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1809775))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1809775), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1809777))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1809775, _1809777))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1809775), _1809779)))], (45450 ^ _779327) ^ [_1680568, _1680570, _1680572, _1680574] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680568)), _1680570) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680572)), _1680574), -(hAPP(hAPP(c_List_Omap(tc_prod(_1680568, _1680572), _1680572), c_Product__Type_Osnd(_1680568, _1680572)), hAPP(hAPP(c_List_Ozip(_1680568, _1680572), _1680570), _1680574)) = _1680574)], (42653 ^ _779327) ^ [_1611486, _1611488, _1611490, _1611492, _1611494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611488, tc_HOL_Obool)), _1611492), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1611488, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1611486, _1611488, hAPP(c_Relation_Oconverse(_1611488, _1611486), _1611490)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1611486, tc_HOL_Obool)), _1611494))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611486, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1611488, _1611486, _1611490), _1611492)), _1611494)))], (45892 ^ _779327) ^ [_1691910, _1691912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691912))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691910), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691912)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691910)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691910)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1691912))))], (37122 ^ _779327) ^ [_1472794, _1472796, _1472798, _1472800] : [-(_1472794 = c_Orderings_Obot__class_Obot(tc_fun(_1472796, tc_HOL_Obool))), 37125 ^ _779327 : [(37126 ^ _779327) ^ [] : [-(hAPP(c_Set_Oimage(_1472798, _1472796, 37133 ^ [_1472794, _1472796, _1472798, _1472800]), _1472800) = _1472794), 37127 ^ _779327 : [(37128 ^ _779327) ^ [_1472935] : [c_Fun_Oinj__on(_1472796, _1472798, _1472935, _1472794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472798, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472796, _1472798, _1472935), _1472794)), _1472800))]]], (37137 ^ _779327) ^ [] : [37138 ^ _779327 : [(37139 ^ _779327) ^ [_1473127] : [hAPP(c_Set_Oimage(_1472798, _1472796, _1473127), _1472800) = _1472794]], 37141 ^ _779327 : [(37144 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472798, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1472796, _1472798, 37140 ^ [_1472794, _1472796, _1472798, _1472800]), _1472794)), _1472800)))], (37142 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1472796, _1472798, 37140 ^ [_1472794, _1472796, _1472798, _1472800], _1472794))]]]]], (17462 ^ _779327) ^ [_1075787] : [c_Int_OBit1(_1075787) = c_Int_OMin, -(_1075787 = c_Int_OMin)], (3860 ^ _779327) ^ [_837904, _837906, _837908, _837910] : [-(c_Hilbert__Choice_OEps(_837910, _837906) = c_Hilbert__Choice_OEps(_837908, _837904)), _837910 = _837908, _837906 = _837904], (18508 ^ _779327) ^ [_1093627, _1093629, _1093631] : [class_Rings_Oring__1(_1093627), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093627), hAPP(c_Groups_Ouminus__class_Ouminus(_1093627), _1093629)), 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)))), _1093631)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1093627), _1093629), 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)))), _1093631)))], (24177 ^ _779327) ^ [_1200429, _1200431, _1200433] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200429), _1200431)), 24188 ^ _779327 : [(24191 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200433), _1200429))], (24189 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200429), _1200433)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200431), _1200433)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1200433), _1200431)))], (14647 ^ _779327) ^ [_1025955] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1025955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025955), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1188 ^ _779327) ^ [_797165, _797167] : [-(class_Rings_Olinordered__ring__strict(_797165)), _797167 = _797165, class_Rings_Olinordered__ring__strict(_797167)], (5746 ^ _779327) ^ [_870215] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _870215))))], (33361 ^ _779327) ^ [_1387039, _1387041, _1387043, _1387045, _1387047] : [class_Groups_Ocomm__monoid__mult(_1387039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387041), _1387043)), -(hBOOL(hAPP(hAPP(c_member(_1387041), _1387045), _1387043))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387041, _1387039), _1387047), hAPP(hAPP(c_Set_Oinsert(_1387041), _1387045), _1387043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387039), hAPP(_1387047, _1387045)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387041, _1387039), _1387047), _1387043)))], (41801 ^ _779327) ^ [_1590332, _1590334, _1590336, _1590338] : [-(c_Hilbert__Choice_OEps(tc_prod(_1590332, _1590334), hAPP(c_Product__Type_Oprod_Oprod__case(_1590332, _1590334, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1590332, tc_fun(_1590334, tc_HOL_Obool), tc_fun(_1590334, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1590334, tc_HOL_Obool), tc_fun(_1590334, tc_HOL_Obool)), _1590332), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1590334)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1590332), c_fconj), hAPP(c_fequal, _1590336)))), hAPP(c_fequal, _1590338)))) = hAPP(hAPP(c_Product__Type_OPair(_1590332, _1590334), _1590336), _1590338))], (26838 ^ _779327) ^ [_1252183, _1252185, _1252187] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252183, tc_HOL_Obool)), _1252185), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1252183, tc_HOL_Obool)), _1252187), _1252185)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252183, tc_HOL_Obool)), _1252185), _1252187))], (42525 ^ _779327) ^ [_1608189, _1608191, _1608193, _1608195, _1608197] : [-(hAPP(c_Relation_Oconverse(_1608189, _1608191), hAPP(hAPP(c_Relation_Orel__comp(_1608189, _1608193, _1608191), _1608195), _1608197)) = hAPP(hAPP(c_Relation_Orel__comp(_1608191, _1608193, _1608189), hAPP(c_Relation_Oconverse(_1608193, _1608191), _1608197)), hAPP(c_Relation_Oconverse(_1608189, _1608193), _1608195)))], (41261 ^ _779327) ^ [_1578279, _1578281, _1578283, _1578285, _1578287, _1578289, _1578291, _1578293, _1578295, _1578297, _1578299] : [hAPP(_1578279, hAPP(_1578281, _1578283)) = hAPP(_1578285, hAPP(_1578287, _1578289)), -(hAPP(hAPP(c_Fun_Ocomp(_1578291, _1578293, _1578295, _1578279), _1578281), _1578283) = hAPP(hAPP(c_Fun_Ocomp(_1578297, _1578293, _1578299, _1578285), _1578287), _1578289))], (40637 ^ _779327) ^ [_1563131, _1563133, _1563135] : [c_Wellfounded_Owf(_1563131, _1563133), -(hBOOL(hAPP(hAPP(c_member(_1563131), _1563135), c_Wellfounded_Oacc(_1563131, _1563133))))], (48317 ^ _779327) ^ [_1745602] : [-(c_List_Oremdups(_1745602, c_List_Olist_ONil(_1745602)) = c_List_Olist_ONil(_1745602))], (6898 ^ _779327) ^ [_887222, _887224] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887222), hAPP(c_Nat_OSuc, _887224)))), 6899 ^ _779327 : [(6902 ^ _779327) ^ [_887310] : [_887222 = hAPP(c_Nat_OSuc, _887310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887310), _887224))], (6900 ^ _779327) ^ [] : [_887222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44474 ^ _779327) ^ [_1653261, _1653263, _1653265] : [hAPP(hAPP(c_List_Olist_OCons(_1653261), _1653263), _1653265) = _1653265], (52690 ^ _779327) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52051 ^ _779327) ^ [_1827058, _1827060, _1827062, _1827064, _1827066, _1827068] : [-(c_Partial__Function_Ofun__lub(_1827058, _1827060, _1827062, _1827064, _1827066, _1827068) = hAPP(_1827064, hAPP(c_Set_OCollect(_1827058), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool), tc_HOL_Obool, _1827058), c_HOL_OEx(tc_fun(_1827062, _1827058))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool), tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool), _1827058), hAPP(c_COMBS(tc_fun(_1827062, _1827058), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1827062, _1827058)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1827062, _1827058), tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1827062, _1827058))), _1827066)))), hAPP(hAPP(c_COMBC(_1827058, tc_fun(tc_fun(_1827062, _1827058), _1827058), tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1827058, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1827062, _1827058), _1827058), tc_fun(tc_fun(_1827062, _1827058), tc_HOL_Obool)), _1827058), c_COMBB(_1827058, tc_HOL_Obool, tc_fun(_1827062, _1827058))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1827062, _1827058), _1827062, _1827058), c_COMBI(tc_fun(_1827062, _1827058))), _1827068)))))))], (34302 ^ _779327) ^ [_1409247, _1409249, _1409251] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1409247), hAPP(hAPP(c_Set_Oinsert(_1409247), _1409249), c_Orderings_Obot__class_Obot(tc_fun(_1409247, tc_HOL_Obool)))), _1409251) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1409247, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1409247, _1409247, _1409251), hAPP(hAPP(c_Set_Oinsert(_1409247), _1409249), c_Orderings_Obot__class_Obot(tc_fun(_1409247, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1409247, tc_HOL_Obool), tc_HOL_Obool))))], (35075 ^ _779327) ^ [_1426449, _1426451, _1426453] : [class_Lattices_Olattice(_1426449), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426449), _1426451), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426449), _1426451), _1426453)) = _1426451)], (17636 ^ _779327) ^ [_1078610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1078610)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078610), c_Int_OPls)))], (38936 ^ _779327) ^ [_1515870, _1515872, _1515874, _1515876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1515870, _1515872)), hAPP(hAPP(c_Product__Type_OSigma(_1515870, _1515872), _1515874), hAPP(c_COMBK(tc_fun(_1515872, tc_HOL_Obool), _1515870), _1515876)))), -(_1515874 = c_Orderings_Obot__class_Obot(tc_fun(_1515870, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515872), _1515876)))], (48969 ^ _779327) ^ [_1761051, _1761053] : [class_Orderings_Olinorder(_1761051), c_List_Olinorder__class_Osorted(_1761051, _1761053), -(c_List_Olinorder__class_Osorted(_1761051, hAPP(c_List_Otl(_1761051), _1761053)))], (10379 ^ _779327) ^ [_947487, _947489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947487)), 10382 ^ _779327 : [(10389 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _947487), _947489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _947487)), hAPP(c_Int_Onat, _947489))))], (10383 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _947487)), hAPP(c_Int_Onat, _947489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _947487), _947489)))]]], (52676 ^ _779327) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (46766 ^ _779327) ^ [_1712505, _1712507, _1712509, _1712511] : [hBOOL(hAPP(c_List_Odistinct(_1712505), _1712507)), -(hBOOL(hAPP(hAPP(c_member(_1712505), _1712509), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1712505, tc_HOL_Obool)), hAPP(c_List_Oset(_1712505), _1712507)), hAPP(hAPP(c_Set_Oinsert(_1712505), hAPP(hAPP(c_List_Onth(_1712505), _1712507), _1712511)), c_Orderings_Obot__class_Obot(tc_fun(_1712505, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1712505), hAPP(hAPP(c_List_Olist__update(_1712505, _1712507), _1712511), _1712509))))], (27116 ^ _779327) ^ [_1257875, _1257877, _1257879] : [class_Lattices_Osemilattice__sup(_1257875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257875), _1257877), _1257879)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257875), _1257877), _1257879) = _1257879)], (44676 ^ _779327) ^ [_1659573, _1659575, _1659577, _1659579, _1659581, _1659583] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659573), tc_List_Olist(_1659573))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659573), tc_List_Olist(_1659573)), hAPP(hAPP(c_List_Olist_OCons(_1659573), _1659575), _1659577)), hAPP(hAPP(c_List_Olist_OCons(_1659573), _1659579), _1659581))), c_List_Olistrel1(_1659573, _1659583)))), 44677 ^ _779327 : [(44684 ^ _779327) ^ [] : [_1659575 = _1659579, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659573), tc_List_Olist(_1659573))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659573), tc_List_Olist(_1659573)), _1659577), _1659581)), c_List_Olistrel1(_1659573, _1659583)))], (44678 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1659573, _1659573)), hAPP(hAPP(c_Product__Type_OPair(_1659573, _1659573), _1659575), _1659579)), _1659583)), _1659577 = _1659581]]], (33791 ^ _779327) ^ [_1397003, _1397005, _1397007, _1397009] : [-(hAPP(c_Relation_OField(_1397003), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1397003, _1397003)), hAPP(hAPP(c_Product__Type_OPair(_1397003, _1397003), _1397005), _1397007)), _1397009)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397003, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1397003), _1397005), hAPP(hAPP(c_Set_Oinsert(_1397003), _1397007), c_Orderings_Obot__class_Obot(tc_fun(_1397003, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1397003), _1397009)))], (29284 ^ _779327) ^ [_1301467, _1301469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301467), _1301469)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1301467), hAPP(c_Nat_OSuc, _1301469)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1301469), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1301467), _1301469)))], (43939 ^ _779327) ^ [_1640455, _1640457, _1640459] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640455, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1640455, tc_HOL_Obool), tc_HOL_Obool)), _1640457), _1640459)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640455, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640455, tc_HOL_Obool), _1640457)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640455, tc_HOL_Obool), _1640459)))], (19015 ^ _779327) ^ [_1103255, _1103257, _1103259, _1103261] : [class_Fields_Olinordered__field(_1103255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103255), _1103257), _1103259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103255), c_Groups_Ozero__class_Ozero(_1103255)), _1103261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103255), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103255), _1103257), _1103261)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103255), _1103259), _1103261))))], (43748 ^ _779327) ^ [_1635760, _1635762, _1635764, _1635766] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635760, tc_fun(_1635762, tc_HOL_Obool)), _1635764), _1635766) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635762, tc_HOL_Obool), hAPP(c_Set_Oimage(_1635760, tc_fun(_1635762, tc_HOL_Obool), _1635766), _1635764)))], (23756 ^ _779327) ^ [_1193132, _1193134, _1193136, _1193138, _1193140] : [-(hAPP(c_New__DSequence_Oneg__bind(_1193132, _1193134, _1193136, _1193138), _1193140) = c_Lazy__Sequence_Ohb__bind(_1193132, _1193134, hAPP(_1193136, _1193140), hAPP(hAPP(c_COMBC(_1193132, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1193134))), _1193138), _1193140)))], (38043 ^ _779327) ^ [_1491929, _1491931, _1491933, _1491935, _1491937] : [c_Fun_Oinj__on(_1491929, _1491931, _1491933, c_Orderings_Otop__class_Otop(tc_fun(_1491929, tc_HOL_Obool))), 38046 ^ _779327 : [(38053 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491929, tc_HOL_Obool)), _1491935), _1491937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491931, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491929, _1491931, _1491933), _1491935)), hAPP(c_Set_Oimage(_1491929, _1491931, _1491933), _1491937))))], (38047 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491931, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491929, _1491931, _1491933), _1491935)), hAPP(c_Set_Oimage(_1491929, _1491931, _1491933), _1491937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491929, tc_HOL_Obool)), _1491935), _1491937)))]]], (15147 ^ _779327) ^ [_1034400] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1034400))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034400)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (35647 ^ _779327) ^ [_1439689, _1439691, _1439693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439689, tc_HOL_Obool)), _1439691), _1439693))), -(hAPP(c_Finite__Set_Ocard(_1439689), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1439689, tc_HOL_Obool)), _1439691), _1439693)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1439689), _1439691)), hAPP(c_Finite__Set_Ocard(_1439689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439689, tc_HOL_Obool)), _1439691), _1439693))))], (4678 ^ _779327) ^ [_850607, _850609, _850611, _850613, _850615, _850617] : [-(c_List_OtakeWhile(_850617, _850613, _850609) = c_List_OtakeWhile(_850615, _850611, _850607)), _850617 = _850615, _850613 = _850611, _850609 = _850607], (22739 ^ _779327) ^ [_1172984, _1172986] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1172984), hAPP(c_Nat_OSuc, _1172986)) = 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)), _1172986)), _1172984))], (28644 ^ _779327) ^ [_1289762, _1289764, _1289766] : [class_Orderings_Obot(_1289762), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1289764, _1289762)), _1289766) = c_Orderings_Obot__class_Obot(_1289762))], (46433 ^ _779327) ^ [_1704562, _1704564, _1704566, _1704568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704562), tc_List_Olist(_1704562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704562), tc_List_Olist(_1704562)), _1704564), _1704566)), c_List_Olistrel1(_1704562, _1704568))), 46438 ^ _779327 : [(46443 ^ _779327) ^ [] : [-(_1704566 = hAPP(hAPP(c_List_Olist__update(_1704562, _1704564), 46437 ^ [_1704562, _1704564, _1704566, _1704568]), 46436 ^ [_1704562, _1704564, _1704566, _1704568]))], (46441 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46437 ^ [_1704562, _1704564, _1704566, _1704568]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704562)), _1704564))))], (46439 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1704562, _1704562)), hAPP(hAPP(c_Product__Type_OPair(_1704562, _1704562), hAPP(hAPP(c_List_Onth(_1704562), _1704564), 46437 ^ [_1704562, _1704564, _1704566, _1704568])), 46436 ^ [_1704562, _1704564, _1704566, _1704568])), _1704568)))]]], (52379 ^ _779327) ^ [_1833133, _1833135, _1833137] : [c_Fun_Oinj__on(_1833133, _1833135, _1833137, c_Orderings_Otop__class_Otop(tc_fun(_1833133, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1833135, _1833133, _1833133, c_Hilbert__Choice_Oinv__into(_1833133, _1833135, c_Orderings_Otop__class_Otop(tc_fun(_1833133, tc_HOL_Obool)), _1833137)), _1833137) = c_Fun_Oid(_1833133))], (52982 ^ _779327) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (22913 ^ _779327) ^ [_1176332, _1176334, _1176336, _1176338] : [class_Orderings_Olinorder(_1176332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176332), _1176334), _1176336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176332), _1176334), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176332), _1176338), _1176336))))], (30849 ^ _779327) ^ [_1337202, _1337204, _1337206] : [30851 ^ _779327 : [(30854 ^ _779327) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1337206, 30850 ^ [_1337202, _1337204, _1337206]))], (30852 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337202), 30850 ^ [_1337202, _1337204, _1337206]), _1337204)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337202, tc_Int_Oint), _1337206), _1337204) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337202, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1337202), c_Int_Onat), _1337206)), _1337204)))], (42873 ^ _779327) ^ [_1616644, _1616646, _1616648] : [c_Wellfounded_Owf(_1616644, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616644, _1616644), tc_HOL_Obool), _1616646), _1616648)), -(c_Wellfounded_Owf(_1616644, _1616648))], (51602 ^ _779327) ^ [_1816575, _1816577, _1816579] : [-(c_List_Olist__ex(_1816575, _1816577, _1816579)), 51603 ^ _779327 : [(51604 ^ _779327) ^ [_1816632] : [hBOOL(hAPP(hAPP(c_member(_1816575), _1816632), hAPP(c_List_Oset(_1816575), _1816579))), hBOOL(hAPP(_1816577, _1816632))]]], (11479 ^ _779327) ^ [_968836, _968838, _968840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _968836), _968838)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968840), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968838), _968836))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _968840), _968836)), hAPP(c_Nat_OSuc, _968838)))], (43044 ^ _779327) ^ [_1621462, _1621464, _1621466, _1621468, _1621470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621462, _1621462)), hAPP(hAPP(c_Product__Type_OPair(_1621462, _1621462), _1621464), _1621466)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621462, _1621462), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1621468)), _1621470))), 43048 ^ _779327 : [(43051 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621462, _1621462)), hAPP(hAPP(c_Product__Type_OPair(_1621462, _1621462), 43047 ^ [_1621462, _1621464, _1621466, _1621468, _1621470]), _1621466)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621462, _1621462), tc_HOL_Obool), _1621468), _1621470))))], (43049 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621462, _1621462)), hAPP(hAPP(c_Product__Type_OPair(_1621462, _1621462), _1621464), 43047 ^ [_1621462, _1621464, _1621466, _1621468, _1621470])), _1621470)))]]], (3604 ^ _779327) ^ [_833764, _833766, _833768, _833770] : [-(c_Relation_ORange(_833770, _833766) = c_Relation_ORange(_833768, _833764)), _833770 = _833768, _833766 = _833764], (45074 ^ _779327) ^ [_1670930, _1670932, _1670934, _1670936] : [-(hAPP(c_List_Oset(_1670930), hAPP(hAPP(c_List_Omap(_1670932, _1670930), _1670934), _1670936)) = hAPP(c_Set_Oimage(_1670932, _1670930, _1670934), hAPP(c_List_Oset(_1670932), _1670936)))], (38844 ^ _779327) ^ [_1513455, _1513457, _1513459, _1513461, _1513463] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1513455, _1513457), _1513459), hAPP(hAPP(c_COMBS(_1513455, tc_fun(_1513457, tc_HOL_Obool), tc_fun(_1513457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513457, tc_HOL_Obool), tc_fun(tc_fun(_1513457, tc_HOL_Obool), tc_fun(_1513457, tc_HOL_Obool)), _1513455), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513457, tc_HOL_Obool))), _1513461)), _1513463)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1513455, _1513457), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1513455, _1513457), _1513459), _1513461)), hAPP(hAPP(c_Product__Type_OSigma(_1513455, _1513457), _1513459), _1513463)))], (7228 ^ _779327) ^ [_892661, _892663, _892665, _892667] : [class_Rings_Olinordered__semidom(_892661), hAPP(hAPP(c_Power_Opower__class_Opower(_892661), _892663), _892665) = hAPP(hAPP(c_Power_Opower__class_Opower(_892661), _892667), _892665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892661), c_Groups_Ozero__class_Ozero(_892661)), _892663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892661), c_Groups_Ozero__class_Ozero(_892661)), _892667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _892665)), -(_892663 = _892667)], (36993 ^ _779327) ^ [_1469756, _1469758, _1469760, _1469762, _1469764, _1469766] : [c_Fun_Oinj__on(_1469756, _1469758, _1469760, _1469762), -(hBOOL(hAPP(hAPP(c_member(_1469758), _1469764), hAPP(c_Set_Oimage(_1469756, _1469758, _1469760), _1469762)))), -(c_Fun_Oinj__on(_1469756, _1469758, c_Fun_Ofun__upd(_1469756, _1469758, _1469760, _1469766, _1469764), _1469762))], (46580 ^ _779327) ^ [_1708293, _1708295, _1708297, _1708299] : [-(hAPP(hAPP(c_List_Odrop(_1708293), _1708295), hAPP(hAPP(c_List_Oappend(_1708293), _1708297), _1708299)) = hAPP(hAPP(c_List_Oappend(_1708293), hAPP(hAPP(c_List_Odrop(_1708293), _1708295), _1708297)), hAPP(hAPP(c_List_Odrop(_1708293), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1708295), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708293)), _1708297))), _1708299)))], (33606 ^ _779327) ^ [_1392042] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1392042)), -(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))), _1392042)), c_FunDef_Omax__weak)))], (26314 ^ _779327) ^ [_1242149, _1242151, _1242153, _1242155, _1242157, _1242159] : [-(hAPP(c_Set_Oimage(_1242149, _1242151, _1242153), hAPP(c_Set_Oimage(_1242155, _1242149, _1242157), _1242159)) = hAPP(c_Set_Oimage(_1242155, _1242151, hAPP(hAPP(c_COMBB(_1242149, _1242151, _1242155), _1242153), _1242157)), _1242159))], (38190 ^ _779327) ^ [_1496389] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496389), c_Orderings_Otop__class_Otop(tc_fun(_1496389, 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(_1496389), c_Orderings_Otop__class_Otop(tc_fun(_1496389, tc_HOL_Obool))))))], (31501 ^ _779327) ^ [_1350513, _1350515] : [hBOOL(hAPP(_1350513, _1350515)), -(hBOOL(hAPP(_1350513, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1350513) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _1350513), c_Nat_OSuc))))], (38333 ^ _779327) ^ [_1500737] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1500737)), c_Int_OInteg)))], (23329 ^ _779327) ^ [_1184570, _1184572] : [_1184570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1184572, _1184570) = _1184572)], (46066 ^ _779327) ^ [_1695877, _1695879, _1695881] : [-(hAPP(hAPP(c_List_Olist__update(_1695877, c_List_Olist_ONil(_1695877)), _1695879), _1695881) = c_List_Olist_ONil(_1695877))], (33816 ^ _779327) ^ [_1397586, _1397588, _1397590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1397586, _1397586), tc_HOL_Obool)), _1397588), _1397590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1397586, tc_HOL_Obool)), hAPP(c_Relation_OField(_1397586), _1397588)), hAPP(c_Relation_OField(_1397586), _1397590))))], (48355 ^ _779327) ^ [_1746233, _1746235] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746233)), c_List_Oremdups(_1746233, _1746235)) = hAPP(c_Finite__Set_Ocard(_1746233), hAPP(c_List_Oset(_1746233), _1746235)))], (41279 ^ _779327) ^ [_1578768, _1578770, _1578772, _1578774, _1578776, _1578778, _1578780, _1578782, _1578784, _1578786] : [-(c_Product__Type_Omap__pair(_1578768, _1578770, _1578772, _1578774, hAPP(c_Fun_Ocomp(_1578776, _1578770, _1578768, _1578778), _1578780), hAPP(c_Fun_Ocomp(_1578782, _1578774, _1578772, _1578784), _1578786)) = hAPP(c_Fun_Ocomp(tc_prod(_1578776, _1578782), tc_prod(_1578770, _1578774), tc_prod(_1578768, _1578772), c_Product__Type_Omap__pair(_1578776, _1578770, _1578782, _1578774, _1578778, _1578784)), c_Product__Type_Omap__pair(_1578768, _1578776, _1578772, _1578782, _1578780, _1578786)))], (33232 ^ _779327) ^ [_1384249, _1384251, _1384253, _1384255, _1384257] : [class_Fields_Ofield__inverse__zero(_1384249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384251), _1384253)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384251, _1384249), hAPP(hAPP(c_COMBS(_1384251, _1384249, _1384249), hAPP(hAPP(c_COMBB(_1384249, tc_fun(_1384249, _1384249), _1384251), c_Rings_Oinverse__class_Odivide(_1384249)), _1384255)), _1384257)), _1384253) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384249), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384251, _1384249), _1384255), _1384253)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384251, _1384249), _1384257), _1384253)))], (34439 ^ _779327) ^ [_1412395, _1412397, _1412399, _1412401, _1412403] : [hAPP(c_Relation_OImage(_1412395, _1412395, _1412397), hAPP(hAPP(c_Set_Oinsert(_1412395), _1412399), c_Orderings_Obot__class_Obot(tc_fun(_1412395, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1412395, _1412395, _1412397), hAPP(hAPP(c_Set_Oinsert(_1412395), _1412401), c_Orderings_Obot__class_Obot(tc_fun(_1412395, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1412395, _1412403, _1412397), hBOOL(hAPP(hAPP(c_member(_1412395), _1412401), _1412403)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1412395, _1412395)), hAPP(hAPP(c_Product__Type_OPair(_1412395, _1412395), _1412399), _1412401)), _1412397)))], (4240 ^ _779327) ^ [_843708, _843710] : [_843710 = _843708, -(c_SetInterval_Oord__class_OatMost(_843710) = c_SetInterval_Oord__class_OatMost(_843708))], (20625 ^ _779327) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (31123 ^ _779327) ^ [_1342921, _1342923, _1342925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342921)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1342923), _1342925)), 31130 ^ _779327 : [(31131 ^ _779327) ^ [_1343117] : [31133 ^ _779327 : [(31139 ^ _779327) ^ [] : [-(_1343117 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 31135 ^ [_1342921, _1342923, _1342925, _1343117]), 31132 ^ [_1342921, _1342923, _1342925, _1343117]))], (31137 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31135 ^ [_1342921, _1342923, _1342925, _1343117]), _1342925)))], (31134 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31132 ^ [_1342921, _1342923, _1342925, _1343117]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1342921))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342923), _1343117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1343117), _1342921))))]]], (5914 ^ _779327) ^ [_872501, _872503, _872505] : [class_Orderings_Olinorder(_872501), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_872501), _872503), _872505))), -(_872503 = _872505), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_872501), _872505), _872503)))], (44946 ^ _779327) ^ [_1667459, _1667461, _1667463] : [-(_1667459 = _1667461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667463)), _1667459) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667463)), _1667461), 44952 ^ _779327 : [(44955 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Onth(_1667463), _1667459), 44951 ^ [_1667459, _1667461, _1667463]) = hAPP(hAPP(c_List_Onth(_1667463), _1667461), 44951 ^ [_1667459, _1667461, _1667463])], (44953 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44951 ^ [_1667459, _1667461, _1667463]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667463)), _1667459))))]]], (23187 ^ _779327) ^ [_1181947] : [class_Orderings_Olinorder(_1181947), -(c_Orderings_Oord_Omin(_1181947, hAPP(c_COMBC(_1181947, _1181947, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1181947))) = c_Orderings_Oord__class_Omax(_1181947))], (17238 ^ _779327) ^ [_1071873, _1071875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071873), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071873)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071875)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071875))], (45478 ^ _779327) ^ [_1681173, _1681175, _1681177, _1681179] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681173)), _1681175) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681177)), _1681179), -(hAPP(hAPP(c_List_Omap(tc_prod(_1681173, _1681177), _1681173), c_Product__Type_Ofst(_1681173, _1681177)), hAPP(hAPP(c_List_Ozip(_1681173, _1681177), _1681175), _1681179)) = _1681175)], (36240 ^ _779327) ^ [_1454186, _1454188, _1454190, _1454192, _1454194] : [class_Fields_Ofield(_1454186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454188), _1454190)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454188), _1454192)), 36254 ^ _779327 : [(36257 ^ _779327) ^ [] : [-(hAPP(_1454194, 36253 ^ [_1454186, _1454188, _1454190, _1454192, _1454194]) = c_Groups_Ozero__class_Ozero(_1454186))], (36255 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1454188), 36253 ^ [_1454186, _1454188, _1454190, _1454192, _1454194]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454188, tc_HOL_Obool)), _1454190), _1454192))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454188, _1454186), _1454194), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1454188, tc_HOL_Obool)), _1454190), _1454192)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1454186), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454188, _1454186), _1454194), _1454190)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454188, _1454186), _1454194), _1454192))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454188, _1454186), _1454194), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454188, tc_HOL_Obool)), _1454190), _1454192))))], (38605 ^ _779327) ^ [_1506994, _1506996, _1506998, _1507000] : [c_Wellfounded_Omax__extp(_1506994, _1506996, _1506998, _1507000), 38608 ^ _779327 : [(38611 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506994), _1507000)))], (38613 ^ _779327) ^ [] : [_1507000 = c_Orderings_Obot__class_Obot(tc_fun(_1506994, tc_HOL_Obool))], (38615 ^ _779327) ^ [_1507210] : [hBOOL(hAPP(hAPP(c_member(_1506994), _1507210), _1506998)), 38619 ^ _779327 : [(38622 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1506996, _1507210), 38618 ^ [_1506994, _1506996, _1506998, _1507000, _1507210])))], (38620 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506994), 38618 ^ [_1506994, _1506996, _1506998, _1507000, _1507210]), _1507000)))]]], (38609 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506994), _1506998)))]]], (19557 ^ _779327) ^ [_1112438, _1112440, _1112442, _1112444] : [class_Fields_Olinordered__field(_1112438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112440), _1112442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), _1112444), c_Groups_Ozero__class_Ozero(_1112438))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), c_Groups_Ozero__class_Ozero(_1112438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112438), _1112440), _1112442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112438), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112438), _1112444), _1112440)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112438), _1112444), _1112442))))], (29947 ^ _779327) ^ [_1314673, _1314675, _1314677, _1314679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314673, tc_HOL_Obool)), _1314675), _1314677)), hBOOL(hAPP(hAPP(c_member(_1314673), _1314679), _1314675)), -(hBOOL(hAPP(hAPP(c_member(_1314673), _1314679), _1314677)))], (22389 ^ _779327) ^ [_1166763, _1166765, _1166767] : [class_Orderings_Olinorder(_1166763), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166763), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166763), _1166765), _1166767)), _1166767)))], (22061 ^ _779327) ^ [_1160324, _1160326, _1160328, _1160330, _1160332] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1160324, _1160326, _1160328), _1160330), _1160332) = hAPP(hAPP(_1160330, hAPP(c_Product__Type_Ofst(_1160324, _1160326), _1160332)), hAPP(c_Product__Type_Osnd(_1160324, _1160326), _1160332)))], (12225 ^ _779327) ^ [] : [-(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))], (41269 ^ _779327) ^ [_1578508, _1578510, _1578512, _1578514, _1578516, _1578518] : [-(hAPP(hAPP(c_Fun_Ocomp(_1578508, _1578510, _1578512, hAPP(c_COMBK(_1578510, _1578508), _1578514)), _1578516), _1578518) = _1578514)], (10687 ^ _779327) ^ [_952822, _952824, _952826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952822), _952826)), _952824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _952822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _952824), _952826))))], (49033 ^ _779327) ^ [_1761973, _1761975, _1761977, _1761979] : [class_Orderings_Olinorder(_1761973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761973), _1761975), _1761977)), c_List_Olinorder__class_Osorted(_1761973, hAPP(hAPP(c_List_Olist_OCons(_1761973), _1761977), _1761979)), -(c_List_Olinorder__class_Osorted(_1761973, hAPP(hAPP(c_List_Olist_OCons(_1761973), _1761975), hAPP(hAPP(c_List_Olist_OCons(_1761973), _1761977), _1761979))))], (2402 ^ _779327) ^ [_814415, _814417] : [_814417 = _814415, -(c_HOL_Obool_Obool__size(_814417) = c_HOL_Obool_Obool__size(_814415))], (24719 ^ _779327) ^ [_1209798, _1209800, _1209802, _1209804, _1209806] : [class_Rings_Ocomm__semiring__1(_1209798), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209798), _1209800), _1209802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209804), _1209806)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209798), hAPP(hAPP(c_Power_Opower__class_Opower(_1209798), _1209800), _1209804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1209798), _1209802), _1209806))))], (4924 ^ _779327) ^ [_854404, _854406] : [_854406 = _854404, -(c_Lazy__Sequence_Oyieldn(_854406) = c_Lazy__Sequence_Oyieldn(_854404))], (9068 ^ _779327) ^ [_925757, _925759, _925761, _925763] : [class_Rings_Ocomm__semiring__1(_925757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925757), _925759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925757), _925761), _925763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925757), _925761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925757), _925759), _925763)))], (39814 ^ _779327) ^ [_1535244, _1535246, _1535248, _1535250] : [-(hBOOL(hAPP(hAPP(c_member(_1535244), _1535246), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535244, tc_HOL_Obool)), _1535248), hAPP(c_Set_OCollect(_1535244), _1535250))))), hBOOL(hAPP(hAPP(c_member(_1535244), _1535246), _1535248)), hBOOL(hAPP(_1535250, _1535246))], (33337 ^ _779327) ^ [_1386590, _1386592, _1386594, _1386596] : [class_Groups_Ocomm__monoid__mult(_1386590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386592), _1386594)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386592, _1386590), hAPP(c_COMBK(_1386590, _1386592), _1386596)), _1386594) = hAPP(hAPP(c_Power_Opower__class_Opower(_1386590), _1386596), hAPP(c_Finite__Set_Ocard(_1386592), _1386594)))], (14653 ^ _779327) ^ [_1026040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026040), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1026040)))], (1208 ^ _779327) ^ [_797415, _797417] : [-(class_Rings_Olinordered__semiring__1(_797415)), _797417 = _797415, class_Rings_Olinordered__semiring__1(_797417)], (52942 ^ _779327) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (46104 ^ _779327) ^ [_1696596, _1696598, _1696600] : [hAPP(hAPP(c_List_Oappend(_1696596), _1696598), _1696600) = c_List_Olist_ONil(_1696596), 46107 ^ _779327 : [(46110 ^ _779327) ^ [] : [-(_1696600 = c_List_Olist_ONil(_1696596))], (46108 ^ _779327) ^ [] : [-(_1696598 = c_List_Olist_ONil(_1696596))]]], (1428 ^ _779327) ^ [_800165, _800167] : [-(class_Lattices_Obounded__lattice__bot(_800165)), _800167 = _800165, class_Lattices_Obounded__lattice__bot(_800167)], (25616 ^ _779327) ^ [_1227763, _1227765] : [class_Rings_Ocomm__semiring__1(_1227763), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1227763), c_Groups_Oone__class_Oone(_1227763)), c_Groups_Oone__class_Oone(_1227763))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227763), c_Nat_Osemiring__1__class_Oof__nat(_1227763)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1227765))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227763), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227763), _1227765)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1227763), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227763), _1227765)), c_Groups_Oone__class_Oone(_1227763))))], (36622 ^ _779327) ^ [_1462359, _1462361, _1462363] : [class_Lattices_Olattice(_1462359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462359), _1462361)), 36629 ^ _779327 : [(36636 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462359, tc_HOL_Obool)), _1462361), hAPP(hAPP(c_Set_Oinsert(_1462359), _1462363), c_Orderings_Obot__class_Obot(tc_fun(_1462359, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1462359, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1462359, hAPP(hAPP(c_Set_Oinsert(_1462359), _1462363), _1462361)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462359), _1462363), c_Big__Operators_Olattice__class_OInf__fin(_1462359, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462359, tc_HOL_Obool)), _1462361), hAPP(hAPP(c_Set_Oinsert(_1462359), _1462363), c_Orderings_Obot__class_Obot(tc_fun(_1462359, tc_HOL_Obool)))))))], (36630 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462359, tc_HOL_Obool)), _1462361), hAPP(hAPP(c_Set_Oinsert(_1462359), _1462363), c_Orderings_Obot__class_Obot(tc_fun(_1462359, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1462359, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1462359, hAPP(hAPP(c_Set_Oinsert(_1462359), _1462363), _1462361)) = _1462363)]]], (26609 ^ _779327) ^ [_1247711] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1247711)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1247711))], (15453 ^ _779327) ^ [_1040442, _1040444, _1040446] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040442), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040444, _1040446)), _1040446) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040442), _1040444), _1040446))], (2974 ^ _779327) ^ [_823825, _823827, _823829, _823831, _823833, _823835] : [-(c_SetInterval_Oord_OgreaterThan(_823835, _823831, _823827) = c_SetInterval_Oord_OgreaterThan(_823833, _823829, _823825)), _823835 = _823833, _823831 = _823829, _823827 = _823825], (5880 ^ _779327) ^ [_871988, _871990] : [5881 ^ _779327 : [(5884 ^ _779327) ^ [] : [_871988 = _871990], (5882 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871988), _871990))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871988), _871990)))], (21493 ^ _779327) ^ [_1149193, _1149195, _1149197] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1149193, _1149195), _1149197)), 21496 ^ _779327 : [(21497 ^ _779327) ^ [_1149278] : [hBOOL(hAPP(hAPP(_1149195, _1149278), _1149197)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1149193, _1149195), _1149278)))]]], (38854 ^ _779327) ^ [_1513883, _1513885, _1513887, _1513889, _1513891, _1513893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513883, _1513885)), hAPP(hAPP(c_Product__Type_OPair(_1513883, _1513885), _1513887), _1513889)), hAPP(hAPP(c_Product__Type_OSigma(_1513883, _1513885), _1513891), _1513893))), 38857 ^ _779327 : [(38860 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513885), _1513889), hAPP(_1513893, _1513887))))], (38858 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513883), _1513887), _1513891)))]]], (39357 ^ _779327) ^ [_1524344, _1524346, _1524348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524344, _1524344), tc_HOL_Obool)), _1524346), hAPP(hAPP(c_Product__Type_OSigma(_1524344, _1524344), _1524348), hAPP(c_COMBK(tc_fun(_1524344, tc_HOL_Obool), _1524344), _1524348)))), 39363 ^ _779327 : [(39366 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524344, _1524344)), hAPP(hAPP(c_Product__Type_OPair(_1524344, _1524344), 39362 ^ [_1524344, _1524346, _1524348]), 39362 ^ [_1524344, _1524346, _1524348])), _1524346))], (39364 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524344), 39362 ^ [_1524344, _1524346, _1524348]), _1524348)))]], -(c_Relation_Orefl__on(_1524344, _1524348, _1524346))], (45341 ^ _779327) ^ [_1677079, _1677081] : [-(hAPP(c_List_Oset(_1677079), _1677081) = hAPP(c_Set_OCollect(_1677079), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1677079), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1677079, 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)), _1677079), 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)), _1677079), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1677079, tc_fun(tc_Nat_Onat, _1677079), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1677079, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1677079), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1677079), c_COMBB(_1677079, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1677079), _1677081))))), 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(_1677079)), _1677081))))))], (41311 ^ _779327) ^ [_1579587, _1579589, _1579591, _1579593, _1579595, _1579597] : [c_Fun_Oinj__on(_1579587, _1579589, hAPP(c_Fun_Ocomp(_1579591, _1579589, _1579587, _1579593), _1579595), _1579597), -(c_Fun_Oinj__on(_1579591, _1579589, _1579593, hAPP(c_Set_Oimage(_1579587, _1579591, _1579595), _1579597)))], (37713 ^ _779327) ^ [_1485436, _1485438] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485436, tc_HOL_Obool)), _1485438), c_Orderings_Otop__class_Otop(tc_fun(_1485436, tc_HOL_Obool)))))], (48315 ^ _779327) ^ [_1745546, _1745548, _1745550, _1745552] : [-(c_List_Oremdups(_1745546, hAPP(hAPP(c_List_Omap(_1745548, _1745546), _1745550), c_List_Oremdups(_1745548, _1745552))) = c_List_Oremdups(_1745546, hAPP(hAPP(c_List_Omap(_1745548, _1745546), _1745550), _1745552)))], (19435 ^ _779327) ^ [_1110149, _1110151, _1110153] : [class_Fields_Olinordered__field(_1110149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110149), _1110151), c_Groups_Ozero__class_Ozero(_1110149))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110149), _1110153), c_Groups_Ozero__class_Ozero(_1110149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110149), c_Groups_Ozero__class_Ozero(_1110149)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110149), _1110151), _1110153))))], (5672 ^ _779327) ^ [_868939, _868941] : [class_Orderings_Oorder(_868939), 5675 ^ _779327 : [(5682 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_868939), hAPP(_868941, 5683 ^ [_868939, _868941])), hAPP(_868941, hAPP(c_Nat_OSuc, 5683 ^ [_868939, _868941])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _868939, _868941))], (5676 ^ _779327) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _868939, _868941), 5679 ^ _779327 : [(5680 ^ _779327) ^ [_869073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_868939), hAPP(_868941, _869073)), hAPP(_868941, hAPP(c_Nat_OSuc, _869073)))))]]]]], (26284 ^ _779327) ^ [_1241616, _1241618] : [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)), _1241616)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1241618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1241616), _1241618)))], (3090 ^ _779327) ^ [_825721, _825723] : [_825723 = _825721, -(c_Int_Oring__1__class_OInts(_825723) = c_Int_Oring__1__class_OInts(_825721))], (40528 ^ _779327) ^ [_1561142, _1561144] : [c_Wellfounded_Owf(_1561142, hAPP(hAPP(c_Relation_Orel__comp(_1561142, _1561142, _1561142), _1561144), _1561144)), -(c_Wellfounded_Owf(_1561142, _1561144))], (42420 ^ _779327) ^ [_1605586, _1605588, _1605590, _1605592] : [hBOOL(hAPP(hAPP(c_member(_1605586), _1605588), c_Wellfounded_Oacc(_1605586, _1605590))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605586, _1605586)), hAPP(hAPP(c_Product__Type_OPair(_1605586, _1605586), _1605592), _1605588)), c_Transitive__Closure_Ortrancl(_1605586, _1605590))), -(hBOOL(hAPP(hAPP(c_member(_1605586), _1605592), c_Wellfounded_Oacc(_1605586, _1605590))))], (3324 ^ _779327) ^ [_829324, _829326, _829328, _829330, _829332, _829334, _829336, _829338] : [-(c_Product__Type_Oapfst(_829338, _829334, _829330, _829326) = c_Product__Type_Oapfst(_829336, _829332, _829328, _829324)), _829338 = _829336, _829334 = _829332, _829330 = _829328, _829326 = _829324], (33642 ^ _779327) ^ [_1393078, _1393080, _1393082, _1393084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1393078, tc_HOL_Obool), tc_fun(_1393078, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1393078, tc_HOL_Obool), tc_fun(_1393078, tc_HOL_Obool)), _1393082), _1393084)), c_Wellfounded_Omax__ext(_1393078, _1393080))), -(c_Wellfounded_Omax__extp(_1393078, hAPP(hAPP(c_COMBC(_1393078, tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_fun(_1393078, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393078, tc_fun(tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_fun(_1393078, tc_HOL_Obool)), _1393078), c_COMBC(_1393078, tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1393078, tc_prod(_1393078, _1393078)), tc_fun(_1393078, tc_fun(tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_HOL_Obool)), _1393078), hAPP(c_COMBB(tc_prod(_1393078, _1393078), tc_fun(tc_fun(tc_prod(_1393078, _1393078), tc_HOL_Obool), tc_HOL_Obool), _1393078), c_member(tc_prod(_1393078, _1393078)))), c_Product__Type_OPair(_1393078, _1393078)))), _1393080), _1393082, _1393084))], (52624 ^ _779327) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (16315 ^ _779327) ^ [_1055850, _1055852, _1055854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055852), 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), _1055852), _1055854))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1055850))), _1055854)))], (17804 ^ _779327) ^ [_1081306, _1081308] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1081306), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1081308)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1081306), 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)))), _1081308)))], (12467 ^ _779327) ^ [_986960, _986962, _986964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986960), _986962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _986962), _986964))))], (52948 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (45314 ^ _779327) ^ [_1676434, _1676436, _1676438] : [hBOOL(hAPP(hAPP(c_member(_1676434), _1676436), hAPP(c_List_Oset(_1676434), _1676438))), 45318 ^ _779327 : [(45321 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1676434), _1676438), 45317 ^ [_1676434, _1676436, _1676438]) = _1676436)], (45319 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45317 ^ [_1676434, _1676436, _1676438]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676434)), _1676438))))]]], (22933 ^ _779327) ^ [_1176690, _1176692, _1176694, _1176696] : [class_Orderings_Olinorder(_1176690), 22936 ^ _779327 : [(22945 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176690), _1176692), _1176694)), _1176696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), _1176692), _1176696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), _1176694), _1176696))], (22937 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1176690), _1176692), _1176694)), _1176696)), 22940 ^ _779327 : [(22943 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), _1176694), _1176696)))], (22941 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176690), _1176692), _1176696)))]]]]], (10705 ^ _779327) ^ [_953173, _953175, _953177, _953179] : [class_Rings_Ocomm__semiring__1(_953173), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953173), _953175), _953177)), _953179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953173), _953175), _953179)), _953177))], (21095 ^ _779327) ^ [_1140867, _1140869, _1140871, _1140873, _1140875] : [class_Complete__Lattice_Ocomplete__lattice(_1140867), 21098 ^ _779327 : [(21099 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140867), _1140869), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1140871, _1140867), _1140873), _1140875))), 21102 ^ _779327 : [(21103 ^ _779327) ^ [_1141048] : [hBOOL(hAPP(hAPP(c_member(_1140871), _1141048), _1140873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140867), _1140869), hAPP(_1140875, _1141048))))]]], (21109 ^ _779327) ^ [] : [21111 ^ _779327 : [(21114 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140867), _1140869), hAPP(_1140875, 21110 ^ [_1140867, _1140869, _1140871, _1140873, _1140875])))], (21112 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1140871), 21110 ^ [_1140867, _1140869, _1140871, _1140873, _1140875]), _1140873)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140867), _1140869), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1140871, _1140867), _1140873), _1140875))))]]], (39467 ^ _779327) ^ [_1527280, _1527282, _1527284] : [class_Lattices_Oab__semigroup__idem__mult(_1527280), hAPP(_1527282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1527280), 39472 ^ [_1527280, _1527282, _1527284]), 39473 ^ [_1527280, _1527282, _1527284])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1527280), hAPP(_1527282, 39472 ^ [_1527280, _1527282, _1527284])), hAPP(_1527282, 39473 ^ [_1527280, _1527282, _1527284])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527280), _1527284)), -(_1527284 = c_Orderings_Obot__class_Obot(tc_fun(_1527280, tc_HOL_Obool))), -(hAPP(_1527282, hAPP(c_Finite__Set_Ofold1(_1527280, c_Groups_Otimes__class_Otimes(_1527280)), _1527284)) = hAPP(c_Finite__Set_Ofold1(_1527280, c_Groups_Otimes__class_Otimes(_1527280)), hAPP(c_Set_Oimage(_1527280, _1527280, _1527282), _1527284)))], (51223 ^ _779327) ^ [_1807647, _1807649, _1807651, _1807653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807647), _1807649)), -(hAPP(hAPP(c_List_Onth(_1807651), c_List_Oreplicate(_1807651, _1807649, _1807653)), _1807647) = _1807653)], (45580 ^ _779327) ^ [_1683889, _1683891, _1683893] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683889), tc_List_Olist(_1683889))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683889), tc_List_Olist(_1683889)), _1683891), c_List_Olist_ONil(_1683889))), c_List_Olex(_1683889, _1683893)))], (7440 ^ _779327) ^ [_896271, _896273, _896275] : [class_Rings_Osemiring__1(_896271), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_896271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _896273), _896275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896271), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_896271), _896273)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_896271), _896275)))], (45215 ^ _779327) ^ [_1674109, _1674111, _1674113] : [c_Fun_Oinj__on(tc_List_Olist(_1674109), tc_List_Olist(_1674111), hAPP(c_List_Omap(_1674109, _1674111), _1674113), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674109), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1674109, _1674111, _1674113, c_Orderings_Otop__class_Otop(tc_fun(_1674109, tc_HOL_Obool))))], (17984 ^ _779327) ^ [_1084624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084624), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084624)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52800 ^ _779327) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (40643 ^ _779327) ^ [_1563245, _1563247] : [c_Wellfounded_Owf(_1563245, _1563247), 40646 ^ _779327 : [(40647 ^ _779327) ^ [_1563314] : [-(hBOOL(hAPP(hAPP(c_member(_1563245), _1563314), c_Wellfounded_Oacc(_1563245, _1563247))))]]], (21037 ^ _779327) ^ [_1139577, _1139579, _1139581, _1139583, _1139585] : [class_Complete__Lattice_Ocomplete__lattice(_1139577), class_Orderings_Olinorder(_1139577), 21044 ^ _779327 : [(21054 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1139579, _1139577), _1139581), _1139583)), _1139585))), 21055 ^ _779327 : [(21056 ^ _779327) ^ [_1139925] : [hBOOL(hAPP(hAPP(c_member(_1139579), _1139925), _1139581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), hAPP(_1139583, _1139925)), _1139585))]]], (21045 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1139579, _1139577), _1139581), _1139583)), _1139585)), 21049 ^ _779327 : [(21052 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), hAPP(_1139583, 21048 ^ [_1139577, _1139579, _1139581, _1139583, _1139585])), _1139585)))], (21050 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1139579), 21048 ^ [_1139577, _1139579, _1139581, _1139583, _1139585]), _1139581)))]]]]], (35565 ^ _779327) ^ [_1437632, _1437634, _1437636] : [class_Orderings_Oorder(_1437632), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437632, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1437632, _1437634, _1437636)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1437632), _1437636)) = c_Orderings_Obot__class_Obot(tc_fun(_1437632, tc_HOL_Obool)))], (41493 ^ _779327) ^ [_1583498, _1583500, _1583502, _1583504, _1583506, _1583508, _1583510, _1583512] : [c_Finite__Set_Ofolding(_1583498, _1583500, _1583502, _1583504), -(hAPP(c_Fun_Ocomp(_1583500, _1583500, _1583506, hAPP(_1583502, _1583508)), hAPP(c_Fun_Ocomp(_1583500, _1583500, _1583506, hAPP(_1583502, _1583510)), _1583512)) = hAPP(c_Fun_Ocomp(_1583500, _1583500, _1583506, hAPP(_1583502, _1583510)), hAPP(c_Fun_Ocomp(_1583500, _1583500, _1583506, hAPP(_1583502, _1583508)), _1583512)))], (14671 ^ _779327) ^ [_1026269, _1026271] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026269), _1026271) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1026271 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14680 ^ _779327 : [(14683 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026269), _1026271)))], (14681 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026269)))]], 14684 ^ _779327 : [(14687 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026271), _1026269)))], (14685 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1026269), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (1088 ^ _779327) ^ [_795801, _795803, _795805, _795807] : [-(c_Predicate_Otransp(_795805, _795801)), c_Predicate_Otransp(_795807, _795803), _795807 = _795805, _795803 = _795801], (18128 ^ _779327) ^ [_1087158] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087158))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1087158)))))], (17514 ^ _779327) ^ [_1076616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1076616)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076616), c_Int_OMin)))], (45777 ^ _779327) ^ [_1689064, _1689066] : [class_Groups_Ocomm__monoid__add(_1689064), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1689064), _1689066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1689064), hAPP(c_List_Onth(_1689064), _1689066)), 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(_1689064)), _1689066))))], (4286 ^ _779327) ^ [_844483, _844485, _844487, _844489] : [-(c_List_Olinorder__class_Osorted__list__of__set(_844489, _844485) = c_List_Olinorder__class_Osorted__list__of__set(_844487, _844483)), _844489 = _844487, _844485 = _844483], (9244 ^ _779327) ^ [_928980, _928982] : [class_Rings_Ocomm__semiring__1(_928980), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928980), _928982), c_Groups_Ozero__class_Ozero(_928980)) = c_Groups_Ozero__class_Ozero(_928980))], (17426 ^ _779327) ^ [_1075191, _1075193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075191), _1075193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075191)), c_Int_OBit1(_1075193))))], (43710 ^ _779327) ^ [_1635069] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1635069, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1635069, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1635069, tc_HOL_Obool)))], (17544 ^ _779327) ^ [_1077091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1077091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1077091))))], (19001 ^ _779327) ^ [_1102986, _1102988, _1102990, _1102992] : [class_Fields_Olinordered__field(_1102986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102986), _1102988), _1102990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102986), _1102992), c_Groups_Ozero__class_Ozero(_1102986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102986), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102986), _1102990), _1102992)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102986), _1102988), _1102992))))], (47830 ^ _779327) ^ [_1734806, _1734808, _1734810] : [47832 ^ _779327 : [(47835 ^ _779327) ^ [] : [hBOOL(hAPP(_1734808, 47831 ^ [_1734806, _1734808, _1734810]))], (47833 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734806), 47831 ^ [_1734806, _1734808, _1734810]), hAPP(c_List_Oset(_1734806), _1734810))))]], -(hBOOL(hAPP(c_List_Olistsp(_1734806, _1734808), _1734810)))], (39898 ^ _779327) ^ [_1537710, _1537712, _1537714, _1537716] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1537710, tc_fun(_1537712, tc_HOL_Obool)), _1537714), _1537716) = hAPP(c_Set_OCollect(_1537712), hAPP(hAPP(c_COMBB(tc_fun(_1537710, tc_HOL_Obool), tc_HOL_Obool, _1537712), c_HOL_OAll(_1537710)), hAPP(hAPP(c_COMBB(tc_fun(_1537710, tc_HOL_Obool), tc_fun(_1537710, tc_HOL_Obool), _1537712), hAPP(c_COMBS(_1537710, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537710), c_fimplies), hAPP(hAPP(c_COMBC(_1537710, tc_fun(_1537710, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537710)), _1537714)))), hAPP(hAPP(c_COMBC(_1537712, tc_fun(_1537710, tc_fun(_1537712, tc_HOL_Obool)), tc_fun(_1537710, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1537712, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1537710, tc_fun(_1537712, tc_HOL_Obool)), tc_fun(_1537710, tc_HOL_Obool)), _1537712), c_COMBB(tc_fun(_1537712, tc_HOL_Obool), tc_HOL_Obool, _1537710)), c_member(_1537712))), _1537716)))))], (13102 ^ _779327) ^ [_998307, _998309, _998311] : [class_Int_Onumber__ring(_998307), class_Rings_Olinordered__idom(_998307), 13109 ^ _779327 : [(13116 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998309), _998311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998307), hAPP(c_Int_Onumber__class_Onumber__of(_998307), _998309)), hAPP(c_Int_Onumber__class_Onumber__of(_998307), _998311))))], (13110 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998307), hAPP(c_Int_Onumber__class_Onumber__of(_998307), _998309)), hAPP(c_Int_Onumber__class_Onumber__of(_998307), _998311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998309), _998311)))]]], (34769 ^ _779327) ^ [_1420040, _1420042, _1420044] : [class_Lattices_Osemilattice__inf(_1420040), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420040), _1420042), _1420044) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1420040), _1420044), _1420042))], (2890 ^ _779327) ^ [_822467, _822469, _822471, _822473, _822475, _822477, _822479, _822481] : [-(c_New__DSequence_Oneg__bind(_822481, _822477, _822473, _822469) = c_New__DSequence_Oneg__bind(_822479, _822475, _822471, _822467)), _822481 = _822479, _822477 = _822475, _822473 = _822471, _822469 = _822467], (35165 ^ _779327) ^ [_1428556, _1428558, _1428560] : [class_Lattices_Oboolean__algebra(_1428556), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1428556), _1428558), _1428560) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1428556), _1428558), hAPP(c_Groups_Ouminus__class_Ouminus(_1428556), _1428560)))], (7476 ^ _779327) ^ [_896991, _896993, _896995] : [class_Rings_Oring__no__zero__divisors(_896991), 7479 ^ _779327 : [(7480 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896991), _896993), _896995) = c_Groups_Ozero__class_Ozero(_896991), -(_896993 = c_Groups_Ozero__class_Ozero(_896991)), -(_896995 = c_Groups_Ozero__class_Ozero(_896991))], (7490 ^ _779327) ^ [] : [7491 ^ _779327 : [(7494 ^ _779327) ^ [] : [_896995 = c_Groups_Ozero__class_Ozero(_896991)], (7492 ^ _779327) ^ [] : [_896993 = c_Groups_Ozero__class_Ozero(_896991)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896991), _896993), _896995) = c_Groups_Ozero__class_Ozero(_896991))]]], (16215 ^ _779327) ^ [_1054124, _1054126] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1054124))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054124)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054126)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7364 ^ _779327) ^ [_894777, _894779, _894781, _894783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894777), _894779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894781), _894783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894777), _894781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894779), _894783))))], (22671 ^ _779327) ^ [] : [-(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))], (31318 ^ _779327) ^ [_1346944, _1346946, _1346948, _1346950, _1346952, _1346954, _1346956, _1346958] : [c_Finite__Set_Ofolding__image__simple(_1346944, _1346946, _1346948, _1346950, _1346952, _1346954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346946), _1346956)), -(hBOOL(hAPP(hAPP(c_member(_1346946), _1346958), _1346956))), -(hAPP(_1346954, hAPP(hAPP(c_Set_Oinsert(_1346946), _1346958), _1346956)) = hAPP(hAPP(_1346948, hAPP(_1346952, _1346958)), hAPP(_1346954, _1346956)))], (30221 ^ _779327) ^ [_1322814, _1322816, _1322818, _1322820] : [hBOOL(hAPP(hAPP(c_member(_1322814), _1322816), _1322818)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322814, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1322814), _1322816), _1322820)), _1322818) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322814, tc_HOL_Obool)), _1322820), _1322818))], (42294 ^ _779327) ^ [_1602770, _1602772] : [-(c_Relation_Orefl__on(_1602770, c_Orderings_Otop__class_Otop(tc_fun(_1602770, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1602770, _1602772)))], (44164 ^ _779327) ^ [_1645429, _1645431, _1645433] : [44166 ^ _779327 : [(44169 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1645429), _1645433), 44165 ^ [_1645429, _1645431, _1645433]))], (44167 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1645429, tc_HOL_Obool)), 44165 ^ [_1645429, _1645431, _1645433]), _1645431)))]], -(hBOOL(hAPP(hAPP(c_member(_1645429), _1645433), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1645429, tc_HOL_Obool), _1645431))))], (45576 ^ _779327) ^ [_1683741, _1683743] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683741), tc_List_Olist(_1683741))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683741), tc_List_Olist(_1683741)), c_List_Olist_ONil(_1683741)), c_List_Olist_ONil(_1683741))), c_List_Olistrel(_1683741, _1683743))))], (6444 ^ _779327) ^ [_880513, _880515, _880517] : [class_Orderings_Olinorder(_880513), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880513), _880515), _880517))), 6451 ^ _779327 : [(6458 ^ _779327) ^ [] : [_880515 = _880517, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880513), _880515), _880517)))], (6452 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880513), _880515), _880517)), -(_880515 = _880517)]]], (52824 ^ _779327) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (48546 ^ _779327) ^ [_1751186, _1751188, _1751190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1751186, tc_HOL_Obool)), hAPP(c_List_Oset(_1751186), hAPP(c_List_Ofilter(_1751186, _1751188), _1751190))), hAPP(c_List_Oset(_1751186), _1751190))))], (17958 ^ _779327) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (5734 ^ _779327) ^ [_870038] : [hAPP(c_Nat_OSuc, _870038) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22113 ^ _779327) ^ [_1161308, _1161310, _1161312, _1161314, _1161316] : [hAPP(c_Product__Type_Ofst(_1161308, _1161310), hAPP(hAPP(c_Product__Type_OPair(_1161308, _1161310), _1161312), _1161314)) = _1161316, -(_1161312 = _1161316)], (16471 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (19701 ^ _779327) ^ [_1115218, _1115220, _1115222, _1115224] : [class_Fields_Olinordered__field__inverse__zero(_1115218), 19704 ^ _779327 : [(19705 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115218), _1115220), _1115222)), _1115224)), 19708 ^ _779327 : [(19715 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115222))), 19718 ^ _779327 : [(19725 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115222), c_Groups_Ozero__class_Ozero(_1115218)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115224)))], (19719 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115222), c_Groups_Ozero__class_Ozero(_1115218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115218), _1115224), _1115222)), _1115220)))]]], (19709 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115218), _1115224), _1115222))))]]], (19731 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1115218), _1115220), _1115222)), _1115224))), 19734 ^ _779327 : [(19737 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115218), _1115224), _1115222)))], (19735 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115222)))]], 19738 ^ _779327 : [(19741 ^ _779327) ^ [] : [19742 ^ _779327 : [(19745 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115218), _1115224), _1115222)), _1115220))], (19743 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115222), c_Groups_Ozero__class_Ozero(_1115218))))]], 19746 ^ _779327 : [(19749 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115224))], (19747 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), _1115222), c_Groups_Ozero__class_Ozero(_1115218)))]]], (19739 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115218), c_Groups_Ozero__class_Ozero(_1115218)), _1115222))]]]]], (26147 ^ _779327) ^ [_1238489, _1238491, _1238493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238489)), 26150 ^ _779327 : [(26151 ^ _779327) ^ [_1238623] : [26153 ^ _779327 : [(26159 ^ _779327) ^ [] : [-(_1238623 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26155 ^ [_1238489, _1238491, _1238493, _1238623]), 26152 ^ [_1238489, _1238491, _1238493, _1238623]))], (26157 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26155 ^ [_1238489, _1238491, _1238493, _1238623]), _1238491)))], (26154 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26152 ^ [_1238489, _1238491, _1238493, _1238623]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1238489))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238493), _1238623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238623), _1238489))))]]], (13306 ^ _779327) ^ [_1001945, _1001947, _1001949] : [class_Int_Onumber__ring(_1001945), -(hAPP(c_Int_Onumber__class_Onumber__of(_1001945), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001947), _1001949)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001945), hAPP(c_Int_Onumber__class_Onumber__of(_1001945), _1001947)), hAPP(c_Int_Onumber__class_Onumber__of(_1001945), _1001949)))], (28568 ^ _779327) ^ [_1288255, _1288257, _1288259, _1288261, _1288263] : [-(hAPP(hAPP(c_Set_Oinsert(_1288255), _1288257), hAPP(hAPP(c_Set_Oinsert(_1288255), _1288259), c_Orderings_Obot__class_Obot(tc_fun(_1288255, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1288255), _1288261), hAPP(hAPP(c_Set_Oinsert(_1288255), _1288263), c_Orderings_Obot__class_Obot(tc_fun(_1288255, tc_HOL_Obool))))), 28569 ^ _779327 : [(28576 ^ _779327) ^ [] : [_1288257 = _1288263, _1288259 = _1288261], (28570 ^ _779327) ^ [] : [_1288257 = _1288261, _1288259 = _1288263]]], (12838 ^ _779327) ^ [_993850, _993852] : [class_Groups_Oordered__ab__group__add(_993850), 12841 ^ _779327 : [(12848 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993850), c_Groups_Ozero__class_Ozero(_993850)), _993852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993850), hAPP(c_Groups_Ouminus__class_Ouminus(_993850), _993852)), c_Groups_Ozero__class_Ozero(_993850))))], (12842 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993850), hAPP(c_Groups_Ouminus__class_Ouminus(_993850), _993852)), c_Groups_Ozero__class_Ozero(_993850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993850), c_Groups_Ozero__class_Ozero(_993850)), _993852)))]]], (29827 ^ _779327) ^ [_1312489, _1312491, _1312493, _1312495, _1312497] : [-(hBOOL(hAPP(hAPP(c_member(_1312489), _1312491), hAPP(c_Set_Oimage(_1312493, _1312489, _1312495), _1312497)))), 29828 ^ _779327 : [(29829 ^ _779327) ^ [_1312559] : [hBOOL(hAPP(hAPP(c_member(_1312493), _1312559), _1312497)), _1312491 = hAPP(_1312495, _1312559)]]], (46866 ^ _779327) ^ [_1714454, _1714456] : [hBOOL(hAPP(c_List_Odistinct(_1714454), _1714456)), -(hAPP(c_Finite__Set_Ocard(_1714454), hAPP(c_List_Oset(_1714454), _1714456)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714454)), _1714456))], (52682 ^ _779327) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (15696 ^ _779327) ^ [_1044881, _1044883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1044881), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 15699 ^ _779327 : [(15702 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1044881), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044883, _1044881))))], (15700 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044883, _1044881)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (45205 ^ _779327) ^ [_1673840, _1673842, _1673844] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673840, tc_HOL_Obool)), hAPP(c_List_Oset(_1673840), c_List_Osublist(_1673840, _1673842, _1673844))), hAPP(c_List_Oset(_1673840), _1673842))))], (17670 ^ _779327) ^ [_1079095] : [class_Int_Onumber__ring(_1079095), c_Int_Oiszero(_1079095, hAPP(c_Int_Onumber__class_Onumber__of(_1079095), c_Int_OBit1(c_Int_OPls)))], (19837 ^ _779327) ^ [_1117644, _1117646, _1117648, _1117650] : [class_Fields_Ofield__inverse__zero(_1117644), -(_1117646 = c_Groups_Ozero__class_Ozero(_1117644)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117644), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117644), _1117648), _1117646)), _1117650) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117644), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117644), _1117648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117644), _1117650), _1117646))), _1117646))], (32966 ^ _779327) ^ [_1379201, _1379203, _1379205, _1379207, _1379209, _1379211] : [-(hBOOL(hAPP(hAPP(c_member(_1379201), _1379203), _1379205))), -(hAPP(c_Set_Oimage(_1379201, _1379207, c_Fun_Ofun__upd(_1379201, _1379207, _1379209, _1379203, _1379211)), _1379205) = hAPP(c_Set_Oimage(_1379201, _1379207, _1379209), _1379205))], (46540 ^ _779327) ^ [_1707365, _1707367, _1707369] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707365)), hAPP(hAPP(c_List_Odrop(_1707365), _1707367), _1707369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707365)), _1707369)), _1707367))], (21278 ^ _779327) ^ [_1145059, _1145061] : [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(_1145061))), 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), _1145059)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1145059)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145061))))], (40534 ^ _779327) ^ [_1561241, _1561243] : [-(hAPP(c_Relation_ORange(_1561241, _1561241), c_Relation_OId__on(_1561241, _1561243)) = _1561243)], (17660 ^ _779327) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (26938 ^ _779327) ^ [_1254393, _1254395] : [class_Lattices_Osemilattice__sup(_1254393), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254393), _1254395), _1254395) = _1254395)], (46044 ^ _779327) ^ [_1695386, _1695388, _1695390] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695386)), hAPP(hAPP(c_List_Oappend(_1695386), _1695388), _1695390)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695386)), _1695388)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695386)), _1695390)))], (34033 ^ _779327) ^ [_1402531, _1402533, _1402535, _1402537, _1402539] : [c_Finite__Set_Ofolding__one__idem(_1402531, _1402533, _1402535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402531), _1402537)), hBOOL(hAPP(hAPP(c_member(_1402531), _1402539), _1402537)), -(hAPP(hAPP(_1402533, _1402539), hAPP(_1402535, _1402537)) = hAPP(_1402535, _1402537))], (46012 ^ _779327) ^ [_1694582, _1694584, _1694586, _1694588] : [-(hAPP(hAPP(c_List_Oappend(_1694582), hAPP(hAPP(c_List_Olist_OCons(_1694582), _1694584), _1694586)), _1694588) = hAPP(hAPP(c_List_Olist_OCons(_1694582), _1694584), hAPP(hAPP(c_List_Oappend(_1694582), _1694586), _1694588)))], (52576 ^ _779327) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (36306 ^ _779327) ^ [_1455686, _1455688, _1455690, _1455692, _1455694, _1455696] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455686, tc_fun(_1455688, tc_HOL_Obool))), _1455690), _1455692), _1455694), _1455696)), -(hBOOL(hAPP(hAPP(_1455690, _1455694), _1455696)))], (36122 ^ _779327) ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006] : [c_Equiv__Relations_Oequiv(_1449994, _1449996, _1449998), c_Equiv__Relations_Ocongruent(_1449994, tc_fun(_1450000, tc_HOL_Obool), _1449998, _1450002), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449994, tc_fun(_1450000, tc_HOL_Obool)), _1450004), _1450002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449994, tc_fun(_1450000, tc_HOL_Obool)), _1450006), _1450002), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449994, tc_HOL_Obool)), _1450004), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449994), _1449996), _1449998))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449994, tc_HOL_Obool)), _1450006), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449994), _1449996), _1449998))), 36144 ^ _779327 : [(36148 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449994), 36146 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006]), _1449996)))], (36150 ^ _779327) ^ [] : [-(hAPP(_1450002, 36143 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006]) = hAPP(_1450002, 36146 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006]))], (36152 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1449994, _1449994)), hAPP(hAPP(c_Product__Type_OPair(_1449994, _1449994), 36143 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006]), 36146 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006])), _1449998))], (36145 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449994), 36143 ^ [_1449994, _1449996, _1449998, _1450000, _1450002, _1450004, _1450006]), _1449996)))]], -(_1450004 = _1450006)], (20965 ^ _779327) ^ [_1138453, _1138455] : [_1138453 = _1138455, -(c_Code__Numeral_OSuc__code__numeral(_1138453) = c_Code__Numeral_OSuc__code__numeral(_1138455))], (29186 ^ _779327) ^ [_1299602, _1299604] : [29187 ^ _779327 : [(29190 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1299602), _1299604)))], (29188 ^ _779327) ^ [] : [_1299604 = c_Orderings_Obot__class_Obot(tc_fun(_1299602, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1299602), _1299604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46259 ^ _779327) ^ [_1699902, _1699904, _1699906, _1699908] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699902)), hAPP(hAPP(c_List_Oappend(_1699902), _1699904), _1699906)), c_List_Olists(_1699902, _1699908))), 46262 ^ _779327 : [(46265 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699902)), _1699906), c_List_Olists(_1699902, _1699908))))], (46263 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699902)), _1699904), c_List_Olists(_1699902, _1699908))))]]], (29278 ^ _779327) ^ [_1301315, _1301317] : [class_Orderings_Olinorder(_1301315), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301315, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1301315), _1301317)), hAPP(hAPP(c_Set_Oinsert(_1301315), _1301317), c_Orderings_Obot__class_Obot(tc_fun(_1301315, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1301315), _1301317))], (43712 ^ _779327) ^ [_1635111, _1635113, _1635115] : [class_Complete__Lattice_Ocomplete__lattice(_1635111), hBOOL(hAPP(hAPP(c_member(_1635111), _1635113), _1635115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1635111), c_Complete__Lattice_OInf__class_OInf(_1635111, _1635115)), _1635113)))], (1488 ^ _779327) ^ [_800915, _800917] : [-(class_Orderings_Otop(_800915)), _800917 = _800915, class_Orderings_Otop(_800917)], (2450 ^ _779327) ^ [_815163, _815165, _815167, _815169] : [-(c_Nitpick_Oinverse__frac(_815169, _815165) = c_Nitpick_Oinverse__frac(_815167, _815163)), _815169 = _815167, _815165 = _815163], (15057 ^ _779327) ^ [_1032868, _1032870, _1032872] : [-(hBOOL(hAPP(_1032868, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032870), _1032872)))), 15060 ^ _779327 : [(15063 ^ _779327) ^ [] : [hBOOL(hAPP(_1032868, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15061 ^ _779327) ^ [] : [-(_1032872 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 15066 ^ _779327 : [(15067 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032872)))], (15073 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 15069 ^ [_1032868, _1032870, _1032872]), _1032872)))], (15077 ^ _779327) ^ [] : [hBOOL(hAPP(_1032868, 15068 ^ [_1032868, _1032870, _1032872]))], (15075 ^ _779327) ^ [] : [-(_1032870 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1032872), 15068 ^ [_1032868, _1032870, _1032872])), 15069 ^ [_1032868, _1032870, _1032872]))], (15071 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15069 ^ [_1032868, _1032870, _1032872])))]], 15078 ^ _779327 : [(15079 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032872), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15085 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 15081 ^ [_1032868, _1032870, _1032872]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15089 ^ _779327) ^ [] : [hBOOL(hAPP(_1032868, 15080 ^ [_1032868, _1032870, _1032872]))], (15087 ^ _779327) ^ [] : [-(_1032870 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1032872), 15080 ^ [_1032868, _1032870, _1032872])), 15081 ^ [_1032868, _1032870, _1032872]))], (15083 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032872), 15081 ^ [_1032868, _1032870, _1032872])))]]], (24595 ^ _779327) ^ [_1207406, _1207408, _1207410] : [class_Divides_Osemiring__div(_1207406), 24598 ^ _779327 : [(24605 ^ _779327) ^ [] : [c_Divides_Odiv__class_Omod(_1207406, _1207410, _1207408) = c_Groups_Ozero__class_Ozero(_1207406), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207406), _1207408), _1207410)))], (24599 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207406), _1207408), _1207410)), -(c_Divides_Odiv__class_Omod(_1207406, _1207410, _1207408) = c_Groups_Ozero__class_Ozero(_1207406))]]], (48359 ^ _779327) ^ [_1746344, _1746346] : [class_Orderings_Olinorder(_1746344), -(c_List_Olinorder__class_Osorted__list__of__set(_1746344, hAPP(c_List_Oset(_1746344), _1746346)) = c_List_Olinorder__class_Osort__key(_1746344, _1746344, c_COMBI(_1746344), c_List_Oremdups(_1746344, _1746346)))], (52305 ^ _779327) ^ [_1831558, _1831560] : [-(c_Equiv__Relations_Opart__equivp(_1831558, _1831560)), 52308 ^ _779327 : [(52309 ^ _779327) ^ [_1831678] : [hBOOL(hAPP(hAPP(_1831560, _1831678), _1831678))]], 52326 ^ _779327 : [(52329 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1831560, 52311 ^ [_1831558, _1831560]), 52311 ^ [_1831558, _1831560])))], (52331 ^ _779327) ^ [] : [-(hAPP(_1831560, 52310 ^ [_1831558, _1831560]) = hAPP(_1831560, 52311 ^ [_1831558, _1831560]))], (52333 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1831560, 52310 ^ [_1831558, _1831560]), 52311 ^ [_1831558, _1831560]))], (52327 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1831560, 52310 ^ [_1831558, _1831560]), 52310 ^ [_1831558, _1831560])))]], 52314 ^ _779327 : [(52317 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1831560, 52310 ^ [_1831558, _1831560]), 52310 ^ [_1831558, _1831560])), hBOOL(hAPP(hAPP(_1831560, 52311 ^ [_1831558, _1831560]), 52311 ^ [_1831558, _1831560])), hAPP(_1831560, 52310 ^ [_1831558, _1831560]) = hAPP(_1831560, 52311 ^ [_1831558, _1831560])], (52315 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1831560, 52310 ^ [_1831558, _1831560]), 52311 ^ [_1831558, _1831560])))]]], (2036 ^ _779327) ^ [_808714, _808716, _808718, _808720] : [-(c_SMT_Oz3mod(_808720, _808716) = c_SMT_Oz3mod(_808718, _808714)), _808720 = _808718, _808716 = _808714], (34575 ^ _779327) ^ [_1415595, _1415597, _1415599, _1415601, _1415603, _1415605] : [c_Equiv__Relations_Oequiv(_1415595, _1415597, _1415599), hBOOL(hAPP(hAPP(c_member(_1415595), _1415601), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415595, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1415595, _1415595, _1415599), hAPP(hAPP(c_Set_Oinsert(_1415595), _1415603), c_Orderings_Obot__class_Obot(tc_fun(_1415595, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1415595, _1415595, _1415599), hAPP(hAPP(c_Set_Oinsert(_1415595), _1415605), c_Orderings_Obot__class_Obot(tc_fun(_1415595, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1415595, _1415595)), hAPP(hAPP(c_Product__Type_OPair(_1415595, _1415595), _1415603), _1415605)), _1415599)))], (17858 ^ _779327) ^ [_1082439, _1082441] : [class_Rings_Osemiring__1(_1082439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082441)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082439), 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)))), _1082441))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082439), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082439), hAPP(c_Int_Onat, _1082441))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1082439), hAPP(c_Int_Onat, _1082441))))], (26014 ^ _779327) ^ [_1235832, _1235834] : [26022 ^ _779327 : [(26025 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1235834, 26021 ^ [_1235832, _1235834])))], (26023 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26021 ^ [_1235832, _1235834]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235832))))]], 26015 ^ _779327 : [(26016 ^ _779327) ^ [_1235900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235900), _1235832)), hBOOL(hAPP(_1235834, _1235900))]]], (52522 ^ _779327) ^ [_1835671, _1835673] : [class_Orderings_Oord(_1835671), -(class_Orderings_Oord(tc_fun(_1835673, _1835671)))], (40134 ^ _779327) ^ [_1547137, _1547139, _1547141] : [class_Lattices_Odistrib__lattice(_1547137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547137), _1547139)), -(_1547139 = c_Orderings_Obot__class_Obot(tc_fun(_1547137, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547137), _1547141)), -(_1547141 = c_Orderings_Obot__class_Obot(tc_fun(_1547137, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1547137), c_Big__Operators_Olattice__class_OSup__fin(_1547137, _1547139)), c_Big__Operators_Olattice__class_OSup__fin(_1547137, _1547141)) = c_Big__Operators_Olattice__class_OSup__fin(_1547137, hAPP(c_Set_OCollect(_1547137), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_HOL_Obool), tc_HOL_Obool, _1547137), c_HOL_OEx(_1547137)), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool)), tc_fun(_1547137, tc_HOL_Obool), _1547137), hAPP(c_COMBB(tc_fun(_1547137, tc_HOL_Obool), tc_HOL_Obool, _1547137), c_HOL_OEx(_1547137))), hAPP(hAPP(c_COMBC(_1547137, tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool)), tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_fun(tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool))), tc_fun(tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool)), tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool))), _1547137), c_COMBS(_1547137, tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_fun(_1547137, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1547137, tc_fun(tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool))), _1547137), hAPP(c_COMBB(tc_fun(_1547137, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool)), _1547137), c_COMBS(_1547137, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool)), tc_fun(_1547137, tc_fun(_1547137, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1547137), hAPP(c_COMBB(tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1547137), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547137), c_fconj))), hAPP(hAPP(c_COMBC(_1547137, tc_fun(_1547137, tc_fun(_1547137, _1547137)), tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547137, _1547137), tc_fun(_1547137, tc_HOL_Obool)), tc_fun(tc_fun(_1547137, tc_fun(_1547137, _1547137)), tc_fun(_1547137, tc_fun(_1547137, tc_HOL_Obool))), _1547137), c_COMBB(tc_fun(_1547137, _1547137), tc_fun(_1547137, tc_HOL_Obool), _1547137)), hAPP(hAPP(c_COMBB(tc_fun(_1547137, tc_HOL_Obool), tc_fun(tc_fun(_1547137, _1547137), tc_fun(_1547137, tc_HOL_Obool)), _1547137), c_COMBB(_1547137, tc_HOL_Obool, _1547137)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1547137)))))), hAPP(hAPP(c_COMBC(_1547137, tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1547137, tc_HOL_Obool), tc_fun(_1547137, tc_HOL_Obool)), _1547137), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1547137)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547137), c_fconj), hAPP(hAPP(c_COMBC(_1547137, tc_fun(_1547137, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547137)), _1547139)))), hAPP(hAPP(c_COMBC(_1547137, tc_fun(_1547137, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547137)), _1547141))))))))], (25548 ^ _779327) ^ [_1225981, _1225983, _1225985, _1225987, _1225989] : [class_Fields_Ofield(_1225981), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1225981), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225983, _1225981), _1225985), _1225987)), _1225989) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225983, _1225981), hAPP(hAPP(c_COMBC(_1225983, _1225981, _1225981), hAPP(hAPP(c_COMBB(_1225981, tc_fun(_1225981, _1225981), _1225983), c_Rings_Oinverse__class_Odivide(_1225981)), _1225985)), _1225989)), _1225987))], (19029 ^ _779327) ^ [_1103524, _1103526, _1103528] : [class_Fields_Olinordered__field(_1103524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103524), _1103526), c_Groups_Ozero__class_Ozero(_1103524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103524), _1103528), c_Groups_Ozero__class_Ozero(_1103524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103524), c_Groups_Ozero__class_Ozero(_1103524)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1103524), _1103526), _1103528))))], (47231 ^ _779327) ^ [_1722331, _1722333] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1722331), hAPP(c_List_Oset(tc_Nat_Onat), _1722333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722331), 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)), _1722333))))], (14465 ^ _779327) ^ [_1023303, _1023305] : [class_Divides_Osemiring__div(_1023303), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1023303), _1023305), c_Groups_Ozero__class_Ozero(_1023303)) = c_Groups_Ozero__class_Ozero(_1023303))], (24019 ^ _779327) ^ [_1197854, _1197856] : [class_Rings_Ocomm__semiring__1(_1197854), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1197854), c_Groups_Ozero__class_Ozero(_1197854)), _1197856)), -(_1197856 = c_Groups_Ozero__class_Ozero(_1197854))], (6504 ^ _779327) ^ [_881315, _881317, _881319, _881321, _881323] : [class_Orderings_Oorder(_881315), class_Orderings_Oorder(_881317), c_Orderings_Oorder__class_Ostrict__mono(_881317, _881315, _881319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881317), _881321), _881323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881315), hAPP(_881319, _881321)), hAPP(_881319, _881323))))], (26899 ^ _779327) ^ [_1253507, _1253509, _1253511, _1253513] : [26901 ^ _779327 : [(26904 ^ _779327) ^ [] : [hBOOL(hAPP(_1253513, 26900 ^ [_1253507, _1253509, _1253511, _1253513]))], (26902 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253507), 26900 ^ [_1253507, _1253509, _1253511, _1253513]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253507, tc_HOL_Obool)), _1253509), _1253511))))]], 26905 ^ _779327 : [(26912 ^ _779327) ^ [_1253824] : [hBOOL(hAPP(hAPP(c_member(_1253507), _1253824), _1253511)), -(hBOOL(hAPP(_1253513, _1253824)))], (26906 ^ _779327) ^ [_1253727] : [hBOOL(hAPP(hAPP(c_member(_1253507), _1253727), _1253509)), -(hBOOL(hAPP(_1253513, _1253727)))]]], (1778 ^ _779327) ^ [_804540, _804542] : [-(class_Nat_Osemiring__char__0(_804540)), _804542 = _804540, class_Nat_Osemiring__char__0(_804542)], (4814 ^ _779327) ^ [_852631, _852633, _852635, _852637, _852639, _852641] : [-(c_Predicate_Oconversep(_852641, _852637, _852633) = c_Predicate_Oconversep(_852639, _852635, _852631)), _852641 = _852639, _852637 = _852635, _852633 = _852631], (43493 ^ _779327) ^ [_1630777, _1630779, _1630781, _1630783, _1630785, _1630787, _1630789] : [c_Finite__Set_Ofun__left__comm(_1630777, _1630779, _1630781), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1630777, _1630779, _1630781, _1630783, _1630785), _1630787)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1630777, _1630779, _1630781, _1630783, _1630785), _1630789)), -(_1630789 = _1630787)], (31099 ^ _779327) ^ [_1342471, _1342473, _1342475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342471)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1342473), _1342475)), 31106 ^ _779327 : [(31107 ^ _779327) ^ [_1342661] : [31109 ^ _779327 : [(31115 ^ _779327) ^ [] : [-(_1342661 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 31111 ^ [_1342471, _1342473, _1342475, _1342661]), 31108 ^ [_1342471, _1342473, _1342475, _1342661]))], (31113 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31111 ^ [_1342471, _1342473, _1342475, _1342661]), _1342475)))], (31110 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31108 ^ [_1342471, _1342473, _1342475, _1342661]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1342471))))]], -(_1342661 = _1342473), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1342661), _1342471) = _1342473]]], (51063 ^ _779327) ^ [_1804619, _1804621, _1804623, _1804625] : [-(hAPP(hAPP(c_List_Omap(_1804619, _1804621), hAPP(c_COMBK(_1804621, _1804619), _1804623)), _1804625) = c_List_Oreplicate(_1804621, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1804619)), _1804625), _1804623))], (5696 ^ _779327) ^ [_869438, _869440, _869442] : [class_Rings_Osemiring__1(_869438), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_869438, _869440, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _869442) = _869442)], (39940 ^ _779327) ^ [_1539440, _1539442] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1539440))), -(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)), _1539440))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1539442)))) = 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)), _1539440))), 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, _1539442))))))], (6849 ^ _779327) ^ [_886385, _886387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886385)), _886387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886385), _886387)))], (45795 ^ _779327) ^ [_1689912] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1689912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45798 ^ _779327 : [(45799 ^ _779327) ^ [_1689987] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1689987), hAPP(c_List_Oset(tc_Nat_Onat), _1689912))), -(_1689987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3994 ^ _779327) ^ [_839929, _839931, _839933, _839935] : [-(c_List_Olistsp(_839935, _839931) = c_List_Olistsp(_839933, _839929)), _839935 = _839933, _839931 = _839929], (38077 ^ _779327) ^ [] : [-(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)))], (15425 ^ _779327) ^ [_1039913, _1039915, _1039917] : [class_Divides_Oring__div(_1039913), -(c_Divides_Odiv__class_Omod(_1039913, hAPP(c_Groups_Ouminus__class_Ouminus(_1039913), _1039915), _1039917) = c_Divides_Odiv__class_Omod(_1039913, hAPP(c_Groups_Ouminus__class_Ouminus(_1039913), c_Divides_Odiv__class_Omod(_1039913, _1039915, _1039917)), _1039917))], (14405 ^ _779327) ^ [_1022230, _1022232] : [class_Int_Onumber__ring(_1022230), 14408 ^ _779327 : [(14415 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1022232)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1022230), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1022232)) = hAPP(c_Int_Onumber__class_Onumber__of(_1022230), _1022232))], (14409 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1022232))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1022230), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1022232)) = c_Groups_Ozero__class_Ozero(_1022230))]]], (17512 ^ _779327) ^ [_1076570] : [-(c_Int_OBit1(_1076570) = 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)), _1076570)), _1076570))], (36933 ^ _779327) ^ [_1468489, _1468491, _1468493, _1468495, _1468497, _1468499] : [c_Fun_Oinj__on(_1468489, _1468491, _1468493, _1468495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468489, tc_HOL_Obool)), _1468497), _1468495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468489, tc_HOL_Obool)), _1468499), _1468495)), -(hAPP(c_Set_Oimage(_1468489, _1468491, _1468493), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468489, tc_HOL_Obool)), _1468497), _1468499)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468491, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468489, _1468491, _1468493), _1468497)), hAPP(c_Set_Oimage(_1468489, _1468491, _1468493), _1468499)))], (53020 ^ _779327) ^ [_1840738, _1840740] : [hBOOL(hAPP(hAPP(c_fequal, _1840738), _1840740)), -(_1840738 = _1840740)], (28874 ^ _779327) ^ [_1293998, _1294000, _1294002] : [class_Orderings_Oorder(_1293998), 28877 ^ _779327 : [(28884 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293998), _1294000), _1294002))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1293998, _1294000, _1294002) = c_Orderings_Obot__class_Obot(tc_fun(_1293998, tc_HOL_Obool)))], (28878 ^ _779327) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1293998, _1294000, _1294002) = c_Orderings_Obot__class_Obot(tc_fun(_1293998, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293998), _1294000), _1294002))]]], (2356 ^ _779327) ^ [_813734, _813736] : [_813736 = _813734, -(c_Nitpick_Oone__frac(_813736) = c_Nitpick_Oone__frac(_813734))], (29194 ^ _779327) ^ [_1299746, _1299748] : [class_Orderings_Oorder(_1299746), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299746, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1299746), _1299748), c_Orderings_Obot__class_Obot(tc_fun(_1299746, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1299746), _1299748)) = hAPP(hAPP(c_Set_Oinsert(_1299746), _1299748), c_Orderings_Obot__class_Obot(tc_fun(_1299746, tc_HOL_Obool))))], (22277 ^ _779327) ^ [_1164316, _1164318, _1164320, _1164322, _1164324, _1164326, _1164328] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164316, _1164318), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1164320), _1164322))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1164324, _1164318), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1164326), _1164328))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164318)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164316), _1164324), _1164318), 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), _1164320), _1164326)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164322), _1164328)), _1164318))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164322), _1164328), _1164318)))))], (32150 ^ _779327) ^ [_1363096, _1363098, _1363100] : [class_Lattices_Olattice(_1363096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363096), _1363098)), -(hBOOL(hAPP(hAPP(c_member(_1363096), _1363100), _1363098))), -(_1363098 = c_Orderings_Obot__class_Obot(tc_fun(_1363096, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1363096, hAPP(hAPP(c_Set_Oinsert(_1363096), _1363100), _1363098)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1363096), _1363100), c_Big__Operators_Olattice__class_OSup__fin(_1363096, _1363098)))], (42172 ^ _779327) ^ [_1599726, _1599728, _1599730] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599726, _1599726)), _1599728), _1599730)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599726, _1599726)), _1599728), c_Transitive__Closure_Ortrancl(_1599726, _1599730))))], (26320 ^ _779327) ^ [_1242367, _1242369, _1242371, _1242373, _1242375] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1242367, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1242367, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1242369, _1242367, _1242371), _1242373)), hAPP(c_Set_Oimage(_1242369, _1242367, _1242371), _1242375))), hAPP(c_Set_Oimage(_1242369, _1242367, _1242371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1242369, tc_HOL_Obool)), _1242373), _1242375)))))], (47237 ^ _779327) ^ [_1722440, _1722442, _1722444] : [-(hAPP(c_List_Orotate(_1722440, _1722442), _1722444) = hAPP(hAPP(c_List_Oappend(_1722440), hAPP(hAPP(c_List_Odrop(_1722440), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1722442, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722440)), _1722444))), _1722444)), hAPP(hAPP(c_List_Otake(_1722440), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1722442, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722440)), _1722444))), _1722444)))], (3552 ^ _779327) ^ [_832990, _832992, _832994, _832996] : [-(c_Wellfounded_Omax__ext(_832996, _832992) = c_Wellfounded_Omax__ext(_832994, _832990)), _832996 = _832994, _832992 = _832990], (45669 ^ _779327) ^ [_1686191] : [-(c_List_Olists(_1686191, c_Orderings_Obot__class_Obot(tc_fun(_1686191, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1686191)), c_List_Olist_ONil(_1686191)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1686191), tc_HOL_Obool))))], (8144 ^ _779327) ^ [_908868, _908870, _908872, _908874] : [class_Rings_Olinordered__semiring__strict(_908868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908868), _908870), _908872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908868), c_Groups_Ozero__class_Ozero(_908868)), _908874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908868), _908870), _908874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_908868), _908872), _908874))))], (14117 ^ _779327) ^ [_1016728, _1016730, _1016732] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016728), _1016730) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016728), _1016732), -(_1016730 = _1016732)], (35321 ^ _779327) ^ [_1432419, _1432421, _1432423, _1432425, _1432427] : [-(_1432419 = c_Orderings_Obot__class_Obot(tc_fun(_1432421, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432423, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432421, tc_fun(_1432423, tc_HOL_Obool)), _1432419), _1432425)), _1432427) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432421, tc_fun(_1432423, tc_HOL_Obool)), _1432419), hAPP(hAPP(c_COMBC(_1432421, tc_fun(_1432423, tc_HOL_Obool), tc_fun(_1432423, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432423, tc_HOL_Obool), tc_fun(tc_fun(_1432423, tc_HOL_Obool), tc_fun(_1432423, tc_HOL_Obool)), _1432421), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432423, tc_HOL_Obool))), _1432425)), _1432427)))], (45546 ^ _779327) ^ [_1682569, _1682571] : [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(_1682569)), _1682571))), _1682571 = c_List_Olist_ONil(_1682569)], (25127 ^ _779327) ^ [_1217408, _1217410] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217408), _1217410)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217408), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217410))))], (43774 ^ _779327) ^ [_1636483, _1636485] : [class_Complete__Lattice_Ocomplete__lattice(_1636483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636483), _1636485)), -(_1636485 = c_Orderings_Obot__class_Obot(tc_fun(_1636483, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1636483, _1636485) = c_Complete__Lattice_OInf__class_OInf(_1636483, _1636485))], (26832 ^ _779327) ^ [_1251965, _1251967, _1251969, _1251971, _1251973] : [-(hAPP(c_Set_Oimage(_1251965, _1251967, _1251969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251965, tc_HOL_Obool)), _1251971), _1251973)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1251967, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1251965, _1251967, _1251969), _1251971)), hAPP(c_Set_Oimage(_1251965, _1251967, _1251969), _1251973)))], (17686 ^ _779327) ^ [] : [-(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))))))], (10673 ^ _779327) ^ [_952535] : [-(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, _952535)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47608 ^ _779327) ^ [_1729688, _1729690, _1729692, _1729694] : [hBOOL(hAPP(hAPP(c_member(_1729688), _1729690), hAPP(c_List_Oset(_1729688), _1729692))), -(c_List_Oremove1(_1729688, _1729690, hAPP(hAPP(c_List_Oappend(_1729688), _1729692), _1729694)) = hAPP(hAPP(c_List_Oappend(_1729688), c_List_Oremove1(_1729688, _1729690, _1729692)), _1729694))], (43696 ^ _779327) ^ [_1634622, _1634624, _1634626] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1634622, tc_HOL_Obool)), _1634624), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1634622, tc_HOL_Obool), _1634626)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1634622, tc_HOL_Obool), tc_fun(_1634622, tc_HOL_Obool)), _1634626), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1634622, tc_HOL_Obool)), _1634624)))], (7326 ^ _779327) ^ [_894132, _894134] : [_894132 = _894134, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894132), _894134)))], (23530 ^ _779327) ^ [_1188780, _1188782, _1188784, _1188786] : [-(c_HOL_OThe(tc_prod(_1188780, _1188782), hAPP(c_Product__Type_Oprod_Oprod__case(_1188780, _1188782, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1188780, tc_fun(_1188782, tc_HOL_Obool), tc_fun(_1188782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1188782, tc_HOL_Obool), tc_fun(_1188782, tc_HOL_Obool)), _1188780), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1188782)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1188780), c_fconj), hAPP(c_fequal, _1188784)))), hAPP(c_fequal, _1188786)))) = hAPP(hAPP(c_Product__Type_OPair(_1188780, _1188782), _1188784), _1188786))], (20977 ^ _779327) ^ [_1138647] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1138647)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1138647)], (43929 ^ _779327) ^ [_1640253, _1640255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1640253), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640253, tc_HOL_Obool), _1640255))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1640253, tc_HOL_Obool)), _1640255)))], (12746 ^ _779327) ^ [_992302] : [class_Groups_Osgn__if(_992302), -(c_Groups_Osgn__class_Osgn(_992302, c_Groups_Ozero__class_Ozero(_992302)) = c_Groups_Ozero__class_Ozero(_992302))], (13410 ^ _779327) ^ [_1004008, _1004010, _1004012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004008), _1004010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004012), _1004008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004008), _1004012)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004010), _1004012))))], (50937 ^ _779327) ^ [_1802122, _1802124, _1802126] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802122)), c_List_Osplice(_1802122, _1802124, _1802126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802122)), _1802124)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802122)), _1802126)))], (52223 ^ _779327) ^ [_1830199, _1830201] : [c_Relation_Osym(_1830199, hAPP(c_Set_OCollect(tc_prod(_1830199, _1830199)), hAPP(c_Product__Type_Oprod_Oprod__case(_1830199, _1830199, tc_HOL_Obool), _1830201))), -(c_Predicate_Osymp(_1830199, _1830201))], (8674 ^ _779327) ^ [_918333, _918335, _918337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918333), _918335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918337), _918335))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918333), _918337)))], (31648 ^ _779327) ^ [_1354363, _1354365] : [31649 ^ _779327 : [(31652 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354365), _1354363))], (31650 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354363), _1354365)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354363, _1354365) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (14205 ^ _779327) ^ [_1018663, _1018665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018663), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018665), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018663), _1018665)))], (15369 ^ _779327) ^ [_1038747, _1038749, _1038751, _1038753, _1038755, _1038757] : [class_Divides_Osemiring__div(_1038747), c_Divides_Odiv__class_Omod(_1038747, _1038749, _1038751) = c_Divides_Odiv__class_Omod(_1038747, _1038753, _1038751), c_Divides_Odiv__class_Omod(_1038747, _1038755, _1038751) = c_Divides_Odiv__class_Omod(_1038747, _1038757, _1038751), -(c_Divides_Odiv__class_Omod(_1038747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038747), _1038749), _1038755), _1038751) = c_Divides_Odiv__class_Omod(_1038747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038747), _1038753), _1038757), _1038751))], (45034 ^ _779327) ^ [_1669751, _1669753, _1669755] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669751)), hAPP(hAPP(c_List_Otake(_1669751), _1669753), _1669755)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669751)), _1669755)), _1669753))], (16521 ^ _779327) ^ [_1059300, _1059302] : [class_Groups_Oordered__ab__group__add__abs(_1059300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059300), hAPP(c_Groups_Oabs__class_Oabs(_1059300), _1059302)), c_Groups_Ozero__class_Ozero(_1059300)))], (26641 ^ _779327) ^ [_1248272, _1248274] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1248272, _1248274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1248274)), _1248272))], (32736 ^ _779327) ^ [_1374624, _1374626] : [class_Orderings_Olinorder(_1374624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374624), _1374626)), -(_1374626 = c_Orderings_Obot__class_Obot(tc_fun(_1374624, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1374624), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374624), 32749 ^ [_1374624, _1374626]), 32750 ^ [_1374624, _1374626])), hAPP(hAPP(c_Set_Oinsert(_1374624), 32749 ^ [_1374624, _1374626]), hAPP(hAPP(c_Set_Oinsert(_1374624), 32750 ^ [_1374624, _1374626]), c_Orderings_Obot__class_Obot(tc_fun(_1374624, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1374624), c_Big__Operators_Olattice_OSup__fin(_1374624, c_Orderings_Oord__class_Omax(_1374624), _1374626)), _1374626)))], (3672 ^ _779327) ^ [_834842, _834844, _834846, _834848] : [-(c_List_Olenlex(_834848, _834844) = c_List_Olenlex(_834846, _834842)), _834848 = _834846, _834844 = _834842], (16852 ^ _779327) ^ [_1065282, _1065284] : [class_Groups_Oordered__ab__group__add__abs(_1065282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065282), _1065284), c_Groups_Ozero__class_Ozero(_1065282))), -(hAPP(c_Groups_Oabs__class_Oabs(_1065282), _1065284) = hAPP(c_Groups_Ouminus__class_Ouminus(_1065282), _1065284))], (50999 ^ _779327) ^ [_1803581, _1803583, _1803585] : [-(_1803581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1803583), c_List_Oreplicate(_1803583, _1803581, _1803585)) = c_List_Oreplicate(_1803583, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1803581), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1803585))], (7250 ^ _779327) ^ [_893036, _893038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893036), _893038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _893036), _893038)))], (15590 ^ _779327) ^ [_1042858] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1042858) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1042858))], (12479 ^ _779327) ^ [_987208, _987210, _987212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987210), _987212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987208), _987210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987208), _987212))))], (11357 ^ _779327) ^ [_966269, _966271, _966273, _966275, _966277, _966279] : [class_Rings_Oordered__ring(_966269), 11360 ^ _779327 : [(11367 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966269), _966271), _966277)), _966273)), _966275)), _966279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), _966271), _966273)), _966275)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), _966277), _966273)), _966279))))], (11361 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), _966271), _966273)), _966275)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), _966277), _966273)), _966279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966269), _966271), _966277)), _966273)), _966275)), _966279)))]]], (27368 ^ _779327) ^ [_1263289, _1263291] : [c_Nat__Transfer_Onat__set(_1263289), c_Nat__Transfer_Onat__set(_1263291), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1263289), _1263291) = 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), _1263289)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1263291))))], (44224 ^ _779327) ^ [_1646907, _1646909] : [-(c_Wellfounded_Owf(_1646907, _1646909)), 44227 ^ _779327 : [(44230 ^ _779327) ^ [_1647127] : [hBOOL(hAPP(hAPP(c_member(_1646907), _1647127), 44225 ^ [_1646907, _1646909])), 44234 ^ _779327 : [(44237 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646907), 44233 ^ [_1646907, _1646909, _1647127]), 44225 ^ [_1646907, _1646909])))], (44235 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646907, _1646907)), hAPP(hAPP(c_Product__Type_OPair(_1646907, _1646907), 44233 ^ [_1646907, _1646909, _1647127]), _1647127)), _1646909)))]]], (44228 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646907), 44226 ^ [_1646907, _1646909]), 44225 ^ [_1646907, _1646909])))]]], (30882 ^ _779327) ^ [_1337916, _1337918, _1337920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337916)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337918), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1337920)), 30889 ^ _779327 : [(30890 ^ _779327) ^ [_1338124] : [30892 ^ _779327 : [(30898 ^ _779327) ^ [] : [-(_1338124 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30894 ^ [_1337916, _1337918, _1337920, _1338124]), 30891 ^ [_1337916, _1337918, _1337920, _1338124]))], (30896 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30894 ^ [_1337916, _1337918, _1337920, _1338124]), _1337920)))], (30893 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30891 ^ [_1337916, _1337918, _1337920, _1338124]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1337916))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1338124), _1337918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338124), _1337916)), _1337918)))]]], (42665 ^ _779327) ^ [_1611822, _1611824, _1611826] : [hAPP(hAPP(c_Relation_Orel__comp(_1611822, _1611822, _1611822), hAPP(c_Relation_Oconverse(_1611822, _1611822), _1611824)), _1611824) = _1611824, hAPP(c_Relation_ODomain(_1611822, _1611822), _1611824) = _1611826, -(c_Equiv__Relations_Oequiv(_1611822, _1611826, _1611824))], (23720 ^ _779327) ^ [_1192406, _1192408] : [-(hAPP(c_New__DSequence_Opos__empty(_1192406), _1192408) = c_Lazy__Sequence_Oempty(_1192406))], (37619 ^ _779327) ^ [_1483413, _1483415, _1483417, _1483419] : [c_Orderings_Otop__class_Otop(tc_fun(_1483413, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1483415, tc_fun(_1483413, tc_HOL_Obool)), _1483417), _1483419), 37622 ^ _779327 : [(37623 ^ _779327) ^ [_1483529] : [hBOOL(hAPP(hAPP(c_member(_1483415), _1483529), _1483417)), -(hAPP(_1483419, _1483529) = c_Orderings_Otop__class_Otop(tc_fun(_1483413, tc_HOL_Obool)))]]], (22149 ^ _779327) ^ [_1162158, _1162160, _1162162, _1162164] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1162158, _1162160), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1162162), _1162164))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1162158, _1162160) = _1162164)], (3106 ^ _779327) ^ [_825955, _825957, _825959, _825961] : [-(c_Predicate_OPowp(_825961, _825957) = c_Predicate_OPowp(_825959, _825955)), _825961 = _825959, _825957 = _825955], (48221 ^ _779327) ^ [_1743559, _1743561] : [-(_1743559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1743561, _1743559, c_List_Olist_ONil(_1743561)) = c_List_Olist_ONil(tc_List_Olist(_1743561)))], (8096 ^ _779327) ^ [_907977, _907979, _907981, _907983] : [class_Rings_Olinordered__ring__strict(_907977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907977), _907979), c_Groups_Ozero__class_Ozero(_907977))), 8103 ^ _779327 : [(8110 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907977), _907983), _907981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907977), _907979), _907981)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907977), _907979), _907983))))], (8104 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907977), _907979), _907981)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907977), _907979), _907983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907977), _907983), _907981)))]]], (2232 ^ _779327) ^ [_811740, _811742, _811744, _811746] : [-(c_Divides_OnegDivAlg(_811746, _811742) = c_Divides_OnegDivAlg(_811744, _811740)), _811746 = _811744, _811742 = _811740], (37959 ^ _779327) ^ [_1490296] : [class_Lattices_Oboolean__algebra(_1490296), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1490296), c_Orderings_Obot__class_Obot(_1490296)) = c_Orderings_Otop__class_Otop(_1490296))], (44612 ^ _779327) ^ [_1657442, _1657444] : [-(c_List_Olistrel1(_1657442, hAPP(c_Relation_Oconverse(_1657442, _1657442), _1657444)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1657442), tc_List_Olist(_1657442)), c_List_Olistrel1(_1657442, _1657444)))], (24397 ^ _779327) ^ [_1203956, _1203958] : [class_Rings_Ocomm__semiring__1(_1203956), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1203956), _1203958), _1203958)))], (25530 ^ _779327) ^ [_1225468, _1225470, _1225472, _1225474, _1225476] : [class_Rings_Osemiring__0(_1225468), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225468), _1225470), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225472, _1225468), _1225474), _1225476)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225472, _1225468), hAPP(hAPP(c_COMBB(_1225468, _1225468, _1225472), hAPP(c_Groups_Otimes__class_Otimes(_1225468), _1225470)), _1225474)), _1225476))], (22291 ^ _779327) ^ [_1164677, _1164679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1164677), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1164679), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1164677, _1164679) = 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), _1164677), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164679)))))], (38423 ^ _779327) ^ [_1502962, _1502964, _1502966, _1502968, _1502970] : [hBOOL(hAPP(hAPP(c_member(_1502962), _1502964), hAPP(c_Set_Ovimage(_1502962, _1502966, _1502968), hAPP(hAPP(c_Set_Oinsert(_1502966), _1502970), c_Orderings_Obot__class_Obot(tc_fun(_1502966, tc_HOL_Obool)))))), -(hAPP(_1502968, _1502964) = _1502970)], (20615 ^ _779327) ^ [_1131863, _1131865] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131863), hAPP(c_Int_Onumber__class_Onumber__of(_1131863), c_Int_OMin)), _1131865) = hAPP(c_Groups_Ouminus__class_Ouminus(_1131863), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131863), c_Groups_Oone__class_Oone(_1131863)), _1131865))), class_Fields_Ofield__inverse__zero(_1131863), class_Int_Onumber__ring(_1131863)], (20233 ^ _779327) ^ [_1124545, _1124547, _1124549, _1124551] : [class_Fields_Olinordered__field(_1124545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124545), c_Groups_Ozero__class_Ozero(_1124545)), _1124547)), 20240 ^ _779327 : [(20247 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124545), _1124549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124545), _1124551), _1124547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124545), _1124549), _1124547)), _1124551)))], (20241 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124545), _1124549), _1124547)), _1124551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124545), _1124549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124545), _1124551), _1124547))))]]], (14579 ^ _779327) ^ [_1024979, _1024981, _1024983, _1024985] : [class_Divides_Osemiring__div(_1024979), -(_1024981 = c_Groups_Ozero__class_Ozero(_1024979)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024979), _1024983), _1024981)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024979), _1024985), _1024981)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024979), _1024983), _1024985))], (44959 ^ _779327) ^ [_1667789, _1667791, _1667793, _1667795] : [_1667789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1667791), hAPP(hAPP(c_List_Olist_OCons(_1667791), _1667793), _1667795)), _1667789) = _1667793)], (10493 ^ _779327) ^ [_949239, _949241] : [hBOOL(hAPP(_949239, hAPP(c_Int_Onat, _949241))), 10496 ^ _779327 : [(10503 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _949241), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_949239, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10497 ^ _779327) ^ [_949339] : [_949241 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _949339), -(hBOOL(hAPP(_949239, _949339)))]]], (48730 ^ _779327) ^ [_1756235, _1756237, _1756239] : [-(c_List_Osublist(_1756235, _1756237, _1756239) = hAPP(hAPP(c_List_Omap(tc_prod(_1756235, tc_Nat_Onat), _1756235), c_Product__Type_Ofst(_1756235, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1756235, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1756235, 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(_1756235, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1756235, tc_Nat_Onat))), _1756239)), hAPP(hAPP(c_List_Ozip(_1756235, tc_Nat_Onat), _1756237), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756235)), _1756237))))))], (36468 ^ _779327) ^ [_1459823, _1459825, _1459827, _1459829, _1459831] : [c_Relation_Orefl__on(_1459823, _1459825, _1459827), c_Relation_Orefl__on(_1459823, _1459829, _1459831), -(c_Relation_Orefl__on(_1459823, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459823, tc_HOL_Obool)), _1459825), _1459829), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1459823, _1459823), tc_HOL_Obool)), _1459827), _1459831)))], (41009 ^ _779327) ^ [_1572616, _1572618] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1572616, _1572618), 41010 ^ [_1572616, _1572618])), -(c_Wellfounded_OwfP(_1572616, _1572618))], (29726 ^ _779327) ^ [_1310573, _1310575, _1310577, _1310579] : [-(hBOOL(hAPP(hAPP(c_member(_1310573), _1310575), _1310577))), -(hBOOL(hAPP(hAPP(c_member(_1310573), _1310575), _1310579))), 29733 ^ _779327 : [(29740 ^ _779327) ^ [] : [_1310577 = _1310579, -(hAPP(hAPP(c_Set_Oinsert(_1310573), _1310575), _1310577) = hAPP(hAPP(c_Set_Oinsert(_1310573), _1310575), _1310579))], (29734 ^ _779327) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1310573), _1310575), _1310577) = hAPP(hAPP(c_Set_Oinsert(_1310573), _1310575), _1310579), -(_1310577 = _1310579)]]], (17166 ^ _779327) ^ [_1070743, _1070745] : [class_Int_Onumber__ring(_1070743), class_Rings_Olinordered__idom(_1070743), 17173 ^ _779327 : [(17180 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070745), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070743), hAPP(c_Int_Onumber__class_Onumber__of(_1070743), _1070745)), c_Groups_Ozero__class_Ozero(_1070743))))], (17174 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070743), hAPP(c_Int_Onumber__class_Onumber__of(_1070743), _1070745)), c_Groups_Ozero__class_Ozero(_1070743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070745), c_Int_OPls)))]]], (41441 ^ _779327) ^ [_1582258, _1582260, _1582262, _1582264, _1582266, _1582268] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1582258, _1582260), _1582258, tc_prod(_1582262, _1582264), c_Product__Type_Ofst(_1582258, _1582260)), c_Product__Type_Omap__pair(_1582262, _1582258, _1582264, _1582260, _1582266, _1582268)) = hAPP(c_Fun_Ocomp(_1582262, _1582258, tc_prod(_1582262, _1582264), _1582266), c_Product__Type_Ofst(_1582262, _1582264)))], (44113 ^ _779327) ^ [_1644375, _1644377, _1644379, _1644381, _1644383, _1644385, _1644387] : [c_Finite__Set_Ofun__left__comm(_1644375, _1644377, _1644379), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1644375, _1644377, _1644379, _1644381, hAPP(hAPP(c_Set_Oinsert(_1644375), _1644383), _1644385)), _1644387)), -(hBOOL(hAPP(hAPP(c_member(_1644375), _1644383), _1644385))), 44125 ^ _779327 : [(44128 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1644375, _1644377, _1644379, _1644381, _1644385), 44124 ^ [_1644375, _1644377, _1644379, _1644381, _1644383, _1644385, _1644387])))], (44126 ^ _779327) ^ [] : [-(_1644387 = hAPP(hAPP(_1644379, _1644383), 44124 ^ [_1644375, _1644377, _1644379, _1644381, _1644383, _1644385, _1644387]))]]], (16309 ^ _779327) ^ [_1055703, _1055705, _1055707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055705), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1055707), 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), _1055707), _1055705))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1055703)))))], (41449 ^ _779327) ^ [] : [-(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))], (28900 ^ _779327) ^ [_1294380, _1294382, _1294384, _1294386] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294380, tc_HOL_Obool)), _1294382), hAPP(hAPP(c_Set_Oinsert(_1294380), _1294384), _1294386)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294380, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294380, tc_HOL_Obool)), _1294382), _1294386)), hAPP(hAPP(c_Set_Oinsert(_1294380), _1294384), c_Orderings_Obot__class_Obot(tc_fun(_1294380, tc_HOL_Obool)))))], (49485 ^ _779327) ^ [_1770710, _1770712, _1770714] : [_1770712 = hAPP(hAPP(c_List_Olist_OCons(_1770710), _1770714), c_List_Olist_ONil(_1770710)), -(hAPP(c_List_Orev(_1770710), _1770712) = hAPP(hAPP(c_List_Olist_OCons(_1770710), _1770714), c_List_Olist_ONil(_1770710)))], (31616 ^ _779327) ^ [_1353796, _1353798, _1353800, _1353802, _1353804, _1353806] : [-(hBOOL(hAPP(hAPP(c_member(_1353796), _1353798), c_SetInterval_Oord_OgreaterThanAtMost(_1353796, _1353800, _1353802, _1353804, _1353806)))), hBOOL(hAPP(hAPP(_1353802, _1353804), _1353798)), hBOOL(hAPP(hAPP(_1353800, _1353798), _1353806))], (9511 ^ _779327) ^ [_933404, _933406] : [class_Rings_Oring__1(_933404), -(hAPP(c_Int_Oring__1__class_Oof__int(_933404), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933406)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_933404), _933406))], (29498 ^ _779327) ^ [_1306136, _1306138, _1306140, _1306142] : [hBOOL(hAPP(hAPP(c_member(_1306136), _1306138), hAPP(hAPP(c_Set_Oinsert(_1306136), _1306140), _1306142))), -(_1306138 = _1306140), -(hBOOL(hAPP(hAPP(c_member(_1306136), _1306138), _1306142)))], (43569 ^ _779327) ^ [_1632190, _1632192, _1632194, _1632196, _1632198, _1632200] : [c_Finite__Set_Ofun__left__comm(_1632190, _1632192, _1632194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632190), _1632196)), -(hBOOL(hAPP(hAPP(c_member(_1632190), _1632198), _1632196))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1632190, _1632192, _1632194), _1632200), hAPP(hAPP(c_Set_Oinsert(_1632190), _1632198), _1632196)) = hAPP(hAPP(_1632194, _1632198), hAPP(hAPP(c_Finite__Set_Ofold(_1632190, _1632192, _1632194), _1632200), _1632196)))], (37787 ^ _779327) ^ [_1486624, _1486626, _1486628, _1486630, _1486632] : [_1486624 = hAPP(_1486626, _1486628), -(hBOOL(hAPP(hAPP(c_member(_1486630), _1486624), hAPP(c_Set_Oimage(_1486632, _1486630, _1486626), c_Orderings_Otop__class_Otop(tc_fun(_1486632, tc_HOL_Obool))))))], (38515 ^ _779327) ^ [_1505177, _1505179, _1505181, _1505183, _1505185, _1505187] : [-(hBOOL(hAPP(hAPP(c_member(_1505177), _1505179), _1505181))), 38518 ^ _779327 : [(38525 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505177), _1505183), _1505181))), -(hAPP(c_Set_Ovimage(_1505185, _1505177, hAPP(hAPP(c_COMBC(_1505185, _1505177, _1505177), hAPP(hAPP(c_COMBC(_1505185, _1505177, tc_fun(_1505177, _1505177)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1505177, tc_fun(_1505177, _1505177)), _1505185), c_If(_1505177)), hAPP(hAPP(c_COMBC(_1505185, tc_fun(_1505185, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505185)), _1505187))), _1505179)), _1505183)), _1505181) = c_Orderings_Obot__class_Obot(tc_fun(_1505185, tc_HOL_Obool)))], (38519 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1505177), _1505183), _1505181)), -(hAPP(c_Set_Ovimage(_1505185, _1505177, hAPP(hAPP(c_COMBC(_1505185, _1505177, _1505177), hAPP(hAPP(c_COMBC(_1505185, _1505177, tc_fun(_1505177, _1505177)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1505177, tc_fun(_1505177, _1505177)), _1505185), c_If(_1505177)), hAPP(hAPP(c_COMBC(_1505185, tc_fun(_1505185, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505185)), _1505187))), _1505179)), _1505183)), _1505181) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1505185, tc_HOL_Obool)), _1505187))]]], (46672 ^ _779327) ^ [_1710661, _1710663, _1710665, _1710667] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710661) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1710663), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1710661)), hAPP(hAPP(c_List_Olist_OCons(_1710663), _1710665), _1710667)) = hAPP(hAPP(c_List_Olist_OCons(_1710663), _1710665), _1710667))], (38230 ^ _779327) ^ [_1498011, _1498013, _1498015, _1498017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498011, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498011, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38231 ^ [_1498011, _1498013, _1498015, _1498017])), _1498013)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498011, 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), 38231 ^ [_1498011, _1498013, _1498015, _1498017]), _1498015))), _1498017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1498011, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498011, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1498013)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1498011, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1498017))))], (17556 ^ _779327) ^ [_1077287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077287), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1077287)), c_Int_OMin)))], (25774 ^ _779327) ^ [_1230888, _1230890, _1230892, _1230894] : [class_Orderings_Olinorder(_1230888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230888), _1230890), _1230892)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1230888, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1230888, _1230890), _1230894)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1230888, _1230890), _1230892)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1230888, _1230892), _1230894))], (15820 ^ _779327) ^ [_1046848, _1046850] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046848, _1046850) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046848), _1046850)), _1046850)))], (26458 ^ _779327) ^ [_1245201, _1245203] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245201, _1245203) = 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), _1245201), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1245203))))], (40903 ^ _779327) ^ [_1569694, _1569696, _1569698, _1569700, _1569702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569694, _1569696)), hAPP(hAPP(c_Product__Type_OPair(_1569694, _1569696), _1569698), _1569700)), _1569702)), -(hBOOL(hAPP(hAPP(c_member(_1569694), _1569698), hAPP(c_Relation_ODomain(_1569694, _1569696), _1569702))))], (35281 ^ _779327) ^ [_1431299, _1431301] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431299, tc_HOL_Obool)), _1431301), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1431299, tc_HOL_Obool)), _1431301)) = c_Orderings_Obot__class_Obot(tc_fun(_1431299, tc_HOL_Obool)))], (10887 ^ _779327) ^ [_956787, _956789, _956791] : [class_Groups_Ogroup__add(_956787), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956787), _956789), _956791) = c_Groups_Ozero__class_Ozero(_956787), -(hAPP(c_Groups_Ouminus__class_Ouminus(_956787), _956789) = _956791)], (23335 ^ _779327) ^ [_1184647, _1184649] : [-(_1184647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1184649, _1184647) = c_Nitpick_Onat__gcd(_1184647, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1184649, _1184647)))], (30171 ^ _779327) ^ [_1321718, _1321720, _1321722, _1321724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321718, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1321718), _1321720), _1321722)), _1321724)), 30174 ^ _779327 : [(30177 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321718, tc_HOL_Obool)), _1321722), _1321724)))], (30175 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321718), _1321720), _1321724)))]]], (50003 ^ _779327) ^ [_1781833, _1781835] : [class_Orderings_Olinorder(_1781833), 50006 ^ _779327 : [(50027 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781833, _1781835)), 50028 ^ _779327 : [(50031 ^ _779327) ^ [_1782393, _1782395] : [_1781835 = hAPP(hAPP(c_List_Olist_OCons(_1781833), _1782393), _1782395), 50037 ^ _779327 : [(50040 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781833), _1782393), 50036 ^ [_1781833, _1781835, _1782393, _1782395]))], (50038 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781833), 50036 ^ [_1781833, _1781835, _1782393, _1782395]), hAPP(c_List_Oset(_1781833), _1782395))))]], c_List_Olinorder__class_Osorted(_1781833, _1782395)], (50029 ^ _779327) ^ [] : [_1781835 = c_List_Olist_ONil(_1781833)]]], (50007 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1781833, _1781835), -(_1781835 = c_List_Olist_ONil(_1781833)), 50016 ^ _779327 : [(50019 ^ _779327) ^ [_1782167] : [hBOOL(hAPP(hAPP(c_member(_1781833), _1782167), hAPP(c_List_Oset(_1781833), 50014 ^ [_1781833, _1781835]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781833), 50015 ^ [_1781833, _1781835]), _1782167)))], (50025 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781833, 50014 ^ [_1781833, _1781835]))], (50017 ^ _779327) ^ [] : [-(_1781835 = hAPP(hAPP(c_List_Olist_OCons(_1781833), 50015 ^ [_1781833, _1781835]), 50014 ^ [_1781833, _1781835]))]]]]], (23341 ^ _779327) ^ [_1184695, _1184697] : [-(c_Nitpick_Onat__lcm(_1184695, _1184697) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184695), _1184697)), c_Nitpick_Onat__gcd(_1184695, _1184697)))], (50555 ^ _779327) ^ [_1794500, _1794502, _1794504, _1794506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794500), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1794502)), _1794504))), 50561 ^ _779327 : [(50564 ^ _779327) ^ [] : [hBOOL(hAPP(_1794506, 50560 ^ [_1794500, _1794502, _1794504, _1794506]))], (50562 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794502), 50560 ^ [_1794500, _1794502, _1794504, _1794506]), hAPP(c_List_Oset(_1794502), _1794504))))]], -(hBOOL(hAPP(_1794506, hAPP(hAPP(c_List_Onth(_1794502), _1794504), _1794500))))], (21304 ^ _779327) ^ [_1145847, _1145849] : [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), _1145847))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1145849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1145847))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1145849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145847))), 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), _1145849))), c_COMBI(tc_Int_Oint))))], (9807 ^ _779327) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (31834 ^ _779327) ^ [_1357856, _1357858, _1357860] : [class_Rings_Oring__1(_1357856), hBOOL(hAPP(hAPP(c_member(_1357856), _1357858), c_Int_Oring__1__class_OInts(_1357856))), hBOOL(hAPP(hAPP(c_member(_1357856), _1357860), c_Int_Oring__1__class_OInts(_1357856))), -(hBOOL(hAPP(hAPP(c_member(_1357856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357856), _1357858), _1357860)), c_Int_Oring__1__class_OInts(_1357856))))], (12221 ^ _779327) ^ [_982610] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982610), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _982610)], (34795 ^ _779327) ^ [_1420586, _1420588] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420586, tc_HOL_Obool)), _1420588), _1420588) = _1420588)], (14179 ^ _779327) ^ [_1018183, _1018185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018183), _1018185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018183), _1018185)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (704 ^ _779327) ^ [_790193, _790195, _790197, _790199] : [-(c_FunDef_Ois__measure(_790197, _790193)), c_FunDef_Ois__measure(_790199, _790195), _790199 = _790197, _790195 = _790193], (8462 ^ _779327) ^ [_914756, _914758, _914760, _914762] : [class_Rings_Olinordered__semiring__strict(_914756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914756), _914758), _914760)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_914756), _914758), _914762))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914756), c_Groups_Ozero__class_Ozero(_914756)), _914758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914756), _914760), _914762)))], (39946 ^ _779327) ^ [_1539523, _1539525] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1539523)), 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)), _1539523))), 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, _1539525))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49427 ^ _779327) ^ [_1769603, _1769605] : [-(c_Fun_Oinj__on(tc_List_Olist(_1769603), tc_List_Olist(_1769603), c_List_Orev(_1769603), _1769605))], (2212 ^ _779327) ^ [_811442, _811444, _811446, _811448] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_811448, _811444) = c_Code__Numeral_Odiv__mod__code__numeral(_811446, _811442)), _811448 = _811446, _811444 = _811442], (15686 ^ _779327) ^ [_1044724, _1044726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044724), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1044726), _1044724)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1044724, _1044726) = _1044724)], (51089 ^ _779327) ^ [_1805100, _1805102, _1805104, _1805106] : [51091 ^ _779327 : [(51094 ^ _779327) ^ [] : [hBOOL(hAPP(_1805106, 51090 ^ [_1805100, _1805102, _1805104, _1805106]))], (51092 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805100), 51090 ^ [_1805100, _1805102, _1805104, _1805106]), hAPP(c_List_Oset(_1805100), c_List_Oreplicate(_1805100, _1805102, _1805104)))))]], -(hBOOL(hAPP(_1805106, _1805104))), -(_1805102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10109 ^ _779327) ^ [_942973, _942975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _942973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _942975)), 10116 ^ _779327 : [(10123 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _942973), _942975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _942973)), hAPP(c_Int_Onat, _942975))))], (10117 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _942973)), hAPP(c_Int_Onat, _942975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _942973), _942975)))]]], (42881 ^ _779327) ^ [_1616810, _1616812] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616810, _1616810), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1616812) = _1616812)], (46184 ^ _779327) ^ [_1698244, _1698246, _1698248, _1698250] : [-(hAPP(hAPP(c_List_Oappend(_1698244), hAPP(hAPP(c_List_Oappend(_1698244), _1698246), _1698248)), _1698250) = hAPP(hAPP(c_List_Oappend(_1698244), _1698246), hAPP(hAPP(c_List_Oappend(_1698244), _1698248), _1698250)))], (52818 ^ _779327) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51334 ^ _779327) ^ [_1810724, _1810726, _1810728, _1810730] : [hBOOL(hAPP(hAPP(c_List_Omember(_1810724), hAPP(hAPP(c_List_Olist_OCons(_1810724), _1810726), _1810728)), _1810730)), -(_1810726 = _1810730), -(hBOOL(hAPP(hAPP(c_List_Omember(_1810724), _1810728), _1810730)))], (25251 ^ _779327) ^ [_1219518, _1219520, _1219522] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219518), _1219522)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219518), _1219520)))], (27687 ^ _779327) ^ [_1270831, _1270833, _1270835, _1270837, _1270839, _1270841] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270831, tc_fun(_1270833, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270835, tc_fun(_1270831, tc_HOL_Obool)), _1270837), _1270839)), _1270841) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270835, tc_fun(_1270833, tc_HOL_Obool)), _1270837), hAPP(hAPP(c_COMBC(_1270835, tc_fun(_1270831, tc_fun(_1270833, tc_HOL_Obool)), tc_fun(_1270833, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270831, tc_HOL_Obool), tc_fun(tc_fun(_1270831, tc_fun(_1270833, tc_HOL_Obool)), tc_fun(_1270833, tc_HOL_Obool)), _1270835), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1270831, tc_fun(_1270833, tc_HOL_Obool))), _1270839)), _1270841)))], (49655 ^ _779327) ^ [_1774329, _1774331] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1774329), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1774329))), _1774331))), 49658 ^ _779327 : [(49665 ^ _779327) ^ [] : [-(_1774331 = c_List_Olist_ONil(tc_List_Olist(_1774329))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1774329))), c_List_Otranspose(_1774329, _1774331)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774329)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1774329)), _1774331), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49659 ^ _779327) ^ [] : [_1774331 = c_List_Olist_ONil(tc_List_Olist(_1774329)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1774329))), c_List_Otranspose(_1774329, _1774331)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5096 ^ _779327) ^ [_857038, _857040, _857042, _857044, _857046, _857048] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_857048, _857044, _857040) = c_SetInterval_Oord__class_OatLeastAtMost(_857046, _857042, _857038)), _857048 = _857046, _857044 = _857042, _857040 = _857038], (41219 ^ _779327) ^ [_1577169, _1577171, _1577173, _1577175, _1577177, _1577179] : [-(hAPP(c_Set_Ovimage(_1577169, tc_prod(_1577171, _1577173), _1577175), hAPP(hAPP(c_Product__Type_OSigma(_1577171, _1577173), _1577177), hAPP(c_COMBK(tc_fun(_1577173, tc_HOL_Obool), _1577171), _1577179))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577169, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1577169, _1577171, hAPP(c_Fun_Ocomp(tc_prod(_1577171, _1577173), _1577171, _1577169, c_Product__Type_Ofst(_1577171, _1577173)), _1577175)), _1577177)), hAPP(c_Set_Ovimage(_1577169, _1577173, hAPP(c_Fun_Ocomp(tc_prod(_1577171, _1577173), _1577173, _1577169, c_Product__Type_Osnd(_1577171, _1577173)), _1577175)), _1577179)))], (34351 ^ _779327) ^ [_1410549, _1410551, _1410553, _1410555] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1410549, _1410549)), hAPP(hAPP(c_Product__Type_OPair(_1410549, _1410549), _1410551), _1410553)), c_Relation_OId__on(_1410549, _1410555)))), _1410551 = _1410553, hBOOL(hAPP(hAPP(c_member(_1410549), _1410551), _1410555))], (4358 ^ _779327) ^ [_845625, _845627, _845629, _845631] : [-(c_List_Otranspose(_845631, _845627) = c_List_Otranspose(_845629, _845625)), _845631 = _845629, _845627 = _845625], (18376 ^ _779327) ^ [_1091482, _1091484] : [class_Rings_Olinordered__idom(_1091482), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091482), c_Groups_Ozero__class_Ozero(_1091482)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091482), _1091484), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (3562 ^ _779327) ^ [_833139, _833141] : [_833141 = _833139, -(c_Rings_Odvd__class_Odvd(_833141) = c_Rings_Odvd__class_Odvd(_833139))], (4776 ^ _779327) ^ [_852078, _852080, _852082, _852084] : [-(c_List_Ofilter(_852084, _852080) = c_List_Ofilter(_852082, _852078)), _852084 = _852082, _852080 = _852078], (49605 ^ _779327) ^ [_1773302, _1773304, _1773306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773302), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773304)), _1773306))), -(hAPP(hAPP(c_List_Onth(_1773304), hAPP(c_List_Orev(_1773304), _1773306)), _1773302) = hAPP(hAPP(c_List_Onth(_1773304), _1773306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773304)), _1773306)), hAPP(c_Nat_OSuc, _1773302))))], (4808 ^ _779327) ^ [_852546, _852548] : [_852548 = _852546, -(c_List_Oappend(_852548) = c_List_Oappend(_852546))], (46668 ^ _779327) ^ [_1710549, _1710551, _1710553, _1710555] : [-(hAPP(c_List_Orotate1(_1710549), c_List_Olist_ONil(_1710549)) = c_List_Olist_ONil(_1710549))], (11945 ^ _779327) ^ [_977421, _977423, _977425, _977427] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_977421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977421), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977421), _977423), _977425)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977421), _977427), _977425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977421), _977423), _977427)))], (26687 ^ _779327) ^ [_1249166, _1249168, _1249170, _1249172, _1249174] : [class_Groups_Ocomm__monoid__add(_1249166), class_Groups_Ocomm__monoid__mult(_1249166), _1249168 = _1249170, c_Nat__Transfer_Onat__set(_1249170), 26705 ^ _779327 : [(26708 ^ _779327) ^ [] : [hAPP(_1249172, 26704 ^ [_1249166, _1249168, _1249170, _1249172, _1249174]) = hAPP(_1249174, 26704 ^ [_1249166, _1249168, _1249170, _1249172, _1249174])], (26706 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26704 ^ [_1249166, _1249168, _1249170, _1249172, _1249174])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1249166), _1249172), _1249168) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1249166), _1249174), _1249170))], (17996 ^ _779327) ^ [_1084820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084820))))], (29200 ^ _779327) ^ [_1299905, _1299907, _1299909, _1299911] : [-(hAPP(c_Set_Oimage(_1299905, _1299907, _1299909), _1299911) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1299905, tc_fun(_1299907, tc_HOL_Obool)), _1299911), hAPP(hAPP(c_COMBC(_1299905, tc_fun(_1299907, tc_HOL_Obool), tc_fun(_1299907, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1299907, tc_fun(tc_fun(_1299907, tc_HOL_Obool), tc_fun(_1299907, tc_HOL_Obool)), _1299905), c_Set_Oinsert(_1299907)), _1299909)), c_Orderings_Obot__class_Obot(tc_fun(_1299907, tc_HOL_Obool)))))], (21352 ^ _779327) ^ [_1146728, _1146730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146728)), 21355 ^ _779327 : [(21362 ^ _779327) ^ [] : [-(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), _1146730), _1146728)))), -(c_Divides_OnegDivAlg(_1146730, _1146728) = hAPP(c_Divides_Oadjust(_1146728), c_Divides_OnegDivAlg(_1146730, 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)))), _1146728))))], (21356 ^ _779327) ^ [] : [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), _1146730), _1146728))), -(c_Divides_OnegDivAlg(_1146730, _1146728) = 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), _1146730), _1146728)))]]], (48008 ^ _779327) ^ [_1738622, _1738624, _1738626, _1738628, _1738630, _1738632, _1738634] : [c_List_Olist__all2(_1738622, _1738624, _1738626, hAPP(hAPP(c_List_Olist_OCons(_1738622), _1738628), _1738630), hAPP(hAPP(c_List_Olist_OCons(_1738624), _1738632), _1738634)), 48011 ^ _779327 : [(48014 ^ _779327) ^ [] : [-(c_List_Olist__all2(_1738622, _1738624, _1738626, _1738630, _1738634))], (48012 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1738626, _1738628), _1738632)))]]], (13909 ^ _779327) ^ [_1012896, _1012898] : [-(_1012896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1012898), _1012896) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012898), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1012898), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1012896), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (49467 ^ _779327) ^ [_1770311, _1770313, _1770315] : [hAPP(hAPP(c_List_Olist_OCons(_1770311), _1770313), c_List_Olist_ONil(_1770311)) = hAPP(c_List_Orev(_1770311), _1770315), -(_1770315 = hAPP(hAPP(c_List_Olist_OCons(_1770311), _1770313), c_List_Olist_ONil(_1770311)))], (15740 ^ _779327) ^ [_1045613] : [class_Int_Onumber__ring(_1045613), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1045613), c_Groups_Oone__class_Oone(_1045613)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045613), c_Int_OMin))], (38079 ^ _779327) ^ [_1492867, _1492869, _1492871, _1492873, _1492875] : [_1492867 = c_Orderings_Obot__class_Obot(tc_fun(_1492869, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1492869, tc_fun(_1492871, tc_HOL_Obool)), _1492867), hAPP(hAPP(c_COMBC(_1492869, tc_fun(_1492871, tc_HOL_Obool), tc_fun(_1492871, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1492871, tc_HOL_Obool), tc_fun(tc_fun(_1492871, tc_HOL_Obool), tc_fun(_1492871, tc_HOL_Obool)), _1492869), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492871, tc_HOL_Obool))), _1492873)), _1492875)) = c_Orderings_Otop__class_Otop(tc_fun(_1492871, tc_HOL_Obool)))], (23181 ^ _779327) ^ [_1181773, _1181775] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1181773)), _1181775) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1181773), 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), _1181773)), _1181775))], (47602 ^ _779327) ^ [_1729570, _1729572, _1729574] : [hBOOL(hAPP(c_List_Odistinct(_1729570), _1729572)), -(hBOOL(hAPP(c_List_Odistinct(_1729570), c_List_Oremove1(_1729570, _1729574, _1729572))))], (49525 ^ _779327) ^ [_1771671, _1771673, _1771675, _1771677, _1771679] : [c_List_Olist__all2(_1771671, _1771673, _1771675, _1771677, _1771679), -(c_List_Olist__all2(_1771671, _1771673, _1771675, hAPP(c_List_Orev(_1771671), _1771677), hAPP(c_List_Orev(_1771673), _1771679)))], (46582 ^ _779327) ^ [_1708396, _1708398, _1708400, _1708402] : [hAPP(hAPP(c_List_Oappend(_1708396), _1708398), _1708400) = _1708402, 46585 ^ _779327 : [(46588 ^ _779327) ^ [] : [-(_1708400 = hAPP(hAPP(c_List_Odrop(_1708396), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708396)), _1708398)), _1708402))], (46586 ^ _779327) ^ [] : [-(_1708398 = hAPP(hAPP(c_List_Otake(_1708396), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708396)), _1708398)), _1708402))]]], (48808 ^ _779327) ^ [_1757759, _1757761, _1757763] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1757759), c_List_Oupt(_1757761, _1757763)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757761), _1757759), _1757763))], (14521 ^ _779327) ^ [_1024101, _1024103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024101)), 14524 ^ _779327 : [(14531 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024103), 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), _1024103), _1024101)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14525 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024103), _1024101)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024103), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25884 ^ _779327) ^ [_1233163, _1233165, _1233167, _1233169] : [class_Groups_Ocomm__monoid__add(_1233163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233165), _1233167)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233163), _1233169), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1233165), _1233167)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1233163), hAPP(_1233169, _1233165)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233163), _1233169), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1233165)), _1233167))))], (16944 ^ _779327) ^ [_1066830, _1066832] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1066830), _1066832)), _1066832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066830), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066830, _1066832)))], (44875 ^ _779327) ^ [_1665392, _1665394, _1665396] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665392)), _1665394), c_Wellfounded_Oacc(tc_List_Olist(_1665392), c_List_Olistrel1(_1665392, _1665396)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1665392)), _1665394), c_List_Olists(_1665392, c_Wellfounded_Oacc(_1665392, _1665396)))))], (48900 ^ _779327) ^ [_1759563, _1759565, _1759567, _1759569, _1759571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1759565), _1759567))), -(hAPP(hAPP(c_List_Onth(_1759569), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1759569), _1759571), c_List_Oupt(_1759567, _1759565))), _1759563) = hAPP(_1759571, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1759567), _1759563)))], (23153 ^ _779327) ^ [_1181039, _1181041, _1181043, _1181045] : [class_Orderings_Olinorder(_1181039), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181039), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181039), _1181041), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181039), _1181043), _1181045))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1181039), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181039), _1181041), _1181043)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1181039), _1181041), _1181045)))))], (15135 ^ _779327) ^ [_1034246, _1034248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034246)), -(c_SMT_Oz3div(_1034248, _1034246) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034248), _1034246))], (51853 ^ _779327) ^ [_1823510, _1823512] : [c_Equiv__Relations_Oequivp(_1823510, _1823512), 51856 ^ _779327 : [(51861 ^ _779327) ^ [] : [-(c_Predicate_Otransp(_1823510, _1823512))], (51859 ^ _779327) ^ [] : [-(c_Predicate_Osymp(_1823510, _1823512))], (51857 ^ _779327) ^ [] : [-(c_Predicate_Oreflp(_1823510, _1823512))]]], (47466 ^ _779327) ^ [_1726953, _1726955, _1726957] : [_1726953 = c_List_Olist_ONil(_1726955), -(c_List_Obutlast(_1726955, hAPP(hAPP(c_List_Oappend(_1726955), _1726957), _1726953)) = c_List_Obutlast(_1726955, _1726957))], (46662 ^ _779327) ^ [_1710378, _1710380, _1710382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710378), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710380)), _1710382))), -(hAPP(hAPP(c_List_Olist_OCons(_1710380), hAPP(hAPP(c_List_Onth(_1710380), _1710382), _1710378)), hAPP(hAPP(c_List_Odrop(_1710380), hAPP(c_Nat_OSuc, _1710378)), _1710382)) = hAPP(hAPP(c_List_Odrop(_1710380), _1710378), _1710382))], (27282 ^ _779327) ^ [_1261055, _1261057] : [c_Nat__Transfer_Onat__set(_1261055), c_Nat__Transfer_Onat__set(_1261057), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1261055), _1261057)))], (41573 ^ _779327) ^ [_1585318, _1585320, _1585322, _1585324, _1585326, _1585328] : [c_Finite__Set_Ofolding(_1585318, _1585320, _1585322, _1585324), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585318), _1585326)), -(hBOOL(hAPP(hAPP(c_member(_1585318), _1585328), _1585326))), -(hAPP(_1585324, hAPP(hAPP(c_Set_Oinsert(_1585318), _1585328), _1585326)) = hAPP(c_Fun_Ocomp(_1585320, _1585320, _1585320, hAPP(_1585324, _1585326)), hAPP(_1585322, _1585328)))], (42775 ^ _779327) ^ [_1614105, _1614107, _1614109] : [42778 ^ _779327 : [(42784 ^ _779327) ^ [] : [42777 ^ [_1614105, _1614107, _1614109] = 42780 ^ [_1614105, _1614107, _1614109]], (42782 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614105, _1614107)), hAPP(hAPP(c_Product__Type_OPair(_1614105, _1614107), 42776 ^ [_1614105, _1614107, _1614109]), 42780 ^ [_1614105, _1614107, _1614109])), _1614109)))], (42779 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614105, _1614107)), hAPP(hAPP(c_Product__Type_OPair(_1614105, _1614107), 42776 ^ [_1614105, _1614107, _1614109]), 42777 ^ [_1614105, _1614107, _1614109])), _1614109)))]], -(c_Relation_Osingle__valued(_1614105, _1614107, _1614109))], (43794 ^ _779327) ^ [_1636882, _1636884] : [class_Complete__Lattice_Ocomplete__lattice(_1636882), -(c_Complete__Lattice_OSup__class_OSup(_1636882, _1636884) = c_Complete__Lattice_OInf__class_OInf(_1636882, hAPP(c_Set_OCollect(_1636882), hAPP(hAPP(c_COMBB(tc_fun(_1636882, tc_HOL_Obool), tc_HOL_Obool, _1636882), c_HOL_OAll(_1636882)), hAPP(hAPP(c_COMBB(tc_fun(_1636882, tc_HOL_Obool), tc_fun(_1636882, tc_HOL_Obool), _1636882), hAPP(c_COMBS(_1636882, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1636882), c_fimplies), hAPP(hAPP(c_COMBC(_1636882, tc_fun(_1636882, tc_HOL_Obool), tc_HOL_Obool), c_member(_1636882)), _1636884)))), hAPP(c_COMBC(_1636882, _1636882, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1636882)))))))], (50252 ^ _779327) ^ [_1787421, _1787423] : [class_Enum_Oenum(_1787421), 50255 ^ _779327 : [(50263 ^ _779327) ^ [] : [50264 ^ _779327 : [(50265 ^ _779327) ^ [_1787601] : [hBOOL(hAPP(_1787423, _1787601))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787421), _1787423)))], (50256 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787421), _1787423)), -(hBOOL(hAPP(_1787423, 50259 ^ [_1787421, _1787423])))]]], (14277 ^ _779327) ^ [_1019963, _1019965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019963), _1019965)), -(c_Nat__Transfer_Otsub(_1019965, _1019963) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019965), _1019963))], (12251 ^ _779327) ^ [_983165] : [_983165 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _983165) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39708 ^ _779327) ^ [_1532777] : [-(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)), _1532777)))))], (29244 ^ _779327) ^ [_1300741] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1300741)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1300741), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (34146 ^ _779327) ^ [_1404887, _1404889, _1404891, _1404893, _1404895] : [-(hAPP(c_Relation_OImage(_1404887, _1404889, _1404891), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404887, tc_HOL_Obool)), _1404893), _1404895)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404889, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404887, _1404889, _1404891), _1404893)), hAPP(c_Relation_OImage(_1404887, _1404889, _1404891), _1404895)))], (15822 ^ _779327) ^ [_1046895] : [class_Int_Onumber__ring(_1046895), -(hAPP(c_Int_Oring__1__class_Oof__int(_1046895), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1046895), c_Int_OMin))], (28421 ^ _779327) ^ [_1285289, _1285291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1285289), _1285291))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285289), _1285291)))], (5254 ^ _779327) ^ [_859521, _859523, _859525, _859527, _859529, _859531] : [-(c_Relation_Orel__comp(_859531, _859527, _859523) = c_Relation_Orel__comp(_859529, _859525, _859521)), _859531 = _859529, _859527 = _859525, _859523 = _859521], (47839 ^ _779327) ^ [_1734996, _1734998, _1735000, _1735002, _1735004] : [class_Orderings_Olinorder(_1734996), -(hAPP(c_List_Oset(_1734998), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734998, _1734996, _1735000), _1735002), _1735004)) = hAPP(hAPP(c_Set_Oinsert(_1734998), _1735002), hAPP(c_List_Oset(_1734998), _1735004)))], (18480 ^ _779327) ^ [_1093173, _1093175] : [class_Rings_Oring__1__no__zero__divisors(_1093173), 18483 ^ _779327 : [(18484 ^ _779327) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1093173), _1093175), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1093173), -(_1093175 = c_Groups_Oone__class_Oone(_1093173)), -(_1093175 = hAPP(c_Groups_Ouminus__class_Ouminus(_1093173), c_Groups_Oone__class_Oone(_1093173)))], (18494 ^ _779327) ^ [] : [18495 ^ _779327 : [(18498 ^ _779327) ^ [] : [_1093175 = hAPP(c_Groups_Ouminus__class_Ouminus(_1093173), c_Groups_Oone__class_Oone(_1093173))], (18496 ^ _779327) ^ [] : [_1093175 = c_Groups_Oone__class_Oone(_1093173)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093173), _1093175), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1093173))]]], (50205 ^ _779327) ^ [_1786209, _1786211, _1786213, _1786215, _1786217] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786209, _1786209)), hAPP(hAPP(c_Product__Type_OPair(_1786209, _1786209), _1786211), _1786213)), c_List_Omeasures(_1786209, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1786209, tc_Nat_Onat)), _1786215), _1786217))))), 50206 ^ _779327 : [(50209 ^ _779327) ^ [] : [hAPP(_1786215, _1786211) = hAPP(_1786215, _1786213), hBOOL(hAPP(hAPP(c_member(tc_prod(_1786209, _1786209)), hAPP(hAPP(c_Product__Type_OPair(_1786209, _1786209), _1786211), _1786213)), c_List_Omeasures(_1786209, _1786217)))], (50207 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1786215, _1786211)), hAPP(_1786215, _1786213)))]]], (18038 ^ _779327) ^ [_1085575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085575)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085575), c_Int_OPls)))], (14553 ^ _779327) ^ [_1024616, _1024618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024616), 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)), _1024618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024616), _1024618)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (44173 ^ _779327) ^ [_1645645, _1645647, _1645649, _1645651] : [class_Lattices_Osemilattice__inf(_1645645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645645), _1645647)), 44183 ^ _779327 : [(44186 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1645645), _1645649), 44182 ^ [_1645645, _1645647, _1645649, _1645651]))], (44184 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1645645), 44182 ^ [_1645645, _1645647, _1645649, _1645651]), _1645647)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1645645), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1645645), _1645649), _1645651)), hAPP(hAPP(c_Finite__Set_Ofold(_1645645, _1645645, c_Lattices_Osemilattice__inf__class_Oinf(_1645645)), _1645651), _1645647))))], (52708 ^ _779327) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (3196 ^ _779327) ^ [_827352, _827354] : [_827354 = _827352, -(c_Int_Oring__1__class_Oof__int(_827354) = c_Int_Oring__1__class_Oof__int(_827352))], (7806 ^ _779327) ^ [_902594, _902596, _902598, _902600] : [class_Rings_Oordered__comm__semiring(_902594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902594), _902596), _902598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902594), c_Groups_Ozero__class_Ozero(_902594)), _902600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902594), _902600), _902596)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902594), _902600), _902598))))], (45657 ^ _779327) ^ [_1686008, _1686010, _1686012] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1686008)), -(c_List_Osublist(_1686010, hAPP(hAPP(c_List_Olist_OCons(_1686010), _1686012), c_List_Olist_ONil(_1686010)), _1686008) = hAPP(hAPP(c_List_Olist_OCons(_1686010), _1686012), c_List_Olist_ONil(_1686010)))], (40382 ^ _779327) ^ [_1555507, _1555509, _1555511, _1555513, _1555515] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1555507, _1555509, _1555511), _1555513), _1555515) = hAPP(c_Set_OCollect(tc_prod(_1555507, _1555511)), hAPP(c_Product__Type_Oprod_Oprod__case(_1555507, _1555511, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1555511, tc_fun(_1555509, tc_HOL_Obool)), tc_fun(_1555511, tc_HOL_Obool), _1555507), hAPP(c_COMBB(tc_fun(_1555509, tc_HOL_Obool), tc_HOL_Obool, _1555511), c_HOL_OEx(_1555509))), hAPP(hAPP(c_COMBC(_1555507, tc_fun(_1555511, tc_fun(_1555509, tc_HOL_Obool)), tc_fun(_1555511, tc_fun(_1555509, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1555509, tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), tc_fun(tc_fun(_1555511, tc_fun(_1555509, tc_HOL_Obool)), tc_fun(_1555511, tc_fun(_1555509, tc_HOL_Obool))), _1555507), c_COMBB(tc_fun(_1555509, tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool), _1555511)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1555509, tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), _1555507), c_COMBS(_1555509, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_HOL_Obool), tc_fun(_1555509, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1555507), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555509), c_fconj)), hAPP(hAPP(c_COMBC(_1555507, tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_fun(tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), _1555507), c_COMBC(_1555509, tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_prod(_1555507, _1555509)), tc_fun(_1555509, tc_fun(tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_HOL_Obool)), _1555507), hAPP(c_COMBB(tc_prod(_1555507, _1555509), tc_fun(tc_fun(tc_prod(_1555507, _1555509), tc_HOL_Obool), tc_HOL_Obool), _1555509), c_member(tc_prod(_1555507, _1555509)))), c_Product__Type_OPair(_1555507, _1555509)))), _1555513))))), hAPP(hAPP(c_COMBC(_1555511, tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_fun(tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_fun(_1555509, tc_HOL_Obool)), _1555511), c_COMBC(_1555509, tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1555509, tc_prod(_1555509, _1555511)), tc_fun(_1555509, tc_fun(tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_HOL_Obool)), _1555511), hAPP(c_COMBB(tc_prod(_1555509, _1555511), tc_fun(tc_fun(tc_prod(_1555509, _1555511), tc_HOL_Obool), tc_HOL_Obool), _1555509), c_member(tc_prod(_1555509, _1555511)))), hAPP(c_COMBC(_1555509, _1555511, tc_prod(_1555509, _1555511)), c_Product__Type_OPair(_1555509, _1555511))))), _1555515))))))], (30581 ^ _779327) ^ [_1331165, _1331167, _1331169, _1331171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331165, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331165, tc_HOL_Obool)), _1331167), hAPP(hAPP(c_Set_Oinsert(_1331165), _1331169), c_Orderings_Obot__class_Obot(tc_fun(_1331165, tc_HOL_Obool))))), _1331171)), hBOOL(hAPP(hAPP(c_member(_1331165), _1331169), _1331167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331165, tc_HOL_Obool)), _1331167), hAPP(hAPP(c_Set_Oinsert(_1331165), _1331169), _1331171))))], (37751 ^ _779327) ^ [] : [-(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))))], (22019 ^ _779327) ^ [_1159261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159261)), 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), _1159261)) = 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), _1159261))))))], (49563 ^ _779327) ^ [_1772356, _1772358] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772356)), hAPP(c_List_Orev(_1772356), _1772358)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772356)), _1772358))], (4896 ^ _779327) ^ [_853930, _853932] : [_853932 = _853930, -(c_Groups_Oone__class_Oone(_853932) = c_Groups_Oone__class_Oone(_853930))], (39742 ^ _779327) ^ [_1533310, _1533312, _1533314] : [-(hAPP(hAPP(c_Set_Oinsert(_1533310), _1533312), hAPP(c_Set_OCollect(_1533310), _1533314)) = hAPP(c_Set_OCollect(_1533310), hAPP(hAPP(c_COMBS(_1533310, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533310), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1533310), c_fNot), hAPP(hAPP(c_COMBC(_1533310, _1533310, tc_HOL_Obool), c_fequal), _1533312)))), _1533314)))], (45279 ^ _779327) ^ [_1675631, _1675633, _1675635, _1675637, _1675639] : [hBOOL(hAPP(hAPP(c_member(_1675631), _1675633), hAPP(c_List_Oset(_1675631), _1675635))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675637), hAPP(_1675639, _1675633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675637), c_List_Olist_Olist__size(_1675631, _1675639, _1675635))))], (12375 ^ _779327) ^ [_985245, _985247] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985245), _985247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _985245 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _985247 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25181 ^ _779327) ^ [_1218334, _1218336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218336)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218334), _1218336)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1218336), _1218334)), -(_1218334 = _1218336)], (1458 ^ _779327) ^ [_800540, _800542] : [-(class_Lattices_Odistrib__lattice(_800540)), _800542 = _800540, class_Lattices_Odistrib__lattice(_800542)], (6716 ^ _779327) ^ [_884458, _884460, _884462, _884464] : [class_Orderings_Oord(_884458), 6719 ^ _779327 : [(6726 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884458), hAPP(_884462, 6727 ^ [_884458, _884460, _884462, _884464])), hAPP(_884464, 6727 ^ [_884458, _884460, _884462, _884464]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884460, _884458)), _884462), _884464)))], (6720 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884460, _884458)), _884462), _884464)), 6723 ^ _779327 : [(6724 ^ _779327) ^ [_884615] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884458), hAPP(_884462, _884615)), hAPP(_884464, _884615))))]]]]], (12642 ^ _779327) ^ [_990338, _990340, _990342, _990344, _990346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990338), _990340)), 12645 ^ _779327 : [(12652 ^ _779327) ^ [] : [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), _990340), _990338)), _990342)), _990344)), _990346)), -(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), _990340), _990342)), _990344)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990338), _990342)), _990346))))], (12646 ^ _779327) ^ [] : [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), _990340), _990342)), _990344)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990338), _990342)), _990346))), -(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), _990340), _990338)), _990342)), _990344)), _990346)))]]], (17390 ^ _779327) ^ [_1074542, _1074544] : [_1074542 = _1074544, -(c_Int_OBit1(_1074542) = c_Int_OBit1(_1074544))], (47104 ^ _779327) ^ [_1719603, _1719605, _1719607] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719603)), hAPP(c_List_Orotate(_1719603, _1719605), _1719607)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719603)), _1719607))], (15345 ^ _779327) ^ [_1038183, _1038185, _1038187, _1038189] : [class_Divides_Osemiring__div(_1038183), -(c_Divides_Odiv__class_Omod(_1038183, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038183), _1038185), _1038187), _1038189) = c_Divides_Odiv__class_Omod(_1038183, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038183), c_Divides_Odiv__class_Omod(_1038183, _1038185, _1038189)), c_Divides_Odiv__class_Omod(_1038183, _1038187, _1038189)), _1038189))], (38800 ^ _779327) ^ [_1512048, _1512050, _1512052] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512048, _1512050), _1512052), hAPP(c_COMBK(tc_fun(_1512050, tc_HOL_Obool), _1512048), c_Orderings_Obot__class_Obot(tc_fun(_1512050, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1512048, _1512050), tc_HOL_Obool)))], (42675 ^ _779327) ^ [_1612001, _1612003] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1612001, _1612001)), _1612003)), c_Wellfounded_Oacyclic(_1612001, _1612003), -(c_Wellfounded_Owf(_1612001, hAPP(c_Relation_Oconverse(_1612001, _1612001), _1612003)))], (5792 ^ _779327) ^ [_870788] : [_870788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _870788), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22067 ^ _779327) ^ [_1160479, _1160481, _1160483, _1160485] : [hAPP(c_Product__Type_Ofst(_1160479, _1160481), _1160483) = hAPP(c_Product__Type_Ofst(_1160479, _1160481), _1160485), hAPP(c_Product__Type_Osnd(_1160479, _1160481), _1160483) = hAPP(c_Product__Type_Osnd(_1160479, _1160481), _1160485), -(_1160483 = _1160485)], (49756 ^ _779327) ^ [_1776477, _1776479, _1776481] : [hBOOL(hAPP(c_List_Odistinct(_1776477), _1776479)), -(hBOOL(hAPP(c_List_Odistinct(_1776477), c_List_OtakeWhile(_1776477, _1776481, _1776479))))], (33068 ^ _779327) ^ [_1381202, _1381204, _1381206, _1381208] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1381202), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381204, tc_Int_Oint), _1381206), _1381208)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381204, _1381202), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1381202, _1381204), c_Int_Oring__1__class_Oof__int(_1381202)), _1381206)), _1381208)), class_Groups_Ocomm__monoid__mult(_1381202), class_Rings_Oring__1(_1381202)], (37207 ^ _779327) ^ [_1474567, _1474569, _1474571, _1474573] : [c_Fun_Oinj__on(_1474567, _1474569, _1474571, _1474573), -(c_Fun_Oinj__on(_1474569, _1474567, c_Fun_Othe__inv__into(_1474567, _1474569, _1474573, _1474571), hAPP(c_Set_Oimage(_1474567, _1474569, _1474571), _1474573)))], (5142 ^ _779327) ^ [_857781, _857783] : [_857783 = _857781, -(c_List_Oset(_857783) = c_List_Oset(_857781))], (52570 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (6929 ^ _779327) ^ [_887727] : [6930 ^ _779327 : [(6931 ^ _779327) ^ [_887769] : [_887727 = hAPP(c_Nat_OSuc, _887769)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887727)))], (51877 ^ _779327) ^ [_1823816, _1823818] : [c_Predicate_Oreflp(_1823816, _1823818), c_Predicate_Osymp(_1823816, _1823818), c_Predicate_Otransp(_1823816, _1823818), -(c_Equiv__Relations_Oequivp(_1823816, _1823818))], (22085 ^ _779327) ^ [_1160836, _1160838, _1160840, _1160842] : [-(_1160836 = _1160838), hAPP(c_Product__Type_Ofst(_1160840, _1160842), _1160836) = hAPP(c_Product__Type_Ofst(_1160840, _1160842), _1160838), hAPP(c_Product__Type_Osnd(_1160840, _1160842), _1160836) = hAPP(c_Product__Type_Osnd(_1160840, _1160842), _1160838)], (4264 ^ _779327) ^ [_844094, _844096, _844098, _844100, _844102, _844104, _844106, _844108, _844110, _844112] : [-(c_List_Olinorder__class_Oinsort__insert__key(_844112, _844108, _844104, _844100, _844096) = c_List_Olinorder__class_Oinsort__insert__key(_844110, _844106, _844102, _844098, _844094)), _844112 = _844110, _844108 = _844106, _844104 = _844102, _844100 = _844098, _844096 = _844094], (31710 ^ _779327) ^ [_1355483, _1355485] : [class_Int_Onumber__ring(_1355483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1355485)), -(hBOOL(hAPP(hAPP(c_member(_1355483), hAPP(c_Int_Onumber__class_Onumber__of(_1355483), _1355485)), c_Nat_Osemiring__1__class_ONats(_1355483))))], (50314 ^ _779327) ^ [_1788758, _1788760] : [class_Lazy__Sequence_Osmall__lazy(_1788758), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1788758), _1788760) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1788758), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1788758)), c_List_Olist_ONil(_1788758)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1788758))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1788760)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1788758, tc_List_Olist(_1788758)), tc_List_Olist(_1788758), c_Lazy__Sequence_Oproduct(_1788758, tc_List_Olist(_1788758), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1788758, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1788760), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1788758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1788760), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1788758, tc_List_Olist(_1788758), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1788758))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1788758), tc_List_Olist(_1788758)), tc_fun(tc_List_Olist(_1788758), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1788758))), _1788758), hAPP(c_COMBB(tc_List_Olist(_1788758), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1788758)), tc_List_Olist(_1788758)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1788758)))), c_List_Olist_OCons(_1788758))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1788758)))))], (42908 ^ _779327) ^ [_1617555, _1617557] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617555, _1617555), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1617557) = c_Relation_OId(_1617555))], (44546 ^ _779327) ^ [_1655465, _1655467, _1655469, _1655471, _1655473, _1655475] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655465), tc_List_Olist(_1655465))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655465), tc_List_Olist(_1655465)), hAPP(hAPP(c_List_Olist_OCons(_1655465), _1655467), _1655469)), hAPP(hAPP(c_List_Olist_OCons(_1655465), _1655471), _1655473))), c_List_Olexord(_1655465, _1655475))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655465, _1655465)), hAPP(hAPP(c_Product__Type_OPair(_1655465, _1655465), _1655467), _1655471)), _1655475))), 44553 ^ _779327 : [(44556 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655465), tc_List_Olist(_1655465))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655465), tc_List_Olist(_1655465)), _1655469), _1655473)), c_List_Olexord(_1655465, _1655475))))], (44554 ^ _779327) ^ [] : [-(_1655467 = _1655471)]]], (9763 ^ _779327) ^ [_937566] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _937566)) = _937566)], (18787 ^ _779327) ^ [_1099069, _1099071] : [class_Rings_Odivision__ring(_1099069), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099069), c_Groups_Ozero__class_Ozero(_1099069)), _1099071) = c_Groups_Ozero__class_Ozero(_1099069))], (43143 ^ _779327) ^ [_1623885, _1623887, _1623889, _1623891] : [class_Orderings_Olinorder(_1623885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623885), _1623887)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1623885, _1623885, c_Orderings_Oord__class_Omin(_1623885)), _1623889), hAPP(hAPP(c_Set_Oinsert(_1623885), _1623891), _1623887)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1623885), _1623891), hAPP(hAPP(c_Finite__Set_Ofold(_1623885, _1623885, c_Orderings_Oord__class_Omin(_1623885)), _1623889), _1623887)))], (40871 ^ _779327) ^ [_1568845, _1568847, _1568849] : [c_Wellfounded_Owf(_1568845, _1568847), c_Wellfounded_Owf(_1568845, _1568849), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568845, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1568845, _1568845), _1568847)), hAPP(c_Relation_ORange(_1568845, _1568845), _1568849)) = c_Orderings_Obot__class_Obot(tc_fun(_1568845, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1568845, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568845, _1568845), tc_HOL_Obool)), _1568847), _1568849)))], (31988 ^ _779327) ^ [_1360448, _1360450] : [class_Rings_Osemiring__1(_1360448), -(hBOOL(hAPP(hAPP(c_member(_1360448), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1360448), _1360450)), c_Nat_Osemiring__1__class_ONats(_1360448))))], (5200 ^ _779327) ^ [_858632, _858634, _858636, _858638] : [-(c_Complete__Lattice_OInf__class_OInf(_858638, _858634) = c_Complete__Lattice_OInf__class_OInf(_858636, _858632)), _858638 = _858636, _858634 = _858632], (52632 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (17898 ^ _779327) ^ [_1083168, _1083170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1083168)), c_Int_OBit0(_1083170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083168), _1083170)))], (39012 ^ _779327) ^ [_1517202, _1517204] : [class_Orderings_Olinorder(_1517202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517202), _1517204)), -(c_Big__Operators_Olattice_OInf__fin(_1517202, c_Orderings_Oord__class_Omin(_1517202), _1517204) = hAPP(c_Finite__Set_Ofold1(_1517202, c_Orderings_Oord__class_Omin(_1517202)), _1517204))], (23784 ^ _779327) ^ [_1193762, _1193764, _1193766, _1193768, _1193770, _1193772, _1193774] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1193762, _1193764, _1193766, _1193768), _1193770), _1193772), _1193774) = c_New__DSequence_Oneg__bind(_1193762, _1193764, hAPP(hAPP(hAPP(_1193766, _1193770), _1193772), _1193774), hAPP(hAPP(c_COMBC(_1193762, 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(_1193764)))), hAPP(hAPP(c_COMBC(_1193762, 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(_1193764))))), hAPP(hAPP(c_COMBC(_1193762, 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(_1193764)))))), _1193768), _1193770)), _1193772)), _1193774)))], (17934 ^ _779327) ^ [_1083834] : [c_Int_OBit0(_1083834) = c_Int_OPls, -(_1083834 = c_Int_OPls)], (39521 ^ _779327) ^ [_1528670, _1528672, _1528674, _1528676, _1528678, _1528680, _1528682, _1528684] : [-(hAPP(c_Product__Type_Omap__pair(_1528670, _1528672, _1528674, _1528676, _1528678, _1528680), hAPP(hAPP(c_Product__Type_OPair(_1528670, _1528674), _1528682), _1528684)) = hAPP(hAPP(c_Product__Type_OPair(_1528672, _1528676), hAPP(_1528678, _1528682)), hAPP(_1528680, _1528684)))], (16764 ^ _779327) ^ [_1063591, _1063593] : [class_Rings_Olinordered__idom(_1063591), -(hAPP(c_Groups_Oabs__class_Oabs(_1063591), _1063593) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063591), _1063593), c_Groups_Osgn__class_Osgn(_1063591, _1063593)))], (22315 ^ _779327) ^ [_1165178, _1165180, _1165182, _1165184, _1165186] : [hBOOL(hAPP(hAPP(_1165178, _1165180), _1165182)), -(hBOOL(hAPP(hAPP(_1165178, hAPP(c_Product__Type_Osnd(_1165184, _1165186), hAPP(hAPP(c_Product__Type_OPair(_1165184, _1165186), _1165182), _1165180))), hAPP(c_Product__Type_Ofst(_1165184, _1165186), hAPP(hAPP(c_Product__Type_OPair(_1165184, _1165186), _1165182), _1165180)))))], (52918 ^ _779327) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (22327 ^ _779327) ^ [_1165499] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1165499) = _1165499)], (49177 ^ _779327) ^ [_1764454, _1764456, _1764458] : [class_Orderings_Olinorder(_1764454), -(c_List_Olinorder__class_Osorted(_1764454, hAPP(c_List_Ofilter(_1764454, hAPP(hAPP(c_COMBC(_1764454, _1764454, tc_HOL_Obool), c_fequal), hAPP(_1764456, _1764458))), _1764458)))], (30165 ^ _779327) ^ [_1321578, _1321580, _1321582] : [hBOOL(hAPP(hAPP(c_member(_1321578), _1321580), hAPP(hAPP(c_Set_Oinsert(_1321578), _1321582), c_Orderings_Obot__class_Obot(tc_fun(_1321578, tc_HOL_Obool))))), -(_1321580 = _1321582)], (26474 ^ _779327) ^ [_1245563, _1245565] : [class_Groups_Oordered__ab__group__add(_1245563), -(hAPP(c_Set_Oimage(_1245563, _1245563, c_Groups_Ouminus__class_Ouminus(_1245563)), hAPP(c_SetInterval_Oord__class_OlessThan(_1245563), _1245565)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1245563), hAPP(c_Groups_Ouminus__class_Ouminus(_1245563), _1245565)))], (36725 ^ _779327) ^ [_1464646, _1464648, _1464650] : [-(c_Fun_Oinj__on(_1464646, _1464648, _1464650, c_Orderings_Obot__class_Obot(tc_fun(_1464646, tc_HOL_Obool))))], (1548 ^ _779327) ^ [_801665, _801667] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801665)), _801667 = _801665, class_Groups_Oordered__cancel__ab__semigroup__add(_801667)], (7304 ^ _779327) ^ [_893829, _893831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _893829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _893831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _893831), _893829))))], (15011 ^ _779327) ^ [_1031908, _1031910, _1031912] : [hBOOL(hAPP(_1031908, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1031910), _1031912))), 15014 ^ _779327 : [(15039 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031912), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 15042 ^ _779327 : [(15043 ^ _779327) ^ [_1032572] : [-(hBOOL(hAPP(_1031908, _1032572))), 15044 ^ _779327 : [(15045 ^ _779327) ^ [_1032646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031912), _1032646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032646), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1031910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031912), _1032572)), _1032646)]]]]], (15021 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031912)), 15024 ^ _779327 : [(15025 ^ _779327) ^ [_1032242] : [-(hBOOL(hAPP(_1031908, _1032242))), 15026 ^ _779327 : [(15027 ^ _779327) ^ [_1032313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032313), _1031912)), _1031910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031912), _1032242)), _1032313)]]]]], (15015 ^ _779327) ^ [] : [_1031912 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1031908, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (35309 ^ _779327) ^ [_1432095, _1432097, _1432099, _1432101, _1432103] : [hBOOL(hAPP(hAPP(c_member(_1432095), _1432097), _1432099)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432101, tc_HOL_Obool)), hAPP(_1432103, _1432097)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432095, tc_fun(_1432101, tc_HOL_Obool)), _1432099), _1432103)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432095, tc_fun(_1432101, tc_HOL_Obool)), _1432099), _1432103))], (42402 ^ _779327) ^ [] : [-(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))))], (39854 ^ _779327) ^ [_1536152, _1536154, _1536156] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1536152, tc_HOL_Obool)), _1536154), _1536156) = hAPP(c_Set_OCollect(_1536152), hAPP(hAPP(c_COMBS(_1536152, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536152), c_fconj), hAPP(hAPP(c_COMBC(_1536152, tc_fun(_1536152, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536152)), _1536154))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536152), c_fNot), hAPP(hAPP(c_COMBC(_1536152, tc_fun(_1536152, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536152)), _1536156)))))], (38198 ^ _779327) ^ [_1496524, _1496526, _1496528, _1496530] : [c_Fun_Oinj__on(_1496524, _1496526, _1496528, c_Orderings_Otop__class_Otop(tc_fun(_1496524, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496526, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1496524, _1496526, _1496528), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496524, tc_HOL_Obool)), _1496530))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496526, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1496524, _1496526, _1496528), _1496530)))))], (31720 ^ _779327) ^ [_1355642, _1355644] : [class_Rings_Olinordered__idom(_1355642), hBOOL(hAPP(hAPP(c_member(_1355642), _1355644), c_Int_Oring__1__class_OInts(_1355642))), 31727 ^ _779327 : [(31734 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355642), _1355644), c_Groups_Ozero__class_Ozero(_1355642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355642), c_Groups_Oone__class_Oone(_1355642)), _1355644)), _1355644)), c_Groups_Ozero__class_Ozero(_1355642))))], (31728 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355642), c_Groups_Oone__class_Oone(_1355642)), _1355644)), _1355644)), c_Groups_Ozero__class_Ozero(_1355642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355642), _1355644), c_Groups_Ozero__class_Ozero(_1355642))))]]], (40832 ^ _779327) ^ [_1568175, _1568177, _1568179, _1568181, _1568183] : [hBOOL(hAPP(hAPP(_1568175, _1568177), _1568179)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1568181, _1568183, _1568175), _1568179)))], (33738 ^ _779327) ^ [_1395989, _1395991, _1395993] : [class_Orderings_Olinorder(_1395989), hAPP(_1395991, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1395989), 33743 ^ [_1395989, _1395991, _1395993]), 33744 ^ [_1395989, _1395991, _1395993])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1395989), hAPP(_1395991, 33743 ^ [_1395989, _1395991, _1395993])), hAPP(_1395991, 33744 ^ [_1395989, _1395991, _1395993])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395989), _1395993)), -(_1395993 = c_Orderings_Obot__class_Obot(tc_fun(_1395989, tc_HOL_Obool))), -(hAPP(_1395991, c_Big__Operators_Olinorder__class_OMin(_1395989, _1395993)) = c_Big__Operators_Olinorder__class_OMin(_1395989, hAPP(c_Set_Oimage(_1395989, _1395989, _1395991), _1395993)))], (40773 ^ _779327) ^ [_1566367, _1566369, _1566371, _1566373] : [c_FunDef_Oreduction__pair(_1566367, _1566369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool)), _1566371), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool), tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool)), _1566369))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool)), _1566373), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool), tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool)), _1566369))), c_Wellfounded_Owf(_1566367, _1566373), -(c_Wellfounded_Owf(_1566367, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566367, _1566367), tc_HOL_Obool)), _1566371), _1566373)))], (22971 ^ _779327) ^ [_1177326, _1177328, _1177330] : [class_Orderings_Olinorder(_1177326), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177326), _1177328), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177326), _1177330), _1177328))))], (35093 ^ _779327) ^ [_1426974, _1426976, _1426978, _1426980] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426974, tc_HOL_Obool)), _1426976), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426974, tc_HOL_Obool)), _1426978), _1426980)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426974, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426974, tc_HOL_Obool)), _1426976), _1426978)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426974, tc_HOL_Obool)), _1426976), _1426980)))], (23716 ^ _779327) ^ [_1192249, _1192251] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1192249), _1192251) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1192249)), hAPP(c_Code__Numeral_Onat__of, _1192251))))], (50096 ^ _779327) ^ [_1783612, _1783614, _1783616, _1783618, _1783620] : [c_Fun_Oinj__on(_1783612, _1783614, _1783616, c_Orderings_Otop__class_Otop(tc_fun(_1783612, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1783612, _1783614), _1783616), hAPP(c_List_OremoveAll(_1783612, _1783618), _1783620)) = hAPP(c_List_OremoveAll(_1783614, hAPP(_1783616, _1783618)), hAPP(hAPP(c_List_Omap(_1783612, _1783614), _1783616), _1783620)))], (18811 ^ _779327) ^ [_1099647, _1099649, _1099651, _1099653] : [class_Rings_Odivision__ring(_1099647), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099647), _1099649), _1099651)), _1099653) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099647), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099647), _1099649), _1099653)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099647), _1099651), _1099653)))], (10809 ^ _779327) ^ [_955374, _955376, _955378] : [class_Rings_Ocomm__semiring__1(_955374), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955374), _955376), _955378) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955374), _955378), _955376))], (25031 ^ _779327) ^ [_1215730, _1215732, _1215734, _1215736] : [class_Orderings_Oorder(_1215730), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1215730, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1215732), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215730), hAPP(_1215732, _1215734)), hAPP(_1215732, _1215736)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215734), _1215736)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215736), _1215734)))], (23598 ^ _779327) ^ [_1190180, _1190182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190180)), hAPP(c_Code__Numeral_Oof__nat, _1190182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190180), _1190182)))], (29578 ^ _779327) ^ [_1307559, _1307561, _1307563, _1307565, _1307567, _1307569] : [hBOOL(hAPP(hAPP(c_member(_1307559), _1307561), _1307563)), hBOOL(hAPP(hAPP(c_member(_1307565), _1307567), hAPP(_1307569, _1307561))), -(hBOOL(hAPP(hAPP(c_member(_1307565), _1307567), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307559, tc_fun(_1307565, tc_HOL_Obool)), _1307563), _1307569))))], (18246 ^ _779327) ^ [_1089199] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1089199)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1089199)))], (13352 ^ _779327) ^ [_1002979, _1002981] : [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), _1002979), _1002981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002981), _1002979)))], (23065 ^ _779327) ^ [_1179046, _1179048, _1179050, _1179052] : [class_Orderings_Olinorder(_1179046), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179046), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179046), _1179048), _1179050)), _1179052) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179046), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179046), _1179048), _1179052)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179046), _1179050), _1179052)))], (48764 ^ _779327) ^ [_1757116, _1757118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757116), _1757118)), -(c_List_Oupt(_1757116, _1757118) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1757116), c_List_Oupt(hAPP(c_Nat_OSuc, _1757116), _1757118)))], (21750 ^ _779327) ^ [_1153806, _1153808, _1153810, _1153812, _1153814, _1153816, _1153818] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153806, _1153808), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1153810), _1153812))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153814, _1153808), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1153816), _1153818))), -(_1153808 = 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), _1153806), _1153814), _1153808), 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), _1153810), _1153816)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153812), _1153818)), _1153808))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153812), _1153818), _1153808)))))], (12902 ^ _779327) ^ [_994934, _994936] : [class_Groups_Oordered__ab__group__add(_994934), 12905 ^ _779327 : [(12912 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994934), c_Groups_Ozero__class_Ozero(_994934)), _994936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994934), hAPP(c_Groups_Ouminus__class_Ouminus(_994934), _994936)), c_Groups_Ozero__class_Ozero(_994934))))], (12906 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994934), hAPP(c_Groups_Ouminus__class_Ouminus(_994934), _994936)), c_Groups_Ozero__class_Ozero(_994934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994934), c_Groups_Ozero__class_Ozero(_994934)), _994936)))]]], (49814 ^ _779327) ^ [_1777654] : [-(c_List_Oembed__list(_1777654) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1777654))], (42066 ^ _779327) ^ [_1596310, _1596312, _1596314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596310, _1596310)), _1596312), _1596314)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596310, _1596310)), _1596312), c_Transitive__Closure_Otrancl(_1596310, _1596314))))], (16461 ^ _779327) ^ [_1058381, _1058383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058381, _1058383)), _1058381)))], (26430 ^ _779327) ^ [_1244660] : [-(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)), _1244660)) = _1244660)], (27869 ^ _779327) ^ [_1274786, _1274788] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1274786, _1274788))))], (37296 ^ _779327) ^ [_1476456, _1476458, _1476460, _1476462, _1476464, _1476466, _1476468] : [c_Finite__Set_Ofolding__image__simple(_1476456, _1476458, _1476460, _1476462, _1476464, _1476466), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476458), _1476468)), -(hAPP(_1476466, _1476468) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476456, _1476458, _1476460), _1476464), _1476462), _1476468))], (8564 ^ _779327) ^ [_916470, _916472] : [class_Rings_Olinordered__semidom(_916470), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916470), c_Groups_Ozero__class_Ozero(_916470)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_916470), _916472))))], (30453 ^ _779327) ^ [_1328389, _1328391, _1328393] : [hBOOL(hAPP(hAPP(c_member(_1328389), _1328391), _1328393)), -(hAPP(hAPP(c_Set_Oinsert(_1328389), _1328391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328389, tc_HOL_Obool)), _1328393), hAPP(hAPP(c_Set_Oinsert(_1328389), _1328391), c_Orderings_Obot__class_Obot(tc_fun(_1328389, tc_HOL_Obool))))) = _1328393)], (52482 ^ _779327) ^ [_1835147, _1835149] : [class_Lattices_Oboolean__algebra(_1835147), -(class_Lattices_Oboolean__algebra(tc_fun(_1835149, _1835147)))], (53048 ^ _779327) ^ [_1841069, _1841071] : [hBOOL(_1841069), hBOOL(_1841071), -(hBOOL(hAPP(hAPP(c_fconj, _1841069), _1841071)))], (38772 ^ _779327) ^ [_1511241, _1511243, _1511245, _1511247, _1511249] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1511241, _1511243), _1511245), hAPP(hAPP(c_COMBS(_1511241, tc_fun(_1511243, tc_HOL_Obool), tc_fun(_1511243, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511243, tc_HOL_Obool), tc_fun(tc_fun(_1511243, tc_HOL_Obool), tc_fun(_1511243, tc_HOL_Obool)), _1511241), c_Groups_Ominus__class_Ominus(tc_fun(_1511243, tc_HOL_Obool))), _1511247)), _1511249)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1511241, _1511243), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1511241, _1511243), _1511245), _1511247)), hAPP(hAPP(c_Product__Type_OSigma(_1511241, _1511243), _1511245), _1511249)))], (37847 ^ _779327) ^ [_1487743, _1487745] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487743, tc_HOL_Obool)), _1487745), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487743, tc_HOL_Obool)), _1487745)) = c_Orderings_Otop__class_Otop(tc_fun(_1487743, tc_HOL_Obool)))], (1968 ^ _779327) ^ [_806915, _806917] : [-(hBOOL(_806915)), _806917 = _806915, hBOOL(_806917)], (49806 ^ _779327) ^ [_1777530] : [c_List_Onat__list(_1777530), -(c_List_Oembed__list(c_List_Oreturn__list(_1777530)) = _1777530)], (10053 ^ _779327) ^ [] : [-(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))))], (16269 ^ _779327) ^ [_1055112, _1055114] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055112))), -(c_SMT_Oz3mod(_1055114, _1055112) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055114, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1055112)))], (42244 ^ _779327) ^ [_1601414, _1601416, _1601418] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601414, _1601414), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601414, _1601414), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1601414, _1601416)), c_Transitive__Closure_Ortrancl(_1601414, _1601418))), c_Transitive__Closure_Ortrancl(_1601414, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601414, _1601414), tc_HOL_Obool)), _1601416), _1601418)))))], (45984 ^ _779327) ^ [_1693951, _1693953, _1693955, _1693957, _1693959] : [-(hAPP(hAPP(c_List_Oappend(_1693951), _1693953), hAPP(hAPP(c_List_Olist_OCons(_1693951), _1693955), c_List_Olist_ONil(_1693951))) = hAPP(hAPP(c_List_Oappend(_1693951), _1693957), hAPP(hAPP(c_List_Olist_OCons(_1693951), _1693959), c_List_Olist_ONil(_1693951)))), _1693953 = _1693957, _1693955 = _1693959], (11705 ^ _779327) ^ [_973276, _973278, _973280] : [class_Groups_Oordered__ab__group__add(_973276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), _973278), _973280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973276), hAPP(c_Groups_Ouminus__class_Ouminus(_973276), _973280)), hAPP(c_Groups_Ouminus__class_Ouminus(_973276), _973278))))], (49885 ^ _779327) ^ [_1779200, _1779202, _1779204] : [hBOOL(hAPP(c_List_Odistinct(_1779200), _1779202)), -(hBOOL(hAPP(c_List_Odistinct(_1779200), c_List_OdropWhile(_1779200, _1779204, _1779202))))], (11203 ^ _779327) ^ [_962937, _962939, _962941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962937), _962939)), _962941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962941), _962939))))], (27915 ^ _779327) ^ [_1275745, _1275747, _1275749, _1275751] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1275745), _1275747), _1275749), _1275751)), -(_1275747 = _1275751), -(hBOOL(hAPP(_1275749, _1275751)))], (39900 ^ _779327) ^ [_1537875, _1537877, _1537879, _1537881, _1537883, _1537885] : [-(hAPP(c_Set_Oimage(_1537875, _1537877, hAPP(hAPP(c_COMBS(_1537875, _1537877, _1537877), hAPP(hAPP(c_COMBS(_1537875, _1537877, tc_fun(_1537877, _1537877)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537877, tc_fun(_1537877, _1537877)), _1537875), c_If(_1537877)), _1537879)), _1537881)), _1537883)), _1537885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1537875, _1537877, _1537881), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537875, tc_HOL_Obool)), _1537885), hAPP(c_Set_OCollect(_1537875), _1537879)))), hAPP(c_Set_Oimage(_1537875, _1537877, _1537883), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537875, tc_HOL_Obool)), _1537885), hAPP(c_Set_OCollect(_1537875), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1537875), c_fNot), _1537879))))))], (46872 ^ _779327) ^ [_1714573, _1714575] : [hAPP(c_Finite__Set_Ocard(_1714573), hAPP(c_List_Oset(_1714573), _1714575)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714573)), _1714575), -(hBOOL(hAPP(c_List_Odistinct(_1714573), _1714575)))], (52876 ^ _779327) ^ [_1839152] : [-(class_Nat_Osize(tc_Option_Ooption(_1839152)))], (17318 ^ _779327) ^ [_1073189, _1073191] : [class_Int_Onumber__ring(_1073189), 17321 ^ _779327 : [(17328 ^ _779327) ^ [] : [c_Int_Oiszero(_1073189, hAPP(c_Int_Onumber__class_Onumber__of(_1073189), 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), _1073191)))), -(c_Groups_Oone__class_Oone(_1073189) = hAPP(c_Int_Onumber__class_Onumber__of(_1073189), _1073191))], (17322 ^ _779327) ^ [] : [c_Groups_Oone__class_Oone(_1073189) = hAPP(c_Int_Onumber__class_Onumber__of(_1073189), _1073191), -(c_Int_Oiszero(_1073189, hAPP(c_Int_Onumber__class_Onumber__of(_1073189), 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), _1073191)))))]]], (14625 ^ _779327) ^ [_1025703, _1025705] : [class_Divides_Osemiring__div(_1025703), -(_1025705 = c_Groups_Ozero__class_Ozero(_1025703)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025703), _1025705), _1025705) = c_Groups_Oone__class_Oone(_1025703))], (45363 ^ _779327) ^ [_1678402, _1678404, _1678406, _1678408] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1678402), tc_List_Olist(_1678402))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678402), tc_List_Olist(_1678402)), _1678404), _1678406)), c_List_Olistrel(_1678402, _1678408)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678402)), _1678404) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678402)), _1678406), 45369 ^ _779327 : [(45372 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1678402, _1678402, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1678402, tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_fun(_1678402, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1678402, tc_fun(tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_fun(_1678402, tc_HOL_Obool)), _1678402), c_COMBC(_1678402, tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1678402, tc_prod(_1678402, _1678402)), tc_fun(_1678402, tc_fun(tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_HOL_Obool)), _1678402), hAPP(c_COMBB(tc_prod(_1678402, _1678402), tc_fun(tc_fun(tc_prod(_1678402, _1678402), tc_HOL_Obool), tc_HOL_Obool), _1678402), c_member(tc_prod(_1678402, _1678402)))), c_Product__Type_OPair(_1678402, _1678402)))), _1678408)), 45368 ^ [_1678402, _1678404, _1678406, _1678408]))], (45370 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678402, _1678402)), 45368 ^ [_1678402, _1678404, _1678406, _1678408]), hAPP(c_List_Oset(tc_prod(_1678402, _1678402)), hAPP(hAPP(c_List_Ozip(_1678402, _1678402), _1678404), _1678406)))))]]], (9192 ^ _779327) ^ [_927958, _927960, _927962, _927964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927958, tc_HOL_Obool)), _927960), _927962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927958, tc_HOL_Obool)), _927962), _927964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927958, tc_HOL_Obool)), _927960), _927964)))], (44147 ^ _779327) ^ [_1645065, _1645067, _1645069, _1645071] : [class_Orderings_Olinorder(_1645065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1645065), _1645067)), 44157 ^ _779327 : [(44160 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1645065), _1645069), 44156 ^ [_1645065, _1645067, _1645069, _1645071]))], (44158 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1645065), 44156 ^ [_1645065, _1645067, _1645069, _1645071]), _1645067)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1645065), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1645065), _1645069), _1645071)), hAPP(hAPP(c_Finite__Set_Ofold(_1645065, _1645065, c_Orderings_Oord__class_Omin(_1645065)), _1645071), _1645067))))], (2330 ^ _779327) ^ [_813351, _813353, _813355, _813357] : [-(c_Orderings_Oord_Omax(_813357, _813353) = c_Orderings_Oord_Omax(_813355, _813351)), _813357 = _813355, _813353 = _813351], (27859 ^ _779327) ^ [_1274635] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1274635))))], (14901 ^ _779327) ^ [_1030014, _1030016, _1030018] : [class_Divides_Osemiring__div(_1030014), -(_1030016 = c_Groups_Ozero__class_Ozero(_1030014)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030014), _1030016), _1030018)), _1030016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030014), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030014), _1030018), _1030016)), c_Groups_Oone__class_Oone(_1030014)))], (2436 ^ _779327) ^ [_814942, _814944, _814946, _814948, _814950, _814952] : [-(c_Nitpick_Oof__frac(_814952, _814948, _814944) = c_Nitpick_Oof__frac(_814950, _814946, _814942)), _814952 = _814950, _814948 = _814946, _814944 = _814942], (48560 ^ _779327) ^ [_1751596, _1751598, _1751600, _1751602] : [-(hBOOL(hAPP(_1751596, _1751598))), -(c_List_Oremove1(_1751600, _1751598, hAPP(c_List_Ofilter(_1751600, _1751596), _1751602)) = hAPP(c_List_Ofilter(_1751600, _1751596), _1751602))], (6821 ^ _779327) ^ [_885923, _885925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885923), _885925)), 6824 ^ _779327 : [(6831 ^ _779327) ^ [] : [_885925 = _885923, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885925), hAPP(c_Nat_OSuc, _885923))))], (6825 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885925), hAPP(c_Nat_OSuc, _885923))), -(_885925 = _885923)]]], (52752 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (37891 ^ _779327) ^ [_1488801, _1488803, _1488805, _1488807] : [c_Fun_Oinj__on(_1488801, _1488803, _1488805, c_Orderings_Otop__class_Otop(tc_fun(_1488801, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1488801, _1488803, c_Orderings_Otop__class_Otop(tc_fun(_1488801, tc_HOL_Obool)), _1488805), hAPP(_1488805, _1488807)) = _1488807)], (17678 ^ _779327) ^ [] : [-(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)))))], (10337 ^ _779327) ^ [] : [-(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))], (45408 ^ _779327) ^ [_1679761, _1679763] : [c_Orderings_Obot__class_Obot(tc_fun(_1679761, tc_HOL_Obool)) = hAPP(c_List_Oset(_1679761), _1679763), -(_1679763 = c_List_Olist_ONil(_1679761))], (48698 ^ _779327) ^ [_1755321, _1755323] : [-(c_List_Ofoldr(tc_List_Olist(_1755321), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1755321)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1755321))), c_List_Otranspose(_1755321, _1755323), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1755321))), hAPP(c_List_Ofilter(tc_List_Olist(_1755321), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1755321)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1755321), tc_List_Olist(_1755321), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1755321)))), _1755323)))], (49990 ^ _779327) ^ [_1781525, _1781527, _1781529, _1781531] : [49992 ^ _779327 : [(49995 ^ _779327) ^ [] : [hBOOL(hAPP(_1781527, hAPP(hAPP(c_List_Onth(_1781529), _1781531), 49991 ^ [_1781525, _1781527, _1781529, _1781531])))], (49993 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49991 ^ [_1781525, _1781527, _1781529, _1781531]), _1781525)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1781525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781529)), _1781531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1781525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781529)), c_List_OtakeWhile(_1781529, _1781527, _1781531)))))], (30325 ^ _779327) ^ [_1324672, _1324674, _1324676] : [class_Orderings_Oord(_1324672), 30328 ^ _779327 : [(30335 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324672), _1324676), _1324674)), -(hBOOL(hAPP(hAPP(c_member(_1324672), _1324674), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1324672), _1324676))))], (30329 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324672), _1324674), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1324672), _1324676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324672), _1324676), _1324674)))]]], (15752 ^ _779327) ^ [_1045812, _1045814] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045812, _1045814) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045812, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1045814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1045812, _1045814)), _1045814))], (35069 ^ _779327) ^ [_1426290, _1426292, _1426294, _1426296] : [class_Lattices_Odistrib__lattice(_1426290), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426290), _1426292), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426290), _1426294), _1426296)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426290), _1426292), _1426294)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426290), _1426292), _1426296)))], (298 ^ _779327) ^ [_783804, _783806, _783808, _783810, _783812, _783814, _783816, _783818] : [-(c_Equiv__Relations_Ocongruent(_783816, _783812, _783808, _783804)), c_Equiv__Relations_Ocongruent(_783818, _783814, _783810, _783806), _783818 = _783816, _783814 = _783812, _783810 = _783808, _783806 = _783804], (25019 ^ _779327) ^ [_1215523, _1215525, _1215527] : [class_Rings_Ocomm__semiring__1(_1215523), 25024 ^ _779327 : [(25027 ^ _779327) ^ [] : [_1215527 = c_Groups_Oone__class_Oone(_1215523)], (25025 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215525))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215523), _1215527), hAPP(hAPP(c_Power_Opower__class_Opower(_1215523), _1215527), _1215525))))], (15451 ^ _779327) ^ [_1040391, _1040393, _1040395] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1040391), _1040393), _1040395) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1040391), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040393, _1040395)), _1040395))], (35231 ^ _779327) ^ [_1429959, _1429961, _1429963, _1429965, _1429967] : [class_Lattices_Osemilattice__inf(_1429959), class_Lattices_Osemilattice__inf(_1429961), c_Orderings_Oorder__class_Omono(_1429961, _1429959, _1429963), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429959), hAPP(_1429963, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1429961), _1429965), _1429967))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1429959), hAPP(_1429963, _1429965)), hAPP(_1429963, _1429967)))))], (37294 ^ _779327) ^ [_1476407, _1476409, _1476411, _1476413, _1476415] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476407, _1476409, _1476411), _1476413), _1476415), c_Orderings_Obot__class_Obot(tc_fun(_1476409, tc_HOL_Obool))) = _1476415)], (21676 ^ _779327) ^ [_1152874, _1152876, _1152878] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1152874, _1152874), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1152876), _1152878))), -(_1152874 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1152878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48552 ^ _779327) ^ [_1751367, _1751369, _1751371] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1751367), tc_List_Olist(_1751367)), c_List_Opartition(_1751367, _1751369, _1751371)) = hAPP(c_List_Ofilter(_1751367, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1751367, c_fNot), _1751369)), _1751371))], (41409 ^ _779327) ^ [_1581514, _1581516, _1581518, _1581520, _1581522, _1581524, _1581526] : [c_Fun_Oinj__on(_1581514, _1581516, _1581518, hAPP(c_Set_Oimage(_1581520, _1581514, _1581522), _1581524)), c_Fun_Oinj__on(_1581520, _1581514, _1581522, _1581524), hBOOL(hAPP(hAPP(c_member(_1581516), _1581526), hAPP(c_Set_Oimage(_1581514, _1581516, _1581518), hAPP(c_Set_Oimage(_1581520, _1581514, _1581522), _1581524)))), -(hAPP(c_Fun_Othe__inv__into(_1581520, _1581516, _1581524, hAPP(c_Fun_Ocomp(_1581514, _1581516, _1581520, _1581518), _1581522)), _1581526) = hAPP(hAPP(c_Fun_Ocomp(_1581514, _1581520, _1581516, c_Fun_Othe__inv__into(_1581520, _1581514, _1581524, _1581522)), c_Fun_Othe__inv__into(_1581514, _1581516, hAPP(c_Set_Oimage(_1581520, _1581514, _1581522), _1581524), _1581518)), _1581526))], (35353 ^ _779327) ^ [_1433138, _1433140, _1433142, _1433144, _1433146, _1433148, _1433150, _1433152] : [c_Equiv__Relations_Oequiv(_1433138, _1433140, _1433142), c_Equiv__Relations_Ocongruent2(_1433138, _1433144, _1433146, _1433142, _1433148, _1433150), hBOOL(hAPP(hAPP(c_member(_1433138), _1433152), _1433140)), -(c_Equiv__Relations_Ocongruent(_1433144, _1433146, _1433148, hAPP(_1433150, _1433152)))], (6837 ^ _779327) ^ [_886164, _886166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886164), _886166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886164)), _886166)))], (7736 ^ _779327) ^ [_901291, _901293, _901295] : [class_Rings_Oordered__cancel__semiring(_901291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901291), c_Groups_Ozero__class_Ozero(_901291)), _901293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901291), _901295), c_Groups_Ozero__class_Ozero(_901291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_901291), _901295), _901293)), c_Groups_Ozero__class_Ozero(_901291))))], (17892 ^ _779327) ^ [_1083046, _1083048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083046), _1083048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1083046)), c_Int_OBit0(_1083048))))], (51693 ^ _779327) ^ [_1818649, _1818651] : [c_Relation_Otrans(_1818649, _1818651), -(c_Relation_Otrans(tc_List_Olist(_1818649), c_List_Olexord(_1818649, _1818651)))], (31948 ^ _779327) ^ [_1359748] : [class_Rings_Osemiring__1(_1359748), -(hBOOL(hAPP(hAPP(c_member(_1359748), c_Groups_Ozero__class_Ozero(_1359748)), c_Nat_Osemiring__1__class_ONats(_1359748))))], (21484 ^ _779327) ^ [_1148989, _1148991, _1148993] : [21486 ^ _779327 : [(21489 ^ _779327) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1148989, _1148991), 21485 ^ [_1148989, _1148991, _1148993]))], (21487 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1148991, 21485 ^ [_1148989, _1148991, _1148993]), _1148993)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1148989, _1148991), _1148993)))], (22267 ^ _779327) ^ [_1164125, _1164127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1164125), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1164127), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1164125), _1164127) = 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), _1164125), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164127)))))], (44207 ^ _779327) ^ [_1646388, _1646390] : [c_Wellfounded_Owf(_1646388, _1646390), 44210 ^ _779327 : [(44211 ^ _779327) ^ [_1646520] : [44212 ^ _779327 : [(44213 ^ _779327) ^ [_1646625] : [hBOOL(hAPP(hAPP(c_member(_1646388), _1646625), _1646520))]], 44215 ^ _779327 : [(44218 ^ _779327) ^ [_1646747] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1646388, _1646388)), hAPP(hAPP(c_Product__Type_OPair(_1646388, _1646388), _1646747), 44214 ^ [_1646388, _1646390, _1646520])), _1646390)), hBOOL(hAPP(hAPP(c_member(_1646388), _1646747), _1646520))], (44216 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646388), 44214 ^ [_1646388, _1646390, _1646520]), _1646520)))]]]]], (29756 ^ _779327) ^ [_1311073, _1311075, _1311077, _1311079] : [29757 ^ _779327 : [(29760 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1311073), _1311075), _1311079))], (29758 ^ _779327) ^ [] : [_1311075 = _1311077]], -(hBOOL(hAPP(hAPP(c_member(_1311073), _1311075), hAPP(hAPP(c_Set_Oinsert(_1311073), _1311077), _1311079))))], (11621 ^ _779327) ^ [_971831, _971833, _971835] : [class_Groups_Ogroup__add(_971831), 11624 ^ _779327 : [(11631 ^ _779327) ^ [] : [_971833 = _971835, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971831), _971833), _971835) = c_Groups_Ozero__class_Ozero(_971831))], (11625 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971831), _971833), _971835) = c_Groups_Ozero__class_Ozero(_971831), -(_971833 = _971835)]]], (46724 ^ _779327) ^ [_1712037, _1712039, _1712041, _1712043] : [-(_1712037 = c_List_Olist_ONil(_1712039)), -(hAPP(c_List_Ohd(_1712041), hAPP(hAPP(c_List_Omap(_1712039, _1712041), _1712043), _1712037)) = hAPP(_1712043, hAPP(c_List_Ohd(_1712039), _1712037)))], (22127 ^ _779327) ^ [_1161578, _1161580, _1161582, _1161584] : [-(hAPP(c_Product__Type_Osnd(_1161578, _1161580), hAPP(hAPP(c_Product__Type_OPair(_1161578, _1161580), _1161582), _1161584)) = _1161584)], (45564 ^ _779327) ^ [_1683089, _1683091, _1683093, _1683095, _1683097, _1683099] : [-(hAPP(hAPP(c_List_Ozip(_1683089, _1683091), hAPP(hAPP(c_List_Olist_OCons(_1683089), _1683093), _1683095)), hAPP(hAPP(c_List_Olist_OCons(_1683091), _1683097), _1683099)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1683089, _1683091)), hAPP(hAPP(c_Product__Type_OPair(_1683089, _1683091), _1683093), _1683097)), hAPP(hAPP(c_List_Ozip(_1683089, _1683091), _1683095), _1683099)))], (30547 ^ _779327) ^ [_1330550, _1330552, _1330554, _1330556] : [c_Finite__Set_Ofolding__one(_1330550, _1330552, _1330554), -(hAPP(_1330554, hAPP(hAPP(c_Set_Oinsert(_1330550), _1330556), c_Orderings_Obot__class_Obot(tc_fun(_1330550, tc_HOL_Obool)))) = _1330556)], (48784 ^ _779327) ^ [_1757416, _1757418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757416), _1757418)), -(c_List_Oupt(_1757418, _1757416) = c_List_Olist_ONil(tc_Nat_Onat))], (13603 ^ _779327) ^ [_1007321, _1007323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007321), _1007323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1007321), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1007323)))], (3212 ^ _779327) ^ [_827586, _827588, _827590, _827592] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_827592, _827588) = c_Inductive_Ocomplete__lattice__class_Olfp(_827590, _827586)), _827592 = _827590, _827588 = _827586], (18284 ^ _779327) ^ [_1089941] : [class_Rings_Osemiring__1(_1089941), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1089941), c_Groups_Ozero__class_Ozero(_1089941)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1089941))], (21136 ^ _779327) ^ [_1141838, _1141840, _1141842, _1141844, _1141846] : [class_Groups_Ominus(_1141838), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1141840, _1141838)), _1141842), _1141844), _1141846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141838), hAPP(_1141842, _1141846)), hAPP(_1141844, _1141846)))], (15774 ^ _779327) ^ [_1046152, _1046154, _1046156] : [-(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), _1046152), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046154), _1046152))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046154, _1046152))), _1046156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1046154), _1046156))], (33533 ^ _779327) ^ [_1390681, _1390683, _1390685, _1390687] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1390681), _1390683)), 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)), _1390681), _1390685)), 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)), _1390683), _1390687)), 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)), _1390683), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1390685), _1390687))), c_FunDef_Omin__strict)))], (48688 ^ _779327) ^ [_1755068, _1755070] : [-(c_Random_Opick(_1755068, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755068), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1755068, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1755068, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1755068)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1755070)) = c_Random_Opick(_1755068, _1755070))], (16916 ^ _779327) ^ [_1066316] : [_1066316 = 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), _1066316)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (46201 ^ _779327) ^ [_1698660, _1698662, _1698664, _1698666, _1698668] : [-(hAPP(hAPP(c_List_Oappend(_1698660), _1698662), _1698664) = hAPP(hAPP(c_List_Oappend(_1698660), _1698666), _1698668)), 46202 ^ _779327 : [(46209 ^ _779327) ^ [_1698884] : [hAPP(hAPP(c_List_Oappend(_1698660), _1698662), _1698884) = _1698666, _1698664 = hAPP(hAPP(c_List_Oappend(_1698660), _1698884), _1698668)], (46203 ^ _779327) ^ [_1698772] : [_1698662 = hAPP(hAPP(c_List_Oappend(_1698660), _1698666), _1698772), hAPP(hAPP(c_List_Oappend(_1698660), _1698772), _1698664) = _1698668]]], (27597 ^ _779327) ^ [_1268247, _1268249, _1268251, _1268253, _1268255, _1268257] : [class_Complete__Lattice_Ocomplete__lattice(_1268247), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268249, _1268247), _1268251), hAPP(hAPP(c_COMBB(tc_fun(_1268253, _1268247), _1268247, _1268249), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268253, _1268247), _1268255)), _1268257)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268253, _1268247), _1268255), hAPP(hAPP(c_COMBB(tc_fun(_1268249, _1268247), _1268247, _1268253), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268249, _1268247), _1268251)), hAPP(c_COMBC(_1268249, _1268253, _1268247), _1268257))))], (7848 ^ _779327) ^ [_903401, _903403, _903405, _903407, _903409] : [class_Rings_Oordered__semiring(_903401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903401), _903403), _903405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903401), _903407), _903409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903401), c_Groups_Ozero__class_Ozero(_903401)), _903403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903401), c_Groups_Ozero__class_Ozero(_903401)), _903407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903401), _903403), _903407)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903401), _903405), _903409))))], (53004 ^ _779327) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (8770 ^ _779327) ^ [_920171, _920173, _920175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920173), _920175)), -(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, _920171)), _920173)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _920171)), _920175))))], (10035 ^ _779327) ^ [_941863, _941865] : [class_Power_Opower(_941863), -(hAPP(hAPP(c_Power_Opower__class_Opower(_941863), _941865), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_941863))], (42320 ^ _779327) ^ [_1603304, _1603306, _1603308, _1603310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603304, _1603304)), hAPP(hAPP(c_Product__Type_OPair(_1603304, _1603304), _1603306), _1603308)), c_Transitive__Closure_Ortrancl(_1603304, _1603310))), -(_1603306 = _1603308), 42327 ^ _779327 : [(42330 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603304, _1603304)), hAPP(hAPP(c_Product__Type_OPair(_1603304, _1603304), _1603306), _1603308)), c_Transitive__Closure_Otrancl(_1603304, _1603310))))], (42328 ^ _779327) ^ [] : [_1603306 = _1603308]]], (45428 ^ _779327) ^ [_1680120, _1680122, _1680124, _1680126] : [_1680126 = c_List_Olist_ONil(_1680120), -(hAPP(hAPP(c_List_Omap(_1680120, _1680122), _1680124), _1680126) = c_List_Olist_ONil(_1680122))], (42733 ^ _779327) ^ [_1613193, _1613195] : [-(c_Relation_Ototal__on(_1613193, c_Orderings_Obot__class_Obot(tc_fun(_1613193, tc_HOL_Obool)), _1613195))], (29354 ^ _779327) ^ [_1303029, _1303031, _1303033] : [class_Orderings_Olinorder(_1303029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303029), _1303031), _1303033)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303029, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1303029), _1303031), c_Orderings_Obot__class_Obot(tc_fun(_1303029, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1303029, _1303031, _1303033)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303029, _1303031), _1303033))], (14589 ^ _779327) ^ [_1025141, _1025143, _1025145] : [class_Divides_Osemiring__div(_1025141), -(_1025143 = c_Groups_Ozero__class_Ozero(_1025141)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025141), _1025143), _1025145)), _1025143) = _1025145)], (37753 ^ _779327) ^ [_1486043, _1486045, _1486047, _1486049, _1486051] : [c_Fun_Oinj__on(_1486043, _1486045, _1486047, c_Orderings_Otop__class_Otop(tc_fun(_1486043, tc_HOL_Obool))), hAPP(_1486047, _1486049) = hAPP(_1486047, _1486051), -(_1486049 = _1486051)], (1668 ^ _779327) ^ [_803165, _803167] : [-(class_Rings_Olinordered__semidom(_803165)), _803167 = _803165, class_Rings_Olinordered__semidom(_803167)], (49764 ^ _779327) ^ [_1776608, _1776610, _1776612, _1776614, _1776616] : [hBOOL(hAPP(hAPP(c_member(_1776608), _1776610), hAPP(c_List_Oset(_1776608), _1776612))), -(hBOOL(hAPP(_1776614, _1776610))), -(c_List_OtakeWhile(_1776608, _1776614, hAPP(hAPP(c_List_Oappend(_1776608), _1776612), _1776616)) = c_List_OtakeWhile(_1776608, _1776614, _1776612))], (9932 ^ _779327) ^ [_940109] : [9934 ^ _779327 : [(9937 ^ _779327) ^ [] : [hBOOL(hAPP(_940109, hAPP(c_Int_Onat, 9933 ^ [_940109])))], (9935 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9933 ^ [_940109])))]], 9938 ^ _779327 : [(9939 ^ _779327) ^ [_940242] : [-(hBOOL(hAPP(_940109, _940242)))]]], (40400 ^ _779327) ^ [_1556569, _1556571, _1556573, _1556575, _1556577, _1556579] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556569, _1556571, _1556573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556569, _1556571), tc_HOL_Obool)), _1556575), _1556577)), _1556579) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556569, _1556573), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1556569, _1556571, _1556573), _1556575), _1556579)), hAPP(hAPP(c_Relation_Orel__comp(_1556569, _1556571, _1556573), _1556577), _1556579)))], (27052 ^ _779327) ^ [_1256722, _1256724, _1256726, _1256728] : [class_Lattices_Osemilattice__sup(_1256722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256722), _1256724), _1256726)), _1256728)), 27059 ^ _779327 : [(27062 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256722), _1256726), _1256728)))], (27060 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256722), _1256724), _1256728)))]]], (3906 ^ _779327) ^ [_838585, _838587] : [_838587 = _838585, -(c_List_Orotate1(_838587) = c_List_Orotate1(_838585))], (45127 ^ _779327) ^ [_1672207, _1672209] : [-(hAPP(hAPP(c_List_Omap(_1672207, _1672207), c_COMBI(_1672207)), _1672209) = _1672209)], (2988 ^ _779327) ^ [_824046, _824048, _824050, _824052, _824054, _824056] : [-(c_SetInterval_Oord_OatMost(_824056, _824052, _824048) = c_SetInterval_Oord_OatMost(_824054, _824050, _824046)), _824056 = _824054, _824052 = _824050, _824048 = _824046], (48651 ^ _779327) ^ [_1753596, _1753598] : [c_List_Otranspose(_1753596, _1753598) = c_List_Olist_ONil(tc_List_Olist(_1753596)), 48654 ^ _779327 : [(48655 ^ _779327) ^ [_1753691] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1753596)), _1753691), hAPP(c_List_Oset(tc_List_Olist(_1753596)), _1753598))), -(_1753691 = c_List_Olist_ONil(_1753596))]]], (12229 ^ _779327) ^ [_982740, _982742] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _982740)), hAPP(c_Nat_OSuc, _982742)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982740), _982742))], (8200 ^ _779327) ^ [_909944, _909946, _909948, _909950] : [class_Rings_Olinordered__ring__strict(_909944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909944), _909946), _909948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909944), _909950), c_Groups_Ozero__class_Ozero(_909944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909944), _909950), _909948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909944), _909950), _909946))))], (18008 ^ _779327) ^ [_1085016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085016), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085016)), c_Int_OPls)))], (30097 ^ _779327) ^ [_1320107, _1320109, _1320111, _1320113, _1320115] : [hBOOL(hAPP(hAPP(c_member(_1320107), _1320109), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1320111, tc_fun(_1320107, tc_HOL_Obool)), _1320113), _1320115))), 30101 ^ _779327 : [(30104 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320107), _1320109), hAPP(_1320115, 30100 ^ [_1320107, _1320109, _1320111, _1320113, _1320115]))))], (30102 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320111), 30100 ^ [_1320107, _1320109, _1320111, _1320113, _1320115]), _1320113)))]]], (17118 ^ _779327) ^ [_1069967, _1069969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069969)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1069967), hAPP(c_Int_Onat, _1069969)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1069967, _1069969)))], (51233 ^ _779327) ^ [_1807878, _1807880, _1807882, _1807884] : [-(hAPP(hAPP(c_List_Oappend(_1807878), c_List_Oreplicate(_1807878, _1807880, _1807882)), hAPP(hAPP(c_List_Olist_OCons(_1807878), _1807882), _1807884)) = hAPP(hAPP(c_List_Olist_OCons(_1807878), _1807882), hAPP(hAPP(c_List_Oappend(_1807878), c_List_Oreplicate(_1807878, _1807880, _1807882)), _1807884)))], (40253 ^ _779327) ^ [_1552218, _1552220] : [-(c_Product__Type_Oapsnd(_1552218, _1552218, _1552220, c_Fun_Oid(_1552218)) = c_Fun_Oid(tc_prod(_1552220, _1552218)))], (10550 ^ _779327) ^ [_950224, _950226, _950228] : [class_Rings_Olinordered__semidom(_950224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950224), c_Groups_Ozero__class_Ozero(_950224)), _950226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950224), _950226), c_Groups_Oone__class_Oone(_950224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950224), _950226), hAPP(hAPP(c_Power_Opower__class_Opower(_950224), _950226), _950228))), hAPP(hAPP(c_Power_Opower__class_Opower(_950224), _950226), _950228))))], (46058 ^ _779327) ^ [_1695738, _1695740, _1695742] : [_1695738 = _1695740, -(_1695738 = hAPP(hAPP(c_List_Oappend(_1695742), c_List_Olist_ONil(_1695742)), _1695740))], (52968 ^ _779327) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (26663 ^ _779327) ^ [_1248714, _1248716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248714)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1248714, _1248716)))], (47442 ^ _779327) ^ [_1726497, _1726499, _1726501] : [-(c_List_Obutlast(_1726497, hAPP(hAPP(c_List_Odrop(_1726497), _1726499), _1726501)) = hAPP(hAPP(c_List_Odrop(_1726497), _1726499), c_List_Obutlast(_1726497, _1726501)))], (25099 ^ _779327) ^ [_1216858, _1216860] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216858), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1216860)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216858)), _1216860)))], (28856 ^ _779327) ^ [_1293720, _1293722, _1293724] : [-(hAPP(hAPP(c_Set_Oinsert(_1293720), _1293722), _1293724) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293720, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1293720), _1293722), c_Orderings_Obot__class_Obot(tc_fun(_1293720, tc_HOL_Obool)))), _1293724))], (21562 ^ _779327) ^ [_1150393, _1150395] : [class_Rings_Oring__1(_1150393), 21565 ^ _779327 : [(21572 ^ _779327) ^ [] : [-(_1150395 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21575 ^ _779327 : [(21582 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150395), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1150393), _1150395) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1150393), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1150393, _1150393)), tc_fun(tc_Int_Oint, _1150393)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1150393, _1150393), _1150393), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1150393, _1150393)), tc_fun(tc_Int_Oint, _1150393)), tc_Int_Oint), c_COMBB(tc_fun(_1150393, _1150393), _1150393, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1150393, tc_fun(tc_fun(_1150393, _1150393), _1150393), tc_Int_Oint), c_HOL_OLet(_1150393, _1150393)), c_Int_Oring__1__class_Oof__int(_1150393)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1150393, _1150393), tc_fun(_1150393, _1150393)), hAPP(hAPP(c_COMBB(tc_fun(_1150393, tc_fun(_1150393, _1150393)), tc_fun(tc_fun(_1150393, _1150393), tc_fun(_1150393, _1150393)), tc_Int_Oint), c_COMBS(_1150393, _1150393, _1150393)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1150393, _1150393), tc_fun(_1150393, tc_fun(_1150393, _1150393))), hAPP(hAPP(c_COMBB(tc_fun(_1150393, tc_fun(_1150393, _1150393)), tc_fun(tc_fun(_1150393, _1150393), tc_fun(_1150393, tc_fun(_1150393, _1150393))), tc_Int_Oint), c_COMBB(_1150393, tc_fun(_1150393, _1150393), _1150393)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1150393, tc_fun(_1150393, _1150393)), tc_Int_Oint), c_If(_1150393)), 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(_1150393, _1150393, _1150393), c_Groups_Oplus__class_Oplus(_1150393)), c_COMBI(_1150393))))), hAPP(hAPP(c_COMBC(_1150393, _1150393, _1150393), hAPP(hAPP(c_COMBB(_1150393, tc_fun(_1150393, _1150393), _1150393), c_Groups_Oplus__class_Oplus(_1150393)), hAPP(hAPP(c_COMBS(_1150393, _1150393, _1150393), c_Groups_Oplus__class_Oplus(_1150393)), c_COMBI(_1150393)))), c_Groups_Oone__class_Oone(_1150393))))), c_Divides_Odivmod__int(_1150395, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (21576 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1150395), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1150393), _1150395) = hAPP(c_Groups_Ouminus__class_Ouminus(_1150393), hAPP(c_Int_Oring__1__class_Oof__int(_1150393), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1150395))))]]], (21566 ^ _779327) ^ [] : [_1150395 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1150393), _1150395) = c_Groups_Ozero__class_Ozero(_1150393))]]], (52113 ^ _779327) ^ [_1828257, _1828259] : [c_Relation_Osym(_1828257, _1828259), -(c_Relation_Osym(_1828257, c_Transitive__Closure_Otrancl(_1828257, _1828259)))], (45627 ^ _779327) ^ [_1685120, _1685122, _1685124, _1685126, _1685128, _1685130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685120, _1685122)), hAPP(hAPP(c_Product__Type_OPair(_1685120, _1685122), _1685124), _1685126)), hAPP(c_List_Oset(tc_prod(_1685120, _1685122)), hAPP(hAPP(c_List_Ozip(_1685120, _1685122), _1685128), _1685130)))), -(hBOOL(hAPP(hAPP(c_member(_1685120), _1685124), hAPP(c_List_Oset(_1685120), _1685128))))], (50514 ^ _779327) ^ [_1793584, _1793586, _1793588, _1793590, _1793592] : [-(hAPP(c_List_Ofilter(_1793584, _1793586), _1793588) = hAPP(hAPP(c_List_Olist_OCons(_1793584), _1793590), _1793592)), 50515 ^ _779327 : [(50516 ^ _779327) ^ [_1793712, _1793714] : [_1793588 = hAPP(hAPP(c_List_Oappend(_1793584), _1793714), hAPP(hAPP(c_List_Olist_OCons(_1793584), _1793590), _1793712)), 50522 ^ _779327 : [(50525 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1793586, 50521 ^ [_1793584, _1793586, _1793588, _1793590, _1793592, _1793712, _1793714])))], (50523 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793584), 50521 ^ [_1793584, _1793586, _1793588, _1793590, _1793592, _1793712, _1793714]), hAPP(c_List_Oset(_1793584), _1793714))))]], hBOOL(hAPP(_1793586, _1793590)), _1793592 = hAPP(c_List_Ofilter(_1793584, _1793586), _1793712)]]], (23550 ^ _779327) ^ [_1189319, _1189321, _1189323, _1189325, _1189327, _1189329, _1189331] : [hBOOL(hAPP(hAPP(_1189319, hAPP(c_Product__Type_Osnd(_1189321, _1189323), _1189325)), hAPP(c_Product__Type_Ofst(_1189321, _1189323), _1189325))), 23557 ^ _779327 : [(23560 ^ _779327) ^ [] : [hBOOL(hAPP(_1189327, hAPP(hAPP(_1189329, 23555 ^ [_1189319, _1189321, _1189323, _1189325, _1189327, _1189329, _1189331]), 23556 ^ [_1189319, _1189321, _1189323, _1189325, _1189327, _1189329, _1189331])))], (23558 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1189319, 23556 ^ [_1189319, _1189321, _1189323, _1189325, _1189327, _1189329, _1189331]), 23555 ^ [_1189319, _1189321, _1189323, _1189325, _1189327, _1189329, _1189331])))]], -(hBOOL(hAPP(_1189327, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189321, _1189323, _1189331), _1189329), _1189325))))], (11557 ^ _779327) ^ [_970684, _970686, _970688, _970690, _970692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970684), _970686)), 11560 ^ _779327 : [(11567 ^ _779327) ^ [] : [_970690 = 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), _970686), _970684)), _970688)), _970692), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970684), _970688)), _970690) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970686), _970688)), _970692))], (11561 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970684), _970688)), _970690) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970686), _970688)), _970692), -(_970690 = 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), _970686), _970684)), _970688)), _970692))]]], (11931 ^ _779327) ^ [_977150, _977152, _977154, _977156, _977158] : [class_Groups_Oordered__ab__semigroup__add(_977150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977150), _977152), _977154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977150), _977156), _977158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977150), _977152), _977156)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977150), _977154), _977158))))], (25746 ^ _779327) ^ [_1230245, _1230247, _1230249, _1230251, _1230253] : [class_Orderings_Olinorder(_1230245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1230245, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1230245, _1230247), _1230249)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1230245, _1230251), _1230253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230245), _1230249), _1230247))), 25757 ^ _779327 : [(25760 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230245), _1230249), _1230253)))], (25758 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230245), _1230251), _1230247)))]]], (3140 ^ _779327) ^ [_826490, _826492] : [_826492 = _826490, -(c_SetInterval_Oord__class_OatLeast(_826492) = c_SetInterval_Oord__class_OatLeast(_826490))], (17432 ^ _779327) ^ [_1075313, _1075315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075313)), c_Int_OBit1(_1075315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075313), _1075315)))], (38846 ^ _779327) ^ [_1513570, _1513572, _1513574, _1513576, _1513578] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1513570, _1513572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513570, tc_HOL_Obool)), _1513574), _1513576)), hAPP(c_COMBK(tc_fun(_1513572, tc_HOL_Obool), _1513570), _1513578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1513570, _1513572), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1513570, _1513572), _1513574), hAPP(c_COMBK(tc_fun(_1513572, tc_HOL_Obool), _1513570), _1513578))), hAPP(hAPP(c_Product__Type_OSigma(_1513570, _1513572), _1513576), hAPP(c_COMBK(tc_fun(_1513572, tc_HOL_Obool), _1513570), _1513578))))], (5928 ^ _779327) ^ [_872636, _872638, _872640] : [class_Orderings_Olinorder(_872636), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872636), _872638), _872640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872636), _872640), _872638)))], (21588 ^ _779327) ^ [_1151306, _1151308, _1151310] : [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), _1151306), _1151308))), -(hBOOL(hAPP(hAPP(_1151310, _1151306), _1151308))), 21595 ^ _779327 : [(21598 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1151310, 21593 ^ [_1151306, _1151308, _1151310]), 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)))), 21594 ^ [_1151306, _1151308, _1151310])))), -(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), 21593 ^ [_1151306, _1151308, _1151310]), 21594 ^ [_1151306, _1151308, _1151310])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 21594 ^ [_1151306, _1151308, _1151310]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21608 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1151310, 21593 ^ [_1151306, _1151308, _1151310]), 21594 ^ [_1151306, _1151308, _1151310]))], (21596 ^ _779327) ^ [] : [-(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), 21593 ^ [_1151306, _1151308, _1151310]), 21594 ^ [_1151306, _1151308, _1151310]))))]]], (15521 ^ _779327) ^ [_1041695, _1041697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041697)), -(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, _1041695, _1041697))))], (1858 ^ _779327) ^ [_805540, _805542] : [-(class_Rings_Omult__zero(_805540)), _805542 = _805540, class_Rings_Omult__zero(_805542)], (48250 ^ _779327) ^ [_1744179, _1744181, _1744183, _1744185] : [48252 ^ _779327 : [(48255 ^ _779327) ^ [] : [hBOOL(hAPP(_1744183, hAPP(hAPP(c_List_Onth(_1744179), _1744181), 48251 ^ [_1744179, _1744181, _1744183, _1744185])))], (48253 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48251 ^ [_1744179, _1744181, _1744183, _1744185]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744179)), _1744181))))]], hBOOL(hAPP(hAPP(c_member(_1744179), _1744185), hAPP(c_List_Oset(_1744179), _1744181))), -(hBOOL(hAPP(_1744183, _1744185)))], (15461 ^ _779327) ^ [_1040629, _1040631] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040629, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040631)) = 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), _1040629), _1040631)))], (50128 ^ _779327) ^ [_1784158, _1784160, _1784162] : [hBOOL(hAPP(hAPP(c_member(_1784158), _1784160), hAPP(c_List_Oset(_1784158), _1784162))), -(c_List_Oinsert(_1784158, _1784160, _1784162) = _1784162)], (21876 ^ _779327) ^ [_1156252, _1156254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156252))), 21879 ^ _779327 : [(21886 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156254))), -(c_Divides_Odivmod__int(_1156252, _1156254) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1156252), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1156254))))], (21880 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1156254)), -(c_Divides_Odivmod__int(_1156252, _1156254) = c_Divides_OnegDivAlg(_1156252, _1156254))]]], (38059 ^ _779327) ^ [_1492270, _1492272, _1492274, _1492276, _1492278] : [c_Fun_Oinj__on(_1492270, _1492272, _1492274, c_Orderings_Otop__class_Otop(tc_fun(_1492270, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1492270, _1492272, _1492274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492270, tc_HOL_Obool)), _1492276), _1492278)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492272, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492270, _1492272, _1492274), _1492276)), hAPP(c_Set_Oimage(_1492270, _1492272, _1492274), _1492278)))], (50775 ^ _779327) ^ [_1798899, _1798901, _1798903] : [50776 ^ _779327 : [(50777 ^ _779327) ^ [_1798976, _1798978] : [_1798903 = hAPP(hAPP(c_List_Oappend(_1798899), _1798978), hAPP(hAPP(c_List_Olist_OCons(_1798899), _1798901), _1798976))]], -(hBOOL(hAPP(hAPP(c_member(_1798899), _1798901), hAPP(c_List_Oset(_1798899), _1798903))))], (24573 ^ _779327) ^ [_1207048, _1207050, _1207052, _1207054] : [class_Rings_Oidom(_1207048), 24576 ^ _779327 : [(24577 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207048), _1207050), _1207052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207048), _1207054), _1207052))), -(_1207052 = c_Groups_Ozero__class_Ozero(_1207048)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207048), _1207050), _1207054)))], (24587 ^ _779327) ^ [] : [24588 ^ _779327 : [(24591 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207048), _1207050), _1207054))], (24589 ^ _779327) ^ [] : [_1207052 = c_Groups_Ozero__class_Ozero(_1207048)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1207048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207048), _1207050), _1207052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207048), _1207054), _1207052))))]]], (12632 ^ _779327) ^ [_990129, _990131, _990133] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _990131), _990133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990129), _990131)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _990129), _990133)))], (52397 ^ _779327) ^ [_1833548, _1833550, _1833552, _1833554, _1833556, _1833558] : [hAPP(c_Set_Oimage(_1833548, _1833550, _1833552), _1833554) = _1833556, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1833550, tc_HOL_Obool)), _1833558), _1833556)), -(hAPP(c_Set_Oimage(_1833548, _1833550, _1833552), hAPP(c_Set_Oimage(_1833550, _1833548, c_Hilbert__Choice_Oinv__into(_1833548, _1833550, _1833554, _1833552)), _1833558)) = _1833558)], (19647 ^ _779327) ^ [_1114187, _1114189, _1114191, _1114193] : [class_Fields_Olinordered__field(_1114187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114187), c_Groups_Ozero__class_Ozero(_1114187)), _1114189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114187), _1114191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114187), _1114193), _1114189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114187), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114187), _1114191), _1114189)), _1114193)))], (43369 ^ _779327) ^ [_1628521, _1628523, _1628525, _1628527] : [class_Complete__Lattice_Ocomplete__lattice(_1628521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628523), _1628525)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628523, _1628521), _1628525), _1628527) = hAPP(hAPP(c_Finite__Set_Ofold(_1628523, _1628521, hAPP(hAPP(c_COMBB(_1628521, tc_fun(_1628521, _1628521), _1628523), c_Lattices_Osemilattice__inf__class_Oinf(_1628521)), _1628527)), c_Orderings_Otop__class_Otop(_1628521)), _1628525))], (53064 ^ _779327) ^ [_1841295, _1841297] : [hBOOL(hAPP(hAPP(c_fconj, _1841295), _1841297)), -(hBOOL(_1841297))], (30779 ^ _779327) ^ [_1335576, _1335578, _1335580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335576), _1335578)), hBOOL(hAPP(hAPP(c_member(_1335576), _1335580), _1335578)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1335576), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1335576, tc_HOL_Obool)), _1335578), hAPP(hAPP(c_Set_Oinsert(_1335576), _1335580), c_Orderings_Obot__class_Obot(tc_fun(_1335576, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1335576), _1335578))], (45558 ^ _779327) ^ [_1682712, _1682714, _1682716] : [-(hAPP(hAPP(c_List_Otake(_1682712), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1682712), _1682714), _1682716)) = hAPP(hAPP(c_List_Olist_OCons(_1682712), _1682714), c_List_Olist_ONil(_1682712)))], (51979 ^ _779327) ^ [_1825607, _1825609] : [c_Relation_Oantisym(_1825607, hAPP(c_Relation_Oconverse(_1825607, _1825607), _1825609)), -(c_Relation_Oantisym(_1825607, _1825609))], (2566 ^ _779327) ^ [_816989, _816991, _816993, _816995, _816997, _816999] : [-(c_Random__Sequence_Oempty(_816999, _816995, _816991) = c_Random__Sequence_Oempty(_816997, _816993, _816989)), _816999 = _816997, _816995 = _816993, _816991 = _816989], (52385 ^ _779327) ^ [_1833284, _1833286, _1833288] : [c_Fun_Oinj__on(_1833284, _1833286, _1833288, c_Orderings_Otop__class_Otop(tc_fun(_1833284, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1833286, _1833284, _1833284, c_Hilbert__Choice_Oinv__into(_1833284, _1833286, c_Orderings_Otop__class_Otop(tc_fun(_1833284, tc_HOL_Obool)), _1833288)), _1833288) = c_Fun_Oid(_1833284))], (5706 ^ _779327) ^ [_869598, _869600, _869602] : [-(c_Nat_Onat_Onat__case(_869598, _869600, _869602, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _869600)], (43319 ^ _779327) ^ [_1627435, _1627437, _1627439] : [class_Orderings_Olinorder(_1627435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627435), _1627437)), -(c_Big__Operators_Olattice_OInf__fin(_1627435, c_Orderings_Oord__class_Omin(_1627435), hAPP(hAPP(c_Set_Oinsert(_1627435), _1627439), _1627437)) = hAPP(hAPP(c_Finite__Set_Ofold(_1627435, _1627435, c_Orderings_Oord__class_Omin(_1627435)), _1627439), _1627437))], (9174 ^ _779327) ^ [_927641, _927643, _927645] : [_927641 = _927643, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927645, tc_HOL_Obool)), _927641), _927643)))], (42810 ^ _779327) ^ [_1614982, _1614984, _1614986] : [42812 ^ _779327 : [(42813 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614982), 42811 ^ [_1614982, _1614984, _1614986]), _1614984)))], (42818 ^ _779327) ^ [] : [42811 ^ [_1614982, _1614984, _1614986] = 42814 ^ [_1614982, _1614984, _1614986]], (42822 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614982, _1614982)), hAPP(hAPP(c_Product__Type_OPair(_1614982, _1614982), 42814 ^ [_1614982, _1614984, _1614986]), 42811 ^ [_1614982, _1614984, _1614986])), _1614986))], (42820 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614982, _1614982)), hAPP(hAPP(c_Product__Type_OPair(_1614982, _1614982), 42811 ^ [_1614982, _1614984, _1614986]), 42814 ^ [_1614982, _1614984, _1614986])), _1614986))], (42816 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614982), 42814 ^ [_1614982, _1614984, _1614986]), _1614984)))]], -(c_Relation_Ototal__on(_1614982, _1614984, _1614986))], (46148 ^ _779327) ^ [_1697369, _1697371, _1697373] : [c_List_Olist_ONil(_1697369) = hAPP(hAPP(c_List_Oappend(_1697369), _1697371), _1697373), 46151 ^ _779327 : [(46154 ^ _779327) ^ [] : [-(_1697373 = c_List_Olist_ONil(_1697369))], (46152 ^ _779327) ^ [] : [-(_1697371 = c_List_Olist_ONil(_1697369))]]], (20097 ^ _779327) ^ [_1122046, _1122048] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122046), _1122048), hAPP(c_Int_Onumber__class_Onumber__of(_1122046), c_Int_OBit1(c_Int_OPls))) = _1122048), class_Fields_Ofield(_1122046), class_Int_Onumber__ring(_1122046)], (34150 ^ _779327) ^ [_1405005, _1405007, _1405009, _1405011, _1405013, _1405015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1405005, _1405007), tc_HOL_Obool)), _1405009), _1405011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405005, tc_HOL_Obool)), _1405013), _1405015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405007, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405005, _1405007, _1405009), _1405013)), hAPP(c_Relation_OImage(_1405005, _1405007, _1405011), _1405015))))], (10195 ^ _779327) ^ [_944345, _944347, _944349] : [class_Rings_Olinordered__idom(_944345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944345), c_Groups_Ozero__class_Ozero(_944345)), _944347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944345), c_Groups_Ozero__class_Ozero(_944345)), _944349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944345), _944349), c_Groups_Oone__class_Oone(_944345))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944345), _944347), _944349)), _944347)))], (37903 ^ _779327) ^ [_1489168, _1489170, _1489172, _1489174] : [hBOOL(hAPP(hAPP(c_member(_1489170), _1489174), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489168, tc_fun(_1489170, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1489168, tc_HOL_Obool))), _1489172))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1489168, tc_fun(_1489170, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1489168, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1489170, tc_HOL_Obool), tc_fun(_1489170, tc_HOL_Obool), _1489168), hAPP(c_COMBC(_1489170, tc_fun(_1489170, tc_HOL_Obool), tc_HOL_Obool), c_member(_1489170))), _1489172)), _1489174)))], (45906 ^ _779327) ^ [_1692174, _1692176, _1692178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1692176))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1692176), _1692174), _1692178)) = 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), _1692176)), _1692178)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1692176), _1692174)))], (46042 ^ _779327) ^ [_1695334, _1695336, _1695338, _1695340] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695334)), hAPP(hAPP(c_List_Olist__update(_1695334, _1695336), _1695338), _1695340)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695334)), _1695336))], (50193 ^ _779327) ^ [_1785930, _1785932, _1785934, _1785936, _1785938] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785930, _1785930)), hAPP(hAPP(c_Product__Type_OPair(_1785930, _1785930), _1785932), _1785934)), c_List_Omeasures(_1785930, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1785930, tc_Nat_Onat)), _1785936), _1785938)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1785936, _1785932)), hAPP(_1785936, _1785934)))), 50200 ^ _779327 : [(50203 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785930, _1785930)), hAPP(hAPP(c_Product__Type_OPair(_1785930, _1785930), _1785932), _1785934)), c_List_Omeasures(_1785930, _1785938))))], (50201 ^ _779327) ^ [] : [-(hAPP(_1785936, _1785932) = hAPP(_1785936, _1785934))]]], (12521 ^ _779327) ^ [_987993, _987995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _987993), _987995))))], (9270 ^ _779327) ^ [_929427, _929429] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929427)), _929429) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _929427), _929429)))], (40460 ^ _779327) ^ [_1558789, _1558791, _1558793, _1558795, _1558797, _1558799, _1558801] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1558789, _1558791, _1558793, hAPP(hAPP(c_COMBC(_1558789, tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_fun(_1558791, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558791, tc_fun(tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_fun(_1558791, tc_HOL_Obool)), _1558789), c_COMBC(_1558791, tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558791, tc_prod(_1558789, _1558791)), tc_fun(_1558791, tc_fun(tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_HOL_Obool)), _1558789), hAPP(c_COMBB(tc_prod(_1558789, _1558791), tc_fun(tc_fun(tc_prod(_1558789, _1558791), tc_HOL_Obool), tc_HOL_Obool), _1558791), c_member(tc_prod(_1558789, _1558791)))), c_Product__Type_OPair(_1558789, _1558791)))), _1558795), hAPP(hAPP(c_COMBC(_1558791, tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_fun(_1558793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558793, tc_fun(tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_fun(_1558793, tc_HOL_Obool)), _1558791), c_COMBC(_1558793, tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558793, tc_prod(_1558791, _1558793)), tc_fun(_1558793, tc_fun(tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_HOL_Obool)), _1558791), hAPP(c_COMBB(tc_prod(_1558791, _1558793), tc_fun(tc_fun(tc_prod(_1558791, _1558793), tc_HOL_Obool), tc_HOL_Obool), _1558793), c_member(tc_prod(_1558791, _1558793)))), c_Product__Type_OPair(_1558791, _1558793)))), _1558797)), _1558799), _1558801)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1558789, _1558793)), hAPP(hAPP(c_Product__Type_OPair(_1558789, _1558793), _1558799), _1558801)), hAPP(hAPP(c_Relation_Orel__comp(_1558789, _1558791, _1558793), _1558795), _1558797))))], (42709 ^ _779327) ^ [_1612804] : [-(c_Relation_Osingle__valued(_1612804, _1612804, c_Relation_OId(_1612804)))], (37809 ^ _779327) ^ [_1487053, _1487055, _1487057, _1487059, _1487061] : [c_Fun_Oinj__on(_1487053, _1487055, _1487057, c_Orderings_Otop__class_Otop(tc_fun(_1487053, tc_HOL_Obool))), 37812 ^ _779327 : [(37819 ^ _779327) ^ [] : [_1487059 = _1487061, -(hAPP(c_Set_Oimage(_1487053, _1487055, _1487057), _1487059) = hAPP(c_Set_Oimage(_1487053, _1487055, _1487057), _1487061))], (37813 ^ _779327) ^ [] : [hAPP(c_Set_Oimage(_1487053, _1487055, _1487057), _1487059) = hAPP(c_Set_Oimage(_1487053, _1487055, _1487057), _1487061), -(_1487059 = _1487061)]]], (27783 ^ _779327) ^ [_1273069, _1273071] : [class_Orderings_Olinorder(_1273069), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1273069, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1273069), _1273071)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1273069), _1273071))], (10009 ^ _779327) ^ [_941429, _941431, _941433, _941435] : [class_Rings_Olinordered__semidom(_941429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941429), c_Groups_Oone__class_Oone(_941429)), _941431)), 10016 ^ _779327 : [(10023 ^ _779327) ^ [] : [_941433 = _941435, -(hAPP(hAPP(c_Power_Opower__class_Opower(_941429), _941431), _941433) = hAPP(hAPP(c_Power_Opower__class_Opower(_941429), _941431), _941435))], (10017 ^ _779327) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_941429), _941431), _941433) = hAPP(hAPP(c_Power_Opower__class_Opower(_941429), _941431), _941435), -(_941433 = _941435)]]], (48584 ^ _779327) ^ [_1752002, _1752004, _1752006, _1752008] : [hBOOL(hAPP(_1752002, _1752004)), -(hAPP(c_List_Ofilter(_1752006, _1752002), hAPP(hAPP(c_List_Olist_OCons(_1752006), _1752004), _1752008)) = hAPP(hAPP(c_List_Olist_OCons(_1752006), _1752004), hAPP(c_List_Ofilter(_1752006, _1752002), _1752008)))], (46498 ^ _779327) ^ [_1706325, _1706327, _1706329, _1706331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706327)), _1706329))), -(hAPP(hAPP(c_List_Olist__update(_1706327, _1706329), _1706325), _1706331) = hAPP(hAPP(c_List_Oappend(_1706327), hAPP(hAPP(c_List_Otake(_1706327), _1706325), _1706329)), hAPP(hAPP(c_List_Olist_OCons(_1706327), _1706331), hAPP(hAPP(c_List_Odrop(_1706327), hAPP(c_Nat_OSuc, _1706325)), _1706329))))], (30459 ^ _779327) ^ [_1328546, _1328548] : [c_Nat__Transfer_Onat__set(_1328546), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1328548), _1328546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328548)))], (52426 ^ _779327) ^ [_1834280, _1834282, _1834284, _1834286] : [hAPP(c_Set_Oimage(_1834280, _1834282, _1834284), c_Orderings_Otop__class_Otop(tc_fun(_1834280, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1834282, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1834280, _1834282, _1834284), hAPP(c_Set_Oimage(_1834282, _1834280, c_Hilbert__Choice_Oinv__into(_1834280, _1834282, c_Orderings_Otop__class_Otop(tc_fun(_1834280, tc_HOL_Obool)), _1834284)), _1834286)) = _1834286)], (14197 ^ _779327) ^ [_1018511] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018511)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1018511))], (13342 ^ _779327) ^ [_1002805, _1002807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002807), _1002805)), _1002807)))], (52648 ^ _779327) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (4570 ^ _779327) ^ [_848893, _848895, _848897, _848899, _848901, _848903] : [-(c_List_OdropWhile(_848903, _848899, _848895) = c_List_OdropWhile(_848901, _848897, _848893)), _848903 = _848901, _848899 = _848897, _848895 = _848893], (31626 ^ _779327) ^ [_1353989, _1353991] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1353989), _1353991)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1353991, _1353989) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52610 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (13378 ^ _779327) ^ [_1003431, _1003433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003431), _1003433)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003431), _1003433) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51205 ^ _779327) ^ [_1807286, _1807288, _1807290, _1807292, _1807294] : [-(c_List_Oreplicate(_1807286, _1807288, _1807290) = c_List_Oreplicate(_1807286, _1807292, _1807294)), _1807288 = _1807292, 51210 ^ _779327 : [(51213 ^ _779327) ^ [] : [_1807290 = _1807294], (51211 ^ _779327) ^ [] : [_1807288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48886 ^ _779327) ^ [_1759228, _1759230] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1759228), hAPP(c_List_Onth(_1759228), _1759230)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759228)), _1759230))) = _1759230)], (52470 ^ _779327) ^ [_1834989, _1834991] : [class_Lattices_Olattice(_1834989), -(class_Lattices_Osemilattice__inf(tc_fun(_1834991, _1834989)))], (18086 ^ _779327) ^ [_1086401, _1086403] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1086401)), c_Int_OBit0(_1086403)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086401), _1086403)))], (35295 ^ _779327) ^ [_1431741, _1431743, _1431745, _1431747] : [class_Orderings_Oorder(_1431741), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431741, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1431741, _1431743, _1431745)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1431741, _1431745, _1431747)) = c_Orderings_Obot__class_Obot(tc_fun(_1431741, tc_HOL_Obool)))], (29650 ^ _779327) ^ [_1309174, _1309176] : [-(hBOOL(hAPP(hAPP(c_member(_1309174), 29651 ^ [_1309174, _1309176]), _1309176))), -(_1309176 = c_Orderings_Obot__class_Obot(tc_fun(_1309174, tc_HOL_Obool)))], (30995 ^ _779327) ^ [_1340543, _1340545] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1340543), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1340545))), 30998 ^ _779327 : [(31001 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340543), _1340545))], (30999 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340545), _1340543)))]]], (25466 ^ _779327) ^ [_1223665, _1223667, _1223669, _1223671] : [class_Rings_Osemiring__1(_1223665), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223665), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223667, tc_Nat_Onat), _1223669), _1223671)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223667, _1223665), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1223665, _1223667), c_Nat_Osemiring__1__class_Oof__nat(_1223665)), _1223669)), _1223671))], (25257 ^ _779327) ^ [_1219637, _1219639, _1219641] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219637), _1219639)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1219637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1219639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219637), _1219641)))))], (19379 ^ _779327) ^ [_1109239, _1109241, _1109243] : [class_Rings_Odivision__ring(_1109239), -(_1109241 = c_Groups_Ozero__class_Ozero(_1109239)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109239), hAPP(c_Groups_Ouminus__class_Ouminus(_1109239), _1109243)), hAPP(c_Groups_Ouminus__class_Ouminus(_1109239), _1109241)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1109239), _1109243), _1109241))], (52602 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (23177 ^ _779327) ^ [_1181663, _1181665] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1181663), _1181665)), _1181665) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1181663), _1181665))], (16553 ^ _779327) ^ [_1059774, _1059776, _1059778] : [class_Groups_Oordered__ab__group__add__abs(_1059774), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059774), hAPP(c_Groups_Oabs__class_Oabs(_1059774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059774), _1059776), _1059778))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059774), hAPP(c_Groups_Oabs__class_Oabs(_1059774), _1059776)), hAPP(c_Groups_Oabs__class_Oabs(_1059774), _1059778)))))], (22755 ^ _779327) ^ [_1173268, _1173270, _1173272, _1173274, _1173276, _1173278] : [-(c_Product__Type_Oprod_Oprod__rec(_1173268, _1173270, _1173272, _1173274, hAPP(hAPP(c_Product__Type_OPair(_1173268, _1173270), _1173276), _1173278)) = hAPP(hAPP(_1173274, _1173276), _1173278))], (42555 ^ _779327) ^ [_1609149, _1609151, _1609153] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1609149, _1609151)), hAPP(c_Relation_Oconverse(_1609151, _1609149), _1609153))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1609151, _1609149)), _1609153)))], (3178 ^ _779327) ^ [_827051, _827053, _827055, _827057, _827059, _827061, _827063, _827065] : [-(c_Nitpick_Oprod(_827065, _827061, _827057, _827053) = c_Nitpick_Oprod(_827063, _827059, _827055, _827051)), _827065 = _827063, _827061 = _827059, _827057 = _827055, _827053 = _827051], (5350 ^ _779327) ^ [_860955, _860957] : [_860957 = _860955, -(c_Lattices_Osemilattice__inf__class_Oinf(_860957) = c_Lattices_Osemilattice__inf__class_Oinf(_860955))], (40819 ^ _779327) ^ [_1567923, _1567925] : [c_Wellfounded_Owf(_1567923, _1567925), -(c_Wellfounded_Owf(tc_List_Olist(_1567923), c_List_Olenlex(_1567923, _1567925)))], (16199 ^ _779327) ^ [_1053841, _1053843] : [-(_1053841 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16202 ^ _779327 : [(16209 ^ _779327) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053843, _1053841) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1053843), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1053841)) = 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), _1053843), _1053841))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16203 ^ _779327) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1053843, _1053841) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1053843), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1053841)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1053843), _1053841)))]]], (37827 ^ _779327) ^ [_1487375] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487375, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1487375, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1487375, tc_HOL_Obool)))], (28070 ^ _779327) ^ [_1278446, _1278448, _1278450, _1278452, _1278454] : [class_Groups_Ocomm__monoid__add(_1278446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278448), _1278450)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278448, _1278446), hAPP(hAPP(c_COMBS(_1278448, _1278446, _1278446), hAPP(hAPP(c_COMBB(_1278446, tc_fun(_1278446, _1278446), _1278448), c_Groups_Oplus__class_Oplus(_1278446)), _1278452)), _1278454)), _1278450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278446), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278448, _1278446), _1278452), _1278450)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278448, _1278446), _1278454), _1278450)))], (25768 ^ _779327) ^ [_1230697, _1230699, _1230701, _1230703, _1230705] : [class_Groups_Ocomm__monoid__add(_1230697), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230697), _1230699), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1230701), _1230703)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1230705), _1230703))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1230697), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1230697, tc_Nat_Onat), _1230699), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1230703))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1230701), _1230705)))], (4498 ^ _779327) ^ [_847751, _847753, _847755, _847757] : [-(c_List_Omeasures(_847757, _847753) = c_List_Omeasures(_847755, _847751)), _847757 = _847755, _847753 = _847751], (3342 ^ _779327) ^ [_829625, _829627, _829629, _829631, _829633, _829635, _829637, _829639] : [-(c_Product__Type_Oapsnd(_829639, _829635, _829631, _829627) = c_Product__Type_Oapsnd(_829637, _829633, _829629, _829625)), _829639 = _829637, _829635 = _829633, _829631 = _829629, _829627 = _829625], (44454 ^ _779327) ^ [_1652070] : [class_Nat_Osize(_1652070), -(c_FunDef_Ois__measure(_1652070, c_Nat_Osize__class_Osize(_1652070)))], (39872 ^ _779327) ^ [_1536564, _1536566, _1536568] : [-(hAPP(hAPP(c_Set_Oinsert(_1536564), _1536566), _1536568) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536564, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1536564), hAPP(hAPP(c_COMBC(_1536564, _1536564, tc_HOL_Obool), c_fequal), _1536566))), _1536568))], (33553 ^ _779327) ^ [_1391099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1391099)), -(_1391099 = 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))), _1391099)), c_FunDef_Omax__strict)))], (4526 ^ _779327) ^ [_848201, _848203] : [_848203 = _848201, -(c_Enum_Oenum__class_Oenum__ex(_848203) = c_Enum_Oenum__class_Oenum__ex(_848201))], (7344 ^ _779327) ^ [_894465, _894467, _894469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894465), _894467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894467), _894469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894465), _894469)))], (48265 ^ _779327) ^ [_1744596, _1744598, _1744600, _1744602, _1744604] : [c_Finite__Set_Ofun__left__comm(_1744596, _1744598, _1744600), -(hAPP(hAPP(c_Finite__Set_Ofold(_1744596, _1744598, _1744600), _1744602), hAPP(c_List_Oset(_1744596), _1744604)) = hAPP(c_List_Ofoldl(_1744598, _1744596, hAPP(c_COMBC(_1744596, _1744598, _1744598), _1744600), _1744602), c_List_Oremdups(_1744596, _1744604)))], (52440 ^ _779327) ^ [_1834594, _1834596] : [class_Lattices_Obounded__lattice(_1834594), -(class_Lattices_Obounded__lattice(tc_fun(_1834596, _1834594)))], (14421 ^ _779327) ^ [_1022470, _1022472, _1022474] : [class_Int_Onumber__ring(_1022470), 14424 ^ _779327 : [(14431 ^ _779327) ^ [] : [c_Int_Oiszero(_1022470, hAPP(c_Int_Onumber__class_Onumber__of(_1022470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022472), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022474)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1022470), _1022472) = hAPP(c_Int_Onumber__class_Onumber__of(_1022470), _1022474))], (14425 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1022470), _1022472) = hAPP(c_Int_Onumber__class_Onumber__of(_1022470), _1022474), -(c_Int_Oiszero(_1022470, hAPP(c_Int_Onumber__class_Onumber__of(_1022470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022472), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022474)))))]]], (4944 ^ _779327) ^ [_854710, _854712] : [_854712 = _854710, -(c_Lazy__Sequence_Oyield(_854712) = c_Lazy__Sequence_Oyield(_854710))], (27378 ^ _779327) ^ [_1263456, _1263458] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1263456, _1263458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1263458), hAPP(c_Nat_OSuc, _1263456)))], (42300 ^ _779327) ^ [_1602877] : [-(c_Transitive__Closure_Ortrancl(_1602877, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1602877, _1602877), tc_HOL_Obool))) = c_Relation_OId(_1602877))], (418 ^ _779327) ^ [_785710, _785712, _785714, _785716, _785718, _785720, _785722, _785724, _785726, _785728, _785730, _785732] : [-(c_Finite__Set_Ofolding__image__simple(_785730, _785726, _785722, _785718, _785714, _785710)), c_Finite__Set_Ofolding__image__simple(_785732, _785728, _785724, _785720, _785716, _785712), _785732 = _785730, _785728 = _785726, _785724 = _785722, _785720 = _785718, _785716 = _785714, _785712 = _785710], (26454 ^ _779327) ^ [_1245126] : [-(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)), _1245126)) = hAPP(c_Int_Onat, _1245126))], (22769 ^ _779327) ^ [_1173681, _1173683, _1173685, _1173687] : [class_Orderings_Olinorder(_1173681), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173681), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173681), _1173683), _1173685)), _1173687) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173681), _1173683), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173681), _1173685), _1173687)))], (25598 ^ _779327) ^ [_1227244, _1227246, _1227248] : [-(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), _1227244)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1227246))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1227248))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1227248), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1227246)))))], (4748 ^ _779327) ^ [_851674, _851676, _851678, _851680] : [-(c_List_Olast(_851680, _851676) = c_List_Olast(_851678, _851674)), _851680 = _851678, _851676 = _851674], (46562 ^ _779327) ^ [_1707926, _1707928, _1707930] : [hAPP(hAPP(c_List_Odrop(_1707926), _1707928), _1707930) = c_List_Olist_ONil(_1707926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707926)), _1707930)), _1707928)))], (46568 ^ _779327) ^ [_1708045, _1708047, _1708049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708045)), _1708049)), _1708047)), -(hAPP(hAPP(c_List_Odrop(_1708045), _1708047), _1708049) = c_List_Olist_ONil(_1708045))], (9032 ^ _779327) ^ [_924797, _924799, _924801, _924803, _924805] : [class_Rings_Ocomm__semiring__1(_924797), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), _924799), _924801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), _924803), _924805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), _924799), _924803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924797), _924801), _924805)))], (28457 ^ _779327) ^ [_1285957, _1285959, _1285961, _1285963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285957), _1285959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1285961), hAPP(c_Set_Oimage(_1285957, _1285961, _1285963), _1285959))), hAPP(c_Finite__Set_Ocard(_1285957), _1285959))))], (27554 ^ _779327) ^ [_1266942, _1266944, _1266946, _1266948, _1266950] : [class_Orderings_Oorder(_1266942), c_Orderings_Oorder__class_Omono(_1266942, tc_fun(_1266944, tc_HOL_Obool), _1266946), -(c_Orderings_Oorder__class_Omono(_1266942, tc_fun(_1266944, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1266942, tc_fun(_1266944, tc_HOL_Obool), tc_fun(_1266944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1266944, tc_HOL_Obool), tc_fun(tc_fun(_1266944, tc_HOL_Obool), tc_fun(_1266944, tc_HOL_Obool)), _1266942), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266944, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1266942, tc_fun(_1266944, tc_HOL_Obool), tc_fun(_1266944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1266944, tc_HOL_Obool), tc_fun(tc_fun(_1266944, tc_HOL_Obool), tc_fun(_1266944, tc_HOL_Obool)), _1266942), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266944, tc_HOL_Obool))), _1266946)), _1266948))), _1266950)))], (35938 ^ _779327) ^ [_1446179, _1446181, _1446183] : [class_Orderings_Olinorder(_1446179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446179), _1446181)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446179), _1446183)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446179, tc_HOL_Obool)), _1446181), _1446183) = c_Orderings_Obot__class_Obot(tc_fun(_1446179, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446179), c_Big__Operators_Olinorder__class_OMax(_1446179, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446179, tc_HOL_Obool)), _1446181), _1446183))), c_Big__Operators_Olinorder__class_OMax(_1446179, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446179, tc_HOL_Obool)), _1446181), _1446183))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446179), c_Big__Operators_Olinorder__class_OMax(_1446179, _1446181)), c_Big__Operators_Olinorder__class_OMax(_1446179, _1446183)))], (29028 ^ _779327) ^ [_1296551, _1296553, _1296555] : [class_Orderings_Oorder(_1296551), 29031 ^ _779327 : [(29038 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296551), _1296553), _1296555))), -(c_Orderings_Obot__class_Obot(tc_fun(_1296551, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1296551, _1296553, _1296555))], (29032 ^ _779327) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1296551, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1296551, _1296553, _1296555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296551), _1296553), _1296555))]]], (34653 ^ _779327) ^ [_1417644, _1417646, _1417648, _1417650] : [class_Lattices_Osemilattice__inf(_1417644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417644), _1417646), _1417648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417644), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1417644), _1417650), _1417646)), _1417648)))], (49212 ^ _779327) ^ [_1765094, _1765096, _1765098] : [class_Orderings_Olinorder(_1765094), 49215 ^ _779327 : [(49234 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1765094, hAPP(hAPP(c_List_Oappend(_1765094), _1765096), _1765098))), c_List_Olinorder__class_Osorted(_1765094, _1765096), c_List_Olinorder__class_Osorted(_1765094, _1765098), 49244 ^ _779327 : [(49250 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1765094), 49243 ^ [_1765094, _1765096, _1765098]), 49246 ^ [_1765094, _1765096, _1765098]))], (49248 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765094), 49246 ^ [_1765094, _1765096, _1765098]), hAPP(c_List_Oset(_1765094), _1765098))))], (49245 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765094), 49243 ^ [_1765094, _1765096, _1765098]), hAPP(c_List_Oset(_1765094), _1765096))))]]], (49216 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1765094, hAPP(hAPP(c_List_Oappend(_1765094), _1765096), _1765098)), 49219 ^ _779327 : [(49224 ^ _779327) ^ [_1765330] : [hBOOL(hAPP(hAPP(c_member(_1765094), _1765330), hAPP(c_List_Oset(_1765094), _1765096))), 49227 ^ _779327 : [(49228 ^ _779327) ^ [_1765440] : [hBOOL(hAPP(hAPP(c_member(_1765094), _1765440), hAPP(c_List_Oset(_1765094), _1765098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1765094), _1765330), _1765440)))]]], (49222 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1765094, _1765098))], (49220 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1765094, _1765096))]]]]], (24453 ^ _779327) ^ [_1204952, _1204954, _1204956, _1204958] : [class_Rings_Ocomm__semiring__1(_1204952), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204952), _1204954), _1204956)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204952), _1204954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204952), _1204956), _1204958))))], (13732 ^ _779327) ^ [_1009693, _1009695, _1009697] : [class_Rings_Olinordered__ring__strict(_1009693), 13735 ^ _779327 : [(13744 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009693), _1009695), _1009695)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009693), _1009697), _1009697))), c_Groups_Ozero__class_Ozero(_1009693)))), _1009695 = c_Groups_Ozero__class_Ozero(_1009693), _1009697 = c_Groups_Ozero__class_Ozero(_1009693)], (13736 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009693), _1009695), _1009695)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009693), _1009697), _1009697))), c_Groups_Ozero__class_Ozero(_1009693))), 13739 ^ _779327 : [(13742 ^ _779327) ^ [] : [-(_1009697 = c_Groups_Ozero__class_Ozero(_1009693))], (13740 ^ _779327) ^ [] : [-(_1009695 = c_Groups_Ozero__class_Ozero(_1009693))]]]]], (25269 ^ _779327) ^ [_1219882, _1219884] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219882)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219884))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219882), _1219884)))], (53098 ^ _779327) ^ [_1841690, _1841692] : [hBOOL(_1841690), -(hBOOL(hAPP(hAPP(c_fimplies, _1841692), _1841690)))], (52768 ^ _779327) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (7452 ^ _779327) ^ [_896531, _896533, _896535] : [class_Power_Opower(_896531), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896531), _896533), hAPP(c_Nat_OSuc, _896535)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896531), _896533), hAPP(hAPP(c_Power_Opower__class_Opower(_896531), _896533), _896535)))], (17420 ^ _779327) ^ [_1075090, _1075092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075090)), c_Int_OBit1(_1075092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075090), _1075092)))], (16293 ^ _779327) ^ [_1055430, _1055432] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055430)))), 16296 ^ _779327 : [(16303 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055432)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055430), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055432)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055430), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055432))))], (16297 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1055432))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055430), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055432)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055430))]]], (2476 ^ _779327) ^ [_815546, _815548, _815550, _815552, _815554, _815556] : [-(c_Nitpick_Oplus__frac(_815556, _815552, _815548) = c_Nitpick_Oplus__frac(_815554, _815550, _815546)), _815556 = _815554, _815552 = _815550, _815548 = _815546], (18032 ^ _779327) ^ [_1085456, _1085458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085456), _1085458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085456)), c_Int_OBit1(_1085458))))], (7031 ^ _779327) ^ [_889374, _889376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889374), _889376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889374), hAPP(c_Nat_OSuc, _889376))))], (11911 ^ _779327) ^ [_976760, _976762, _976764, _976766] : [class_Groups_Oordered__ab__semigroup__add(_976760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976760), _976762), _976764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976760), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976760), _976762), _976766)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976760), _976764), _976766))))], (16752 ^ _779327) ^ [_1063389, _1063391] : [class_Int_Onumber__ring(_1063389), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063389), hAPP(c_Int_Onumber__class_Onumber__of(_1063389), c_Int_OPls)), _1063391) = _1063391)], (28600 ^ _779327) ^ [_1288881, _1288883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288881, tc_HOL_Obool)), _1288883), c_Orderings_Obot__class_Obot(tc_fun(_1288881, tc_HOL_Obool)))), -(_1288883 = c_Orderings_Obot__class_Obot(tc_fun(_1288881, tc_HOL_Obool)))], (10827 ^ _779327) ^ [_955753, _955755] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _955753), _955755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _955753)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _955755)))], (7464 ^ _779327) ^ [_896793, _896795] : [class_Rings_Omult__zero(_896793), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896793), c_Groups_Ozero__class_Ozero(_896793)), _896795) = c_Groups_Ozero__class_Ozero(_896793))], (23512 ^ _779327) ^ [_1188486, _1188488, _1188490, _1188492, _1188494, _1188496] : [c_Nitpick_Opair__box_OPairBox(_1188486, _1188488, _1188490, _1188492) = c_Nitpick_Opair__box_OPairBox(_1188486, _1188488, _1188494, _1188496), 23515 ^ _779327 : [(23518 ^ _779327) ^ [] : [-(_1188492 = _1188496)], (23516 ^ _779327) ^ [] : [-(_1188490 = _1188494)]]], (45436 ^ _779327) ^ [_1680290, _1680292, _1680294, _1680296] : [c_List_Olist_ONil(_1680290) = hAPP(hAPP(c_List_Omap(_1680292, _1680290), _1680294), _1680296), -(_1680296 = c_List_Olist_ONil(_1680292))], (49786 ^ _779327) ^ [_1777086, _1777088] : [-(_1777086 = c_List_Olist_ONil(_1777088)), hBOOL(hAPP(c_List_Odistinct(_1777088), _1777086)), -(c_List_OtakeWhile(_1777088, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777088), c_fNot), hAPP(hAPP(c_COMBC(_1777088, _1777088, tc_HOL_Obool), c_fequal), c_List_Olast(_1777088, _1777086))), _1777086) = c_List_Obutlast(_1777088, _1777086))], (46820 ^ _779327) ^ [_1713612] : [-(hAPP(c_List_Otl(_1713612), c_List_Olist_ONil(_1713612)) = c_List_Olist_ONil(_1713612))], (34213 ^ _779327) ^ [] : [-(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))))))], (52730 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52598 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (49617 ^ _779327) ^ [_1773678, _1773680, _1773682, _1773684] : [class_Orderings_Olinorder(_1773678), c_List_Olinorder__class_Osorted(_1773678, hAPP(c_List_Orev(_1773678), _1773680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1773682), _1773684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773678)), _1773680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1773678), hAPP(hAPP(c_List_Onth(_1773678), _1773680), _1773684)), hAPP(hAPP(c_List_Onth(_1773678), _1773680), _1773682))))], (42051 ^ _779327) ^ [_1596004, _1596006] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596004, _1596004)), hAPP(hAPP(c_Product__Type_OPair(_1596004, _1596004), 42052 ^ [_1596004, _1596006]), 42052 ^ [_1596004, _1596006])), c_Transitive__Closure_Otrancl(_1596004, _1596006)))), -(c_Wellfounded_Oacyclic(_1596004, _1596006))], (1978 ^ _779327) ^ [_807036, _807038, _807040, _807042, _807044, _807046] : [-(c_Hoare__Mirabelle_Otriple__valid(_807044, _807040, _807036)), c_Hoare__Mirabelle_Otriple__valid(_807046, _807042, _807038), _807046 = _807044, _807042 = _807040, _807038 = _807036], (35101 ^ _779327) ^ [_1427252, _1427254, _1427256] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427252, tc_HOL_Obool)), _1427254), _1427256) = c_Orderings_Obot__class_Obot(tc_fun(_1427252, tc_HOL_Obool)), 35104 ^ _779327 : [(35105 ^ _779327) ^ [_1427376] : [hBOOL(hAPP(hAPP(c_member(_1427252), _1427376), _1427254)), 35108 ^ _779327 : [(35109 ^ _779327) ^ [_1427466] : [hBOOL(hAPP(hAPP(c_member(_1427252), _1427466), _1427256)), _1427376 = _1427466]]]]], (51436 ^ _779327) ^ [_1813162, _1813164, _1813166] : [-(c_FunDef_OTHE__default(_1813164, _1813166, _1813162) = c_HOL_OThe(_1813164, _1813162)), 51437 ^ _779327 : [(51438 ^ _779327) ^ [_1813226] : [hBOOL(hAPP(_1813162, _1813226)), 51442 ^ _779327 : [(51445 ^ _779327) ^ [] : [51441 ^ [_1813162, _1813164, _1813166, _1813226] = _1813226], (51443 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1813162, 51441 ^ [_1813162, _1813164, _1813166, _1813226])))]]]]], (21828 ^ _779327) ^ [_1155483, _1155485] : [_1155483 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1155483, _1155485) = 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)))], (9062 ^ _779327) ^ [_925614, _925616, _925618, _925620] : [class_Rings_Ocomm__semiring__1(_925614), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925614), _925616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925614), _925618), _925620)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925614), _925616), _925618)), _925620))], (27046 ^ _779327) ^ [_1256611, _1256613, _1256615, _1256617] : [hBOOL(hAPP(_1256611, _1256613)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256615, tc_HOL_Obool)), _1256617), _1256611), _1256613)))], (31608 ^ _779327) ^ [_1353643, _1353645, _1353647, _1353649, _1353651, _1353653] : [hBOOL(hAPP(hAPP(c_member(_1353643), _1353645), c_SetInterval_Oord_OgreaterThanAtMost(_1353643, _1353647, _1353649, _1353651, _1353653))), 31611 ^ _779327 : [(31614 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1353647, _1353645), _1353653)))], (31612 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1353649, _1353651), _1353645)))]]], (27867 ^ _779327) ^ [_1274755, _1274757] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1274755, _1274757))))], (27552 ^ _779327) ^ [_1266870, _1266872, _1266874] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1266870, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1266872)), _1266874) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266870, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1266870, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1266872)), _1266874)), hAPP(_1266874, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52021 ^ _779327) ^ [_1826423, _1826425] : [52024 ^ _779327 : [(52029 ^ _779327) ^ [] : [52022 ^ [_1826423, _1826425] = 52023 ^ [_1826423, _1826425]], (52027 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826423, _1826423)), hAPP(hAPP(c_Product__Type_OPair(_1826423, _1826423), 52023 ^ [_1826423, _1826425]), 52022 ^ [_1826423, _1826425])), _1826425)))], (52025 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826423, _1826423)), hAPP(hAPP(c_Product__Type_OPair(_1826423, _1826423), 52022 ^ [_1826423, _1826425]), 52023 ^ [_1826423, _1826425])), _1826425)))]], -(c_Relation_Oantisym(_1826423, _1826425))], (50406 ^ _779327) ^ [_1790864, _1790866] : [class_Orderings_Olinorder(_1790864), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790864), _1790866)), 50414 ^ _779327 : [(50417 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1790864, 50413 ^ [_1790864, _1790866]))], (50419 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1790864), 50413 ^ [_1790864, _1790866])))], (50421 ^ _779327) ^ [_1791190] : [-(_1791190 = 50413 ^ [_1790864, _1790866]), hAPP(c_List_Oset(_1790864), _1791190) = _1790866, c_List_Olinorder__class_Osorted(_1790864, _1791190), hBOOL(hAPP(c_List_Odistinct(_1790864), _1791190))], (50415 ^ _779327) ^ [] : [-(hAPP(c_List_Oset(_1790864), 50413 ^ [_1790864, _1790866]) = _1790866)]]], (25484 ^ _779327) ^ [_1224240, _1224242, _1224244, _1224246] : [class_Rings_Oring__1(_1224240), -(hAPP(c_Int_Oring__1__class_Oof__int(_1224240), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224242, tc_Int_Oint), _1224244), _1224246)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224242, _1224240), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1224240, _1224242), c_Int_Oring__1__class_Oof__int(_1224240)), _1224244)), _1224246))], (4726 ^ _779327) ^ [_851355, _851357] : [_851357 = _851355, -(c_List_Otl(_851357) = c_List_Otl(_851355))], (47792 ^ _779327) ^ [_1733976, _1733978, _1733980, _1733982] : [class_Orderings_Olinorder(_1733976), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733976, _1733976, c_COMBI(_1733976)), _1733978), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733976, _1733976, c_COMBI(_1733976)), _1733980), _1733982)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733976, _1733976, c_COMBI(_1733976)), _1733980), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733976, _1733976, c_COMBI(_1733976)), _1733978), _1733982)))], (33153 ^ _779327) ^ [_1382851, _1382853, _1382855] : [class_Groups_Ocomm__monoid__mult(_1382851), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382853, _1382851), _1382855), c_Orderings_Obot__class_Obot(tc_fun(_1382853, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1382851))], (1768 ^ _779327) ^ [_804415, _804417] : [-(class_Rings_Ocomm__semiring(_804415)), _804417 = _804415, class_Rings_Ocomm__semiring(_804417)], (5216 ^ _779327) ^ [_858866, _858868] : [_858868 = _858866, -(c_Groups_Ominus__class_Ominus(_858868) = c_Groups_Ominus__class_Ominus(_858866))], (34709 ^ _779327) ^ [_1418732, _1418734, _1418736, _1418738] : [class_Lattices_Olattice(_1418732), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418732), _1418734), _1418736)), _1418738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418732), _1418734), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418732), _1418736), _1418738)))], (42898 ^ _779327) ^ [_1617259, _1617261, _1617263, _1617265] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617259, _1617259)), _1617261), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617259, _1617259), tc_HOL_Obool), _1617263), _1617265))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617259, _1617259)), _1617261), c_Transitive__Closure_Ortrancl(_1617259, _1617265))))], (11171 ^ _779327) ^ [_962151, _962153, _962155] : [class_Int_Onumber__ring(_962151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962151), hAPP(c_Groups_Ouminus__class_Ouminus(_962151), hAPP(c_Int_Onumber__class_Onumber__of(_962151), _962153))), _962155) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962151), hAPP(c_Int_Onumber__class_Onumber__of(_962151), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _962153))), _962155))], (15251 ^ _779327) ^ [_1036336, _1036338, _1036340] : [class_Divides_Osemiring__div(_1036336), -(c_Divides_Odiv__class_Omod(_1036336, c_Divides_Odiv__class_Omod(_1036336, _1036338, _1036340), _1036340) = c_Divides_Odiv__class_Omod(_1036336, _1036338, _1036340))], (52970 ^ _779327) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (15966 ^ _779327) ^ [_1049479, _1049481, _1049483] : [hBOOL(hAPP(_1049479, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1049481), _1049483))), 15971 ^ _779327 : [(15974 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1049479, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15972 ^ _779327) ^ [] : [-(_1049483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15976 ^ _779327 : [(15981 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1049479, 15975 ^ [_1049479, _1049481, _1049483])))], (15979 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049481), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049483), hAPP(c_Nat_OSuc, 15975 ^ [_1049479, _1049481, _1049483])))))], (15977 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049483), 15975 ^ [_1049479, _1049481, _1049483])), _1049481)))]]], (51402 ^ _779327) ^ [_1812153, _1812155, _1812157, _1812159] : [class_Groups_Ocomm__monoid__add(_1812153), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1812155, tc_HOL_Obool)), _1812157)), 51412 ^ _779327 : [(51415 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1812155), 51411 ^ [_1812153, _1812155, _1812157, _1812159]))], (51413 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1812155, tc_HOL_Obool)), 51411 ^ [_1812153, _1812155, _1812157, _1812159]), _1812157)))]], 51419 ^ _779327 : [(51423 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1812155, tc_HOL_Obool)), 51421 ^ [_1812153, _1812155, _1812157, _1812159]), _1812157)))], (51420 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1812155, tc_HOL_Obool)), 51418 ^ [_1812153, _1812155, _1812157, _1812159]), _1812157)))], (51432 ^ _779327) ^ [] : [hAPP(_1812159, 51426 ^ [_1812153, _1812155, _1812157, _1812159]) = c_Groups_Ozero__class_Ozero(_1812153)], (51428 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812155), 51426 ^ [_1812153, _1812155, _1812157, _1812159]), 51418 ^ [_1812153, _1812155, _1812157, _1812159])))], (51430 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812155), 51426 ^ [_1812153, _1812155, _1812157, _1812159]), 51421 ^ [_1812153, _1812155, _1812157, _1812159])))], (51425 ^ _779327) ^ [] : [51418 ^ [_1812153, _1812155, _1812157, _1812159] = 51421 ^ [_1812153, _1812155, _1812157, _1812159]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1812155, _1812153), _1812159), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1812155, tc_HOL_Obool), _1812157)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1812155, tc_HOL_Obool), _1812153), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1812155, _1812153), _1812159)), _1812157))], (51013 ^ _779327) ^ [_1803802, _1803804, _1803806, _1803808] : [-(hBOOL(hAPP(hAPP(c_member(_1803802), _1803804), hAPP(c_List_Oset(_1803802), c_List_Oreplicate(_1803802, _1803806, _1803808))))), _1803804 = _1803808, -(_1803806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25287 ^ _779327) ^ [_1220224, _1220226] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1220224), _1220226)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1220224), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1220226), _1220224)) = _1220226)], (49740 ^ _779327) ^ [_1776209, _1776211, _1776213, _1776215] : [hBOOL(hAPP(_1776209, _1776211)), -(c_List_OtakeWhile(_1776213, _1776209, hAPP(hAPP(c_List_Olist_OCons(_1776213), _1776211), _1776215)) = hAPP(hAPP(c_List_Olist_OCons(_1776213), _1776211), c_List_OtakeWhile(_1776213, _1776209, _1776215)))], (18562 ^ _779327) ^ [_1094704, _1094706, _1094708] : [class_Rings_Olinordered__idom(_1094704), 18565 ^ _779327 : [(18566 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094704), c_Groups_Ozero__class_Ozero(_1094704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094704), hAPP(hAPP(c_Power_Opower__class_Opower(_1094704), _1094706), 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(_1094704), _1094708), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1094706 = c_Groups_Ozero__class_Ozero(_1094704), _1094708 = c_Groups_Ozero__class_Ozero(_1094704)], (18576 ^ _779327) ^ [] : [18577 ^ _779327 : [(18580 ^ _779327) ^ [] : [-(_1094708 = c_Groups_Ozero__class_Ozero(_1094704))], (18578 ^ _779327) ^ [] : [-(_1094706 = c_Groups_Ozero__class_Ozero(_1094704))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094704), c_Groups_Ozero__class_Ozero(_1094704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094704), hAPP(hAPP(c_Power_Opower__class_Opower(_1094704), _1094706), 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(_1094704), _1094708), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (25518 ^ _779327) ^ [_1224946, _1224948, _1224950, _1224952, _1224954, _1224956, _1224958] : [class_Rings_Osemiring__0(_1224946), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224946), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224948, _1224946), _1224950), _1224952)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224954, _1224946), _1224956), _1224958)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224948, _1224946), hAPP(hAPP(c_COMBC(_1224948, tc_fun(_1224954, tc_HOL_Obool), _1224946), hAPP(hAPP(c_COMBB(tc_fun(_1224954, _1224946), tc_fun(tc_fun(_1224954, tc_HOL_Obool), _1224946), _1224948), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224954, _1224946)), hAPP(hAPP(c_COMBC(_1224948, tc_fun(_1224954, _1224946), tc_fun(_1224954, _1224946)), hAPP(hAPP(c_COMBB(tc_fun(_1224946, _1224946), tc_fun(tc_fun(_1224954, _1224946), tc_fun(_1224954, _1224946)), _1224948), c_COMBB(_1224946, _1224946, _1224954)), hAPP(hAPP(c_COMBB(_1224946, tc_fun(_1224946, _1224946), _1224948), c_Groups_Otimes__class_Otimes(_1224946)), _1224950))), _1224956))), _1224958)), _1224952))], (38395 ^ _779327) ^ [_1502131, _1502133, _1502135, _1502137, _1502139] : [hBOOL(hAPP(hAPP(c_member(_1502135), hAPP(_1502137, _1502133)), _1502139)), -(hBOOL(hAPP(hAPP(c_member(_1502131), _1502133), hAPP(c_Set_Ovimage(_1502131, _1502135, _1502137), _1502139))))], (30607 ^ _779327) ^ [_1331773, _1331775, _1331777, _1331779] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331773, tc_HOL_Obool)), _1331775), hAPP(hAPP(c_Set_Oinsert(_1331773), _1331777), _1331779)))), 30610 ^ _779327 : [(30613 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331773, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331773, tc_HOL_Obool)), _1331775), hAPP(hAPP(c_Set_Oinsert(_1331773), _1331777), c_Orderings_Obot__class_Obot(tc_fun(_1331773, tc_HOL_Obool))))), _1331779))], (30611 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331773), _1331777), _1331775)))]], 30614 ^ _779327 : [(30617 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1331773, tc_HOL_Obool)), _1331775), _1331779))], (30615 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1331773), _1331777), _1331775))]]], (18050 ^ _779327) ^ [_1085783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085783)))], (30647 ^ _779327) ^ [_1332589, _1332591, _1332593] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332589), _1332591)), -(hBOOL(hAPP(hAPP(c_member(_1332589), _1332593), _1332591))), -(hAPP(c_Finite__Set_Ocard(_1332589), hAPP(hAPP(c_Set_Oinsert(_1332589), _1332593), _1332591)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1332589), _1332591)))], (46010 ^ _779327) ^ [_1694514, _1694516, _1694518, _1694520, _1694522] : [-(hAPP(hAPP(c_List_Olist__update(_1694514, hAPP(hAPP(c_List_Olist_OCons(_1694514), _1694516), _1694518)), hAPP(c_Nat_OSuc, _1694520)), _1694522) = hAPP(hAPP(c_List_Olist_OCons(_1694514), _1694516), hAPP(hAPP(c_List_Olist__update(_1694514, _1694518), _1694520), _1694522)))], (36300 ^ _779327) ^ [_1455553, _1455555, _1455557, _1455559, _1455561, _1455563] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455553, tc_fun(_1455555, tc_HOL_Obool))), _1455557), _1455559), _1455561), _1455563)), -(hBOOL(hAPP(hAPP(_1455559, _1455561), _1455563)))], (24239 ^ _779327) ^ [_1201428, _1201430, _1201432] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201428), _1201430)), _1201430 = _1201432, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201428), _1201432)))], (51768 ^ _779327) ^ [_1820335, _1820337] : [c_Relation_Otrans(_1820335, _1820337), -(c_Relation_Otrans(_1820335, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1820335, _1820335), tc_HOL_Obool)), _1820337), c_Relation_OId(_1820335))))], (24877 ^ _779327) ^ [_1212801, _1212803, _1212805, _1212807] : [class_Rings_Ocomm__ring(_1212801), class_Rings_Odvd(_1212801), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212801), _1212803), _1212805)), 24888 ^ _779327 : [(24895 ^ _779327) ^ [_1213227, _1213229] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212801), _1212803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212801), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212801), _1213229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212801), _1213227), _1212805))), _1212807))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212801), _1212803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212801), _1213229), _1212807))))], (24889 ^ _779327) ^ [_1213054, _1213056] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212801), _1212803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212801), _1213056), _1212807))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212801), _1212803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212801), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212801), _1213056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212801), _1213054), _1212805))), _1212807))))]]], (23424 ^ _779327) ^ [_1186239, _1186241, _1186243] : [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), _1186239), _1186241))), -(hBOOL(hAPP(hAPP(_1186243, _1186239), _1186241))), 23431 ^ _779327 : [(23434 ^ _779327) ^ [] : [-(23430 ^ [_1186239, _1186241, _1186243] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1186243, 23430 ^ [_1186239, _1186241, _1186243]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23429 ^ [_1186239, _1186241, _1186243], 23430 ^ [_1186239, _1186241, _1186243]))))], (23440 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1186243, 23429 ^ [_1186239, _1186241, _1186243]), 23430 ^ [_1186239, _1186241, _1186243]))], (23432 ^ _779327) ^ [] : [-(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), 23429 ^ [_1186239, _1186241, _1186243]), 23430 ^ [_1186239, _1186241, _1186243]))))]]], (43890 ^ _779327) ^ [_1639428, _1639430, _1639432, _1639434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639428, tc_fun(_1639430, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1639428, tc_HOL_Obool), _1639432)), _1639434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1639428, tc_HOL_Obool), tc_fun(_1639430, tc_HOL_Obool)), _1639432), hAPP(hAPP(c_COMBC(tc_fun(_1639428, tc_HOL_Obool), tc_fun(_1639428, tc_fun(_1639430, tc_HOL_Obool)), tc_fun(_1639430, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639428, tc_fun(_1639430, tc_HOL_Obool))), _1639434)))], (29012 ^ _779327) ^ [_1296332, _1296334, _1296336] : [class_Orderings_Oorder(_1296332), 29015 ^ _779327 : [(29022 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296332), _1296334), _1296336))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1296332, _1296334, _1296336) = c_Orderings_Obot__class_Obot(tc_fun(_1296332, tc_HOL_Obool)))], (29016 ^ _779327) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1296332, _1296334, _1296336) = c_Orderings_Obot__class_Obot(tc_fun(_1296332, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296332), _1296334), _1296336))]]], (40271 ^ _779327) ^ [_1552545, _1552547, _1552549, _1552551] : [-(c_Product__Type_Oapsnd(_1552545, _1552547, _1552549, _1552551) = c_Product__Type_Omap__pair(_1552549, _1552549, _1552545, _1552547, c_Fun_Oid(_1552549), _1552551))], (34815 ^ _779327) ^ [_1421076, _1421078, _1421080, _1421082] : [class_Lattices_Osemilattice__inf(_1421076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421076), _1421078), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421076), _1421080), _1421082))), 34822 ^ _779327 : [(34825 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421076), _1421078), _1421082)))], (34823 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421076), _1421078), _1421080)))]]], (42529 ^ _779327) ^ [_1608333, _1608335, _1608337, _1608339, _1608341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608333, _1608335)), hAPP(hAPP(c_Product__Type_OPair(_1608333, _1608335), _1608337), _1608339)), hAPP(c_Relation_Oconverse(_1608335, _1608333), _1608341))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608335, _1608333)), hAPP(hAPP(c_Product__Type_OPair(_1608335, _1608333), _1608339), _1608337)), _1608341)))], (25542 ^ _779327) ^ [_1225832, _1225834, _1225836, _1225838] : [class_Groups_Oab__group__add(_1225832), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225834, _1225832), hAPP(hAPP(c_COMBB(_1225832, _1225832, _1225834), c_Groups_Ouminus__class_Ouminus(_1225832)), _1225836)), _1225838) = hAPP(c_Groups_Ouminus__class_Ouminus(_1225832), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1225834, _1225832), _1225836), _1225838)))], (23632 ^ _779327) ^ [_1190766, _1190768, _1190770, _1190772] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1190766, _1190768, _1190770, _1190772) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1190766, _1190768), _1190770), _1190772)))], (22395 ^ _779327) ^ [_1166870, _1166872, _1166874] : [class_Orderings_Olinorder(_1166870), 22398 ^ _779327 : [(22405 ^ _779327) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166870), _1166872), _1166874) = _1166872, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166870), _1166872), _1166874)))], (22399 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166870), _1166872), _1166874)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1166870), _1166872), _1166874) = _1166872)]]], (14191 ^ _779327) ^ [_1018399, _1018401] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018399), _1018401) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018399), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1018401)))], (52584 ^ _779327) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (9879 ^ _779327) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19425 ^ _779327) ^ [_1110020, _1110022] : [c_Nat__Transfer_Ois__nat(_1110020), c_Nat__Transfer_Ois__nat(_1110022), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1110020, _1110022)))], (28282 ^ _779327) ^ [_1282704, _1282706] : [class_Finite__Set_Ofinite(_1282704), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282704), _1282706)))], (15574 ^ _779327) ^ [_1042578, _1042580] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1042578), _1042580) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042578, _1042580) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18502 ^ _779327) ^ [_1093480, _1093482, _1093484] : [class_Rings_Ocomm__semiring__1(_1093480), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093480), _1093482), 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)))), _1093484)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093480), hAPP(hAPP(c_Power_Opower__class_Opower(_1093480), _1093482), _1093484)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093480), _1093482), _1093484)))], (38155 ^ _779327) ^ [_1494745, _1494747, _1494749] : [hBOOL(hAPP(hAPP(c_member(_1494745), _1494747), c_Wellfounded_Oacc(_1494745, _1494749))), 38158 ^ _779327 : [(38159 ^ _779327) ^ [_1494859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494745, _1494745)), hAPP(hAPP(c_Product__Type_OPair(_1494745, _1494745), _1494859), _1494747)), _1494749)), -(hBOOL(hAPP(hAPP(c_member(_1494745), _1494859), c_Wellfounded_Oacc(_1494745, _1494749))))]]], (16834 ^ _779327) ^ [_1064795, _1064797, _1064799, _1064801, _1064803] : [class_Groups_Oordered__ab__group__add__abs(_1064795), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064795), hAPP(c_Groups_Oabs__class_Oabs(_1064795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064795), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064795), _1064797), _1064799)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064795), _1064801), _1064803)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064795), hAPP(c_Groups_Oabs__class_Oabs(_1064795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064795), _1064797), _1064801))), hAPP(c_Groups_Oabs__class_Oabs(_1064795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064795), _1064799), _1064803))))))], (27318 ^ _779327) ^ [_1262144, _1262146, _1262148, _1262150] : [class_Orderings_Olinorder(_1262144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262144), _1262146), _1262148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262144), _1262148), _1262150)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262144, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1262144, _1262146), _1262148)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1262144, _1262148), _1262150)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1262144, _1262146), _1262150))], (28708 ^ _779327) ^ [_1290943, _1290945, _1290947, _1290949] : [28710 ^ _779327 : [(28713 ^ _779327) ^ [] : [hAPP(_1290949, 28709 ^ [_1290943, _1290945, _1290947, _1290949]) = c_Orderings_Obot__class_Obot(tc_fun(_1290943, tc_HOL_Obool))], (28711 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290945), 28709 ^ [_1290943, _1290945, _1290947, _1290949]), _1290947)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1290943, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290945, tc_fun(_1290943, tc_HOL_Obool)), _1290947), _1290949))], (33098 ^ _779327) ^ [_1381839, _1381841, _1381843, _1381845] : [class_Fields_Olinordered__field(_1381839), -(hAPP(c_Groups_Oabs__class_Oabs(_1381839), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381841, _1381839), _1381843), _1381845)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381841, _1381839), hAPP(hAPP(c_COMBB(_1381839, _1381839, _1381841), c_Groups_Oabs__class_Oabs(_1381839)), _1381843)), _1381845))], (28550 ^ _779327) ^ [_1287874, _1287876, _1287878] : [c_Orderings_Obot__class_Obot(tc_fun(_1287874, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1287874), _1287876), _1287878)], (23610 ^ _779327) ^ [_1190396, _1190398] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190396)), hAPP(c_Code__Numeral_Oof__nat, _1190398)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1190396), _1190398)))], (51265 ^ _779327) ^ [_1809070, _1809072, _1809074] : [-(_1809070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1809072), c_List_Oreplicate(_1809072, _1809070, _1809074)) = hAPP(hAPP(c_Set_Oinsert(_1809072), _1809074), c_Orderings_Obot__class_Obot(tc_fun(_1809072, tc_HOL_Obool))))], (37947 ^ _779327) ^ [_1490058, _1490060, _1490062, _1490064] : [c_Fun_Oinj__on(_1490058, _1490060, _1490062, c_Orderings_Otop__class_Otop(tc_fun(_1490058, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1490058, tc_fun(_1490064, _1490060), hAPP(hAPP(c_COMBB(_1490060, tc_fun(_1490064, _1490060), _1490058), c_COMBK(_1490060, _1490064)), _1490062), c_Orderings_Otop__class_Otop(tc_fun(_1490058, tc_HOL_Obool))))], (49403 ^ _779327) ^ [_1768853, _1768855, _1768857] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1768853), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1768853))), _1768855))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768857), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1768853))), _1768855))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1768853), _1768853), hAPP(hAPP(c_COMBC(tc_List_Olist(_1768853), tc_Nat_Onat, _1768853), c_List_Onth(_1768853)), _1768857)), hAPP(c_List_Ofilter(tc_List_Olist(_1768853), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1768853)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768857)), c_Nat_Osize__class_Osize(tc_List_Olist(_1768853)))), c_List_Otranspose(_1768853, _1768855))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1768853)), _1768855), _1768857))], (46445 ^ _779327) ^ [_1704910, _1704912, _1704914, _1704916] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1704910), tc_List_Olist(_1704910))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1704910), tc_List_Olist(_1704910)), _1704912), _1704914)), c_List_Olistrel1(_1704910, _1704916)))), 46446 ^ _779327 : [(46447 ^ _779327) ^ [_1705043, _1705045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1704910, _1704910)), hAPP(hAPP(c_Product__Type_OPair(_1704910, _1704910), hAPP(hAPP(c_List_Onth(_1704910), _1704912), _1705043)), _1705045)), _1704916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704910)), _1704912))), _1704914 = hAPP(hAPP(c_List_Olist__update(_1704910, _1704912), _1705043), _1705045)]]], (15830 ^ _779327) ^ [_1047020] : [-(c_Int_Osucc(_1047020) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1047020), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47694 ^ _779327) ^ [_1731974, _1731976] : [-(hBOOL(hAPP(c_List_Olistsp(_1731974, _1731976), c_List_Olist_ONil(_1731974))))], (34183 ^ _779327) ^ [_1405880, _1405882, _1405884, _1405886, _1405888] : [-(hBOOL(hAPP(hAPP(c_member(_1405880), _1405882), hAPP(c_Relation_OImage(_1405884, _1405880, _1405886), _1405888)))), 34184 ^ _779327 : [(34185 ^ _779327) ^ [_1405966] : [hBOOL(hAPP(hAPP(c_member(_1405884), _1405966), _1405888)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1405884, _1405880)), hAPP(hAPP(c_Product__Type_OPair(_1405884, _1405880), _1405966), _1405882)), _1405886))]]], (45076 ^ _779327) ^ [_1670985, _1670987, _1670989, _1670991] : [c_Fun_Oinj__on(_1670985, _1670987, _1670989, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670985, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1670985), tc_fun(_1670985, tc_HOL_Obool), c_List_Oset(_1670985)), _1670991))), -(c_Fun_Oinj__on(tc_List_Olist(_1670985), tc_List_Olist(_1670987), hAPP(c_List_Omap(_1670985, _1670987), _1670989), _1670991))], (35523 ^ _779327) ^ [_1436711, _1436713, _1436715] : [class_Orderings_Oorder(_1436711), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436711, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1436711, _1436713, _1436715)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1436711), _1436715)) = c_Orderings_Obot__class_Obot(tc_fun(_1436711, tc_HOL_Obool)))], (43983 ^ _779327) ^ [_1641421, _1641423, _1641425] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641421, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641421, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1641421, tc_HOL_Obool), tc_HOL_Obool)), _1641423), _1641425))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1641421, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641421, tc_HOL_Obool), _1641423)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641421, tc_HOL_Obool), _1641425)))))], (38838 ^ _779327) ^ [_1513312, _1513314, _1513316] : [c_Equiv__Relations_Oequiv(_1513312, _1513314, _1513316), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1513312, _1513312), tc_HOL_Obool)), _1513316), hAPP(hAPP(c_Product__Type_OSigma(_1513312, _1513312), _1513314), hAPP(c_COMBK(tc_fun(_1513312, tc_HOL_Obool), _1513312), _1513314)))))], (3814 ^ _779327) ^ [_837153, _837155, _837157, _837159] : [-(c_List_Olistrel1(_837159, _837155) = c_List_Olistrel1(_837157, _837153)), _837159 = _837157, _837155 = _837153], (806 ^ _779327) ^ [_791652, _791654, _791656, _791658] : [-(c_Wellfounded_Owf(_791656, _791652)), c_Wellfounded_Owf(_791658, _791654), _791658 = _791656, _791654 = _791652], (27352 ^ _779327) ^ [_1262959, _1262961, _1262963, _1262965] : [class_Orderings_Olinorder(_1262959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262959), _1262961), _1262963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262959), _1262963), _1262965)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262959, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262959, _1262961, _1262963)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1262959, _1262963, _1262965)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1262959, _1262961, _1262965))], (37723 ^ _779327) ^ [_1485621, _1485623] : [class_Orderings_Otop(_1485621), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1485621), _1485623), c_Orderings_Otop__class_Otop(_1485621))))], (37029 ^ _779327) ^ [_1470425, _1470427, _1470429, _1470431, _1470433] : [c_Fun_Oinj__on(_1470425, _1470427, _1470429, hAPP(hAPP(c_Set_Oinsert(_1470425), _1470431), _1470433)), 37032 ^ _779327 : [(37035 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1470427), hAPP(_1470429, _1470431)), hAPP(c_Set_Oimage(_1470425, _1470427, _1470429), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470425, tc_HOL_Obool)), _1470433), hAPP(hAPP(c_Set_Oinsert(_1470425), _1470431), c_Orderings_Obot__class_Obot(tc_fun(_1470425, tc_HOL_Obool)))))))], (37033 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1470425, _1470427, _1470429, _1470433))]]], (33092 ^ _779327) ^ [_1381724, _1381726, _1381728] : [class_Groups_Ocomm__monoid__mult(_1381724), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381726, _1381724), hAPP(c_COMBK(_1381724, _1381726), c_Groups_Oone__class_Oone(_1381724))), _1381728) = c_Groups_Oone__class_Oone(_1381724))], (9074 ^ _779327) ^ [_925900, _925902, _925904] : [class_Rings_Ocomm__semiring__1(_925900), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925900), _925902), _925904) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_925900), _925904), _925902))], (25079 ^ _779327) ^ [_1216488, _1216490] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1216488)), _1216490))), 25082 ^ _779327 : [(25085 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1216488), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216490)))], (25083 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216488)))]], 25086 ^ _779327 : [(25089 ^ _779327) ^ [] : [_1216490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25087 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216488))]]], (50320 ^ _779327) ^ [_1789119, _1789121, _1789123] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1789119, _1789121), _1789123) = c_Lazy__Sequence_Oproduct(_1789119, _1789121, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1789119, _1789123), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1789121, _1789123))), class_Lazy__Sequence_Osmall__lazy(_1789119), class_Lazy__Sequence_Osmall__lazy(_1789121)], (31702 ^ _779327) ^ [_1355335, _1355337] : [31703 ^ _779327 : [(31706 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355337), _1355335))], (31704 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355335), _1355337)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1355335, _1355337))], (5418 ^ _779327) ^ [_861987, _861989, _861991, _861993, _861995, _861997] : [-(c_Set_Oimage(_861997, _861993, _861989) = c_Set_Oimage(_861995, _861991, _861987)), _861997 = _861995, _861993 = _861991, _861989 = _861987], (47171 ^ _779327) ^ [_1720973, _1720975] : [class_Complete__Lattice_Ocomplete__lattice(_1720973), -(c_Complete__Lattice_OSup__class_OSup(_1720973, hAPP(c_List_Oset(_1720973), _1720975)) = hAPP(c_List_Ofoldl(_1720973, _1720973, c_Lattices_Osemilattice__sup__class_Osup(_1720973), c_Orderings_Obot__class_Obot(_1720973)), _1720975))], (37691 ^ _779327) ^ [_1485061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1485061)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1485061), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1485061), c_Orderings_Otop__class_Otop(tc_fun(_1485061, tc_HOL_Obool)))))], (44717 ^ _779327) ^ [_1660731, _1660733, _1660735, _1660737, _1660739] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660731), tc_List_Olist(_1660731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660731), tc_List_Olist(_1660731)), _1660733), _1660735)), c_List_Olistrel(_1660731, c_Transitive__Closure_Ortrancl(_1660731, _1660737)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660731), tc_List_Olist(_1660731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660731), tc_List_Olist(_1660731)), _1660735), _1660739)), c_List_Olistrel(_1660731, c_Transitive__Closure_Ortrancl(_1660731, _1660737)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660731), tc_List_Olist(_1660731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660731), tc_List_Olist(_1660731)), _1660733), _1660739)), c_List_Olistrel(_1660731, c_Transitive__Closure_Ortrancl(_1660731, _1660737)))))], (18414 ^ _779327) ^ [_1092161, _1092163] : [class_Rings_Olinordered__idom(_1092161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092161), hAPP(hAPP(c_Power_Opower__class_Opower(_1092161), _1092163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1092161)))], (23566 ^ _779327) ^ [_1189760] : [-(_1189760 = 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)), _1189760)))], (36590 ^ _779327) ^ [_1461936, _1461938] : [class_Lattices_Olattice(_1461936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461936), _1461938)), -(_1461938 = c_Orderings_Obot__class_Obot(tc_fun(_1461936, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1461936), c_Big__Operators_Olattice__class_OInf__fin(_1461936, _1461938)), c_Big__Operators_Olattice__class_OSup__fin(_1461936, _1461938))))], (34539 ^ _779327) ^ [_1414711, _1414713, _1414715, _1414717, _1414719, _1414721] : [c_Equiv__Relations_Oequiv(_1414711, _1414713, _1414715), c_Equiv__Relations_Ocongruent(_1414711, tc_fun(_1414717, tc_HOL_Obool), _1414715, _1414719), hBOOL(hAPP(hAPP(c_member(_1414711), _1414721), _1414713)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414711, tc_fun(_1414717, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1414711, _1414711, _1414715), hAPP(hAPP(c_Set_Oinsert(_1414711), _1414721), c_Orderings_Obot__class_Obot(tc_fun(_1414711, tc_HOL_Obool))))), _1414719) = hAPP(_1414719, _1414721))], (27636 ^ _779327) ^ [_1269361, _1269363, _1269365] : [class_Orderings_Olinorder(_1269361), 27639 ^ _779327 : [(27646 ^ _779327) ^ [] : [_1269363 = _1269365, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1269361), _1269363) = hAPP(c_SetInterval_Oord__class_OatLeast(_1269361), _1269365))], (27640 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1269361), _1269363) = hAPP(c_SetInterval_Oord__class_OatLeast(_1269361), _1269365), -(_1269363 = _1269365)]]], (29118 ^ _779327) ^ [_1298086, _1298088] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1298088, _1298086) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1298086), _1298088)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1298088), _1298086)))], (34318 ^ _779327) ^ [_1409687, _1409689, _1409691, _1409693] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1409687, tc_HOL_Obool)), _1409689), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1409687), _1409691), _1409693))), 34322 ^ _779327 : [(34325 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409687), 34321 ^ [_1409687, _1409689, _1409691, _1409693]), _1409691)))], (34323 ^ _779327) ^ [] : [-(_1409689 = hAPP(c_Relation_OImage(_1409687, _1409687, _1409693), hAPP(hAPP(c_Set_Oinsert(_1409687), 34321 ^ [_1409687, _1409689, _1409691, _1409693]), c_Orderings_Obot__class_Obot(tc_fun(_1409687, tc_HOL_Obool)))))]]], (52754 ^ _779327) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (20205 ^ _779327) ^ [_1124007, _1124009, _1124011, _1124013] : [class_Fields_Olinordered__field(_1124007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124007), c_Groups_Ozero__class_Ozero(_1124007)), _1124009)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124007), _1124011), _1124009)), _1124013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124007), _1124011), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124007), _1124013), _1124009))))], (37457 ^ _779327) ^ [_1479971, _1479973, _1479975, _1479977, _1479979] : [class_Groups_Oab__semigroup__mult(_1479971), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1479971, _1479971, c_Groups_Otimes__class_Otimes(_1479971), _1479973, _1479975), _1479977)), hBOOL(hAPP(hAPP(c_member(_1479971), _1479979), _1479975)), -(hBOOL(hAPP(hAPP(c_member(_1479971), _1479973), _1479975))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1479971, _1479971, c_Groups_Otimes__class_Otimes(_1479971), _1479979, hAPP(hAPP(c_Set_Oinsert(_1479971), _1479973), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479971, tc_HOL_Obool)), _1479975), hAPP(hAPP(c_Set_Oinsert(_1479971), _1479979), c_Orderings_Obot__class_Obot(tc_fun(_1479971, tc_HOL_Obool)))))), _1479977)))], (49719 ^ _779327) ^ [_1775729, _1775731, _1775733] : [49721 ^ _779327 : [(49724 ^ _779327) ^ [] : [hBOOL(hAPP(_1775731, 49720 ^ [_1775729, _1775731, _1775733]))], (49722 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775729), 49720 ^ [_1775729, _1775731, _1775733]), hAPP(c_List_Oset(_1775729), _1775733))))]], -(c_List_OtakeWhile(_1775729, _1775731, _1775733) = _1775733)], (26854 ^ _779327) ^ [_1252457, _1252459, _1252461] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252457, tc_HOL_Obool)), _1252459), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252457, tc_HOL_Obool)), _1252459), _1252461)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1252457, tc_HOL_Obool)), _1252459), _1252461))], (23945 ^ _779327) ^ [_1196590, _1196592, _1196594] : [class_Rings_Ocomm__ring__1(_1196590), 23948 ^ _779327 : [(23955 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196590), _1196592), _1196594)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196590), hAPP(c_Groups_Ouminus__class_Ouminus(_1196590), _1196592)), _1196594)))], (23949 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196590), hAPP(c_Groups_Ouminus__class_Ouminus(_1196590), _1196592)), _1196594)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196590), _1196592), _1196594)))]]], (27883 ^ _779327) ^ [_1275079] : [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)), _1275079))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1275079)))], (34811 ^ _779327) ^ [_1420919, _1420921, _1420923, _1420925] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420919, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420919, tc_HOL_Obool)), _1420921), _1420923)), _1420925) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420919, tc_HOL_Obool)), _1420921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1420919, tc_HOL_Obool)), _1420923), _1420925)))], (8908 ^ _779327) ^ [_922709, _922711, _922713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922709, tc_HOL_Obool)), _922711), _922713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922709, tc_HOL_Obool)), _922713), _922711)), -(_922711 = _922713)], (37177 ^ _779327) ^ [_1474028] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1474028))], (22625 ^ _779327) ^ [_1170932] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170932) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23384 ^ _779327) ^ [_1185527, _1185529, _1185531, _1185533] : [hBOOL(hAPP(_1185527, _1185529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1185531, tc_HOL_Obool)), _1185527), _1185533)), -(hBOOL(hAPP(_1185533, _1185529)))], (7123 ^ _779327) ^ [_890813, _890815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890813), _890815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890813), hAPP(c_Nat_OSuc, _890815))))], (50373 ^ _779327) ^ [_1790054, _1790056, _1790058, _1790060, _1790062] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790054)), _1790056) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790058)), _1790060), 50379 ^ _779327 : [(50382 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1790062, hAPP(hAPP(c_List_Onth(_1790054), _1790056), 50378 ^ [_1790054, _1790056, _1790058, _1790060, _1790062])), hAPP(hAPP(c_List_Onth(_1790058), _1790060), 50378 ^ [_1790054, _1790056, _1790058, _1790060, _1790062])))], (50380 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50378 ^ [_1790054, _1790056, _1790058, _1790060, _1790062]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790054)), _1790056))))]], -(c_List_Olist__all2(_1790054, _1790058, _1790062, _1790056, _1790060))], (37481 ^ _779327) ^ [_1480424, _1480426, _1480428, _1480430] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480424, _1480426, _1480428, _1480430, c_Orderings_Obot__class_Obot(tc_fun(_1480424, tc_HOL_Obool))), _1480430)))], (21796 ^ _779327) ^ [_1154805, _1154807, _1154809, _1154811, _1154813] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1154805, _1154807), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1154809), _1154811))), -(_1154807 = 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), _1154813), _1154805), _1154807), 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), _1154813), _1154809)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1154813), _1154811)), _1154807))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1154813), _1154811), _1154807)))))], (12081 ^ _779327) ^ [_979718, _979720, _979722, _979724] : [class_Groups_Oordered__cancel__ab__semigroup__add(_979718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979718), _979720), _979722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979718), _979720), _979724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979718), _979722), _979724))))], (13166 ^ _779327) ^ [_999463, _999465] : [class_Groups_Olinordered__ab__group__add(_999463), 13169 ^ _779327 : [(13176 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999463), _999465), c_Groups_Ozero__class_Ozero(_999463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999463), _999465), _999465)), c_Groups_Ozero__class_Ozero(_999463))))], (13170 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999463), _999465), _999465)), c_Groups_Ozero__class_Ozero(_999463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999463), _999465), c_Groups_Ozero__class_Ozero(_999463))))]]], (49455 ^ _779327) ^ [_1770105, _1770107] : [hAPP(c_List_Orev(_1770105), _1770107) = c_List_Olist_ONil(_1770105), -(_1770107 = c_List_Olist_ONil(_1770105))], (5650 ^ _779327) ^ [_868541, _868543] : [hAPP(c_Nat_OSuc, _868541) = hAPP(c_Nat_OSuc, _868543), -(_868541 = _868543)], (21029 ^ _779327) ^ [_1139457, _1139459] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139457), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139459)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139457)) = 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), _1139459), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1139457)))), 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)))], (11373 ^ _779327) ^ [_966708, _966710, _966712, _966714, _966716, _966718] : [class_Rings_Oordered__ring(_966708), 11376 ^ _779327 : [(11383 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966708), _966714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966708), _966716), _966710)), _966712)), _966718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), _966710), _966712)), _966714)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), _966716), _966712)), _966718))))], (11377 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), _966710), _966712)), _966714)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), _966716), _966712)), _966718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966708), _966714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966708), _966716), _966710)), _966712)), _966718))))]]], (18278 ^ _779327) ^ [_1089834] : [class_Int_Onumber__ring(_1089834), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089834), c_Groups_Oone__class_Oone(_1089834)), c_Groups_Oone__class_Oone(_1089834)) = hAPP(c_Int_Onumber__class_Onumber__of(_1089834), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (13622 ^ _779327) ^ [_1007685, _1007687] : [13623 ^ _779327 : [(13624 ^ _779327) ^ [_1007738] : [_1007687 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1007685), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1007738))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1007685), _1007687)))], (12147 ^ _779327) ^ [_981121, _981123, _981125, _981127] : [class_Rings_Ocomm__semiring__1(_981121), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981121), _981123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981121), _981125), _981127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981121), _981123), _981125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981121), _981123), _981127)))], (29328 ^ _779327) ^ [_1302442, _1302444, _1302446] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302442), _1302444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1302442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1302442, tc_HOL_Obool)), _1302444), hAPP(hAPP(c_Set_Oinsert(_1302442), _1302446), c_Orderings_Obot__class_Obot(tc_fun(_1302442, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1302442), _1302444))))], (4930 ^ _779327) ^ [_854489, _854491, _854493, _854495, _854497, _854499] : [-(c_Lazy__Sequence_Oanamorph(_854499, _854495, _854491) = c_Lazy__Sequence_Oanamorph(_854497, _854493, _854489)), _854499 = _854497, _854495 = _854493, _854491 = _854489], (48566 ^ _779327) ^ [_1751654, _1751656, _1751658, _1751660] : [-(hAPP(c_List_Ofilter(_1751654, _1751656), c_List_Oremove1(_1751654, _1751658, _1751660)) = c_List_Oremove1(_1751654, _1751658, hAPP(c_List_Ofilter(_1751654, _1751656), _1751660)))], (19613 ^ _779327) ^ [_1113537, _1113539, _1113541, _1113543] : [class_Fields_Olinordered__field(_1113537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113537), _1113539), c_Groups_Ozero__class_Ozero(_1113537))), 19620 ^ _779327 : [(19627 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113537), _1113543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113537), _1113541), _1113539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113537), _1113541), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113537), _1113543), _1113539))))], (19621 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113537), _1113541), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1113537), _1113543), _1113539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113537), _1113543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113537), _1113541), _1113539))))]]], (35759 ^ _779327) ^ [_1442309, _1442311, _1442313, _1442315] : [35761 ^ _779327 : [(35764 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1442309, _1442309, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1442309, tc_fun(_1442309, _1442311), tc_fun(_1442309, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442311, tc_HOL_Obool), tc_fun(tc_fun(_1442309, _1442311), tc_fun(_1442309, tc_HOL_Obool)), _1442309), c_COMBB(_1442311, tc_HOL_Obool, _1442309)), hAPP(hAPP(c_COMBB(_1442311, tc_fun(_1442311, tc_HOL_Obool), _1442309), c_fequal), _1442315))), _1442315)), 35760 ^ [_1442309, _1442311, _1442313, _1442315]))], (35762 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442309, _1442309)), 35760 ^ [_1442309, _1442311, _1442313, _1442315]), _1442313)))]], -(c_Equiv__Relations_Ocongruent(_1442309, _1442311, _1442313, _1442315))], (13390 ^ _779327) ^ [_1003655, _1003657, _1003659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003655), _1003657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003655), _1003659)), 13397 ^ _779327 : [(13404 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003657), _1003659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003657), _1003655)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003659), _1003655))))], (13398 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003657), _1003655)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003659), _1003655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003657), _1003659)))]]], (20147 ^ _779327) ^ [_1122886, _1122888, _1122890, _1122892] : [class_Fields_Olinordered__field(_1122886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122886), _1122888), _1122890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122886), c_Groups_Ozero__class_Ozero(_1122886)), _1122892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122886), c_Groups_Ozero__class_Ozero(_1122886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122886), _1122890), _1122888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122886), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122886), _1122892), _1122890)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122886), _1122892), _1122888))))], (16321 ^ _779327) ^ [_1056003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056003), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056003)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (40958 ^ _779327) ^ [_1571042, _1571044, _1571046, _1571048] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571042, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1571042, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1571042, _1571044), _1571046)), hAPP(c_Relation_ODomain(_1571042, _1571044), _1571048))), hAPP(c_Relation_ODomain(_1571042, _1571044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1571042, _1571044), tc_HOL_Obool)), _1571046), _1571048)))))], (1888 ^ _779327) ^ [_805915, _805917] : [-(class_Orderings_Oord(_805915)), _805917 = _805915, class_Orderings_Oord(_805917)], (6430 ^ _779327) ^ [_880297, _880299, _880301] : [class_Orderings_Oorder(_880297), -(_880299 = _880301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880297), _880299), _880301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880297), _880299), _880301)))], (4150 ^ _779327) ^ [_842343, _842345, _842347, _842349] : [-(c_Random_Opick(_842349, _842345) = c_Random_Opick(_842347, _842343)), _842349 = _842347, _842345 = _842343], (7316 ^ _779327) ^ [_894016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894016), _894016))))], (35133 ^ _779327) ^ [_1427826, _1427828] : [class_Lattices_Obounded__lattice__bot(_1427826), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1427826), _1427828), c_Orderings_Obot__class_Obot(_1427826)) = c_Orderings_Obot__class_Obot(_1427826))], (28960 ^ _779327) ^ [_1295428, _1295430, _1295432, _1295434] : [class_Orderings_Oorder(_1295428), 28963 ^ _779327 : [(28972 ^ _779327) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1295428, _1295430, _1295432) = hAPP(hAPP(c_Set_Oinsert(_1295428), _1295434), c_Orderings_Obot__class_Obot(tc_fun(_1295428, tc_HOL_Obool)))), _1295430 = _1295432, _1295432 = _1295434], (28964 ^ _779327) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1295428, _1295430, _1295432) = hAPP(hAPP(c_Set_Oinsert(_1295428), _1295434), c_Orderings_Obot__class_Obot(tc_fun(_1295428, tc_HOL_Obool))), 28967 ^ _779327 : [(28970 ^ _779327) ^ [] : [-(_1295432 = _1295434)], (28968 ^ _779327) ^ [] : [-(_1295430 = _1295432)]]]]], (22515 ^ _779327) ^ [_1168955, _1168957, _1168959, _1168961] : [class_Orderings_Olinorder(_1168955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168955), _1168957), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168955), _1168959), _1168961))), 22522 ^ _779327 : [(22525 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168955), _1168957), _1168961)))], (22523 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168955), _1168957), _1168959)))]]], (21938 ^ _779327) ^ [_1157527, _1157529, _1157531, _1157533, _1157535, _1157537, _1157539] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1157527, _1157529, tc_fun(_1157531, tc_HOL_Obool)), _1157533), hAPP(hAPP(c_Product__Type_OPair(_1157527, _1157529), _1157535), _1157537)), _1157539)), -(hBOOL(hAPP(hAPP(hAPP(_1157533, _1157535), _1157537), _1157539)))], (38543 ^ _779327) ^ [_1505908, _1505910, _1505912, _1505914, _1505916, _1505918] : [c_Typedef_Otype__definition(_1505908, _1505910, _1505912, _1505914, _1505916), -(hBOOL(hAPP(hAPP(c_member(_1505910), hAPP(_1505912, _1505918)), _1505916)))], (51114 ^ _779327) ^ [_1805580, _1805582, _1805584, _1805586] : [51121 ^ _779327 : [(51124 ^ _779327) ^ [] : [_1805582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51122 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1805586, _1805584)))]], 51115 ^ _779327 : [(51116 ^ _779327) ^ [_1805652] : [hBOOL(hAPP(hAPP(c_member(_1805580), _1805652), hAPP(c_List_Oset(_1805580), c_List_Oreplicate(_1805580, _1805582, _1805584)))), hBOOL(hAPP(_1805586, _1805652))]]], (8692 ^ _779327) ^ [_918690, _918692, _918694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918690), _918692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918690), _918694))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918692), _918694)))], (48521 ^ _779327) ^ [_1750669, _1750671, _1750673] : [hBOOL(hAPP(c_List_Odistinct(_1750669), _1750671)), -(hBOOL(hAPP(c_List_Odistinct(_1750669), hAPP(c_List_Ofilter(_1750669, _1750673), _1750671))))], (31820 ^ _779327) ^ [_1357601, _1357603, _1357605] : [class_Rings_Oring__1(_1357601), hBOOL(hAPP(hAPP(c_member(_1357601), _1357603), c_Int_Oring__1__class_OInts(_1357601))), hBOOL(hAPP(hAPP(c_member(_1357601), _1357605), c_Int_Oring__1__class_OInts(_1357601))), -(hBOOL(hAPP(hAPP(c_member(_1357601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357601), _1357603), _1357605)), c_Int_Oring__1__class_OInts(_1357601))))], (12610 ^ _779327) ^ [_989704, _989706, _989708] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989704), _989706)), _989708) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989704), _989708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _989706), _989708)))], (50535 ^ _779327) ^ [_1794110, _1794112, _1794114, _1794116] : [class_Orderings_Oorder(_1794110), class_Enum_Oenum(_1794112), 50542 ^ _779327 : [(50549 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1794112), hAPP(hAPP(c_COMBS(_1794112, _1794110, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1794110, tc_fun(_1794110, tc_HOL_Obool), _1794112), c_Orderings_Oord__class_Oless__eq(_1794110)), _1794114)), _1794116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794112, _1794110)), _1794114), _1794116)))], (50543 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794112, _1794110)), _1794114), _1794116)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1794112), hAPP(hAPP(c_COMBS(_1794112, _1794110, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1794110, tc_fun(_1794110, tc_HOL_Obool), _1794112), c_Orderings_Oord__class_Oless__eq(_1794110)), _1794114)), _1794116))))]]], (18865 ^ _779327) ^ [_1100739] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1100739)))], (27791 ^ _779327) ^ [_1273262, _1273264, _1273266] : [class_Orderings_Olinorder(_1273262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273262), _1273264), _1273266)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273262, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1273262, _1273264), _1273266)), hAPP(c_SetInterval_Oord__class_OatLeast(_1273262), _1273266)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1273262), _1273264))], (24063 ^ _779327) ^ [_1198576, _1198578] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198576), _1198578)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198578), _1198576))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198578), _1198576)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198576), _1198578)))], (52634 ^ _779327) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (39720 ^ _779327) ^ [_1533034, _1533036] : [-(hBOOL(hAPP(_1533036, 39721 ^ [_1533034, _1533036]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1533034, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1533034), _1533036))], (616 ^ _779327) ^ [_788757, _788759, _788761, _788763, _788765, _788767, _788769, _788771] : [-(c_Finite__Set_Ofolding(_788769, _788765, _788761, _788757)), c_Finite__Set_Ofolding(_788771, _788767, _788763, _788759), _788771 = _788769, _788767 = _788765, _788763 = _788761, _788759 = _788757], (45822 ^ _779327) ^ [_1690413, _1690415, _1690417, _1690419, _1690421, _1690423] : [-(hAPP(c_List_Olist_Olist__case(_1690413, _1690415, _1690417, _1690419), hAPP(hAPP(c_List_Olist_OCons(_1690415), _1690421), _1690423)) = hAPP(hAPP(_1690419, _1690421), _1690423))], (34296 ^ _779327) ^ [_1409076, _1409078, _1409080, _1409082] : [hBOOL(hAPP(hAPP(c_member(_1409076), _1409078), _1409080)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1409076, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1409076, _1409076, _1409082), hAPP(hAPP(c_Set_Oinsert(_1409076), _1409078), c_Orderings_Obot__class_Obot(tc_fun(_1409076, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1409076), _1409080), _1409082))))], (18350 ^ _779327) ^ [] : [-(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)))))], (45693 ^ _779327) ^ [_1686674, _1686676, _1686678, _1686680] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686674) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1686676), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686674)), hAPP(hAPP(c_List_Olist_OCons(_1686676), _1686678), _1686680)) = c_List_Olist_ONil(_1686676))], (40989 ^ _779327) ^ [_1572257, _1572259] : [c_Wellfounded_Owf(_1572257, hAPP(c_Set_OCollect(tc_prod(_1572257, _1572257)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572257, _1572257, tc_HOL_Obool), _1572259))), -(c_Wellfounded_OwfP(_1572257, _1572259))], (17446 ^ _779327) ^ [_1075564] : [c_Int_OBit1(_1075564) = c_Int_OPls], (10043 ^ _779327) ^ [_941976, _941978] : [_941976 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _941976), _941978), -(_941978 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_941976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6056 ^ _779327) ^ [_874678, _874680, _874682, _874684] : [class_Orderings_Oord(_874678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874678), _874680), _874682)), _874682 = _874684, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874678), _874680), _874684)))], (24853 ^ _779327) ^ [_1212188, _1212190, _1212192, _1212194] : [class_Rings_Ocomm__ring(_1212188), class_Rings_Odvd(_1212188), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212188), _1212190), _1212192)), 24864 ^ _779327 : [(24871 ^ _779327) ^ [_1212614, _1212616] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212188), _1212190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212188), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212188), _1212616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212188), _1212614), _1212192))), _1212194))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212188), _1212190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212188), _1212616), _1212194))))], (24865 ^ _779327) ^ [_1212441, _1212443] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212188), _1212190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212188), _1212443), _1212194))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212188), _1212190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212188), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1212188), _1212443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212188), _1212441), _1212192))), _1212194))))]]], (25417 ^ _779327) ^ [_1222527, _1222529] : [class_Orderings_Oorder(_1222527), 25424 ^ _779327 : [(25427 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222527), hAPP(_1222529, 25422 ^ [_1222527, _1222529])), hAPP(_1222529, 25423 ^ [_1222527, _1222529])))], (25425 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 25422 ^ [_1222527, _1222529]), 25423 ^ [_1222527, _1222529])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1222527, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1222529))], (33943 ^ _779327) ^ [_1400277, _1400279, _1400281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400277, tc_HOL_Obool)), _1400279), _1400281)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1400277, tc_HOL_Obool)), _1400279), hAPP(c_Set_OPow(_1400277), _1400281))))], (51790 ^ _779327) ^ [_1821642, _1821644, _1821646, _1821648] : [class_Complete__Lattice_Ocomplete__lattice(_1821642), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1821644, _1821642), _1821646), _1821648) = c_Complete__Lattice_OInf__class_OInf(_1821642, hAPP(c_Set_OCollect(_1821642), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool), tc_HOL_Obool, _1821642), c_HOL_OEx(tc_fun(_1821644, _1821642))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool), tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool), _1821642), hAPP(c_COMBS(tc_fun(_1821644, _1821642), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1821644, _1821642)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1821644, _1821642), tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1821644, _1821642))), _1821646)))), hAPP(hAPP(c_COMBC(_1821642, tc_fun(tc_fun(_1821644, _1821642), _1821642), tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1821642, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1821644, _1821642), _1821642), tc_fun(tc_fun(_1821644, _1821642), tc_HOL_Obool)), _1821642), c_COMBB(_1821642, tc_HOL_Obool, tc_fun(_1821644, _1821642))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1821644, _1821642), _1821644, _1821642), c_COMBI(tc_fun(_1821644, _1821642))), _1821648)))))))], (38946 ^ _779327) ^ [_1516049, _1516051, _1516053, _1516055] : [_1516049 = c_Orderings_Obot__class_Obot(tc_fun(_1516051, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1516053, _1516051), _1516053, c_Product__Type_Ofst(_1516053, _1516051)), hAPP(hAPP(c_Product__Type_OSigma(_1516053, _1516051), _1516055), hAPP(c_COMBK(tc_fun(_1516051, tc_HOL_Obool), _1516053), _1516049))) = c_Orderings_Obot__class_Obot(tc_fun(_1516053, tc_HOL_Obool)))], (6322 ^ _779327) ^ [_878760, _878762, _878764] : [class_Orderings_Olinorder(_878760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878760), _878762), _878764)), 6329 ^ _779327 : [(6336 ^ _779327) ^ [] : [_878762 = _878764, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878760), _878762), _878764))], (6330 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878760), _878762), _878764))), -(_878762 = _878764)]]], (14299 ^ _779327) ^ [_1020293] : [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), _1020293))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1020293) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1020293)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46600 ^ _779327) ^ [_1708790, _1708792, _1708794, _1708796] : [-(hAPP(hAPP(c_List_Odrop(_1708790), _1708792), hAPP(hAPP(c_List_Olist_OCons(_1708790), _1708794), _1708796)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1708790), hAPP(hAPP(c_List_Olist_OCons(_1708790), _1708794), _1708796), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1708790), tc_List_Olist(_1708790)), c_List_Odrop(_1708790)), _1708796), _1708792))], (29068 ^ _779327) ^ [_1297178, _1297180, _1297182, _1297184, _1297186] : [_1297178 = c_Orderings_Obot__class_Obot(tc_fun(_1297180, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1297182), _1297184), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297180, tc_fun(_1297182, tc_HOL_Obool)), _1297178), _1297186)) = hAPP(hAPP(c_Set_Oinsert(_1297182), _1297184), c_Orderings_Obot__class_Obot(tc_fun(_1297182, tc_HOL_Obool))))], (47207 ^ _779327) ^ [_1721719, _1721721, _1721723] : [class_Orderings_Olinorder(_1721719), -(c_Big__Operators_Olattice_OInf__fin(_1721719, c_Orderings_Oord__class_Omin(_1721719), hAPP(c_List_Oset(_1721719), hAPP(hAPP(c_List_Olist_OCons(_1721719), _1721721), _1721723))) = hAPP(c_List_Ofoldl(_1721719, _1721719, c_Orderings_Oord__class_Omin(_1721719), _1721721), _1721723))], (31511 ^ _779327) ^ [_1350643, _1350645, _1350647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350643, tc_HOL_Obool)), _1350645), hAPP(_1350647, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1350643, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), _1350647)), _1350645))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1350643, tc_HOL_Obool), _1350647)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), _1350647), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350643, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1350643, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), _1350647)), _1350645))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1350643, tc_HOL_Obool), _1350647)))), hAPP(_1350647, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1350643, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1350643, tc_HOL_Obool), tc_fun(tc_fun(_1350643, tc_HOL_Obool), tc_fun(_1350643, tc_HOL_Obool)), tc_fun(_1350643, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350643, tc_HOL_Obool))), _1350647)), _1350645))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1350643, tc_HOL_Obool), _1350647)))))))], (18534 ^ _779327) ^ [_1094164, _1094166, _1094168] : [class_Rings_Olinordered__idom(_1094164), 18537 ^ _779327 : [(18546 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094164), hAPP(hAPP(c_Power_Opower__class_Opower(_1094164), _1094166), 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(_1094164), _1094168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094164)))), _1094166 = c_Groups_Ozero__class_Ozero(_1094164), _1094168 = c_Groups_Ozero__class_Ozero(_1094164)], (18538 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094164), hAPP(hAPP(c_Power_Opower__class_Opower(_1094164), _1094166), 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(_1094164), _1094168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094164))), 18541 ^ _779327 : [(18544 ^ _779327) ^ [] : [-(_1094168 = c_Groups_Ozero__class_Ozero(_1094164))], (18542 ^ _779327) ^ [] : [-(_1094166 = c_Groups_Ozero__class_Ozero(_1094164))]]]]], (27681 ^ _779327) ^ [_1270492, _1270494, _1270496, _1270498, _1270500] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270492, tc_fun(_1270494, tc_HOL_Obool)), _1270496), hAPP(hAPP(c_COMBS(_1270492, tc_fun(_1270494, tc_HOL_Obool), tc_fun(_1270494, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270494, tc_HOL_Obool), tc_fun(tc_fun(_1270494, tc_HOL_Obool), tc_fun(_1270494, tc_HOL_Obool)), _1270492), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270494, tc_HOL_Obool))), _1270498)), _1270500)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270494, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270492, tc_fun(_1270494, tc_HOL_Obool)), _1270496), _1270498)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270492, tc_fun(_1270494, tc_HOL_Obool)), _1270496), _1270500)))], (52053 ^ _779327) ^ [_1827271, _1827273] : [c_Relation_Osym(_1827271, _1827273), c_Relation_Otrans(_1827271, _1827273), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1827271, _1827271), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1827271, _1827271, _1827271), hAPP(c_Relation_Oconverse(_1827271, _1827271), _1827273)), _1827273)), _1827273)))], (27078 ^ _779327) ^ [_1257216, _1257218, _1257220, _1257222] : [class_Lattices_Osemilattice__sup(_1257216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257216), _1257218), _1257220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257216), _1257222), _1257220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257216), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257216), _1257218), _1257222)), _1257220)))], (38097 ^ _779327) ^ [_1493388, _1493390, _1493392, _1493394, _1493396] : [-(_1493388 = c_Orderings_Obot__class_Obot(tc_fun(_1493390, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493390, tc_fun(_1493392, tc_HOL_Obool)), _1493388), hAPP(hAPP(c_COMBB(tc_fun(_1493392, tc_HOL_Obool), tc_fun(_1493392, tc_HOL_Obool), _1493390), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493392, tc_HOL_Obool)), _1493394)), _1493396)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493392, tc_HOL_Obool)), _1493394), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493390, tc_fun(_1493392, tc_HOL_Obool)), _1493388), _1493396)))], (23692 ^ _779327) ^ [_1191794] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1191794)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1191794))], (24317 ^ _779327) ^ [_1202648, _1202650] : [24324 ^ _779327 : [(24327 ^ _779327) ^ [] : [_1202648 = _1202650], (24325 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202648), _1202650)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202648), _1202650)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202650), _1202648)))], (37749 ^ _779327) ^ [] : [-(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)))], (8282 ^ _779327) ^ [_911340, _911342] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_911340), c_Groups_Ozero__class_Ozero(_911340)), hAPP(c_Nat_OSuc, _911342)) = c_Groups_Ozero__class_Ozero(_911340)), class_Power_Opower(_911340), class_Rings_Osemiring__0(_911340)], (18967 ^ _779327) ^ [_1102396, _1102398, _1102400] : [class_Fields_Olinordered__field__inverse__zero(_1102396), 18970 ^ _779327 : [(18985 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102396), _1102398), _1102400)))), 18986 ^ _779327 : [(18993 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), _1102398), c_Groups_Ozero__class_Ozero(_1102396))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), _1102400), c_Groups_Ozero__class_Ozero(_1102396)))], (18987 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), _1102398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), _1102400))]]], (18971 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1102396), _1102398), _1102400))), 18976 ^ _779327 : [(18979 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), _1102400)))], (18977 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), c_Groups_Ozero__class_Ozero(_1102396)), _1102398)))]], 18980 ^ _779327 : [(18983 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), _1102400), c_Groups_Ozero__class_Ozero(_1102396))))], (18981 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102396), _1102398), c_Groups_Ozero__class_Ozero(_1102396))))]]]]], (29893 ^ _779327) ^ [_1313630, _1313632, _1313634, _1313636] : [_1313630 = _1313632, hBOOL(hAPP(hAPP(c_member(_1313634), _1313632), _1313636)), -(hBOOL(hAPP(hAPP(c_member(_1313634), _1313630), _1313636)))], (29054 ^ _779327) ^ [] : [-(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)))], (32266 ^ _779327) ^ [_1365398, _1365400, _1365402] : [class_Orderings_Olinorder(_1365398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365398), _1365400)), hBOOL(hAPP(hAPP(c_member(_1365398), _1365402), _1365400)), 32277 ^ _779327 : [(32284 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365398, tc_HOL_Obool)), _1365400), hAPP(hAPP(c_Set_Oinsert(_1365398), _1365402), c_Orderings_Obot__class_Obot(tc_fun(_1365398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365398, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1365398, _1365400) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365398), _1365402), c_Big__Operators_Olinorder__class_OMin(_1365398, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365398, tc_HOL_Obool)), _1365400), hAPP(hAPP(c_Set_Oinsert(_1365398), _1365402), c_Orderings_Obot__class_Obot(tc_fun(_1365398, tc_HOL_Obool)))))))], (32278 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365398, tc_HOL_Obool)), _1365400), hAPP(hAPP(c_Set_Oinsert(_1365398), _1365402), c_Orderings_Obot__class_Obot(tc_fun(_1365398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365398, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1365398, _1365400) = _1365402)]]], (27585 ^ _779327) ^ [_1267739, _1267741, _1267743, _1267745, _1267747, _1267749] : [class_Complete__Lattice_Ocomplete__lattice(_1267739), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267741, tc_fun(_1267743, _1267739)), _1267745), _1267747), _1267749) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267741, _1267739), _1267745), hAPP(hAPP(c_COMBC(_1267741, _1267743, _1267739), _1267747), _1267749)))], (72 ^ _779327) ^ [_780299, _780301] : [-(class_Fields_Olinordered__field__inverse__zero(_780299)), _780301 = _780299, class_Fields_Olinordered__field__inverse__zero(_780301)], (48313 ^ _779327) ^ [_1745512, _1745514] : [-(c_List_Oremdups(_1745512, c_List_Oremdups(_1745512, _1745514)) = c_List_Oremdups(_1745512, _1745514))], (30683 ^ _779327) ^ [_1333295, _1333297, _1333299, _1333301] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333295, tc_HOL_Obool)), _1333297), hAPP(hAPP(c_Set_Oinsert(_1333295), _1333299), _1333301)))), 30686 ^ _779327 : [(30689 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333295, tc_HOL_Obool)), _1333297), _1333301))], (30687 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333295), _1333299), _1333301)))]], 30690 ^ _779327 : [(30693 ^ _779327) ^ [] : [30694 ^ _779327 : [(30697 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1333295, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333295, tc_HOL_Obool)), _1333297), hAPP(hAPP(c_Set_Oinsert(_1333295), _1333299), c_Orderings_Obot__class_Obot(tc_fun(_1333295, tc_HOL_Obool))))), _1333301))], (30695 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333295), _1333299), _1333297)))]], 30698 ^ _779327 : [(30701 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1333295, tc_HOL_Obool)), _1333297), _1333301))], (30699 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333295), _1333299), _1333297))]]], (30691 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333295), _1333299), _1333301))]]], (45882 ^ _779327) ^ [_1691771, _1691773] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1691771), _1691773))), -(c_List_Oupto(_1691771, _1691773) = c_List_Olist_ONil(tc_Int_Oint))], (8082 ^ _779327) ^ [_907722, _907724, _907726] : [class_Rings_Olinordered__semiring__strict(_907722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907722), c_Groups_Ozero__class_Ozero(_907722)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907722), _907724), _907726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907722), c_Groups_Ozero__class_Ozero(_907722)), _907726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907722), c_Groups_Ozero__class_Ozero(_907722)), _907724)))], (12011 ^ _779327) ^ [_978527, _978529] : [class_Rings_Ocomm__semiring__1(_978527), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978527), _978529), c_Groups_Ozero__class_Ozero(_978527)) = _978529)], (27935 ^ _779327) ^ [_1276049, _1276051, _1276053, _1276055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276049, tc_HOL_Obool)), _1276051), _1276053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276049, tc_HOL_Obool)), _1276051), hAPP(hAPP(c_Set_Oinsert(_1276049), _1276055), _1276053))))], (21272 ^ _779327) ^ [_1144914, _1144916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1144914)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144916))), -(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(_1144916))), 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), _1144914)), c_Int_Onat))))))], (17952 ^ _779327) ^ [_1084077] : [c_Int_OPls = _1084077, -(c_Int_OPls = c_Int_OBit0(_1084077))], (29937 ^ _779327) ^ [_1314488, _1314490, _1314492, _1314494] : [hBOOL(hAPP(hAPP(c_member(_1314488), _1314490), _1314492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314488, tc_HOL_Obool)), _1314492), _1314494)), -(hBOOL(hAPP(hAPP(c_member(_1314488), _1314490), _1314494)))], (2748 ^ _779327) ^ [_820054, _820056] : [_820056 = _820054, -(c_Lazy__Sequence_Ohit__bound(_820056) = c_Lazy__Sequence_Ohit__bound(_820054))], (51509 ^ _779327) ^ [_1814737, _1814739, _1814741] : [c_List_Oall__interval__int(_1814737, _1814739, _1814741), -(c_List_Olist__all(tc_Int_Oint, _1814737, c_List_Oupto(_1814739, _1814741)))], (5758 ^ _779327) ^ [_870355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _870355)), _870355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22239 ^ _779327) ^ [_1163739, _1163741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163739)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163741), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1163739, _1163741) = 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), _1163739), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163741)))))], (11497 ^ _779327) ^ [_969139, _969141, _969143, _969145, _969147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969139), _969141)), 11500 ^ _779327 : [(11507 ^ _779327) ^ [] : [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), _969141), _969139)), _969143)), _969145)), _969147)), -(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), _969141), _969143)), _969145)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969139), _969143)), _969147))))], (11501 ^ _779327) ^ [] : [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), _969141), _969143)), _969145)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969139), _969143)), _969147))), -(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), _969141), _969139)), _969143)), _969145)), _969147)))]]], (40267 ^ _779327) ^ [_1552460] : [-(hAPP(c_Set_Oimage(_1552460, _1552460, c_Fun_Oid(_1552460)), c_Orderings_Otop__class_Otop(tc_fun(_1552460, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1552460, tc_HOL_Obool)))], (26167 ^ _779327) ^ [_1238897, _1238899, _1238901, _1238903] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1238897), _1238899)), 26170 ^ _779327 : [(26171 ^ _779327) ^ [_1239051] : [26173 ^ _779327 : [(26179 ^ _779327) ^ [] : [-(_1239051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26175 ^ [_1238897, _1238899, _1238901, _1238903, _1239051]), 26172 ^ [_1238897, _1238899, _1238901, _1238903, _1239051]))], (26177 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26175 ^ [_1238897, _1238899, _1238901, _1238903, _1239051]), _1238901)))], (26174 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26172 ^ [_1238897, _1238899, _1238901, _1238903, _1239051]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1238899))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1238897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239051), _1238903))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1238897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239051), _1238899)), _1238903))))]]], (42585 ^ _779327) ^ [_1609764, _1609766] : [-(hAPP(c_Relation_OField(_1609764), hAPP(c_Relation_Oconverse(_1609764, _1609764), _1609766)) = hAPP(c_Relation_OField(_1609764), _1609766))], (2296 ^ _779327) ^ [_812816, _812818] : [_812818 = _812816, -(c_Int_Opred(_812818) = c_Int_Opred(_812816))], (25151 ^ _779327) ^ [_1217831, _1217833, _1217835] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217831), _1217833)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217831), _1217835)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217831), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217833, _1217835))))], (38571 ^ _779327) ^ [_1506383, _1506385, _1506387, _1506389, _1506391, _1506393, _1506395] : [c_Typedef_Otype__definition(_1506383, _1506385, _1506387, _1506389, _1506391), hBOOL(hAPP(hAPP(c_member(_1506385), _1506393), _1506391)), hBOOL(hAPP(hAPP(c_member(_1506385), _1506395), _1506391)), 38582 ^ _779327 : [(38589 ^ _779327) ^ [] : [_1506393 = _1506395, -(hAPP(_1506389, _1506393) = hAPP(_1506389, _1506395))], (38583 ^ _779327) ^ [] : [hAPP(_1506389, _1506393) = hAPP(_1506389, _1506395), -(_1506393 = _1506395)]]], (31316 ^ _779327) ^ [_1346906, _1346908, _1346910, _1346912] : [-(c_Nitpick_Ofold__graph_H(_1346906, _1346908, _1346910, _1346912, c_Orderings_Obot__class_Obot(tc_fun(_1346906, tc_HOL_Obool)), _1346912))], (12530 ^ _779327) ^ [_988151, _988153] : [12531 ^ _779327 : [(12532 ^ _779327) ^ [_988201] : [_988153 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988151), _988201)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988151), _988153)))], (44331 ^ _779327) ^ [_1649279, _1649281, _1649283] : [hBOOL(hAPP(hAPP(c_member(_1649279), _1649281), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1649279, tc_HOL_Obool), _1649283))), 44335 ^ _779327 : [(44338 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1649279, tc_HOL_Obool)), 44334 ^ [_1649279, _1649281, _1649283]), _1649283)))], (44336 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1649279), _1649281), 44334 ^ [_1649279, _1649281, _1649283])))]]], (46730 ^ _779327) ^ [_1712097, _1712099, _1712101] : [-(_1712097 = c_List_Olist_ONil(_1712099)), -(hAPP(c_List_Ohd(_1712099), hAPP(hAPP(c_List_Oappend(_1712099), _1712097), _1712101)) = hAPP(c_List_Ohd(_1712099), _1712097))], (51977 ^ _779327) ^ [_1825567] : [-(c_Relation_Oantisym(_1825567, c_Relation_OId(_1825567)))], (5748 ^ _779327) ^ [_870252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870252), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16816 ^ _779327) ^ [_1064400, _1064402, _1064404] : [class_Rings_Oordered__ring__abs(_1064400), -(hAPP(c_Groups_Oabs__class_Oabs(_1064400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064400), _1064402), _1064404)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064400), hAPP(c_Groups_Oabs__class_Oabs(_1064400), _1064402)), hAPP(c_Groups_Oabs__class_Oabs(_1064400), _1064404))), 16823 ^ _779327 : [(16826 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064400), _1064402), c_Groups_Ozero__class_Ozero(_1064400)))], (16824 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064400), c_Groups_Ozero__class_Ozero(_1064400)), _1064402))]], 16827 ^ _779327 : [(16830 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064400), _1064404), c_Groups_Ozero__class_Ozero(_1064400)))], (16828 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1064400), c_Groups_Ozero__class_Ozero(_1064400)), _1064404))]]], (37795 ^ _779327) ^ [] : [-(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)))], (31692 ^ _779327) ^ [_1355174, _1355176] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1355174, _1355176), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355174), _1355176)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355176), _1355174)))], (51637 ^ _779327) ^ [_1817392, _1817394] : [51638 ^ _779327 : [(51639 ^ _779327) ^ [_1817458] : [hBOOL(hAPP(_1817394, _1817458))]], 51641 ^ _779327 : [(51644 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1817394, 51640 ^ [_1817392, _1817394])))], (51642 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1817392), 51640 ^ [_1817392, _1817394]), c_Orderings_Otop__class_Otop(tc_fun(_1817392, tc_HOL_Obool)))))]]], (3432 ^ _779327) ^ [_831084, _831086] : [_831086 = _831084, -(c_Random__Sequence_Osingle(_831086) = c_Random__Sequence_Osingle(_831084))], (18766 ^ _779327) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (1738 ^ _779327) ^ [_804040, _804042] : [-(class_Rings_Ocomm__semiring__1(_804040)), _804042 = _804040, class_Rings_Ocomm__semiring__1(_804042)], (50114 ^ _779327) ^ [_1783950, _1783952, _1783954] : [-(hBOOL(hAPP(hAPP(c_member(_1783950), _1783952), hAPP(c_List_Oset(_1783950), _1783954)))), -(c_List_Oinsert(_1783950, _1783952, _1783954) = hAPP(hAPP(c_List_Olist_OCons(_1783950), _1783952), _1783954))], (18096 ^ _779327) ^ [_1086618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1086618)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086618), c_Int_OMin)))], (8608 ^ _779327) ^ [_917171, _917173] : [-(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), _917171), _917173)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _917171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _917173))], (1102 ^ _779327) ^ [_795994, _795996, _795998, _796000] : [-(c_Equiv__Relations_Opart__equivp(_795998, _795994)), c_Equiv__Relations_Opart__equivp(_796000, _795996), _796000 = _795998, _795996 = _795994], (34361 ^ _779327) ^ [_1410746, _1410748, _1410750, _1410752] : [c_Equiv__Relations_Oequiv(_1410746, _1410748, _1410750), hBOOL(hAPP(hAPP(c_member(_1410746), _1410752), _1410748)), -(hBOOL(hAPP(hAPP(c_member(_1410746), _1410752), hAPP(c_Relation_OImage(_1410746, _1410746, _1410750), hAPP(hAPP(c_Set_Oinsert(_1410746), _1410752), c_Orderings_Obot__class_Obot(tc_fun(_1410746, tc_HOL_Obool)))))))], (34981 ^ _779327) ^ [_1424029, _1424031, _1424033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424029, tc_HOL_Obool)), _1424031), _1424033)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424029, tc_HOL_Obool)), _1424033), _1424031) = _1424031)], (13224 ^ _779327) ^ [_1000509, _1000511] : [class_Rings_Olinordered__idom(_1000509), 13227 ^ _779327 : [(13234 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000509), _1000511), c_Groups_Ozero__class_Ozero(_1000509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000509), _1000511), _1000511)), c_Groups_Ozero__class_Ozero(_1000509))))], (13228 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000509), _1000511), _1000511)), c_Groups_Ozero__class_Ozero(_1000509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000509), _1000511), c_Groups_Ozero__class_Ozero(_1000509))))]]], (968 ^ _779327) ^ [_794105, _794107, _794109, _794111] : [-(c_Wellfounded_Oacyclic(_794109, _794105)), c_Wellfounded_Oacyclic(_794111, _794107), _794111 = _794109, _794107 = _794105], (38115 ^ _779327) ^ [_1493824, _1493826, _1493828, _1493830, _1493832] : [_1493824 = c_Orderings_Obot__class_Obot(tc_fun(_1493826, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1493826, tc_fun(_1493828, tc_HOL_Obool)), _1493824), hAPP(hAPP(c_COMBC(_1493826, tc_fun(_1493828, tc_HOL_Obool), tc_fun(_1493828, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493828, tc_HOL_Obool), tc_fun(tc_fun(_1493828, tc_HOL_Obool), tc_fun(_1493828, tc_HOL_Obool)), _1493826), c_Groups_Ominus__class_Ominus(tc_fun(_1493828, tc_HOL_Obool))), _1493830)), _1493832)) = c_Orderings_Otop__class_Otop(tc_fun(_1493828, tc_HOL_Obool)))], (30043 ^ _779327) ^ [_1317041, _1317043, _1317045, _1317047] : [_1317045 = _1317047, -(hAPP(hAPP(c_COMBC(_1317041, tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_fun(_1317043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317043, tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_fun(_1317043, tc_HOL_Obool)), _1317041), c_COMBC(_1317043, tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317043, tc_prod(_1317041, _1317043)), tc_fun(_1317043, tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), _1317041), hAPP(c_COMBB(tc_prod(_1317041, _1317043), tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool), _1317043), c_member(tc_prod(_1317041, _1317043)))), c_Product__Type_OPair(_1317041, _1317043)))), _1317045) = hAPP(hAPP(c_COMBC(_1317041, tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_fun(_1317043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317043, tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_fun(_1317043, tc_HOL_Obool)), _1317041), c_COMBC(_1317043, tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1317043, tc_prod(_1317041, _1317043)), tc_fun(_1317043, tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool)), _1317041), hAPP(c_COMBB(tc_prod(_1317041, _1317043), tc_fun(tc_fun(tc_prod(_1317041, _1317043), tc_HOL_Obool), tc_HOL_Obool), _1317043), c_member(tc_prod(_1317041, _1317043)))), c_Product__Type_OPair(_1317041, _1317043)))), _1317047))], (51699 ^ _779327) ^ [_1818736] : [-(c_Relation_Otrans(_1818736, c_Relation_OId(_1818736)))], (27426 ^ _779327) ^ [_1264427, _1264429, _1264431, _1264433] : [class_Orderings_Olinorder(_1264427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264427), _1264429), _1264431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264427), _1264431), _1264433)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264427, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1264427, _1264429, _1264431)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1264427, _1264431, _1264433)) = c_SetInterval_Oord__class_OatLeastAtMost(_1264427, _1264429, _1264433))], (31031 ^ _779327) ^ [_1341192, _1341194, _1341196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341192)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1341194), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1341196)), 31041 ^ _779327 : [(31047 ^ _779327) ^ [] : [-(_1341194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 31043 ^ [_1341192, _1341194, _1341196]), 31040 ^ [_1341192, _1341194, _1341196]))], (31045 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31043 ^ [_1341192, _1341194, _1341196]), _1341196)))], (31042 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 31040 ^ [_1341192, _1341194, _1341196]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1341192))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1341194), _1341192) = _1341194)], (23578 ^ _779327) ^ [_1189889, _1189891] : [hAPP(c_Code__Numeral_Oof__nat, _1189889) = hAPP(c_Code__Numeral_Oof__nat, _1189891), -(_1189889 = _1189891)], (37306 ^ _779327) ^ [_1476653, _1476655, _1476657, _1476659, _1476661] : [class_Groups_Ocomm__monoid__mult(_1476653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476655), _1476657)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476653, _1476655, c_Groups_Otimes__class_Otimes(_1476653)), hAPP(hAPP(c_COMBS(_1476655, _1476653, _1476653), hAPP(hAPP(c_COMBB(_1476653, tc_fun(_1476653, _1476653), _1476655), c_Groups_Otimes__class_Otimes(_1476653)), _1476659)), _1476661)), c_Groups_Oone__class_Oone(_1476653)), _1476657) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1476653), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476653, _1476655, c_Groups_Otimes__class_Otimes(_1476653)), _1476659), c_Groups_Oone__class_Oone(_1476653)), _1476657)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1476653, _1476655, c_Groups_Otimes__class_Otimes(_1476653)), _1476661), c_Groups_Oone__class_Oone(_1476653)), _1476657)))], (28678 ^ _779327) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (51332 ^ _779327) ^ [_1810676] : [-(c_List_Omember(_1810676) = c_List_Oset(_1810676))], (36668 ^ _779327) ^ [_1463306, _1463308, _1463310] : [class_Lattices_Olattice(_1463306), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463306), _1463308)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463306), _1463310)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463306, tc_HOL_Obool)), _1463308), _1463310) = c_Orderings_Obot__class_Obot(tc_fun(_1463306, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463306), c_Big__Operators_Olattice__class_OInf__fin(_1463306, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463306, tc_HOL_Obool)), _1463308), _1463310))), c_Big__Operators_Olattice__class_OInf__fin(_1463306, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463306, tc_HOL_Obool)), _1463308), _1463310))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1463306), c_Big__Operators_Olattice__class_OInf__fin(_1463306, _1463308)), c_Big__Operators_Olattice__class_OInf__fin(_1463306, _1463310)))], (51711 ^ _779327) ^ [_1818900] : [-(c_Relation_Otrans(tc_fun(_1818900, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1818900)))], (47259 ^ _779327) ^ [_1723099, _1723101, _1723103, _1723105] : [-(_1723099 = c_List_Olist_ONil(_1723101)), 47262 ^ _779327 : [(47269 ^ _779327) ^ [] : [-(_1723103 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723101)), _1723099)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1723101, hAPP(hAPP(c_List_Olist__update(_1723101, _1723099), _1723103), _1723105)) = c_List_Olast(_1723101, _1723099))], (47263 ^ _779327) ^ [] : [_1723103 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723101)), _1723099)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1723101, hAPP(hAPP(c_List_Olist__update(_1723101, _1723099), _1723103), _1723105)) = _1723105)]]], (23638 ^ _779327) ^ [_1190917, _1190919, _1190921, _1190923, _1190925] : [_1190917 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1190919, _1190921, _1190923, _1190925), _1190917) = c_Lazy__Sequence_Oempty(_1190921))], (29226 ^ _779327) ^ [_1300461, _1300463, _1300465] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1300461, _1300463) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1300465), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 29229 ^ _779327 : [(29232 ^ _779327) ^ [] : [-(_1300463 = _1300465)], (29230 ^ _779327) ^ [] : [-(_1300461 = _1300463)]]], (21220 ^ _779327) ^ [_1143655, _1143657, _1143659, _1143661] : [-(c_Nat_Onat_Onat__case(_1143655, _1143657, _1143659, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143661)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1143655), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1143661))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1143655, _1143655), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1143655, tc_fun(_1143655, _1143655)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1143655, tc_fun(_1143655, _1143655)), tc_Int_Oint), c_If(_1143655)), c_Nat__Numeral_Oneg)), _1143657)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1143655, tc_Int_Oint), _1143659), c_Int_Onat))))], (22005 ^ _779327) ^ [_1158948, _1158950, _1158952, _1158954, _1158956, _1158958] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1158948, _1158950, _1158952), _1158954), hAPP(hAPP(c_Product__Type_OPair(_1158948, _1158950), _1158956), _1158958)) = hAPP(hAPP(_1158954, _1158956), _1158958))], (42916 ^ _779327) ^ [_1617737, _1617739, _1617741] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617737, _1617737)), hAPP(hAPP(c_Product__Type_OPair(_1617737, _1617737), _1617739), _1617739)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617737, _1617737), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1617741))))], (40472 ^ _779327) ^ [_1560065, _1560067, _1560069] : [c_Wellfounded_Owf(_1560065, _1560067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1560065, _1560065), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1560065, _1560065, _1560065), _1560067), _1560069)), _1560067)), -(c_FunDef_Oreduction__pair(_1560065, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1560065, _1560065), tc_HOL_Obool), tc_fun(tc_prod(_1560065, _1560065), tc_HOL_Obool)), _1560067), _1560069)))], (17488 ^ _779327) ^ [_1076190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1076190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1076190)))], (3728 ^ _779327) ^ [_835774, _835776, _835778, _835780, _835782, _835784, _835786, _835788, _835790, _835792] : [-(c_Fun_Ofun__upd(_835792, _835788, _835784, _835780, _835776) = c_Fun_Ofun__upd(_835790, _835786, _835782, _835778, _835774)), _835792 = _835790, _835788 = _835786, _835784 = _835782, _835780 = _835778, _835776 = _835774], (6867 ^ _779327) ^ [_886703, _886705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886703), _886705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886703), hAPP(c_Nat_OSuc, _886705))))], (30371 ^ _779327) ^ [_1325497, _1325499, _1325501, _1325503, _1325505] : [class_Complete__Lattice_Ocomplete__lattice(_1325497), hBOOL(hAPP(hAPP(c_member(_1325499), _1325501), _1325503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325497), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1325499, _1325497), _1325503), _1325505)), hAPP(_1325505, _1325501))))], (1338 ^ _779327) ^ [_799040, _799042] : [-(class_Groups_Osgn__if(_799040)), _799042 = _799040, class_Groups_Osgn__if(_799042)], (3222 ^ _779327) ^ [_827735, _827737] : [_827737 = _827735, -(c_Wellfounded_Omeasure(_827737) = c_Wellfounded_Omeasure(_827735))], (17688 ^ _779327) ^ [_1079356] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1079356))) = 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)))), _1079356))], (4640 ^ _779327) ^ [_850054, _850056] : [_850056 = _850054, -(c_Lazy__Sequence_Oempty(_850056) = c_Lazy__Sequence_Oempty(_850054))], (4416 ^ _779327) ^ [_846476, _846478] : [_846478 = _846476, -(c_List_Omonoid__add__class_Olistsum(_846478) = c_List_Omonoid__add__class_Olistsum(_846476))], (15443 ^ _779327) ^ [_1040271] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1040271) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19449 ^ _779327) ^ [_1110404, _1110406, _1110408] : [class_Fields_Olinordered__field(_1110404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110404), _1110406), c_Groups_Ozero__class_Ozero(_1110404))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110404), c_Groups_Ozero__class_Ozero(_1110404)), _1110408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110404), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1110404), _1110406), _1110408)), c_Groups_Ozero__class_Ozero(_1110404))))], (39826 ^ _779327) ^ [_1535552, _1535554, _1535556] : [hBOOL(hAPP(_1535552, _1535554)), -(hAPP(c_Set_OCollect(_1535556), hAPP(hAPP(c_COMBS(_1535556, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535556), c_fconj), hAPP(hAPP(c_COMBC(_1535556, _1535556, tc_HOL_Obool), c_fequal), _1535554))), _1535552)) = hAPP(hAPP(c_Set_Oinsert(_1535556), _1535554), c_Orderings_Obot__class_Obot(tc_fun(_1535556, tc_HOL_Obool))))], (43812 ^ _779327) ^ [_1637371, _1637373, _1637375, _1637377] : [-(hAPP(c_Set_Oimage(_1637371, _1637373, _1637375), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637371, tc_HOL_Obool), _1637377)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637371, tc_HOL_Obool), tc_fun(_1637373, tc_HOL_Obool)), _1637377), c_Set_Oimage(_1637371, _1637373, _1637375)))], (41451 ^ _779327) ^ [] : [-(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))], (41750 ^ _779327) ^ [_1589385, _1589387, _1589389] : [-(hAPP(c_New__DSequence_Opos__single(_1589385, _1589387), _1589389) = hAPP(c_Lazy__Sequence_Osingle(_1589385), _1589387))], (17186 ^ _779327) ^ [_1071057, _1071059] : [class_Int_Onumber__ring(_1071057), class_Rings_Olinordered__idom(_1071057), 17193 ^ _779327 : [(17200 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071057), c_Groups_Ozero__class_Ozero(_1071057)), hAPP(c_Int_Onumber__class_Onumber__of(_1071057), _1071059))))], (17194 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071057), c_Groups_Ozero__class_Ozero(_1071057)), hAPP(c_Int_Onumber__class_Onumber__of(_1071057), _1071059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1071059)))]]], (33732 ^ _779327) ^ [_1395796, _1395798, _1395800, _1395802, _1395804, _1395806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395802, _1395802)), hAPP(hAPP(c_Product__Type_OPair(_1395802, _1395802), hAPP(_1395806, _1395798)), hAPP(_1395806, _1395800))), _1395804)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395796, _1395796)), hAPP(hAPP(c_Product__Type_OPair(_1395796, _1395796), _1395798), _1395800)), hAPP(hAPP(c_Relation_Oinv__image(_1395802, _1395796), _1395804), _1395806))))], (39032 ^ _779327) ^ [_1517546, _1517548, _1517550] : [c_Relation_Orefl__on(_1517546, _1517548, _1517550), 39035 ^ _779327 : [(39038 ^ _779327) ^ [_1517728] : [hBOOL(hAPP(hAPP(c_member(_1517546), _1517728), _1517548)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517546, _1517546)), hAPP(hAPP(c_Product__Type_OPair(_1517546, _1517546), _1517728), _1517728)), _1517550)))], (39036 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517546, _1517546), tc_HOL_Obool)), _1517550), hAPP(hAPP(c_Product__Type_OSigma(_1517546, _1517546), _1517548), hAPP(c_COMBK(tc_fun(_1517546, tc_HOL_Obool), _1517546), _1517548)))))]]], (14129 ^ _779327) ^ [_1016932, _1016934, _1016936] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016932), _1016934)), _1016936) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1016934), _1016936)))], (31051 ^ _779327) ^ [_1341552, _1341554, _1341556, _1341558] : [hBOOL(hAPP(hAPP(c_member(_1341552), _1341554), c_SetInterval_Oord_OlessThan(_1341552, _1341556, _1341558))), -(hBOOL(hAPP(hAPP(_1341556, _1341554), _1341558)))], (30037 ^ _779327) ^ [_1316492, _1316494, _1316496, _1316498] : [hAPP(hAPP(c_COMBC(_1316492, tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_fun(_1316494, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1316494, tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_fun(_1316494, tc_HOL_Obool)), _1316492), c_COMBC(_1316494, tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1316494, tc_prod(_1316492, _1316494)), tc_fun(_1316494, tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), _1316492), hAPP(c_COMBB(tc_prod(_1316492, _1316494), tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool), _1316494), c_member(tc_prod(_1316492, _1316494)))), c_Product__Type_OPair(_1316492, _1316494)))), _1316496) = hAPP(hAPP(c_COMBC(_1316492, tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_fun(_1316494, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1316494, tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_fun(_1316494, tc_HOL_Obool)), _1316492), c_COMBC(_1316494, tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1316494, tc_prod(_1316492, _1316494)), tc_fun(_1316494, tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool)), _1316492), hAPP(c_COMBB(tc_prod(_1316492, _1316494), tc_fun(tc_fun(tc_prod(_1316492, _1316494), tc_HOL_Obool), tc_HOL_Obool), _1316494), c_member(tc_prod(_1316492, _1316494)))), c_Product__Type_OPair(_1316492, _1316494)))), _1316498), -(_1316496 = _1316498)], (23534 ^ _779327) ^ [_1188964, _1188966] : [-(c_Divides_Odivmod__nat(_1188964, _1188966) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1188964, _1188966)))], (26069 ^ _779327) ^ [_1236979, _1236981, _1236983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236979)), 26072 ^ _779327 : [(26073 ^ _779327) ^ [_1237113] : [26075 ^ _779327 : [(26081 ^ _779327) ^ [] : [-(_1237113 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26077 ^ [_1236979, _1236981, _1236983, _1237113]), 26074 ^ [_1236979, _1236981, _1236983, _1237113]))], (26079 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26077 ^ [_1236979, _1236981, _1236983, _1237113]), _1236981)))], (26076 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26074 ^ [_1236979, _1236981, _1236983, _1237113]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1236979))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237113), _1236983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1237113), _1236979)), _1236983)))]]], (12978 ^ _779327) ^ [_996139, _996141] : [class_Rings_Ocomm__ring__1(_996139), -(hAPP(c_Groups_Ouminus__class_Ouminus(_996139), _996141) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996139), hAPP(c_Groups_Ouminus__class_Ouminus(_996139), c_Groups_Oone__class_Oone(_996139))), _996141))], (48790 ^ _779327) ^ [_1757524, _1757526] : [c_List_Oupt(_1757524, _1757526) = c_List_Olist_ONil(tc_Nat_Onat), -(_1757526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757526), _1757524)))], (8186 ^ _779327) ^ [_909675, _909677, _909679, _909681] : [class_Rings_Olinordered__ring__strict(_909675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909675), _909677), _909679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909675), _909681), c_Groups_Ozero__class_Ozero(_909675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909675), _909679), _909681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_909675), _909677), _909681))))], (7570 ^ _779327) ^ [_898408, _898410, _898412] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898408), _898410) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _898408), _898412), -(_898410 = _898412), -(_898408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31994 ^ _779327) ^ [_1360551, _1360553] : [class_Int_Oring__char__0(_1360551), hBOOL(hAPP(hAPP(c_member(_1360551), _1360553), c_Int_Oring__1__class_OInts(_1360551))), 32001 ^ _779327 : [(32008 ^ _779327) ^ [] : [_1360553 = c_Groups_Ozero__class_Ozero(_1360551), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360551), _1360553), _1360553) = c_Groups_Ozero__class_Ozero(_1360551))], (32002 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360551), _1360553), _1360553) = c_Groups_Ozero__class_Ozero(_1360551), -(_1360553 = c_Groups_Ozero__class_Ozero(_1360551))]]], (26538 ^ _779327) ^ [_1246620] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1246620)) = hAPP(c_Nat_OSuc, _1246620))], (36070 ^ _779327) ^ [_1448738, _1448740, _1448742, _1448744, _1448746, _1448748, _1448750, _1448752, _1448754, _1448756] : [c_Equiv__Relations_Ocongruent2(_1448738, _1448740, _1448742, _1448744, _1448746, _1448748), hBOOL(hAPP(hAPP(c_member(tc_prod(_1448738, _1448738)), hAPP(hAPP(c_Product__Type_OPair(_1448738, _1448738), _1448750), _1448752)), _1448744)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1448740, _1448740)), hAPP(hAPP(c_Product__Type_OPair(_1448740, _1448740), _1448754), _1448756)), _1448746)), -(hAPP(hAPP(_1448748, _1448750), _1448754) = hAPP(hAPP(_1448748, _1448752), _1448756))], (17438 ^ _779327) ^ [_1075414, _1075416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075414), _1075416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1075414)), c_Int_OBit1(_1075416))))], (37197 ^ _779327) ^ [_1474386, _1474388, _1474390, _1474392, _1474394] : [c_Fun_Oinj__on(_1474386, _1474388, _1474390, _1474392), hBOOL(hAPP(hAPP(c_member(_1474386), _1474394), _1474392)), -(hAPP(c_Fun_Othe__inv__into(_1474386, _1474388, _1474392, _1474390), hAPP(_1474390, _1474394)) = _1474394)], (3456 ^ _779327) ^ [_831470, _831472, _831474, _831476, _831478, _831480, _831482, _831484] : [-(c_New__Random__Sequence_Oneg__bind(_831484, _831480, _831476, _831472) = c_New__Random__Sequence_Oneg__bind(_831482, _831478, _831474, _831470)), _831484 = _831482, _831480 = _831478, _831476 = _831474, _831472 = _831470], (44761 ^ _779327) ^ [_1662100, _1662102, _1662104, _1662106] : [c_List_Olistrelp(_1662100, hAPP(hAPP(c_COMBC(_1662100, tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_fun(_1662100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662100, tc_fun(tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_fun(_1662100, tc_HOL_Obool)), _1662100), c_COMBC(_1662100, tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662100, tc_prod(_1662100, _1662100)), tc_fun(_1662100, tc_fun(tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_HOL_Obool)), _1662100), hAPP(c_COMBB(tc_prod(_1662100, _1662100), tc_fun(tc_fun(tc_prod(_1662100, _1662100), tc_HOL_Obool), tc_HOL_Obool), _1662100), c_member(tc_prod(_1662100, _1662100)))), c_Product__Type_OPair(_1662100, _1662100)))), _1662102), _1662104, _1662106), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662100), tc_List_Olist(_1662100))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662100), tc_List_Olist(_1662100)), _1662104), _1662106)), c_List_Olistrel(_1662100, _1662102))))], (52714 ^ _779327) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (12566 ^ _779327) ^ [_988872, _988874, _988876, _988878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988872), _988874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988876), _988878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988872), _988876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988874), _988878))))], (29140 ^ _779327) ^ [_1298544, _1298546, _1298548, _1298550, _1298552] : [_1298544 = c_Orderings_Obot__class_Obot(tc_fun(_1298546, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298548, tc_HOL_Obool)), _1298550), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298546, tc_fun(_1298548, tc_HOL_Obool)), _1298544), _1298552)) = _1298550)], (42480 ^ _779327) ^ [_1607088, _1607090] : [-(c_Relation_Oirrefl(_1607088, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1607088, _1607088), tc_HOL_Obool)), _1607090), c_Relation_OId(_1607088))))], (45235 ^ _779327) ^ [_1674583, _1674585, _1674587] : [45237 ^ _779327 : [(45240 ^ _779327) ^ [] : [hBOOL(hAPP(_1674587, 45236 ^ [_1674583, _1674585, _1674587]))], (45238 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1674583), 45236 ^ [_1674583, _1674585, _1674587]), hAPP(c_List_Oset(_1674583), _1674585))))]], 45241 ^ _779327 : [(45242 ^ _779327) ^ [_1674767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1674767), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674583)), _1674585))), -(hBOOL(hAPP(_1674587, hAPP(hAPP(c_List_Onth(_1674583), _1674585), _1674767))))]]], (1948 ^ _779327) ^ [_806665, _806667] : [-(class_Rings_Odvd(_806665)), _806667 = _806665, class_Rings_Odvd(_806667)], (34144 ^ _779327) ^ [_1404803, _1404805, _1404807, _1404809, _1404811, _1404813] : [-(hAPP(c_Relation_OImage(_1404803, _1404805, _1404807), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404809, tc_fun(_1404803, tc_HOL_Obool)), _1404811), _1404813)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404809, tc_fun(_1404805, tc_HOL_Obool)), _1404811), hAPP(hAPP(c_COMBB(tc_fun(_1404803, tc_HOL_Obool), tc_fun(_1404805, tc_HOL_Obool), _1404809), c_Relation_OImage(_1404803, _1404805, _1404807)), _1404813)))], (19153 ^ _779327) ^ [_1105724, _1105726, _1105728, _1105730] : [class_Rings_Odivision__ring(_1105724), -(_1105726 = c_Groups_Ozero__class_Ozero(_1105724)), 19160 ^ _779327 : [(19167 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105724), _1105728), _1105726) = _1105730, -(_1105728 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105724), _1105730), _1105726))], (19161 ^ _779327) ^ [] : [_1105728 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105724), _1105730), _1105726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105724), _1105728), _1105726) = _1105730)]]], (40070 ^ _779327) ^ [_1544580, _1544582, _1544584] : [class_Groups_Olinordered__ab__semigroup__add(_1544580), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544580), _1544582)), -(_1544582 = c_Orderings_Obot__class_Obot(tc_fun(_1544580, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1544580), _1544584), c_Big__Operators_Olinorder__class_OMin(_1544580, _1544582)) = c_Big__Operators_Olinorder__class_OMin(_1544580, hAPP(c_Set_OCollect(_1544580), hAPP(hAPP(c_COMBB(tc_fun(_1544580, tc_HOL_Obool), tc_HOL_Obool, _1544580), c_HOL_OEx(_1544580)), hAPP(hAPP(c_COMBC(_1544580, tc_fun(_1544580, tc_HOL_Obool), tc_fun(_1544580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544580, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1544580, tc_HOL_Obool), tc_fun(_1544580, tc_HOL_Obool)), _1544580), c_COMBS(_1544580, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544580, tc_HOL_Obool), tc_fun(_1544580, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1544580), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544580), c_fconj)), hAPP(hAPP(c_COMBC(_1544580, tc_fun(_1544580, _1544580), tc_fun(_1544580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544580, tc_HOL_Obool), tc_fun(tc_fun(_1544580, _1544580), tc_fun(_1544580, tc_HOL_Obool)), _1544580), c_COMBB(_1544580, tc_HOL_Obool, _1544580)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1544580), _1544584))))), hAPP(hAPP(c_COMBC(_1544580, tc_fun(_1544580, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544580)), _1544582))))))], (40587 ^ _779327) ^ [_1562185, _1562187, _1562189] : [c_Wellfounded_Owf(_1562185, _1562187), -(c_Wellfounded_Owf(_1562185, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1562185, _1562185), tc_HOL_Obool)), _1562187), _1562189)))], (6362 ^ _779327) ^ [_879335, _879337, _879339] : [class_Orderings_Opreorder(_879335), _879337 = _879339, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879335), _879337), _879339)))], (25560 ^ _779327) ^ [_1226337, _1226339, _1226341] : [class_Orderings_Olinorder(_1226337), 25563 ^ _779327 : [(25570 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226337), _1226339), _1226341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226337, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226337), _1226339)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226337), _1226341))))], (25564 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226337, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226337), _1226339)), hAPP(c_SetInterval_Oord__class_OlessThan(_1226337), _1226341))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226337), _1226339), _1226341)))]]], (17574 ^ _779327) ^ [_1077596, _1077598] : [c_Int_Oiszero(_1077596, hAPP(c_Int_Onumber__class_Onumber__of(_1077596), c_Int_OBit1(_1077598))), class_Int_Onumber__ring(_1077596), class_Int_Oring__char__0(_1077596)], (17284 ^ _779327) ^ [_1072645, _1072647] : [class_Int_Onumber__ring(_1072645), 17287 ^ _779327 : [(17294 ^ _779327) ^ [] : [c_Int_Oiszero(_1072645, hAPP(c_Int_Onumber__class_Onumber__of(_1072645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072647), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1072645), _1072647) = c_Groups_Ozero__class_Ozero(_1072645))], (17288 ^ _779327) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1072645), _1072647) = c_Groups_Ozero__class_Ozero(_1072645), -(c_Int_Oiszero(_1072645, hAPP(c_Int_Onumber__class_Onumber__of(_1072645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1072647), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (17840 ^ _779327) ^ [_1082048, _1082050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082048)), -(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)))), _1082050))), 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)))), _1082048)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1082050), _1082048))], (27825 ^ _779327) ^ [_1273998, _1274000, _1274002] : [class_Complete__Lattice_Ocomplete__lattice(_1273998), c_Orderings_Oorder__class_Omono(_1273998, _1273998, _1274000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273998), _1274002), hAPP(_1274000, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273998), _1274002), c_Inductive_Ocomplete__lattice__class_Ogfp(_1273998, _1274000))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273998), _1274002), c_Inductive_Ocomplete__lattice__class_Ogfp(_1273998, _1274000))))], (48894 ^ _779327) ^ [_1759420, _1759422, _1759424, _1759426] : [class_Groups_Ocomm__monoid__add(_1759420), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1759420), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1759420), _1759422), c_List_Oupt(_1759424, _1759426))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1759420), _1759422), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1759424, _1759426))))], (45544 ^ _779327) ^ [_1682490, _1682492] : [-(hAPP(hAPP(c_List_Ozip(_1682490, _1682490), _1682492), _1682492) = hAPP(hAPP(c_List_Omap(_1682490, tc_prod(_1682490, _1682490)), hAPP(hAPP(c_COMBS(_1682490, _1682490, tc_prod(_1682490, _1682490)), c_Product__Type_OPair(_1682490, _1682490)), c_COMBI(_1682490))), _1682492))], (39686 ^ _779327) ^ [_1532251, _1532253] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1532251)), -(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)), _1532251))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1532253))))) = 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)), _1532251))), 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, _1532253))))))], (38862 ^ _779327) ^ [_1514088, _1514090, _1514092, _1514094, _1514096, _1514098] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514088, _1514090)), hAPP(hAPP(c_Product__Type_OPair(_1514088, _1514090), _1514092), _1514094)), hAPP(hAPP(c_Product__Type_OSigma(_1514088, _1514090), _1514096), _1514098))), -(hBOOL(hAPP(hAPP(c_member(_1514090), _1514094), hAPP(_1514098, _1514092))))], (22453 ^ _779327) ^ [_1167864, _1167866, _1167868] : [class_Orderings_Olinorder(_1167864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167864), _1167866), _1167868)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167864), _1167866), _1167868) = _1167866)], (49569 ^ _779327) ^ [_1772535, _1772537, _1772539, _1772541] : [hAPP(c_List_Orev(_1772535), _1772537) = hAPP(hAPP(c_List_Olist_OCons(_1772535), _1772539), _1772541), -(_1772537 = hAPP(hAPP(c_List_Oappend(_1772535), hAPP(c_List_Orev(_1772535), _1772541)), hAPP(hAPP(c_List_Olist_OCons(_1772535), _1772539), c_List_Olist_ONil(_1772535))))], (14929 ^ _779327) ^ [_1030482, _1030484] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1030482) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1030484), 14932 ^ _779327 : [(14939 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030482)))), 14942 ^ _779327 : [(14949 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030484)))), -(_1030482 = _1030484)], (14943 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030484))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030482) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (14933 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030484)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (52664 ^ _779327) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (20928 ^ _779327) ^ [_1137839, _1137841] : [-(c_Random_Olog(_1137839, _1137841) = 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(_1137839, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1137841), _1137839)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1137839), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1137841), _1137839)))], (36642 ^ _779327) ^ [_1462829, _1462831, _1462833] : [class_Lattices_Olattice(_1462829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462829), _1462831)), -(_1462831 = c_Orderings_Obot__class_Obot(tc_fun(_1462829, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462829), _1462833)), -(_1462833 = c_Orderings_Obot__class_Obot(tc_fun(_1462829, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462829, tc_HOL_Obool)), _1462831), _1462833) = c_Orderings_Obot__class_Obot(tc_fun(_1462829, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1462829, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462829, tc_HOL_Obool)), _1462831), _1462833)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1462829), c_Big__Operators_Olattice__class_OInf__fin(_1462829, _1462831)), c_Big__Operators_Olattice__class_OInf__fin(_1462829, _1462833)))], (29234 ^ _779327) ^ [_1300584, _1300586, _1300588] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1300584, _1300586) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1300588), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1300584 = _1300586, _1300586 = _1300588], (42084 ^ _779327) ^ [_1596679, _1596681] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596679, _1596679)), _1596681)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596679, _1596679)), c_Transitive__Closure_Otrancl(_1596679, _1596681))))], (21368 ^ _779327) ^ [_1146992, _1146994] : [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), _1146992))), 21371 ^ _779327 : [(21378 ^ _779327) ^ [] : [-(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), _1146994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146994), 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), _1146992)))))], (21372 ^ _779327) ^ [] : [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), _1146994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992)) = 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), _1146994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1146992))))]]], (15153 ^ _779327) ^ [_1034491] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1034491)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1034491)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1034491)))], (26348 ^ _779327) ^ [_1242932, _1242934, _1242936, _1242938] : [class_Groups_Ocomm__monoid__add(_1242932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242934), _1242936)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242932), _1242938), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1242934, _1242936)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1242932), hAPP(_1242938, _1242934)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1242932), _1242938), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1242934, _1242936))))], (47052 ^ _779327) ^ [_1718476, _1718478, _1718480] : [hBOOL(hAPP(c_List_Odistinct(_1718476), hAPP(c_List_Orotate(_1718476, _1718478), _1718480))), -(hBOOL(hAPP(c_List_Odistinct(_1718476), _1718480)))], (22321 ^ _779327) ^ [_1165341] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1165341)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1165341)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16405 ^ _779327) ^ [_1057259, _1057261, _1057263] : [class_Groups_Oordered__ab__group__add__abs(_1057259), -(hAPP(c_Groups_Oabs__class_Oabs(_1057259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057259), hAPP(c_Groups_Oabs__class_Oabs(_1057259), _1057261)), hAPP(c_Groups_Oabs__class_Oabs(_1057259), _1057263))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057259), hAPP(c_Groups_Oabs__class_Oabs(_1057259), _1057261)), hAPP(c_Groups_Oabs__class_Oabs(_1057259), _1057263)))], (46403 ^ _779327) ^ [_1703663, _1703665, _1703667, _1703669, _1703671, _1703673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703663), tc_List_Olist(_1703663))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1703663), tc_List_Olist(_1703663)), hAPP(hAPP(c_List_Oappend(_1703663), _1703665), hAPP(hAPP(c_List_Olist_OCons(_1703663), _1703667), c_List_Olist_ONil(_1703663)))), hAPP(hAPP(c_List_Oappend(_1703663), _1703669), hAPP(hAPP(c_List_Olist_OCons(_1703663), _1703671), c_List_Olist_ONil(_1703663))))), c_List_Olistrel1(_1703663, _1703673))), 46408 ^ _779327 : [(46411 ^ _779327) ^ [] : [-(_1703667 = _1703671)], (46409 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703663), tc_List_Olist(_1703663))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1703663), tc_List_Olist(_1703663)), _1703665), _1703669)), c_List_Olistrel1(_1703663, _1703673))))]], 46412 ^ _779327 : [(46415 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1703663, _1703663)), hAPP(hAPP(c_Product__Type_OPair(_1703663, _1703663), _1703667), _1703671)), _1703673)))], (46413 ^ _779327) ^ [] : [-(_1703665 = _1703669)]]], (52668 ^ _779327) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52706 ^ _779327) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (37703 ^ _779327) ^ [_1485297] : [class_Finite__Set_Ofinite(_1485297), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1485297), c_Orderings_Otop__class_Otop(tc_fun(_1485297, tc_HOL_Obool)))))], (52688 ^ _779327) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (28427 ^ _779327) ^ [_1285388, _1285390, _1285392] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285388), _1285390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1285388), _1285390)), hAPP(c_Finite__Set_Ocard(_1285388), hAPP(hAPP(c_Set_Oinsert(_1285388), _1285392), _1285390)))))], (42611 ^ _779327) ^ [_1610275, _1610277, _1610279] : [c_Equiv__Relations_Oequiv(_1610275, _1610277, _1610279), -(hAPP(hAPP(c_Relation_Orel__comp(_1610275, _1610275, _1610275), hAPP(c_Relation_Oconverse(_1610275, _1610275), _1610279)), _1610279) = _1610279)], (18344 ^ _779327) ^ [_1090895, _1090897, _1090899] : [class_Groups_Omonoid__mult(_1090895), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090895), _1090897), 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)))), _1090899)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1090895), hAPP(hAPP(c_Power_Opower__class_Opower(_1090895), _1090897), _1090899)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17960 ^ _779327) ^ [_1084188, _1084190] : [c_Int_OBit1(_1084188) = c_Int_OBit0(_1084190)], (10899 ^ _779327) ^ [_956999, _957001, _957003] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956999), _957001)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956999), _957003)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _957001), _957003))], (39146 ^ _779327) ^ [_1520511, _1520513, _1520515] : [class_Lattices_Oab__semigroup__idem__mult(_1520511), -(_1520513 = c_Orderings_Obot__class_Obot(tc_fun(_1520511, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520511), _1520513)), -(hAPP(c_Finite__Set_Ofold1(_1520511, c_Groups_Otimes__class_Otimes(_1520511)), hAPP(hAPP(c_Set_Oinsert(_1520511), _1520515), _1520513)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1520511), _1520515), hAPP(c_Finite__Set_Ofold1(_1520511, c_Groups_Otimes__class_Otimes(_1520511)), _1520513)))], (21236 ^ _779327) ^ [_1144053, _1144055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1144053)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1144055))), -(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(_1144055))), 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), _1144053)), c_Int_Onat))))))], (28638 ^ _779327) ^ [_1289655, _1289657, _1289659] : [hBOOL(hAPP(hAPP(c_member(_1289657), _1289655), c_Orderings_Obot__class_Obot(tc_fun(_1289657, tc_HOL_Obool)))), -(hBOOL(hAPP(_1289659, _1289655)))], (27871 ^ _779327) ^ [_1274817, _1274819] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1274817, _1274819))))], (39404 ^ _779327) ^ [_1525645, _1525647, _1525649, _1525651, _1525653, _1525655] : [class_Groups_Ocomm__monoid__mult(_1525645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525647), _1525649)), 39414 ^ _779327 : [(39417 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525651), hAPP(_1525653, 39413 ^ [_1525645, _1525647, _1525649, _1525651, _1525653, _1525655])))], (39415 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525647), 39413 ^ [_1525645, _1525647, _1525649, _1525651, _1525653, _1525655]), _1525649)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1525645, _1525647, c_Groups_Otimes__class_Otimes(_1525645)), hAPP(hAPP(c_COMBS(_1525647, tc_fun(_1525651, tc_HOL_Obool), _1525645), hAPP(hAPP(c_COMBC(_1525647, _1525645, tc_fun(tc_fun(_1525651, tc_HOL_Obool), _1525645)), hAPP(hAPP(c_COMBB(tc_fun(_1525651, _1525645), tc_fun(_1525645, tc_fun(tc_fun(_1525651, tc_HOL_Obool), _1525645)), _1525647), c_Finite__Set_Ofold__image(_1525645, _1525651, c_Groups_Otimes__class_Otimes(_1525645))), _1525655)), c_Groups_Oone__class_Oone(_1525645))), _1525653)), c_Groups_Oone__class_Oone(_1525645)), _1525649) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1525645, tc_prod(_1525647, _1525651), c_Groups_Otimes__class_Otimes(_1525645)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525647, _1525651, _1525645), _1525655)), c_Groups_Oone__class_Oone(_1525645)), hAPP(hAPP(c_Product__Type_OSigma(_1525647, _1525651), _1525649), _1525653)))], (30941 ^ _779327) ^ [_1339170, _1339172, _1339174, _1339176, _1339178, _1339180, _1339182] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339170, tc_fun(_1339172, tc_fun(_1339174, tc_HOL_Obool))), _1339176), _1339178), _1339180), _1339182))), 30942 ^ _779327 : [(30943 ^ _779327) ^ [_1339255] : [hBOOL(hAPP(hAPP(c_member(_1339170), _1339255), _1339176)), hBOOL(hAPP(hAPP(hAPP(_1339178, _1339255), _1339180), _1339182))]]], (48629 ^ _779327) ^ [_1753009, _1753011, _1753013, _1753015] : [-(c_List_Otranspose(_1753009, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753011), tc_List_Olist(_1753009)), hAPP(c_List_Omap(_1753011, _1753009), _1753013)), _1753015)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753011), tc_List_Olist(_1753009)), hAPP(c_List_Omap(_1753011, _1753009), _1753013)), c_List_Otranspose(_1753011, _1753015)))], (46974 ^ _779327) ^ [_1716891, _1716893, _1716895] : [-(hBOOL(hAPP(c_List_Odistinct(_1716891), hAPP(hAPP(c_List_Oappend(_1716891), _1716893), _1716895)))), hBOOL(hAPP(c_List_Odistinct(_1716891), _1716893)), hBOOL(hAPP(c_List_Odistinct(_1716891), _1716895)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1716891, tc_HOL_Obool)), hAPP(c_List_Oset(_1716891), _1716893)), hAPP(c_List_Oset(_1716891), _1716895)) = c_Orderings_Obot__class_Obot(tc_fun(_1716891, tc_HOL_Obool))], (29967 ^ _779327) ^ [_1315061, _1315063, _1315065, _1315067] : [hBOOL(hAPP(hAPP(c_member(_1315061), _1315063), _1315065)), -(hBOOL(hAPP(hAPP(c_member(_1315061), _1315063), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315061, tc_HOL_Obool)), _1315067), _1315065))))], (30843 ^ _779327) ^ [_1337061, _1337063, _1337065, _1337067, _1337069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1337061, _1337063)), hAPP(hAPP(c_Product__Type_OPair(_1337061, _1337063), _1337067), _1337069)), _1337065)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1337061, _1337063, _1337065), _1337067), _1337069)))], (33672 ^ _779327) ^ [_1394021, _1394023, _1394025, _1394027] : [c_FunDef_Oreduction__pair(_1394021, _1394023), -(c_FunDef_Oreduction__pair(_1394025, hAPP(hAPP(c_FunDef_Orp__inv__image(_1394021, _1394025), _1394023), _1394027)))], (1518 ^ _779327) ^ [_801290, _801292] : [-(class_Lazy__Sequence_Osmall__lazy(_801290)), _801292 = _801290, class_Lazy__Sequence_Osmall__lazy(_801292)], (35407 ^ _779327) ^ [_1434191, _1434193, _1434195, _1434197] : [class_Orderings_Oorder(_1434191), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1434191, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434191, _1434193), _1434195)), c_SetInterval_Oord__class_OatLeastAtMost(_1434191, _1434195, _1434197)) = c_Orderings_Obot__class_Obot(tc_fun(_1434191, tc_HOL_Obool)))], (39324 ^ _779327) ^ [_1523715, _1523717, _1523719] : [class_Orderings_Olinorder(_1523715), -(_1523717 = c_Orderings_Obot__class_Obot(tc_fun(_1523715, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523715, tc_HOL_Obool)), _1523717), _1523719)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523715), _1523719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1523715), hAPP(c_Finite__Set_Ofold1(_1523715, c_Orderings_Oord__class_Omin(_1523715)), _1523719)), hAPP(c_Finite__Set_Ofold1(_1523715, c_Orderings_Oord__class_Omin(_1523715)), _1523717))))], (49730 ^ _779327) ^ [_1775991, _1775993, _1775995, _1775997, _1775999] : [-(hAPP(hAPP(c_List_Ozip(_1775991, _1775993), c_List_OtakeWhile(_1775991, _1775995, _1775997)), _1775999) = c_List_OtakeWhile(tc_prod(_1775991, _1775993), hAPP(c_Fun_Ocomp(_1775991, tc_HOL_Obool, tc_prod(_1775991, _1775993), _1775995), c_Product__Type_Ofst(_1775991, _1775993)), hAPP(hAPP(c_List_Ozip(_1775991, _1775993), _1775997), _1775999)))], (4962 ^ _779327) ^ [_854965, _854967] : [_854967 = _854965, -(c_List_Omember(_854967) = c_List_Omember(_854965))], (36919 ^ _779327) ^ [_1468242, _1468244, _1468246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468242), _1468244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468242, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468242, _1468242, _1468246), _1468244)), _1468244)), c_Fun_Oinj__on(_1468242, _1468242, _1468246, _1468244), -(hAPP(c_Set_Oimage(_1468242, _1468242, _1468246), _1468244) = _1468244)], (27440 ^ _779327) ^ [_1264692, _1264694, _1264696] : [class_Orderings_Olinorder(_1264692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264692), _1264694), _1264696)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264692, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1264692), _1264694)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1264692, _1264694, _1264696)) = hAPP(c_SetInterval_Oord__class_OatMost(_1264692), _1264696))], (40046 ^ _779327) ^ [_1543583] : [-(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)))), _1543583))))], (11851 ^ _779327) ^ [_975698, _975700, _975702] : [class_Rings_Oring(_975698), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975698), hAPP(c_Groups_Ouminus__class_Ouminus(_975698), _975700)), hAPP(c_Groups_Ouminus__class_Ouminus(_975698), _975702)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975698), _975700), _975702))], (19817 ^ _779327) ^ [_1117288, _1117290, _1117292, _1117294] : [class_Fields_Ofield__inverse__zero(_1117288), -(_1117290 = c_Groups_Ozero__class_Ozero(_1117288)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117288), _1117292), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117288), _1117294), _1117290)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117288), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117288), _1117294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117288), _1117292), _1117290))), _1117290))], (27256 ^ _779327) ^ [_1260518, _1260520, _1260522, _1260524, _1260526] : [c_Orderings_Oorder__class_Omono(tc_fun(_1260518, tc_HOL_Obool), tc_fun(_1260520, tc_HOL_Obool), _1260522), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260520, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260520, tc_HOL_Obool)), hAPP(_1260522, _1260524)), hAPP(_1260522, _1260526))), hAPP(_1260522, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260518, tc_HOL_Obool)), _1260524), _1260526)))))], (53092 ^ _779327) ^ [_1841650, _1841652] : [-(hBOOL(_1841650)), -(hBOOL(hAPP(hAPP(c_fimplies, _1841650), _1841652)))], (30211 ^ _779327) ^ [_1322554, _1322556, _1322558, _1322560, _1322562, _1322564] : [hBOOL(hAPP(hAPP(c_member(_1322554), _1322556), _1322558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322560, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1322554, _1322560, _1322562), _1322558)), hAPP(_1322564, hAPP(c_Set_Oimage(_1322554, _1322560, _1322562), _1322558)))), -(hBOOL(hAPP(hAPP(c_member(_1322560), hAPP(_1322562, _1322556)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1322560, tc_HOL_Obool), _1322564))))], (32362 ^ _779327) ^ [_1367406, _1367408, _1367410] : [class_Orderings_Olinorder(_1367406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367406), _1367408)), hBOOL(hAPP(hAPP(c_member(_1367406), _1367410), _1367408)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367406), _1367410), c_Big__Operators_Olinorder__class_OMin(_1367406, _1367408)) = c_Big__Operators_Olinorder__class_OMin(_1367406, _1367408))], (27366 ^ _779327) ^ [_1263224, _1263226, _1263228] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1263224, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1263224, tc_HOL_Obool)), _1263226), _1263228)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263224, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1263224, tc_HOL_Obool)), _1263226)), _1263228))], (40015 ^ _779327) ^ [_1542454, _1542456, _1542458, _1542460] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542454), hAPP(c_Set_OCollect(_1542454), _1542456))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542458), hAPP(c_Set_OCollect(_1542458), hAPP(hAPP(c_COMBB(tc_fun(_1542454, tc_HOL_Obool), tc_HOL_Obool, _1542458), c_HOL_OEx(_1542454)), hAPP(hAPP(c_COMBC(_1542458, tc_fun(_1542454, tc_HOL_Obool), tc_fun(_1542454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542454, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1542454, tc_HOL_Obool), tc_fun(_1542454, tc_HOL_Obool)), _1542458), c_COMBS(_1542454, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542454, tc_HOL_Obool), tc_fun(_1542454, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1542458), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542454), c_fconj)), hAPP(hAPP(c_COMBC(_1542458, tc_fun(_1542454, _1542458), tc_fun(_1542454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542458, tc_HOL_Obool), tc_fun(tc_fun(_1542454, _1542458), tc_fun(_1542454, tc_HOL_Obool)), _1542458), c_COMBB(_1542458, tc_HOL_Obool, _1542454)), c_fequal)), _1542460)))), _1542456))))))], (32486 ^ _779327) ^ [_1369525, _1369527] : [class_Groups_Olinordered__ab__group__add(_1369525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369525), _1369527)), -(_1369527 = c_Orderings_Obot__class_Obot(tc_fun(_1369525, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1369525), c_Big__Operators_Olinorder__class_OMin(_1369525, _1369527)) = c_Big__Operators_Olinorder__class_OMax(_1369525, hAPP(c_Set_Oimage(_1369525, _1369525, c_Groups_Ouminus__class_Ouminus(_1369525)), _1369527)))], (8530 ^ _779327) ^ [_915928, _915930, _915932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _915928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _915928), _915930)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _915928), _915932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915930), _915932)))], (45639 ^ _779327) ^ [_1685482, _1685484, _1685486, _1685488, _1685490, _1685492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685482, _1685484)), hAPP(hAPP(c_Product__Type_OPair(_1685482, _1685484), _1685486), _1685488)), hAPP(c_List_Oset(tc_prod(_1685482, _1685484)), hAPP(hAPP(c_List_Ozip(_1685482, _1685484), _1685490), _1685492)))), 45642 ^ _779327 : [(45645 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685484), _1685488), hAPP(c_List_Oset(_1685484), _1685492))))], (45643 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685482), _1685486), hAPP(c_List_Oset(_1685482), _1685490))))]]], (16373 ^ _779327) ^ [_1056767, _1056769, _1056771] : [class_Groups_Oordered__ab__group__add__abs(_1056767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056767), hAPP(c_Groups_Oabs__class_Oabs(_1056767), _1056769)), _1056771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056767), _1056769), _1056771)))], (4508 ^ _779327) ^ [_847900, _847902, _847904, _847906, _847908, _847910, _847912, _847914] : [-(c_List_Ofoldl(_847914, _847910, _847906, _847902) = c_List_Ofoldl(_847912, _847908, _847904, _847900)), _847914 = _847912, _847910 = _847908, _847906 = _847904, _847902 = _847900], (26635 ^ _779327) ^ [_1248191, _1248193] : [c_Nat__Transfer_Ois__nat(_1248191), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1248191, _1248193)))], (43921 ^ _779327) ^ [_1640083, _1640085, _1640087] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640083, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1640083, tc_HOL_Obool)), _1640085), _1640087)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640083, tc_HOL_Obool)), _1640085), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640083, tc_HOL_Obool), _1640087)))], (33222 ^ _779327) ^ [_1383982, _1383984, _1383986, _1383988, _1383990] : [class_Groups_Ocomm__monoid__mult(_1383982), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383984), _1383986)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383984, _1383982), hAPP(hAPP(c_COMBS(_1383984, _1383982, _1383982), hAPP(hAPP(c_COMBB(_1383982, tc_fun(_1383982, _1383982), _1383984), c_Groups_Otimes__class_Otimes(_1383982)), _1383988)), _1383990)), _1383986) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383982), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383984, _1383982), _1383988), _1383986)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383984, _1383982), _1383990), _1383986)))], (22433 ^ _779327) ^ [_1167506, _1167508, _1167510, _1167512] : [class_Orderings_Olinorder(_1167506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167506), _1167508), _1167510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167506), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1167506), _1167508), _1167512)), _1167510)))], (43820 ^ _779327) ^ [_1637675, _1637677, _1637679] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1637675, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1637675, tc_HOL_Obool), _1637677)), _1637679) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1637675, tc_HOL_Obool), tc_fun(_1637675, tc_HOL_Obool)), _1637677), hAPP(hAPP(c_COMBC(tc_fun(_1637675, tc_HOL_Obool), tc_fun(_1637675, tc_HOL_Obool), tc_fun(_1637675, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1637675, tc_HOL_Obool))), _1637679)))], (21064 ^ _779327) ^ [_1140110, _1140112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1140110)), _1140112)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1140110), _1140112)))], (25975 ^ _779327) ^ [_1235057, _1235059] : [25983 ^ _779327 : [(25986 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1235059, 25982 ^ [_1235057, _1235059])))], (25984 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25982 ^ [_1235057, _1235059]), _1235057)))]], 25976 ^ _779327 : [(25977 ^ _779327) ^ [_1235126] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1235126), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1235057))), hBOOL(hAPP(_1235059, _1235126))]]], (47072 ^ _779327) ^ [_1718947, _1718949, _1718951, _1718953] : [class_Groups_Osemigroup__add(_1718947), -(hAPP(c_List_Ofoldl(_1718947, _1718947, c_Groups_Oplus__class_Oplus(_1718947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1718947), _1718949), _1718951)), _1718953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1718947), _1718949), hAPP(c_List_Ofoldl(_1718947, _1718947, c_Groups_Oplus__class_Oplus(_1718947), _1718951), _1718953)))], (32466 ^ _779327) ^ [_1369055, _1369057, _1369059] : [class_Orderings_Olinorder(_1369055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369055), _1369057)), 32473 ^ _779327 : [(32480 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369055, tc_HOL_Obool)), _1369057), hAPP(hAPP(c_Set_Oinsert(_1369055), _1369059), c_Orderings_Obot__class_Obot(tc_fun(_1369055, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369055, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1369055, hAPP(hAPP(c_Set_Oinsert(_1369055), _1369059), _1369057)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369055), _1369059), c_Big__Operators_Olinorder__class_OMin(_1369055, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369055, tc_HOL_Obool)), _1369057), hAPP(hAPP(c_Set_Oinsert(_1369055), _1369059), c_Orderings_Obot__class_Obot(tc_fun(_1369055, tc_HOL_Obool)))))))], (32474 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369055, tc_HOL_Obool)), _1369057), hAPP(hAPP(c_Set_Oinsert(_1369055), _1369059), c_Orderings_Obot__class_Obot(tc_fun(_1369055, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369055, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1369055, hAPP(hAPP(c_Set_Oinsert(_1369055), _1369059), _1369057)) = _1369059)]]], (28846 ^ _779327) ^ [_1293546, _1293548, _1293550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1293546, tc_HOL_Obool)), _1293548), hAPP(hAPP(c_Set_Oinsert(_1293546), _1293550), c_Orderings_Obot__class_Obot(tc_fun(_1293546, tc_HOL_Obool))))), -(_1293548 = c_Orderings_Obot__class_Obot(tc_fun(_1293546, tc_HOL_Obool))), -(_1293548 = hAPP(hAPP(c_Set_Oinsert(_1293546), _1293550), c_Orderings_Obot__class_Obot(tc_fun(_1293546, tc_HOL_Obool))))], (31314 ^ _779327) ^ [_1346868, _1346870, _1346872, _1346874] : [-(c_Nitpick_Ofold__graph_H(_1346868, _1346870, _1346872, _1346874, c_Orderings_Obot__class_Obot(tc_fun(_1346868, tc_HOL_Obool)), _1346874))], (5066 ^ _779327) ^ [_856583, _856585, _856587, _856589, _856591, _856593] : [-(c_Lazy__Sequence_Oappend(_856593, _856589, _856585) = c_Lazy__Sequence_Oappend(_856591, _856587, _856583)), _856593 = _856591, _856589 = _856587, _856585 = _856583], (27839 ^ _779327) ^ [_1274247, _1274249, _1274251] : [class_Complete__Lattice_Ocomplete__lattice(_1274247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274247), _1274249), hAPP(_1274251, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274247), _1274249), c_Inductive_Ocomplete__lattice__class_Ogfp(_1274247, _1274251))))), c_Orderings_Oorder__class_Omono(_1274247, _1274247, _1274251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274247), _1274249), c_Inductive_Ocomplete__lattice__class_Ogfp(_1274247, _1274251))), hAPP(_1274251, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274247), _1274249), c_Inductive_Ocomplete__lattice__class_Ogfp(_1274247, _1274251))))))], (14835 ^ _779327) ^ [_1028839, _1028841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028839), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1028841), _1028839)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028839), _1028841) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6793 ^ _779327) ^ [_885521, _885523, _885525] : [class_Orderings_Olinorder(_885521), 6796 ^ _779327 : [(6803 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885521), _885525), _885523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885521), _885523), _885525))], (6797 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885521), _885523), _885525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885521), _885525), _885523)))]]], (33563 ^ _779327) ^ [_1391205] : [-(_1391205 = 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)), _1391205), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (22983 ^ _779327) ^ [_1177540, _1177542, _1177544, _1177546] : [class_Orderings_Olinorder(_1177540), 22986 ^ _779327 : [(22987 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177540), _1177544), _1177546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), _1177544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), _1177546)))], (22997 ^ _779327) ^ [] : [22998 ^ _779327 : [(23001 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), _1177546))], (22999 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), _1177544))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177540), _1177542), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1177540), _1177544), _1177546))))]]], (40712 ^ _779327) ^ [_1564859, _1564861, _1564863] : [c_Wellfounded_Owf(_1564859, _1564861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564859, tc_HOL_Obool)), _1564863), hAPP(c_Relation_OImage(_1564859, _1564859, _1564861), _1564863))), -(_1564863 = c_Orderings_Obot__class_Obot(tc_fun(_1564859, tc_HOL_Obool)))], (28772 ^ _779327) ^ [_1292255, _1292257, _1292259] : [class_Lattices_Obounded__lattice__bot(_1292255), 28775 ^ _779327 : [(28784 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292255), _1292257), _1292259) = c_Orderings_Obot__class_Obot(_1292255)), _1292257 = c_Orderings_Obot__class_Obot(_1292255), _1292259 = c_Orderings_Obot__class_Obot(_1292255)], (28776 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292255), _1292257), _1292259) = c_Orderings_Obot__class_Obot(_1292255), 28779 ^ _779327 : [(28782 ^ _779327) ^ [] : [-(_1292259 = c_Orderings_Obot__class_Obot(_1292255))], (28780 ^ _779327) ^ [] : [-(_1292257 = c_Orderings_Obot__class_Obot(_1292255))]]]]], (46700 ^ _779327) ^ [_1711411, _1711413, _1711415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711413)), _1711415))), -(_1711415 = hAPP(hAPP(c_List_Oappend(_1711413), hAPP(hAPP(c_List_Otake(_1711413), _1711411), _1711415)), hAPP(hAPP(c_List_Olist_OCons(_1711413), hAPP(hAPP(c_List_Onth(_1711413), _1711415), _1711411)), hAPP(hAPP(c_List_Odrop(_1711413), hAPP(c_Nat_OSuc, _1711411)), _1711415))))], (36223 ^ _779327) ^ [_1453842, _1453844, _1453846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1453842), _1453844)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453842), _1453846)), 36233 ^ _779327 : [(36236 ^ _779327) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36234 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1453842), 36232 ^ [_1453842, _1453844, _1453846]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453842, tc_HOL_Obool)), _1453844), _1453846))))]], -(hAPP(c_Finite__Set_Ocard(_1453842), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1453842, tc_HOL_Obool)), _1453844), _1453846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1453842), _1453844)), hAPP(c_Finite__Set_Ocard(_1453842), _1453846)))], (44051 ^ _779327) ^ [_1642690, _1642692] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1642690, tc_HOL_Obool), _1642692) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1642690, tc_HOL_Obool), tc_fun(_1642690, tc_HOL_Obool)), _1642692), c_COMBI(tc_fun(_1642690, tc_HOL_Obool))))], (13971 ^ _779327) ^ [_1013988, _1013990, _1013992] : [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), _1013988), _1013990)), _1013992))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013992), _1013988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013990)))], (33473 ^ _779327) ^ [_1389442, _1389444, _1389446, _1389448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1389442), _1389444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1389446), _1389448)), -(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), _1389442), _1389446)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1389444), _1389448))), c_FunDef_Opair__less)))], (34637 ^ _779327) ^ [_1417243, _1417245, _1417247, _1417249, _1417251] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417243, tc_fun(_1417245, tc_HOL_Obool)), _1417247), hAPP(hAPP(c_COMBC(_1417243, tc_fun(_1417245, tc_HOL_Obool), tc_fun(_1417245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1417245, tc_HOL_Obool), tc_fun(tc_fun(_1417245, tc_HOL_Obool), tc_fun(_1417245, tc_HOL_Obool)), _1417243), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417245, tc_HOL_Obool))), _1417249)), _1417251)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417245, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417243, tc_fun(_1417245, tc_HOL_Obool)), _1417247), _1417249)), _1417251))], (18688 ^ _779327) ^ [_1097342] : [_1097342 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1097342) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28354 ^ _779327) ^ [_1283971, _1283973, _1283975] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283971), _1283973)), 28357 ^ _779327 : [(28364 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283971), _1283975)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283971, tc_HOL_Obool)), _1283975), _1283973))))], (28358 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283971, tc_HOL_Obool)), _1283975), _1283973))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283971), _1283975)))]]], (6546 ^ _779327) ^ [_882013, _882015, _882017, _882019, _882021] : [class_Orderings_Oorder(_882013), class_Orderings_Olinorder(_882015), c_Orderings_Oorder__class_Ostrict__mono(_882015, _882013, _882017), 6557 ^ _779327 : [(6564 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882015), _882019), _882021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882013), hAPP(_882017, _882019)), hAPP(_882017, _882021))))], (6558 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882013), hAPP(_882017, _882019)), hAPP(_882017, _882021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_882015), _882019), _882021)))]]], (9399 ^ _779327) ^ [_931616, _931618] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931616), _931618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931618), _931616)))], (3310 ^ _779327) ^ [_829103, _829105, _829107, _829109, _829111, _829113] : [-(c_Predicate_ORangeP(_829113, _829109, _829105) = c_Predicate_ORangeP(_829111, _829107, _829103)), _829113 = _829111, _829109 = _829107, _829105 = _829103], (30523 ^ _779327) ^ [_1330042, _1330044, _1330046, _1330048, _1330050] : [_1330042 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1330044, tc_HOL_Obool), _1330046), c_Orderings_Oorder__class_Omono(tc_fun(_1330044, tc_HOL_Obool), tc_fun(_1330044, tc_HOL_Obool), _1330046), hBOOL(hAPP(hAPP(c_member(_1330044), _1330048), _1330050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330044, tc_HOL_Obool)), _1330050), hAPP(_1330046, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330044, tc_HOL_Obool)), _1330050), _1330042)))), -(hBOOL(hAPP(hAPP(c_member(_1330044), _1330048), _1330042)))], (31880 ^ _779327) ^ [_1358665, _1358667] : [class_Rings_Oring__1(_1358665), -(hBOOL(hAPP(hAPP(c_member(_1358665), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1358665), _1358667)), c_Int_Oring__1__class_OInts(_1358665))))], (49449 ^ _779327) ^ [_1769993, _1769995] : [_1769995 = c_List_Olist_ONil(_1769993), -(c_List_Olist_ONil(_1769993) = hAPP(c_List_Orev(_1769993), _1769995))], (17904 ^ _779327) ^ [_1083269, _1083271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083269), _1083271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1083269)), c_Int_OBit0(_1083271))))], (42906 ^ _779327) ^ [_1617474, _1617476, _1617478, _1617480] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617474, _1617474), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1617476), _1617478)), _1617480) = hAPP(hAPP(c_Relation_Orel__comp(_1617474, _1617474, _1617474), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617474, _1617474), tc_HOL_Obool), _1617476), _1617480)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1617474, _1617474), tc_HOL_Obool), _1617478), _1617480)))], (27542 ^ _779327) ^ [_1266675, _1266677, _1266679] : [class_Orderings_Olinorder(_1266675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266675), _1266677), _1266679)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266675, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1266675, _1266677, _1266679)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1266675), _1266679)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1266675), _1266677))], (31471 ^ _779327) ^ [_1350035, _1350037, _1350039] : [class_Orderings_Owellorder(_1350035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350035), _1350037), c_Orderings_Oord__class_OLeast(_1350035, _1350039))), hBOOL(hAPP(_1350039, _1350037))], (9777 ^ _779327) ^ [_937785, _937787] : [class_Groups_Ocomm__monoid__mult(_937785), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937785), _937787), c_Groups_Oone__class_Oone(_937785)) = _937787)], (48413 ^ _779327) ^ [_1747457, _1747459, _1747461, _1747463] : [-(hAPP(hAPP(c_List_Omap(_1747457, _1747459), _1747461), c_List_Oconcat(_1747457, _1747463)) = c_List_Oconcat(_1747459, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747457), tc_List_Olist(_1747459)), hAPP(c_List_Omap(_1747457, _1747459), _1747461)), _1747463)))], (51891 ^ _779327) ^ [_1823997, _1823999, _1824001, _1824003] : [c_Predicate_Osymp(_1823997, _1823999), hBOOL(hAPP(hAPP(_1823999, _1824001), _1824003)), -(hBOOL(hAPP(hAPP(_1823999, _1824003), _1824001)))], (22039 ^ _779327) ^ [_1159703, _1159705, _1159707, _1159709, _1159711] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1159703, _1159705), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1159707), _1159709))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159705)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159711), _1159703), _1159705), 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), _1159711), _1159707)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159711), _1159709)), _1159705))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1159711), _1159709), _1159705)))))], (46459 ^ _779327) ^ [_1705355] : [c_List_Onat__list(_1705355), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1705355)))], (21076 ^ _779327) ^ [_1140346, _1140348, _1140350, _1140352, _1140354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140346, tc_HOL_Obool)), _1140348), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1140350, tc_fun(_1140346, tc_HOL_Obool)), _1140352), _1140354))), 21079 ^ _779327 : [(21080 ^ _779327) ^ [_1140479] : [hBOOL(hAPP(hAPP(c_member(_1140350), _1140479), _1140352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140346, tc_HOL_Obool)), _1140348), hAPP(_1140354, _1140479))))]]], (10129 ^ _779327) ^ [_943288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943288)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _943288)) = _943288)], (37877 ^ _779327) ^ [_1488378, _1488380, _1488382, _1488384] : [hBOOL(hAPP(hAPP(c_member(_1488380), _1488384), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488378, tc_fun(_1488380, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488378, tc_HOL_Obool))), _1488382))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488378, tc_fun(_1488380, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1488378, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1488380, tc_HOL_Obool), tc_fun(_1488380, tc_HOL_Obool), _1488378), hAPP(c_COMBC(_1488380, tc_fun(_1488380, tc_HOL_Obool), tc_HOL_Obool), c_member(_1488380))), _1488382)), _1488384)))], (13569 ^ _779327) ^ [_1006668, _1006670, _1006672, _1006674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006668), _1006670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1006672), _1006674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1006668), _1006672)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1006670), _1006674))))], (43071 ^ _779327) ^ [_1622342, _1622344, _1622346, _1622348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622342, _1622342)), hAPP(hAPP(c_Product__Type_OPair(_1622342, _1622342), _1622344), _1622346)), c_Transitive__Closure_Otrancl(_1622342, _1622348))), 43075 ^ _779327 : [(43078 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622342, _1622342)), hAPP(hAPP(c_Product__Type_OPair(_1622342, _1622342), 43074 ^ [_1622342, _1622344, _1622346, _1622348]), _1622346)), _1622348)))], (43076 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622342, _1622342)), hAPP(hAPP(c_Product__Type_OPair(_1622342, _1622342), _1622344), 43074 ^ [_1622342, _1622344, _1622346, _1622348])), c_Transitive__Closure_Ortrancl(_1622342, _1622348))))]]], (35057 ^ _779327) ^ [_1425972, _1425974, _1425976, _1425978] : [class_Lattices_Odistrib__lattice(_1425972), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425972), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425972), _1425974), _1425976)), _1425978) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425972), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425972), _1425974), _1425978)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1425972), _1425976), _1425978)))], (33016 ^ _779327) ^ [_1380315, _1380317, _1380319, _1380321, _1380323] : [c_Fun_Ofun__upd(_1380315, _1380317, _1380319, _1380321, _1380323) = _1380319, -(hAPP(_1380319, _1380321) = _1380323)], (36354 ^ _779327) ^ [_1456809, _1456811, _1456813, _1456815, _1456817] : [class_Groups_Ocomm__monoid__add(_1456809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456811), _1456813)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456811), _1456815)), 36368 ^ _779327 : [(36371 ^ _779327) ^ [] : [hAPP(_1456817, 36367 ^ [_1456809, _1456811, _1456813, _1456815, _1456817]) = c_Groups_Ozero__class_Ozero(_1456809)], (36369 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456811), 36367 ^ [_1456809, _1456811, _1456813, _1456815, _1456817]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456811, tc_HOL_Obool)), _1456813), _1456815))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456811, _1456809), _1456817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456811, tc_HOL_Obool)), _1456813), _1456815)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456809), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456811, _1456809), _1456817), _1456813)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456811, _1456809), _1456817), _1456815)))], (23923 ^ _779327) ^ [_1196229, _1196231] : [class_Rings_Ocomm__semiring__1(_1196229), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1196229), c_Groups_Oone__class_Oone(_1196229)), _1196231)))], (36536 ^ _779327) ^ [_1461065, _1461067, _1461069] : [class_Lattices_Olattice(_1461065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461065), _1461067)), -(_1461067 = c_Orderings_Obot__class_Obot(tc_fun(_1461065, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1461065, hAPP(hAPP(c_Set_Oinsert(_1461065), _1461069), _1461067)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1461065), _1461069), c_Big__Operators_Olattice__class_OInf__fin(_1461065, _1461067)))], (14479 ^ _779327) ^ [_1023530] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023530)))], (52778 ^ _779327) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (38812 ^ _779327) ^ [_1512535, _1512537, _1512539, _1512541, _1512543] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1512535, _1512537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512535, tc_HOL_Obool)), _1512539), _1512541)), _1512543) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512535, _1512537), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1512535, _1512537), _1512539), _1512543)), hAPP(hAPP(c_Product__Type_OSigma(_1512535, _1512537), _1512541), _1512543)))], (18188 ^ _779327) ^ [_1088174, _1088176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088174), _1088176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1088174)), c_Int_OBit1(_1088176))))], (26643 ^ _779327) ^ [_1248313, _1248315] : [class_Orderings_Olinorder(_1248313), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1248313, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1248313), _1248315)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1248313), _1248315))], (19485 ^ _779327) ^ [_1111082, _1111084, _1111086, _1111088, _1111090] : [class_Fields_Olinordered__field(_1111082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111082), c_Groups_Ozero__class_Ozero(_1111082)), _1111084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111082), _1111084), _1111086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111082), c_Groups_Ozero__class_Ozero(_1111082)), _1111088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111082), _1111088), _1111090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111082), _1111084), _1111090)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1111082), _1111086), _1111088))))], (51364 ^ _779327) ^ [_1811291, _1811293, _1811295] : [c_List_Olist__ex1(_1811291, _1811293, _1811295), 51368 ^ _779327 : [(51373 ^ _779327) ^ [_1811537] : [-(_1811537 = 51367 ^ [_1811291, _1811293, _1811295]), hBOOL(hAPP(hAPP(c_member(_1811291), _1811537), hAPP(c_List_Oset(_1811291), _1811295))), hBOOL(hAPP(_1811293, _1811537))], (51371 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1811293, 51367 ^ [_1811291, _1811293, _1811295])))], (51369 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811291), 51367 ^ [_1811291, _1811293, _1811295]), hAPP(c_List_Oset(_1811291), _1811295))))]]], (37845 ^ _779327) ^ [_1487694, _1487696] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487694, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487694, tc_HOL_Obool)), _1487696)), _1487696) = c_Orderings_Otop__class_Otop(tc_fun(_1487694, tc_HOL_Obool)))], (8664 ^ _779327) ^ [_918134, _918136, _918138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918134), _918136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918134), _918138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918136), _918138))))], (51713 ^ _779327) ^ [_1818928, _1818930] : [-(c_Relation_Otrans(_1818928, c_Transitive__Closure_Ortrancl(_1818928, _1818930)))], (39824 ^ _779327) ^ [_1535447, _1535449, _1535451] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535447, tc_HOL_Obool)), _1535449), _1535451) = hAPP(c_Set_OCollect(_1535447), hAPP(hAPP(c_COMBS(_1535447, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535447), c_fconj), hAPP(hAPP(c_COMBC(_1535447, tc_fun(_1535447, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535447)), _1535449))), hAPP(hAPP(c_COMBC(_1535447, tc_fun(_1535447, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535447)), _1535451))))], (30079 ^ _779327) ^ [_1319477, _1319479, _1319481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319477, tc_HOL_Obool)), _1319479), _1319481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319477, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1319477, tc_fun(_1319477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319477)), _1319479)), hAPP(hAPP(c_COMBC(_1319477, tc_fun(_1319477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319477)), _1319481))))], (34270 ^ _779327) ^ [_1408514, _1408516] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408514), c_Orderings_Obot__class_Obot(tc_fun(_1408514, tc_HOL_Obool))), _1408516) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408514, tc_HOL_Obool), tc_HOL_Obool)))], (48394 ^ _779327) ^ [_1747088, _1747090] : [48396 ^ _779327 : [(48399 ^ _779327) ^ [] : [48395 ^ [_1747088, _1747090] = c_List_Olist_ONil(_1747088)], (48397 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1747088)), 48395 ^ [_1747088, _1747090]), hAPP(c_List_Oset(tc_List_Olist(_1747088)), _1747090))))]], -(c_List_Oconcat(_1747088, _1747090) = c_List_Olist_ONil(_1747088))], (50140 ^ _779327) ^ [_1784407, _1784409, _1784411, _1784413] : [-(c_List_Oconcat(_1784407, hAPP(hAPP(c_List_Omap(_1784409, tc_List_Olist(_1784407)), _1784411), _1784413)) = c_List_Omaps(_1784409, _1784407, _1784411, _1784413))], (18602 ^ _779327) ^ [_1095564, _1095566, _1095568] : [class_Rings_Ocomm__semiring__1(_1095564), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095564), _1095566), 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)))), _1095568))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095564), _1095566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095564), hAPP(hAPP(c_Power_Opower__class_Opower(_1095564), _1095566), _1095568)), hAPP(hAPP(c_Power_Opower__class_Opower(_1095564), _1095566), _1095568))))], (39454 ^ _779327) ^ [_1526993, _1526995, _1526997, _1526999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526993), _1526995)), 39460 ^ _779327 : [(39463 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526997), hAPP(_1526999, 39459 ^ [_1526993, _1526995, _1526997, _1526999])))], (39461 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526993), 39459 ^ [_1526993, _1526995, _1526997, _1526999]), _1526995)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1526993, _1526997)), hAPP(hAPP(c_Product__Type_OSigma(_1526993, _1526997), _1526995), _1526999))))], (50046 ^ _779327) ^ [_1782702, _1782704, _1782706, _1782708, _1782710] : [c_Fun_Oinj__on(_1782702, _1782704, _1782706, hAPP(hAPP(c_Set_Oinsert(_1782702), _1782708), hAPP(c_List_Oset(_1782702), _1782710))), -(hAPP(hAPP(c_List_Omap(_1782702, _1782704), _1782706), hAPP(c_List_OremoveAll(_1782702, _1782708), _1782710)) = hAPP(c_List_OremoveAll(_1782704, hAPP(_1782706, _1782708)), hAPP(hAPP(c_List_Omap(_1782702, _1782704), _1782706), _1782710)))], (12219 ^ _779327) ^ [_982581] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982581), _982581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34329 ^ _779327) ^ [_1410039, _1410041] : [-(c_Relation_OId__on(_1410039, _1410041) = hAPP(c_Product__Type_Oprod_Oprod__case(_1410039, _1410039, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1410039, tc_HOL_Obool, tc_fun(_1410039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410039, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1410039, tc_HOL_Obool)), _1410039), c_COMBC(_1410039, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410039, tc_HOL_Obool), tc_fun(_1410039, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1410039), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1410039), c_fconj)), c_fequal))), _1410041)))], (37977 ^ _779327) ^ [_1490597, _1490599, _1490601, _1490603, _1490605] : [c_Fun_Oinj__on(_1490597, _1490599, _1490601, c_Orderings_Otop__class_Otop(tc_fun(_1490597, tc_HOL_Obool))), 37980 ^ _779327 : [(37987 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1490597), _1490603), _1490605)), -(hBOOL(hAPP(hAPP(c_member(_1490599), hAPP(_1490601, _1490603)), hAPP(c_Set_Oimage(_1490597, _1490599, _1490601), _1490605))))], (37981 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1490599), hAPP(_1490601, _1490603)), hAPP(c_Set_Oimage(_1490597, _1490599, _1490601), _1490605))), -(hBOOL(hAPP(hAPP(c_member(_1490597), _1490603), _1490605)))]]], (9306 ^ _779327) ^ [_930119] : [-(hBOOL(hAPP(_930119, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9313 ^ [_930119])))), 9307 ^ _779327 : [(9308 ^ _779327) ^ [_930171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930171)), hBOOL(hAPP(_930119, _930171))]]], (33569 ^ _779327) ^ [_1391250, _1391252, _1391254, _1391256] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1391250), _1391252)), 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)), _1391250), _1391254)), 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)), _1391252), _1391256)), 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)), _1391252), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1391254), _1391256))), c_FunDef_Omin__weak)))], (7332 ^ _779327) ^ [_894219, _894221, _894223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894219), _894221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894219), _894223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894221), _894223))))], (36947 ^ _779327) ^ [_1468824, _1468826, _1468828, _1468830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468824), _1468826)), hAPP(c_Finite__Set_Ocard(_1468828), hAPP(c_Set_Oimage(_1468824, _1468828, _1468830), _1468826)) = hAPP(c_Finite__Set_Ocard(_1468824), _1468826), -(c_Fun_Oinj__on(_1468824, _1468828, _1468830, _1468826))], (13662 ^ _779327) ^ [_1008422, _1008424, _1008426] : [class_Groups_Oordered__comm__monoid__add(_1008422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008422), c_Groups_Ozero__class_Ozero(_1008422)), _1008424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008422), c_Groups_Ozero__class_Ozero(_1008422)), _1008426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008422), c_Groups_Ozero__class_Ozero(_1008422)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008422), _1008424), _1008426))))], (17680 ^ _779327) ^ [_1079215, _1079217] : [class_Groups_Omonoid__mult(_1079215), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079215), _1079217), 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(_1079215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079215), _1079217), _1079217)), _1079217))], (48016 ^ _779327) ^ [_1738785, _1738787, _1738789, _1738791, _1738793, _1738795, _1738797] : [-(c_List_Olist__all2(_1738785, _1738787, _1738789, hAPP(hAPP(c_List_Olist_OCons(_1738785), _1738791), _1738793), hAPP(hAPP(c_List_Olist_OCons(_1738787), _1738795), _1738797))), hBOOL(hAPP(hAPP(_1738789, _1738791), _1738795)), c_List_Olist__all2(_1738785, _1738787, _1738789, _1738793, _1738797)], (27262 ^ _779327) ^ [_1260697, _1260699, _1260701, _1260703] : [class_Lattices_Osemilattice__sup(_1260697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260697), _1260699), _1260701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260697), _1260699), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260697), _1260701), _1260703))))], (16796 ^ _779327) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (37781 ^ _779327) ^ [_1486520, _1486522, _1486524, _1486526] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1486520, _1486522, _1486524), _1486526)), _1486524 = c_Orderings_Obot__class_Obot(tc_fun(_1486520, tc_HOL_Obool))], (11769 ^ _779327) ^ [_974236, _974238] : [class_Groups_Olinordered__ab__group__add(_974236), 11772 ^ _779327 : [(11779 ^ _779327) ^ [] : [_974238 = c_Groups_Ozero__class_Ozero(_974236), -(hAPP(c_Groups_Ouminus__class_Ouminus(_974236), _974238) = _974238)], (11773 ^ _779327) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_974236), _974238) = _974238, -(_974238 = c_Groups_Ozero__class_Ozero(_974236))]]], (42004 ^ _779327) ^ [_1595037, _1595039, _1595041, _1595043, _1595045, _1595047, _1595049, _1595051] : [class_Groups_Ocomm__monoid__add(_1595037), c_Fun_Oinj__on(_1595039, _1595041, _1595043, _1595045), _1595047 = hAPP(c_Set_Oimage(_1595039, _1595041, _1595043), _1595045), 42018 ^ _779327 : [(42021 ^ _779327) ^ [] : [hAPP(_1595049, 42017 ^ [_1595037, _1595039, _1595041, _1595043, _1595045, _1595047, _1595049, _1595051]) = hAPP(_1595051, hAPP(_1595043, 42017 ^ [_1595037, _1595039, _1595041, _1595043, _1595045, _1595047, _1595049, _1595051]))], (42019 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1595039), 42017 ^ [_1595037, _1595039, _1595041, _1595043, _1595045, _1595047, _1595049, _1595051]), _1595045)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1595041, _1595037), _1595051), _1595047) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1595039, _1595037), _1595049), _1595045))], (32652 ^ _779327) ^ [_1372980, _1372982, _1372984] : [class_Orderings_Olinorder(_1372980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372980), _1372982)), hBOOL(hAPP(hAPP(c_member(_1372980), _1372984), _1372982)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372980), _1372984), c_Big__Operators_Olattice_OSup__fin(_1372980, c_Orderings_Oord__class_Omax(_1372980), _1372982)) = _1372984)], (17940 ^ _779327) ^ [_1083909] : [_1083909 = c_Int_OPls, -(c_Int_OBit0(_1083909) = c_Int_OPls)], (29056 ^ _779327) ^ [_1296966, _1296968, _1296970, _1296972] : [_1296966 = c_Orderings_Obot__class_Obot(tc_fun(_1296968, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1296968, _1296970, hAPP(c_COMBK(_1296970, _1296968), _1296972)), _1296966) = c_Orderings_Obot__class_Obot(tc_fun(_1296970, tc_HOL_Obool)))], (26358 ^ _779327) ^ [_1243151, _1243153, _1243155, _1243157] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1243151, tc_Nat_Onat), _1243153), _1243155) = hAPP(c_Nat_OSuc, _1243157), 26362 ^ _779327 : [(26365 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1243153, 26361 ^ [_1243151, _1243153, _1243155, _1243157]))))], (26363 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1243151), 26361 ^ [_1243151, _1243153, _1243155, _1243157]), _1243155)))]]], (14437 ^ _779327) ^ [_1022753, _1022755, _1022757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022753, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022753, tc_HOL_Obool)), _1022755), _1022757)), _1022757) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022753, tc_HOL_Obool)), _1022755), _1022757))], (51911 ^ _779327) ^ [_1824306, _1824308, _1824310, _1824312] : [c_Wellfounded_Omax__extp(_1824306, _1824308, _1824310, _1824312), 51914 ^ _779327 : [(51917 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1824306), _1824312)))], (51919 ^ _779327) ^ [] : [_1824312 = c_Orderings_Obot__class_Obot(tc_fun(_1824306, tc_HOL_Obool))], (51921 ^ _779327) ^ [_1824522] : [hBOOL(hAPP(hAPP(c_member(_1824306), _1824522), _1824310)), 51925 ^ _779327 : [(51928 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1824308, _1824522), 51924 ^ [_1824306, _1824308, _1824310, _1824312, _1824522])))], (51926 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1824306), 51924 ^ [_1824306, _1824308, _1824310, _1824312, _1824522]), _1824312)))]]], (51915 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1824306), _1824310)))]]], (45826 ^ _779327) ^ [_1690507, _1690509] : [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), _1690507), _1690509))), 45829 ^ _779327 : [(45836 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1690507), _1690509))), -(c_List_Oupto(_1690507, _1690509) = c_List_Olist_ONil(tc_Int_Oint))], (45830 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1690507), _1690509)), -(c_List_Oupto(_1690507, _1690509) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1690507), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1690507), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1690509)))]]], (47253 ^ _779327) ^ [_1722916, _1722918, _1722920] : [47254 ^ _779327 : [(47255 ^ _779327) ^ [_1723005, _1723007] : [_1722918 = hAPP(hAPP(c_List_Olist_OCons(_1722916), _1723007), _1723005)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1722916), tc_List_Olist(_1722916))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722916), tc_List_Olist(_1722916)), c_List_Olist_ONil(_1722916)), _1722918)), c_List_Olexord(_1722916, _1722920))))], (42985 ^ _779327) ^ [_1619590, _1619592, _1619594, _1619596, _1619598] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619590, _1619590)), hAPP(hAPP(c_Product__Type_OPair(_1619590, _1619590), _1619592), _1619594)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1619590, _1619590), tc_HOL_Obool), _1619596), _1619598))), 42990 ^ _779327 : [(42993 ^ _779327) ^ [] : [-(_1619592 = _1619594)], (42991 ^ _779327) ^ [] : [-(_1619596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 42996 ^ _779327 : [(43001 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619590, _1619590)), hAPP(hAPP(c_Product__Type_OPair(_1619590, _1619590), 42994 ^ [_1619590, _1619592, _1619594, _1619596, _1619598]), _1619594)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1619590, _1619590), tc_HOL_Obool), 42995 ^ [_1619590, _1619592, _1619594, _1619596, _1619598]), _1619598))))], (42999 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619590, _1619590)), hAPP(hAPP(c_Product__Type_OPair(_1619590, _1619590), _1619592), 42994 ^ [_1619590, _1619592, _1619594, _1619596, _1619598])), _1619598)))], (42997 ^ _779327) ^ [] : [-(_1619596 = hAPP(c_Nat_OSuc, 42995 ^ [_1619590, _1619592, _1619594, _1619596, _1619598]))]]], (52782 ^ _779327) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (20981 ^ _779327) ^ [_1138708, _1138710, _1138712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1138708), _1138710)), -(c_Random_Ominus__shift(_1138712, _1138708, _1138710) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1138712), _1138708)), _1138710))], (52828 ^ _779327) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (5714 ^ _779327) ^ [_869739] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869739), hAPP(c_Nat_OSuc, _869739))))], (16263 ^ _779327) ^ [_1055023, _1055025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055023)), -(c_SMT_Oz3mod(_1055025, _1055023) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1055025, _1055023))], (16495 ^ _779327) ^ [_1058892, _1058894] : [class_Groups_Oordered__ab__group__add__abs(_1058892), 16498 ^ _779327 : [(16505 ^ _779327) ^ [] : [_1058894 = c_Groups_Ozero__class_Ozero(_1058892), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058892), hAPP(c_Groups_Oabs__class_Oabs(_1058892), _1058894)), c_Groups_Ozero__class_Ozero(_1058892))))], (16499 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058892), hAPP(c_Groups_Oabs__class_Oabs(_1058892), _1058894)), c_Groups_Ozero__class_Ozero(_1058892))), -(_1058894 = c_Groups_Ozero__class_Ozero(_1058892))]]], (4032 ^ _779327) ^ [_840528, _840530, _840532, _840534] : [-(c_Product__Type_OSigma(_840534, _840530) = c_Product__Type_OSigma(_840532, _840528)), _840534 = _840532, _840530 = _840528], (12822 ^ _779327) ^ [_993582, _993584] : [class_Groups_Olinordered__ab__group__add(_993582), 12825 ^ _779327 : [(12832 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993582), _993584), c_Groups_Ozero__class_Ozero(_993582))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993582), _993584), hAPP(c_Groups_Ouminus__class_Ouminus(_993582), _993584))))], (12826 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993582), _993584), hAPP(c_Groups_Ouminus__class_Ouminus(_993582), _993584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993582), _993584), c_Groups_Ozero__class_Ozero(_993582))))]]], (1468 ^ _779327) ^ [_800665, _800667] : [-(class_Lattices_Oboolean__algebra(_800665)), _800667 = _800665, class_Lattices_Oboolean__algebra(_800667)], (40853 ^ _779327) ^ [_1568552, _1568554] : [c_Wellfounded_Owf(_1568552, _1568554), -(c_Wellfounded_Owf(tc_List_Olist(_1568552), c_List_Olex(_1568552, _1568554)))], (52670 ^ _779327) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (31233 ^ _779327) ^ [_1345101, _1345103, _1345105, _1345107] : [hBOOL(hAPP(hAPP(_1345105, _1345103), _1345107)), -(hBOOL(hAPP(hAPP(c_member(_1345101), _1345103), c_SetInterval_Oord_OatMost(_1345101, _1345105, _1345107))))], (6140 ^ _779327) ^ [_876048, _876050, _876052, _876054] : [class_Orderings_Oord(_876048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876048), _876050), _876052)), _876052 = _876054, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876048), _876050), _876054)))], (45671 ^ _779327) ^ [_1686256, _1686258, _1686260, _1686262] : [_1686256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1686258), _1686256), hAPP(hAPP(c_List_Olist_OCons(_1686258), _1686260), _1686262)) = c_List_Olist_ONil(_1686258))], (21702 ^ _779327) ^ [_1153141, _1153143, _1153145, _1153147] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153141, _1153143), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1153145), _1153147))), -(_1153143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1153141, _1153143) = _1153147)], (27416 ^ _779327) ^ [_1264228, _1264230, _1264232] : [class_Orderings_Olinorder(_1264228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264228), _1264230), _1264232)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264228, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1264228), _1264230)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1264228, _1264230), _1264232)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1264228), _1264232))], (10153 ^ _779327) ^ [_943662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943662)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _943662)) = _943662)], (33165 ^ _779327) ^ [_1383069, _1383071, _1383073, _1383075] : [class_Groups_Ocomm__monoid__mult(_1383069), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1383071), _1383073))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1383071, _1383069), _1383075), _1383073) = c_Groups_Oone__class_Oone(_1383069))], (2754 ^ _779327) ^ [_820139, _820141, _820143, _820145] : [-(c_Quickcheck_Obeyond(_820145, _820141) = c_Quickcheck_Obeyond(_820143, _820139)), _820145 = _820143, _820141 = _820139], (40052 ^ _779327) ^ [_1544012] : [-(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)))), _1544012)) = 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), _1544012), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (52900 ^ _779327) ^ [_1839461, _1839463] : [-(class_Enum_Oenum(tc_prod(_1839461, _1839463))), class_Enum_Oenum(_1839461), class_Enum_Oenum(_1839463)], (36743 ^ _779327) ^ [_1464938, _1464940, _1464942, _1464944, _1464946, _1464948] : [c_Fun_Oinj__on(_1464938, _1464940, _1464942, _1464944), -(_1464946 = _1464948), hBOOL(hAPP(hAPP(c_member(_1464938), _1464946), _1464944)), hBOOL(hAPP(hAPP(c_member(_1464938), _1464948), _1464944)), hAPP(_1464942, _1464946) = hAPP(_1464942, _1464948)], (17666 ^ _779327) ^ [_1079044] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1079044)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1079044)))], (7438 ^ _779327) ^ [_896234, _896236] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _896234), _896236) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _896236), _896234))], (39342 ^ _779327) ^ [_1524041, _1524043, _1524045, _1524047] : [c_Big__Operators_Osemilattice__big(_1524041, _1524043, _1524045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524041), _1524047)), -(hAPP(_1524045, _1524047) = hAPP(c_Finite__Set_Ofold1(_1524041, _1524043), _1524047))], (42025 ^ _779327) ^ [_1595544, _1595546] : [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), _1595544), _1595546)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1595544), _1595546)))], (9451 ^ _779327) ^ [_932463, _932465, _932467] : [class_Rings_Oring__1(_932463), -(hAPP(c_Int_Oring__1__class_Oof__int(_932463), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _932465), _932467)) = hAPP(hAPP(c_Power_Opower__class_Opower(_932463), hAPP(c_Int_Oring__1__class_Oof__int(_932463), _932465)), _932467))], (24431 ^ _779327) ^ [_1204543, _1204545, _1204547, _1204549] : [class_Rings_Ocomm__semiring__1(_1204543), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204543), _1204545), _1204547)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1204543), hAPP(hAPP(c_Power_Opower__class_Opower(_1204543), _1204545), _1204549)), hAPP(hAPP(c_Power_Opower__class_Opower(_1204543), _1204547), _1204549))))], (566 ^ _779327) ^ [_788026, _788028, _788030, _788032] : [-(c_Relation_Oirrefl(_788030, _788026)), c_Relation_Oirrefl(_788032, _788028), _788032 = _788030, _788028 = _788026], (41557 ^ _779327) ^ [_1585012, _1585014, _1585016, _1585018] : [c_Finite__Set_Ofolding(_1585012, _1585014, _1585016, _1585018), -(hAPP(_1585018, c_Orderings_Obot__class_Obot(tc_fun(_1585012, tc_HOL_Obool))) = c_Fun_Oid(_1585014))], (46397 ^ _779327) ^ [_1703443, _1703445, _1703447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703443), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703445)), _1703447))), -(hAPP(hAPP(c_List_Otake(_1703445), hAPP(c_Nat_OSuc, _1703443)), _1703447) = hAPP(hAPP(c_List_Oappend(_1703445), hAPP(hAPP(c_List_Otake(_1703445), _1703443), _1703447)), hAPP(hAPP(c_List_Olist_OCons(_1703445), hAPP(hAPP(c_List_Onth(_1703445), _1703447), _1703443)), c_List_Olist_ONil(_1703445))))], (35637 ^ _779327) ^ [_1439432, _1439434, _1439436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1439432), _1439434)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1439432), _1439436)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1439432), _1439434)), hAPP(c_Finite__Set_Ocard(_1439432), _1439436)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1439432), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439432, tc_HOL_Obool)), _1439434), _1439436))), hAPP(c_Finite__Set_Ocard(_1439432), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439432, tc_HOL_Obool)), _1439434), _1439436))))], (42603 ^ _779327) ^ [_1610125, _1610127] : [-(c_Transitive__Closure_Otrancl(_1610125, hAPP(c_Relation_Oconverse(_1610125, _1610125), _1610127)) = hAPP(c_Relation_Oconverse(_1610125, _1610125), c_Transitive__Closure_Otrancl(_1610125, _1610127)))], (32920 ^ _779327) ^ [_1378047, _1378049] : [class_Orderings_Olinorder(_1378047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378047), _1378049)), -(_1378049 = c_Orderings_Obot__class_Obot(tc_fun(_1378047, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1378047), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1378047), 32933 ^ [_1378047, _1378049]), 32934 ^ [_1378047, _1378049])), hAPP(hAPP(c_Set_Oinsert(_1378047), 32933 ^ [_1378047, _1378049]), hAPP(hAPP(c_Set_Oinsert(_1378047), 32934 ^ [_1378047, _1378049]), c_Orderings_Obot__class_Obot(tc_fun(_1378047, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1378047), c_Big__Operators_Olattice_OInf__fin(_1378047, c_Orderings_Oord__class_Omin(_1378047), _1378049)), _1378049)))], (13646 ^ _779327) ^ [_1008124, _1008126] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1008124), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1008126)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008124), _1008126)))], (40931 ^ _779327) ^ [_1570320, _1570322, _1570324, _1570326] : [-(hAPP(c_Relation_ODomain(_1570320, _1570322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570320, _1570322), tc_HOL_Obool)), _1570324), _1570326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1570320, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1570320, _1570322), _1570324)), hAPP(c_Relation_ODomain(_1570320, _1570322), _1570326)))], (4672 ^ _779327) ^ [_850522, _850524] : [_850524 = _850522, -(c_List_Odistinct(_850524) = c_List_Odistinct(_850522))], (28584 ^ _779327) ^ [_1288571, _1288573, _1288575] : [hAPP(hAPP(c_Set_Oinsert(_1288571), _1288573), c_Orderings_Obot__class_Obot(tc_fun(_1288571, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1288571), _1288575), c_Orderings_Obot__class_Obot(tc_fun(_1288571, tc_HOL_Obool))), -(_1288573 = _1288575)], (31069 ^ _779327) ^ [_1341906, _1341908, _1341910, _1341912] : [hBOOL(hAPP(hAPP(_1341910, _1341912), _1341908)), -(hBOOL(hAPP(hAPP(c_member(_1341906), _1341908), c_SetInterval_Oord_OgreaterThan(_1341906, _1341910, _1341912))))], (27208 ^ _779327) ^ [_1259458, _1259460, _1259462] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259458, tc_HOL_Obool)), _1259460), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259458, tc_HOL_Obool)), _1259460), _1259462))))], (52834 ^ _779327) ^ [_1838618] : [class_Lazy__Sequence_Osmall__lazy(_1838618), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1838618)))], (3378 ^ _779327) ^ [_830227, _830229] : [_830229 = _830227, -(c_Nitpick_Odenom(_830229) = c_Nitpick_Odenom(_830227))], (38257 ^ _779327) ^ [_1498949, _1498951] : [c_Equiv__Relations_Oequiv(_1498949, c_Orderings_Otop__class_Otop(tc_fun(_1498949, tc_HOL_Obool)), _1498951), -(c_Equiv__Relations_Oequivp(_1498949, hAPP(hAPP(c_COMBC(_1498949, tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_fun(_1498949, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498949, tc_fun(tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_fun(_1498949, tc_HOL_Obool)), _1498949), c_COMBC(_1498949, tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498949, tc_prod(_1498949, _1498949)), tc_fun(_1498949, tc_fun(tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_HOL_Obool)), _1498949), hAPP(c_COMBB(tc_prod(_1498949, _1498949), tc_fun(tc_fun(tc_prod(_1498949, _1498949), tc_HOL_Obool), tc_HOL_Obool), _1498949), c_member(tc_prod(_1498949, _1498949)))), c_Product__Type_OPair(_1498949, _1498949)))), _1498951)))], (27410 ^ _779327) ^ [_1264067, _1264069, _1264071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1264067), _1264069)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1264067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1264069), _1264071)) = 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, _1264067), _1264069)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1264069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1264069), _1264071))))], (50068 ^ _779327) ^ [_1783119, _1783121] : [-(c_List_OremoveAll(_1783119, _1783121) = c_List_Ofilter(_1783119, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1783119), c_fNot), hAPP(c_fequal, _1783121))))], (24143 ^ _779327) ^ [_1199884, _1199886] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199884), _1199886))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199884), _1199886)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199886), _1199884)))], (9617 ^ _779327) ^ [_935119, _935121, _935123] : [class_Rings_Olinordered__semidom(_935119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935119), c_Groups_Oone__class_Oone(_935119)), _935121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _935123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935119), c_Groups_Oone__class_Oone(_935119)), hAPP(hAPP(c_Power_Opower__class_Opower(_935119), _935121), _935123))))], (5730 ^ _779327) ^ [_869968] : [hAPP(c_Nat_OSuc, _869968) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51703 ^ _779327) ^ [_1818789, _1818791] : [c_Relation_Otrans(_1818789, _1818791), -(c_Transitive__Closure_Otrancl(_1818789, _1818791) = _1818791)], (46878 ^ _779327) ^ [_1714692, _1714694, _1714696, _1714698] : [hBOOL(hAPP(c_List_Odistinct(_1714692), _1714694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714696), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714692)), _1714694))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714698), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714692)), _1714694))), 46889 ^ _779327 : [(46896 ^ _779327) ^ [] : [_1714696 = _1714698, -(hAPP(hAPP(c_List_Onth(_1714692), _1714694), _1714696) = hAPP(hAPP(c_List_Onth(_1714692), _1714694), _1714698))], (46890 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Onth(_1714692), _1714694), _1714696) = hAPP(hAPP(c_List_Onth(_1714692), _1714694), _1714698), -(_1714696 = _1714698)]]], (1918 ^ _779327) ^ [_806290, _806292] : [-(class_Groups_Ozero(_806290)), _806292 = _806290, class_Groups_Ozero(_806292)], (37565 ^ _779327) ^ [_1482203, _1482205, _1482207] : [hBOOL(hAPP(hAPP(c_member(_1482203), _1482207), c_Wellfounded_Oacc(_1482203, _1482205))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1482203, hAPP(hAPP(c_COMBC(_1482203, tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_fun(_1482203, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482203, tc_fun(tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_fun(_1482203, tc_HOL_Obool)), _1482203), c_COMBC(_1482203, tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482203, tc_prod(_1482203, _1482203)), tc_fun(_1482203, tc_fun(tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_HOL_Obool)), _1482203), hAPP(c_COMBB(tc_prod(_1482203, _1482203), tc_fun(tc_fun(tc_prod(_1482203, _1482203), tc_HOL_Obool), tc_HOL_Obool), _1482203), c_member(tc_prod(_1482203, _1482203)))), c_Product__Type_OPair(_1482203, _1482203)))), _1482205)), _1482207)))], (21222 ^ _779327) ^ [_1143757, _1143759, _1143761, _1143763] : [-(hAPP(c_Nat_Onat_Onat__rec(_1143757, _1143759, _1143761), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1143763)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1143757), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1143763))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1143757, _1143757), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1143757, tc_fun(_1143757, _1143757)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1143757, tc_fun(_1143757, _1143757)), tc_Int_Oint), c_If(_1143757)), c_Nat__Numeral_Oneg)), _1143759)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1143757, _1143757), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1143757, _1143757), tc_Int_Oint), _1143761), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1143757, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1143757, _1143759, _1143761)), c_Int_Onat)))))], (39525 ^ _779327) ^ [_1528864, _1528866, _1528868, _1528870, _1528872, _1528874, _1528876, _1528878, _1528880, _1528882] : [hAPP(c_Set_Oimage(_1528864, _1528866, _1528868), _1528870) = _1528872, hAPP(c_Set_Oimage(_1528874, _1528876, _1528878), _1528880) = _1528882, -(hAPP(c_Set_Oimage(tc_prod(_1528864, _1528874), tc_prod(_1528866, _1528876), c_Product__Type_Omap__pair(_1528864, _1528866, _1528874, _1528876, _1528868, _1528878)), hAPP(hAPP(c_Product__Type_OSigma(_1528864, _1528874), _1528870), hAPP(c_COMBK(tc_fun(_1528874, tc_HOL_Obool), _1528864), _1528880))) = hAPP(hAPP(c_Product__Type_OSigma(_1528866, _1528876), _1528872), hAPP(c_COMBK(tc_fun(_1528876, tc_HOL_Obool), _1528866), _1528882)))], (34195 ^ _779327) ^ [_1406261, _1406263, _1406265, _1406267, _1406269] : [hBOOL(hAPP(hAPP(c_member(_1406261), _1406263), hAPP(c_Relation_OImage(_1406265, _1406261, _1406267), hAPP(hAPP(c_Set_Oinsert(_1406265), _1406269), c_Orderings_Obot__class_Obot(tc_fun(_1406265, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1406265, _1406261)), hAPP(hAPP(c_Product__Type_OPair(_1406265, _1406261), _1406269), _1406263)), _1406267)))], (9088 ^ _779327) ^ [_926116] : [_926116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _926116) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28254 ^ _779327) ^ [_1282140, _1282142, _1282144] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282140), _1282142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282140, tc_HOL_Obool)), _1282142), _1282144)), -(hAPP(c_Finite__Set_Ocard(_1282140), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282140, tc_HOL_Obool)), _1282144), _1282142)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1282140), _1282144)), hAPP(c_Finite__Set_Ocard(_1282140), _1282142)))], (9262 ^ _779327) ^ [_929298, _929300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _929298), _929300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929298)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929300))))], (29002 ^ _779327) ^ [_1296169, _1296171, _1296173] : [class_Orderings_Oorder(_1296169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296169), _1296171), _1296173)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1296169, _1296173, _1296171) = c_Orderings_Obot__class_Obot(tc_fun(_1296169, tc_HOL_Obool)))], (40885 ^ _779327) ^ [_1569116, _1569118, _1569120, _1569122] : [40887 ^ _779327 : [(40890 ^ _779327) ^ [] : [c_Wellfounded_Owf(_1569118, hAPP(_1569120, 40886 ^ [_1569116, _1569118, _1569120, _1569122]))], (40888 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1569116, 40886 ^ [_1569116, _1569118, _1569120, _1569122])))]], -(c_Wellfounded_Owf(tc_prod(_1569122, _1569118), c_Recdef_Osame__fst(_1569122, _1569118, _1569116, _1569120)))], (44632 ^ _779327) ^ [_1658130, _1658132, _1658134, _1658136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658130), tc_List_Olist(_1658130))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658130), tc_List_Olist(_1658130)), _1658132), _1658134)), c_List_Olistrel1(_1658130, _1658136))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658130)), _1658132) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658130)), _1658134))], (48337 ^ _779327) ^ [_1745929, _1745931] : [_1745931 = c_List_Olist_ONil(_1745929), -(c_List_Oremdups(_1745929, _1745931) = c_List_Olist_ONil(_1745929))], (49493 ^ _779327) ^ [_1770899, _1770901] : [-(hAPP(c_List_Orev(_1770899), c_List_Oconcat(_1770899, _1770901)) = c_List_Oconcat(_1770899, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1770899), tc_List_Olist(_1770899)), c_List_Orev(_1770899)), hAPP(c_List_Orev(tc_List_Olist(_1770899)), _1770901))))], (23786 ^ _779327) ^ [_1193903, _1193905, _1193907] : [hBOOL(hAPP(c_Predicate_OPowp(_1193903, _1193905), _1193907)), 23789 ^ _779327 : [(23790 ^ _779327) ^ [_1193987] : [hBOOL(hAPP(hAPP(c_member(_1193903), _1193987), _1193907)), -(hBOOL(hAPP(_1193905, _1193987)))]]], (46698 ^ _779327) ^ [_1711304, _1711306, _1711308, _1711310, _1711312] : [-(hAPP(hAPP(c_List_Ozip(_1711304, _1711306), _1711308), hAPP(hAPP(c_List_Oappend(_1711306), _1711310), _1711312)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1711304, _1711306)), hAPP(hAPP(c_List_Ozip(_1711304, _1711306), hAPP(hAPP(c_List_Otake(_1711304), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711306)), _1711310)), _1711308)), _1711310)), hAPP(hAPP(c_List_Ozip(_1711304, _1711306), hAPP(hAPP(c_List_Odrop(_1711304), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711306)), _1711310)), _1711308)), _1711312)))], (49151 ^ _779327) ^ [_1763917, _1763919, _1763921, _1763923, _1763925] : [class_Orderings_Olinorder(_1763917), c_List_Olinorder__class_Osorted(_1763917, hAPP(hAPP(c_List_Omap(_1763919, _1763917), _1763921), _1763923)), -(c_List_Olinorder__class_Osorted(_1763917, hAPP(hAPP(c_List_Omap(_1763919, _1763917), _1763921), c_List_Olinorder__class_Oinsort__insert__key(_1763919, _1763917, _1763921, _1763925, _1763923))))], (41766 ^ _779327) ^ [_1589695, _1589697] : [-(c_Hilbert__Choice_OEps(_1589695, hAPP(hAPP(c_COMBC(_1589695, _1589695, tc_HOL_Obool), c_fequal), _1589697)) = _1589697)], (12281 ^ _779327) ^ [_983592, _983594, _983596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _983592), _983594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983592), _983596)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983594), _983596))))], (46846 ^ _779327) ^ [_1714024, _1714026, _1714028] : [-(hAPP(hAPP(c_List_Odrop(_1714024), hAPP(c_Nat_OSuc, _1714026)), _1714028) = hAPP(hAPP(c_List_Odrop(_1714024), _1714026), hAPP(c_List_Otl(_1714024), _1714028)))], (49964 ^ _779327) ^ [_1781000, _1781002, _1781004] : [49966 ^ _779327 : [(49969 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1781002, 49965 ^ [_1781000, _1781002, _1781004])))], (49967 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781000), 49965 ^ [_1781000, _1781002, _1781004]), hAPP(c_List_Oset(_1781000), c_List_OdropWhile(_1781000, _1781002, _1781004)))))]], -(c_List_OtakeWhile(_1781000, _1781002, _1781004) = hAPP(c_List_Ofilter(_1781000, _1781002), _1781004))], (27298 ^ _779327) ^ [_1261479, _1261481, _1261483, _1261485, _1261487] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261479, tc_HOL_Obool)), _1261481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261483, tc_fun(_1261479, tc_HOL_Obool)), _1261485), _1261487)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261483, tc_fun(_1261479, tc_HOL_Obool)), _1261485), hAPP(hAPP(c_COMBB(tc_fun(_1261479, tc_HOL_Obool), tc_fun(_1261479, tc_HOL_Obool), _1261483), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261479, tc_HOL_Obool)), _1261481)), _1261487)))], (47782 ^ _779327) ^ [_1733767, _1733769, _1733771, _1733773] : [-(hBOOL(hAPP(c_List_Olistsp(_1733767, hAPP(hAPP(c_COMBS(_1733767, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1733767), c_fconj), _1733769)), _1733771)), _1733773))), hBOOL(hAPP(c_List_Olistsp(_1733767, _1733769), _1733773)), hBOOL(hAPP(c_List_Olistsp(_1733767, _1733771), _1733773))], (2942 ^ _779327) ^ [_823303, _823305, _823307, _823309, _823311, _823313, _823315, _823317] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_823317, _823313, _823309, _823305) = c_SetInterval_Oord_OgreaterThanLessThan(_823315, _823311, _823307, _823303)), _823317 = _823315, _823313 = _823311, _823309 = _823307, _823305 = _823303], (42703 ^ _779327) ^ [_1612687, _1612689, _1612691] : [c_Relation_Ototal__on(_1612687, _1612689, _1612691), -(c_Relation_Ototal__on(_1612687, _1612689, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1612687, _1612687), tc_HOL_Obool)), _1612691), c_Relation_OId(_1612687))))], (11839 ^ _779327) ^ [_975440, _975442, _975444] : [class_Rings_Oring(_975440), -(hAPP(c_Groups_Ouminus__class_Ouminus(_975440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975440), _975442), _975444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975440), hAPP(c_Groups_Ouminus__class_Ouminus(_975440), _975442)), _975444))], (1878 ^ _779327) ^ [_805790, _805792] : [-(class_Rings_Osemiring(_805790)), _805792 = _805790, class_Rings_Osemiring(_805792)], (42398 ^ _779327) ^ [_1605206] : [-(hAPP(c_Relation_ORange(_1605206, _1605206), c_Relation_OId(_1605206)) = c_Orderings_Otop__class_Otop(tc_fun(_1605206, tc_HOL_Obool)))], (44735 ^ _779327) ^ [_1661316, _1661318, _1661320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1661316, _1661316), tc_HOL_Obool)), _1661318), _1661320)), c_Relation_Orefl__on(_1661316, c_Orderings_Otop__class_Otop(tc_fun(_1661316, tc_HOL_Obool)), _1661320), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1661316), tc_List_Olist(_1661316)), tc_HOL_Obool)), c_List_Olistrel1(_1661316, _1661318)), c_List_Olistrel(_1661316, _1661320))))], (12596 ^ _779327) ^ [_989436, _989438, _989440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989436), _989438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989436), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989440), _989438))))], (51297 ^ _779327) ^ [_1809619, _1809621, _1809623, _1809625] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1809619, _1809621), c_Lazy__Sequence_Olazy__sequence_OInsert(_1809619, _1809623, _1809625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1809621, _1809623)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1809619, _1809621), _1809625))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48411 ^ _779327) ^ [_1747425] : [-(c_List_Oconcat(_1747425, c_List_Olist_ONil(tc_List_Olist(_1747425))) = c_List_Olist_ONil(_1747425))], (4712 ^ _779327) ^ [_851134, _851136, _851138, _851140, _851142, _851144] : [-(c_List_Osplice(_851144, _851140, _851136) = c_List_Osplice(_851142, _851138, _851134)), _851144 = _851142, _851140 = _851138, _851136 = _851134], (38549 ^ _779327) ^ [_1506019, _1506021, _1506023, _1506025, _1506027, _1506029, _1506031] : [c_Typedef_Otype__definition(_1506019, _1506021, _1506023, _1506025, _1506027), 38552 ^ _779327 : [(38559 ^ _779327) ^ [] : [_1506029 = _1506031, -(hAPP(_1506023, _1506029) = hAPP(_1506023, _1506031))], (38553 ^ _779327) ^ [] : [hAPP(_1506023, _1506029) = hAPP(_1506023, _1506031), -(_1506029 = _1506031)]]], (38377 ^ _779327) ^ [_1501718, _1501720, _1501722, _1501724, _1501726] : [hBOOL(hAPP(hAPP(c_member(_1501718), hAPP(_1501720, _1501722)), _1501724)), -(hBOOL(hAPP(hAPP(c_member(_1501726), _1501722), hAPP(c_Set_Ovimage(_1501726, _1501718, _1501720), _1501724))))], (16710 ^ _779327) ^ [_1062760, _1062762] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062760), _1062762))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1062760, _1062762) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1062760), _1062762), _1062762))], (23345 ^ _779327) ^ [_1184766, _1184768] : [-(c_Nitpick_Onumber__of__frac(_1184766, _1184768) = c_Nitpick_OAbs__Frac(_1184766, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184768), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (47774 ^ _779327) ^ [_1733594, _1733596, _1733598, _1733600] : [hBOOL(hAPP(c_List_Olistsp(_1733594, hAPP(hAPP(c_COMBS(_1733594, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1733594), c_fconj), _1733596)), _1733598)), _1733600)), 47777 ^ _779327 : [(47780 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1733594, _1733598), _1733600)))], (47778 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1733594, _1733596), _1733600)))]]], (15772 ^ _779327) ^ [_1046079, _1046081, _1046083] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046079), _1046081)), _1046083) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046079), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1046081), _1046083))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046079), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1046081, _1046083))), _1046083)))], (51251 ^ _779327) ^ [_1808850, _1808852, _1808854] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1808850), hAPP(c_COMBK(_1808850, tc_Nat_Onat), _1808852)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1808854)) = c_List_Oreplicate(_1808850, _1808854, _1808852))], (3614 ^ _779327) ^ [_833913, _833915, _833917, _833919, _833921, _833923] : [-(c_Set_Ovimage(_833923, _833919, _833915) = c_Set_Ovimage(_833921, _833917, _833913)), _833923 = _833921, _833919 = _833917, _833915 = _833913], (47472 ^ _779327) ^ [_1727058, _1727060, _1727062] : [-(_1727058 = c_List_Olist_ONil(_1727060)), -(c_List_Obutlast(_1727060, hAPP(hAPP(c_List_Oappend(_1727060), _1727062), _1727058)) = hAPP(hAPP(c_List_Oappend(_1727060), _1727062), c_List_Obutlast(_1727060, _1727058)))], (43003 ^ _779327) ^ [_1620032, _1620034, _1620036, _1620038, _1620040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620032, _1620032)), hAPP(hAPP(c_Product__Type_OPair(_1620032, _1620032), _1620034), _1620036)), c_Transitive__Closure_Ortrancl(_1620032, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620032, _1620032), tc_HOL_Obool)), _1620038), _1620040)))), 43009 ^ _779327 : [(43015 ^ _779327) ^ [] : [43008 ^ [_1620032, _1620034, _1620036, _1620038, _1620040] = 43011 ^ [_1620032, _1620034, _1620036, _1620038, _1620040]], (43013 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620032, _1620032)), hAPP(hAPP(c_Product__Type_OPair(_1620032, _1620032), 43008 ^ [_1620032, _1620034, _1620036, _1620038, _1620040]), 43011 ^ [_1620032, _1620034, _1620036, _1620038, _1620040])), _1620040)))], (43010 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620032, _1620032)), hAPP(hAPP(c_Product__Type_OPair(_1620032, _1620032), _1620034), 43008 ^ [_1620032, _1620034, _1620036, _1620038, _1620040])), c_Transitive__Closure_Ortrancl(_1620032, _1620038))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620032, _1620032)), hAPP(hAPP(c_Product__Type_OPair(_1620032, _1620032), _1620034), _1620036)), c_Transitive__Closure_Ortrancl(_1620032, _1620038))))], (3980 ^ _779327) ^ [_839708, _839710, _839712, _839714, _839716, _839718] : [-(c_List_Olist_Olist__size(_839718, _839714, _839710) = c_List_Olist_Olist__size(_839716, _839712, _839708)), _839718 = _839716, _839714 = _839712, _839710 = _839708], (24365 ^ _779327) ^ [_1203453, _1203455] : [_1203453 = _1203455, 24368 ^ _779327 : [(24371 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203455), _1203453)))], (24369 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203453), _1203455)))]]], (8540 ^ _779327) ^ [_916124, _916126] : [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), _916124), _916126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _916124))), -(_916126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37799 ^ _779327) ^ [_1486866, _1486868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486866), c_Orderings_Otop__class_Otop(tc_fun(_1486866, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1486866), _1486868) = hAPP(c_Finite__Set_Ocard(_1486866), c_Orderings_Otop__class_Otop(tc_fun(_1486866, tc_HOL_Obool))), -(_1486868 = c_Orderings_Otop__class_Otop(tc_fun(_1486866, tc_HOL_Obool)))], (49681 ^ _779327) ^ [_1774948, _1774950] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1774948), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1774948))), _1774950))), -(c_List_Otranspose(_1774948, c_List_Otranspose(_1774948, _1774950)) = c_List_OtakeWhile(tc_List_Olist(_1774948), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1774948)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1774948), tc_List_Olist(_1774948), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1774948))), _1774950))], (1298 ^ _779327) ^ [_798540, _798542] : [-(class_Divides_Oring__div(_798540)), _798542 = _798540, class_Divides_Oring__div(_798542)], (27350 ^ _779327) ^ [_1262913, _1262915] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1262913), _1262915) = 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)), _1262913)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1262915))))], (27743 ^ _779327) ^ [_1272113, _1272115, _1272117, _1272119, _1272121] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272113, tc_fun(_1272115, tc_HOL_Obool)), _1272117), hAPP(hAPP(c_COMBB(tc_fun(_1272115, tc_HOL_Obool), tc_fun(_1272115, tc_HOL_Obool), _1272113), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272115, tc_HOL_Obool)), _1272119)), _1272121)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272115, tc_HOL_Obool)), _1272119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1272113, tc_fun(_1272115, tc_HOL_Obool)), _1272117), _1272121)))], (31886 ^ _779327) ^ [_1358768, _1358770] : [class_Rings_Oring__1(_1358768), -(hBOOL(hAPP(hAPP(c_member(_1358768), hAPP(c_Int_Oring__1__class_Oof__int(_1358768), _1358770)), c_Int_Oring__1__class_OInts(_1358768))))], (17690 ^ _779327) ^ [] : [-(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)))))], (51217 ^ _779327) ^ [_1807485, _1807487, _1807489, _1807491, _1807493] : [-(c_Predicate_Oconversep(_1807485, _1807487, c_Predicate_Opred__comp(_1807485, _1807489, _1807487, _1807491, _1807493)) = c_Predicate_Opred__comp(_1807487, _1807489, _1807485, c_Predicate_Oconversep(_1807489, _1807487, _1807493), c_Predicate_Oconversep(_1807485, _1807489, _1807491)))], (37396 ^ _779327) ^ [_1478605, _1478607, _1478609, _1478611] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478605), _1478607)), -(hAPP(c_Set_Oimage(_1478605, _1478609, _1478611), _1478607) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1478609, tc_HOL_Obool), _1478605, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478609, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1478605, tc_fun(_1478609, tc_HOL_Obool), tc_fun(_1478609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1478609, tc_fun(tc_fun(_1478609, tc_HOL_Obool), tc_fun(_1478609, tc_HOL_Obool)), _1478605), c_Set_Oinsert(_1478609)), _1478611)), c_Orderings_Obot__class_Obot(tc_fun(_1478609, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1478609, tc_HOL_Obool))), _1478607))], (11971 ^ _779327) ^ [_977906, _977908] : [class_Groups_Ocomm__monoid__add(_977906), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977906), c_Groups_Ozero__class_Ozero(_977906)), _977908) = _977908)], (20944 ^ _779327) ^ [_1138042, _1138044, _1138046] : [class_Fields_Olinordered__field(_1138042), 20950 ^ _779327 : [(20953 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138042), _1138044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138042), _1138046), 20949 ^ [_1138042, _1138044, _1138046])))], (20951 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138042), c_Groups_Ozero__class_Ozero(_1138042)), 20949 ^ [_1138042, _1138044, _1138046])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138042), _1138044), _1138046)))], (51497 ^ _779327) ^ [_1814522, _1814524, _1814526] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814522) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1814522, _1814524, _1814526)], (7536 ^ _779327) ^ [_897840, _897842, _897844] : [class_Rings_Olinordered__semidom(_897840), 7539 ^ _779327 : [(7546 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _897842), _897844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897840), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_897840), _897842)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_897840), _897844))))], (7540 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897840), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_897840), _897842)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_897840), _897844))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _897842), _897844)))]]], (14855 ^ _779327) ^ [_1029181, _1029183, _1029185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029181), _1029183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029185), 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), _1029183), _1029185)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029181), _1029185))))], (23592 ^ _779327) ^ [_1190083, _1190085] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1190083)), hAPP(c_Code__Numeral_Oof__nat, _1190085)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190083), _1190085)))], (10083 ^ _779327) ^ [_942547, _942549] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _942547)), hAPP(c_Int_Onat, _942549)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _942549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _942547), _942549))], (33612 ^ _779327) ^ [_1392137] : [-(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)), _1392137), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (40220 ^ _779327) ^ [_1551599, _1551601, _1551603, _1551605, _1551607] : [_1551599 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1551601, tc_HOL_Obool), _1551603), c_Orderings_Oorder__class_Omono(tc_fun(_1551601, tc_HOL_Obool), tc_fun(_1551601, tc_HOL_Obool), _1551603), hBOOL(hAPP(hAPP(c_member(_1551601), _1551605), _1551599)), 40234 ^ _779327 : [(40237 ^ _779327) ^ [] : [hBOOL(hAPP(_1551607, 40233 ^ [_1551599, _1551601, _1551603, _1551605, _1551607]))], (40235 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551601), 40233 ^ [_1551599, _1551601, _1551603, _1551605, _1551607]), hAPP(_1551603, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551601, tc_HOL_Obool)), _1551599), hAPP(c_Set_OCollect(_1551601), _1551607))))))]], -(hBOOL(hAPP(_1551607, _1551605)))], (27224 ^ _779327) ^ [_1259812, _1259814, _1259816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259812, tc_HOL_Obool)), _1259814), _1259816)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259812, tc_HOL_Obool)), _1259814), _1259816) = _1259816)], (19575 ^ _779327) ^ [_1112797, _1112799, _1112801, _1112803] : [class_Fields_Olinordered__field(_1112797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112797), _1112799), _1112801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112797), c_Groups_Ozero__class_Ozero(_1112797)), _1112803)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112797), c_Groups_Ozero__class_Ozero(_1112797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112797), _1112801), _1112799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112797), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112797), _1112803), _1112801)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1112797), _1112803), _1112799))))], (10177 ^ _779327) ^ [_944022, _944024, _944026] : [class_Rings_Olinordered__idom(_944022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944022), c_Groups_Ozero__class_Ozero(_944022)), _944024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944022), c_Groups_Ozero__class_Ozero(_944022)), _944026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944022), _944026), c_Groups_Oone__class_Oone(_944022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944022), _944026), _944024)), _944024)))], (46180 ^ _779327) ^ [_1698079, _1698081, _1698083, _1698085, _1698087, _1698089] : [-(hAPP(hAPP(c_List_Omap(_1698079, _1698081), _1698083), hAPP(hAPP(c_List_Olist__update(_1698079, _1698085), _1698087), _1698089)) = hAPP(hAPP(c_List_Olist__update(_1698081, hAPP(hAPP(c_List_Omap(_1698079, _1698081), _1698083), _1698085)), _1698087), hAPP(_1698083, _1698089)))], (48227 ^ _779327) ^ [_1743607, _1743609] : [-(c_Enum_On__lists(_1743607, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1743609) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1743607)), c_List_Olist_ONil(_1743607)), c_List_Olist_ONil(tc_List_Olist(_1743607))))], (5870 ^ _779327) ^ [_871876, _871878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _871876), _871878)), -(_871876 = _871878), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871876), _871878)))], (50585 ^ _779327) ^ [_1795039, _1795041] : [class_Enum_Oenum(_1795039), 50588 ^ _779327 : [(50596 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1795039), _1795041)), 50599 ^ _779327 : [(50600 ^ _779327) ^ [_1795257] : [-(hBOOL(hAPP(_1795041, _1795257)))]]], (50589 ^ _779327) ^ [] : [hBOOL(hAPP(_1795041, 50590 ^ [_1795039, _1795041])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1795039), _1795041)))]]], (5764 ^ _779327) ^ [_870446, _870448] : [-(_870446 = _870448), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870446), _870448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870448), _870446)))], (8684 ^ _779327) ^ [_918510, _918512, _918514] : [8685 ^ _779327 : [(8688 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918510), _918514))], (8686 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _918512)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918510), _918512)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _918514), _918512))))], (36333 ^ _779327) ^ [_1456314, _1456316, _1456318, _1456320, _1456322] : [class_Groups_Ocomm__monoid__add(_1456314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456316), _1456318)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456316), _1456320)), 36347 ^ _779327 : [(36350 ^ _779327) ^ [] : [hAPP(_1456322, 36346 ^ [_1456314, _1456316, _1456318, _1456320, _1456322]) = c_Groups_Ozero__class_Ozero(_1456314)], (36348 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456316), 36346 ^ [_1456314, _1456316, _1456318, _1456320, _1456322]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456316, tc_HOL_Obool)), _1456318), _1456320))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456316, _1456314), _1456322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456316, tc_HOL_Obool)), _1456318), _1456320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456314), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456316, _1456314), _1456322), _1456318)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456316, _1456314), _1456322), _1456320)))], (47304 ^ _779327) ^ [_1723980, _1723982, _1723984] : [-(_1723980 = c_List_Olist_ONil(_1723982)), -(c_List_Olast(_1723982, hAPP(hAPP(c_List_Olist_OCons(_1723982), _1723984), _1723980)) = c_List_Olast(_1723982, _1723980))], (37436 ^ _779327) ^ [_1479428, _1479430, _1479432, _1479434, _1479436] : [class_Groups_Ocomm__monoid__mult(_1479428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479430), _1479432)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479430), _1479434)), 37450 ^ _779327 : [(37453 ^ _779327) ^ [] : [hAPP(_1479436, 37449 ^ [_1479428, _1479430, _1479432, _1479434, _1479436]) = c_Groups_Oone__class_Oone(_1479428)], (37451 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479430), 37449 ^ [_1479428, _1479430, _1479432, _1479434, _1479436]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479430, tc_HOL_Obool)), _1479432), _1479434))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1479428, _1479430, c_Groups_Otimes__class_Otimes(_1479428)), _1479436), c_Groups_Oone__class_Oone(_1479428)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479430, tc_HOL_Obool)), _1479432), _1479434)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1479428), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1479428, _1479430, c_Groups_Otimes__class_Otimes(_1479428)), _1479436), c_Groups_Oone__class_Oone(_1479428)), _1479432)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1479428, _1479430, c_Groups_Otimes__class_Otimes(_1479428)), _1479436), c_Groups_Oone__class_Oone(_1479428)), _1479434)))], (28447 ^ _779327) ^ [_1285766, _1285768, _1285770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285766), _1285768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1285766, tc_HOL_Obool)), _1285770), _1285768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1285766), _1285770)), hAPP(c_Finite__Set_Ocard(_1285766), _1285768))))], (39780 ^ _779327) ^ [_1534224, _1534226, _1534228] : [hBOOL(hAPP(hAPP(c_member(_1534224), _1534226), hAPP(c_Set_OCollect(_1534224), _1534228))), -(hBOOL(hAPP(_1534228, _1534226)))], (7938 ^ _779327) ^ [_905109, _905111, _905113, _905115] : [class_Rings_Olinordered__ring__strict(_905109), 7941 ^ _779327 : [(7956 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905109), _905111), _905113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905109), _905115), _905113)))), 7957 ^ _779327 : [(7964 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905113), c_Groups_Ozero__class_Ozero(_905109))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905115), _905111))], (7958 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), c_Groups_Ozero__class_Ozero(_905109)), _905113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905111), _905115))]]], (7942 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905109), _905111), _905113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_905109), _905115), _905113))), 7947 ^ _779327 : [(7950 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905111), _905115)))], (7948 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), c_Groups_Ozero__class_Ozero(_905109)), _905113)))]], 7951 ^ _779327 : [(7954 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905115), _905111)))], (7952 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905109), _905113), c_Groups_Ozero__class_Ozero(_905109))))]]]]], (30351 ^ _779327) ^ [_1325171, _1325173, _1325175, _1325177, _1325179] : [class_Complete__Lattice_Ocomplete__lattice(_1325171), hBOOL(hAPP(hAPP(c_member(_1325173), _1325175), _1325177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325171), hAPP(_1325179, _1325175)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1325173, _1325171), _1325177), _1325179))))], (4488 ^ _779327) ^ [_847602, _847604, _847606, _847608] : [-(c_List_Olex(_847608, _847604) = c_List_Olex(_847606, _847602)), _847608 = _847606, _847604 = _847602], (39698 ^ _779327) ^ [_1532535, _1532537, _1532539] : [39699 ^ _779327 : [(39702 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1532535), hAPP(c_Set_OCollect(_1532535), _1532539)))], (39700 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1532535), hAPP(c_Set_OCollect(_1532535), _1532537)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532535), hAPP(c_Set_OCollect(_1532535), hAPP(hAPP(c_COMBS(_1532535, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532535), c_fconj), _1532537)), _1532539)))))], (23594 ^ _779327) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6630 ^ _779327) ^ [_883202, _883204, _883206] : [class_Orderings_Oorder(_883202), 6633 ^ _779327 : [(6642 ^ _779327) ^ [] : [-(_883204 = _883206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883202), _883204), _883206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883202), _883206), _883204))], (6634 ^ _779327) ^ [] : [_883204 = _883206, 6637 ^ _779327 : [(6640 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883202), _883206), _883204)))], (6638 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883202), _883204), _883206)))]]]]], (36973 ^ _779327) ^ [_1469291, _1469293, _1469295, _1469297, _1469299, _1469301] : [c_Fun_Oinj__on(_1469291, _1469293, _1469295, _1469297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469291, tc_HOL_Obool)), _1469299), _1469297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469291, tc_HOL_Obool)), _1469301), _1469297)), -(hAPP(c_Set_Oimage(_1469291, _1469293, _1469295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469291, tc_HOL_Obool)), _1469299), _1469301)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469293, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469291, _1469293, _1469295), _1469299)), hAPP(c_Set_Oimage(_1469291, _1469293, _1469295), _1469301)))], (44650 ^ _779327) ^ [_1658728, _1658730, _1658732, _1658734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658728), tc_List_Olist(_1658728))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658728), tc_List_Olist(_1658728)), _1658730), _1658732)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1658728), tc_List_Olist(_1658728)), c_List_Olistrel1(_1658728, _1658734)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658728), tc_List_Olist(_1658728))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658728), tc_List_Olist(_1658728)), _1658730), _1658732)), c_List_Olistrel1(_1658728, hAPP(c_Relation_Oconverse(_1658728, _1658728), _1658734)))))], (24811 ^ _779327) ^ [_1211447, _1211449, _1211451] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211449), _1211451))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211447), _1211449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1211451), _1211449)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211447), _1211451)))], (48746 ^ _779327) ^ [_1756792, _1756794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756792), _1756794)), -(c_List_Oupt(_1756792, hAPP(c_Nat_OSuc, _1756794)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1756792, _1756794)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1756794), c_List_Olist_ONil(tc_Nat_Onat))))], (28530 ^ _779327) ^ [_1287478, _1287480, _1287482, _1287484] : [28531 ^ _779327 : [(28534 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1287482), _1287484)))], (28532 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1287478), _1287480)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1287478, _1287482)), c_Sum__Type_OPlus(_1287478, _1287482, _1287480, _1287484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16942 ^ _779327) ^ [_1066794, _1066796] : [-(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), _1066794)), _1066796))))], (638 ^ _779327) ^ [_789110, _789112, _789114, _789116, _789118, _789120] : [-(c_Finite__Set_Ofolding__one__idem(_789118, _789114, _789110)), c_Finite__Set_Ofolding__one__idem(_789120, _789116, _789112), _789120 = _789118, _789116 = _789114, _789112 = _789110], (27857 ^ _779327) ^ [_1274604, _1274606] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1274604, _1274606))))], (52732 ^ _779327) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (40536 ^ _779327) ^ [_1561275] : [-(c_Wellfounded_Owf(tc_fun(_1561275, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1561275)))], (6843 ^ _779327) ^ [_886267, _886269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886267), _886269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886267), hAPP(c_Nat_OSuc, _886269))))], (11161 ^ _779327) ^ [_961908, _961910, _961912, _961914] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961908), _961910), _961912)), hAPP(c_Int_Onumber__class_Onumber__of(_961908), _961914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961908), _961910), hAPP(c_Int_Onumber__class_Onumber__of(_961908), _961914))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961908), _961912), hAPP(c_Int_Onumber__class_Onumber__of(_961908), _961914)))), class_Int_Onumber(_961908), class_Rings_Osemiring(_961908)], (17852 ^ _779327) ^ [_1082312, _1082314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1082312)), -(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)))), _1082314)), 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)))), _1082312)) = 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, _1082314, _1082312))))], (33279 ^ _779327) ^ [_1385209, _1385211, _1385213, _1385215, _1385217] : [class_Groups_Ocomm__monoid__mult(_1385209), class_Rings_Odvd(_1385209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385211), _1385213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385211, tc_HOL_Obool)), _1385215), _1385213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1385209), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385211, _1385209), _1385217), _1385215)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385211, _1385209), _1385217), _1385213))))], (37851 ^ _779327) ^ [_1487841, _1487843] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1487841), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1487843), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 37858 ^ _779327 : [(37865 ^ _779327) ^ [] : [_1487841 = _1487843, -(hAPP(c_Code__Numeral_Oof__nat, _1487841) = hAPP(c_Code__Numeral_Oof__nat, _1487843))], (37859 ^ _779327) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1487841) = hAPP(c_Code__Numeral_Oof__nat, _1487843), -(_1487841 = _1487843)]]], (1828 ^ _779327) ^ [_805165, _805167] : [-(class_Groups_Omonoid__add(_805165)), _805167 = _805165, class_Groups_Omonoid__add(_805167)], (52794 ^ _779327) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (36909 ^ _779327) ^ [_1468063, _1468065, _1468067] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1468063), _1468065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468063, tc_HOL_Obool)), _1468065), hAPP(c_Set_Oimage(_1468063, _1468063, _1468067), _1468065))), -(c_Fun_Oinj__on(_1468063, _1468063, _1468067, _1468065))], (12536 ^ _779327) ^ [_988283, _988285, _988287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988283), _988285)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988283), _988287))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988285), _988287)))], (45677 ^ _779327) ^ [_1686367, _1686369, _1686371, _1686373] : [-(_1686367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1686369), _1686367), hAPP(hAPP(c_List_Olist_OCons(_1686369), _1686371), _1686373)) = hAPP(hAPP(c_List_Olist_OCons(_1686369), _1686371), hAPP(hAPP(c_List_Otake(_1686369), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1686367), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1686373)))], (51784 ^ _779327) ^ [_1821199, _1821201, _1821203, _1821205] : [class_Complete__Lattice_Ocomplete__lattice(_1821199), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1821201, _1821199), _1821203), _1821205) = c_Complete__Lattice_OSup__class_OSup(_1821199, hAPP(c_Set_OCollect(_1821199), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool), tc_HOL_Obool, _1821199), c_HOL_OEx(tc_fun(_1821201, _1821199))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool), tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool), _1821199), hAPP(c_COMBS(tc_fun(_1821201, _1821199), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1821201, _1821199)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1821201, _1821199), tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1821201, _1821199))), _1821203)))), hAPP(hAPP(c_COMBC(_1821199, tc_fun(tc_fun(_1821201, _1821199), _1821199), tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1821199, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1821201, _1821199), _1821199), tc_fun(tc_fun(_1821201, _1821199), tc_HOL_Obool)), _1821199), c_COMBB(_1821199, tc_HOL_Obool, tc_fun(_1821201, _1821199))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1821201, _1821199), _1821201, _1821199), c_COMBI(tc_fun(_1821201, _1821199))), _1821205)))))))], (52976 ^ _779327) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (40722 ^ _779327) ^ [_1565036, _1565038, _1565040] : [c_Wellfounded_Owf(_1565036, _1565038), c_Wellfounded_Owf(_1565036, _1565040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565036, _1565036), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565036, _1565036, _1565036), _1565038), _1565040)), _1565038)), -(c_Wellfounded_Owf(_1565036, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565036, _1565036), tc_HOL_Obool)), _1565038), _1565040)))], (24757 ^ _779327) ^ [_1210573] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1210573), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1210573 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26318 ^ _779327) ^ [_1242290, _1242292, _1242294, _1242296, _1242298, _1242300] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1242290, tc_fun(_1242292, tc_HOL_Obool)), _1242294), hAPP(hAPP(c_COMBB(_1242296, tc_fun(_1242292, tc_HOL_Obool), _1242290), _1242298), _1242300)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1242296, tc_fun(_1242292, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1242290, _1242296, _1242300), _1242294)), _1242298))], (518 ^ _779327) ^ [_787228, _787230, _787232, _787234, _787236, _787238, _787240, _787242, _787244, _787246] : [-(c_Finite__Set_Ofolding__image(_787244, _787240, _787236, _787232, _787228)), c_Finite__Set_Ofolding__image(_787246, _787242, _787238, _787234, _787230), _787246 = _787244, _787242 = _787240, _787238 = _787236, _787234 = _787232, _787230 = _787228], (37501 ^ _779327) ^ [_1480830, _1480832, _1480834, _1480836, _1480838] : [class_Groups_Oab__semigroup__mult(_1480830), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480830, _1480830, c_Groups_Otimes__class_Otimes(_1480830), _1480832, _1480834), _1480836)), -(hBOOL(hAPP(hAPP(c_member(_1480830), _1480832), _1480834))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1480830, _1480830, c_Groups_Otimes__class_Otimes(_1480830), _1480838, hAPP(hAPP(c_Set_Oinsert(_1480830), _1480832), _1480834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1480830), _1480838), _1480836))))], (25554 ^ _779327) ^ [_1226164, _1226166, _1226168, _1226170] : [class_Groups_Oordered__ab__group__add__abs(_1226164), -(hAPP(c_Groups_Oabs__class_Oabs(_1226164), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1226166, _1226164), hAPP(hAPP(c_COMBB(_1226164, _1226164, _1226166), c_Groups_Oabs__class_Oabs(_1226164)), _1226168)), _1226170)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1226166, _1226164), hAPP(hAPP(c_COMBB(_1226164, _1226164, _1226166), c_Groups_Oabs__class_Oabs(_1226164)), _1226168)), _1226170))], (43630 ^ _779327) ^ [_1633400, _1633402, _1633404, _1633406] : [hBOOL(hAPP(hAPP(c_member(_1633400), _1633402), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1633400, tc_HOL_Obool), _1633404))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1633400, tc_HOL_Obool)), _1633406), _1633404)), -(hBOOL(hAPP(hAPP(c_member(_1633400), _1633402), _1633406)))], (42166 ^ _779327) ^ [_1599299, _1599301, _1599303, _1599305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599299, _1599299)), hAPP(hAPP(c_Product__Type_OPair(_1599299, _1599299), _1599303), _1599305)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool)), _1599301), c_Relation_OId(_1599299)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1599299, tc_fun(_1599299, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1599299, tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_fun(_1599299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599299, tc_fun(tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_fun(_1599299, tc_HOL_Obool)), _1599299), c_COMBC(_1599299, tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1599299, tc_prod(_1599299, _1599299)), tc_fun(_1599299, tc_fun(tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_HOL_Obool)), _1599299), hAPP(c_COMBB(tc_prod(_1599299, _1599299), tc_fun(tc_fun(tc_prod(_1599299, _1599299), tc_HOL_Obool), tc_HOL_Obool), _1599299), c_member(tc_prod(_1599299, _1599299)))), c_Product__Type_OPair(_1599299, _1599299)))), _1599301)), c_fequal), _1599303), _1599305)))], (37575 ^ _779327) ^ [_1482628, _1482630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482628, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1482628, tc_HOL_Obool))), _1482630) = _1482630)], (38174 ^ _779327) ^ [_1495238, _1495240] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1495238, 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(_1495238, tc_HOL_Obool)), tc_fun(_1495238, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1495238, tc_HOL_Obool)), tc_fun(_1495238, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1495238, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1495240)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1495238, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1495240))], (16946 ^ _779327) ^ [_1066877, _1066879] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066877), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1066879), _1066877)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1066879), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066879, _1066877)))], (11895 ^ _779327) ^ [_976453, _976455, _976457, _976459] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_976453), 11898 ^ _779327 : [(11905 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976453), _976457), _976459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976453), _976455), _976457)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976453), _976455), _976459))))], (11899 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976453), _976455), _976457)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976453), _976455), _976459))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976453), _976457), _976459)))]]], (39519 ^ _779327) ^ [_1528610, _1528612, _1528614, _1528616, _1528618, _1528620, _1528622] : [-(hAPP(c_Product__Type_Osnd(_1528610, _1528612), hAPP(c_Product__Type_Omap__pair(_1528614, _1528610, _1528616, _1528612, _1528618, _1528620), _1528622)) = hAPP(_1528620, hAPP(c_Product__Type_Osnd(_1528614, _1528616), _1528622)))], (15501 ^ _779327) ^ [_1041382] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1041382), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1041382)], (45129 ^ _779327) ^ [_1672243] : [-(hAPP(c_List_Omap(_1672243, _1672243), c_Fun_Oid(_1672243)) = c_Fun_Oid(tc_List_Olist(_1672243)))], (9715 ^ _779327) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (4552 ^ _779327) ^ [_848592, _848594, _848596, _848598, _848600, _848602, _848604, _848606] : [-(c_Lazy__Sequence_Oproduct(_848606, _848602, _848598, _848594) = c_Lazy__Sequence_Oproduct(_848604, _848600, _848596, _848592)), _848606 = _848604, _848602 = _848600, _848598 = _848596, _848594 = _848592], (27236 ^ _779327) ^ [_1260054, _1260056, _1260058, _1260060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260054, tc_HOL_Obool)), _1260056), _1260058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260054, tc_HOL_Obool)), _1260060), _1260058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260054, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260054, tc_HOL_Obool)), _1260056), _1260060)), _1260058)))], (39928 ^ _779327) ^ [_1538958, _1538960, _1538962, _1538964] : [-(hAPP(c_Relation_OImage(_1538958, _1538960, _1538962), hAPP(hAPP(c_Set_Oinsert(_1538958), _1538964), c_Orderings_Obot__class_Obot(tc_fun(_1538958, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1538960), hAPP(hAPP(c_COMBC(_1538960, tc_fun(tc_prod(_1538958, _1538960), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1538958, _1538960), tc_fun(tc_fun(tc_prod(_1538958, _1538960), tc_HOL_Obool), tc_HOL_Obool), _1538960), c_member(tc_prod(_1538958, _1538960))), hAPP(c_Product__Type_OPair(_1538958, _1538960), _1538964))), _1538962)))], (46942 ^ _779327) ^ [_1716206, _1716208, _1716210, _1716212] : [-(hBOOL(hAPP(c_List_Odistinct(_1716206), hAPP(hAPP(c_List_Omap(_1716208, _1716206), _1716210), _1716212)))), hBOOL(hAPP(c_List_Odistinct(_1716208), _1716212)), c_Fun_Oinj__on(_1716208, _1716206, _1716210, hAPP(c_List_Oset(_1716208), _1716212))], (42541 ^ _779327) ^ [_1608699, _1608701, _1608703, _1608705, _1608707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608699, _1608701)), hAPP(hAPP(c_Product__Type_OPair(_1608699, _1608701), _1608703), _1608705)), hAPP(c_Relation_Oconverse(_1608701, _1608699), _1608707))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608701, _1608699)), hAPP(hAPP(c_Product__Type_OPair(_1608701, _1608699), _1608705), _1608703)), _1608707)))], (36853 ^ _779327) ^ [_1466875, _1466877, _1466879, _1466881] : [36855 ^ _779327 : [(36859 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466875), 36857 ^ [_1466875, _1466877, _1466879, _1466881]), _1466881)))], (36861 ^ _779327) ^ [] : [-(hAPP(_1466879, 36854 ^ [_1466875, _1466877, _1466879, _1466881]) = hAPP(_1466879, 36857 ^ [_1466875, _1466877, _1466879, _1466881]))], (36863 ^ _779327) ^ [] : [36854 ^ [_1466875, _1466877, _1466879, _1466881] = 36857 ^ [_1466875, _1466877, _1466879, _1466881]], (36856 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466875), 36854 ^ [_1466875, _1466877, _1466879, _1466881]), _1466881)))]], -(c_Fun_Oinj__on(_1466875, _1466877, _1466879, _1466881))], (45540 ^ _779327) ^ [_1682366, _1682368] : [-(hAPP(hAPP(c_List_Otake(_1682366), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1682368) = c_List_Olist_ONil(_1682366))], (24797 ^ _779327) ^ [_1211208, _1211210, _1211212] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211208), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211210), _1211212))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211208), _1211212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1211212), _1211210)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1211208), _1211210)))], (45486 ^ _779327) ^ [_1681361, _1681363] : [-(c_List_Olistrelp(_1681361, _1681363, c_List_Olist_ONil(_1681361), c_List_Olist_ONil(_1681361)))], (20867 ^ _779327) ^ [_1136603, _1136605, _1136607] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1136603, _1136605, _1136607, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1136605)], (2362 ^ _779327) ^ [_813819, _813821, _813823, _813825] : [-(c_Nitpick_Onumber__of__frac(_813825, _813821) = c_Nitpick_Onumber__of__frac(_813823, _813819)), _813825 = _813823, _813821 = _813819], (35818 ^ _779327) ^ [_1443835, _1443837, _1443839, _1443841, _1443843] : [class_Groups_Ocomm__monoid__mult(_1443835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443837), _1443839)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443837), _1443841)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443837, tc_HOL_Obool)), _1443839), _1443841) = c_Orderings_Obot__class_Obot(tc_fun(_1443837, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443837, _1443835), _1443843), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443837, tc_HOL_Obool)), _1443839), _1443841)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443835), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443837, _1443835), _1443843), _1443839)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443837, _1443835), _1443843), _1443841)))], (16936 ^ _779327) ^ [_1066603, _1066605] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1066603), _1066605))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066603))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066605))))], (42430 ^ _779327) ^ [_1605807, _1605809, _1605811, _1605813] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605807, _1605807)), hAPP(hAPP(c_Product__Type_OPair(_1605807, _1605807), _1605809), _1605811)), c_Transitive__Closure_Ortrancl(_1605807, _1605813))), hBOOL(hAPP(hAPP(c_member(_1605807), _1605811), c_Wellfounded_Oacc(_1605807, _1605813))), -(hBOOL(hAPP(hAPP(c_member(_1605807), _1605809), c_Wellfounded_Oacc(_1605807, _1605813))))], (46516 ^ _779327) ^ [_1706823, _1706825, _1706827, _1706829, _1706831] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1706823, _1706825)), _1706827), hAPP(hAPP(c_List_Ozip(_1706823, _1706825), _1706829), _1706831)) = hAPP(hAPP(c_List_Ozip(_1706823, _1706825), hAPP(hAPP(c_List_Odrop(_1706823), _1706827), _1706829)), hAPP(hAPP(c_List_Odrop(_1706825), _1706827), _1706831)))], (16938 ^ _779327) ^ [_1066658, _1066660, _1066662] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066660), _1066662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1066660), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1066658), _1066660), _1066662))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1066658, _1066660)))], (47562 ^ _779327) ^ [_1728902, _1728904, _1728906, _1728908] : [-(_1728902 = _1728904), -(c_List_Oremove1(_1728906, _1728902, hAPP(hAPP(c_List_Olist_OCons(_1728906), _1728904), _1728908)) = hAPP(hAPP(c_List_Olist_OCons(_1728906), _1728904), c_List_Oremove1(_1728906, _1728902, _1728908)))], (36084 ^ _779327) ^ [_1449075, _1449077, _1449079, _1449081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449075), _1449077)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1449075), _1449079)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449075, tc_Nat_Onat), _1449081), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449075, tc_HOL_Obool)), _1449077), _1449079)) = 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(_1449075, tc_Nat_Onat), _1449081), _1449077)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449075, tc_Nat_Onat), _1449081), _1449079))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449075, tc_Nat_Onat), _1449081), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449075, tc_HOL_Obool)), _1449077), _1449079))))], (51253 ^ _779327) ^ [_1808911, _1808913, _1808915] : [_1808911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1808913), c_List_Oreplicate(_1808913, _1808911, _1808915)) = c_Orderings_Obot__class_Obot(tc_fun(_1808913, tc_HOL_Obool)))], (40911 ^ _779327) ^ [_1569893, _1569895, _1569897] : [hAPP(c_Relation_ODomain(_1569893, _1569895), _1569897) = c_Orderings_Obot__class_Obot(tc_fun(_1569893, tc_HOL_Obool)), -(_1569897 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569893, _1569895), tc_HOL_Obool)))], (28415 ^ _779327) ^ [_1285244, _1285246] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285244), _1285246))), -(hAPP(c_Finite__Set_Ocard(_1285244), _1285246) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16601 ^ _779327) ^ [_1060886, _1060888, _1060890] : [class_Groups_Oordered__ab__group__add__abs(_1060886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060886), _1060888), _1060890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060886), hAPP(c_Groups_Ouminus__class_Ouminus(_1060886), _1060888)), _1060890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060886), hAPP(c_Groups_Oabs__class_Oabs(_1060886), _1060888)), _1060890)))], (38674 ^ _779327) ^ [_1508562, _1508564, _1508566, _1508568, _1508570] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1508562, _1508564, hAPP(hAPP(c_Set_Oinsert(_1508562), _1508566), _1508568)), _1508570)), 38679 ^ _779327 : [(38684 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1508562), 38677 ^ [_1508562, _1508564, _1508566, _1508568, _1508570]), 38678 ^ [_1508562, _1508564, _1508566, _1508568, _1508570]))], (38682 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1508562, _1508562, _1508564, 38677 ^ [_1508562, _1508564, _1508566, _1508568, _1508570], 38678 ^ [_1508562, _1508564, _1508566, _1508568, _1508570]), _1508570)))], (38680 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1508562), _1508566), _1508568) = hAPP(hAPP(c_Set_Oinsert(_1508562), 38677 ^ [_1508562, _1508564, _1508566, _1508568, _1508570]), 38678 ^ [_1508562, _1508564, _1508566, _1508568, _1508570]))]]], (12313 ^ _779327) ^ [_984149, _984151, _984153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984149), _984151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984149), _984153)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984151), _984149)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984153), _984149)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984151), _984153))], (40917 ^ _779327) ^ [_1570006, _1570008, _1570010] : [_1570010 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570006, _1570008), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1570006, _1570008), _1570010) = c_Orderings_Obot__class_Obot(tc_fun(_1570006, tc_HOL_Obool)))], (22619 ^ _779327) ^ [_1170773, _1170775, _1170777, _1170779] : [class_Groups_Oordered__ab__group__add(_1170773), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1170773), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170773), _1170775), _1170777)), _1170779) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1170773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1170773), _1170775), _1170779)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1170773), _1170777), _1170779)))], (15549 ^ _779327) ^ [_1042147, _1042149] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1042147), _1042149)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042147)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042149)))], (10719 ^ _779327) ^ [_953510, _953512, _953514, _953516] : [class_Int_Onumber__ring(_953510), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953510), hAPP(c_Int_Onumber__class_Onumber__of(_953510), _953512)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953510), hAPP(c_Int_Onumber__class_Onumber__of(_953510), _953514)), _953516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953510), hAPP(c_Int_Onumber__class_Onumber__of(_953510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _953512), _953514))), _953516))], (11535 ^ _779327) ^ [_970092, _970094, _970096, _970098, _970100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970092), _970094)), 11538 ^ _779327 : [(11545 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970098), 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), _970094), _970092)), _970096)), _970100))), -(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), _970092), _970096)), _970098)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970094), _970096)), _970100))))], (11539 ^ _779327) ^ [] : [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), _970092), _970096)), _970098)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970094), _970096)), _970100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970098), 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), _970094), _970092)), _970096)), _970100))))]]], (50062 ^ _779327) ^ [_1783059, _1783061, _1783063, _1783065] : [-(hBOOL(hAPP(_1783059, _1783061))), -(hAPP(c_List_OremoveAll(_1783063, _1783061), hAPP(c_List_Ofilter(_1783063, _1783059), _1783065)) = hAPP(c_List_Ofilter(_1783063, _1783059), _1783065))], (448 ^ _779327) ^ [_786255, _786257, _786259, _786261, _786263, _786265] : [-(c_Orderings_Oorder__class_Omono(_786263, _786259, _786255)), c_Orderings_Oorder__class_Omono(_786265, _786261, _786257), _786265 = _786263, _786261 = _786259, _786257 = _786255], (30813 ^ _779327) ^ [_1336393, _1336395, _1336397, _1336399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1336393), _1336395)), hBOOL(hAPP(hAPP(c_member(_1336393), _1336397), _1336395)), -(hBOOL(hAPP(hAPP(c_member(_1336393), _1336397), _1336399))), -(hAPP(c_Finite__Set_Ocard(_1336393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336393, tc_HOL_Obool)), _1336395), hAPP(hAPP(c_Set_Oinsert(_1336393), _1336397), _1336399))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1336393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336393, tc_HOL_Obool)), _1336395), _1336399))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (51584 ^ _779327) ^ [_1816243, _1816245, _1816247] : [c_List_Olist__ex(_1816243, _1816247, _1816245), 51588 ^ _779327 : [(51591 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1816247, 51587 ^ [_1816243, _1816245, _1816247])))], (51589 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1816243), 51587 ^ [_1816243, _1816245, _1816247]), hAPP(c_List_Oset(_1816243), _1816245))))]]], (39434 ^ _779327) ^ [_1526539, _1526541] : [class_Groups_Oab__semigroup__mult(_1526539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526539), _1526541)), -(_1526541 = c_Orderings_Obot__class_Obot(tc_fun(_1526539, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1526539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1526539), 39447 ^ [_1526539, _1526541]), 39448 ^ [_1526539, _1526541])), hAPP(hAPP(c_Set_Oinsert(_1526539), 39447 ^ [_1526539, _1526541]), hAPP(hAPP(c_Set_Oinsert(_1526539), 39448 ^ [_1526539, _1526541]), c_Orderings_Obot__class_Obot(tc_fun(_1526539, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1526539), hAPP(c_Finite__Set_Ofold1(_1526539, c_Groups_Otimes__class_Otimes(_1526539)), _1526541)), _1526541)))], (22775 ^ _779327) ^ [_1173824, _1173826, _1173828, _1173830] : [class_Orderings_Olinorder(_1173824), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173824), _1173826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173824), _1173828), _1173830)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173824), _1173828), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1173824), _1173826), _1173830)))], (40795 ^ _779327) ^ [_1566921, _1566923, _1566925, _1566927] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566921, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1566921, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1566923, _1566921), _1566925)), hAPP(c_Relation_ORange(_1566923, _1566921), _1566927))), hAPP(c_Relation_ORange(_1566923, _1566921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1566923, _1566921), tc_HOL_Obool)), _1566925), _1566927)))))], (43035 ^ _779327) ^ [_1621150, _1621152, _1621154, _1621156, _1621158] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621150, _1621150)), hAPP(hAPP(c_Product__Type_OPair(_1621150, _1621150), _1621152), _1621154)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621150, _1621150), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1621156)), _1621158))), 43039 ^ _779327 : [(43042 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621150, _1621150)), hAPP(hAPP(c_Product__Type_OPair(_1621150, _1621150), 43038 ^ [_1621150, _1621152, _1621154, _1621156, _1621158]), _1621154)), _1621158)))], (43040 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621150, _1621150)), hAPP(hAPP(c_Product__Type_OPair(_1621150, _1621150), _1621152), 43038 ^ [_1621150, _1621152, _1621154, _1621156, _1621158])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1621150, _1621150), tc_HOL_Obool), _1621156), _1621158))))]]], (50341 ^ _779327) ^ [_1789546, _1789548, _1789550, _1789552, _1789554, _1789556] : [-(c_New__Random__Sequence_Opos__union(_1789546, _1789548, _1789550, _1789552, _1789554, _1789556) = c_New__DSequence_Opos__union(_1789546, hAPP(hAPP(hAPP(_1789548, _1789552), _1789554), _1789556), hAPP(hAPP(hAPP(_1789550, _1789552), _1789554), _1789556)))], (42448 ^ _779327) ^ [_1606244, _1606246, _1606248, _1606250] : [-(c_Wellfounded_Owf(_1606244, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1606244, _1606244)), hAPP(hAPP(c_Product__Type_OPair(_1606244, _1606244), _1606246), _1606248)), _1606250))), c_Wellfounded_Owf(_1606244, _1606250), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606244, _1606244)), hAPP(hAPP(c_Product__Type_OPair(_1606244, _1606244), _1606248), _1606246)), c_Transitive__Closure_Ortrancl(_1606244, _1606250))))], (1258 ^ _779327) ^ [_798040, _798042] : [-(class_Groups_Oab__group__add(_798040)), _798042 = _798040, class_Groups_Oab__group__add(_798042)], (43810 ^ _779327) ^ [_1637320, _1637322] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1637320, tc_HOL_Obool), _1637322) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1637320, tc_HOL_Obool), tc_fun(_1637320, tc_HOL_Obool)), _1637322), c_COMBI(tc_fun(_1637320, tc_HOL_Obool))))], (50146 ^ _779327) ^ [_1784551, _1784553] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1784551)), _1784553)), 50152 ^ _779327 : [(50155 ^ _779327) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1784551), 50151 ^ [_1784551, _1784553]))], (50153 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1784551)), 50151 ^ [_1784551, _1784553]), hAPP(c_List_Oset(tc_List_Olist(_1784551)), _1784553))))]], 50159 ^ _779327 : [(50163 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1784551)), 50161 ^ [_1784551, _1784553]), hAPP(c_List_Oset(tc_List_Olist(_1784551)), _1784553))))], (50165 ^ _779327) ^ [] : [50158 ^ [_1784551, _1784553] = 50161 ^ [_1784551, _1784553]], (50167 ^ _779327) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1784551, tc_HOL_Obool)), hAPP(c_List_Oset(_1784551), 50158 ^ [_1784551, _1784553])), hAPP(c_List_Oset(_1784551), 50161 ^ [_1784551, _1784553])) = c_Orderings_Obot__class_Obot(tc_fun(_1784551, tc_HOL_Obool))], (50160 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1784551)), 50158 ^ [_1784551, _1784553]), hAPP(c_List_Oset(tc_List_Olist(_1784551)), _1784553))))]], -(hBOOL(hAPP(c_List_Odistinct(_1784551), c_List_Oconcat(_1784551, _1784553))))], (22077 ^ _779327) ^ [_1160685, _1160687, _1160689, _1160691] : [_1160685 = _1160687, 22080 ^ _779327 : [(22083 ^ _779327) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1160689, _1160691), _1160685) = hAPP(c_Product__Type_Osnd(_1160689, _1160691), _1160687))], (22081 ^ _779327) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1160689, _1160691), _1160685) = hAPP(c_Product__Type_Ofst(_1160689, _1160691), _1160687))]]], (27564 ^ _779327) ^ [_1267269, _1267271] : [-(hAPP(c_Set_Oimage(_1267269, _1267269, c_COMBI(_1267269)), _1267271) = _1267271)], (39640 ^ _779327) ^ [_1531301] : [class_Orderings_Olinorder(_1531301), -(c_Finite__Set_Ofun__left__comm__idem(_1531301, _1531301, c_Orderings_Oord__class_Omin(_1531301)))], (6522 ^ _779327) ^ [_881612, _881614, _881616, _881618, _881620] : [class_Orderings_Oorder(_881612), class_Orderings_Olinorder(_881614), c_Orderings_Oorder__class_Ostrict__mono(_881614, _881612, _881616), 6533 ^ _779327 : [(6540 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881614), _881618), _881620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881612), hAPP(_881616, _881618)), hAPP(_881616, _881620))))], (6534 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881612), hAPP(_881616, _881618)), hAPP(_881616, _881620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881614), _881618), _881620)))]]], (34003 ^ _779327) ^ [_1401618, _1401620, _1401622, _1401624] : [-(hAPP(c_Set_OPow(_1401618), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401620, tc_fun(_1401618, tc_HOL_Obool)), _1401622), _1401624)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1401620, tc_fun(tc_fun(_1401618, tc_HOL_Obool), tc_HOL_Obool)), _1401622), hAPP(hAPP(c_COMBB(tc_fun(_1401618, tc_HOL_Obool), tc_fun(tc_fun(_1401618, tc_HOL_Obool), tc_HOL_Obool), _1401620), c_Set_OPow(_1401618)), _1401624)))], (4532 ^ _779327) ^ [_848286, _848288] : [_848288 = _848286, -(c_If(_848288) = c_If(_848286))], (28717 ^ _779327) ^ [_1291173, _1291175, _1291177] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1291173, tc_fun(_1291175, tc_HOL_Obool)), _1291177), hAPP(c_COMBK(tc_fun(_1291175, tc_HOL_Obool), _1291173), c_Orderings_Obot__class_Obot(tc_fun(_1291175, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1291175, tc_HOL_Obool)))], (34243 ^ _779327) ^ [_1407691, _1407693, _1407695, _1407697] : [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), _1407691), _1407693)), 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), _1407695), _1407697)), 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), _1407691), _1407697)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407695), _1407693))))], (13438 ^ _779327) ^ [_1004488, _1004490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004488)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004490))))], (9411 ^ _779327) ^ [_931778, _931780, _931782] : [class_Int_Oring__char__0(_931778), 9414 ^ _779327 : [(9421 ^ _779327) ^ [] : [_931780 = _931782, -(hAPP(c_Int_Oring__1__class_Oof__int(_931778), _931780) = hAPP(c_Int_Oring__1__class_Oof__int(_931778), _931782))], (9415 ^ _779327) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_931778), _931780) = hAPP(c_Int_Oring__1__class_Oof__int(_931778), _931782), -(_931780 = _931782)]]], (47620 ^ _779327) ^ [_1729925, _1729927, _1729929] : [hBOOL(hAPP(hAPP(c_member(_1729925), _1729927), hAPP(c_List_Oset(_1729925), _1729929))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729925)), c_List_Oremove1(_1729925, _1729927, _1729929)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729925)), _1729929)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29849 ^ _779327) ^ [_1312932, _1312934] : [hAPP(c_Int_ORep__Integ, _1312932) = hAPP(c_Int_ORep__Integ, _1312934), -(_1312932 = _1312934)], (35063 ^ _779327) ^ [_1426131, _1426133, _1426135, _1426137] : [class_Lattices_Odistrib__lattice(_1426131), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426131), _1426133), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426131), _1426135), _1426137)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1426131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426131), _1426133), _1426135)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1426131), _1426133), _1426137)))], (23037 ^ _779327) ^ [_1178448, _1178450, _1178452, _1178454] : [class_Orderings_Olinorder(_1178448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178448), _1178450), _1178452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178448), _1178450), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1178448), _1178454), _1178452))))], (24249 ^ _779327) ^ [_1201581, _1201583, _1201585] : [_1201581 = _1201583, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201583), _1201585)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201581), _1201585)))], (9022 ^ _779327) ^ [_924604, _924606, _924608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924604), _924606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _924608)), -(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), _924608)), _924604)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924608)), _924606))))], (47183 ^ _779327) ^ [_1721203, _1721205, _1721207] : [class_Lattices_Olattice(_1721203), -(c_Big__Operators_Olattice__class_OSup__fin(_1721203, hAPP(c_List_Oset(_1721203), hAPP(hAPP(c_List_Olist_OCons(_1721203), _1721205), _1721207))) = hAPP(c_List_Ofoldl(_1721203, _1721203, c_Lattices_Osemilattice__sup__class_Osup(_1721203), _1721205), _1721207))], (41231 ^ _779327) ^ [_1577498, _1577500, _1577502, _1577504] : [c_Finite__Set_Ofun__left__comm__idem(_1577498, _1577500, _1577502), -(hAPP(c_Fun_Ocomp(_1577500, _1577500, _1577500, hAPP(_1577502, _1577504)), hAPP(_1577502, _1577504)) = hAPP(_1577502, _1577504))], (45856 ^ _779327) ^ [_1691231, _1691233] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691231, _1691233)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1691231, _1691233))], (41032 ^ _779327) ^ [_1573003, _1573005, _1573007, _1573009] : [hBOOL(hAPP(c_Predicate_ODomainP(_1573003, _1573005, _1573007), _1573009)), -(hBOOL(hAPP(hAPP(_1573007, _1573009), 41035 ^ [_1573003, _1573005, _1573007, _1573009])))], (41277 ^ _779327) ^ [_1578679, _1578681, _1578683, _1578685, _1578687, _1578689, _1578691, _1578693, _1578695, _1578697, _1578699] : [-(hAPP(c_Product__Type_Omap__pair(_1578679, _1578681, _1578683, _1578685, _1578687, _1578689), hAPP(c_Product__Type_Omap__pair(_1578691, _1578679, _1578693, _1578683, _1578695, _1578697), _1578699)) = hAPP(c_Product__Type_Omap__pair(_1578691, _1578681, _1578693, _1578685, hAPP(c_Fun_Ocomp(_1578679, _1578681, _1578691, _1578687), _1578695), hAPP(c_Fun_Ocomp(_1578683, _1578685, _1578693, _1578689), _1578697)), _1578699))], (52804 ^ _779327) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (24305 ^ _779327) ^ [_1202442, _1202444] : [-(_1202442 = _1202444), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202442), _1202444)), 24312 ^ _779327 : [(24315 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202444), _1202442))], (24313 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202442), _1202444)))]]], (13830 ^ _779327) ^ [_1011567, _1011569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011567)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011569)))), 13833 ^ _779327 : [(13836 ^ _779327) ^ [] : [-(_1011569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13834 ^ _779327) ^ [] : [-(_1011567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27664 ^ _779327) ^ [_1269902, _1269904, _1269906, _1269908, _1269910] : [27666 ^ _779327 : [(27669 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269902, tc_HOL_Obool)), hAPP(_1269908, 27665 ^ [_1269902, _1269904, _1269906, _1269908, _1269910])), _1269910))], (27667 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1269904), 27665 ^ [_1269902, _1269904, _1269906, _1269908, _1269910]), _1269906)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269902, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1269904, tc_fun(_1269902, tc_HOL_Obool)), _1269906), _1269908)), _1269910)))], (5400 ^ _779327) ^ [_861732, _861734] : [_861734 = _861732, -(c_Fun_Oid(_861734) = c_Fun_Oid(_861732))], (24283 ^ _779327) ^ [_1202124, _1202126] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202124), _1202126)), 24286 ^ _779327 : [(24293 ^ _779327) ^ [] : [_1202126 = _1202124, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202126), _1202124)))], (24287 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1202126), _1202124)), -(_1202126 = _1202124)]]], (26420 ^ _779327) ^ [_1244419, _1244421] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1244419, _1244421)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244419), hAPP(c_Nat_OSuc, _1244421)))], (48151 ^ _779327) ^ [_1741886, _1741888, _1741890, _1741892, _1741894, _1741896, _1741898, _1741900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741886), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741888)), _1741890))), c_List_Olist__all2(_1741888, _1741892, _1741894, _1741890, _1741896), hBOOL(hAPP(hAPP(_1741894, _1741898), _1741900)), -(c_List_Olist__all2(_1741888, _1741892, _1741894, hAPP(hAPP(c_List_Olist__update(_1741888, _1741890), _1741886), _1741898), hAPP(hAPP(c_List_Olist__update(_1741892, _1741896), _1741886), _1741900)))], (28698 ^ _779327) ^ [_1290714, _1290716, _1290718, _1290720] : [c_Orderings_Obot__class_Obot(tc_fun(_1290714, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1290716, tc_fun(_1290714, tc_HOL_Obool)), _1290718), _1290720), 28701 ^ _779327 : [(28702 ^ _779327) ^ [_1290830] : [hBOOL(hAPP(hAPP(c_member(_1290716), _1290830), _1290718)), -(hAPP(_1290720, _1290830) = c_Orderings_Obot__class_Obot(tc_fun(_1290714, tc_HOL_Obool)))]]], (5670 ^ _779327) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (48800 ^ _779327) ^ [_1757626, _1757628] : [48801 ^ _779327 : [(48804 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757628), _1757626))], (48802 ^ _779327) ^ [] : [_1757628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1757626, _1757628) = c_List_Olist_ONil(tc_Nat_Onat))], (42142 ^ _779327) ^ [_1598130, _1598132, _1598134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598130, _1598130), tc_HOL_Obool)), _1598132), hAPP(hAPP(c_Product__Type_OSigma(_1598130, _1598130), _1598134), hAPP(c_COMBK(tc_fun(_1598130, tc_HOL_Obool), _1598130), _1598134)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598130, _1598130), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1598130, _1598132)), hAPP(hAPP(c_Product__Type_OSigma(_1598130, _1598130), _1598134), hAPP(c_COMBK(tc_fun(_1598130, tc_HOL_Obool), _1598130), _1598134)))))], (10361 ^ _779327) ^ [_947206] : [class_Power_Opower(_947206), -(c_Power_Opower__class_Opower(_947206) = c_Power_Opower_Opower(_947206, c_Groups_Oone__class_Oone(_947206), c_Groups_Otimes__class_Otimes(_947206)))], (35547 ^ _779327) ^ [_1437251, _1437253, _1437255] : [class_Orderings_Oorder(_1437251), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437251, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1437251), _1437253)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1437251, _1437253, _1437255)) = c_Orderings_Obot__class_Obot(tc_fun(_1437251, tc_HOL_Obool)))], (40550 ^ _779327) ^ [_1561509, _1561511, _1561513, _1561515, _1561517, _1561519, _1561521] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1561509, _1561511, _1561513, _1561515, _1561517), _1561519), _1561521)), 40554 ^ _779327 : [(40557 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1561517, 40553 ^ [_1561509, _1561511, _1561513, _1561515, _1561517, _1561519, _1561521]), _1561521)))], (40555 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1561515, _1561519), 40553 ^ [_1561509, _1561511, _1561513, _1561515, _1561517, _1561519, _1561521])))]]], (21284 ^ _779327) ^ [_1145210, _1145212, _1145214, _1145216, _1145218] : [-(c_Nat_Onat_Onat__case(_1145210, _1145212, _1145214, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1145216)), _1145218)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1145210), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1145216))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1145210, _1145210), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1145210, tc_fun(_1145210, _1145210)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1145210, tc_fun(_1145210, _1145210)), tc_Int_Oint), c_If(_1145210)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1145210, _1145212, _1145214, _1145218))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1145210, tc_Int_Oint), _1145214), 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)), _1145218)))))], (35681 ^ _779327) ^ [_1440523, _1440525] : [class_Orderings_Oorder(_1440523), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440523, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1440523), _1440525)), hAPP(c_SetInterval_Oord__class_OatLeast(_1440523), _1440525)) = hAPP(hAPP(c_Set_Oinsert(_1440523), _1440525), c_Orderings_Obot__class_Obot(tc_fun(_1440523, tc_HOL_Obool))))], (53012 ^ _779327) ^ [_1840541, _1840543, _1840545, _1840547] : [-(hAPP(hAPP(c_COMBK(_1840541, _1840543), _1840545), _1840547) = _1840545)], (26422 ^ _779327) ^ [_1244461, _1244463, _1244465] : [-(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)), _1244461)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244463), _1244465)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244463), _1244461)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244465), _1244461)))], (10029 ^ _779327) ^ [_941768, _941770] : [class_Rings_Ocomm__semiring__1(_941768), -(hAPP(hAPP(c_Power_Opower__class_Opower(_941768), _941770), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_941768))], (23494 ^ _779327) ^ [] : [-(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)))], (34453 ^ _779327) ^ [_1412728, _1412730, _1412732, _1412734, _1412736] : [c_Equiv__Relations_Oequiv(_1412728, _1412730, _1412732), hBOOL(hAPP(hAPP(c_member(_1412728), _1412734), _1412730)), hBOOL(hAPP(hAPP(c_member(_1412728), _1412736), _1412730)), 34464 ^ _779327 : [(34471 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1412728, _1412728)), hAPP(hAPP(c_Product__Type_OPair(_1412728, _1412728), _1412734), _1412736)), _1412732)), -(hAPP(c_Relation_OImage(_1412728, _1412728, _1412732), hAPP(hAPP(c_Set_Oinsert(_1412728), _1412734), c_Orderings_Obot__class_Obot(tc_fun(_1412728, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1412728, _1412728, _1412732), hAPP(hAPP(c_Set_Oinsert(_1412728), _1412736), c_Orderings_Obot__class_Obot(tc_fun(_1412728, tc_HOL_Obool)))))], (34465 ^ _779327) ^ [] : [hAPP(c_Relation_OImage(_1412728, _1412728, _1412732), hAPP(hAPP(c_Set_Oinsert(_1412728), _1412734), c_Orderings_Obot__class_Obot(tc_fun(_1412728, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1412728, _1412728, _1412732), hAPP(hAPP(c_Set_Oinsert(_1412728), _1412736), c_Orderings_Obot__class_Obot(tc_fun(_1412728, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1412728, _1412728)), hAPP(hAPP(c_Product__Type_OPair(_1412728, _1412728), _1412734), _1412736)), _1412732)))]]], (3146 ^ _779327) ^ [_826575, _826577] : [_826577 = _826575, -(c_Int_OBit0(_826577) = c_Int_OBit0(_826575))], (34005 ^ _779327) ^ [_1401700, _1401702, _1401704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401700, tc_HOL_Obool)), _1401702), _1401704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1401700, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1401700), _1401702)), hAPP(c_Set_OPow(_1401700), _1401704))))], (13838 ^ _779327) ^ [_1011694, _1011696] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011694)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1011696))))), _1011694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1011696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12560 ^ _779327) ^ [_988749, _988751, _988753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988749), _988751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988749), _988753)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988751), _988753))))], (40084 ^ _779327) ^ [_1545066, _1545068, _1545070] : [class_Lattices_Odistrib__lattice(_1545066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545066), _1545068)), -(_1545068 = c_Orderings_Obot__class_Obot(tc_fun(_1545066, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545066), _1545070)), -(_1545070 = c_Orderings_Obot__class_Obot(tc_fun(_1545066, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1545066), c_Big__Operators_Olattice__class_OInf__fin(_1545066, _1545068)), c_Big__Operators_Olattice__class_OInf__fin(_1545066, _1545070)) = c_Big__Operators_Olattice__class_OInf__fin(_1545066, hAPP(c_Set_OCollect(_1545066), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool, _1545066), c_HOL_OEx(_1545066)), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool)), tc_fun(_1545066, tc_HOL_Obool), _1545066), hAPP(c_COMBB(tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool, _1545066), c_HOL_OEx(_1545066))), hAPP(hAPP(c_COMBC(_1545066, tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool)), tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_fun(tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool))), tc_fun(tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool)), tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool))), _1545066), c_COMBS(_1545066, tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_fun(_1545066, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1545066, tc_fun(tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool))), _1545066), hAPP(c_COMBB(tc_fun(_1545066, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool)), _1545066), c_COMBS(_1545066, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool)), tc_fun(_1545066, tc_fun(_1545066, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1545066), hAPP(c_COMBB(tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1545066), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545066), c_fconj))), hAPP(hAPP(c_COMBC(_1545066, tc_fun(_1545066, tc_fun(_1545066, _1545066)), tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1545066, _1545066), tc_fun(_1545066, tc_HOL_Obool)), tc_fun(tc_fun(_1545066, tc_fun(_1545066, _1545066)), tc_fun(_1545066, tc_fun(_1545066, tc_HOL_Obool))), _1545066), c_COMBB(tc_fun(_1545066, _1545066), tc_fun(_1545066, tc_HOL_Obool), _1545066)), hAPP(hAPP(c_COMBB(tc_fun(_1545066, tc_HOL_Obool), tc_fun(tc_fun(_1545066, _1545066), tc_fun(_1545066, tc_HOL_Obool)), _1545066), c_COMBB(_1545066, tc_HOL_Obool, _1545066)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1545066)))))), hAPP(hAPP(c_COMBC(_1545066, tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545066, tc_HOL_Obool), tc_fun(_1545066, tc_HOL_Obool)), _1545066), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545066)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545066), c_fconj), hAPP(hAPP(c_COMBC(_1545066, tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545066)), _1545068)))), hAPP(hAPP(c_COMBC(_1545066, tc_fun(_1545066, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545066)), _1545070))))))))], (11283 ^ _779327) ^ [_964485, _964487, _964489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964485), _964487)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964487), _964489)), _964485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964487), _964485)), _964489))], (6196 ^ _779327) ^ [_876924, _876926, _876928, _876930] : [class_Orderings_Oord(_876924), _876926 = _876928, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876924), _876928), _876930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_876924), _876926), _876930)))], (15441 ^ _779327) ^ [_1040244] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040244, _1040244) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52912 ^ _779327) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (5002 ^ _779327) ^ [_855569, _855571] : [_855571 = _855569, -(c_Orderings_Oord__class_Oless(_855571) = c_Orderings_Oord__class_Oless(_855569))], (17048 ^ _779327) ^ [_1068642, _1068644, _1068646] : [hBOOL(hAPP(_1068642, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1068644, _1068646))), 17051 ^ _779327 : [(17058 ^ _779327) ^ [] : [-(_1068646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 17061 ^ _779327 : [(17062 ^ _779327) ^ [_1068890, _1068892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068890), _1068646)), _1068644 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1068646), _1068892)), _1068890), -(hBOOL(hAPP(_1068642, _1068890)))]]], (17052 ^ _779327) ^ [] : [_1068646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1068642, _1068644)))]]], (7402 ^ _779327) ^ [_895503, _895505, _895507, _895509] : [class_Groups_Ocomm__monoid__mult(_895503), -(hAPP(hAPP(c_Power_Opower__class_Opower(_895503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895503), _895505), _895507)), _895509) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895503), hAPP(hAPP(c_Power_Opower__class_Opower(_895503), _895505), _895509)), hAPP(hAPP(c_Power_Opower__class_Opower(_895503), _895507), _895509)))], (6945 ^ _779327) ^ [_888036, _888038, _888040, _888042, _888044] : [class_Orderings_Oorder(_888036), class_Orderings_Oorder(_888038), c_Orderings_Oorder__class_Omono(_888038, _888036, _888040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888038), _888042), _888044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888036), hAPP(_888040, _888042)), hAPP(_888040, _888044))))], (52672 ^ _779327) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (19255 ^ _779327) ^ [_1107334, _1107336, _1107338, _1107340] : [class_Fields_Ofield__inverse__zero(_1107334), 19258 ^ _779327 : [(19259 ^ _779327) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107334), _1107336), _1107338) = _1107340, 19262 ^ _779327 : [(19269 ^ _779327) ^ [] : [_1107338 = c_Groups_Ozero__class_Ozero(_1107334), -(_1107340 = c_Groups_Ozero__class_Ozero(_1107334))], (19263 ^ _779327) ^ [] : [-(_1107338 = c_Groups_Ozero__class_Ozero(_1107334)), -(_1107336 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107334), _1107340), _1107338))]]], (19275 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107334), _1107336), _1107338) = _1107340), 19278 ^ _779327 : [(19281 ^ _779327) ^ [] : [_1107336 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107334), _1107340), _1107338)], (19279 ^ _779327) ^ [] : [_1107338 = c_Groups_Ozero__class_Ozero(_1107334)]], 19282 ^ _779327 : [(19285 ^ _779327) ^ [] : [_1107340 = c_Groups_Ozero__class_Ozero(_1107334)], (19283 ^ _779327) ^ [] : [-(_1107338 = c_Groups_Ozero__class_Ozero(_1107334))]]]]], (29572 ^ _779327) ^ [_1307499, _1307501, _1307503] : [-(hBOOL(hAPP(hAPP(c_member(_1307499), _1307501), _1307503))), -(hBOOL(hAPP(hAPP(c_member(_1307499), _1307501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1307499, tc_HOL_Obool)), _1307503))))], (45267 ^ _779327) ^ [_1675376, _1675378, _1675380, _1675382, _1675384] : [-(c_List_Olist_Olist__size(_1675376, _1675378, hAPP(hAPP(c_List_Omap(_1675380, _1675376), _1675382), _1675384)) = c_List_Olist_Olist__size(_1675380, hAPP(c_Fun_Ocomp(_1675376, tc_Nat_Onat, _1675380, _1675378), _1675382), _1675384))], (19661 ^ _779327) ^ [_1114456, _1114458, _1114460, _1114462] : [class_Fields_Olinordered__field(_1114456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114456), c_Groups_Ozero__class_Ozero(_1114456)), _1114458)), 19668 ^ _779327 : [(19675 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114456), _1114460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114456), _1114462), _1114458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114456), _1114460), _1114458)), _1114462)))], (19669 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1114456), _1114460), _1114458)), _1114462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114456), _1114460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114456), _1114462), _1114458))))]]], (30019 ^ _779327) ^ [_1316135, _1316137, _1316139, _1316141, _1316143] : [hBOOL(hAPP(hAPP(c_member(_1316135), _1316137), c_SetInterval_Oord_OatLeastAtMost(_1316135, _1316139, _1316141, _1316143))), 30022 ^ _779327 : [(30025 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1316139, _1316137), _1316143)))], (30023 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1316139, _1316141), _1316137)))]]], (3896 ^ _779327) ^ [_838436, _838438, _838440, _838442] : [-(c_Nat_Ocompow(_838442, _838438) = c_Nat_Ocompow(_838440, _838436)), _838442 = _838440, _838438 = _838436], (8638 ^ _779327) ^ [_917676, _917678, _917680] : [class_Rings_Olinordered__semidom(_917676), 8641 ^ _779327 : [(8648 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917678), _917680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917676), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917676), _917678)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917676), _917680))))], (8642 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917676), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917676), _917678)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_917676), _917680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917678), _917680)))]]], (24921 ^ _779327) ^ [_1213778, _1213780, _1213782, _1213784] : [class_Divides_Osemiring__div(_1213778), -(_1213780 = c_Groups_Ozero__class_Ozero(_1213778)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213778), _1213780), _1213782)), 24932 ^ _779327 : [(24939 ^ _779327) ^ [] : [_1213782 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213778), _1213784), _1213780), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1213778), _1213782), _1213780) = _1213784)], (24933 ^ _779327) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1213778), _1213782), _1213780) = _1213784, -(_1213782 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213778), _1213784), _1213780))]]], (52039 ^ _779327) ^ [_1826864, _1826866] : [c_Relation_Oantisym(_1826864, _1826866), -(c_Relation_Oantisym(_1826864, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1826864, _1826864), tc_HOL_Obool)), _1826866), c_Relation_OId(_1826864))))], (23476 ^ _779327) ^ [_1187410, _1187412, _1187414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1187410), c_Nitpick_Oplus__frac(_1187410, _1187412, c_Nitpick_Ouminus__frac(_1187410, _1187414)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1187410, _1187412, _1187414))], (48882 ^ _779327) ^ [_1759155, _1759157] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1759155, _1759157) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1759155), _1759157)))], (42194 ^ _779327) ^ [_1600230, _1600232] : [-(c_Transitive__Closure_Otrancl(_1600230, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1600230, _1600230), tc_HOL_Obool)), _1600232), c_Relation_OId(_1600230))) = c_Transitive__Closure_Ortrancl(_1600230, _1600232))], (48810 ^ _779327) ^ [_1757804, _1757806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757804), _1757806)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1757804, _1757806)) = _1757804)], (7169 ^ _779327) ^ [_891577, _891579] : [class_Rings_Olinordered__semidom(_891577), 7172 ^ _779327 : [(7179 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _891579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891577), c_Groups_Ozero__class_Ozero(_891577)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_891577), _891579))))], (7173 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891577), c_Groups_Ozero__class_Ozero(_891577)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_891577), _891579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _891579)))]]], (46552 ^ _779327) ^ [_1707638, _1707640, _1707642, _1707644] : [-(hAPP(hAPP(c_List_Odrop(_1707638), hAPP(c_Nat_OSuc, _1707640)), hAPP(hAPP(c_List_Olist_OCons(_1707638), _1707642), _1707644)) = hAPP(hAPP(c_List_Odrop(_1707638), _1707640), _1707644))], (26426 ^ _779327) ^ [_1244579, _1244581] : [-(hAPP(c_Finite__Set_Ocard(_1244579), _1244581) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1244579, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1244579), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1244581))], (46080 ^ _779327) ^ [_1696168, _1696170, _1696172] : [hAPP(hAPP(c_List_Oappend(_1696168), _1696170), _1696172) = _1696172, -(_1696170 = c_List_Olist_ONil(_1696168))], (8896 ^ _779327) ^ [_922447, _922449, _922451] : [class_Rings_Ocomm__semiring__1(_922447), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922447), _922449), hAPP(hAPP(c_Power_Opower__class_Opower(_922447), _922449), _922451)) = hAPP(hAPP(c_Power_Opower__class_Opower(_922447), _922449), hAPP(c_Nat_OSuc, _922451)))], (23624 ^ _779327) ^ [_1190673, _1190675] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1190673)), hAPP(c_Code__Numeral_Oof__nat, _1190675)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190673), _1190675)))], (4732 ^ _779327) ^ [_851440, _851442, _851444, _851446] : [-(c_List_Oconcat(_851446, _851442) = c_List_Oconcat(_851444, _851440)), _851446 = _851444, _851442 = _851440], (26764 ^ _779327) ^ [_1250646, _1250648, _1250650, _1250652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250646, _1250648)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250650, _1250652)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250650), _1250652)), 26767 ^ _779327 : [(26770 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250650), _1250646)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250648), _1250652)), 26777 ^ _779327 : [(26784 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250648), _1250652)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250652), _1250648)))], (26778 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250650), _1250646)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250646), _1250650)))]]], (26768 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1250646), _1250648)))]]], (10373 ^ _779327) ^ [_947396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _947396))))], (48263 ^ _779327) ^ [_1744475, _1744477, _1744479, _1744481] : [-(c_Lazy__Sequence_Oproduct(_1744475, _1744477, _1744479, _1744481) = hAPP(c_Lazy__Sequence_Obind(_1744475, tc_prod(_1744475, _1744477), _1744479), hAPP(hAPP(c_COMBB(tc_fun(_1744477, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1744475, _1744477))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1744475, _1744477)), _1744475), c_Lazy__Sequence_Obind(_1744477, tc_prod(_1744475, _1744477), _1744481)), hAPP(hAPP(c_COMBB(tc_fun(_1744477, tc_prod(_1744475, _1744477)), tc_fun(_1744477, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1744475, _1744477))), _1744475), hAPP(c_COMBB(tc_prod(_1744475, _1744477), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1744475, _1744477)), _1744477), c_Lazy__Sequence_Osingle(tc_prod(_1744475, _1744477)))), c_Product__Type_OPair(_1744475, _1744477)))))], (25962 ^ _779327) ^ [_1234827, _1234829] : [25970 ^ _779327 : [(25973 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1234829, 25969 ^ [_1234827, _1234829])))], (25971 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25969 ^ [_1234827, _1234829]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1234827))))]], 25963 ^ _779327 : [(25964 ^ _779327) ^ [_1234896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1234896), _1234827)), hBOOL(hAPP(_1234829, _1234896))]]], (50622 ^ _779327) ^ [_1795731, _1795733, _1795735] : [class_Orderings_Olinorder(_1795731), 50628 ^ _779327 : [(50631 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795731), _1795735), 50627 ^ [_1795731, _1795733, _1795735]))], (50629 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795731), 50627 ^ [_1795731, _1795733, _1795735]), hAPP(c_List_Oset(_1795731), _1795733))))]], c_List_Olinorder__class_Osorted(_1795731, _1795733), -(c_List_Olinorder__class_Osorted(_1795731, hAPP(hAPP(c_List_Olist_OCons(_1795731), _1795735), _1795733)))], (48384 ^ _779327) ^ [_1746882, _1746884] : [c_List_Oconcat(_1746882, _1746884) = c_List_Olist_ONil(_1746882), 48387 ^ _779327 : [(48388 ^ _779327) ^ [_1746973] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1746882)), _1746973), hAPP(c_List_Oset(tc_List_Olist(_1746882)), _1746884))), -(_1746973 = c_List_Olist_ONil(_1746882))]]], (2222 ^ _779327) ^ [_811591, _811593, _811595, _811597] : [-(c_Divides_Odivmod__int(_811597, _811593) = c_Divides_Odivmod__int(_811595, _811591)), _811597 = _811595, _811593 = _811591], (35493 ^ _779327) ^ [_1436004, _1436006, _1436008, _1436010] : [class_Orderings_Oorder(_1436004), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436004, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1436004, _1436006, _1436008)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1436004, _1436008), _1436010)) = c_Orderings_Obot__class_Obot(tc_fun(_1436004, tc_HOL_Obool)))], (29818 ^ _779327) ^ [_1312305, _1312307, _1312309, _1312311, _1312313] : [hBOOL(hAPP(hAPP(c_member(_1312305), _1312307), hAPP(c_Set_Oimage(_1312309, _1312305, _1312311), _1312313))), 29822 ^ _779327 : [(29825 ^ _779327) ^ [] : [-(_1312307 = hAPP(_1312311, 29821 ^ [_1312305, _1312307, _1312309, _1312311, _1312313]))], (29823 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312309), 29821 ^ [_1312305, _1312307, _1312309, _1312311, _1312313]), _1312313)))]]], (14265 ^ _779327) ^ [_1019742, _1019744, _1019746, _1019748] : [class_Groups_Ouminus(_1019742), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019744, _1019742)), _1019746), _1019748) = hAPP(c_Groups_Ouminus__class_Ouminus(_1019742), hAPP(_1019746, _1019748)))], (12658 ^ _779327) ^ [_990729, _990731, _990733, _990735, _990737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990729), _990731)), 12661 ^ _779327 : [(12668 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990735), 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), _990731), _990729)), _990733)), _990737))), -(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), _990729), _990733)), _990735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990731), _990733)), _990737))))], (12662 ^ _779327) ^ [] : [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), _990729), _990733)), _990735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990731), _990733)), _990737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990735), 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), _990731), _990729)), _990733)), _990737))))]]], (2144 ^ _779327) ^ [_810388, _810390, _810392, _810394, _810396, _810398] : [-(c_Nat_Onat_Onat__rec(_810398, _810394, _810390) = c_Nat_Onat_Onat__rec(_810396, _810392, _810388)), _810398 = _810396, _810394 = _810392, _810390 = _810388], (26308 ^ _779327) ^ [_1242058, _1242060] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1242058) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1242060), -(_1242058 = _1242060)], (49461 ^ _779327) ^ [_1770196, _1770198] : [_1770198 = c_List_Olist_ONil(_1770196), -(hAPP(c_List_Orev(_1770196), _1770198) = c_List_Olist_ONil(_1770196))], (21916 ^ _779327) ^ [_1156966, _1156968, _1156970, _1156972, _1156974, _1156976, _1156978, _1156980] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1156966, _1156968, _1156970), _1156972), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1156974, _1156976, tc_prod(_1156966, _1156968)), _1156978), _1156980)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1156974, _1156976, _1156970), hAPP(hAPP(c_COMBB(tc_fun(_1156976, tc_prod(_1156966, _1156968)), tc_fun(_1156976, _1156970), _1156974), hAPP(c_COMBB(tc_prod(_1156966, _1156968), _1156970, _1156976), hAPP(c_Product__Type_Oprod_Oprod__case(_1156966, _1156968, _1156970), _1156972))), _1156978)), _1156980))], (9236 ^ _779327) ^ [_928818, _928820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _928818), _928820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _928818)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _928820))))], (52452 ^ _779327) ^ [_1834752, _1834754] : [class_Lattices_Obounded__lattice(_1834752), -(class_Lattices_Obounded__lattice__top(tc_fun(_1834754, _1834752)))], (2068 ^ _779327) ^ [_809182, _809184, _809186, _809188] : [-(c_Random_Olog(_809188, _809184) = c_Random_Olog(_809186, _809182)), _809188 = _809186, _809184 = _809182], (50475 ^ _779327) ^ [_1792516, _1792518, _1792520, _1792522, _1792524] : [-(hAPP(hAPP(c_List_Olist_OCons(_1792516), _1792518), _1792520) = hAPP(c_List_Ofilter(_1792516, _1792522), _1792524)), 50476 ^ _779327 : [(50477 ^ _779327) ^ [_1792644, _1792646] : [_1792524 = hAPP(hAPP(c_List_Oappend(_1792516), _1792646), hAPP(hAPP(c_List_Olist_OCons(_1792516), _1792518), _1792644)), 50483 ^ _779327 : [(50486 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1792522, 50482 ^ [_1792516, _1792518, _1792520, _1792522, _1792524, _1792644, _1792646])))], (50484 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792516), 50482 ^ [_1792516, _1792518, _1792520, _1792522, _1792524, _1792644, _1792646]), hAPP(c_List_Oset(_1792516), _1792646))))]], hBOOL(hAPP(_1792522, _1792518)), _1792520 = hAPP(c_List_Ofilter(_1792516, _1792522), _1792644)]]], (238 ^ _779327) ^ [_782884, _782886] : [-(class_Fields_Olinordered__field(_782884)), _782886 = _782884, class_Fields_Olinordered__field(_782886)], (28840 ^ _779327) ^ [_1293437, _1293439, _1293441] : [class_Groups_Ocomm__monoid__add(_1293437), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293439, _1293437), _1293441), c_Orderings_Obot__class_Obot(tc_fun(_1293439, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1293437))], (26998 ^ _779327) ^ [_1255563, _1255565, _1255567, _1255569] : [class_Lattices_Osemilattice__sup(_1255563), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255563), _1255565), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255563), _1255567), _1255569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255563), _1255567), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255563), _1255565), _1255569)))], (25512 ^ _779327) ^ [_1224745, _1224747, _1224749, _1224751, _1224753] : [class_Groups_Ocomm__monoid__add(_1224745), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224747, _1224745), hAPP(hAPP(c_COMBS(_1224747, _1224745, _1224745), hAPP(hAPP(c_COMBB(_1224745, tc_fun(_1224745, _1224745), _1224747), c_Groups_Oplus__class_Oplus(_1224745)), _1224749)), _1224751)), _1224753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224745), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224747, _1224745), _1224749), _1224753)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224747, _1224745), _1224751), _1224753)))], (45143 ^ _779327) ^ [_1672655, _1672657, _1672659, _1672661, _1672663, _1672665] : [-(hBOOL(hAPP(hAPP(c_member(_1672655), _1672657), hAPP(c_List_Oset(_1672655), _1672659)))), -(hAPP(hAPP(c_List_Omap(_1672655, _1672661), c_Fun_Ofun__upd(_1672655, _1672661, _1672663, _1672657, _1672665)), _1672659) = hAPP(hAPP(c_List_Omap(_1672655, _1672661), _1672663), _1672659))], (17676 ^ _779327) ^ [] : [-(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)))], (3516 ^ _779327) ^ [_832458, _832460, _832462, _832464] : [-(c_New__DSequence_Oneg__single(_832464, _832460) = c_New__DSequence_Oneg__single(_832462, _832458)), _832464 = _832462, _832460 = _832458], (5774 ^ _779327) ^ [_870495, _870497] : [5775 ^ _779327 : [(5778 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870497), _870495))], (5776 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _870495), _870497))]], _870495 = _870497], (24645 ^ _779327) ^ [_1208289, _1208291, _1208293, _1208295] : [class_Divides_Osemiring__div(_1208289), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1208289), _1208291), _1208293)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208289), _1208295), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208289), _1208293), _1208291)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208289), _1208295), _1208293)), _1208291))], (20087 ^ _779327) ^ [_1121845, _1121847, _1121849] : [class_Fields_Olinordered__field__inverse__zero(_1121845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121845), c_Groups_Ozero__class_Ozero(_1121845)), _1121847)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121845), hAPP(c_Groups_Oabs__class_Oabs(_1121845), _1121849)), _1121847) = hAPP(c_Groups_Oabs__class_Oabs(_1121845), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121845), _1121849), _1121847)))], (13999 ^ _779327) ^ [_1014460, _1014462, _1014464, _1014466, _1014468] : [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), _1014460), _1014462)), _1014464)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014460), _1014466)), _1014468))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014464), _1014460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014468), _1014460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014462), _1014466)))], (52726 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (27865 ^ _779327) ^ [_1274724, _1274726] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1274724, _1274726))))], (14379 ^ _779327) ^ [_1021728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021728), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1021728 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 14382 ^ [_1021728]))))], (18108 ^ _779327) ^ [_1086826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1086826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1086826)))], (31302 ^ _779327) ^ [_1346650, _1346652, _1346654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346650, tc_HOL_Obool)), _1346652), hAPP(hAPP(c_Set_Oinsert(_1346650), _1346654), c_Orderings_Obot__class_Obot(tc_fun(_1346650, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1346650, _1346654, _1346652) = c_HOL_OThe(_1346650, hAPP(hAPP(c_COMBC(_1346650, tc_fun(_1346650, tc_HOL_Obool), tc_HOL_Obool), c_member(_1346650)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346650, tc_HOL_Obool)), _1346652), hAPP(hAPP(c_Set_Oinsert(_1346650), _1346654), c_Orderings_Obot__class_Obot(tc_fun(_1346650, tc_HOL_Obool)))))))], (41834 ^ _779327) ^ [_1591252, _1591254, _1591256] : [41836 ^ _779327 : [(41839 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1591252), 41835 ^ [_1591252, _1591254, _1591256]), c_Wellfounded_Oacc(_1591252, _1591256)))], (41837 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591252, _1591252)), hAPP(hAPP(c_Product__Type_OPair(_1591252, _1591252), 41835 ^ [_1591252, _1591254, _1591256]), _1591254)), _1591256)))]], -(hBOOL(hAPP(hAPP(c_member(_1591252), _1591254), c_Wellfounded_Oacc(_1591252, _1591256))))], (37037 ^ _779327) ^ [_1470644, _1470646, _1470648, _1470650, _1470652] : [-(c_Fun_Oinj__on(_1470644, _1470646, _1470648, hAPP(hAPP(c_Set_Oinsert(_1470644), _1470650), _1470652))), c_Fun_Oinj__on(_1470644, _1470646, _1470648, _1470652), -(hBOOL(hAPP(hAPP(c_member(_1470646), hAPP(_1470648, _1470650)), hAPP(c_Set_Oimage(_1470644, _1470646, _1470648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470644, tc_HOL_Obool)), _1470652), hAPP(hAPP(c_Set_Oinsert(_1470644), _1470650), c_Orderings_Obot__class_Obot(tc_fun(_1470644, tc_HOL_Obool))))))))], (38415 ^ _779327) ^ [_1502742, _1502744, _1502746, _1502748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502742, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1502744, _1502742, _1502746), hAPP(c_Set_Ovimage(_1502744, _1502742, _1502746), _1502748))), _1502748)))], (11301 ^ _779327) ^ [_964892, _964894] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _964892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _964894)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964892), _964894)))], (10135 ^ _779327) ^ [_943394, _943396] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943394) = _943396, 10138 ^ _779327 : [(10141 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943396)))], (10139 ^ _779327) ^ [] : [-(_943394 = hAPP(c_Int_Onat, _943396))]]], (29218 ^ _779327) ^ [_1300310, _1300312] : [_1300310 = _1300312, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1300310, _1300312) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1300310), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (18248 ^ _779327) ^ [_1089232, _1089234] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1089232)), c_Int_OBit1(_1089234)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1089232)), _1089234)))], (40484 ^ _779327) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (29618 ^ _779327) ^ [_1308371, _1308373, _1308375, _1308377, _1308379, _1308381] : [hBOOL(hAPP(hAPP(c_member(_1308371), _1308373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1308375, tc_fun(_1308371, tc_HOL_Obool)), _1308377), _1308379))), hBOOL(hAPP(hAPP(c_member(_1308375), _1308381), _1308377)), -(hBOOL(hAPP(hAPP(c_member(_1308371), _1308373), hAPP(_1308379, _1308381))))], (1168 ^ _779327) ^ [_796915, _796917] : [-(class_Groups_Olinordered__ab__group__add(_796915)), _796917 = _796915, class_Groups_Olinordered__ab__group__add(_796917)], (15600 ^ _779327) ^ [_1042989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042989)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1042989) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042989), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52832 ^ _779327) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (41487 ^ _779327) ^ [_1583353, _1583355, _1583357, _1583359, _1583361, _1583363] : [c_Finite__Set_Ofolding(_1583353, _1583355, _1583357, _1583359), -(hAPP(c_Fun_Ocomp(_1583355, _1583355, _1583355, hAPP(_1583357, _1583361)), hAPP(_1583357, _1583363)) = hAPP(c_Fun_Ocomp(_1583355, _1583355, _1583355, hAPP(_1583357, _1583363)), hAPP(_1583357, _1583361)))], (52738 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (14225 ^ _779327) ^ [_1019057, _1019059, _1019061] : [class_Lattices_Oab__semigroup__idem__mult(_1019057), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019057), _1019059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019057), _1019059), _1019061)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019057), _1019059), _1019061))], (34107 ^ _779327) ^ [_1403989, _1403991, _1403993, _1403995, _1403997] : [class_Groups_Ocomm__monoid__add(_1403989), class_Groups_Oordered__cancel__ab__semigroup__add(_1403989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403991), _1403993)), -(_1403993 = c_Orderings_Obot__class_Obot(tc_fun(_1403991, tc_HOL_Obool))), 34125 ^ _779327 : [(34128 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403989), hAPP(_1403995, 34124 ^ [_1403989, _1403991, _1403993, _1403995, _1403997])), hAPP(_1403997, 34124 ^ [_1403989, _1403991, _1403993, _1403995, _1403997])))], (34126 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403991), 34124 ^ [_1403989, _1403991, _1403993, _1403995, _1403997]), _1403993)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403989), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1403991, _1403989), _1403995), _1403993)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1403991, _1403989), _1403997), _1403993))))], (9557 ^ _779327) ^ [_934135, _934137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _934137)), -(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), _934135), _934137))))], (42252 ^ _779327) ^ [_1601652, _1601654] : [-(hAPP(c_Relation_ORange(_1601652, _1601652), c_Transitive__Closure_Ortrancl(_1601652, _1601654)) = c_Orderings_Otop__class_Otop(tc_fun(_1601652, tc_HOL_Obool)))], (40960 ^ _779327) ^ [_1571124, _1571126] : [-(hAPP(c_Relation_OField(_1571124), _1571126) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571124, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1571124, _1571124), _1571126)), hAPP(c_Relation_ORange(_1571124, _1571124), _1571126)))], (48868 ^ _779327) ^ [_1758873, _1758875] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1758873, _1758875)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1758873), hAPP(c_Nat_OSuc, _1758875)))], (13420 ^ _779327) ^ [_1004210, _1004212] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004210)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1004212), 13423 ^ _779327 : [(13426 ^ _779327) ^ [] : [-(_1004212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13424 ^ _779327) ^ [] : [-(_1004210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50444 ^ _779327) ^ [_1791655, _1791657, _1791659, _1791661, _1791663] : [class_Orderings_Olinorder(_1791655), 50450 ^ _779327 : [(50453 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791655), hAPP(_1791661, _1791663)), hAPP(_1791661, 50449 ^ [_1791655, _1791657, _1791659, _1791661, _1791663])))], (50451 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791657), 50449 ^ [_1791655, _1791657, _1791659, _1791661, _1791663]), hAPP(c_List_Oset(_1791657), _1791659))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1791657, _1791655, _1791661), _1791663), _1791659) = hAPP(hAPP(c_List_Olist_OCons(_1791657), _1791663), _1791659))], (14147 ^ _779327) ^ [_1017389, _1017391, _1017393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017389, tc_HOL_Obool)), _1017391), _1017393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017389, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017389, tc_HOL_Obool)), _1017393)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017389, tc_HOL_Obool)), _1017391))))], (2340 ^ _779327) ^ [_813500, _813502] : [_813502 = _813500, -(c_Nitpick_Ozero__frac(_813502) = c_Nitpick_Ozero__frac(_813500))], (50286 ^ _779327) ^ [_1787907, _1787909, _1787911] : [class_Enum_Oenum(_1787907), class_Enum_Oenum(_1787909), 50293 ^ _779327 : [(50300 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787909), hAPP(hAPP(c_COMBB(tc_fun(_1787907, tc_HOL_Obool), tc_HOL_Obool, _1787909), c_Enum_Oenum__class_Oenum__ex(_1787907)), hAPP(hAPP(c_COMBB(tc_fun(_1787907, tc_prod(_1787909, _1787907)), tc_fun(_1787907, tc_HOL_Obool), _1787909), hAPP(c_COMBB(tc_prod(_1787909, _1787907), tc_HOL_Obool, _1787907), _1787911)), c_Product__Type_OPair(_1787909, _1787907))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1787909, _1787907)), _1787911)))], (50294 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1787909, _1787907)), _1787911)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1787909), hAPP(hAPP(c_COMBB(tc_fun(_1787907, tc_HOL_Obool), tc_HOL_Obool, _1787909), c_Enum_Oenum__class_Oenum__ex(_1787907)), hAPP(hAPP(c_COMBB(tc_fun(_1787907, tc_prod(_1787909, _1787907)), tc_fun(_1787907, tc_HOL_Obool), _1787909), hAPP(c_COMBB(tc_prod(_1787909, _1787907), tc_HOL_Obool, _1787907), _1787911)), c_Product__Type_OPair(_1787909, _1787907))))))]]], (17976 ^ _779327) ^ [_1084492] : [c_Int_OMin = c_Int_OBit0(_1084492)], (12227 ^ _779327) ^ [_982683, _982685, _982687] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _982683)), _982685)), hAPP(c_Nat_OSuc, _982687)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _982683), _982685)), _982687))], (24229 ^ _779327) ^ [_1201279, _1201281] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201279), _1201281)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1201281), _1201279)), -(_1201279 = _1201281)], (7338 ^ _779327) ^ [_894342, _894344, _894346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _894342), _894344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894346), _894342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _894346), _894344))))], (9645 ^ _779327) ^ [_935625, _935627, _935629, _935631] : [class_Rings_Olinordered__semidom(_935625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935625), c_Groups_Oone__class_Oone(_935625)), _935627)), 9652 ^ _779327 : [(9659 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935629), _935631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935625), hAPP(hAPP(c_Power_Opower__class_Opower(_935625), _935627), _935629)), hAPP(hAPP(c_Power_Opower__class_Opower(_935625), _935627), _935631))))], (9653 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935625), hAPP(hAPP(c_Power_Opower__class_Opower(_935625), _935627), _935629)), hAPP(hAPP(c_Power_Opower__class_Opower(_935625), _935627), _935631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935629), _935631)))]]], (12608 ^ _779327) ^ [_989658, _989660] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _989658)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _989660)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _989658), _989660)))], (45769 ^ _779327) ^ [_1688857, _1688859, _1688861, _1688863] : [class_Rings_Osemiring__1(_1688857), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1688857), hAPP(hAPP(c_List_Omap(_1688859, _1688857), hAPP(c_COMBK(_1688857, _1688859), _1688861)), _1688863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1688857), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1688857), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688859)), _1688863))), _1688861))], (18823 ^ _779327) ^ [_1099901, _1099903, _1099905] : [class_Rings_Odivision__ring(_1099901), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1099901), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099901), _1099903), _1099905)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099901), hAPP(c_Groups_Ouminus__class_Ouminus(_1099901), _1099903)), _1099905))], (9877 ^ _779327) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48921 ^ _779327) ^ [_1760236, _1760238, _1760240, _1760242, _1760244] : [class_Orderings_Olinorder(_1760236), hBOOL(hAPP(hAPP(c_member(_1760238), _1760240), hAPP(c_List_Oset(_1760238), _1760242))), c_List_Olinorder__class_Osorted(_1760236, hAPP(hAPP(c_List_Omap(_1760238, _1760236), _1760244), _1760242)), hAPP(c_List_Ohd(_1760238), hAPP(c_List_Ofilter(_1760238, hAPP(hAPP(c_COMBB(_1760236, tc_HOL_Obool, _1760238), hAPP(c_fequal, hAPP(_1760244, _1760240))), _1760244)), _1760242)) = _1760240, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1760238, _1760236, _1760244), _1760240), c_List_Oremove1(_1760238, _1760240, _1760242)) = _1760242)], (41709 ^ _779327) ^ [_1588410, _1588412, _1588414, _1588416, _1588418, _1588420] : [c_Finite__Set_Ofolding__idem(_1588410, _1588412, _1588414, _1588416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1588410), _1588418)), -(hAPP(_1588416, hAPP(hAPP(c_Set_Oinsert(_1588410), _1588420), _1588418)) = hAPP(c_Fun_Ocomp(_1588412, _1588412, _1588412, hAPP(_1588416, _1588418)), hAPP(_1588414, _1588420)))], (31275 ^ _779327) ^ [_1346025, _1346027, _1346029, _1346031, _1346033] : [class_Groups_Oordered__comm__monoid__add(_1346025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346027), _1346029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1346027, tc_HOL_Obool)), _1346031), _1346029)), 31289 ^ _779327 : [(31292 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346025), c_Groups_Ozero__class_Ozero(_1346025)), hAPP(_1346033, 31288 ^ [_1346025, _1346027, _1346029, _1346031, _1346033])))], (31290 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346027), 31288 ^ [_1346025, _1346027, _1346029, _1346031, _1346033]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1346027, tc_HOL_Obool)), _1346029), _1346031))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346025), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346027, _1346025), _1346033), _1346031)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346027, _1346025), _1346033), _1346029))))], (16423 ^ _779327) ^ [_1057684, _1057686, _1057688] : [class_Groups_Oordered__ab__group__add__abs(_1057684), -(hAPP(c_Groups_Oabs__class_Oabs(_1057684), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057684), _1057686), _1057688)) = hAPP(c_Groups_Oabs__class_Oabs(_1057684), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057684), _1057688), _1057686)))], (10263 ^ _779327) ^ [_945541, _945543, _945545, _945547] : [class_Rings_Olinordered__semidom(_945541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945541), c_Groups_Oone__class_Oone(_945541)), _945543)), 10270 ^ _779327 : [(10277 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945545), _945547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945541), hAPP(hAPP(c_Power_Opower__class_Opower(_945541), _945543), _945545)), hAPP(hAPP(c_Power_Opower__class_Opower(_945541), _945543), _945547))))], (10271 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945541), hAPP(hAPP(c_Power_Opower__class_Opower(_945541), _945543), _945545)), hAPP(hAPP(c_Power_Opower__class_Opower(_945541), _945543), _945547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945545), _945547)))]]], (33004 ^ _779327) ^ [_1380136, _1380138, _1380140, _1380142, _1380144, _1380146] : [_1380136 = _1380138, -(hAPP(c_Fun_Ofun__upd(_1380140, _1380142, _1380144, _1380138, _1380146), _1380136) = _1380146)], (45221 ^ _779327) ^ [_1674258, _1674260, _1674262] : [c_Fun_Oinj__on(tc_List_Olist(_1674258), tc_List_Olist(_1674260), hAPP(c_List_Omap(_1674258, _1674260), _1674262), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674258), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1674258, _1674260, _1674262, c_Orderings_Otop__class_Otop(tc_fun(_1674258, tc_HOL_Obool))))], (45390 ^ _779327) ^ [_1679384, _1679386, _1679388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679384), tc_List_Olist(_1679384))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679384), tc_List_Olist(_1679384)), c_List_Olist_ONil(_1679384)), _1679386)), c_List_Olistrel(_1679384, _1679388))), -(_1679386 = c_List_Olist_ONil(_1679384))], (48959 ^ _779327) ^ [_1760904, _1760906, _1760908] : [class_Orderings_Olinorder(_1760904), c_List_Olinorder__class_Osorted(_1760904, _1760906), -(c_List_Olinorder__class_Osorted(_1760904, c_List_Olinorder__class_Oinsort__insert__key(_1760904, _1760904, c_COMBI(_1760904), _1760908, _1760906)))], (51701 ^ _779327) ^ [_1818761, _1818763] : [-(c_Relation_Otrans(_1818761, c_Transitive__Closure_Otrancl(_1818761, _1818763)))], (18805 ^ _779327) ^ [_1099470, _1099472, _1099474, _1099476, _1099478] : [class_Fields_Ofield__inverse__zero(_1099470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099470), _1099472), _1099474)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099470), _1099476), _1099478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1099470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099470), _1099472), _1099476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099470), _1099474), _1099478)))], (14505 ^ _779327) ^ [_1023870, _1023872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023872)), -(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), _1023870), _1023872))))], (2684 ^ _779327) ^ [_818930, _818932, _818934, _818936] : [-(c_Code__Numeral_Onat__of__aux(_818936, _818932) = c_Code__Numeral_Onat__of__aux(_818934, _818930)), _818936 = _818934, _818932 = _818930], (46754 ^ _779327) ^ [_1712387, _1712389] : [-(_1712387 = c_List_Olist_ONil(_1712389)), -(hAPP(c_List_Ohd(_1712389), _1712387) = hAPP(hAPP(c_List_Onth(_1712389), _1712387), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14921 ^ _779327) ^ [_1030342] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1030342))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1030342) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6809 ^ _779327) ^ [_885730, _885732] : [class_Orderings_Opreorder(_885730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885730), _885732), _885732))], (48631 ^ _779327) ^ [_1753082, _1753084, _1753086] : [-(hAPP(c_List_Oset(_1753082), hAPP(c_List_Ofilter(_1753082, _1753084), _1753086)) = hAPP(c_Set_OCollect(_1753082), hAPP(hAPP(c_COMBS(_1753082, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1753082), c_fconj), hAPP(hAPP(c_COMBC(_1753082, tc_fun(_1753082, tc_HOL_Obool), tc_HOL_Obool), c_member(_1753082)), hAPP(c_List_Oset(_1753082), _1753086)))), _1753084)))], (40593 ^ _779327) ^ [_1562292, _1562294, _1562296] : [c_Wellfounded_Owf(_1562292, _1562294), -(c_Wellfounded_Owf(_1562292, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1562292, _1562292), tc_HOL_Obool)), _1562296), _1562294)))], (2522 ^ _779327) ^ [_816305, _816307, _816309, _816311, _816313, _816315, _816317, _816319] : [-(c_Random__Sequence_ORandom(_816319, _816315, _816311, _816307) = c_Random__Sequence_ORandom(_816317, _816313, _816309, _816305)), _816319 = _816317, _816315 = _816313, _816311 = _816309, _816307 = _816305], (48301 ^ _779327) ^ [_1745280, _1745282] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745280)), c_List_Oremdups(_1745280, _1745282)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745280)), _1745282), -(c_List_Oremdups(_1745280, _1745282) = _1745282)], (37923 ^ _779327) ^ [_1489662, _1489664] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1489662, _1489664)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1489662, _1489664), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1489664), c_Orderings_Otop__class_Otop(tc_fun(_1489664, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1489662), c_Orderings_Otop__class_Otop(tc_fun(_1489662, tc_HOL_Obool)))))], (48195 ^ _779327) ^ [_1742837] : [-(c_Enum_Osublists(_1742837, c_List_Olist_ONil(_1742837)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1742837)), c_List_Olist_ONil(_1742837)), c_List_Olist_ONil(tc_List_Olist(_1742837))))], (14563 ^ _779327) ^ [_1024777] : [-(_1024777 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024777), _1024777) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23115 ^ _779327) ^ [_1180149, _1180151, _1180153, _1180155, _1180157, _1180159] : [-(hAPP(c_Product__Type_Oapfst(_1180149, _1180151, _1180153, _1180155), hAPP(hAPP(c_Product__Type_OPair(_1180149, _1180153), _1180157), _1180159)) = hAPP(hAPP(c_Product__Type_OPair(_1180151, _1180153), hAPP(_1180155, _1180157)), _1180159))], (31003 ^ _779327) ^ [_1340688, _1340690] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1340688), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1340690)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340690), _1340688)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1340688), _1340690)))], (44316 ^ _779327) ^ [_1648879, _1648881, _1648883, _1648885, _1648887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648879, tc_HOL_Obool)), _1648881), _1648883)), 44322 ^ _779327 : [(44327 ^ _779327) ^ [] : [hBOOL(hAPP(_1648887, 44321 ^ [_1648879, _1648881, _1648883, _1648885, _1648887]))], (44325 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1648885, 44321 ^ [_1648879, _1648881, _1648883, _1648885, _1648887])))], (44323 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648879), 44321 ^ [_1648879, _1648881, _1648883, _1648885, _1648887]), _1648881)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648879, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648879, tc_HOL_Obool)), _1648881), hAPP(c_Set_OCollect(_1648879), _1648885))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648879, tc_HOL_Obool)), _1648883), hAPP(c_Set_OCollect(_1648879), _1648887)))))], (3932 ^ _779327) ^ [_838968, _838970, _838972, _838974] : [-(c_Big__Operators_Olinorder__class_OMin(_838974, _838970) = c_Big__Operators_Olinorder__class_OMin(_838972, _838968)), _838974 = _838972, _838970 = _838968], (19071 ^ _779327) ^ [_1104289, _1104291, _1104293] : [class_Fields_Olinordered__field(_1104289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104289), c_Groups_Ozero__class_Ozero(_1104289)), _1104291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104289), c_Groups_Ozero__class_Ozero(_1104289)), _1104293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104289), c_Groups_Ozero__class_Ozero(_1104289)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104289), _1104291), _1104293))))], (11319 ^ _779327) ^ [_965256, _965258, _965260] : [class_Rings_Oring__1(_965256), -(hAPP(c_Int_Oring__1__class_Oof__int(_965256), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _965258), _965260)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965256), hAPP(c_Int_Oring__1__class_Oof__int(_965256), _965258)), hAPP(c_Int_Oring__1__class_Oof__int(_965256), _965260)))], (41083 ^ _779327) ^ [_1574529] : [-(_1574529 = hAPP(c_Int_OAbs__Integ, 41081 ^ [_1574529]))], (47903 ^ _779327) ^ [_1736385, _1736387, _1736389] : [class_Orderings_Olinorder(_1736385), -(hBOOL(hAPP(hAPP(c_member(_1736385), _1736387), hAPP(c_List_Oset(_1736385), _1736389)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1736385, _1736385, c_COMBI(_1736385), _1736387, _1736389) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1736385, _1736385, c_COMBI(_1736385)), _1736387), _1736389))], (43163 ^ _779327) ^ [_1624331, _1624333, _1624335, _1624337, _1624339, _1624341] : [c_Finite__Set_Ofun__left__comm__idem(_1624331, _1624333, _1624335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624331), _1624337)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1624331, _1624333, _1624335), _1624339), hAPP(hAPP(c_Set_Oinsert(_1624331), _1624341), _1624337)) = hAPP(hAPP(c_Finite__Set_Ofold(_1624331, _1624333, _1624335), hAPP(hAPP(_1624335, _1624341), _1624339)), _1624337))], (36261 ^ _779327) ^ [_1454682, _1454684, _1454686, _1454688, _1454690] : [class_Groups_Ocomm__monoid__mult(_1454682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454684), _1454686)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454684), _1454688)), 36275 ^ _779327 : [(36278 ^ _779327) ^ [] : [hAPP(_1454690, 36274 ^ [_1454682, _1454684, _1454686, _1454688, _1454690]) = c_Groups_Oone__class_Oone(_1454682)], (36276 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1454684), 36274 ^ [_1454682, _1454684, _1454686, _1454688, _1454690]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454684, tc_HOL_Obool)), _1454686), _1454688))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454684, _1454682), _1454690), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1454684, tc_HOL_Obool)), _1454686), _1454688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1454682), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454684, _1454682), _1454690), _1454686)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454684, _1454682), _1454690), _1454688)))], (51796 ^ _779327) ^ [_1822085, _1822087, _1822089, _1822091] : [class_Complete__Lattice_Ocomplete__lattice(_1822085), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1822087, _1822085), _1822089), _1822091) = c_Complete__Lattice_OInf__class_OInf(_1822085, hAPP(c_Set_OCollect(_1822085), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool), tc_HOL_Obool, _1822085), c_HOL_OEx(tc_fun(_1822087, _1822085))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool), tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool), _1822085), hAPP(c_COMBS(tc_fun(_1822087, _1822085), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1822087, _1822085)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1822087, _1822085), tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1822087, _1822085))), _1822089)))), hAPP(hAPP(c_COMBC(_1822085, tc_fun(tc_fun(_1822087, _1822085), _1822085), tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1822085, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1822087, _1822085), _1822085), tc_fun(tc_fun(_1822087, _1822085), tc_HOL_Obool)), _1822085), c_COMBB(_1822085, tc_HOL_Obool, tc_fun(_1822087, _1822085))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1822087, _1822085), _1822087, _1822085), c_COMBI(tc_fun(_1822087, _1822085))), _1822091)))))))], (15203 ^ _779327) ^ [_1035405, _1035407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1035405), _1035407)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035405), _1035407) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (40516 ^ _779327) ^ [_1560887, _1560889, _1560891, _1560893, _1560895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560887, _1560889)), hAPP(hAPP(c_Product__Type_OPair(_1560887, _1560889), _1560891), _1560893)), _1560895)), -(hBOOL(hAPP(hAPP(c_member(_1560889), _1560893), hAPP(c_Relation_ORange(_1560887, _1560889), _1560895))))], (5014 ^ _779327) ^ [_855739, _855741, _855743, _855745] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855745, _855741) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855743, _855739)), _855745 = _855743, _855741 = _855739], (29080 ^ _779327) ^ [_1297433, _1297435] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297433, tc_fun(_1297433, tc_HOL_Obool)), _1297435), hAPP(hAPP(c_COMBC(_1297433, tc_fun(_1297433, tc_HOL_Obool), tc_fun(_1297433, tc_HOL_Obool)), c_Set_Oinsert(_1297433)), c_Orderings_Obot__class_Obot(tc_fun(_1297433, tc_HOL_Obool)))) = _1297435)], (41371 ^ _779327) ^ [_1580751, _1580753, _1580755, _1580757, _1580759, _1580761] : [class_Groups_Ocomm__monoid__mult(_1580751), c_Fun_Oinj__on(_1580753, _1580755, _1580757, _1580759), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1580755, _1580751), _1580761), hAPP(c_Set_Oimage(_1580753, _1580755, _1580757), _1580759)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1580753, _1580751), hAPP(c_Fun_Ocomp(_1580755, _1580751, _1580753, _1580761), _1580757)), _1580759))], (31407 ^ _779327) ^ [_1349064, _1349066] : [class_Orderings_Owellorder(_1349064), 31412 ^ _779327 : [(31413 ^ _779327) ^ [_1349158] : [hBOOL(hAPP(_1349066, _1349158))]], -(hBOOL(hAPP(_1349066, c_Orderings_Oord__class_OLeast(_1349064, _1349066))))], (52780 ^ _779327) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (32290 ^ _779327) ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946] : [c_Nitpick_Ofold__graph_H(_1365934, _1365936, _1365938, _1365940, _1365942, hAPP(hAPP(_1365938, _1365944), _1365946)), 32295 ^ _779327 : [(32298 ^ _779327) ^ [] : [-(hAPP(hAPP(_1365938, _1365944), _1365946) = _1365940)], (32296 ^ _779327) ^ [] : [-(_1365942 = c_Orderings_Obot__class_Obot(tc_fun(_1365934, tc_HOL_Obool)))]], 32301 ^ _779327 : [(32306 ^ _779327) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1365934, _1365936, _1365938, _1365940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365934, tc_HOL_Obool)), _1365942), hAPP(hAPP(c_Set_Oinsert(_1365934), 32299 ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946]), c_Orderings_Obot__class_Obot(tc_fun(_1365934, tc_HOL_Obool)))), 32300 ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946]))], (32304 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365934), 32299 ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946]), _1365942)))], (32302 ^ _779327) ^ [] : [-(hAPP(hAPP(_1365938, _1365944), _1365946) = hAPP(hAPP(_1365938, 32299 ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946]), 32300 ^ [_1365934, _1365936, _1365938, _1365940, _1365942, _1365944, _1365946]))]]], (48331 ^ _779327) ^ [_1745842, _1745844] : [c_List_Oremdups(_1745842, _1745844) = c_List_Olist_ONil(_1745842), -(_1745844 = c_List_Olist_ONil(_1745842))], (34673 ^ _779327) ^ [_1418002, _1418004, _1418006, _1418008] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418002, tc_HOL_Obool)), _1418004), _1418006), _1418008)), -(hBOOL(hAPP(_1418006, _1418008)))], (41453 ^ _779327) ^ [_1582588, _1582590, _1582592, _1582594, _1582596, _1582598] : [c_Finite__Set_Ofolding(_1582588, _1582590, _1582592, _1582594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582588), _1582596)), hBOOL(hAPP(hAPP(c_member(_1582588), _1582598), _1582596)), -(hAPP(_1582594, _1582596) = hAPP(c_Fun_Ocomp(_1582590, _1582590, _1582590, hAPP(_1582594, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1582588, tc_HOL_Obool)), _1582596), hAPP(hAPP(c_Set_Oinsert(_1582588), _1582598), c_Orderings_Obot__class_Obot(tc_fun(_1582588, tc_HOL_Obool)))))), hAPP(_1582592, _1582598)))], (16361 ^ _779327) ^ [_1056563, _1056565] : [class_Groups_Oordered__ab__group__add__abs(_1056563), -(hAPP(c_Groups_Oabs__class_Oabs(_1056563), hAPP(c_Groups_Oabs__class_Oabs(_1056563), _1056565)) = hAPP(c_Groups_Oabs__class_Oabs(_1056563), _1056565))], (25600 ^ _779327) ^ [_1227325, _1227327, _1227329, _1227331] : [class_Groups_Oab__group__add(_1227325), 25603 ^ _779327 : [(25610 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227327), _1227329))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227325), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1227325, _1227325), hAPP(hAPP(c_COMBB(_1227325, tc_fun(_1227325, _1227325), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1227325)), _1227331)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227325, tc_Nat_Onat), _1227331), 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, _1227327, _1227329)) = c_Groups_Ozero__class_Ozero(_1227325))], (25604 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227327), _1227329)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1227325), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1227325, _1227325), hAPP(hAPP(c_COMBB(_1227325, tc_fun(_1227325, _1227325), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1227325)), _1227331)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1227325, tc_Nat_Onat), _1227331), 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, _1227327, _1227329)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227325), hAPP(_1227331, _1227327)), hAPP(_1227331, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1227329), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (12049 ^ _779327) ^ [_979104, _979106, _979108, _979110] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_979104), 12052 ^ _779327 : [(12059 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979104), _979106), _979110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979104), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979104), _979106), _979108)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979104), _979110), _979108))))], (12053 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979104), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979104), _979106), _979108)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979104), _979110), _979108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979104), _979106), _979110)))]]], (42494 ^ _779327) ^ [_1607360, _1607362, _1607364, _1607366, _1607368] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607360, _1607360)), hAPP(hAPP(c_Product__Type_OPair(_1607360, _1607360), _1607362), _1607364)), c_Transitive__Closure_Ortrancl(_1607360, _1607366))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607360, _1607360), tc_HOL_Obool)), _1607366), hAPP(hAPP(c_Product__Type_OSigma(_1607360, _1607360), _1607368), hAPP(c_COMBK(tc_fun(_1607360, tc_HOL_Obool), _1607360), _1607368)))), -(_1607362 = _1607364), -(hBOOL(hAPP(hAPP(c_member(_1607360), _1607362), _1607368)))], (34959 ^ _779327) ^ [_1423598, _1423600, _1423602] : [class_Lattices_Osemilattice__inf(_1423598), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1423598), _1423600), _1423602)), _1423600)))], (27508 ^ _779327) ^ [_1266027, _1266029, _1266031, _1266033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266027, _1266029)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266031, _1266033))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266027), _1266029)), 27515 ^ _779327 : [(27518 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266029), _1266033)))], (27516 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1266031), _1266027)))]]], (5708 ^ _779327) ^ [_869630, _869632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _869630), _869632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _869630)), hAPP(c_Nat_OSuc, _869632))))], (39852 ^ _779327) ^ [_1536106, _1536108] : [-(hAPP(c_Set_OCollect(_1536106), hAPP(c_fequal, _1536108)) = hAPP(hAPP(c_Set_Oinsert(_1536106), _1536108), c_Orderings_Obot__class_Obot(tc_fun(_1536106, tc_HOL_Obool))))], (6292 ^ _779327) ^ [_878283, _878285, _878287] : [class_Orderings_Oorder(_878283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_878283), _878285), _878287)), _878287 = _878285], (11921 ^ _779327) ^ [_976955, _976957, _976959, _976961] : [class_Groups_Oordered__ab__semigroup__add(_976955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976955), _976957), _976959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976955), _976961), _976957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976955), _976961), _976959))))], (4378 ^ _779327) ^ [_845923, _845925, _845927, _845929] : [-(c_Product__Type_Ofst(_845929, _845925) = c_Product__Type_Ofst(_845927, _845923)), _845929 = _845927, _845925 = _845923], (51930 ^ _779327) ^ [_1824706, _1824708, _1824710, _1824712] : [-(c_Wellfounded_Omax__extp(_1824706, _1824708, _1824710, _1824712)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1824706), _1824710)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1824706), _1824712)), -(_1824712 = c_Orderings_Obot__class_Obot(tc_fun(_1824706, tc_HOL_Obool))), 51944 ^ _779327 : [(51947 ^ _779327) ^ [_1825051] : [hBOOL(hAPP(hAPP(c_member(_1824706), _1825051), _1824712)), hBOOL(hAPP(hAPP(_1824708, 51943 ^ [_1824706, _1824708, _1824710, _1824712]), _1825051))], (51945 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1824706), 51943 ^ [_1824706, _1824708, _1824710, _1824712]), _1824710)))]]], (33062 ^ _779327) ^ [_1381001, _1381003, _1381005, _1381007, _1381009] : [class_Groups_Ocomm__monoid__mult(_1381001), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381003, _1381001), hAPP(hAPP(c_COMBS(_1381003, _1381001, _1381001), hAPP(hAPP(c_COMBB(_1381001, tc_fun(_1381001, _1381001), _1381003), c_Groups_Otimes__class_Otimes(_1381001)), _1381005)), _1381007)), _1381009) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381001), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381003, _1381001), _1381005), _1381009)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381003, _1381001), _1381007), _1381009)))], (41022 ^ _779327) ^ [_1572823, _1572825, _1572827] : [c_Wellfounded_OwfP(_1572823, _1572825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572823, tc_fun(_1572823, tc_HOL_Obool))), _1572827), _1572825)), -(c_Wellfounded_OwfP(_1572823, _1572827))], (27146 ^ _779327) ^ [_1258394, _1258396, _1258398, _1258400] : [class_Lattices_Osemilattice__sup(_1258394), 27149 ^ _779327 : [(27158 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258394), _1258396), _1258398)), _1258400))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), _1258396), _1258400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), _1258398), _1258400))], (27150 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1258394), _1258396), _1258398)), _1258400)), 27153 ^ _779327 : [(27156 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), _1258398), _1258400)))], (27154 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258394), _1258396), _1258400)))]]]]], (37221 ^ _779327) ^ [_1474903, _1474905, _1474907, _1474909, _1474911] : [c_Fun_Oinj__on(_1474903, _1474905, _1474907, _1474909), hBOOL(hAPP(hAPP(c_member(_1474905), _1474911), hAPP(c_Set_Oimage(_1474903, _1474905, _1474907), _1474909))), -(hAPP(_1474907, hAPP(c_Fun_Othe__inv__into(_1474903, _1474905, _1474909, _1474907), _1474911)) = _1474911)], (31342 ^ _779327) ^ [_1347451, _1347453, _1347455, _1347457, _1347459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1347451, _1347453)), hAPP(_1347451, _1347455))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1347457, _1347457)), hAPP(hAPP(c_Product__Type_OPair(_1347457, _1347457), _1347453), _1347455)), _1347459)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1347457, _1347457)), hAPP(hAPP(c_Product__Type_OPair(_1347457, _1347457), _1347453), _1347455)), c_Wellfounded_Omlex__prod(_1347457, _1347451, _1347459))))], (14363 ^ _779327) ^ [_1021479, _1021481] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021479)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1021479)), _1021481) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021479)), _1021481)))], (41445 ^ _779327) ^ [_1582400, _1582402, _1582404, _1582406, _1582408, _1582410] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582400, tc_fun(_1582402, tc_HOL_Obool)), _1582404), hAPP(c_Fun_Ocomp(_1582406, tc_fun(_1582402, tc_HOL_Obool), _1582400, _1582408), _1582410)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1582406, tc_fun(_1582402, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1582400, _1582406, _1582410), _1582404)), _1582408))], (9100 ^ _779327) ^ [_926298] : [_926298 = 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), _926298)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41281 ^ _779327) ^ [_1578863, _1578865, _1578867, _1578869, _1578871, _1578873, _1578875, _1578877, _1578879, _1578881] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1578863, _1578865), tc_prod(_1578867, _1578869), tc_prod(_1578871, _1578873), c_Product__Type_Omap__pair(_1578863, _1578867, _1578865, _1578869, _1578875, _1578877)), c_Product__Type_Omap__pair(_1578871, _1578863, _1578873, _1578865, _1578879, _1578881)) = c_Product__Type_Omap__pair(_1578871, _1578867, _1578873, _1578869, hAPP(c_Fun_Ocomp(_1578863, _1578867, _1578871, _1578875), _1578879), hAPP(c_Fun_Ocomp(_1578865, _1578869, _1578873, _1578877), _1578881)))], (22851 ^ _779327) ^ [_1175241, _1175243, _1175245, _1175247, _1175249] : [class_Orderings_Olinorder(_1175241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175241), _1175243), _1175245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175241), _1175247), _1175249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175241), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175241), _1175243), _1175247)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175241), _1175245), _1175249))))], (52680 ^ _779327) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (39355 ^ _779327) ^ [_1524258, _1524260, _1524262, _1524264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524260, _1524258), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1524258, tc_prod(_1524260, _1524258), 39351 ^ [_1524258, _1524260, _1524262, _1524264]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524260, tc_fun(_1524258, tc_HOL_Obool)), _1524262), _1524264))), hAPP(hAPP(c_Product__Type_OSigma(_1524260, _1524258), _1524262), _1524264))))], (48716 ^ _779327) ^ [_1755922, _1755924] : [class_Groups_Omonoid__add(_1755922), -(hAPP(c_List_Ofoldl(_1755922, _1755922, c_Groups_Oplus__class_Oplus(_1755922), c_Groups_Ozero__class_Ozero(_1755922)), _1755924) = c_List_Ofoldr(_1755922, _1755922, c_Groups_Oplus__class_Oplus(_1755922), _1755924, c_Groups_Ozero__class_Ozero(_1755922)))], (15882 ^ _779327) ^ [_1047908, _1047910, _1047912] : [-(hBOOL(hAPP(_1047908, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1047910), _1047912)))), 15885 ^ _779327 : [(15888 ^ _779327) ^ [] : [hBOOL(hAPP(_1047908, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15886 ^ _779327) ^ [] : [-(_1047912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 15889 ^ _779327 : [(15894 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15892 ^ [_1047908, _1047910, _1047912]), _1047912)))], (15896 ^ _779327) ^ [] : [-(_1047910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047912), 15891 ^ [_1047908, _1047910, _1047912])), 15892 ^ [_1047908, _1047910, _1047912]))], (15898 ^ _779327) ^ [] : [hBOOL(hAPP(_1047908, 15891 ^ [_1047908, _1047910, _1047912]))], (15890 ^ _779327) ^ [] : [_1047912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (30309 ^ _779327) ^ [_1324404, _1324406, _1324408] : [class_Orderings_Oord(_1324404), 30312 ^ _779327 : [(30319 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324404), _1324408), _1324406)), -(hBOOL(hAPP(hAPP(c_member(_1324404), _1324406), hAPP(c_SetInterval_Oord__class_OatLeast(_1324404), _1324408))))], (30313 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324404), _1324406), hAPP(c_SetInterval_Oord__class_OatLeast(_1324404), _1324408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324404), _1324408), _1324406)))]]], (50330 ^ _779327) ^ [_1789282, _1789284, _1789286, _1789288] : [-(hAPP(c_New__DSequence_Opos__union(_1789282, _1789284, _1789286), _1789288) = c_Lazy__Sequence_Oappend(_1789282, hAPP(_1789284, _1789288), hAPP(_1789286, _1789288)))], (10 ^ _779327) ^ [_779450, _779452, _779454] : [-(_779454 = _779450), _779454 = _779452, _779452 = _779450], (41917 ^ _779327) ^ [_1593191, _1593193, _1593195, _1593197, _1593199, _1593201] : [class_Groups_Oab__semigroup__mult(_1593191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593193), _1593195)), 41927 ^ _779327 : [(41930 ^ _779327) ^ [] : [hAPP(_1593197, 41926 ^ [_1593191, _1593193, _1593195, _1593197, _1593199, _1593201]) = hAPP(_1593199, 41926 ^ [_1593191, _1593193, _1593195, _1593197, _1593199, _1593201])], (41928 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1593193), 41926 ^ [_1593191, _1593193, _1593195, _1593197, _1593199, _1593201]), _1593195)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1593191, _1593193, c_Groups_Otimes__class_Otimes(_1593191)), _1593197), _1593201), _1593195) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1593191, _1593193, c_Groups_Otimes__class_Otimes(_1593191)), _1593199), _1593201), _1593195))], (22133 ^ _779327) ^ [_1161754, _1161756, _1161758, _1161760, _1161762, _1161764] : [hAPP(c_Product__Type_Oapsnd(_1161754, _1161756, _1161758, _1161760), _1161762) = hAPP(c_Product__Type_Oapsnd(_1161754, _1161756, _1161758, _1161764), _1161762), -(hAPP(_1161760, hAPP(c_Product__Type_Osnd(_1161758, _1161754), _1161762)) = hAPP(_1161764, hAPP(c_Product__Type_Osnd(_1161758, _1161754), _1161762)))], (42314 ^ _779327) ^ [_1603160, _1603162, _1603164] : [_1603162 = _1603164, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603160, _1603160)), hAPP(hAPP(c_Product__Type_OPair(_1603160, _1603160), _1603162), _1603164)), c_Relation_OId(_1603160))))], (10339 ^ _779327) ^ [_946905, _946907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946905)), 10342 ^ _779327 : [(10351 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _946905), _946907) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _946905 = c_Groups_Oone__class_Oone(tc_Int_Oint), _946907 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (10343 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _946905), _946907) = c_Groups_Oone__class_Oone(tc_Int_Oint), 10346 ^ _779327 : [(10349 ^ _779327) ^ [] : [-(_946907 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10347 ^ _779327) ^ [] : [-(_946905 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (52742 ^ _779327) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (14999 ^ _779327) ^ [_1031749] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1031749))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1031749)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27925 ^ _779327) ^ [_1275859, _1275861, _1275863, _1275865] : [27926 ^ _779327 : [(27929 ^ _779327) ^ [] : [hBOOL(hAPP(_1275863, _1275865))], (27927 ^ _779327) ^ [] : [_1275861 = _1275865]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1275859), _1275861), _1275863), _1275865)))], (17600 ^ _779327) ^ [_1077987] : [-(c_Int_Opred(_1077987) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077987), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (42045 ^ _779327) ^ [_1595876, _1595878] : [c_Wellfounded_Oacyclic(_1595876, _1595878), 42048 ^ _779327 : [(42049 ^ _779327) ^ [_1595961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595876, _1595876)), hAPP(hAPP(c_Product__Type_OPair(_1595876, _1595876), _1595961), _1595961)), c_Transitive__Closure_Otrancl(_1595876, _1595878)))]]], (15551 ^ _779327) ^ [_1042193, _1042195] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042193)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1042195)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1042193), _1042195)))], (53076 ^ _779327) ^ [_1841469, _1841471] : [hBOOL(_1841469), -(hBOOL(hAPP(hAPP(c_fdisj, _1841471), _1841469)))], (23468 ^ _779327) ^ [_1187231, _1187233] : [-(c_Nitpick_Ouminus__frac(_1187231, _1187233) = c_Nitpick_OAbs__Frac(_1187231, 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(_1187231), _1187233))), hAPP(c_Nitpick_Odenom(_1187231), _1187233))))], (52686 ^ _779327) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (42735 ^ _779327) ^ [_1613242, _1613244, _1613246] : [c_Relation_Ototal__on(_1613242, _1613244, hAPP(c_Relation_Oconverse(_1613242, _1613242), _1613246)), -(c_Relation_Ototal__on(_1613242, _1613244, _1613246))], (48736 ^ _779327) ^ [_1756580, _1756582] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1756580), _1756582) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1756580, _1756582)))], (39714 ^ _779327) ^ [_1532926, _1532928] : [c_Orderings_Obot__class_Obot(tc_fun(_1532926, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1532926), _1532928), 39717 ^ _779327 : [(39718 ^ _779327) ^ [_1533011] : [hBOOL(hAPP(_1532928, _1533011))]]], (48509 ^ _779327) ^ [_1750120, _1750122, _1750124, _1750126] : [-(c_List_Otranspose(_1750120, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1750120)), hAPP(hAPP(c_List_Olist_OCons(_1750120), _1750122), _1750124)), _1750126)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1750120)), hAPP(hAPP(c_List_Olist_OCons(_1750120), _1750122), c_List_Oconcat(_1750120, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750120), tc_List_Olist(_1750120)), c_List_Olist_Olist__case(tc_List_Olist(_1750120), _1750120, c_List_Olist_ONil(_1750120), hAPP(hAPP(c_COMBB(tc_List_Olist(_1750120), tc_fun(tc_List_Olist(_1750120), tc_List_Olist(_1750120)), _1750120), c_COMBK(tc_List_Olist(_1750120), tc_List_Olist(_1750120))), hAPP(hAPP(c_COMBC(_1750120, tc_List_Olist(_1750120), tc_List_Olist(_1750120)), c_List_Olist_OCons(_1750120)), c_List_Olist_ONil(_1750120))))), _1750126)))), c_List_Otranspose(_1750120, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1750120)), _1750124), c_List_Oconcat(tc_List_Olist(_1750120), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750120), tc_List_Olist(tc_List_Olist(_1750120))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1750120)), _1750120, c_List_Olist_ONil(tc_List_Olist(_1750120)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1750120), tc_List_Olist(tc_List_Olist(_1750120))), _1750120), hAPP(hAPP(c_COMBC(tc_List_Olist(_1750120), tc_List_Olist(tc_List_Olist(_1750120)), tc_List_Olist(tc_List_Olist(_1750120))), c_List_Olist_OCons(tc_List_Olist(_1750120))), c_List_Olist_ONil(tc_List_Olist(_1750120)))))), _1750126))))))], (20545 ^ _779327) ^ [_1130465, _1130467, _1130469, _1130471] : [class_Fields_Olinordered__field__inverse__zero(_1130465), class_Int_Onumber(_1130465), 20552 ^ _779327 : [(20553 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130465), _1130467), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))), _1130471)), 20556 ^ _779327 : [(20563 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)))), 20566 ^ _779327 : [(20573 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)), c_Groups_Ozero__class_Ozero(_1130465)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), _1130471)))], (20567 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)), c_Groups_Ozero__class_Ozero(_1130465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130465), _1130471), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))), _1130467)))]]], (20557 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), _1130467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130465), _1130471), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)))))]]], (20579 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130465), _1130467), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))), _1130471))), 20582 ^ _779327 : [(20585 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), _1130467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130465), _1130471), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))))], (20583 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))))]], 20586 ^ _779327 : [(20589 ^ _779327) ^ [] : [20590 ^ _779327 : [(20593 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130465), _1130471), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469))), _1130467))], (20591 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)), c_Groups_Ozero__class_Ozero(_1130465))))]], 20594 ^ _779327 : [(20597 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), _1130471))], (20595 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)), c_Groups_Ozero__class_Ozero(_1130465)))]]], (20587 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130465), c_Groups_Ozero__class_Ozero(_1130465)), hAPP(c_Int_Onumber__class_Onumber__of(_1130465), _1130469)))]]]]], (51055 ^ _779327) ^ [_1804495, _1804497, _1804499] : [_1804497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1804495) = c_List_Oreplicate(_1804495, _1804497, _1804499))], (5704 ^ _779327) ^ [_869564, _869566, _869568] : [-(hAPP(c_Nat_Onat_Onat__rec(_869564, _869566, _869568), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _869566)], (31215 ^ _779327) ^ [_1344763, _1344765] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344763), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344765))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344763), _1344765)))], (17662 ^ _779327) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (12349 ^ _779327) ^ [_984823, _984825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984823), _984825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _984823)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _984825))))], (34162 ^ _779327) ^ [_1405321, _1405323, _1405325, _1405327, _1405329, _1405331] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1405321, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405323, _1405321, _1405325), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1405327, tc_fun(_1405323, tc_HOL_Obool)), _1405329), _1405331))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1405327, tc_fun(_1405321, tc_HOL_Obool)), _1405329), hAPP(hAPP(c_COMBB(tc_fun(_1405323, tc_HOL_Obool), tc_fun(_1405321, tc_HOL_Obool), _1405327), c_Relation_OImage(_1405323, _1405321, _1405325)), _1405331)))))], (44496 ^ _779327) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43339 ^ _779327) ^ [_1627817, _1627819, _1627821] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1627817), _1627819)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627817, tc_HOL_Obool)), _1627821), _1627819) = hAPP(hAPP(c_Finite__Set_Ofold(_1627817, tc_fun(_1627817, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1627817, tc_HOL_Obool), tc_fun(tc_fun(_1627817, tc_HOL_Obool), tc_fun(_1627817, tc_HOL_Obool)), _1627817), hAPP(c_COMBC(tc_fun(_1627817, tc_HOL_Obool), tc_fun(_1627817, tc_HOL_Obool), tc_fun(_1627817, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1627817, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1627817, tc_fun(_1627817, tc_HOL_Obool), tc_fun(_1627817, tc_HOL_Obool)), c_Set_Oinsert(_1627817)), c_Orderings_Obot__class_Obot(tc_fun(_1627817, tc_HOL_Obool))))), _1627821), _1627819))], (21118 ^ _779327) ^ [_1141361, _1141363, _1141365, _1141367, _1141369, _1141371] : [class_Complete__Lattice_Ocomplete__lattice(_1141361), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141363, tc_fun(_1141365, _1141361)), _1141367), _1141369), _1141371) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141363, _1141361), _1141367), hAPP(hAPP(c_COMBC(_1141363, _1141365, _1141361), _1141369), _1141371)))], (19299 ^ _779327) ^ [_1107990, _1107992, _1107994, _1107996] : [class_Fields_Ofield__inverse__zero(_1107990), -(_1107992 = c_Groups_Ozero__class_Ozero(_1107990)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107990), _1107992), _1107994)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107990), _1107992), _1107996)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1107990), _1107994), _1107996))], (35327 ^ _779327) ^ [_1432564, _1432566, _1432568, _1432570, _1432572] : [_1432564 = c_Orderings_Obot__class_Obot(tc_fun(_1432566, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432568, tc_HOL_Obool)), _1432570), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432566, tc_fun(_1432568, tc_HOL_Obool)), _1432564), _1432572)) = _1432570)], (3084 ^ _779327) ^ [_825636, _825638] : [_825638 = _825636, -(c_Nat_Osemiring__1__class_ONats(_825638) = c_Nat_Osemiring__1__class_ONats(_825636))], (1278 ^ _779327) ^ [_798290, _798292] : [-(class_Rings_Ocomm__ring__1(_798290)), _798292 = _798290, class_Rings_Ocomm__ring__1(_798292)], (47346 ^ _779327) ^ [_1724521, _1724523] : [-(_1724521 = c_List_Olist_ONil(_1724523)), -(hBOOL(hAPP(hAPP(c_member(_1724523), c_List_Olast(_1724523, _1724521)), hAPP(c_List_Oset(_1724523), _1724521))))], (45442 ^ _779327) ^ [_1680393, _1680395, _1680397, _1680399] : [_1680399 = c_List_Olist_ONil(_1680395), -(c_List_Olist_ONil(_1680393) = hAPP(hAPP(c_List_Omap(_1680395, _1680393), _1680397), _1680399))], (35786 ^ _779327) ^ [_1443079, _1443081, _1443083, _1443085, _1443087] : [class_Groups_Oab__group__add(_1443079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443081), _1443083)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443081), _1443085)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443081, _1443079), _1443087), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443081, tc_HOL_Obool)), _1443083), _1443085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1443079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1443079), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443081, _1443079), _1443087), _1443083)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443081, _1443079), _1443087), _1443085))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443081, _1443079), _1443087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443081, tc_HOL_Obool)), _1443083), _1443085))))], (43115 ^ _779327) ^ [_1623250, _1623252, _1623254, _1623256, _1623258] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1623250, _1623252, _1623254), _1623256), _1623258) = c_HOL_OThe(_1623252, c_Finite__Set_Ofold__graph(_1623250, _1623252, _1623254, _1623256, _1623258)))], (26685 ^ _779327) ^ [_1249125, _1249127] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1249125, _1249127)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1249127), _1249125)))], (3030 ^ _779327) ^ [_824709, _824711, _824713, _824715] : [-(c_Orderings_Oord__class_OLeast(_824715, _824711) = c_Orderings_Oord__class_OLeast(_824713, _824709)), _824715 = _824713, _824711 = _824709], (13890 ^ _779327) ^ [_1012559, _1012561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012559), _1012561)), -(_1012561 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1012559), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 13893 ^ [_1012559, _1012561]))))], (22811 ^ _779327) ^ [_1174578, _1174580] : [class_Orderings_Olinorder(_1174578), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1174578), _1174580), _1174580) = _1174580)], (46518 ^ _779327) ^ [_1706899, _1706901] : [-(hAPP(hAPP(c_List_Odrop(_1706899), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1706901) = _1706901)], (15594 ^ _779327) ^ [_1042905] : [class_Int_Onumber__ring(_1042905), c_Int_Oiszero(_1042905, hAPP(c_Int_Onumber__class_Onumber__of(_1042905), c_Int_OMin))], (11093 ^ _779327) ^ [_960388, _960390, _960392] : [class_Groups_Oab__group__add(_960388), -(hAPP(c_Groups_Ouminus__class_Ouminus(_960388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960388), _960390), _960392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960388), hAPP(c_Groups_Ouminus__class_Ouminus(_960388), _960390)), hAPP(c_Groups_Ouminus__class_Ouminus(_960388), _960392)))], (23815 ^ _779327) ^ [_1194447, _1194449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1194447)), 23818 ^ _779327 : [(23825 ^ _779327) ^ [] : [_1194449 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194447), _1194449)), _1194447)))], (23819 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1194447), _1194449)), _1194447)), -(_1194449 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16487 ^ _779327) ^ [] : [c_Int_OMin = c_Int_OPls], (1728 ^ _779327) ^ [_803915, _803917] : [-(class_Groups_Ocomm__monoid__add(_803915)), _803917 = _803915, class_Groups_Ocomm__monoid__add(_803917)], (33448 ^ _779327) ^ [_1388944, _1388946, _1388948, _1388950, _1388952] : [class_Groups_Oordered__ab__group__add(_1388944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388946), _1388948)), 33458 ^ _779327 : [(33461 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388944), c_Groups_Ozero__class_Ozero(_1388944)), hAPP(_1388950, 33457 ^ [_1388944, _1388946, _1388948, _1388950, _1388952])))], (33459 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388946), 33457 ^ [_1388944, _1388946, _1388948, _1388950, _1388952]), _1388948)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388946, _1388944), _1388950), _1388948) = c_Groups_Ozero__class_Ozero(_1388944), hBOOL(hAPP(hAPP(c_member(_1388946), _1388952), _1388948)), -(hAPP(_1388950, _1388952) = c_Groups_Ozero__class_Ozero(_1388944))], (48623 ^ _779327) ^ [_1752766, _1752768, _1752770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752766), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1752768))), c_List_Otranspose(_1752768, _1752770)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1752768)), c_List_Otranspose(_1752768, _1752770)), _1752766) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1752768), _1752768), hAPP(hAPP(c_COMBC(tc_List_Olist(_1752768), tc_Nat_Onat, _1752768), c_List_Onth(_1752768)), _1752766)), hAPP(c_List_Ofilter(tc_List_Olist(_1752768), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1752768)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752766)), c_Nat_Osize__class_Osize(tc_List_Olist(_1752768)))), _1752770)))], (51279 ^ _779327) ^ [_1809339, _1809341, _1809343, _1809345, _1809347] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1809339, _1809341, _1809343) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1809339, _1809345, _1809347), 51282 ^ _779327 : [(51285 ^ _779327) ^ [] : [-(_1809343 = _1809347)], (51283 ^ _779327) ^ [] : [-(_1809341 = _1809345)]]], (29508 ^ _779327) ^ [_1306276, _1306278, _1306280, _1306282] : [29509 ^ _779327 : [(29512 ^ _779327) ^ [] : [_1306278 = _1306282], (29510 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1306276), _1306278), _1306280))]], -(hBOOL(hAPP(hAPP(c_member(_1306276), _1306278), hAPP(hAPP(c_Set_Oinsert(_1306276), _1306282), _1306280))))], (37535 ^ _779327) ^ [_1481453, _1481455, _1481457, _1481459, _1481461] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1481453, _1481453, _1481455, _1481457, _1481459), _1481461)), -(hBOOL(hAPP(hAPP(c_member(_1481453), _1481457), _1481459))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1481453, _1481455, hAPP(hAPP(c_Set_Oinsert(_1481453), _1481457), _1481459)), _1481461)))], (28766 ^ _779327) ^ [_1292160, _1292162] : [class_Lattices_Obounded__lattice__bot(_1292160), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292160), _1292162), c_Orderings_Obot__class_Obot(_1292160)) = _1292162)], (45870 ^ _779327) ^ [_1691502, _1691504, _1691506, _1691508] : [class_Groups_Ocomm__monoid__add(_1691502), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1691502), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1691502), _1691504), c_List_Oupto(_1691506, _1691508))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1691502), _1691504), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691506, _1691508))))], (32448 ^ _779327) ^ [_1368818, _1368820, _1368822] : [class_Orderings_Olinorder(_1368818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368818), _1368820)), -(hBOOL(hAPP(hAPP(c_member(_1368818), _1368822), _1368820))), -(_1368820 = c_Orderings_Obot__class_Obot(tc_fun(_1368818, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1368818, hAPP(hAPP(c_Set_Oinsert(_1368818), _1368822), _1368820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368818), _1368822), c_Big__Operators_Olinorder__class_OMin(_1368818, _1368820)))], (34855 ^ _779327) ^ [_1421819, _1421821, _1421823, _1421825] : [class_Lattices_Osemilattice__inf(_1421819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421819), _1421821), _1421823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421819), _1421821), _1421825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421819), _1421821), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1421819), _1421823), _1421825))))], (27296 ^ _779327) ^ [_1261389, _1261391, _1261393, _1261395, _1261397] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261389, tc_HOL_Obool)), _1261391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261393, tc_fun(_1261389, tc_HOL_Obool)), _1261395), _1261397)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1261393, tc_fun(_1261389, tc_HOL_Obool)), _1261395), hAPP(hAPP(c_COMBB(tc_fun(_1261389, tc_HOL_Obool), tc_fun(_1261389, tc_HOL_Obool), _1261393), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261389, tc_HOL_Obool)), _1261391)), _1261397)))], (46046 ^ _779327) ^ [_1695466, _1695468, _1695470, _1695472, _1695474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695466), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695468)), _1695470))), -(hAPP(hAPP(c_List_Olist__update(_1695468, hAPP(hAPP(c_List_Oappend(_1695468), _1695470), _1695472)), _1695466), _1695474) = hAPP(hAPP(c_List_Oappend(_1695468), hAPP(hAPP(c_List_Olist__update(_1695468, _1695470), _1695466), _1695474)), _1695472))], (42723 ^ _779327) ^ [_1613026, _1613028, _1613030, _1613032, _1613034] : [c_Relation_Osingle__valued(_1613026, _1613028, _1613030), c_Relation_Osingle__valued(_1613028, _1613032, _1613034), -(c_Relation_Osingle__valued(_1613026, _1613032, hAPP(hAPP(c_Relation_Orel__comp(_1613026, _1613028, _1613032), _1613030), _1613034)))], (25812 ^ _779327) ^ [_1231822, _1231824, _1231826, _1231828, _1231830] : [class_Groups_Oab__group__add(_1231822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231824), _1231826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231826), _1231828)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231822), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231822), _1231830), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231824), _1231828))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231822), _1231830), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231824), _1231826))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1231822), _1231830), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1231826), _1231828)))], (10608 ^ _779327) ^ [_951368, _951370] : [class_Rings_Olinordered__idom(_951368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951368), c_Groups_Ozero__class_Ozero(_951368)), _951370)), -(c_Groups_Osgn__class_Osgn(_951368, _951370) = c_Groups_Oone__class_Oone(_951368))], (37933 ^ _779327) ^ [_1489822] : [class_Nat_Osemiring__char__0(_1489822), -(c_Fun_Oinj__on(tc_Nat_Onat, _1489822, c_Nat_Osemiring__1__class_Oof__nat(_1489822), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29764 ^ _779327) ^ [_1311238, _1311240, _1311242] : [-(hBOOL(hAPP(hAPP(c_member(_1311238), _1311240), hAPP(hAPP(c_Set_Oinsert(_1311238), _1311240), _1311242))))], (50343 ^ _779327) ^ [_1789617, _1789619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789617), _1789619)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789617, _1789619) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (25490 ^ _779327) ^ [_1224389, _1224391, _1224393] : [class_Orderings_Olinorder(_1224389), 25493 ^ _779327 : [(25500 ^ _779327) ^ [] : [_1224391 = _1224393, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1224389), _1224391) = hAPP(c_SetInterval_Oord__class_OlessThan(_1224389), _1224393))], (25494 ^ _779327) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1224389), _1224391) = hAPP(c_SetInterval_Oord__class_OlessThan(_1224389), _1224393), -(_1224391 = _1224393)]]], (43979 ^ _779327) ^ [_1641218, _1641220, _1641222] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1641218, tc_HOL_Obool)), _1641220), _1641222) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1641218, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1641218, tc_HOL_Obool)), _1641220), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1641218, tc_HOL_Obool)), _1641222), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1641218, tc_HOL_Obool), tc_HOL_Obool))))))], (50602 ^ _779327) ^ [_1795292, _1795294, _1795296] : [class_Enum_Oenum(_1795292), class_Enum_Oenum(_1795294), 50609 ^ _779327 : [(50616 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1795294), hAPP(hAPP(c_COMBB(tc_fun(_1795292, tc_HOL_Obool), tc_HOL_Obool, _1795294), c_Enum_Oenum__class_Oenum__all(_1795292)), hAPP(hAPP(c_COMBB(tc_fun(_1795292, tc_prod(_1795294, _1795292)), tc_fun(_1795292, tc_HOL_Obool), _1795294), hAPP(c_COMBB(tc_prod(_1795294, _1795292), tc_HOL_Obool, _1795292), _1795296)), c_Product__Type_OPair(_1795294, _1795292))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1795294, _1795292)), _1795296)))], (50610 ^ _779327) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1795294, _1795292)), _1795296)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1795294), hAPP(hAPP(c_COMBB(tc_fun(_1795292, tc_HOL_Obool), tc_HOL_Obool, _1795294), c_Enum_Oenum__class_Oenum__all(_1795292)), hAPP(hAPP(c_COMBB(tc_fun(_1795292, tc_prod(_1795294, _1795292)), tc_fun(_1795292, tc_HOL_Obool), _1795294), hAPP(c_COMBB(tc_prod(_1795294, _1795292), tc_HOL_Obool, _1795292), _1795296)), c_Product__Type_OPair(_1795294, _1795292))))))]]], (5858 ^ _779327) ^ [_871691, _871693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _871691), _871693)), _871691 = _871693], (21124 ^ _779327) ^ [_1141512, _1141514, _1141516, _1141518, _1141520, _1141522] : [class_Complete__Lattice_Ocomplete__lattice(_1141512), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141514, _1141512), _1141516), hAPP(hAPP(c_COMBB(tc_fun(_1141518, _1141512), _1141512, _1141514), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141518, _1141512), _1141520)), _1141522)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141518, _1141512), _1141520), hAPP(hAPP(c_COMBB(tc_fun(_1141514, _1141512), _1141512, _1141518), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1141514, _1141512), _1141516)), hAPP(c_COMBC(_1141514, _1141518, _1141512), _1141522))))], (29989 ^ _779327) ^ [_1315498, _1315500, _1315502, _1315504] : [29990 ^ _779327 : [(29993 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1315498), _1315500), _1315504))], (29991 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1315498), _1315500), _1315502))]], -(hBOOL(hAPP(hAPP(c_member(_1315498), _1315500), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315498, tc_HOL_Obool)), _1315502), _1315504))))], (51480 ^ _779327) ^ [_1814165, _1814167] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1814165)), _1814167)), 51484 ^ _779327 : [(51485 ^ _779327) ^ [_1814266] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1814165)), _1814266), _1814167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814165)), _1814266)), 51483 ^ [_1814165, _1814167])))]]], (18779 ^ _779327) ^ [] : [-(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))], (12886 ^ _779327) ^ [_994666, _994668] : [class_Rings_Olinordered__idom(_994666), 12889 ^ _779327 : [(12896 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994666), _994668), c_Groups_Ozero__class_Ozero(_994666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994666), _994668), hAPP(c_Groups_Ouminus__class_Ouminus(_994666), _994668))))], (12890 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994666), _994668), hAPP(c_Groups_Ouminus__class_Ouminus(_994666), _994668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994666), _994668), c_Groups_Ozero__class_Ozero(_994666))))]]], (23532 ^ _779327) ^ [_1188886, _1188888, _1188890] : [-(c_HOL_OThe(tc_prod(_1188886, _1188888), _1188890) = c_HOL_OThe(tc_prod(_1188886, _1188888), hAPP(c_Product__Type_Oprod_Oprod__case(_1188886, _1188888, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1188888, tc_prod(_1188886, _1188888)), tc_fun(_1188888, tc_HOL_Obool), _1188886), hAPP(c_COMBB(tc_prod(_1188886, _1188888), tc_HOL_Obool, _1188888), _1188890)), c_Product__Type_OPair(_1188886, _1188888)))))], (17266 ^ _779327) ^ [_1072372, _1072374] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072372), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072372)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1072374)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072372), _1072374)))], (49495 ^ _779327) ^ [_1770957, _1770959, _1770961, _1770963] : [-(hAPP(c_List_Orev(_1770957), hAPP(hAPP(c_List_Omap(_1770959, _1770957), _1770961), _1770963)) = hAPP(hAPP(c_List_Omap(_1770959, _1770957), _1770961), hAPP(c_List_Orev(_1770959), _1770963)))], (29855 ^ _779327) ^ [_1313017, _1313019] : [_1313017 = _1313019, -(hAPP(c_Int_ORep__Integ, _1313017) = hAPP(c_Int_ORep__Integ, _1313019))], (15734 ^ _779327) ^ [_1045516] : [class_Int_Onumber__ring(_1045516), -(hAPP(c_Int_Onumber__class_Onumber__of(_1045516), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1045516), c_Groups_Oone__class_Oone(_1045516)))], (14599 ^ _779327) ^ [_1025269, _1025271, _1025273] : [class_Divides_Osemiring__div(_1025269), -(_1025271 = c_Groups_Ozero__class_Ozero(_1025269)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025269), _1025273), _1025271)), _1025271) = _1025273)], (8026 ^ _779327) ^ [_906702, _906704, _906706] : [class_Rings_Olinordered__semiring__strict(_906702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906702), c_Groups_Ozero__class_Ozero(_906702)), _906704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906702), c_Groups_Ozero__class_Ozero(_906702)), _906706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906702), c_Groups_Ozero__class_Ozero(_906702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_906702), _906704), _906706))))], (24109 ^ _779327) ^ [_1199348, _1199350] : [_1199350 = _1199348, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199348), _1199350)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199350), _1199348)))], (37657 ^ _779327) ^ [_1484352, _1484354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1484352), c_Orderings_Otop__class_Otop(tc_fun(_1484352, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484354), c_Orderings_Otop__class_Otop(tc_fun(_1484354, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1484352, _1484354)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1484352, _1484354), tc_HOL_Obool)))))], (12387 ^ _779327) ^ [_985417] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _985417) = _985417)], (10540 ^ _779327) ^ [_950067, _950069] : [class_Rings_Oring__1(_950067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950069)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_950067), hAPP(c_Int_Onat, _950069)) = hAPP(c_Int_Oring__1__class_Oof__int(_950067), _950069))], (27620 ^ _779327) ^ [_1268916, _1268918, _1268920, _1268922, _1268924] : [27622 ^ _779327 : [(27628 ^ _779327) ^ [] : [hBOOL(hAPP(_1268924, 27624 ^ [_1268916, _1268918, _1268920, _1268922, _1268924]))], (27626 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1268916), 27624 ^ [_1268916, _1268918, _1268920, _1268922, _1268924]), hAPP(_1268922, 27621 ^ [_1268916, _1268918, _1268920, _1268922, _1268924]))))], (27623 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1268918), 27621 ^ [_1268916, _1268918, _1268920, _1268922, _1268924]), _1268920)))]], 27629 ^ _779327 : [(27630 ^ _779327) ^ [_1269226] : [hBOOL(hAPP(hAPP(c_member(_1268916), _1269226), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1268918, tc_fun(_1268916, tc_HOL_Obool)), _1268920), _1268922))), -(hBOOL(hAPP(_1268924, _1269226)))]]], (24029 ^ _779327) ^ [_1198003, _1198005] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198003), _1198005)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198005), _1198003))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198005), _1198003)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198003), _1198005)))], (13897 ^ _779327) ^ [_1012678, _1012680] : [13898 ^ _779327 : [(13899 ^ _779327) ^ [_1012734] : [_1012680 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1012678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1012734)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012678), _1012680)))], (5736 ^ _779327) ^ [_870064, _870066] : [class_Orderings_Opreorder(_870064), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870064), _870066), _870066)))], (28950 ^ _779327) ^ [_1295263, _1295265, _1295267] : [class_Orderings_Oorder(_1295263), _1295265 = _1295267, -(c_SetInterval_Oord__class_OatLeastAtMost(_1295263, _1295265, _1295267) = hAPP(hAPP(c_Set_Oinsert(_1295263), _1295265), c_Orderings_Obot__class_Obot(tc_fun(_1295263, tc_HOL_Obool))))], (46696 ^ _779327) ^ [_1711197, _1711199, _1711201, _1711203, _1711205] : [-(hAPP(hAPP(c_List_Ozip(_1711197, _1711199), hAPP(hAPP(c_List_Oappend(_1711197), _1711201), _1711203)), _1711205) = hAPP(hAPP(c_List_Oappend(tc_prod(_1711197, _1711199)), hAPP(hAPP(c_List_Ozip(_1711197, _1711199), _1711201), hAPP(hAPP(c_List_Otake(_1711199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711197)), _1711201)), _1711205))), hAPP(hAPP(c_List_Ozip(_1711197, _1711199), _1711203), hAPP(hAPP(c_List_Odrop(_1711199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711197)), _1711201)), _1711205))))], (11255 ^ _779327) ^ [_963952, _963954, _963956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963952), _963954)), 11258 ^ _779327 : [(11265 ^ _779327) ^ [] : [_963954 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963956), _963952), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963954), _963952) = _963956)], (11259 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963954), _963952) = _963956, -(_963954 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963956), _963952))]]], (18370 ^ _779327) ^ [_1091351] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1091351))), 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), _1091351), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (40923 ^ _779327) ^ [_1570125, _1570127] : [-(hAPP(c_Relation_ODomain(_1570125, _1570127), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570125, _1570127), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1570125, tc_HOL_Obool)))], (41423 ^ _779327) ^ [_1581877, _1581879, _1581881, _1581883, _1581885, _1581887, _1581889] : [class_Groups_Oab__semigroup__mult(_1581877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581879), _1581881)), c_Fun_Oinj__on(_1581879, _1581883, _1581885, _1581881), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1581877, _1581883, c_Groups_Otimes__class_Otimes(_1581877)), _1581887), _1581889), hAPP(c_Set_Oimage(_1581879, _1581883, _1581885), _1581881)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1581877, _1581879, c_Groups_Otimes__class_Otimes(_1581877)), hAPP(c_Fun_Ocomp(_1581883, _1581877, _1581879, _1581887), _1581885)), _1581889), _1581881))], (16467 ^ _779327) ^ [_1058500, _1058502, _1058504] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058500, _1058502)), _1058504) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058500), _1058504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1058502), _1058504)))], (45448 ^ _779327) ^ [_1680502, _1680504, _1680506] : [-(hAPP(hAPP(c_List_Ozip(_1680502, _1680504), hAPP(hAPP(c_List_Omap(tc_prod(_1680502, _1680504), _1680502), c_Product__Type_Ofst(_1680502, _1680504)), _1680506)), hAPP(hAPP(c_List_Omap(tc_prod(_1680502, _1680504), _1680504), c_Product__Type_Osnd(_1680502, _1680504)), _1680506)) = _1680506)], (52964 ^ _779327) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (6975 ^ _779327) ^ [_888508, _888510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888508), hAPP(c_Nat_OSuc, _888510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888508), _888510))), -(_888508 = _888510)], (40763 ^ _779327) ^ [_1566046, _1566048] : [-(c_FunDef_Oreduction__pair(_1566046, _1566048)), c_Wellfounded_Owf(_1566046, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool), tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool)), _1566048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1566046, _1566046, _1566046), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool), tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool)), _1566048)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool), tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool)), _1566048))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool), tc_fun(tc_prod(_1566046, _1566046), tc_HOL_Obool)), _1566048)))], (44396 ^ _779327) ^ [_1650854, _1650856, _1650858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1650854), _1650856)), hBOOL(hAPP(_1650858, c_Orderings_Obot__class_Obot(tc_fun(_1650854, tc_HOL_Obool)))), 44407 ^ _779327 : [(44410 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1650854), 44405 ^ [_1650854, _1650856, _1650858]), 44406 ^ [_1650854, _1650856, _1650858]))], (44412 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1650858, 44406 ^ [_1650854, _1650856, _1650858])))], (44414 ^ _779327) ^ [] : [hBOOL(hAPP(_1650858, hAPP(hAPP(c_Set_Oinsert(_1650854), 44405 ^ [_1650854, _1650856, _1650858]), 44406 ^ [_1650854, _1650856, _1650858])))], (44408 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1650854), 44406 ^ [_1650854, _1650856, _1650858])))]], -(hBOOL(hAPP(_1650858, _1650856)))], (2818 ^ _779327) ^ [_821263, _821265, _821267, _821269, _821271, _821273, _821275, _821277] : [-(c_New__DSequence_Oneg__decr__bind(_821277, _821273, _821269, _821265) = c_New__DSequence_Oneg__decr__bind(_821275, _821271, _821267, _821263)), _821277 = _821275, _821273 = _821271, _821269 = _821267, _821265 = _821263], (16637 ^ _779327) ^ [_1061511, _1061513] : [class_Groups_Oordered__ab__group__add__abs(_1061511), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1061511), hAPP(c_Groups_Ouminus__class_Ouminus(_1061511), _1061513)), hAPP(c_Groups_Oabs__class_Oabs(_1061511), _1061513))))], (11075 ^ _779327) ^ [_960011, _960013, _960015] : [class_Groups_Oab__group__add(_960011), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960011), _960013), _960015) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960011), _960013), hAPP(c_Groups_Ouminus__class_Ouminus(_960011), _960015)))], (18176 ^ _779327) ^ [_1087951, _1087953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087951), _1087953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1087951)), c_Int_OBit1(_1087953))))], (41097 ^ _779327) ^ [_1574751, _1574753] : [c_Wellfounded_Owf(_1574751, _1574753), -(c_Wellfounded_Oacyclic(_1574751, _1574753))], (43861 ^ _779327) ^ [_1638878, _1638880, _1638882] : [class_Complete__Lattice_Ocomplete__lattice(_1638878), class_Orderings_Olinorder(_1638878), 43868 ^ _779327 : [(43878 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638878), _1638880), c_Complete__Lattice_OSup__class_OSup(_1638878, _1638882)))), 43879 ^ _779327 : [(43880 ^ _779327) ^ [_1639184] : [hBOOL(hAPP(hAPP(c_member(_1638878), _1639184), _1638882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638878), _1638880), _1639184))]]], (43869 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638878), _1638880), c_Complete__Lattice_OSup__class_OSup(_1638878, _1638882))), 43873 ^ _779327 : [(43876 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1638878), _1638880), 43872 ^ [_1638878, _1638880, _1638882])))], (43874 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1638878), 43872 ^ [_1638878, _1638880, _1638882]), _1638882)))]]]]], (40368 ^ _779327) ^ [_1555240, _1555242] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1555240), _1555242)), -(_1555242 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1555240, 40372 ^ [_1555240, _1555242]), 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)), 40371 ^ [_1555240, _1555242]))))], (16888 ^ _779327) ^ [_1065852, _1065854, _1065856] : [class_Rings_Olinordered__idom(_1065852), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065852), c_Groups_Ozero__class_Ozero(_1065852)), hAPP(hAPP(c_Power_Opower__class_Opower(_1065852), hAPP(c_Groups_Oabs__class_Oabs(_1065852), _1065854)), _1065856))))], (51491 ^ _779327) ^ [_1814405] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1814405)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1814405)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47136 ^ _779327) ^ [_1720288, _1720290] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720288), _1720290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1720288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 47142 ^ _779327 : [(47145 ^ _779327) ^ [] : [47141 ^ [_1720288, _1720290] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47143 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47141 ^ [_1720288, _1720290]), hAPP(c_List_Oset(tc_Nat_Onat), _1720290))))]]], (20739 ^ _779327) ^ [_1134245, _1134247, _1134249, _1134251] : [class_Fields_Olinordered__field__inverse__zero(_1134245), class_Int_Onumber(_1134245), 20746 ^ _779327 : [(20747 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134245), _1134249), _1134251))), 20750 ^ _779327 : [(20757 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), c_Groups_Ozero__class_Ozero(_1134245)), _1134251))), 20760 ^ _779327 : [(20767 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), _1134251), c_Groups_Ozero__class_Ozero(_1134245)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), c_Groups_Ozero__class_Ozero(_1134245))))], (20761 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), _1134251), c_Groups_Ozero__class_Ozero(_1134245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), _1134249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), _1134251))))]]], (20751 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), c_Groups_Ozero__class_Ozero(_1134245)), _1134251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), _1134251)), _1134249)))]]], (20773 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134245), _1134249), _1134251)))), 20776 ^ _779327 : [(20779 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), _1134251)), _1134249))], (20777 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), c_Groups_Ozero__class_Ozero(_1134245)), _1134251)))]], 20780 ^ _779327 : [(20783 ^ _779327) ^ [] : [20784 ^ _779327 : [(20787 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), _1134249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), _1134251)))], (20785 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), _1134251), c_Groups_Ozero__class_Ozero(_1134245))))]], 20788 ^ _779327 : [(20791 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134245), hAPP(c_Int_Onumber__class_Onumber__of(_1134245), _1134247)), c_Groups_Ozero__class_Ozero(_1134245)))], (20789 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), _1134251), c_Groups_Ozero__class_Ozero(_1134245)))]]], (20781 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134245), c_Groups_Ozero__class_Ozero(_1134245)), _1134251))]]]]], (40674 ^ _779327) ^ [_1564015, _1564017] : [-(hAPP(c_Relation_ORange(_1564015, _1564017), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564015, _1564017), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1564017, tc_HOL_Obool)))], (16327 ^ _779327) ^ [_1056100] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056100), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056100)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1056100)))], (49373 ^ _779327) ^ [_1768270, _1768272, _1768274, _1768276, _1768278] : [class_Orderings_Olinorder(_1768270), c_Fun_Oinj__on(_1768272, _1768270, _1768274, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1768272, tc_HOL_Obool)), hAPP(c_List_Oset(_1768272), _1768276)), hAPP(c_List_Oset(_1768272), _1768278))), c_List_Olinorder__class_Osorted(_1768270, hAPP(hAPP(c_List_Omap(_1768272, _1768270), _1768274), _1768276)), hBOOL(hAPP(c_List_Odistinct(_1768270), hAPP(hAPP(c_List_Omap(_1768272, _1768270), _1768274), _1768276))), c_List_Olinorder__class_Osorted(_1768270, hAPP(hAPP(c_List_Omap(_1768272, _1768270), _1768274), _1768278)), hBOOL(hAPP(c_List_Odistinct(_1768270), hAPP(hAPP(c_List_Omap(_1768272, _1768270), _1768274), _1768278))), hAPP(c_List_Oset(_1768272), _1768276) = hAPP(c_List_Oset(_1768272), _1768278), -(_1768276 = _1768278)], (9789 ^ _779327) ^ [_937975, _937977] : [class_Groups_Ocomm__monoid__mult(_937975), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937975), c_Groups_Oone__class_Oone(_937975)), _937977) = _937977)], (50386 ^ _779327) ^ [_1790412, _1790414, _1790416] : [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), _1790412), _1790414))), -(hBOOL(hAPP(hAPP(_1790416, _1790412), _1790414))), 50393 ^ _779327 : [(50396 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50391 ^ [_1790412, _1790414, _1790416]), 50392 ^ [_1790412, _1790414, _1790416]))), -(hBOOL(hAPP(hAPP(_1790416, 50391 ^ [_1790412, _1790414, _1790416]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50392 ^ [_1790412, _1790414, _1790416]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50402 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(_1790416, 50391 ^ [_1790412, _1790414, _1790416]), 50392 ^ [_1790412, _1790414, _1790416]))], (50394 ^ _779327) ^ [] : [-(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), 50391 ^ [_1790412, _1790414, _1790416]), 50392 ^ [_1790412, _1790414, _1790416]))))]]], (7526 ^ _779327) ^ [_897681, _897683, _897685] : [class_Rings_Oring__1__no__zero__divisors(_897681), -(_897683 = c_Groups_Ozero__class_Ozero(_897681)), hAPP(hAPP(c_Power_Opower__class_Opower(_897681), _897683), _897685) = c_Groups_Ozero__class_Ozero(_897681)], (22049 ^ _779327) ^ [_1159972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1159972)), 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), _1159972)) = 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), _1159972))))))], (36833 ^ _779327) ^ [_1466440, _1466442] : [-(c_Fun_Oinj__on(_1466440, _1466440, c_COMBI(_1466440), _1466442))], (13794 ^ _779327) ^ [_1010916] : [class_Rings_Olinordered__semidom(_1010916), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010916), c_Groups_Ozero__class_Ozero(_1010916)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010916), c_Groups_Oone__class_Oone(_1010916)), c_Groups_Oone__class_Oone(_1010916)))))], (1498 ^ _779327) ^ [_801040, _801042] : [-(class_Orderings_Obot(_801040)), _801042 = _801040, class_Orderings_Obot(_801042)], (52391 ^ _779327) ^ [_1833413, _1833415, _1833417] : [hAPP(c_Fun_Ocomp(_1833415, _1833413, _1833413, c_Hilbert__Choice_Oinv__into(_1833413, _1833415, c_Orderings_Otop__class_Otop(tc_fun(_1833413, tc_HOL_Obool)), _1833417)), _1833417) = c_Fun_Oid(_1833413), -(c_Fun_Oinj__on(_1833413, _1833415, _1833417, c_Orderings_Otop__class_Otop(tc_fun(_1833413, tc_HOL_Obool))))], (48511 ^ _779327) ^ [_1750346, _1750348] : [-(c_List_Oconcat(_1750346, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750346), tc_List_Olist(_1750346)), c_List_Olist_Olist__case(tc_List_Olist(_1750346), _1750346, c_List_Olist_ONil(_1750346), hAPP(hAPP(c_COMBB(tc_List_Olist(_1750346), tc_fun(tc_List_Olist(_1750346), tc_List_Olist(_1750346)), _1750346), c_COMBK(tc_List_Olist(_1750346), tc_List_Olist(_1750346))), hAPP(hAPP(c_COMBC(_1750346, tc_List_Olist(_1750346), tc_List_Olist(_1750346)), c_List_Olist_OCons(_1750346)), c_List_Olist_ONil(_1750346))))), _1750348)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1750346), _1750346), c_List_Ohd(_1750346)), hAPP(c_List_Ofilter(tc_List_Olist(_1750346), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1750346)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1750346), tc_List_Olist(_1750346), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1750346)))), _1750348)))], (28656 ^ _779327) ^ [_1289974, _1289976, _1289978] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289974, tc_HOL_Obool)), _1289976), _1289978) = c_Orderings_Obot__class_Obot(tc_fun(_1289974, tc_HOL_Obool)), 28659 ^ _779327 : [(28662 ^ _779327) ^ [] : [-(_1289978 = c_Orderings_Obot__class_Obot(tc_fun(_1289974, tc_HOL_Obool)))], (28660 ^ _779327) ^ [] : [-(_1289976 = c_Orderings_Obot__class_Obot(tc_fun(_1289974, tc_HOL_Obool)))]]], (25642 ^ _779327) ^ [_1228457, _1228459] : [hAPP(_1228457, 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), _1228457), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228459)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1228457), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1228459)))], (11833 ^ _779327) ^ [_975311, _975313, _975315] : [class_Rings_Oring(_975311), -(hAPP(c_Groups_Ouminus__class_Ouminus(_975311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975311), _975313), _975315)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975311), _975313), hAPP(c_Groups_Ouminus__class_Ouminus(_975311), _975315)))], (23634 ^ _779327) ^ [_1190811, _1190813] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1190811, _1190813) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1190811), hAPP(c_Code__Numeral_Onat__of, _1190813))))], (25904 ^ _779327) ^ [_1233621, _1233623, _1233625, _1233627] : [class_Groups_Ocomm__monoid__add(_1233621), 25907 ^ _779327 : [(25914 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233623), _1233625))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233621), _1233627), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1233625), hAPP(c_Nat_OSuc, _1233623))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1233621), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233621), _1233627), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1233625), _1233623))), hAPP(_1233627, _1233623)))], (25908 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233623), _1233625)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1233621), _1233627), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1233625), hAPP(c_Nat_OSuc, _1233623))) = c_Groups_Ozero__class_Ozero(_1233621))]]], (13957 ^ _779327) ^ [_1013759, _1013761, _1013763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013759)), _1013759 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1013761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013759), _1013763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013761), _1013759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1013763)))], (15415 ^ _779327) ^ [_1039726, _1039728, _1039730, _1039732] : [class_Divides_Oring__div(_1039726), c_Divides_Odiv__class_Omod(_1039726, _1039728, _1039730) = c_Divides_Odiv__class_Omod(_1039726, _1039732, _1039730), -(c_Divides_Odiv__class_Omod(_1039726, hAPP(c_Groups_Ouminus__class_Ouminus(_1039726), _1039728), _1039730) = c_Divides_Odiv__class_Omod(_1039726, hAPP(c_Groups_Ouminus__class_Ouminus(_1039726), _1039732), _1039730))], (17382 ^ _779327) ^ [_1074411] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1074411)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1074411))))], (30657 ^ _779327) ^ [_1332768, _1332770, _1332772, _1332774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1332768, tc_HOL_Obool)), _1332770), hAPP(hAPP(c_Set_Oinsert(_1332768), _1332772), _1332774))), 30660 ^ _779327 : [(30667 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332768), _1332772), _1332774))), 30670 ^ _779327 : [(30677 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1332768), _1332772), _1332770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332768, tc_HOL_Obool)), _1332770), _1332774)))], (30671 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332768), _1332772), _1332770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1332768, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1332768, tc_HOL_Obool)), _1332770), hAPP(hAPP(c_Set_Oinsert(_1332768), _1332772), c_Orderings_Obot__class_Obot(tc_fun(_1332768, tc_HOL_Obool))))), _1332774)))]]], (30661 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332768), _1332772), _1332774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1332768, tc_HOL_Obool)), _1332770), _1332774)))]]], (16053 ^ _779327) ^ [_1051024, _1051026, _1051028, _1051030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051026), _1051028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051028), 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), _1051026), _1051024)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1051026), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1051030, _1051024))), _1051028))))], (37003 ^ _779327) ^ [_1469904, _1469906, _1469908, _1469910, _1469912, _1469914] : [c_Fun_Oinj__on(_1469904, _1469906, _1469908, _1469910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469906, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469904, _1469906, _1469908), _1469910)), _1469912)), c_Fun_Oinj__on(_1469906, _1469904, _1469914, _1469912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469904, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469906, _1469904, _1469914), _1469912)), _1469910)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469904), _1469910)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469906), _1469912)), -(hAPP(c_Finite__Set_Ocard(_1469904), _1469910) = hAPP(c_Finite__Set_Ocard(_1469906), _1469912))], (17584 ^ _779327) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (1178 ^ _779327) ^ [_797040, _797042] : [-(class_Rings_Oring__1__no__zero__divisors(_797040)), _797042 = _797040, class_Rings_Oring__1__no__zero__divisors(_797042)], (22865 ^ _779327) ^ [_1175512, _1175514, _1175516, _1175518] : [class_Orderings_Olinorder(_1175512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175512), _1175514), _1175516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175512), _1175518), _1175516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175512), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1175512), _1175514), _1175518)), _1175516)))], (50082 ^ _779327) ^ [_1783363, _1783365] : [-(hAPP(c_List_OremoveAll(_1783363, _1783365), c_List_Olist_ONil(_1783363)) = c_List_Olist_ONil(_1783363))], (18258 ^ _779327) ^ [_1089461] : [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), _1089461))), 18261 ^ _779327 : [(18264 ^ _779327) ^ [] : [-(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(_1089461)))))], (18262 ^ _779327) ^ [] : [-(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(_1089461)))))]]], (40838 ^ _779327) ^ [_1568301, _1568303, _1568305, _1568307] : [hBOOL(hAPP(c_Predicate_ORangeP(_1568301, _1568303, _1568305), _1568307)), -(hBOOL(hAPP(hAPP(_1568305, 40841 ^ [_1568301, _1568303, _1568305, _1568307]), _1568307)))], (41381 ^ _779327) ^ [_1580964, _1580966, _1580968, _1580970, _1580972] : [class_Groups_Ocomm__monoid__add(_1580964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580966), _1580968)), c_Fun_Oinj__on(_1580966, _1580966, _1580970, _1580968), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580966, _1580964), _1580972), hAPP(c_Set_Oimage(_1580966, _1580966, _1580970), _1580968)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580966, _1580964), hAPP(c_Fun_Ocomp(_1580966, _1580964, _1580966, _1580972), _1580970)), _1580968))], (6312 ^ _779327) ^ [_878575, _878577, _878579, _878581, _878583] : [class_Orderings_Oord(_878575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878577, _878575)), _878579), _878581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878575), hAPP(_878579, _878583)), hAPP(_878581, _878583))))], (23295 ^ _779327) ^ [_1183791] : [class_Orderings_Olinorder(_1183791), -(c_Orderings_Oord_Omax(_1183791, hAPP(c_COMBC(_1183791, _1183791, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1183791))) = c_Orderings_Oord__class_Omin(_1183791))], (34413 ^ _779327) ^ [_1411858, _1411860, _1411862, _1411864, _1411866, _1411868, _1411870] : [c_Equiv__Relations_Oequiv(_1411858, _1411860, _1411862), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411858, tc_HOL_Obool)), _1411864), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411858), _1411860), _1411862))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411858, tc_HOL_Obool)), _1411866), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411858), _1411860), _1411862))), hBOOL(hAPP(hAPP(c_member(_1411858), _1411868), _1411864)), hBOOL(hAPP(hAPP(c_member(_1411858), _1411870), _1411866)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1411858, _1411858)), hAPP(hAPP(c_Product__Type_OPair(_1411858, _1411858), _1411868), _1411870)), _1411862)), -(_1411864 = _1411866)], (38768 ^ _779327) ^ [_1511048, _1511050, _1511052, _1511054, _1511056] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1511048, _1511050), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511048, tc_HOL_Obool)), _1511052), _1511054)), _1511056) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1511048, _1511050), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1511048, _1511050), _1511052), _1511056)), hAPP(hAPP(c_Product__Type_OSigma(_1511048, _1511050), _1511054), _1511056)))], (33159 ^ _779327) ^ [_1382960, _1382962, _1382964] : [class_Groups_Ocomm__monoid__mult(_1382960), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382962, _1382960), _1382964), c_Orderings_Obot__class_Obot(tc_fun(_1382962, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1382960))], (51061 ^ _779327) ^ [_1804588, _1804590] : [-(c_List_Oreplicate(_1804588, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1804590) = c_List_Olist_ONil(_1804588))], (22473 ^ _779327) ^ [_1168186, _1168188, _1168190, _1168192] : [class_Orderings_Olinorder(_1168186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168186), _1168188), _1168190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168186), _1168188), _1168192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168186), _1168188), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1168186), _1168190), _1168192))))], (10618 ^ _779327) ^ [_951523, _951525] : [class_Rings_Olinordered__idom(_951523), 10621 ^ _779327 : [(10628 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951523), c_Groups_Ozero__class_Ozero(_951523)), _951525)), -(c_Groups_Osgn__class_Osgn(_951523, _951525) = c_Groups_Oone__class_Oone(_951523))], (10622 ^ _779327) ^ [] : [c_Groups_Osgn__class_Osgn(_951523, _951525) = c_Groups_Oone__class_Oone(_951523), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951523), c_Groups_Ozero__class_Ozero(_951523)), _951525)))]]], (17910 ^ _779327) ^ [_1083391, _1083393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1083391)), c_Int_OBit0(_1083393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083391), _1083393)))], (32014 ^ _779327) ^ [_1360862, _1360864, _1360866] : [class_Orderings_Olinorder(_1360862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1360862, tc_HOL_Obool)), _1360864), _1360866)), -(_1360864 = c_Orderings_Obot__class_Obot(tc_fun(_1360862, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360862), _1360866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360862), c_Big__Operators_Olinorder__class_OMax(_1360862, _1360864)), c_Big__Operators_Olinorder__class_OMax(_1360862, _1360866))))], (50457 ^ _779327) ^ [_1791998, _1792000, _1792002, _1792004, _1792006] : [hAPP(hAPP(c_List_Olist_OCons(_1791998), _1792000), _1792002) = hAPP(c_List_Ofilter(_1791998, _1792004), _1792006), 50462 ^ _779327 : [(50471 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1792004, _1792000)))], (50473 ^ _779327) ^ [] : [-(_1792002 = hAPP(c_List_Ofilter(_1791998, _1792004), 50461 ^ [_1791998, _1792000, _1792002, _1792004, _1792006]))], (50465 ^ _779327) ^ [_1792312] : [hBOOL(hAPP(hAPP(c_member(_1791998), _1792312), hAPP(c_List_Oset(_1791998), 50460 ^ [_1791998, _1792000, _1792002, _1792004, _1792006]))), hBOOL(hAPP(_1792004, _1792312))], (50463 ^ _779327) ^ [] : [-(_1792006 = hAPP(hAPP(c_List_Oappend(_1791998), 50460 ^ [_1791998, _1792000, _1792002, _1792004, _1792006]), hAPP(hAPP(c_List_Olist_OCons(_1791998), _1792000), 50461 ^ [_1791998, _1792000, _1792002, _1792004, _1792006])))]]], (46962 ^ _779327) ^ [_1716570, _1716572, _1716574] : [-(hAPP(c_List_Otl(_1716570), hAPP(hAPP(c_List_Oappend(_1716570), _1716572), _1716574)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1716570), _1716570, hAPP(c_List_Otl(_1716570), _1716574), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1716570), tc_List_Olist(_1716570)), _1716570), hAPP(hAPP(c_COMBC(tc_List_Olist(_1716570), tc_List_Olist(_1716570), tc_List_Olist(_1716570)), c_List_Oappend(_1716570)), _1716574))), _1716572))], (1868 ^ _779327) ^ [_805665, _805667] : [-(class_Orderings_Oorder(_805665)), _805667 = _805665, class_Orderings_Oorder(_805667)], (1558 ^ _779327) ^ [_801790, _801792] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801790)), _801792 = _801790, class_Groups_Oordered__ab__semigroup__add__imp__le(_801792)], (48862 ^ _779327) ^ [_1758762, _1758764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758762), _1758764)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1758762, _1758764)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1758764), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23131 ^ _779327) ^ [_1180596, _1180598, _1180600, _1180602, _1180604] : [-(hAPP(c_Product__Type_Osnd(_1180596, _1180598), hAPP(c_Product__Type_Oapfst(_1180600, _1180596, _1180598, _1180602), _1180604)) = hAPP(c_Product__Type_Osnd(_1180600, _1180598), _1180604))], (47728 ^ _779327) ^ [_1732648, _1732650, _1732652, _1732654] : [-(hBOOL(hAPP(c_List_Olistsp(_1732648, _1732650), hAPP(hAPP(c_List_Olist_OCons(_1732648), _1732652), _1732654)))), hBOOL(hAPP(_1732650, _1732652)), hBOOL(hAPP(c_List_Olistsp(_1732648, _1732650), _1732654))], (49796 ^ _779327) ^ [_1777283, _1777285, _1777287, _1777289, _1777291] : [class_Orderings_Olinorder(_1777283), c_List_Olinorder__class_Osorted(_1777283, hAPP(c_List_Orev(_1777283), hAPP(hAPP(c_List_Omap(_1777285, _1777283), _1777287), _1777289))), -(hAPP(c_List_Ofilter(_1777285, hAPP(hAPP(c_COMBB(_1777283, tc_HOL_Obool, _1777285), hAPP(c_Orderings_Oord__class_Oless(_1777283), _1777291)), _1777287)), _1777289) = c_List_OtakeWhile(_1777285, hAPP(hAPP(c_COMBB(_1777283, tc_HOL_Obool, _1777285), hAPP(c_Orderings_Oord__class_Oless(_1777283), _1777291)), _1777287), _1777289))], (42647 ^ _779327) ^ [_1611295, _1611297, _1611299, _1611301, _1611303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611295, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1611297, _1611295, _1611299), _1611301)), _1611303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611297, tc_HOL_Obool)), _1611301), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1611297, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1611295, _1611297, hAPP(c_Relation_Oconverse(_1611297, _1611295), _1611299)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1611295, tc_HOL_Obool)), _1611303))))))], (15447 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (40615 ^ _779327) ^ [_1562731, _1562733, _1562735, _1562737] : [c_Wellfounded_Owf(_1562731, _1562733), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562731, _1562731)), hAPP(hAPP(c_Product__Type_OPair(_1562731, _1562731), _1562735), _1562737)), _1562733)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1562731, _1562731)), hAPP(hAPP(c_Product__Type_OPair(_1562731, _1562731), _1562737), _1562735)), _1562733))], (20601 ^ _779327) ^ [_1131579, _1131581, _1131583, _1131585] : [class_Fields_Ofield(_1131579), -(_1131581 = c_Groups_Ozero__class_Ozero(_1131579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1131583), _1131585)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1131579), _1131581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1131585), _1131583)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131579), hAPP(hAPP(c_Power_Opower__class_Opower(_1131579), _1131581), _1131585)), hAPP(hAPP(c_Power_Opower__class_Opower(_1131579), _1131581), _1131583)))], (33899 ^ _779327) ^ [_1399387, _1399389, _1399391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1399387), _1399389)), hBOOL(hAPP(_1399391, _1399389)), 33910 ^ _779327 : [(33913 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399387), 33908 ^ [_1399387, _1399389, _1399391]), 33909 ^ [_1399387, _1399389, _1399391])))], (33915 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1399391, 33909 ^ [_1399387, _1399389, _1399391])))], (33917 ^ _779327) ^ [] : [hBOOL(hAPP(_1399391, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399387, tc_HOL_Obool)), 33909 ^ [_1399387, _1399389, _1399391]), hAPP(hAPP(c_Set_Oinsert(_1399387), 33908 ^ [_1399387, _1399389, _1399391]), c_Orderings_Obot__class_Obot(tc_fun(_1399387, tc_HOL_Obool))))))], (33911 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1399387), 33909 ^ [_1399387, _1399389, _1399391])))]], -(hBOOL(hAPP(_1399391, c_Orderings_Obot__class_Obot(tc_fun(_1399387, tc_HOL_Obool)))))], (5958 ^ _779327) ^ [_873101, _873103, _873105, _873107] : [class_Orderings_Oorder(_873101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873101), _873103), _873105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873101), _873107), _873103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873101), _873107), _873105)))], (24353 ^ _779327) ^ [_1203243, _1203245] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203243), _1203245))), 24354 ^ _779327 : [(24355 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203243), _1203245)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1203245), _1203243)))], (24361 ^ _779327) ^ [] : [_1203243 = _1203245]]], (51593 ^ _779327) ^ [_1816421, _1816423, _1816425] : [c_List_Olist__ex(_1816421, _1816423, _1816425), 51597 ^ _779327 : [(51600 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1816423, 51596 ^ [_1816421, _1816423, _1816425])))], (51598 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1816421), 51596 ^ [_1816421, _1816423, _1816425]), hAPP(c_List_Oset(_1816421), _1816425))))]]], (28812 ^ _779327) ^ [_1292925, _1292927, _1292929, _1292931] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1292925), _1292927)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292929), _1292931)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1292925, _1292929)), c_Sum__Type_OPlus(_1292925, _1292929, _1292927, _1292931))))], (29536 ^ _779327) ^ [_1306819, _1306821, _1306823, _1306825] : [hBOOL(hAPP(hAPP(c_member(_1306819), _1306821), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306819, tc_HOL_Obool)), _1306823), _1306825))), -(hBOOL(hAPP(hAPP(c_member(_1306819), _1306821), _1306823))), -(hBOOL(hAPP(hAPP(c_member(_1306819), _1306821), _1306825)))], (29404 ^ _779327) ^ [_1304032] : [-(hAPP(c_Int_Onat, _1304032) = 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, _1304032)), 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)))))))], (34685 ^ _779327) ^ [_1418224, _1418226] : [class_Lattices_Olattice(_1418224), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1418224), _1418226), _1418226) = _1418226)], (18710 ^ _779327) ^ [] : [-(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)))], (42883 ^ _779327) ^ [_1616847, _1616849, _1616851] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1616847, _1616847, _1616847), _1616849), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616847, _1616847), tc_HOL_Obool), _1616851), _1616849)) = hAPP(hAPP(c_Relation_Orel__comp(_1616847, _1616847, _1616847), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1616847, _1616847), tc_HOL_Obool), _1616851), _1616849)), _1616849))], (45864 ^ _779327) ^ [_1691359, _1691361, _1691363, _1691365] : [class_Groups_Ocomm__monoid__add(_1691359), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1691359), _1691361), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1691363, _1691365))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1691359), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1691359), _1691361), c_List_Oupto(_1691363, _1691365))))], (45617 ^ _779327) ^ [_1684885, _1684887, _1684889, _1684891] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1684885, _1684885)), hAPP(hAPP(c_Product__Type_OPair(_1684885, _1684885), _1684887), _1684889)), hAPP(c_List_Oset(tc_prod(_1684885, _1684885)), hAPP(hAPP(c_List_Ozip(_1684885, _1684885), _1684891), _1684891))))), hBOOL(hAPP(hAPP(c_member(_1684885), _1684887), hAPP(c_List_Oset(_1684885), _1684891))), _1684887 = _1684889], (52274 ^ _779327) ^ [_1830977, _1830979] : [c_Equiv__Relations_Opart__equivp(_1830977, _1830979), 52278 ^ _779327 : [(52291 ^ _779327) ^ [_1831319, _1831321] : [-(hBOOL(hAPP(hAPP(_1830979, _1831321), _1831319))), hBOOL(hAPP(hAPP(_1830979, _1831321), _1831321)), hBOOL(hAPP(hAPP(_1830979, _1831319), _1831319)), hAPP(_1830979, _1831321) = hAPP(_1830979, _1831319)], (52281 ^ _779327) ^ [_1831150, _1831152] : [hBOOL(hAPP(hAPP(_1830979, _1831152), _1831150)), 52284 ^ _779327 : [(52289 ^ _779327) ^ [] : [-(hAPP(_1830979, _1831152) = hAPP(_1830979, _1831150))], (52287 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1830979, _1831150), _1831150)))], (52285 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1830979, _1831152), _1831152)))]]], (52279 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(_1830979, 52277 ^ [_1830977, _1830979]), 52277 ^ [_1830977, _1830979])))]]], (19847 ^ _779327) ^ [_1117822, _1117824, _1117826, _1117828] : [class_Fields_Ofield(_1117822), -(_1117824 = c_Groups_Ozero__class_Ozero(_1117822)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117822), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117822), _1117826), _1117824)), _1117828) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117822), _1117826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117822), _1117824), _1117828))), _1117824))], (36290 ^ _779327) ^ [_1455350, _1455352, _1455354, _1455356, _1455358, _1455360] : [hBOOL(hAPP(hAPP(_1455350, _1455352), _1455354)), hBOOL(hAPP(hAPP(_1455356, _1455352), _1455354)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455358, tc_fun(_1455360, tc_HOL_Obool))), _1455350), _1455356), _1455352), _1455354)))], (29402 ^ _779327) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45518 ^ _779327) ^ [_1681980, _1681982, _1681984, _1681986, _1681988] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1681980, _1681982)), _1681984), hAPP(hAPP(c_List_Ozip(_1681980, _1681982), _1681986), _1681988)) = hAPP(hAPP(c_List_Ozip(_1681980, _1681982), hAPP(hAPP(c_List_Otake(_1681980), _1681984), _1681986)), hAPP(hAPP(c_List_Otake(_1681982), _1681984), _1681988)))], (24689 ^ _779327) ^ [_1209213, _1209215, _1209217] : [class_Divides_Oring__div(_1209213), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1209213), _1209215), _1209217)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209213), _1209217), hAPP(c_Groups_Ouminus__class_Ouminus(_1209213), _1209215)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1209213), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1209213), _1209217), _1209215)))], (21956 ^ _779327) ^ [_1157936, _1157938, _1157940, _1157942, _1157944, _1157946] : [hAPP(hAPP(c_Product__Type_OPair(_1157936, _1157938), _1157940), _1157942) = hAPP(hAPP(c_Product__Type_OPair(_1157936, _1157938), _1157944), _1157946), 21959 ^ _779327 : [(21962 ^ _779327) ^ [] : [-(_1157942 = _1157946)], (21960 ^ _779327) ^ [] : [-(_1157940 = _1157944)]]], (5180 ^ _779327) ^ [_858334, _858336, _858338, _858340] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858340, _858336) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858338, _858334)), _858340 = _858338, _858336 = _858334], (9000 ^ _779327) ^ [_924204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924204)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28344 ^ _779327) ^ [_1283792, _1283794, _1283796] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283792), _1283794)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283792), _1283796)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283792), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283792, tc_HOL_Obool)), _1283794), _1283796))))], (6484 ^ _779327) ^ [_881075, _881077, _881079] : [class_Orderings_Olinorder(_881075), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881075), _881077), _881079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881075), _881079), _881077)))], (21722 ^ _779327) ^ [_1153397, _1153399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153397), 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)), _1153399)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1153397, _1153399), c_Divides_OnegDivAlg(_1153397, _1153399))))], (41873 ^ _779327) ^ [_1592052, _1592054, _1592056, _1592058] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1592052, tc_HOL_Obool), tc_fun(_1592052, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1592052, tc_HOL_Obool), tc_fun(_1592052, tc_HOL_Obool)), _1592054), _1592056)), c_Wellfounded_Omax__ext(_1592052, _1592058))), 41876 ^ _779327 : [(41879 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1592052), _1592056)))], (41881 ^ _779327) ^ [] : [_1592056 = c_Orderings_Obot__class_Obot(tc_fun(_1592052, tc_HOL_Obool))], (41883 ^ _779327) ^ [_1592346] : [hBOOL(hAPP(hAPP(c_member(_1592052), _1592346), _1592054)), 41887 ^ _779327 : [(41890 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592052, _1592052)), hAPP(hAPP(c_Product__Type_OPair(_1592052, _1592052), _1592346), 41886 ^ [_1592052, _1592054, _1592056, _1592058, _1592346])), _1592058)))], (41888 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592052), 41886 ^ [_1592052, _1592054, _1592056, _1592058, _1592346]), _1592056)))]]], (41877 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1592052), _1592054)))]]], (50138 ^ _779327) ^ [_1784359, _1784361, _1784363, _1784365] : [-(c_List_Omaps(_1784359, _1784361, _1784363, _1784365) = c_List_Oconcat(_1784361, hAPP(hAPP(c_List_Omap(_1784359, tc_List_Olist(_1784361)), _1784363), _1784365)))], (29476 ^ _779327) ^ [_1305641, _1305643, _1305645, _1305647, _1305649, _1305651, _1305653, _1305655] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1305641, tc_fun(_1305643, tc_fun(_1305645, tc_HOL_Obool))), _1305647), _1305649), _1305651), _1305653)), hBOOL(hAPP(hAPP(c_member(_1305641), _1305655), _1305647)), -(hBOOL(hAPP(hAPP(hAPP(_1305649, _1305655), _1305651), _1305653)))], (41655 ^ _779327) ^ [_1587315, _1587317, _1587319, _1587321, _1587323, _1587325] : [c_Finite__Set_Ofolding__idem(_1587315, _1587317, _1587319, _1587321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587315), _1587323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587315), _1587325)), -(hAPP(_1587321, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1587315, tc_HOL_Obool)), _1587323), _1587325)) = hAPP(c_Fun_Ocomp(_1587317, _1587317, _1587317, hAPP(_1587321, _1587323)), hAPP(_1587321, _1587325)))], (52169 ^ _779327) ^ [_1829413, _1829415, _1829417] : [c_Equiv__Relations_Oequiv(_1829413, _1829415, _1829417), 52172 ^ _779327 : [(52177 ^ _779327) ^ [] : [-(c_Relation_Otrans(_1829413, _1829417))], (52175 ^ _779327) ^ [] : [-(c_Relation_Osym(_1829413, _1829417))], (52173 ^ _779327) ^ [] : [-(c_Relation_Orefl__on(_1829413, _1829415, _1829417))]]], (21400 ^ _779327) ^ [_1147609, _1147611] : [21401 ^ _779327 : [(21404 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147611), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21402 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1147609), _1147611))]], -(c_Divides_OposDivAlg(_1147609, _1147611) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1147609))], (18869 ^ _779327) ^ [_1100782, _1100784] : [c_Nat__Transfer_Ois__nat(_1100782), c_Nat__Transfer_Ois__nat(_1100784), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1100782), _1100784)))], (12554 ^ _779327) ^ [_988638, _988640, _988642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988638), _988640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988638), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _988642), _988640))))], (3016 ^ _779327) ^ [_824488, _824490, _824492, _824494, _824496, _824498] : [-(c_Partial__Function_Oflat__lub(_824498, _824494, _824490) = c_Partial__Function_Oflat__lub(_824496, _824492, _824488)), _824498 = _824496, _824494 = _824492, _824490 = _824488], (28043 ^ _779327) ^ [_1277908] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1277908)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1277908)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1277908)))], (15612 ^ _779327) ^ [_1043221, _1043223, _1043225] : [class_Divides_Osemiring__div(_1043221), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043221), _1043223), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1043221), _1043225), _1043223))), c_Divides_Odiv__class_Omod(_1043221, _1043225, _1043223)) = _1043225)], (49441 ^ _779327) ^ [_1769855] : [-(hAPP(c_List_Orev(_1769855), c_List_Olist_ONil(_1769855)) = c_List_Olist_ONil(_1769855))], (30067 ^ _779327) ^ [_1319121, _1319123, _1319125, _1319127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1319121, _1319123)), hAPP(hAPP(c_Product__Type_OPair(_1319121, _1319123), _1319125), _1319127)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1319121, _1319123), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1319121, tc_fun(_1319123, tc_HOL_Obool))), _1319125), _1319127)))], (21530 ^ _779327) ^ [_1149895, _1149897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149897)), -(c_Divides_OposDivAlg(_1149895, _1149897) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1149895), _1149897)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1149895, _1149897)))], (2158 ^ _779327) ^ [_810609, _810611, _810613, _810615, _810617, _810619, _810621, _810623] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_810623, _810619, _810615, _810611) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_810621, _810617, _810613, _810609)), _810623 = _810621, _810619 = _810617, _810615 = _810613, _810611 = _810609], (46036 ^ _779327) ^ [_1695159, _1695161, _1695163, _1695165, _1695167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695159), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695161)), _1695163))), -(hAPP(hAPP(c_List_Olist__update(_1695161, hAPP(hAPP(c_List_Oappend(_1695161), _1695163), _1695165)), _1695159), _1695167) = hAPP(hAPP(c_List_Oappend(_1695161), hAPP(hAPP(c_List_Olist__update(_1695161, _1695163), _1695159), _1695167)), _1695165))], (5582 ^ _779327) ^ [_864487, _864489] : [_864489 = _864487, -(tc_Hoare__Mirabelle_Otriple(_864489) = tc_Hoare__Mirabelle_Otriple(_864487))], (40398 ^ _779327) ^ [_1556478, _1556480, _1556482, _1556484, _1556486, _1556488] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1556478, _1556480, _1556482), _1556484), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556480, _1556482), tc_HOL_Obool)), _1556486), _1556488)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556478, _1556482), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1556478, _1556480, _1556482), _1556484), _1556486)), hAPP(hAPP(c_Relation_Orel__comp(_1556478, _1556480, _1556482), _1556484), _1556488)))], (27591 ^ _779327) ^ [_1267890, _1267892, _1267894, _1267896, _1267898, _1267900] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267890, tc_fun(_1267892, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267894, tc_fun(_1267890, tc_HOL_Obool)), _1267896), _1267898)), _1267900) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267894, tc_fun(_1267892, tc_HOL_Obool)), _1267896), hAPP(hAPP(c_COMBC(_1267894, tc_fun(_1267890, tc_fun(_1267892, tc_HOL_Obool)), tc_fun(_1267892, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267890, tc_HOL_Obool), tc_fun(tc_fun(_1267890, tc_fun(_1267892, tc_HOL_Obool)), tc_fun(_1267892, tc_HOL_Obool)), _1267894), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1267890, tc_fun(_1267892, tc_HOL_Obool))), _1267898)), _1267900)))], (40005 ^ _779327) ^ [_1541958, _1541960] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541958), _1541960)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1541958, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1541958, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1541958, tc_HOL_Obool), tc_fun(_1541958, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1541958, tc_HOL_Obool))), _1541960)))))], (23718 ^ _779327) ^ [_1192295, _1192297, _1192299, _1192301, _1192303, _1192305, _1192307] : [-(c_New__Random__Sequence_Opos__decr__bind(_1192295, _1192297, _1192299, _1192301, _1192303, _1192305, _1192307) = c_New__DSequence_Opos__decr__bind(_1192295, _1192297, hAPP(hAPP(hAPP(_1192299, _1192303), _1192305), _1192307), hAPP(hAPP(c_COMBC(_1192295, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1192297))), hAPP(hAPP(c_COMBC(_1192295, 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(_1192297)))), hAPP(hAPP(c_COMBC(_1192295, 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(_1192297))))), _1192301), _1192303)), _1192305)), _1192307)))], (21086 ^ _779327) ^ [_1140604, _1140606, _1140608, _1140610, _1140612] : [21088 ^ _779327 : [(21091 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140604, tc_HOL_Obool)), _1140606), hAPP(_1140612, 21087 ^ [_1140604, _1140606, _1140608, _1140610, _1140612])))], (21089 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1140608), 21087 ^ [_1140604, _1140606, _1140608, _1140610, _1140612]), _1140610)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140604, tc_HOL_Obool)), _1140606), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1140608, tc_fun(_1140604, tc_HOL_Obool)), _1140610), _1140612))))], (41175 ^ _779327) ^ [_1575960, _1575962] : [41177 ^ _779327 : [(41180 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1575962), 41176 ^ [_1575960, _1575962]))], (41178 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 41176 ^ [_1575960, _1575962]), _1575960)))]], -(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)), _1575962), _1575960))], (25323 ^ _779327) ^ [_1220906, _1220908] : [class_Orderings_Oorder(_1220906), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1220906, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1220908), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1220906, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220908))], (1116 ^ _779327) ^ [_796187, _796189, _796191, _796193, _796195, _796197, _796199, _796201] : [-(c_Fun_Oinj__on(_796199, _796195, _796191, _796187)), c_Fun_Oinj__on(_796201, _796197, _796193, _796189), _796201 = _796199, _796197 = _796195, _796193 = _796191, _796189 = _796187], (39608 ^ _779327) ^ [_1530801] : [class_Lattices_Osemilattice__sup(_1530801), -(c_Finite__Set_Ofun__left__comm__idem(_1530801, _1530801, c_Lattices_Osemilattice__sup__class_Osup(_1530801)))], (27716 ^ _779327) ^ [_1271595, _1271597, _1271599, _1271601, _1271603] : [class_Complete__Lattice_Ocomplete__lattice(_1271595), class_Orderings_Olinorder(_1271595), 27723 ^ _779327 : [(27733 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271595), _1271597), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271599, _1271595), _1271601), _1271603)))), 27734 ^ _779327 : [(27735 ^ _779327) ^ [_1271943] : [hBOOL(hAPP(hAPP(c_member(_1271599), _1271943), _1271601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271595), _1271597), hAPP(_1271603, _1271943)))]]], (27724 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271595), _1271597), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271599, _1271595), _1271601), _1271603))), 27728 ^ _779327 : [(27731 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271595), _1271597), hAPP(_1271603, 27727 ^ [_1271595, _1271597, _1271599, _1271601, _1271603]))))], (27729 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1271599), 27727 ^ [_1271595, _1271597, _1271599, _1271601, _1271603]), _1271601)))]]]]], (12245 ^ _779327) ^ [_983048, _983050, _983052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _983048), _983050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _983048), _983052)), _983050)))], (35487 ^ _779327) ^ [_1435845, _1435847, _1435849, _1435851, _1435853] : [class_Orderings_Olinorder(_1435845), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435845, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1435845, _1435847, _1435849)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1435845, _1435851, _1435853)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1435845, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1435845), _1435847), _1435851), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1435845), _1435849), _1435853)))], (2176 ^ _779327) ^ [_810910, _810912] : [_810912 = _810910, -(c_Divides_Oadjust(_810912) = c_Divides_Oadjust(_810910))], (3750 ^ _779327) ^ [_836163, _836165, _836167, _836169] : [-(c_Random_Oselect(_836169, _836165) = c_Random_Oselect(_836167, _836163)), _836169 = _836167, _836165 = _836163], (14537 ^ _779327) ^ [_1024360, _1024362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024360), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14540 ^ _779327 : [(14547 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024362), _1024360)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14541 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024362), _1024360)), 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)), _1024362)))]]], (5164 ^ _779327) ^ [_858100, _858102, _858104, _858106] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_858106, _858102) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_858104, _858100)), _858106 = _858104, _858102 = _858100], (16455 ^ _779327) ^ [_1058286, _1058288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058286), _1058288)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1058286, _1058288) = _1058286)], (49183 ^ _779327) ^ [_1764569, _1764571, _1764573] : [class_Orderings_Olinorder(_1764569), 49186 ^ _779327 : [(49199 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1764569, hAPP(hAPP(c_List_Olist_OCons(_1764569), _1764571), _1764573))), c_List_Olinorder__class_Osorted(_1764569, _1764573), 49205 ^ _779327 : [(49208 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1764569), _1764571), 49204 ^ [_1764569, _1764571, _1764573]))], (49206 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764569), 49204 ^ [_1764569, _1764571, _1764573]), hAPP(c_List_Oset(_1764569), _1764573))))]]], (49187 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1764569, hAPP(hAPP(c_List_Olist_OCons(_1764569), _1764571), _1764573)), 49190 ^ _779327 : [(49193 ^ _779327) ^ [_1764755] : [hBOOL(hAPP(hAPP(c_member(_1764569), _1764755), hAPP(c_List_Oset(_1764569), _1764573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1764569), _1764571), _1764755)))], (49191 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1764569, _1764573))]]]]], (18614 ^ _779327) ^ [_1095857, _1095859] : [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), _1095857))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1095859))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1095857))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095859)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095857)))], (27498 ^ _779327) ^ [_1265811, _1265813, _1265815] : [class_Orderings_Olinorder(_1265811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265811), _1265813), _1265815)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265811, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1265811), _1265813)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1265811, _1265813, _1265815)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1265811), _1265815))], (48281 ^ _779327) ^ [_1744928, _1744930] : [hBOOL(hAPP(c_List_Odistinct(_1744928), _1744930)), -(c_List_Oremdups(_1744928, _1744930) = _1744930)], (48740 ^ _779327) ^ [_1756654, _1756656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1756654), _1756656)), -(c_List_Oupt(_1756654, hAPP(c_Nat_OSuc, _1756656)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1756654, _1756656)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1756656), c_List_Olist_ONil(tc_Nat_Onat))))], (44983 ^ _779327) ^ [_1668183, _1668185] : [-(c_Random_Oselect(_1668183, _1668185) = 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(_1668183, 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(_1668183)), _1668185)))), hAPP(hAPP(c_COMBB(_1668183, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1668183, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1668183, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1668183, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1668183), _1668185)), c_Code__Numeral_Onat__of))))], (18334 ^ _779327) ^ [_1090711, _1090713] : [class_Rings_Oring__1(_1090711), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090711), hAPP(c_Groups_Ouminus__class_Ouminus(_1090711), _1090713)), 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(_1090711), _1090713), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29376 ^ _779327) ^ [_1303521, _1303523] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1303521), _1303523)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1303523, _1303521) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (37849 ^ _779327) ^ [_1487792, _1487794] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487792, tc_HOL_Obool)), _1487794) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487792, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1487792, tc_HOL_Obool))), _1487794))], (17038 ^ _779327) ^ [_1068459, _1068461] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1068459), hAPP(hAPP(c_Power_Opower__class_Opower(_1068459), hAPP(c_Int_Onumber__class_Onumber__of(_1068459), c_Int_OMin)), _1068461)) = c_Groups_Oone__class_Oone(_1068459)), class_Int_Onumber__ring(_1068459), class_Rings_Olinordered__idom(_1068459)], (17816 ^ _779327) ^ [_1081562] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081562) = 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(_1081562)))))], (44428 ^ _779327) ^ [_1651584, _1651586, _1651588] : [c_FunDef_Ois__measure(_1651584, _1651586), -(c_FunDef_Ois__measure(tc_prod(_1651584, _1651588), hAPP(hAPP(c_COMBB(_1651584, tc_Nat_Onat, tc_prod(_1651584, _1651588)), _1651586), c_Product__Type_Ofst(_1651584, _1651588))))], (37219 ^ _779327) ^ [_1474803, _1474805, _1474807, _1474809, _1474811] : [-(hAPP(c_Fun_Othe__inv__into(_1474803, _1474805, _1474807, _1474809), _1474811) = c_HOL_OThe(_1474803, hAPP(hAPP(c_COMBS(_1474803, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1474803), c_fconj), hAPP(hAPP(c_COMBC(_1474803, tc_fun(_1474803, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474803)), _1474807))), hAPP(hAPP(c_COMBC(_1474803, _1474805, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1474805, tc_fun(_1474805, tc_HOL_Obool), _1474803), c_fequal), _1474809)), _1474811))))], (42685 ^ _779327) ^ [_1612156, _1612158, _1612160] : [-(hAPP(c_Relation_Oconverse(_1612156, _1612158), _1612160) = hAPP(c_Set_OCollect(tc_prod(_1612158, _1612156)), hAPP(c_Product__Type_Oprod_Oprod__case(_1612158, _1612156, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1612158, tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_fun(_1612156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612156, tc_fun(tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_fun(_1612156, tc_HOL_Obool)), _1612158), c_COMBC(_1612156, tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612156, tc_prod(_1612156, _1612158)), tc_fun(_1612156, tc_fun(tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_HOL_Obool)), _1612158), hAPP(c_COMBB(tc_prod(_1612156, _1612158), tc_fun(tc_fun(tc_prod(_1612156, _1612158), tc_HOL_Obool), tc_HOL_Obool), _1612156), c_member(tc_prod(_1612156, _1612158)))), hAPP(c_COMBC(_1612156, _1612158, tc_prod(_1612156, _1612158)), c_Product__Type_OPair(_1612156, _1612158))))), _1612160))))], (44813 ^ _779327) ^ [_1663825, _1663827, _1663829, _1663831, _1663833] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663825), tc_List_Olist(_1663825))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663825), tc_List_Olist(_1663825)), hAPP(hAPP(c_List_Olist_OCons(_1663825), _1663827), _1663829)), _1663831)), c_List_Olistrel(_1663825, _1663833))), 44818 ^ _779327 : [(44823 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663825), tc_List_Olist(_1663825))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663825), tc_List_Olist(_1663825)), _1663829), 44817 ^ [_1663825, _1663827, _1663829, _1663831, _1663833])), c_List_Olistrel(_1663825, _1663833))))], (44821 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663825, _1663825)), hAPP(hAPP(c_Product__Type_OPair(_1663825, _1663825), _1663827), 44816 ^ [_1663825, _1663827, _1663829, _1663831, _1663833])), _1663833)))], (44819 ^ _779327) ^ [] : [-(_1663831 = hAPP(hAPP(c_List_Olist_OCons(_1663825), 44816 ^ [_1663825, _1663827, _1663829, _1663831, _1663833]), 44817 ^ [_1663825, _1663827, _1663829, _1663831, _1663833]))]]], (13182 ^ _779327) ^ [_999746, _999748, _999750] : [class_Groups_Oordered__comm__monoid__add(_999746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999746), c_Groups_Ozero__class_Ozero(_999746)), _999748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999746), c_Groups_Ozero__class_Ozero(_999746)), _999750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999746), c_Groups_Ozero__class_Ozero(_999746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999746), _999748), _999750))))], (17474 ^ _779327) ^ [_1075943] : [-(c_Int_Osucc(c_Int_Opred(_1075943)) = _1075943)], (49047 ^ _779327) ^ [_1762226, _1762228, _1762230, _1762232] : [class_Orderings_Olinorder(_1762226), 49050 ^ _779327 : [(49059 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1762226, hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762228), hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762230), _1762232)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762226), _1762228), _1762230)), c_List_Olinorder__class_Osorted(_1762226, hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762230), _1762232))], (49051 ^ _779327) ^ [] : [c_List_Olinorder__class_Osorted(_1762226, hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762228), hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762230), _1762232))), 49054 ^ _779327 : [(49057 ^ _779327) ^ [] : [-(c_List_Olinorder__class_Osorted(_1762226, hAPP(hAPP(c_List_Olist_OCons(_1762226), _1762230), _1762232)))], (49055 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762226), _1762228), _1762230)))]]]]], (51546 ^ _779327) ^ [_1815359, _1815361, _1815363, _1815365] : [-(hAPP(c_Relation_OImage(_1815359, _1815361, hAPP(c_Set_OCollect(tc_prod(_1815359, _1815361)), hAPP(c_Product__Type_Oprod_Oprod__case(_1815359, _1815361, tc_HOL_Obool), _1815363))), _1815365) = hAPP(c_Set_OCollect(_1815361), hAPP(hAPP(c_COMBB(tc_fun(_1815359, tc_HOL_Obool), tc_HOL_Obool, _1815361), c_HOL_OEx(_1815359)), hAPP(hAPP(c_COMBB(tc_fun(_1815359, tc_HOL_Obool), tc_fun(_1815359, tc_HOL_Obool), _1815361), hAPP(c_COMBS(_1815359, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1815359), c_fconj), hAPP(hAPP(c_COMBC(_1815359, tc_fun(_1815359, tc_HOL_Obool), tc_HOL_Obool), c_member(_1815359)), _1815365)))), hAPP(c_COMBC(_1815359, _1815361, tc_HOL_Obool), _1815363)))))], (29146 ^ _779327) ^ [_1298677, _1298679, _1298681, _1298683, _1298685] : [-(_1298677 = c_Orderings_Obot__class_Obot(tc_fun(_1298679, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298681, tc_HOL_Obool)), _1298683), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298679, tc_fun(_1298681, tc_HOL_Obool)), _1298677), _1298685)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1298679, tc_fun(_1298681, tc_HOL_Obool)), _1298677), hAPP(hAPP(c_COMBB(tc_fun(_1298681, tc_HOL_Obool), tc_fun(_1298681, tc_HOL_Obool), _1298679), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298681, tc_HOL_Obool)), _1298683)), _1298685)))], (11111 ^ _779327) ^ [_960739, _960741] : [class_Groups_Ogroup__add(_960739), -(hAPP(c_Groups_Ouminus__class_Ouminus(_960739), hAPP(c_Groups_Ouminus__class_Ouminus(_960739), _960741)) = _960741)], (11341 ^ _779327) ^ [_965830, _965832, _965834, _965836, _965838, _965840] : [class_Rings_Oordered__ring(_965830), 11344 ^ _779327 : [(11351 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965830), _965836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965830), _965838), _965832)), _965834)), _965840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), _965832), _965834)), _965836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), _965838), _965834)), _965840))))], (11345 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), _965832), _965834)), _965836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), _965838), _965834)), _965840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965830), _965836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965830), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965830), _965838), _965832)), _965834)), _965840))))]]], (6098 ^ _779327) ^ [_875363, _875365, _875367, _875369] : [class_Orderings_Opreorder(_875363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875363), _875365), _875367)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875363), _875367), _875369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_875363), _875365), _875369)))], (4004 ^ _779327) ^ [_840078, _840080, _840082, _840084] : [-(c_List_Olists(_840084, _840080) = c_List_Olists(_840082, _840078)), _840084 = _840082, _840080 = _840078], (4404 ^ _779327) ^ [_846306, _846308] : [_846308 = _846306, -(c_List_Oembed__list(_846308) = c_List_Oembed__list(_846306))], (24901 ^ _779327) ^ [_1213414, _1213416, _1213418] : [class_Divides_Osemiring__div(_1213414), class_Int_Onumber(_1213414), 24908 ^ _779327 : [(24915 ^ _779327) ^ [] : [c_Divides_Odiv__class_Omod(_1213414, hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213418), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213416)) = c_Groups_Ozero__class_Ozero(_1213414), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213414), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213416)), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213418))))], (24909 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213414), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213416)), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213418))), -(c_Divides_Odiv__class_Omod(_1213414, hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213418), hAPP(c_Int_Onumber__class_Onumber__of(_1213414), _1213416)) = c_Groups_Ozero__class_Ozero(_1213414))]]], (9328 ^ _779327) ^ [_930466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _930466)), 9332 ^ _779327 : [(9335 ^ _779327) ^ [] : [-(_930466 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9331 ^ [_930466]))], (9333 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9331 ^ [_930466])))]]], (40964 ^ _779327) ^ [_1571266, _1571268, _1571270, _1571272] : [hBOOL(hAPP(c_Predicate_ODomainP(_1571266, _1571268, hAPP(hAPP(c_COMBC(_1571266, tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_fun(_1571268, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571268, tc_fun(tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_fun(_1571268, tc_HOL_Obool)), _1571266), c_COMBC(_1571268, tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1571268, tc_prod(_1571266, _1571268)), tc_fun(_1571268, tc_fun(tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_HOL_Obool)), _1571266), hAPP(c_COMBB(tc_prod(_1571266, _1571268), tc_fun(tc_fun(tc_prod(_1571266, _1571268), tc_HOL_Obool), tc_HOL_Obool), _1571268), c_member(tc_prod(_1571266, _1571268)))), c_Product__Type_OPair(_1571266, _1571268)))), _1571270)), _1571272)), -(hBOOL(hAPP(hAPP(c_member(_1571266), _1571272), hAPP(c_Relation_ODomain(_1571266, _1571268), _1571270))))], (52822 ^ _779327) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (45596 ^ _779327) ^ [_1684351, _1684353, _1684355] : [-(_1684351 = _1684353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684355)), _1684351) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684355)), _1684353), 45602 ^ _779327 : [(45605 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1684355, _1684355, tc_HOL_Obool), c_fequal), 45601 ^ [_1684351, _1684353, _1684355]))], (45603 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1684355, _1684355)), 45601 ^ [_1684351, _1684353, _1684355]), hAPP(c_List_Oset(tc_prod(_1684355, _1684355)), hAPP(hAPP(c_List_Ozip(_1684355, _1684355), _1684351), _1684353)))))]]], (47488 ^ _779327) ^ [_1727395, _1727397, _1727399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727397)), _1727399))), -(hAPP(hAPP(c_List_Otake(_1727397), _1727395), c_List_Obutlast(_1727397, _1727399)) = hAPP(hAPP(c_List_Otake(_1727397), _1727395), _1727399))], (52337 ^ _779327) ^ [_1832226, _1832228, _1832230, _1832232] : [c_Equiv__Relations_Opart__equivp(_1832226, _1832228), hBOOL(hAPP(hAPP(_1832228, _1832230), _1832232)), -(hBOOL(hAPP(hAPP(_1832228, _1832232), _1832230)))], (33056 ^ _779327) ^ [_1380900, _1380902, _1380904, _1380906, _1380908] : [hAPP(_1380900, _1380902) = _1380904, -(c_Fun_Ofun__upd(_1380906, _1380908, _1380900, _1380902, _1380904) = _1380900)], (28234 ^ _779327) ^ [_1281714, _1281716, _1281718] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281714), _1281716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281714, tc_HOL_Obool)), _1281718), _1281716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1281714), _1281718)), hAPP(c_Finite__Set_Ocard(_1281714), _1281716))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1281714, tc_HOL_Obool)), _1281718), _1281716)))], (52147 ^ _779327) ^ [_1828942, _1828944] : [52150 ^ _779327 : [(52153 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1828942, _1828942)), hAPP(hAPP(c_Product__Type_OPair(_1828942, _1828942), 52149 ^ [_1828942, _1828944]), 52148 ^ [_1828942, _1828944])), _1828944))], (52151 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828942, _1828942)), hAPP(hAPP(c_Product__Type_OPair(_1828942, _1828942), 52148 ^ [_1828942, _1828944]), 52149 ^ [_1828942, _1828944])), _1828944)))]], -(c_Relation_Osym(_1828942, _1828944))], (52121 ^ _779327) ^ [_1828368, _1828370] : [c_Relation_Osym(_1828368, _1828370), -(c_Relation_Osym(_1828368, c_Transitive__Closure_Ortrancl(_1828368, _1828370)))], (9369 ^ _779327) ^ [_931111, _931113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931111), _931113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _931113), _931111)), -(_931111 = _931113)], (52063 ^ _779327) ^ [_1827458, _1827460, _1827462, _1827464] : [c_Relation_Osym(_1827458, _1827460), -(c_Relation_Osym(_1827462, hAPP(hAPP(c_Relation_Oinv__image(_1827458, _1827462), _1827460), _1827464)))], (846 ^ _779327) ^ [_792290, _792292, _792294, _792296] : [-(c_List_Olinorder__class_Osorted(_792294, _792290)), c_List_Olinorder__class_Osorted(_792296, _792292), _792296 = _792294, _792292 = _792290], (32992 ^ _779327) ^ [_1379886, _1379888, _1379890, _1379892] : [-(c_Fun_Ofun__upd(_1379886, _1379888, _1379890, _1379892, hAPP(_1379890, _1379892)) = _1379890)], (44532 ^ _779327) ^ [_1655154, _1655156, _1655158, _1655160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1655154), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1655156), _1655158))), -(hAPP(c_Random_Opick(_1655156, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1655156)), _1655158), _1655160)), _1655154) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1655156), _1655158))], (4422 ^ _779327) ^ [_846561, _846563, _846565, _846567, _846569, _846571] : [-(c_List_Oremove1(_846571, _846567, _846563) = c_List_Oremove1(_846569, _846565, _846561)), _846571 = _846569, _846567 = _846565, _846563 = _846561], (52946 ^ _779327) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (48191 ^ _779327) ^ [_1742731, _1742733] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1742731), tc_fun(_1742731, tc_HOL_Obool), c_List_Oset(_1742731)), hAPP(c_List_Oset(tc_List_Olist(_1742731)), c_Enum_Osublists(_1742731, _1742733))) = hAPP(c_Set_OPow(_1742731), hAPP(c_List_Oset(_1742731), _1742733)))], (4206 ^ _779327) ^ [_843181, _843183] : [_843183 = _843181, -(c_SetInterval_Oord__class_OlessThan(_843183) = c_SetInterval_Oord__class_OlessThan(_843181))], (39075 ^ _779327) ^ [_1518946, _1518948, _1518950, _1518952] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518946, _1518948), _1518950), _1518952) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518946, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), _1518950), hAPP(hAPP(c_COMBS(_1518946, tc_fun(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518948, tc_HOL_Obool), tc_fun(tc_fun(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), _1518946), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), _1518952)), hAPP(hAPP(c_COMBC(_1518946, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1518948, tc_fun(tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), _1518946), c_COMBC(_1518948, tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1518948, tc_prod(_1518946, _1518948)), tc_fun(_1518948, tc_fun(tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))), _1518946), hAPP(c_COMBB(tc_prod(_1518946, _1518948), tc_fun(tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool), tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool)), _1518948), c_Set_Oinsert(tc_prod(_1518946, _1518948)))), c_Product__Type_OPair(_1518946, _1518948)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518946, _1518948), tc_HOL_Obool))))))], (5636 ^ _779327) ^ [_868324] : [hAPP(c_Nat_OSuc, _868324) = _868324], (23448 ^ _779327) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16081 ^ _779327) ^ [_1051560, _1051562, _1051564, _1051566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051562), _1051564)), -(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), _1051564), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1051566, _1051560))), _1051562))))], (18682 ^ _779327) ^ [_1097213, _1097215] : [class_Int_Onumber__ring(_1097213), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1097213), hAPP(c_Int_Onumber__class_Onumber__of(_1097213), 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)))), _1097215))) = hAPP(c_Int_Onumber__class_Onumber__of(_1097213), c_Int_OMin))], (46920 ^ _779327) ^ [_1715602, _1715604] : [46922 ^ _779327 : [(46926 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46924 ^ [_1715602, _1715604]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715602)), _1715604))))], (46928 ^ _779327) ^ [] : [46921 ^ [_1715602, _1715604] = 46924 ^ [_1715602, _1715604]], (46930 ^ _779327) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1715602), _1715604), 46921 ^ [_1715602, _1715604]) = hAPP(hAPP(c_List_Onth(_1715602), _1715604), 46924 ^ [_1715602, _1715604]))], (46923 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46921 ^ [_1715602, _1715604]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715602)), _1715604))))]], -(hBOOL(hAPP(c_List_Odistinct(_1715602), _1715604)))], (11187 ^ _779327) ^ [_962539, _962541, _962543, _962545] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962539), hAPP(c_Int_Onumber__class_Onumber__of(_962539), _962541)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962539), _962543), _962545)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962539), hAPP(c_Int_Onumber__class_Onumber__of(_962539), _962541)), _962543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962539), hAPP(c_Int_Onumber__class_Onumber__of(_962539), _962541)), _962545))), class_Int_Onumber(_962539), class_Rings_Osemiring(_962539)], (19057 ^ _779327) ^ [_1104034, _1104036, _1104038] : [class_Fields_Olinordered__field(_1104034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104034), c_Groups_Ozero__class_Ozero(_1104034)), _1104036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104034), _1104038), c_Groups_Ozero__class_Ozero(_1104034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104034), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1104034), _1104036), _1104038)), c_Groups_Ozero__class_Ozero(_1104034))))], (8832 ^ _779327) ^ [_921338, _921340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _921338)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _921340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _921338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _921338), _921340))))], (21350 ^ _779327) ^ [_1146696, _1146698, _1146700] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1146696, _1146698, _1146700, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1146698)], (51259 ^ _779327) ^ [_1809012, _1809014, _1809016] : [-(_1809012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1809014), c_List_Oreplicate(_1809014, _1809012, _1809016)) = hAPP(hAPP(c_Set_Oinsert(_1809014), _1809016), c_Orderings_Obot__class_Obot(tc_fun(_1809014, tc_HOL_Obool))))], (15093 ^ _779327) ^ [_1033582, _1033584, _1033586, _1033588] : [_1033582 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033584), _1033586)), _1033588), -(_1033584 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033582), _1033584) = _1033586), 15100 ^ _779327 : [(15103 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033588), _1033584))], (15101 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033584)))]], 15108 ^ _779327 : [(15111 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033584), _1033588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033588), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15109 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033584))]]], (5124 ^ _779327) ^ [_857480, _857482, _857484, _857486, _857488, _857490, _857492, _857494] : [-(c_Wellfounded_Olex__prod(_857494, _857490, _857486, _857482) = c_Wellfounded_Olex__prod(_857492, _857488, _857484, _857480)), _857494 = _857492, _857490 = _857488, _857486 = _857484, _857482 = _857480], (47798 ^ _779327) ^ [_1734151, _1734153, _1734155, _1734157, _1734159, _1734161] : [class_Orderings_Olinorder(_1734151), -(hAPP(_1734153, _1734155) = hAPP(_1734153, _1734157)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734159, _1734151, _1734153), _1734157), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734159, _1734151, _1734153), _1734155), _1734161)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734159, _1734151, _1734153), _1734155), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734159, _1734151, _1734153), _1734157), _1734161)))], (14223 ^ _779327) ^ [_1019008, _1019010] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1019008)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1019010)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019008), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1019010))))], (47626 ^ _779327) ^ [_1730070, _1730072, _1730074] : [-(hBOOL(hAPP(hAPP(c_member(_1730070), _1730072), hAPP(c_List_Oset(_1730070), _1730074)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730070)), c_List_Oremove1(_1730070, _1730072, _1730074)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730070)), _1730074))], (42210 ^ _779327) ^ [_1600634, _1600636] : [-(c_Transitive__Closure_Ortrancl(_1600634, _1600636) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1600634, _1600634), tc_HOL_Obool)), c_Relation_OId(_1600634)), hAPP(hAPP(c_Relation_Orel__comp(_1600634, _1600634, _1600634), c_Transitive__Closure_Ortrancl(_1600634, _1600636)), _1600636)))], (43935 ^ _779327) ^ [_1640364, _1640366] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1640364, tc_HOL_Obool), tc_HOL_Obool)), _1640366), hAPP(c_Set_OPow(_1640364), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1640364, tc_HOL_Obool), _1640366)))))], (29784 ^ _779327) ^ [_1311664, _1311666, _1311668] : [-(hBOOL(hAPP(hAPP(c_member(_1311664), _1311666), _1311668))), -(hBOOL(hAPP(hAPP(c_member(_1311664), _1311666), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1311664, tc_HOL_Obool)), _1311668))))], (52572 ^ _779327) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (40285 ^ _779327) ^ [_1552824, _1552826, _1552828, _1552830] : [class_Groups_Ocomm__monoid__mult(_1552824), c_Fun_Oinj__on(_1552826, _1552824, _1552828, _1552830), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552826, _1552824), _1552828), _1552830) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1552824, _1552824), c_Fun_Oid(_1552824)), hAPP(c_Set_Oimage(_1552826, _1552824, _1552828), _1552830)))], (50217 ^ _779327) ^ [_1786532, _1786534, _1786536, _1786538, _1786540, _1786542, _1786544, _1786546] : [50219 ^ _779327 : [(50222 ^ _779327) ^ [] : [hAPP(c_Fun_Ocomp(_1786536, _1786536, _1786538, hAPP(_1786540, 50218 ^ [_1786532, _1786534, _1786536, _1786538, _1786540, _1786542, _1786544, _1786546])), _1786542) = hAPP(c_Fun_Ocomp(_1786538, _1786536, _1786538, _1786542), hAPP(_1786544, 50218 ^ [_1786532, _1786534, _1786536, _1786538, _1786540, _1786542, _1786544, _1786546]))], (50220 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786532), 50218 ^ [_1786532, _1786534, _1786536, _1786538, _1786540, _1786542, _1786544, _1786546]), hAPP(c_List_Oset(_1786532), _1786534))))]], -(hAPP(c_List_Ofoldl(_1786536, _1786532, hAPP(c_COMBC(_1786532, _1786536, _1786536), _1786540), hAPP(_1786542, _1786546)), _1786534) = hAPP(_1786542, hAPP(c_List_Ofoldl(_1786538, _1786532, hAPP(c_COMBC(_1786532, _1786538, _1786538), _1786544), _1786546), _1786534)))], (43830 ^ _779327) ^ [_1638039] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1638039, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1638039, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1638039, tc_HOL_Obool)))], (46323 ^ _779327) ^ [_1701649, _1701651, _1701653, _1701655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701651)), _1701653))), 46326 ^ _779327 : [(46333 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Onth(_1701651), _1701653), _1701649) = _1701655, -(hAPP(hAPP(c_List_Olist__update(_1701651, _1701653), _1701649), _1701655) = _1701653)], (46327 ^ _779327) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1701651, _1701653), _1701649), _1701655) = _1701653, -(hAPP(hAPP(c_List_Onth(_1701651), _1701653), _1701649) = _1701655)]]], (31666 ^ _779327) ^ [_1354687, _1354689] : [31667 ^ _779327 : [(31670 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354689), _1354687))], (31668 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354687), _1354689)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1354687, _1354689) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (12361 ^ _779327) ^ [_985030, _985032] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985030), _985032) = _985030, -(_985032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21146 ^ _779327) ^ [_1142052] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1142052)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142052)), 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))))], (15295 ^ _779327) ^ [_1037082, _1037084, _1037086, _1037088] : [class_Divides_Osemiring__div(_1037082), -(c_Divides_Odiv__class_Omod(_1037082, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037082), _1037084), _1037086), _1037088) = c_Divides_Odiv__class_Omod(_1037082, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037082), c_Divides_Odiv__class_Omod(_1037082, _1037084, _1037088)), _1037086), _1037088))], (24517 ^ _779327) ^ [_1206119, _1206121] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206121), _1206119))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1206119), _1206121)))], (49780 ^ _779327) ^ [_1776919, _1776921, _1776923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776919)), c_List_OtakeWhile(_1776919, _1776921, _1776923))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776919)), _1776923))), hBOOL(hAPP(_1776921, hAPP(hAPP(c_List_Onth(_1776919), _1776923), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776919)), c_List_OtakeWhile(_1776919, _1776921, _1776923)))))], (34021 ^ _779327) ^ [_1402183, _1402185, _1402187] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1402183, tc_HOL_Obool)), _1402187), hAPP(c_Set_OPow(_1402183), _1402185))), -(hBOOL(hAPP(c_Predicate_OPowp(_1402183, hAPP(hAPP(c_COMBC(_1402183, tc_fun(_1402183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1402183)), _1402185)), _1402187)))], (33385 ^ _779327) ^ [_1387558, _1387560, _1387562, _1387564, _1387566] : [class_Groups_Ocomm__monoid__mult(_1387558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387560), _1387562)), hBOOL(hAPP(hAPP(c_member(_1387560), _1387564), _1387562)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387560, _1387558), _1387566), _1387562) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387558), hAPP(_1387566, _1387564)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387560, _1387558), _1387566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387560, tc_HOL_Obool)), _1387562), hAPP(hAPP(c_Set_Oinsert(_1387560), _1387564), c_Orderings_Obot__class_Obot(tc_fun(_1387560, tc_HOL_Obool)))))))], (47036 ^ _779327) ^ [_1718232, _1718234] : [class_Lattices_Oab__semigroup__idem__mult(_1718232), -(_1718234 = c_List_Olist_ONil(_1718232)), -(hAPP(c_Finite__Set_Ofold1(_1718232, c_Groups_Otimes__class_Otimes(_1718232)), hAPP(c_List_Oset(_1718232), _1718234)) = hAPP(c_List_Ofoldl(_1718232, _1718232, c_Groups_Otimes__class_Otimes(_1718232), hAPP(c_List_Ohd(_1718232), _1718234)), hAPP(c_List_Otl(_1718232), _1718234)))], (1148 ^ _779327) ^ [_796665, _796667] : [-(class_Rings_Olinordered__semiring__1__strict(_796665)), _796667 = _796665, class_Rings_Olinordered__semiring__1__strict(_796667)], (42298 ^ _779327) ^ [_1602838, _1602840] : [-(hAPP(c_Relation_ODomain(_1602838, _1602838), c_Transitive__Closure_Ortrancl(_1602838, _1602840)) = c_Orderings_Otop__class_Otop(tc_fun(_1602838, tc_HOL_Obool)))], (35982 ^ _779327) ^ [_1447004, _1447006, _1447008] : [class_Orderings_Olinorder(_1447004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447004), _1447006)), -(_1447006 = c_Orderings_Obot__class_Obot(tc_fun(_1447004, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447004), _1447008)), -(_1447008 = c_Orderings_Obot__class_Obot(tc_fun(_1447004, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447004, tc_HOL_Obool)), _1447006), _1447008) = c_Orderings_Obot__class_Obot(tc_fun(_1447004, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1447004, c_Orderings_Oord__class_Omin(_1447004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1447004, tc_HOL_Obool)), _1447006), _1447008)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1447004), c_Big__Operators_Olattice_OInf__fin(_1447004, c_Orderings_Oord__class_Omin(_1447004), _1447006)), c_Big__Operators_Olattice_OInf__fin(_1447004, c_Orderings_Oord__class_Omin(_1447004), _1447008)))], (8764 ^ _779327) ^ [_920040, _920042, _920044] : [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, _920040)), _920042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _920040)), _920044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920042), _920044)))], (52928 ^ _779327) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (31764 ^ _779327) ^ [_1356531, _1356533, _1356535] : [class_Orderings_Olinorder(_1356531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356531), _1356533)), hBOOL(hAPP(hAPP(c_member(_1356531), _1356535), _1356533)), 31775 ^ _779327 : [(31782 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356531, tc_HOL_Obool)), _1356533), hAPP(hAPP(c_Set_Oinsert(_1356531), _1356535), c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1356531, _1356533) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356531), _1356535), c_Big__Operators_Olinorder__class_OMax(_1356531, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356531, tc_HOL_Obool)), _1356533), hAPP(hAPP(c_Set_Oinsert(_1356531), _1356535), c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool)))))))], (31776 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356531, tc_HOL_Obool)), _1356533), hAPP(hAPP(c_Set_Oinsert(_1356531), _1356535), c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1356531, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1356531, _1356533) = _1356535)]]], (15553 ^ _779327) ^ [_1042254, _1042256] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1042254, _1042256) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1042254 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042256), 15556 ^ [_1042254, _1042256]))], (11411 ^ _779327) ^ [_967515, _967517, _967519] : [hBOOL(hAPP(_967515, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967517), _967519))), 11414 ^ _779327 : [(11421 ^ _779327) ^ [_967700] : [_967517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967519), _967700), -(hBOOL(hAPP(_967515, _967700)))], (11415 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _967517), _967519)), -(hBOOL(hAPP(_967515, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (5466 ^ _779327) ^ [_862743, _862745, _862747, _862749] : [-(tc_sum(_862749, _862745) = tc_sum(_862747, _862743)), _862749 = _862747, _862745 = _862743], (31570 ^ _779327) ^ [_1352821, _1352823, _1352825] : [-(hAPP(c_Finite__Set_Ocard(_1352821), _1352823) = hAPP(c_Nat_OSuc, _1352825)), 31571 ^ _779327 : [(31572 ^ _779327) ^ [_1352921, _1352923] : [_1352823 = hAPP(hAPP(c_Set_Oinsert(_1352821), _1352923), _1352921), -(hBOOL(hAPP(hAPP(c_member(_1352821), _1352923), _1352921))), hAPP(c_Finite__Set_Ocard(_1352821), _1352921) = _1352825, 31583 ^ _779327 : [(31586 ^ _779327) ^ [] : [_1352921 = c_Orderings_Obot__class_Obot(tc_fun(_1352821, tc_HOL_Obool))], (31584 ^ _779327) ^ [] : [-(_1352825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (26880 ^ _779327) ^ [_1253083, _1253085, _1253087, _1253089] : [26894 ^ _779327 : [(26897 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1253089, 26893 ^ [_1253083, _1253085, _1253087, _1253089])))], (26895 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253083), 26893 ^ [_1253083, _1253085, _1253087, _1253089]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253083, tc_HOL_Obool)), _1253085), _1253087))))]], 26881 ^ _779327 : [(26888 ^ _779327) ^ [_1253292] : [hBOOL(hAPP(hAPP(c_member(_1253083), _1253292), _1253087)), hBOOL(hAPP(_1253089, _1253292))], (26882 ^ _779327) ^ [_1253196] : [hBOOL(hAPP(hAPP(c_member(_1253083), _1253196), _1253085)), hBOOL(hAPP(_1253089, _1253196))]]], (21224 ^ _779327) ^ [_1143894] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1143894))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1143894)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44928 ^ _779327) ^ [_1667000, _1667002, _1667004, _1667006] : [-(hAPP(hAPP(c_List_Onth(_1667000), hAPP(hAPP(c_List_Olist_OCons(_1667000), _1667002), _1667004)), hAPP(c_Nat_OSuc, _1667006)) = hAPP(hAPP(c_List_Onth(_1667000), _1667004), _1667006))], (23506 ^ _779327) ^ [_1188080, _1188082, _1188084, _1188086] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1188080), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1188082, _1188084, _1188080, _1188086) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1188084, _1188086)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1188082, _1188084, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1188080), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1188086))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082))))), tc_prod(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1188082)), hAPP(hAPP(c_COMBB(_1188082, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1188082)))), tc_prod(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1188082)), c_Product__Type_Ofst(_1188082, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (34793 ^ _779327) ^ [_1420537, _1420539, _1420541] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420537, tc_HOL_Obool)), _1420539), _1420541) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420537, tc_HOL_Obool)), _1420541), _1420539))], (44353 ^ _779327) ^ [_1649849, _1649851, _1649853, _1649855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649849, _1649851)), _1649853), hAPP(c_Relation_Oconverse(_1649851, _1649849), _1649855))), 44358 ^ _779327 : [(44361 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649851, _1649849)), hAPP(hAPP(c_Product__Type_OPair(_1649851, _1649849), 44356 ^ [_1649849, _1649851, _1649853, _1649855]), 44357 ^ [_1649849, _1649851, _1649853, _1649855])), _1649855)))], (44359 ^ _779327) ^ [] : [-(_1649853 = hAPP(hAPP(c_Product__Type_OPair(_1649849, _1649851), 44357 ^ [_1649849, _1649851, _1649853, _1649855]), 44356 ^ [_1649849, _1649851, _1649853, _1649855]))]]], (35041 ^ _779327) ^ [_1425610, _1425612, _1425614, _1425616] : [-(hBOOL(hAPP(hAPP(c_member(_1425610), _1425612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425610, tc_HOL_Obool)), _1425614), _1425616)))), hBOOL(hAPP(hAPP(c_member(_1425610), _1425612), _1425614)), hBOOL(hAPP(hAPP(c_member(_1425610), _1425612), _1425616))], (46856 ^ _779327) ^ [_1714260, _1714262, _1714264] : [-(hBOOL(hAPP(c_List_Odistinct(_1714260), hAPP(hAPP(c_List_Olist_OCons(_1714260), _1714262), _1714264)))), -(hBOOL(hAPP(hAPP(c_member(_1714260), _1714262), hAPP(c_List_Oset(_1714260), _1714264)))), hBOOL(hAPP(c_List_Odistinct(_1714260), _1714264))], (29903 ^ _779327) ^ [_1313813, _1313815, _1313817] : [hAPP(hAPP(c_COMBC(_1313813, tc_fun(_1313813, tc_HOL_Obool), tc_HOL_Obool), c_member(_1313813)), _1313815) = hAPP(hAPP(c_COMBC(_1313813, tc_fun(_1313813, tc_HOL_Obool), tc_HOL_Obool), c_member(_1313813)), _1313817), -(_1313815 = _1313817)], (16643 ^ _779327) ^ [_1061620, _1061622, _1061624] : [class_Rings_Olinordered__idom(_1061620), 16646 ^ _779327 : [(16655 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), hAPP(c_Groups_Oabs__class_Oabs(_1061620), _1061622)), _1061624))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), _1061622), _1061624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), hAPP(c_Groups_Ouminus__class_Ouminus(_1061620), _1061622)), _1061624))], (16647 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), hAPP(c_Groups_Oabs__class_Oabs(_1061620), _1061622)), _1061624)), 16650 ^ _779327 : [(16653 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), hAPP(c_Groups_Ouminus__class_Ouminus(_1061620), _1061622)), _1061624)))], (16651 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1061620), _1061622), _1061624)))]]]]], (52488 ^ _779327) ^ [_1835226, _1835228] : [class_Orderings_Opreorder(_1835226), -(class_Orderings_Opreorder(tc_fun(_1835228, _1835226)))], (23694 ^ _779327) ^ [_1191841, _1191843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1191841), _1191843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1191841)), hAPP(c_Code__Numeral_Onat__of, _1191843))))], (48939 ^ _779327) ^ [_1760615] : [class_Orderings_Olinorder(_1760615), -(c_List_Olinorder__class_Osorted(_1760615, c_List_Olist_ONil(_1760615)))], (26918 ^ _779327) ^ [_1253929, _1253931, _1253933, _1253935] : [26922 ^ _779327 : [(26925 ^ _779327) ^ [] : [hBOOL(hAPP(_1253935, 26921 ^ [_1253929, _1253931, _1253933, _1253935]))], (26923 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253929), 26921 ^ [_1253929, _1253931, _1253933, _1253935]), _1253931)))]], 26927 ^ _779327 : [(26930 ^ _779327) ^ [] : [hBOOL(hAPP(_1253935, 26926 ^ [_1253929, _1253931, _1253933, _1253935]))], (26928 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253929), 26926 ^ [_1253929, _1253931, _1253933, _1253935]), _1253933)))]], 26931 ^ _779327 : [(26932 ^ _779327) ^ [_1254262] : [hBOOL(hAPP(hAPP(c_member(_1253929), _1254262), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253929, tc_HOL_Obool)), _1253931), _1253933))), -(hBOOL(hAPP(_1253935, _1254262)))]]], (15457 ^ _779327) ^ [_1040544, _1040546] : [-(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, _1040544, _1040546)), _1040546) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040544), _1040546))], (34221 ^ _779327) ^ [] : [-(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))))))], (17506 ^ _779327) ^ [_1076469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076469), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076469)), c_Int_OPls)))], (12357 ^ _779327) ^ [_984960] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984960), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _984960)], (35343 ^ _779327) ^ [_1432971, _1432973] : [c_Nat__Transfer_Onat__set(_1432971), c_Nat__Transfer_Onat__set(_1432973), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1432971), _1432973) = 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), _1432971)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1432973))))], (48293 ^ _779327) ^ [_1745112, _1745114, _1745116] : [hBOOL(hAPP(c_List_Odistinct(_1745112), _1745114)), -(c_List_Oremove1(_1745112, _1745116, c_List_Oremdups(_1745112, _1745114)) = c_List_Oremdups(_1745112, c_List_Oremove1(_1745112, _1745116, _1745114)))], (21070 ^ _779327) ^ [_1140213, _1140215] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1140213), _1140215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1140213)), _1140215)))], (52654 ^ _779327) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (41481 ^ _779327) ^ [_1583190, _1583192, _1583194, _1583196, _1583198, _1583200, _1583202, _1583204, _1583206, _1583208, _1583210] : [c_Finite__Set_Ofolding(_1583190, _1583192, _1583194, _1583196), -(hAPP(c_Fun_Ocomp(_1583198, _1583200, _1583202, _1583204), hAPP(c_Fun_Ocomp(_1583206, _1583198, _1583202, _1583208), _1583210)) = hAPP(c_Fun_Ocomp(_1583206, _1583200, _1583202, hAPP(c_Fun_Ocomp(_1583198, _1583200, _1583206, _1583204), _1583208)), _1583210))], (14845 ^ _779327) ^ [_1029000, _1029002, _1029004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029000), _1029002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029000), _1029004)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029002), _1029004))))], (16141 ^ _779327) ^ [_1052702, _1052704, _1052706] : [-(hBOOL(hAPP(_1052702, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1052704, _1052706)))), 16144 ^ _779327 : [(16147 ^ _779327) ^ [] : [hBOOL(hAPP(_1052702, _1052704))], (16145 ^ _779327) ^ [] : [-(_1052706 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 16150 ^ _779327 : [(16151 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052706)))], (16157 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 16153 ^ [_1052702, _1052704, _1052706]), _1052706)))], (16161 ^ _779327) ^ [] : [hBOOL(hAPP(_1052702, 16153 ^ [_1052702, _1052704, _1052706]))], (16159 ^ _779327) ^ [] : [-(_1052704 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052706), 16152 ^ [_1052702, _1052704, _1052706])), 16153 ^ [_1052702, _1052704, _1052706]))], (16155 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16153 ^ [_1052702, _1052704, _1052706])))]], 16162 ^ _779327 : [(16163 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052706), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16169 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 16165 ^ [_1052702, _1052704, _1052706]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16173 ^ _779327) ^ [] : [hBOOL(hAPP(_1052702, 16165 ^ [_1052702, _1052704, _1052706]))], (16171 ^ _779327) ^ [] : [-(_1052704 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052706), 16164 ^ [_1052702, _1052704, _1052706])), 16165 ^ [_1052702, _1052704, _1052706]))], (16167 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052706), 16165 ^ [_1052702, _1052704, _1052706])))]]], (62 ^ _779327) ^ [_780174, _780176] : [-(class_Rings_Odivision__ring(_780174)), _780176 = _780174, class_Rings_Odivision__ring(_780176)], (44711 ^ _779327) ^ [_1660562, _1660564, _1660566, _1660568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660562), tc_List_Olist(_1660562))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660562), tc_List_Olist(_1660562)), _1660564), _1660566)), c_List_Olistrel(_1660562, _1660568))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660562)), _1660564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660562)), _1660566))], (16441 ^ _779327) ^ [_1058009, _1058011, _1058013] : [class_Rings_Olinordered__idom(_1058009), -(hAPP(c_Groups_Oabs__class_Oabs(_1058009), hAPP(hAPP(c_Power_Opower__class_Opower(_1058009), _1058011), _1058013)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1058009), hAPP(c_Groups_Oabs__class_Oabs(_1058009), _1058011)), _1058013))], (50666 ^ _779327) ^ [_1796602, _1796604, _1796606] : [c_List_Olist__ex(_1796602, _1796604, _1796606), -(c_List_Olist__ex(_1796602, _1796604, hAPP(c_List_Orev(_1796602), _1796606)))], (20918 ^ _779327) ^ [_1137660] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1137660)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1137660)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51275 ^ _779327) ^ [_1809219, _1809221, _1809223] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809219)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1809219, _1809221, _1809223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1809219)), _1809223)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47008 ^ _779327) ^ [_1717553, _1717555, _1717557, _1717559] : [class_Groups_Ocomm__monoid__add(_1717553), 47011 ^ _779327 : [(47018 ^ _779327) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1717555), _1717557))), -(c_Nitpick_Osetsum_H(_1717555, _1717553, _1717559, _1717557) = c_Groups_Ozero__class_Ozero(_1717553))], (47012 ^ _779327) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1717555), _1717557)), -(c_Nitpick_Osetsum_H(_1717555, _1717553, _1717559, _1717557) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717553), hAPP(hAPP(c_List_Omap(_1717555, _1717553), _1717559), c_Hilbert__Choice_OEps(tc_List_Olist(_1717555), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717555), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1717555)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717555), tc_fun(_1717555, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1717555, tc_HOL_Obool), tc_fun(tc_fun(_1717555, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1717555)), c_fequal), c_List_Oset(_1717555))), _1717557))), c_List_Odistinct(_1717555))))))]]], (52830 ^ _779327) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (32408 ^ _779327) ^ [_1368155, _1368157, _1368159] : [class_Orderings_Olinorder(_1368155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368155), _1368157)), -(_1368159 = c_Orderings_Obot__class_Obot(tc_fun(_1368155, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368155, tc_HOL_Obool)), _1368159), _1368157)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368155), c_Big__Operators_Olinorder__class_OMin(_1368155, _1368159)), c_Big__Operators_Olinorder__class_OMin(_1368155, _1368157)) = c_Big__Operators_Olinorder__class_OMin(_1368155, _1368157))], (45757 ^ _779327) ^ [_1688551, _1688553] : [class_Groups_Oordered__ab__group__add__abs(_1688551), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688551), hAPP(c_Groups_Oabs__class_Oabs(_1688551), hAPP(c_List_Omonoid__add__class_Olistsum(_1688551), _1688553))), hAPP(c_List_Omonoid__add__class_Olistsum(_1688551), hAPP(hAPP(c_List_Omap(_1688551, _1688551), c_Groups_Oabs__class_Oabs(_1688551)), _1688553)))))], (43756 ^ _779327) ^ [_1636077, _1636079, _1636081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636077, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636077, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1636077, tc_HOL_Obool), _1636079)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1636077, tc_HOL_Obool), _1636081))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1636077, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1636077, tc_HOL_Obool), tc_HOL_Obool)), _1636079), _1636081)))))], (26962 ^ _779327) ^ [_1254793, _1254795, _1254797] : [class_Lattices_Osemilattice__sup(_1254793), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254793), _1254795), _1254797) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1254793), _1254797), _1254795))], (37071 ^ _779327) ^ [_1471526, _1471528, _1471530, _1471532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1471526), _1471528)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471530), _1471532)), 37078 ^ _779327 : [(37079 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1471526), _1471528)), hAPP(c_Finite__Set_Ocard(_1471530), _1471532)))), 37080 ^ _779327 : [(37081 ^ _779327) ^ [_1471737] : [c_Fun_Oinj__on(_1471526, _1471530, _1471737, _1471528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471526, _1471530, _1471737), _1471528)), _1471532))]]], (37089 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1471526), _1471528)), hAPP(c_Finite__Set_Ocard(_1471530), _1471532))), 37093 ^ _779327 : [(37096 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471526, _1471530, 37092 ^ [_1471526, _1471528, _1471530, _1471532]), _1471528)), _1471532)))], (37094 ^ _779327) ^ [] : [-(c_Fun_Oinj__on(_1471526, _1471530, 37092 ^ [_1471526, _1471528, _1471530, _1471532], _1471528))]]]]], (44538 ^ _779327) ^ [_1655297, _1655299, _1655301, _1655303] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1655297), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1655299), _1655301)))), -(hAPP(c_Random_Opick(_1655299, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1655299)), _1655301), _1655303)), _1655297) = hAPP(c_Random_Opick(_1655299, _1655303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1655297), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1655299), _1655301))))], (51075 ^ _779327) ^ [_1804806, _1804808, _1804810, _1804812] : [-(hAPP(hAPP(c_List_Otake(_1804806), _1804808), c_List_Oreplicate(_1804806, _1804810, _1804812)) = c_List_Oreplicate(_1804806, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1804808), _1804810), _1804812))], (4706 ^ _779327) ^ [_851049, _851051] : [_851051 = _851049, -(c_Enum_Oenum__class_Oenum__all(_851051) = c_Enum_Oenum__class_Oenum__all(_851049))], (33975 ^ _779327) ^ [_1400941, _1400943, _1400945] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1400941, tc_HOL_Obool)), _1400943), hAPP(c_Set_OPow(_1400941), _1400945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400941, tc_HOL_Obool)), _1400943), _1400945)))], (3264 ^ _779327) ^ [_828360, _828362, _828364, _828366, _828368, _828370, _828372, _828374] : [-(c_Recdef_Osame__fst(_828374, _828370, _828366, _828362) = c_Recdef_Osame__fst(_828372, _828368, _828364, _828360)), _828374 = _828372, _828370 = _828368, _828366 = _828364, _828362 = _828360], (44598 ^ _779327) ^ [_1657085, _1657087, _1657089, _1657091] : [-(c_List_Olist_Olist__size(_1657085, _1657087, hAPP(hAPP(c_List_Olist_OCons(_1657085), _1657089), _1657091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1657087, _1657089)), c_List_Olist_Olist__size(_1657085, _1657087, _1657091))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51715 ^ _779327) ^ [_1818956, _1818958, _1818960, _1818962, _1818964] : [c_Relation_Otrans(_1818956, _1818958), hBOOL(hAPP(hAPP(c_member(tc_prod(_1818956, _1818956)), hAPP(hAPP(c_Product__Type_OPair(_1818956, _1818956), _1818960), _1818962)), _1818958)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1818956, _1818956)), hAPP(hAPP(c_Product__Type_OPair(_1818956, _1818956), _1818962), _1818964)), _1818958)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1818956, _1818956)), hAPP(hAPP(c_Product__Type_OPair(_1818956, _1818956), _1818960), _1818964)), _1818958)))], (42188 ^ _779327) ^ [_1600115, _1600117] : [-(c_Transitive__Closure_Otrancl(_1600115, c_Transitive__Closure_Ortrancl(_1600115, _1600117)) = c_Transitive__Closure_Ortrancl(_1600115, _1600117))], (18068 ^ _779327) ^ [_1086071, _1086073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086071), _1086073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086071)), c_Int_OBit0(_1086073))))], (44272 ^ _779327) ^ [_1647997, _1647999, _1648001, _1648003, _1648005, _1648007, _1648009] : [c_Finite__Set_Ofolding__image__simple__idem(_1647997, _1647999, _1648001, _1648003, _1648005, _1648007), -(hAPP(hAPP(_1648001, _1648009), _1648009) = _1648009)], (42180 ^ _779327) ^ [_1599900, _1599902] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599900, _1599900)), hAPP(hAPP(c_Product__Type_OPair(_1599900, _1599900), _1599902), _1599902)), c_Relation_OId(_1599900))))], (45709 ^ _779327) ^ [_1687161, _1687163, _1687165] : [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, _1687161), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1687161)), _1687163)))), -(hBOOL(hAPP(hAPP(c_member(_1687161), hAPP(c_Product__Type_Ofst(_1687161, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1687161, _1687163), _1687165))), hAPP(c_List_Oset(_1687161), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1687161), _1687161), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1687161)), _1687163)))))], (10634 ^ _779327) ^ [_951770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _951770)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _951770)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _951770)))], (39059 ^ _779327) ^ [_1518365, _1518367, _1518369, _1518371] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518365), _1518367)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518365, _1518365), tc_HOL_Obool)), _1518369), hAPP(hAPP(c_Product__Type_OSigma(_1518365, _1518365), _1518367), hAPP(c_COMBK(tc_fun(_1518365, tc_HOL_Obool), _1518365), _1518367)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1518365, tc_HOL_Obool)), _1518371), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1518365), _1518367), _1518369))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1518365), _1518371)))], (49027 ^ _779327) ^ [_1761896] : [class_Orderings_Olinorder(_1761896), -(c_List_Olinorder__class_Osorted(_1761896, c_List_Olist_ONil(_1761896)))], (25139 ^ _779327) ^ [_1217627, _1217629] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217627), _1217629)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1217627)), _1217629)))], (22197 ^ _779327) ^ [_1163004, _1163006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163006)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1163004), _1163006) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1163004, _1163006)))], (38165 ^ _779327) ^ [_1494998, _1495000, _1495002] : [38167 ^ _779327 : [(38170 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1494998), 38166 ^ [_1494998, _1495000, _1495002]), c_Wellfounded_Oacc(_1494998, _1495002)))], (38168 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494998, _1494998)), hAPP(hAPP(c_Product__Type_OPair(_1494998, _1494998), 38166 ^ [_1494998, _1495000, _1495002]), _1495000)), _1495002)))]], -(hBOOL(hAPP(hAPP(c_member(_1494998), _1495000), c_Wellfounded_Oacc(_1494998, _1495002))))], (29088 ^ _779327) ^ [_1297674, _1297676, _1297678, _1297680, _1297682] : [-(_1297674 = c_Orderings_Obot__class_Obot(tc_fun(_1297676, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297676, tc_fun(_1297678, tc_HOL_Obool)), _1297674), hAPP(hAPP(c_COMBB(tc_fun(_1297678, tc_HOL_Obool), tc_fun(_1297678, tc_HOL_Obool), _1297676), hAPP(c_Set_Oinsert(_1297678), _1297680)), _1297682)) = hAPP(hAPP(c_Set_Oinsert(_1297678), _1297680), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1297676, tc_fun(_1297678, tc_HOL_Obool)), _1297674), _1297682)))], (33648 ^ _779327) ^ [_1393484, _1393486] : [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), _1393484), _1393486)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1393484), _1393486)))], (48686 ^ _779327) ^ [_1754925, _1754927, _1754929, _1754931] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1754925, tc_Nat_Onat), _1754925), c_Product__Type_Ofst(_1754925, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1754925, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1754925, tc_Nat_Onat)), _1754927), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1754925, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1754925, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1754925, tc_Nat_Onat), _1754929), _1754931))) = hAPP(hAPP(c_List_Omap(tc_prod(_1754925, tc_Nat_Onat), _1754925), c_Product__Type_Ofst(_1754925, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1754925, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1754925, tc_Nat_Onat)), _1754927), c_Product__Type_Osnd(_1754925, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1754925, tc_Nat_Onat), _1754929), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1754931)))))], (896 ^ _779327) ^ [_793021, _793023, _793025, _793027, _793029, _793031] : [-(c_List_Oall__interval__int(_793029, _793025, _793021)), c_List_Oall__interval__int(_793031, _793027, _793023), _793031 = _793029, _793027 = _793025, _793023 = _793021], (30973 ^ _779327) ^ [_1339966, _1339968, _1339970, _1339972, _1339974, _1339976, _1339978] : [30975 ^ _779327 : [(30978 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1339974, 30974 ^ [_1339966, _1339968, _1339970, _1339972, _1339974, _1339976, _1339978]), _1339976), _1339978))], (30976 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339966), 30974 ^ [_1339966, _1339968, _1339970, _1339972, _1339974, _1339976, _1339978]), _1339972)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1339966, tc_fun(_1339968, tc_fun(_1339970, tc_HOL_Obool))), _1339972), _1339974), _1339976), _1339978)))], (32900 ^ _779327) ^ [_1377559, _1377561, _1377563] : [class_Orderings_Olinorder(_1377559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377559), _1377561)), 32907 ^ _779327 : [(32914 ^ _779327) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377559, tc_HOL_Obool)), _1377561), hAPP(hAPP(c_Set_Oinsert(_1377559), _1377563), c_Orderings_Obot__class_Obot(tc_fun(_1377559, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377559, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1377559, c_Orderings_Oord__class_Omin(_1377559), hAPP(hAPP(c_Set_Oinsert(_1377559), _1377563), _1377561)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1377559), _1377563), c_Big__Operators_Olattice_OInf__fin(_1377559, c_Orderings_Oord__class_Omin(_1377559), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377559, tc_HOL_Obool)), _1377561), hAPP(hAPP(c_Set_Oinsert(_1377559), _1377563), c_Orderings_Obot__class_Obot(tc_fun(_1377559, tc_HOL_Obool)))))))], (32908 ^ _779327) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377559, tc_HOL_Obool)), _1377561), hAPP(hAPP(c_Set_Oinsert(_1377559), _1377563), c_Orderings_Obot__class_Obot(tc_fun(_1377559, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1377559, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1377559, c_Orderings_Oord__class_Omin(_1377559), hAPP(hAPP(c_Set_Oinsert(_1377559), _1377563), _1377561)) = _1377563)]]], (28045 ^ _779327) ^ [_1277949, _1277951, _1277953] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1277949), _1277951)), 28048 ^ _779327 : [(28049 ^ _779327) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1277949, tc_Nat_Onat), _1277953), _1277951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 28052 ^ _779327 : [(28053 ^ _779327) ^ [_1278111] : [hBOOL(hAPP(hAPP(c_member(_1277949), _1278111), _1277951)), -(hAPP(_1277953, _1278111) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (28059 ^ _779327) ^ [] : [28061 ^ _779327 : [(28064 ^ _779327) ^ [] : [hAPP(_1277953, 28060 ^ [_1277949, _1277951, _1277953]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28062 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277949), 28060 ^ [_1277949, _1277951, _1277953]), _1277951)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1277949, tc_Nat_Onat), _1277953), _1277951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42076 ^ _779327) ^ [_1596517, _1596519] : [-(hAPP(c_Relation_ORange(_1596517, _1596517), c_Transitive__Closure_Otrancl(_1596517, _1596519)) = hAPP(c_Relation_ORange(_1596517, _1596517), _1596519))], (4968 ^ _779327) ^ [_855050, _855052, _855054, _855056] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_855056, _855052) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_855054, _855050)), _855056 = _855054, _855052 = _855050], (28934 ^ _779327) ^ [_1295038, _1295040, _1295042] : [class_Orderings_Oorder(_1295038), 28937 ^ _779327 : [(28944 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295038), _1295040), _1295042))), -(c_Orderings_Obot__class_Obot(tc_fun(_1295038, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1295038, _1295040), _1295042))], (28938 ^ _779327) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1295038, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1295038, _1295040), _1295042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295038), _1295040), _1295042))]]], (51614 ^ _779327) ^ [_1816955, _1816957, _1816959, _1816961] : [c_Relation_Otrans(_1816955, _1816957), -(c_Relation_Otrans(_1816959, hAPP(hAPP(c_Relation_Oinv__image(_1816955, _1816959), _1816957), _1816961)))], (34585 ^ _779327) ^ [_1415896, _1415898, _1415900, _1415902] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415896, tc_HOL_Obool)), _1415898), _1415900), _1415902)), 34588 ^ _779327 : [(34591 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1415900, _1415902)))], (34589 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1415898, _1415902)))]]], (25117 ^ _779327) ^ [_1217218, _1217220, _1217222] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217218), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1217220), _1217222))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217218), _1217222)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1217218), _1217220)))], (44498 ^ _779327) ^ [_1653668, _1653670, _1653672] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653668)), hAPP(hAPP(c_List_Olist_OCons(_1653668), _1653670), _1653672)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653668)), _1653672)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11087 ^ _779327) ^ [_960249, _960251, _960253] : [class_Groups_Ogroup__add(_960249), -(hAPP(c_Groups_Ouminus__class_Ouminus(_960249), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960249), _960251), _960253)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960249), hAPP(c_Groups_Ouminus__class_Ouminus(_960249), _960253)), hAPP(c_Groups_Ouminus__class_Ouminus(_960249), _960251)))], (30423 ^ _779327) ^ [_1326735, _1326737, _1326739, _1326741, _1326743, _1326745] : [hBOOL(hAPP(hAPP(c_member(_1326735), _1326737), _1326739)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1326735, tc_fun(_1326741, tc_HOL_Obool)), _1326739), hAPP(hAPP(c_COMBB(tc_fun(_1326741, tc_HOL_Obool), tc_fun(_1326741, tc_HOL_Obool), _1326735), hAPP(c_Set_Oinsert(_1326741), _1326743)), _1326745)) = hAPP(hAPP(c_Set_Oinsert(_1326741), _1326743), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1326735, tc_fun(_1326741, tc_HOL_Obool)), _1326739), _1326745)))], (10640 ^ _779327) ^ [_951873, _951875, _951877] : [class_Fields_Olinordered__field__inverse__zero(_951873), 10646 ^ _779327 : [(10651 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951873), 10645 ^ [_951873, _951875, _951877]), _951875)), _951877))], (10649 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951873), 10645 ^ [_951873, _951875, _951877]), c_Groups_Oone__class_Oone(_951873))))], (10647 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951873), c_Groups_Ozero__class_Ozero(_951873)), 10645 ^ [_951873, _951875, _951877])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951873), _951875), _951877)))], (3912 ^ _779327) ^ [_838670, _838672, _838674, _838676] : [-(c_Big__Operators_Olattice__class_OSup__fin(_838676, _838672) = c_Big__Operators_Olattice__class_OSup__fin(_838674, _838670)), _838676 = _838674, _838672 = _838670], (41669 ^ _779327) ^ [_1587596, _1587598, _1587600, _1587602, _1587604, _1587606] : [c_Finite__Set_Ofolding__idem(_1587596, _1587598, _1587600, _1587602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587596), _1587604)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1587596, tc_HOL_Obool)), _1587606), _1587604)), -(hAPP(c_Fun_Ocomp(_1587598, _1587598, _1587598, hAPP(_1587602, _1587604)), hAPP(_1587602, _1587606)) = hAPP(_1587602, _1587604))], (37559 ^ _779327) ^ [_1481862, _1481864, _1481866] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1481862, hAPP(hAPP(c_COMBC(_1481862, tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_fun(_1481862, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481862, tc_fun(tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_fun(_1481862, tc_HOL_Obool)), _1481862), c_COMBC(_1481862, tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481862, tc_prod(_1481862, _1481862)), tc_fun(_1481862, tc_fun(tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_HOL_Obool)), _1481862), hAPP(c_COMBB(tc_prod(_1481862, _1481862), tc_fun(tc_fun(tc_prod(_1481862, _1481862), tc_HOL_Obool), tc_HOL_Obool), _1481862), c_member(tc_prod(_1481862, _1481862)))), c_Product__Type_OPair(_1481862, _1481862)))), _1481864)), _1481866)), -(hBOOL(hAPP(hAPP(c_member(_1481862), _1481866), c_Wellfounded_Oacc(_1481862, _1481864))))], (42591 ^ _779327) ^ [_1609949, _1609951] : [c_Wellfounded_Oacyclic(_1609949, hAPP(c_Relation_Oconverse(_1609949, _1609949), _1609951)), -(c_Wellfounded_Oacyclic(_1609949, _1609951))], (33509 ^ _779327) ^ [_1390197, _1390199, _1390201, _1390203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1390197), _1390199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1390201), _1390203)), -(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), _1390197), _1390201)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390199), _1390203))), c_FunDef_Opair__leq)))], (43117 ^ _779327) ^ [_1623300, _1623302, _1623304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623300), _1623302)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623300, tc_HOL_Obool)), _1623302), _1623304) = hAPP(hAPP(c_Finite__Set_Ofold(_1623300, tc_fun(_1623300, tc_HOL_Obool), c_Set_Oinsert(_1623300)), _1623304), _1623302))], (23482 ^ _779327) ^ [_1187545, _1187547, _1187549] : [c_Nitpick_Oless__eq__frac(_1187545, _1187547, _1187549), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1187545), c_Nitpick_Oplus__frac(_1187545, _1187547, c_Nitpick_Ouminus__frac(_1187545, _1187549)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30027 ^ _779327) ^ [_1316284, _1316286, _1316288, _1316290, _1316292] : [-(hBOOL(hAPP(hAPP(c_member(_1316284), _1316286), c_SetInterval_Oord_OatLeastAtMost(_1316284, _1316288, _1316290, _1316292)))), hBOOL(hAPP(hAPP(_1316288, _1316290), _1316286)), hBOOL(hAPP(hAPP(_1316288, _1316286), _1316292))], (23077 ^ _779327) ^ [_1179364, _1179366, _1179368, _1179370] : [class_Orderings_Olinorder(_1179364), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179364), _1179366), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179364), _1179368), _1179370)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1179364), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179364), _1179366), _1179368)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179364), _1179366), _1179370)))], (40995 ^ _779327) ^ [_1572366, _1572368, _1572370, _1572372, _1572374] : [hBOOL(hAPP(hAPP(_1572366, _1572368), _1572370)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1572372, _1572374, _1572366), _1572368)))], (41237 ^ _779327) ^ [_1577615, _1577617, _1577619, _1577621, _1577623, _1577625] : [-(hAPP(c_Set_Ovimage(_1577615, _1577617, hAPP(c_Fun_Ocomp(_1577619, _1577617, _1577615, _1577621), _1577623)), _1577625) = hAPP(c_Set_Ovimage(_1577615, _1577619, _1577623), hAPP(c_Set_Ovimage(_1577619, _1577617, _1577621), _1577625)))], (26396 ^ _779327) ^ [_1244009, _1244011] : [class_Groups_Oordered__ab__group__add(_1244009), -(hAPP(c_Set_Oimage(_1244009, _1244009, c_Groups_Ouminus__class_Ouminus(_1244009)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1244009), _1244011)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1244009), hAPP(c_Groups_Ouminus__class_Ouminus(_1244009), _1244011)))], (17500 ^ _779327) ^ [_1076374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1076374)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076374), c_Int_OPls)))], (51548 ^ _779327) ^ [_1815485, _1815487, _1815489, _1815491, _1815493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1815485), tc_List_Olist(_1815485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1815485), tc_List_Olist(_1815485)), _1815487), _1815489)), c_List_Olexord(_1815485, _1815491))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1815485), tc_List_Olist(_1815485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1815485), tc_List_Olist(_1815485)), _1815489), _1815493)), c_List_Olexord(_1815485, _1815491))), c_Relation_Otrans(_1815485, _1815491), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1815485), tc_List_Olist(_1815485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1815485), tc_List_Olist(_1815485)), _1815487), _1815493)), c_List_Olexord(_1815485, _1815491))))], (46722 ^ _779327) ^ [_1712001, _1712003, _1712005] : [-(hAPP(c_List_Ohd(_1712001), hAPP(hAPP(c_List_Olist_OCons(_1712001), _1712003), _1712005)) = _1712003)], (42214 ^ _779327) ^ [_1600735, _1600737] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1600735, _1600735, _1600735), _1600737), c_Transitive__Closure_Ortrancl(_1600735, _1600737)) = hAPP(hAPP(c_Relation_Orel__comp(_1600735, _1600735, _1600735), c_Transitive__Closure_Ortrancl(_1600735, _1600737)), _1600737))], (7470 ^ _779327) ^ [_896892, _896894] : [class_Rings_Omult__zero(_896892), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896892), _896894), c_Groups_Ozero__class_Ozero(_896892)) = c_Groups_Ozero__class_Ozero(_896892))], (34641 ^ _779327) ^ [_1417442, _1417444, _1417446] : [-(hAPP(c_Set_OPow(_1417442), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417442, tc_HOL_Obool)), _1417444), _1417446)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1417442, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417442), _1417444)), hAPP(c_Set_OPow(_1417442), _1417446)))], (5502 ^ _779327) ^ [_863275, _863277] : [_863277 = _863275, -(tc_Lazy__Sequence_Olazy__sequence(_863277) = tc_Lazy__Sequence_Olazy__sequence(_863275))], (46471 ^ _779327) ^ [_1705507, _1705509, _1705511, _1705513] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705507), tc_List_Olist(_1705507))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705507), tc_List_Olist(_1705507)), _1705509), _1705511)), c_List_Olistrel1(_1705507, _1705513))), 46476 ^ _779327 : [(46483 ^ _779327) ^ [] : [-(_1705511 = hAPP(hAPP(c_List_Oappend(_1705507), 46478 ^ [_1705507, _1705509, _1705511, _1705513]), hAPP(hAPP(c_List_Olist_OCons(_1705507), 46475 ^ [_1705507, _1705509, _1705511, _1705513]), 46479 ^ [_1705507, _1705509, _1705511, _1705513])))], (46481 ^ _779327) ^ [] : [-(_1705509 = hAPP(hAPP(c_List_Oappend(_1705507), 46478 ^ [_1705507, _1705509, _1705511, _1705513]), hAPP(hAPP(c_List_Olist_OCons(_1705507), 46474 ^ [_1705507, _1705509, _1705511, _1705513]), 46479 ^ [_1705507, _1705509, _1705511, _1705513])))], (46477 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1705507, _1705507)), hAPP(hAPP(c_Product__Type_OPair(_1705507, _1705507), 46474 ^ [_1705507, _1705509, _1705511, _1705513]), 46475 ^ [_1705507, _1705509, _1705511, _1705513])), _1705513)))]]], (34231 ^ _779327) ^ [_1407278, _1407280, _1407282, _1407284] : [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), _1407278), _1407280)), 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), _1407282), _1407284)), 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), _1407278), _1407284)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1407282), _1407280))))], (27210 ^ _779327) ^ [_1259506, _1259508, _1259510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259506, tc_HOL_Obool)), _1259508), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259506, tc_HOL_Obool)), _1259510), _1259508))))], (40633 ^ _779327) ^ [_1563081] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1563081)))], (4436 ^ _779327) ^ [_846782, _846784, _846786, _846788] : [-(c_List_OremoveAll(_846788, _846784) = c_List_OremoveAll(_846786, _846782)), _846788 = _846786, _846784 = _846782], (47478 ^ _779327) ^ [_1727122, _1727124, _1727126, _1727128] : [47479 ^ _779327 : [(47482 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1727122), _1727124), hAPP(c_List_Oset(_1727122), c_List_Obutlast(_1727122, _1727128))))], (47480 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1727122), _1727124), hAPP(c_List_Oset(_1727122), c_List_Obutlast(_1727122, _1727126))))]], -(hBOOL(hAPP(hAPP(c_member(_1727122), _1727124), hAPP(c_List_Oset(_1727122), c_List_Obutlast(_1727122, hAPP(hAPP(c_List_Oappend(_1727122), _1727126), _1727128))))))], (7458 ^ _779327) ^ [_896662, _896664, _896666] : [class_Groups_Omonoid__mult(_896662), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896662), _896664), hAPP(c_Nat_OSuc, _896666)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896662), hAPP(hAPP(c_Power_Opower__class_Opower(_896662), _896664), _896666)), _896664))], (44422 ^ _779327) ^ [_1651467, _1651469, _1651471] : [c_FunDef_Ois__measure(_1651467, _1651469), -(c_FunDef_Ois__measure(tc_prod(_1651471, _1651467), hAPP(hAPP(c_COMBB(_1651467, tc_Nat_Onat, tc_prod(_1651471, _1651467)), _1651469), c_Product__Type_Osnd(_1651471, _1651467))))], (50658 ^ _779327) ^ [_1796467, _1796469] : [c_List_Olist__ex(_1796467, _1796469, c_List_Olist_ONil(_1796467))], (29374 ^ _779327) ^ [_1303451, _1303453] : [-(c_Set_Othe__elem(_1303451, _1303453) = c_HOL_OThe(_1303451, hAPP(hAPP(c_COMBB(tc_fun(_1303451, tc_HOL_Obool), tc_HOL_Obool, _1303451), hAPP(c_fequal, _1303453)), hAPP(hAPP(c_COMBC(_1303451, tc_fun(_1303451, tc_HOL_Obool), tc_fun(_1303451, tc_HOL_Obool)), c_Set_Oinsert(_1303451)), c_Orderings_Obot__class_Obot(tc_fun(_1303451, tc_HOL_Obool))))))], (21770 ^ _779327) ^ [_1154343, _1154345, _1154347, _1154349] : [_1154343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1154345), _1154347)), _1154349), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1154343, _1154345), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1154347), _1154349)))), 21777 ^ _779327 : [(21780 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154349), _1154345))], (21778 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154345)))]], 21785 ^ _779327 : [(21788 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154345), _1154349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1154349), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21786 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1154345))]]], (38970 ^ _779327) ^ [_1516534, _1516536, _1516538] : [-(hAPP(c_Finite__Set_Ofold1(_1516534, _1516536), _1516538) = c_HOL_OThe(_1516534, c_Finite__Set_Ofold1Set(_1516534, _1516536, _1516538)))], (9242 ^ _779327) ^ [_928929, _928931, _928933] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _928929), _928931)), _928933) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _928929), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _928931), _928933)))], (16922 ^ _779327) ^ [_1066415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066415), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066415) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1066415))], (44785 ^ _779327) ^ [_1663249, _1663251, _1663253, _1663255, _1663257, _1663259] : [hBOOL(hAPP(hAPP(_1663249, _1663251), _1663253)), c_List_Olistrelp(_1663255, _1663249, _1663257, _1663259), -(c_List_Olistrelp(_1663255, _1663249, hAPP(hAPP(c_List_Olist_OCons(_1663255), _1663251), _1663257), hAPP(hAPP(c_List_Olist_OCons(_1663255), _1663253), _1663259)))], (37993 ^ _779327) ^ [_1490908, _1490910, _1490912, _1490914] : [c_Fun_Oinj__on(_1490908, _1490910, _1490912, c_Orderings_Otop__class_Otop(tc_fun(_1490908, tc_HOL_Obool))), 37996 ^ _779327 : [(38010 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490910), _1490914), hAPP(c_Set_Oimage(_1490908, _1490910, _1490912), c_Orderings_Otop__class_Otop(tc_fun(_1490908, tc_HOL_Obool)))))), 38011 ^ _779327 : [(38012 ^ _779327) ^ [_1491311] : [_1490914 = hAPP(_1490912, _1491311), 38016 ^ _779327 : [(38019 ^ _779327) ^ [] : [38015 ^ [_1490908, _1490910, _1490912, _1490914, _1491311] = _1491311], (38017 ^ _779327) ^ [] : [-(_1490914 = hAPP(_1490912, 38015 ^ [_1490908, _1490910, _1490912, _1490914, _1491311]))]]]]], (37997 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1490910), _1490914), hAPP(c_Set_Oimage(_1490908, _1490910, _1490912), c_Orderings_Otop__class_Otop(tc_fun(_1490908, tc_HOL_Obool))))), 38001 ^ _779327 : [(38004 ^ _779327) ^ [_1491173] : [_1490914 = hAPP(_1490912, _1491173), -(_1491173 = 38000 ^ [_1490908, _1490910, _1490912, _1490914])], (38002 ^ _779327) ^ [] : [-(_1490914 = hAPP(_1490912, 38000 ^ [_1490908, _1490910, _1490912, _1490914]))]]]]], (51827 ^ _779327) ^ [_1823054, _1823056] : [c_Predicate_Otransp(_1823054, _1823056), -(c_Relation_Otrans(_1823054, hAPP(c_Set_OCollect(tc_prod(_1823054, _1823054)), hAPP(c_Product__Type_Oprod_Oprod__case(_1823054, _1823054, tc_HOL_Obool), _1823056))))], (51344 ^ _779327) ^ [_1810858, _1810860, _1810862, _1810864] : [51345 ^ _779327 : [(51348 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1810858), _1810862), _1810864))], (51346 ^ _779327) ^ [] : [_1810860 = _1810864]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1810858), hAPP(hAPP(c_List_Olist_OCons(_1810858), _1810860), _1810862)), _1810864)))], (50791 ^ _779327) ^ [_1799291, _1799293, _1799295] : [50793 ^ _779327 : [(50796 ^ _779327) ^ [] : [hBOOL(hAPP(_1799293, hAPP(hAPP(c_List_Onth(_1799291), _1799295), 50792 ^ [_1799291, _1799293, _1799295])))], (50794 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50792 ^ [_1799291, _1799293, _1799295]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799291)), _1799295))))]], -(c_List_Olist__all(_1799291, _1799293, _1799295))], (51778 ^ _779327) ^ [_1820756, _1820758, _1820760, _1820762] : [class_Complete__Lattice_Ocomplete__lattice(_1820756), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1820758, _1820756), _1820760), _1820762) = c_Complete__Lattice_OSup__class_OSup(_1820756, hAPP(c_Set_OCollect(_1820756), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool), tc_HOL_Obool, _1820756), c_HOL_OEx(tc_fun(_1820758, _1820756))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool), tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool), _1820756), hAPP(c_COMBS(tc_fun(_1820758, _1820756), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1820758, _1820756)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1820758, _1820756), tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1820758, _1820756))), _1820760)))), hAPP(hAPP(c_COMBC(_1820756, tc_fun(tc_fun(_1820758, _1820756), _1820756), tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1820756, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1820758, _1820756), _1820756), tc_fun(tc_fun(_1820758, _1820756), tc_HOL_Obool)), _1820756), c_COMBB(_1820756, tc_HOL_Obool, tc_fun(_1820758, _1820756))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1820758, _1820756), _1820758, _1820756), c_COMBI(tc_fun(_1820758, _1820756))), _1820762)))))))], (51743 ^ _779327) ^ [_1819726, _1819728] : [51746 ^ _779327 : [(51752 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1819726, _1819726)), hAPP(hAPP(c_Product__Type_OPair(_1819726, _1819726), 51744 ^ [_1819726, _1819728]), 51748 ^ [_1819726, _1819728])), _1819728))], (51750 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819726, _1819726)), hAPP(hAPP(c_Product__Type_OPair(_1819726, _1819726), 51745 ^ [_1819726, _1819728]), 51748 ^ [_1819726, _1819728])), _1819728)))], (51747 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819726, _1819726)), hAPP(hAPP(c_Product__Type_OPair(_1819726, _1819726), 51744 ^ [_1819726, _1819728]), 51745 ^ [_1819726, _1819728])), _1819728)))]], -(c_Relation_Otrans(_1819726, _1819728))], (50767 ^ _779327) ^ [_1798740, _1798742, _1798744] : [hBOOL(hAPP(hAPP(c_member(_1798740), _1798742), hAPP(c_List_Oset(_1798740), _1798744))), -(_1798744 = hAPP(hAPP(c_List_Oappend(_1798740), 50770 ^ [_1798740, _1798742, _1798744]), hAPP(hAPP(c_List_Olist_OCons(_1798740), _1798742), 50771 ^ [_1798740, _1798742, _1798744])))], (46178 ^ _779327) ^ [_1698005, _1698007, _1698009, _1698011, _1698013] : [-(hAPP(hAPP(c_List_Omap(_1698005, _1698007), _1698009), hAPP(hAPP(c_List_Oappend(_1698005), _1698011), _1698013)) = hAPP(hAPP(c_List_Oappend(_1698007), hAPP(hAPP(c_List_Omap(_1698005, _1698007), _1698009), _1698011)), hAPP(hAPP(c_List_Omap(_1698005, _1698007), _1698009), _1698013)))], (23199 ^ _779327) ^ [] : [-(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)))))], (30441 ^ _779327) ^ [_1327709, _1327711, _1327713, _1327715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool)), _1327713), _1327715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327709, tc_fun(_1327711, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1327709, tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_fun(_1327711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327711, tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_fun(_1327711, tc_HOL_Obool)), _1327709), c_COMBC(_1327711, tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327711, tc_prod(_1327709, _1327711)), tc_fun(_1327711, tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), _1327709), hAPP(c_COMBB(tc_prod(_1327709, _1327711), tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool), _1327711), c_member(tc_prod(_1327709, _1327711)))), c_Product__Type_OPair(_1327709, _1327711)))), _1327713)), hAPP(hAPP(c_COMBC(_1327709, tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_fun(_1327711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327711, tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_fun(_1327711, tc_HOL_Obool)), _1327709), c_COMBC(_1327711, tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1327711, tc_prod(_1327709, _1327711)), tc_fun(_1327711, tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool)), _1327709), hAPP(c_COMBB(tc_prod(_1327709, _1327711), tc_fun(tc_fun(tc_prod(_1327709, _1327711), tc_HOL_Obool), tc_HOL_Obool), _1327711), c_member(tc_prod(_1327709, _1327711)))), c_Product__Type_OPair(_1327709, _1327711)))), _1327715))))], (41787 ^ _779327) ^ [_1590057, _1590059] : [41788 ^ _779327 : [(41789 ^ _779327) ^ [_1590103] : [hBOOL(hAPP(_1590057, _1590103))]], -(hBOOL(hAPP(_1590057, c_Hilbert__Choice_OEps(_1590059, _1590057))))], (43955 ^ _779327) ^ [_1640804] : [class_Complete__Lattice_Ocomplete__lattice(_1640804), -(c_Complete__Lattice_OSup__class_OSup(_1640804, c_Orderings_Obot__class_Obot(tc_fun(_1640804, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1640804))], (4692 ^ _779327) ^ [_850828, _850830, _850832, _850834, _850836, _850838] : [-(c_List_Olinorder__class_Oinsort__key(_850838, _850834, _850830) = c_List_Olinorder__class_Oinsort__key(_850836, _850832, _850828)), _850838 = _850836, _850834 = _850832, _850830 = _850828], (18712 ^ _779327) ^ [_1097696, _1097698] : [class_Fields_Olinordered__field__inverse__zero(_1097696), class_Int_Onumber__ring(_1097696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097696), c_Groups_Ozero__class_Ozero(_1097696)), _1097698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097696), c_Groups_Ozero__class_Ozero(_1097696)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1097696), _1097698), hAPP(c_Int_Onumber__class_Onumber__of(_1097696), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (38830 ^ _779327) ^ [_1513147, _1513149, _1513151, _1513153] : [_1513147 = c_Finite__Set_Ofold1(_1513149, _1513151), -(hAPP(_1513147, hAPP(hAPP(c_Set_Oinsert(_1513149), _1513153), c_Orderings_Obot__class_Obot(tc_fun(_1513149, tc_HOL_Obool)))) = _1513153)], (45705 ^ _779327) ^ [_1686886, _1686888, _1686890, _1686892] : [-(hAPP(c_List_Oset(tc_prod(_1686886, _1686888)), hAPP(hAPP(c_List_Ozip(_1686886, _1686888), _1686890), _1686892)) = hAPP(c_Set_OCollect(tc_prod(_1686886, _1686888)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1686886, _1686888)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1686886, _1686888), 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(_1686886, _1686888)), 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(_1686886, _1686888)), 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(_1686886, _1686888), tc_fun(tc_Nat_Onat, tc_prod(_1686886, _1686888)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1686886, _1686888), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1686886, _1686888)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1686886, _1686888)), c_COMBB(tc_prod(_1686886, _1686888), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1686888, tc_prod(_1686886, _1686888)), hAPP(hAPP(c_COMBB(_1686886, tc_fun(_1686888, tc_prod(_1686886, _1686888)), tc_Nat_Onat), c_Product__Type_OPair(_1686886, _1686888)), hAPP(c_List_Onth(_1686886), _1686890))), hAPP(c_List_Onth(_1686888), _1686892)))))), 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(_1686886)), _1686890)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686888)), _1686892)))))))], (11047 ^ _779327) ^ [_959532, _959534, _959536] : [class_Groups_Ogroup__add(_959532), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959532), _959534), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959532), hAPP(c_Groups_Ouminus__class_Ouminus(_959532), _959534)), _959536)) = _959536)], (12582 ^ _779327) ^ [_989174, _989176, _989178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989174), _989176)), _989178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989174), _989178)))], (24129 ^ _779327) ^ [_1199654, _1199656] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199654), _1199656)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199656), _1199654))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199656), _1199654)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1199654), _1199656)))], (26047 ^ _779327) ^ [_1236530, _1236532] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1236530), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236532), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1236530, _1236532))], (6993 ^ _779327) ^ [_888778, _888780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _888778)), hAPP(c_Nat_OSuc, _888780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888778), _888780)))], (31401 ^ _779327) ^ [_1348971, _1348973] : [class_Complete__Lattice_Ocomplete__lattice(_1348971), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1348971, hAPP(c_COMBK(_1348971, _1348971), _1348973)) = _1348973)], (48515 ^ _779327) ^ [_1750544, _1750546, _1750548, _1750550, _1750552] : [class_Orderings_Olinorder(_1750544), -(hAPP(c_List_Ofilter(_1750546, _1750548), c_List_Olinorder__class_Osort__key(_1750546, _1750544, _1750550, _1750552)) = c_List_Olinorder__class_Osort__key(_1750546, _1750544, _1750550, hAPP(c_List_Ofilter(_1750546, _1750548), _1750552)))], (1348 ^ _779327) ^ [_799165, _799167] : [-(class_Groups_Oabs__if(_799165)), _799167 = _799165, class_Groups_Oabs__if(_799167)], (37515 ^ _779327) ^ [_1481070, _1481072, _1481074, _1481076, _1481078, _1481080, _1481082] : [c_Big__Operators_Ocomm__monoid__big(_1481070, _1481072, _1481074, _1481076, _1481078), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1481072), _1481080))), -(hAPP(hAPP(_1481078, _1481082), _1481080) = _1481076)], (26588 ^ _779327) ^ [_1247376] : [c_Nat__Transfer_Onat__set(_1247376), 26591 ^ _779327 : [(26592 ^ _779327) ^ [_1247442] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1247442), _1247376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247442)))]]], (23758 ^ _779327) ^ [_1193193, _1193195, _1193197, _1193199, _1193201, _1193203] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1193193, _1193195, _1193197, _1193199), _1193201), _1193203) = hAPP(_1193199, hAPP(hAPP(c_Product__Type_OPair(_1193193, _1193195), _1193201), _1193203)))], (37797 ^ _779327) ^ [_1486820, _1486822] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486820, tc_HOL_Obool)), _1486822), c_Orderings_Otop__class_Otop(tc_fun(_1486820, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1486820, tc_HOL_Obool)))], (17550 ^ _779327) ^ [_1077192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1077192)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077192), c_Int_OMin)))], (49915 ^ _779327) ^ [_1779787, _1779789, _1779791, _1779793, _1779795] : [-(c_List_OdropWhile(_1779787, _1779789, _1779791) = hAPP(hAPP(c_List_Olist_OCons(_1779787), _1779793), _1779795)), _1779791 = hAPP(hAPP(c_List_Oappend(_1779787), c_List_OtakeWhile(_1779787, _1779789, _1779791)), hAPP(hAPP(c_List_Olist_OCons(_1779787), _1779793), _1779795)), -(hBOOL(hAPP(_1779789, _1779793)))], (35559 ^ _779327) ^ [_1437505, _1437507, _1437509] : [class_Orderings_Oorder(_1437505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1437505, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1437505, _1437507, _1437509)), hAPP(c_SetInterval_Oord__class_OatLeast(_1437505), _1437509)) = c_Orderings_Obot__class_Obot(tc_fun(_1437505, tc_HOL_Obool)))], (17734 ^ _779327) ^ [_1080046, _1080048] : [class_Int_Onumber__ring(_1080046), class_Rings_Olinordered__idom(_1080046), 17741 ^ _779327 : [(17748 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080048), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080046), hAPP(c_Int_Onumber__class_Onumber__of(_1080046), _1080048)), c_Groups_Oone__class_Oone(_1080046))))], (17742 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080046), hAPP(c_Int_Onumber__class_Onumber__of(_1080046), _1080048)), c_Groups_Oone__class_Oone(_1080046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080048), c_Int_OBit1(c_Int_OPls))))]]], (38766 ^ _779327) ^ [_1510999, _1511001, _1511003] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1510999, _1511001), c_Orderings_Obot__class_Obot(tc_fun(_1510999, tc_HOL_Obool))), _1511003) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1510999, _1511001), tc_HOL_Obool)))], (41209 ^ _779327) ^ [_1576900, _1576902, _1576904, _1576906, _1576908, _1576910] : [hBOOL(hAPP(hAPP(c_member(_1576900), _1576902), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1576904, _1576906, tc_fun(_1576900, tc_HOL_Obool)), _1576908), _1576910))), 41214 ^ _779327 : [(41217 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576900), _1576902), hAPP(hAPP(_1576908, 41212 ^ [_1576900, _1576902, _1576904, _1576906, _1576908, _1576910]), 41213 ^ [_1576900, _1576902, _1576904, _1576906, _1576908, _1576910]))))], (41215 ^ _779327) ^ [] : [-(_1576910 = hAPP(hAPP(c_Product__Type_OPair(_1576904, _1576906), 41212 ^ [_1576900, _1576902, _1576904, _1576906, _1576908, _1576910]), 41213 ^ [_1576900, _1576902, _1576904, _1576906, _1576908, _1576910]))]]], (26259 ^ _779327) ^ [_1241047, _1241049, _1241051, _1241053, _1241055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241047, tc_HOL_Obool)), _1241049), hAPP(c_Set_Oimage(_1241051, _1241047, _1241053), _1241055))), 26263 ^ _779327 : [(26266 ^ _779327) ^ [] : [-(_1241049 = hAPP(c_Set_Oimage(_1241051, _1241047, _1241053), 26262 ^ [_1241047, _1241049, _1241051, _1241053, _1241055]))], (26264 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241051, tc_HOL_Obool)), 26262 ^ [_1241047, _1241049, _1241051, _1241053, _1241055]), _1241055)))]]], (27807 ^ _779327) ^ [_1273584, _1273586] : [class_Groups_Oordered__ab__group__add(_1273584), -(hAPP(c_Set_Oimage(_1273584, _1273584, c_Groups_Ouminus__class_Ouminus(_1273584)), hAPP(c_SetInterval_Oord__class_OatLeast(_1273584), _1273586)) = hAPP(c_SetInterval_Oord__class_OatMost(_1273584), hAPP(c_Groups_Ouminus__class_Ouminus(_1273584), _1273586)))], (36044 ^ _779327) ^ [_1448243, _1448245, _1448247] : [class_Orderings_Olinorder(_1448243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448243), _1448245)), -(_1448245 = c_Orderings_Obot__class_Obot(tc_fun(_1448243, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1448243), _1448247)), -(_1448247 = c_Orderings_Obot__class_Obot(tc_fun(_1448243, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448243, tc_HOL_Obool)), _1448245), _1448247) = c_Orderings_Obot__class_Obot(tc_fun(_1448243, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1448243, c_Orderings_Oord__class_Omax(_1448243), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1448243, tc_HOL_Obool)), _1448245), _1448247)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1448243), c_Big__Operators_Olattice_OSup__fin(_1448243, c_Orderings_Oord__class_Omax(_1448243), _1448245)), c_Big__Operators_Olattice_OSup__fin(_1448243, c_Orderings_Oord__class_Omax(_1448243), _1448247)))], (18088 ^ _779327) ^ [_1086444, _1086446] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1086444)), c_Int_OBit1(_1086446)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086444), _1086446)))], (51147 ^ _779327) ^ [_1806237, _1806239, _1806241, _1806243, _1806245] : [hBOOL(hAPP(hAPP(_1806237, _1806239), _1806241)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1806243, _1806245, _1806237), _1806241), _1806239)))], (48906 ^ _779327) ^ [_1759726, _1759728, _1759730] : [48907 ^ _779327 : [(48910 ^ _779327) ^ [] : [_1759730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48908 ^ _779327) ^ [] : [-(_1759726 = c_List_Olist_ONil(tc_List_Olist(_1759728)))]], 48914 ^ _779327 : [(48917 ^ _779327) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759728)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1759728)), _1759726), 48913 ^ [_1759726, _1759728, _1759730])) = _1759730], (48915 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48913 ^ [_1759726, _1759728, _1759730]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1759728))), _1759726))))]], -(c_List_Otranspose(_1759728, _1759726) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1759728)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1759728)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1759728), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1759728)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1759728)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1759728), hAPP(hAPP(c_COMBB(tc_List_Olist(_1759728), tc_fun(tc_Nat_Onat, _1759728), tc_Nat_Onat), c_List_Onth(_1759728)), hAPP(c_List_Onth(tc_List_Olist(_1759728)), _1759726))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1759728))), _1759726)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1759730)))], (50943 ^ _779327) ^ [_1802294, _1802296] : [c_List_Olist__ex1(_1802294, _1802296, c_List_Olist_ONil(_1802294))], (34975 ^ _779327) ^ [_1423908, _1423910, _1423912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423908, tc_HOL_Obool)), _1423910), _1423912)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423908, tc_HOL_Obool)), _1423910), _1423912) = _1423910)], (29496 ^ _779327) ^ [_1306099, _1306101] : [hBOOL(hAPP(hAPP(c_member(_1306099), _1306101), c_Orderings_Obot__class_Obot(tc_fun(_1306099, tc_HOL_Obool))))], (22705 ^ _779327) ^ [_1172375, _1172377, _1172379] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1172375, _1172377), _1172379))), _1172375 = 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), _1172379)), _1172377)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1172379)), 22712 ^ _779327 : [(22715 ^ _779327) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1172379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22713 ^ _779327) ^ [] : [-(_1172377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22716 ^ _779327 : [(22719 ^ _779327) ^ [] : [22720 ^ _779327 : [(22723 ^ _779327) ^ [] : [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), _1172379))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1172379)), _1172377))], (22721 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172377)))]], 22728 ^ _779327 : [(22731 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172377), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1172379))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1172379)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22729 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172377))]]], (22717 ^ _779327) ^ [] : [_1172377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (10847 ^ _779327) ^ [_956111, _956113] : [class_Groups_Ogroup__add(_956111), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956111), c_Groups_Ozero__class_Ozero(_956111)), _956113) = hAPP(c_Groups_Ouminus__class_Ouminus(_956111), _956113))], (52952 ^ _779327) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (31982 ^ _779327) ^ [_1360353] : [class_Rings_Osemiring__1(_1360353), -(hBOOL(hAPP(hAPP(c_member(_1360353), c_Groups_Oone__class_Oone(_1360353)), c_Nat_Osemiring__1__class_ONats(_1360353))))], (17306 ^ _779327) ^ [_1073007] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1073007), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1073007)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1073007)))], (41748 ^ _779327) ^ [_1589337, _1589339, _1589341, _1589343, _1589345] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1589337), _1589339), _1589341), _1589343), _1589345) = c_New__DSequence_Opos__single(_1589337, _1589339))], (51687 ^ _779327) ^ [_1818558, _1818560] : [c_Relation_Otrans(_1818558, _1818560), -(c_Relation_Otrans(_1818558, hAPP(c_Relation_Oconverse(_1818558, _1818558), _1818560)))], (11551 ^ _779327) ^ [_970483, _970485, _970487, _970489, _970491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970483), _970485)), -(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), _970483), _970487)), _970489)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970485), _970487)), _970491)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _970489), 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), _970485), _970483)), _970487)), _970491)))], (4014 ^ _779327) ^ [_840227, _840229, _840231, _840233, _840235, _840237, _840239, _840241] : [-(c_Enum_Oproduct(_840241, _840237, _840233, _840229) = c_Enum_Oproduct(_840239, _840235, _840231, _840227)), _840241 = _840239, _840237 = _840235, _840233 = _840231, _840229 = _840227], (47570 ^ _779327) ^ [_1729001, _1729003, _1729005, _1729007] : [-(c_List_Oremove1(_1729001, _1729003, c_List_Oremove1(_1729001, _1729005, _1729007)) = c_List_Oremove1(_1729001, _1729005, c_List_Oremove1(_1729001, _1729003, _1729007)))], (38481 ^ _779327) ^ [_1504284, _1504286, _1504288, _1504290] : [-(hBOOL(hAPP(hAPP(c_member(_1504284), _1504286), _1504288))), -(hAPP(c_Set_Ovimage(_1504290, _1504284, hAPP(c_COMBK(_1504284, _1504290), _1504286)), _1504288) = c_Orderings_Obot__class_Obot(tc_fun(_1504290, tc_HOL_Obool)))], (27853 ^ _779327) ^ [_1274540, _1274542] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1274540), _1274542))))], (47354 ^ _779327) ^ [_1724622, _1724624, _1724626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724622), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724624)), _1724626))), -(c_List_Olast(_1724624, hAPP(hAPP(c_List_Odrop(_1724624), _1724622), _1724626)) = c_List_Olast(_1724624, _1724626))], (49557 ^ _779327) ^ [_1772251, _1772253] : [class_Groups_Ocomm__monoid__add(_1772251), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1772251), hAPP(c_List_Orev(_1772251), _1772253)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1772251), _1772253))], (2312 ^ _779327) ^ [_813050, _813052, _813054, _813056, _813058, _813060, _813062, _813064] : [-(c_Random_Oiterate(_813064, _813060, _813056, _813052) = c_Random_Oiterate(_813062, _813058, _813054, _813050)), _813064 = _813062, _813060 = _813058, _813056 = _813054, _813052 = _813050], (11303 ^ _779327) ^ [_964938, _964940, _964942] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _964938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _964940)), _964942)) = 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), _964938), _964940))), _964942))], (35800 ^ _779327) ^ [_1443440, _1443442, _1443444, _1443446, _1443448] : [class_Groups_Ocomm__monoid__mult(_1443440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443442), _1443444)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443442), _1443446)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1443442, tc_HOL_Obool)), _1443444), _1443446) = c_Orderings_Obot__class_Obot(tc_fun(_1443442, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443442, _1443440), _1443448), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443442, tc_HOL_Obool)), _1443444), _1443446)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443440), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443442, _1443440), _1443448), _1443444)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1443442, _1443440), _1443448), _1443446)))], (23596 ^ _779327) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29927 ^ _779327) ^ [_1314303, _1314305, _1314307, _1314309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314303, tc_HOL_Obool)), _1314305), _1314307)), hBOOL(hAPP(hAPP(c_member(_1314303), _1314309), _1314305)), -(hBOOL(hAPP(hAPP(c_member(_1314303), _1314309), _1314307)))], (30906 ^ _779327) ^ [_1338400, _1338402, _1338404, _1338406, _1338408, _1338410] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338400, tc_fun(_1338402, tc_HOL_Obool))), _1338404), _1338406), _1338408), _1338410)), -(hBOOL(hAPP(hAPP(_1338404, _1338408), _1338410))), -(hBOOL(hAPP(hAPP(_1338406, _1338408), _1338410)))], (7708 ^ _779327) ^ [_900781, _900783, _900785] : [class_Rings_Oordered__cancel__semiring(_900781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900781), c_Groups_Ozero__class_Ozero(_900781)), _900783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900781), c_Groups_Ozero__class_Ozero(_900781)), _900785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900781), c_Groups_Ozero__class_Ozero(_900781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_900781), _900783), _900785))))], (45233 ^ _779327) ^ [_1674518, _1674520] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1674518), hAPP(c_List_Oset(_1674518), _1674520))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674518)), _1674520))))], (31063 ^ _779327) ^ [_1341797, _1341799, _1341801, _1341803] : [hBOOL(hAPP(hAPP(c_member(_1341797), _1341799), c_SetInterval_Oord_OgreaterThan(_1341797, _1341801, _1341803))), -(hBOOL(hAPP(hAPP(_1341801, _1341803), _1341799)))], (52666 ^ _779327) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (29644 ^ _779327) ^ [_1308980, _1308982, _1308984, _1308986, _1308988, _1308990, _1308992] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1308980, _1308982)), hAPP(hAPP(c_Product__Type_OPair(_1308980, _1308982), _1308984), _1308986)), _1308988)), -(hBOOL(hAPP(hAPP(c_member(_1308990), hAPP(hAPP(_1308992, _1308984), _1308986)), hAPP(c_Set_Oimage(tc_prod(_1308980, _1308982), _1308990, hAPP(c_Product__Type_Oprod_Oprod__case(_1308980, _1308982, _1308990), _1308992)), _1308988))))], (35097 ^ _779327) ^ [_1427142, _1427144] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427142, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1427142, tc_HOL_Obool))), _1427144) = c_Orderings_Obot__class_Obot(tc_fun(_1427142, tc_HOL_Obool)))], (37611 ^ _779327) ^ [_1483195] : [c_Orderings_Otop__class_Otop(tc_fun(_1483195, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1483195, tc_HOL_Obool))], (45609 ^ _779327) ^ [_1684686, _1684688, _1684690, _1684692] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1684686, _1684686)), hAPP(hAPP(c_Product__Type_OPair(_1684686, _1684686), _1684688), _1684690)), hAPP(c_List_Oset(tc_prod(_1684686, _1684686)), hAPP(hAPP(c_List_Ozip(_1684686, _1684686), _1684692), _1684692)))), 45612 ^ _779327 : [(45615 ^ _779327) ^ [] : [-(_1684688 = _1684690)], (45613 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684686), _1684688), hAPP(c_List_Oset(_1684686), _1684692))))]]], (12936 ^ _779327) ^ [_995505, _995507, _995509] : [class_Int_Onumber(_995505), class_Orderings_Olinorder(_995505), 12943 ^ _779327 : [(12950 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995505), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995509)), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995507)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995505), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995507)), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995509))))], (12944 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995505), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995507)), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995505), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995509)), hAPP(c_Int_Onumber__class_Onumber__of(_995505), _995507)))]]], (32246 ^ _779327) ^ [_1364954, _1364956] : [class_Lattices_Olattice(_1364954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364954), _1364956)), -(_1364956 = c_Orderings_Obot__class_Obot(tc_fun(_1364954, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1364954), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1364954), 32259 ^ [_1364954, _1364956]), 32260 ^ [_1364954, _1364956])), hAPP(hAPP(c_Set_Oinsert(_1364954), 32259 ^ [_1364954, _1364956]), hAPP(hAPP(c_Set_Oinsert(_1364954), 32260 ^ [_1364954, _1364956]), c_Orderings_Obot__class_Obot(tc_fun(_1364954, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1364954), c_Big__Operators_Olattice__class_OSup__fin(_1364954, _1364956)), _1364956)))], (45763 ^ _779327) ^ [_1688692, _1688694, _1688696, _1688698] : [class_Groups_Oab__group__add(_1688692), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1688692), hAPP(c_List_Omonoid__add__class_Olistsum(_1688692), hAPP(hAPP(c_List_Omap(_1688694, _1688692), _1688696), _1688698))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1688692), hAPP(hAPP(c_List_Omap(_1688694, _1688692), hAPP(c_Fun_Ocomp(_1688692, _1688692, _1688694, c_Groups_Ouminus__class_Ouminus(_1688692)), _1688696)), _1688698)))], (43105 ^ _779327) ^ [_1623061, _1623063, _1623065, _1623067, _1623069, _1623071] : [c_Finite__Set_Ofolding(_1623061, _1623063, _1623065, _1623067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623061), _1623069)), -(hAPP(hAPP(_1623067, _1623069), _1623071) = hAPP(hAPP(c_Finite__Set_Ofold(_1623061, _1623063, _1623065), _1623071), _1623069))], (11955 ^ _779327) ^ [_977616, _977618, _977620, _977622] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_977616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977616), _977618), _977620)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977616), _977618), _977622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977616), _977620), _977622)))], (33704 ^ _779327) ^ [_1395148, _1395150, _1395152] : [class_Orderings_Olinorder(_1395148), hAPP(_1395150, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1395148), 33709 ^ [_1395148, _1395150, _1395152]), 33710 ^ [_1395148, _1395150, _1395152])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1395148), hAPP(_1395150, 33709 ^ [_1395148, _1395150, _1395152])), hAPP(_1395150, 33710 ^ [_1395148, _1395150, _1395152])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395148), _1395152)), -(_1395152 = c_Orderings_Obot__class_Obot(tc_fun(_1395148, tc_HOL_Obool))), -(hAPP(_1395150, c_Big__Operators_Olinorder__class_OMax(_1395148, _1395152)) = c_Big__Operators_Olinorder__class_OMax(_1395148, hAPP(c_Set_Oimage(_1395148, _1395148, _1395150), _1395152)))], (36803 ^ _779327) ^ [_1465961, _1465963, _1465965, _1465967, _1465969] : [c_Fun_Oinj__on(_1465961, _1465963, _1465965, _1465967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465961, tc_HOL_Obool)), _1465969), _1465967)), -(c_Fun_Oinj__on(_1465961, _1465963, _1465965, _1465969))], (34290 ^ _779327) ^ [_1408953, _1408955, _1408957] : [_1408955 = c_Orderings_Obot__class_Obot(tc_fun(_1408953, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1408953), _1408955), _1408957) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1408953, tc_HOL_Obool), tc_HOL_Obool)))], (22301 ^ _779327) ^ [_1164864, _1164866, _1164868, _1164870, _1164872] : [-(c_Product__Type_Oprod_Oprod__size(_1164864, _1164866, _1164868, _1164870, _1164872) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1164868, hAPP(c_Product__Type_Ofst(_1164864, _1164866), _1164872))), hAPP(_1164870, hAPP(c_Product__Type_Osnd(_1164864, _1164866), _1164872)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42074 ^ _779327) ^ [_1596477, _1596479] : [-(hAPP(c_Relation_ODomain(_1596477, _1596477), c_Transitive__Closure_Otrancl(_1596477, _1596479)) = hAPP(c_Relation_ODomain(_1596477, _1596477), _1596479))], (47923 ^ _779327) ^ [_1736708, _1736710, _1736712] : [class_Orderings_Olinorder(_1736708), hBOOL(hAPP(hAPP(c_member(_1736708), _1736710), hAPP(c_List_Oset(_1736708), _1736712))), -(c_List_Olinorder__class_Oinsort__insert__key(_1736708, _1736708, c_COMBI(_1736708), _1736710, _1736712) = _1736712)], (52734 ^ _779327) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (42535 ^ _779327) ^ [_1608504, _1608506, _1608508, _1608510, _1608512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608504, _1608506)), hAPP(hAPP(c_Product__Type_OPair(_1608504, _1608506), _1608508), _1608510)), _1608512)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608506, _1608504)), hAPP(hAPP(c_Product__Type_OPair(_1608506, _1608504), _1608510), _1608508)), hAPP(c_Relation_Oconverse(_1608504, _1608506), _1608512))))], (33038 ^ _779327) ^ [_1380724, _1380726, _1380728, _1380730, _1380732, _1380734] : [-(_1380724 = _1380726), -(hAPP(c_Fun_Ofun__upd(_1380728, _1380730, _1380732, _1380726, _1380734), _1380724) = hAPP(_1380732, _1380724))], (47275 ^ _779327) ^ [_1723389, _1723391, _1723393, _1723395, _1723397] : [class_Groups_Omonoid__add(_1723389), class_Groups_Oordered__ab__semigroup__add(_1723389), 47285 ^ _779327 : [(47288 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723389), hAPP(_1723395, 47284 ^ [_1723389, _1723391, _1723393, _1723395, _1723397])), hAPP(_1723397, 47284 ^ [_1723389, _1723391, _1723393, _1723395, _1723397])))], (47286 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723391), 47284 ^ [_1723389, _1723391, _1723393, _1723395, _1723397]), hAPP(c_List_Oset(_1723391), _1723393))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723389), hAPP(c_List_Omonoid__add__class_Olistsum(_1723389), hAPP(hAPP(c_List_Omap(_1723391, _1723389), _1723395), _1723393))), hAPP(c_List_Omonoid__add__class_Olistsum(_1723389), hAPP(hAPP(c_List_Omap(_1723391, _1723389), _1723397), _1723393)))))], (21436 ^ _779327) ^ [_1148120, _1148122] : [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), _1148120))), 21439 ^ _779327 : [(21446 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148122)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148120)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148122), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148120)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148120)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148122), 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), _1148120)))))], (21440 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148122)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148120))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148122), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148120)) = 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), _1148122)))]]], (5752 ^ _779327) ^ [_870323] : [-(_870323 = 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)), _870323)))], (14217 ^ _779327) ^ [_1018879, _1018881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1018879), _1018881)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018881)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1018879)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1018881), _1018879)))], (2730 ^ _779327) ^ [_819753, _819755, _819757, _819759, _819761, _819763, _819765, _819767] : [-(c_New__DSequence_Opos__decr__bind(_819767, _819763, _819759, _819755) = c_New__DSequence_Opos__decr__bind(_819765, _819761, _819757, _819753)), _819767 = _819765, _819763 = _819761, _819759 = _819757, _819755 = _819753], (49862 ^ _779327) ^ [_1778785, _1778787, _1778789] : [49864 ^ _779327 : [(49867 ^ _779327) ^ [] : [hBOOL(hAPP(_1778787, 49863 ^ [_1778785, _1778787, _1778789]))], (49865 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778785), 49863 ^ [_1778785, _1778787, _1778789]), hAPP(c_List_Oset(_1778785), _1778789))))]], -(c_List_OdropWhile(_1778785, _1778787, _1778789) = c_List_Olist_ONil(_1778785))], (45064 ^ _779327) ^ [_1670667, _1670669, _1670671, _1670673] : [hBOOL(hAPP(hAPP(c_member(_1670667), _1670669), hAPP(c_List_Oset(_1670667), hAPP(hAPP(c_List_Otake(_1670667), _1670671), _1670673)))), -(hBOOL(hAPP(hAPP(c_member(_1670667), _1670669), hAPP(c_List_Oset(_1670667), _1670673))))], (33030 ^ _779327) ^ [_1380566, _1380568, _1380570, _1380572, _1380574] : [-(hAPP(c_Fun_Ofun__upd(_1380566, _1380568, _1380570, _1380572, _1380574), _1380572) = _1380574)], (31227 ^ _779327) ^ [_1344992, _1344994, _1344996, _1344998] : [hBOOL(hAPP(hAPP(c_member(_1344992), _1344994), c_SetInterval_Oord_OatMost(_1344992, _1344996, _1344998))), -(hBOOL(hAPP(hAPP(_1344996, _1344994), _1344998)))], (18781 ^ _779327) ^ [_1098970, _1098972] : [class_Rings_Odivision__ring__inverse__zero(_1098970), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1098970), _1098972), c_Groups_Ozero__class_Ozero(_1098970)) = c_Groups_Ozero__class_Ozero(_1098970))], (51383 ^ _779327) ^ [_1811724, _1811726, _1811728] : [-(c_List_Olist__ex1(_1811724, _1811726, _1811728)), 51384 ^ _779327 : [(51385 ^ _779327) ^ [_1811818] : [hBOOL(hAPP(hAPP(c_member(_1811724), _1811818), hAPP(c_List_Oset(_1811724), _1811728))), hBOOL(hAPP(_1811726, _1811818)), 51393 ^ _779327 : [(51398 ^ _779327) ^ [] : [51392 ^ [_1811724, _1811726, _1811728, _1811818] = _1811818], (51396 ^ _779327) ^ [] : [-(hBOOL(hAPP(_1811726, 51392 ^ [_1811724, _1811726, _1811728, _1811818])))], (51394 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811724), 51392 ^ [_1811724, _1811726, _1811728, _1811818]), hAPP(c_List_Oset(_1811724), _1811728))))]]]]], (24043 ^ _779327) ^ [_1198233, _1198235, _1198237] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198233), _1198235)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198235), _1198233))), 24058 ^ _779327 : [(24061 ^ _779327) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198237), _1198233))], (24059 ^ _779327) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198233), _1198237)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198235), _1198237)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1198237), _1198235)))], (43241 ^ _779327) ^ [_1625966, _1625968, _1625970, _1625972] : [class_Orderings_Olinorder(_1625966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625966), _1625968)), hBOOL(hAPP(hAPP(c_member(_1625966), _1625970), _1625968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625966), hAPP(hAPP(c_Finite__Set_Ofold(_1625966, _1625966, c_Orderings_Oord__class_Omin(_1625966)), _1625972), _1625968)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1625966), _1625970), _1625972))))], (44418 ^ _779327) ^ [_1651341, _1651343] : [-(c_List_Olenlex(_1651341, _1651343) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1651341)), tc_List_Olist(_1651341)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1651341), c_Wellfounded_Oless__than, c_List_Olex(_1651341, _1651343))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1651341), tc_List_Olist(_1651341), tc_prod(tc_Nat_Onat, tc_List_Olist(_1651341))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1651341), tc_prod(tc_Nat_Onat, tc_List_Olist(_1651341))), tc_List_Olist(_1651341)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1651341))), c_Nat_Osize__class_Osize(tc_List_Olist(_1651341)))), c_COMBI(tc_List_Olist(_1651341)))))]], input).
% 46.38/45.04 ncf('1',plain,[c_Hoare__Mirabelle_Otriple__valid(t_a, v_n, 53119 ^ [])],start(53123 ^ 0)).
% 46.38/45.04 ncf('1.1',plain,[-(c_Hoare__Mirabelle_Otriple__valid(t_a, v_n, 53119 ^ [])), c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_n), 53119 ^ [])],extension(5595 ^ 1,bind([[_867382, _867384, _867386], [t_a, v_n, 53119 ^ []]]))).
% 46.38/45.04 ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_n), 53119 ^ [])), hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 53119 ^ []), v_ts))],extension(53114 ^ 2,bind([[_1841912], [53119 ^ []]]))).
% 46.38/45.04 ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), 53119 ^ []), v_ts)))],extension(53121 ^ 3)).
% 46.38/45.04 %-----------------------------------------------------
% 46.38/45.04 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------