TSTP Solution File: SWW300+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW300+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n007.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 12:25:54 EDT 2023
% Result : Theorem 45.26s 43.94s
% Output : Proof 45.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWW300+1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.12 % Command : nanocop.sh %s %d
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 18 22:21:08 EDT 2023
% 0.11/0.33 % CPUTime :
% 45.26/43.94
% 45.26/43.94 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 45.26/43.94 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.26/43.94 %-----------------------------------------------------
% 45.26/43.94 ncf(matrix, plain, [(52580 ^ _2080023) ^ [_2080080] : [v_P_H(_2080080, 52575 ^ []), -(v_Q(_2080080, 52578 ^ []))], (52586 ^ _2080023) ^ [] : [v_Q(52574 ^ [], 52578 ^ [])], (52577 ^ _2080023) ^ [] : [-(v_P(52574 ^ [], 52575 ^ []))], !, (52443 ^ _776545) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (24341 ^ _776545) ^ [_1216793, _1216795, _1216797, _1216799] : [class_Divides_Osemiring__div(_1216793), -(_1216795 = c_Groups_Ozero__class_Ozero(_1216793)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216793), _1216797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216793), _1216799), _1216795))), _1216795) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216793), _1216799), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216793), _1216797), _1216795)))], (3848 ^ _776545) ^ [_834340, _834342] : [_834342 = _834340, -(c_List_Odistinct(_834342) = c_List_Odistinct(_834340))], (19241 ^ _776545) ^ [_1123680, _1123682, _1123684] : [hAPP(c_Finite__Set_Ocard(_1123680), _1123682) = hAPP(c_Nat_OSuc, _1123684), 19246 ^ _776545 : [(19249 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1123680), 19244 ^ [_1123680, _1123682, _1123684]), 19245 ^ [_1123680, _1123682, _1123684]))], (19251 ^ _776545) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1123680), 19245 ^ [_1123680, _1123682, _1123684]) = _1123684)], (19253 ^ _776545) ^ [] : [_1123684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(19245 ^ [_1123680, _1123682, _1123684] = c_Orderings_Obot__class_Obot(tc_fun(_1123680, tc_HOL_Obool)))], (19247 ^ _776545) ^ [] : [-(_1123682 = hAPP(hAPP(c_Set_Oinsert(_1123680), 19244 ^ [_1123680, _1123682, _1123684]), 19245 ^ [_1123680, _1123682, _1123684]))]]], (48814 ^ _776545) ^ [_1760438, _1760440] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760438), _1760440))), -(c_Lazy__Sequence_Osmall__lazy_H(_1760438, _1760440) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1760440), c_Lazy__Sequence_Osmall__lazy_H(_1760438, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1760440), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (38476 ^ _776545) ^ [_1514220, _1514222] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1514220, _1514222), 38477 ^ [_1514220, _1514222])), -(c_Wellfounded_OwfP(_1514220, _1514222))], (29005 ^ _776545) ^ [_1296488, _1296490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296488), _1296490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296488)), c_Int_OBit0(_1296490))))], (24012 ^ _776545) ^ [_1211272] : [class_Rings_Osemiring__1(_1211272), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211272), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1211272))], (52381 ^ _776545) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (21361 ^ _776545) ^ [_1163282, _1163284, _1163286] : [class_Rings_Ocomm__semiring__1(_1163282), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163282), _1163284), hAPP(hAPP(c_Power_Opower__class_Opower(_1163282), _1163284), _1163286)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163282), _1163284), hAPP(c_Nat_OSuc, _1163286)))], (50457 ^ _776545) ^ [_1796633, _1796635, _1796637] : [c_Fun_Obij__betw(_1796633, _1796635, _1796637, c_Orderings_Otop__class_Otop(tc_fun(_1796633, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1796635, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1796633, _1796635, _1796637), c_Orderings_Otop__class_Otop(tc_fun(_1796633, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796635, tc_HOL_Obool)))], (38951 ^ _776545) ^ [_1526092, _1526094, _1526096] : [-(hAPP(c_Relation_ODomain(_1526092, _1526094), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1526092, _1526094), tc_HOL_Obool), _1526096)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1526092, _1526094), tc_HOL_Obool), tc_fun(_1526092, tc_HOL_Obool)), _1526096), c_Relation_ODomain(_1526092, _1526094)))], (27625 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (45104 ^ _776545) ^ [_1679799, _1679801, _1679803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1679799), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1679801), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1679801)), _1679803)))), -(hBOOL(hAPP(hAPP(c_member(_1679801), hAPP(c_Random_Opick(_1679801, _1679803), _1679799)), hAPP(c_List_Oset(_1679801), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1679801), _1679801), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1679801)), _1679803)))))], (18554 ^ _776545) ^ [_1110446, _1110448, _1110450] : [hBOOL(hAPP(_1110446, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110448), _1110450))), 18557 ^ _776545 : [(18564 ^ _776545) ^ [_1110631] : [_1110448 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110450), _1110631), -(hBOOL(hAPP(_1110446, _1110631)))], (18558 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110448), _1110450)), -(hBOOL(hAPP(_1110446, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (22653 ^ _776545) ^ [_1186978, _1186980, _1186982, _1186984] : [class_Groups_Omonoid__mult(_1186978), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186978), _1186980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1186982), _1186984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186978), hAPP(hAPP(c_Power_Opower__class_Opower(_1186978), _1186980), _1186982)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186978), _1186980), _1186984)))], (47383 ^ _776545) ^ [_1729289, _1729291, _1729293] : [c_List_OdropWhile(_1729289, _1729291, _1729293) = c_List_Olist_ONil(_1729289), 47386 ^ _776545 : [(47387 ^ _776545) ^ [_1729380] : [hBOOL(hAPP(hAPP(c_member(_1729289), _1729380), hAPP(c_List_Oset(_1729289), _1729293))), -(hBOOL(hAPP(_1729291, _1729380)))]]], (38138 ^ _776545) ^ [_1506925, _1506927] : [c_Wellfounded_Owf(_1506925, _1506927), -(c_Wellfounded_Owf(tc_fun(_1506925, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1506925, _1506927)))], (24812 ^ _776545) ^ [_1225428, _1225430, _1225432, _1225434] : [class_Divides_Osemiring__div(_1225428), -(c_Divides_Odiv__class_Omod(_1225428, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225428), c_Divides_Odiv__class_Omod(_1225428, _1225430, _1225432)), _1225434), _1225432) = c_Divides_Odiv__class_Omod(_1225428, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225428), _1225430), _1225434), _1225432))], (42653 ^ _776545) ^ [_1625730, _1625732, _1625734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1625732))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1625732), _1625730), _1625734)) = 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), _1625732)), _1625734)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1625732), _1625730)))], (18950 ^ _776545) ^ [_1117887, _1117889, _1117891] : [class_Rings_Olinordered__ring__strict(_1117887), 18953 ^ _776545 : [(18962 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117887), _1117889), _1117889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117887), _1117891), _1117891)) = c_Groups_Ozero__class_Ozero(_1117887)), _1117889 = c_Groups_Ozero__class_Ozero(_1117887), _1117891 = c_Groups_Ozero__class_Ozero(_1117887)], (18954 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117887), _1117889), _1117889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117887), _1117891), _1117891)) = c_Groups_Ozero__class_Ozero(_1117887), 18957 ^ _776545 : [(18960 ^ _776545) ^ [] : [-(_1117891 = c_Groups_Ozero__class_Ozero(_1117887))], (18958 ^ _776545) ^ [] : [-(_1117889 = c_Groups_Ozero__class_Ozero(_1117887))]]]]], (10361 ^ _776545) ^ [_954470, _954472, _954474] : [class_Lattices_Oboolean__algebra(_954470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954470), _954472), _954474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954470), hAPP(c_Groups_Ouminus__class_Ouminus(_954470), _954474)), hAPP(c_Groups_Ouminus__class_Ouminus(_954470), _954472))))], (22615 ^ _776545) ^ [_1186282, _1186284, _1186286, _1186288] : [class_Rings_Olinordered__semidom(_1186282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186282), c_Groups_Oone__class_Oone(_1186282)), _1186284)), 22622 ^ _776545 : [(22629 ^ _776545) ^ [] : [_1186286 = _1186288, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186282), _1186284), _1186286) = hAPP(hAPP(c_Power_Opower__class_Opower(_1186282), _1186284), _1186288))], (22623 ^ _776545) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1186282), _1186284), _1186286) = hAPP(hAPP(c_Power_Opower__class_Opower(_1186282), _1186284), _1186288), -(_1186286 = _1186288)]]], (39095 ^ _776545) ^ [_1529749, _1529751, _1529753] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1529749, _1529751), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529749, _1529751), _1529753), hAPP(c_COMBK(tc_fun(_1529751, tc_HOL_Obool), _1529749), c_Orderings_Otop__class_Otop(tc_fun(_1529751, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1529749, _1529751), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529749, tc_HOL_Obool)), _1529753)), hAPP(c_COMBK(tc_fun(_1529751, tc_HOL_Obool), _1529749), c_Orderings_Otop__class_Otop(tc_fun(_1529751, tc_HOL_Obool)))))], (8221 ^ _776545) ^ [_917185, _917187] : [class_Lattices_Obounded__lattice__top(_917185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917185), c_Orderings_Otop__class_Otop(_917185)), _917187) = _917187)], (18192 ^ _776545) ^ [_1103660, _1103662, _1103664] : [class_Groups_Oordered__comm__monoid__add(_1103660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103660), _1103662), c_Groups_Ozero__class_Ozero(_1103660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103660), _1103664), c_Groups_Ozero__class_Ozero(_1103660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103660), _1103662), _1103664)), c_Groups_Ozero__class_Ozero(_1103660))))], (24770 ^ _776545) ^ [_1224561, _1224563, _1224565] : [class_Divides_Osemiring__div(_1224561), -(c_Divides_Odiv__class_Omod(_1224561, c_Divides_Odiv__class_Omod(_1224561, _1224563, _1224565), _1224565) = c_Divides_Odiv__class_Omod(_1224561, _1224563, _1224565))], (16166 ^ _776545) ^ [_1068765, _1068767] : [class_Groups_Ocomm__monoid__add(_1068765), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068765), c_Groups_Ozero__class_Ozero(_1068765)), _1068767) = _1068767)], (28759 ^ _776545) ^ [_1292108, _1292110] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292108), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292110)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292108), 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)))), _1292110)))], (33703 ^ _776545) ^ [_1399469, _1399471, _1399473, _1399475, _1399477] : [class_Groups_Ocomm__monoid__add(_1399469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399471), _1399473)), 33710 ^ _776545 : [(33717 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399471), _1399475), _1399473))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399471, _1399469), hAPP(hAPP(c_COMBC(_1399471, _1399469, _1399469), hAPP(hAPP(c_COMBS(_1399471, _1399469, tc_fun(_1399469, _1399469)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399469, tc_fun(_1399469, _1399469)), _1399471), c_If(_1399469)), hAPP(c_fequal, _1399475))), _1399477)), c_Groups_Ozero__class_Ozero(_1399469))), _1399473) = c_Groups_Ozero__class_Ozero(_1399469))], (33711 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399471), _1399475), _1399473)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399471, _1399469), hAPP(hAPP(c_COMBC(_1399471, _1399469, _1399469), hAPP(hAPP(c_COMBS(_1399471, _1399469, tc_fun(_1399469, _1399469)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399469, tc_fun(_1399469, _1399469)), _1399471), c_If(_1399469)), hAPP(c_fequal, _1399475))), _1399477)), c_Groups_Ozero__class_Ozero(_1399469))), _1399473) = hAPP(_1399477, _1399475))]]], (8805 ^ _776545) ^ [_927839, _927841, _927843, _927845] : [class_Lattices_Odistrib__lattice(_927839), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927839), _927841), _927843)), _927845) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927839), _927841), _927845)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927839), _927843), _927845)))], (45794 ^ _776545) ^ [_1695386, _1695388, _1695390, _1695392] : [_1695386 = _1695388, -(hAPP(c_List_OremoveAll(_1695390, _1695386), hAPP(hAPP(c_List_Olist_OCons(_1695390), _1695388), _1695392)) = hAPP(c_List_OremoveAll(_1695390, _1695386), _1695392))], (41706 ^ _776545) ^ [_1597801, _1597803, _1597805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597801), c_Nitpick_Oplus__frac(_1597801, _1597803, c_Nitpick_Ouminus__frac(_1597801, _1597805)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1597801, _1597803, _1597805))], (5540 ^ _776545) ^ [_861170, _861172, _861174, _861176] : [-(tc_fun(_861176, _861172) = tc_fun(_861174, _861170)), _861176 = _861174, _861172 = _861170], (3006 ^ _776545) ^ [_821173, _821175] : [_821175 = _821173, -(c_Nitpick_Odenom(_821175) = c_Nitpick_Odenom(_821173))], (22595 ^ _776545) ^ [_1185944, _1185946, _1185948] : [class_Rings_Olinordered__semidom(_1185944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185944), c_Groups_Oone__class_Oone(_1185944)), _1185946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185944), c_Groups_Oone__class_Oone(_1185944)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185944), _1185946), _1185948))))], (2930 ^ _776545) ^ [_820029, _820031, _820033, _820035, _820037, _820039] : [-(c_Nitpick_Oof__frac(_820039, _820035, _820031) = c_Nitpick_Oof__frac(_820037, _820033, _820029)), _820039 = _820037, _820035 = _820033, _820031 = _820029], (43751 ^ _776545) ^ [_1649616, _1649618, _1649620, _1649622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649616), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649618)), _1649620))), -(hAPP(hAPP(c_List_Onth(_1649618), hAPP(hAPP(c_List_Oappend(_1649618), _1649620), _1649622)), _1649616) = hAPP(hAPP(c_List_Onth(_1649618), _1649620), _1649616))], (14987 ^ _776545) ^ [_1046979, _1046981, _1046983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046979), _1046981)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046983), _1046981)), _1046979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046983), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046981), _1046979)))], (14734 ^ _776545) ^ [_1042103, _1042105, _1042107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042103), _1042105)), _1042107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042105), _1042107)))], (36278 ^ _776545) ^ [_1461277, _1461279, _1461281, _1461283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1461277), _1461279)), -(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), _1461277), _1461281)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1461279), _1461283))), c_FunDef_Opair__less)))], (49634 ^ _776545) ^ [_1779607, _1779609] : [c_Relation_Oantisym(_1779607, _1779609), -(c_Relation_Oantisym(_1779607, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779607, _1779607), tc_HOL_Obool)), _1779609), c_Relation_OId(_1779607))))], (44729 ^ _776545) ^ [_1670782] : [-(hAPP(c_List_Omap(_1670782, _1670782), c_COMBI(_1670782)) = c_Fun_Oid(tc_List_Olist(_1670782)))], (34327 ^ _776545) ^ [_1415366, _1415368] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415366)), hAPP(c_Nat_OSuc, _1415368)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415366))), 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)), _1415368)))))], (34347 ^ _776545) ^ [_1415902, _1415904] : [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), _1415902))), 34350 ^ _776545 : [(34357 ^ _776545) ^ [] : [-(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), _1415904)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415904), 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), _1415902)))))], (34351 ^ _776545) ^ [] : [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), _1415904)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415904), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902)) = 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), _1415904)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1415902))))]]], (29139 ^ _776545) ^ [_1298826, _1298828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298826)), c_Int_OBit1(_1298828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298826), _1298828)))], (43510 ^ _776545) ^ [_1644250, _1644252, _1644254, _1644256, _1644258] : [hAPP(hAPP(c_List_Oappend(_1644250), _1644252), _1644254) = hAPP(hAPP(c_List_Oappend(_1644250), _1644256), _1644258), 43516 ^ _776545 : [(43519 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1644250), 43513 ^ [_1644250, _1644252, _1644254, _1644256, _1644258]), _1644254) = _1644258)], (43517 ^ _776545) ^ [] : [-(_1644252 = hAPP(hAPP(c_List_Oappend(_1644250), _1644256), 43513 ^ [_1644250, _1644252, _1644254, _1644256, _1644258]))]], 43520 ^ _776545 : [(43523 ^ _776545) ^ [] : [-(_1644254 = hAPP(hAPP(c_List_Oappend(_1644250), 43513 ^ [_1644250, _1644252, _1644254, _1644256, _1644258]), _1644258))], (43521 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1644250), _1644252), 43513 ^ [_1644250, _1644252, _1644254, _1644256, _1644258]) = _1644256)]]], (30008 ^ _776545) ^ [_1314736, _1314738] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1314736), _1314738) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1314736), _1314738))], (8163 ^ _776545) ^ [_915852, _915854, _915856] : [class_Orderings_Olinorder(_915852), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_915852), _915854), _915856)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915852, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_915852), _915854)), c_SetInterval_Oord__class_OgreaterThanAtMost(_915852, _915854, _915856)) = hAPP(c_SetInterval_Oord__class_OatMost(_915852), _915856))], (22169 ^ _776545) ^ [_1178606, _1178608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178606)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178606), _1178608)))], (47257 ^ _776545) ^ [_1726655, _1726657, _1726659, _1726661, _1726663] : [-(hAPP(hAPP(c_List_Ozip(_1726655, _1726657), _1726659), c_List_OtakeWhile(_1726657, _1726661, _1726663)) = c_List_OtakeWhile(tc_prod(_1726655, _1726657), hAPP(c_Fun_Ocomp(_1726657, tc_HOL_Obool, tc_prod(_1726655, _1726657), _1726661), c_Product__Type_Osnd(_1726655, _1726657)), hAPP(hAPP(c_List_Ozip(_1726655, _1726657), _1726659), _1726663)))], (7646 ^ _776545) ^ [_903496, _903498, _903500, _903502] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903496, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903496, tc_HOL_Obool)), _903498), _903500)), _903502) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903496, tc_HOL_Obool)), _903498), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903496, tc_HOL_Obool)), _903500), _903502)))], (11694 ^ _776545) ^ [_981126, _981128, _981130, _981132, _981134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981126), _981128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981130, tc_HOL_Obool)), _981132), hAPP(c_Set_Oimage(_981126, _981130, _981134), _981128))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981130), _981132)))], (33162 ^ _776545) ^ [_1384033, _1384035, _1384037] : [hBOOL(hAPP(hAPP(c_member(_1384033), _1384035), hAPP(c_Set_OCollect(_1384033), _1384037))), -(hBOOL(hAPP(_1384037, _1384035)))], (22165 ^ _776545) ^ [_1178510, _1178512] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178510)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178512)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178510), _1178512)))], (41365 ^ _776545) ^ [_1588710, _1588712, _1588714, _1588716, _1588718] : [c_Relation_Osingle__valued(_1588710, _1588710, _1588712), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588710, _1588710)), hAPP(hAPP(c_Product__Type_OPair(_1588710, _1588710), _1588714), _1588716)), c_Transitive__Closure_Ortrancl(_1588710, _1588712))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588710, _1588710)), hAPP(hAPP(c_Product__Type_OPair(_1588710, _1588710), _1588714), _1588718)), c_Transitive__Closure_Ortrancl(_1588710, _1588712))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588710, _1588710)), hAPP(hAPP(c_Product__Type_OPair(_1588710, _1588710), _1588716), _1588718)), c_Transitive__Closure_Ortrancl(_1588710, _1588712)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588710, _1588710)), hAPP(hAPP(c_Product__Type_OPair(_1588710, _1588710), _1588718), _1588716)), c_Transitive__Closure_Ortrancl(_1588710, _1588712))))], (26771 ^ _776545) ^ [_1259380] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1259380) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1259380))], (32560 ^ _776545) ^ [_1365444, _1365446, _1365448, _1365450, _1365452] : [-(_1365444 = c_Orderings_Obot__class_Obot(tc_fun(_1365446, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365446, tc_fun(_1365448, tc_HOL_Obool)), _1365444), hAPP(hAPP(c_COMBB(tc_fun(_1365448, tc_HOL_Obool), tc_fun(_1365448, tc_HOL_Obool), _1365446), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365448, tc_HOL_Obool)), _1365450)), _1365452)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365448, tc_HOL_Obool)), _1365450), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365446, tc_fun(_1365448, tc_HOL_Obool)), _1365444), _1365452)))], (26457 ^ _776545) ^ [_1254006, _1254008, _1254010] : [-(hBOOL(hAPP(_1254006, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254008, _1254010)))), 26460 ^ _776545 : [(26463 ^ _776545) ^ [] : [hBOOL(hAPP(_1254006, _1254008))], (26461 ^ _776545) ^ [] : [-(_1254010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 26464 ^ _776545 : [(26469 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26467 ^ [_1254006, _1254008, _1254010]), _1254010)))], (26471 ^ _776545) ^ [] : [-(_1254008 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254010), 26466 ^ [_1254006, _1254008, _1254010])), 26467 ^ [_1254006, _1254008, _1254010]))], (26473 ^ _776545) ^ [] : [hBOOL(hAPP(_1254006, 26467 ^ [_1254006, _1254008, _1254010]))], (26465 ^ _776545) ^ [] : [_1254010 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23858 ^ _776545) ^ [_1208682, _1208684] : [class_Rings_Olinordered__semidom(_1208682), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208682), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208682), _1208684)), c_Groups_Ozero__class_Ozero(_1208682)))], (15886 ^ _776545) ^ [_1064105, _1064107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064107)), -(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), _1064107), _1064105))))], (26230 ^ _776545) ^ [_1250308, _1250310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250308)), _1250310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250308), hAPP(c_Int_Onat, _1250310))))], (1544 ^ _776545) ^ [_798709, _798711] : [-(class_Groups_Oordered__ab__semigroup__add(_798709)), _798711 = _798709, class_Groups_Oordered__ab__semigroup__add(_798711)], (8297 ^ _776545) ^ [_918581, _918583, _918585, _918587] : [class_Lattices_Olattice(_918581), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918581), _918583), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918581), _918585), _918587)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918581), _918585), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918581), _918583), _918587)))], (22659 ^ _776545) ^ [_1187133, _1187135, _1187137, _1187139] : [class_Fields_Ofield(_1187133), -(_1187135 = c_Groups_Ozero__class_Ozero(_1187133)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187133), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187133), _1187137), _1187135)), _1187139) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187133), hAPP(hAPP(c_Power_Opower__class_Opower(_1187133), _1187137), _1187139)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187133), _1187135), _1187139)))], (10980 ^ _776545) ^ [_966343, _966345, _966347] : [class_Rings_Olinordered__idom(_966343), -(_966345 = _966347), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966343), _966345), _966347))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966343), _966347), _966345)))], (26917 ^ _776545) ^ [_1261385, _1261387, _1261389] : [class_Rings_Olinordered__idom(_1261385), 26920 ^ _776545 : [(26927 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261387), _1261389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261385), hAPP(c_Int_Oring__1__class_Oof__int(_1261385), _1261387)), hAPP(c_Int_Oring__1__class_Oof__int(_1261385), _1261389))))], (26921 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261385), hAPP(c_Int_Oring__1__class_Oof__int(_1261385), _1261387)), hAPP(c_Int_Oring__1__class_Oof__int(_1261385), _1261389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261387), _1261389)))]]], (29163 ^ _776545) ^ [_1299272, _1299274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299272)), c_Int_OBit0(_1299274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299272), _1299274)))], (27631 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (43563 ^ _776545) ^ [_1645601, _1645603] : [-(hAPP(hAPP(c_List_Oappend(_1645601), c_List_Olist_ONil(_1645601)), _1645603) = _1645603)], (32468 ^ _776545) ^ [_1361220, _1361222, _1361224, _1361226, _1361228] : [-(_1361220 = c_Orderings_Obot__class_Obot(tc_fun(_1361222, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361222, tc_fun(_1361224, tc_HOL_Obool)), _1361220), hAPP(hAPP(c_COMBB(tc_fun(_1361224, tc_HOL_Obool), tc_fun(_1361224, tc_HOL_Obool), _1361222), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361224, tc_HOL_Obool)), _1361226)), _1361228)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361224, tc_HOL_Obool)), _1361226), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361222, tc_fun(_1361224, tc_HOL_Obool)), _1361220), _1361228)))], (2376 ^ _776545) ^ [_811258, _811260, _811262, _811264, _811266, _811268, _811270, _811272, _811274, _811276] : [-(c_Nitpick_Opair__box_Opair__box__rec(_811276, _811272, _811268, _811264, _811260) = c_Nitpick_Opair__box_Opair__box__rec(_811274, _811270, _811266, _811262, _811258)), _811276 = _811274, _811272 = _811270, _811268 = _811266, _811264 = _811262, _811260 = _811258], (6248 ^ _776545) ^ [_876972] : [class_Complete__Lattice_Ocomplete__lattice(_876972), -(c_Complete__Lattice_OSup__class_OSup(_876972, c_Orderings_Obot__class_Obot(tc_fun(_876972, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_876972))], (19324 ^ _776545) ^ [_1125447] : [class_Rings_Oring__1(_1125447), -(hBOOL(hAPP(hAPP(c_member(_1125447), c_Groups_Ozero__class_Ozero(_1125447)), c_Int_Oring__1__class_OInts(_1125447))))], (10949 ^ _776545) ^ [_965695, _965697, _965699] : [-(hAPP(c_Set_OPow(_965695), hAPP(hAPP(c_Set_Oinsert(_965695), _965697), _965699)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_965695, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_965695), _965699)), hAPP(c_Set_Oimage(tc_fun(_965695, tc_HOL_Obool), tc_fun(_965695, tc_HOL_Obool), hAPP(c_Set_Oinsert(_965695), _965697)), hAPP(c_Set_OPow(_965695), _965699))))], (43866 ^ _776545) ^ [_1652960, _1652962, _1652964] : [-(hAPP(hAPP(c_List_Oappend(_1652960), hAPP(hAPP(c_List_Otake(_1652960), _1652962), _1652964)), hAPP(hAPP(c_List_Odrop(_1652960), _1652962), _1652964)) = _1652964)], (29615 ^ _776545) ^ [_1307374, _1307376] : [-(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), _1307374)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1307376))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1307374))) = 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), _1307376)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307374)))], (25784 ^ _776545) ^ [_1243124, _1243126] : [-(_1243124 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25787 ^ _776545 : [(25794 ^ _776545) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243126, _1243124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243124)) = 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), _1243126), _1243124))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25788 ^ _776545) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243126, _1243124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243124)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243126), _1243124)))]]], (19585 ^ _776545) ^ [_1130462, _1130464] : [class_Rings_Olinordered__idom(_1130462), 19588 ^ _776545 : [(19595 ^ _776545) ^ [] : [_1130464 = c_Groups_Ozero__class_Ozero(_1130462), -(c_Groups_Osgn__class_Osgn(_1130462, _1130464) = c_Groups_Ozero__class_Ozero(_1130462))], (19589 ^ _776545) ^ [] : [c_Groups_Osgn__class_Osgn(_1130462, _1130464) = c_Groups_Ozero__class_Ozero(_1130462), -(_1130464 = c_Groups_Ozero__class_Ozero(_1130462))]]], (26985 ^ _776545) ^ [_1262633, _1262635] : [class_Rings_Oring__1(_1262633), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262633), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262635)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1262633), hAPP(c_Int_Oring__1__class_Oof__int(_1262633), _1262635)))], (29812 ^ _776545) ^ [_1311064, _1311066, _1311068] : [29814 ^ _776545 : [(29819 ^ _776545) ^ [] : [hBOOL(hAPP(_1311066, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 29813 ^ [_1311064, _1311066, _1311068]), _1311064)))], (29817 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1311066, 29813 ^ [_1311064, _1311066, _1311068])))], (29815 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29813 ^ [_1311064, _1311066, _1311068]), _1311064)))]], hBOOL(hAPP(_1311066, _1311068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1311068), _1311064)), -(hBOOL(hAPP(_1311066, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32864 ^ _776545) ^ [_1374817, _1374819, _1374821, _1374823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool)), _1374821), _1374823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374817, tc_fun(_1374819, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1374817, tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_fun(_1374819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374819, tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_fun(_1374819, tc_HOL_Obool)), _1374817), c_COMBC(_1374819, tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374819, tc_prod(_1374817, _1374819)), tc_fun(_1374819, tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), _1374817), hAPP(c_COMBB(tc_prod(_1374817, _1374819), tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool), _1374819), c_member(tc_prod(_1374817, _1374819)))), c_Product__Type_OPair(_1374817, _1374819)))), _1374821)), hAPP(hAPP(c_COMBC(_1374817, tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_fun(_1374819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374819, tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_fun(_1374819, tc_HOL_Obool)), _1374817), c_COMBC(_1374819, tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374819, tc_prod(_1374817, _1374819)), tc_fun(_1374819, tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool)), _1374817), hAPP(c_COMBB(tc_prod(_1374817, _1374819), tc_fun(tc_fun(tc_prod(_1374817, _1374819), tc_HOL_Obool), tc_HOL_Obool), _1374819), c_member(tc_prod(_1374817, _1374819)))), c_Product__Type_OPair(_1374817, _1374819)))), _1374823))))], (33064 ^ _776545) ^ [_1380617, _1380619, _1380621, _1380623, _1380625, _1380627] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380617, tc_fun(_1380619, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380621, _1380617, _1380623), _1380625)), _1380627) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380621, tc_fun(_1380619, tc_HOL_Obool)), _1380625), hAPP(hAPP(c_COMBB(_1380617, tc_fun(_1380619, tc_HOL_Obool), _1380621), _1380627), _1380623)))], (2196 ^ _776545) ^ [_808442, _808444, _808446, _808448] : [-(c_Random_Olog(_808448, _808444) = c_Random_Olog(_808446, _808442)), _808448 = _808446, _808444 = _808442], (28451 ^ _776545) ^ [_1287202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1287202)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1287202), c_Int_OMin)))], (52267 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (14486 ^ _776545) ^ [_1038071, _1038073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038071), _1038073)), _1038071 = _1038073], (16346 ^ _776545) ^ [_1071480] : [class_Rings_Ozero__neq__one(_1071480), c_Groups_Oone__class_Oone(_1071480) = c_Groups_Ozero__class_Ozero(_1071480)], (32209 ^ _776545) ^ [_1355436, _1355438, _1355440] : [class_Orderings_Olinorder(_1355436), hAPP(_1355438, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355436), 32214 ^ [_1355436, _1355438, _1355440]), 32215 ^ [_1355436, _1355438, _1355440])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355436), hAPP(_1355438, 32214 ^ [_1355436, _1355438, _1355440])), hAPP(_1355438, 32215 ^ [_1355436, _1355438, _1355440])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355436), _1355440)), -(_1355440 = c_Orderings_Obot__class_Obot(tc_fun(_1355436, tc_HOL_Obool))), -(hAPP(_1355438, c_Big__Operators_Olattice_OSup__fin(_1355436, c_Orderings_Oord__class_Omax(_1355436), _1355440)) = c_Big__Operators_Olattice_OSup__fin(_1355436, c_Orderings_Oord__class_Omax(_1355436), hAPP(c_Set_Oimage(_1355436, _1355436, _1355438), _1355440)))], (34860 ^ _776545) ^ [_1427088, _1427090, _1427092, _1427094, _1427096, _1427098] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427088, _1427090, _1427092), _1427094), hAPP(hAPP(c_Product__Type_OPair(_1427088, _1427090), _1427096), _1427098)) = hAPP(hAPP(_1427094, _1427096), _1427098))], (10911 ^ _776545) ^ [_964886, _964888, _964890, _964892] : [c_Finite__Set_Ofolding__one(_964886, _964888, _964890), -(hAPP(_964890, hAPP(hAPP(c_Set_Oinsert(_964886), _964892), c_Orderings_Obot__class_Obot(tc_fun(_964886, tc_HOL_Obool)))) = _964892)], (12626 ^ _776545) ^ [_998988, _998990, _998992, _998994, _998996] : [c_Finite__Set_Ofolding__one__idem(_998988, _998990, _998992), hAPP(_998994, hAPP(hAPP(_998990, 12631 ^ [_998988, _998990, _998992, _998994, _998996]), 12632 ^ [_998988, _998990, _998992, _998994, _998996])) = hAPP(hAPP(_998990, hAPP(_998994, 12631 ^ [_998988, _998990, _998992, _998994, _998996])), hAPP(_998994, 12632 ^ [_998988, _998990, _998992, _998994, _998996])), hBOOL(hAPP(c_Finite__Set_Ofinite(_998988), _998996)), -(_998996 = c_Orderings_Obot__class_Obot(tc_fun(_998988, tc_HOL_Obool))), -(hAPP(_998994, hAPP(_998992, _998996)) = hAPP(_998992, hAPP(c_Set_Oimage(_998988, _998988, _998994), _998996)))], (38108 ^ _776545) ^ [_1506436, _1506438, _1506440, _1506442] : [c_Wellfounded_Owf(_1506436, _1506438), -(c_Wellfounded_Owf(_1506440, hAPP(hAPP(c_Relation_Oinv__image(_1506436, _1506440), _1506438), _1506442)))], (48256 ^ _776545) ^ [_1748500, _1748502, _1748504] : [c_FunDef_Ois__measure(_1748500, _1748502), -(c_FunDef_Ois__measure(tc_prod(_1748504, _1748500), hAPP(hAPP(c_COMBB(_1748500, tc_Nat_Onat, tc_prod(_1748504, _1748500)), _1748502), c_Product__Type_Osnd(_1748504, _1748500))))], (31359 ^ _776545) ^ [_1339446, _1339448, _1339450] : [class_Orderings_Olinorder(_1339446), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339446), _1339448), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339446), _1339448), _1339450)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339446), _1339448), _1339450))], (30468 ^ _776545) ^ [_1323170, _1323172, _1323174] : [class_Orderings_Olinorder(_1323170), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323170), _1323172)), -(_1323172 = c_Orderings_Obot__class_Obot(tc_fun(_1323170, tc_HOL_Obool))), 30479 ^ _776545 : [(30489 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323170), hAPP(c_Finite__Set_Ofold1(_1323170, c_Orderings_Oord__class_Omin(_1323170)), _1323172)), _1323174))), 30490 ^ _776545 : [(30491 ^ _776545) ^ [_1323559] : [hBOOL(hAPP(hAPP(c_member(_1323170), _1323559), _1323172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323170), _1323559), _1323174))]]], (30480 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323170), hAPP(c_Finite__Set_Ofold1(_1323170, c_Orderings_Oord__class_Omin(_1323170)), _1323172)), _1323174)), 30484 ^ _776545 : [(30487 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323170), 30483 ^ [_1323170, _1323172, _1323174]), _1323174)))], (30485 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323170), 30483 ^ [_1323170, _1323172, _1323174]), _1323172)))]]]]], (50145 ^ _776545) ^ [_1789761, _1789763, _1789765, _1789767, _1789769, _1789771, _1789773] : [c_Fun_Oinj__on(_1789761, _1789763, _1789765, hAPP(c_Set_Oimage(_1789767, _1789761, _1789769), _1789771)), c_Fun_Oinj__on(_1789767, _1789761, _1789769, _1789771), hBOOL(hAPP(hAPP(c_member(_1789763), _1789773), hAPP(c_Set_Oimage(_1789761, _1789763, _1789765), hAPP(c_Set_Oimage(_1789767, _1789761, _1789769), _1789771)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1789767, _1789763, _1789771, hAPP(c_Fun_Ocomp(_1789761, _1789763, _1789767, _1789765), _1789769)), _1789773) = hAPP(hAPP(c_Fun_Ocomp(_1789761, _1789767, _1789763, c_Hilbert__Choice_Oinv__into(_1789767, _1789761, _1789771, _1789769)), c_Hilbert__Choice_Oinv__into(_1789761, _1789763, hAPP(c_Set_Oimage(_1789767, _1789761, _1789769), _1789771), _1789765)), _1789773))], (31495 ^ _776545) ^ [_1342049, _1342051, _1342053, _1342055] : [class_Orderings_Olinorder(_1342049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342049), _1342051), _1342053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342049), _1342051), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342049), _1342053), _1342055))))], (39065 ^ _776545) ^ [_1528950, _1528952, _1528954] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528950, _1528952), c_Orderings_Obot__class_Obot(tc_fun(_1528950, tc_HOL_Obool))), _1528954) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528950, _1528952), tc_HOL_Obool)))], (31383 ^ _776545) ^ [_1339982, _1339984, _1339986, _1339988] : [class_Orderings_Olinorder(_1339982), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339982), _1339984), _1339986)), _1339988) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339982), _1339984), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339982), _1339986), _1339988)))], (29285 ^ _776545) ^ [_1301336] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301336), 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, _1301336)))], (16430 ^ _776545) ^ [_1072709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072709), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29879 ^ _776545) ^ [_1312382, _1312384] : [29880 ^ _776545 : [(29883 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1312384), _1312382))], (29881 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1312382), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1312382, _1312384) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40925 ^ _776545) ^ [_1578043, _1578045, _1578047, _1578049, _1578051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578043, _1578043)), hAPP(hAPP(c_Product__Type_OPair(_1578043, _1578043), _1578045), _1578047)), c_Transitive__Closure_Ortrancl(_1578043, _1578049))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578043, _1578043)), hAPP(hAPP(c_Product__Type_OPair(_1578043, _1578043), _1578047), _1578051)), c_Transitive__Closure_Otrancl(_1578043, _1578049))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578043, _1578043)), hAPP(hAPP(c_Product__Type_OPair(_1578043, _1578043), _1578045), _1578051)), c_Transitive__Closure_Otrancl(_1578043, _1578049))))], (23489 ^ _776545) ^ [_1202349, _1202351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202349), _1202351)), -(c_Nat__Transfer_Otsub(_1202351, _1202349) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202351), _1202349))], (30760 ^ _776545) ^ [_1328301, _1328303, _1328305] : [class_Orderings_Olinorder(_1328301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328301), _1328303)), -(c_Big__Operators_Olattice_OInf__fin(_1328301, c_Orderings_Oord__class_Omin(_1328301), hAPP(hAPP(c_Set_Oinsert(_1328301), _1328305), _1328303)) = hAPP(hAPP(c_Finite__Set_Ofold(_1328301, _1328301, c_Orderings_Oord__class_Omin(_1328301)), _1328305), _1328303))], (52211 ^ _776545) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (48327 ^ _776545) ^ [_1749845, _1749847, _1749849] : [48329 ^ _776545 : [(48332 ^ _776545) ^ [] : [hBOOL(hAPP(_1749847, 48328 ^ [_1749845, _1749847, _1749849]))], (48330 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749845), 48328 ^ [_1749845, _1749847, _1749849]), hAPP(c_List_Oset(_1749845), _1749849))))]], -(c_List_Olist__all(_1749845, _1749847, _1749849))], (44711 ^ _776545) ^ [_1670353, _1670355, _1670357, _1670359] : [-(_1670353 = c_List_Olist_ONil(_1670355)), -(c_List_Olast(_1670357, hAPP(hAPP(c_List_Omap(_1670355, _1670357), _1670359), _1670353)) = hAPP(_1670359, c_List_Olast(_1670355, _1670353)))], (35493 ^ _776545) ^ [_1438790, _1438792, _1438794, _1438796] : [-(hAPP(c_Product__Type_Osnd(_1438790, _1438792), hAPP(hAPP(c_Product__Type_OPair(_1438790, _1438792), _1438794), _1438796)) = _1438796)], (41457 ^ _776545) ^ [_1590941, _1590943, _1590945, _1590947, _1590949, _1590951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590941, _1590941)), hAPP(hAPP(c_Product__Type_OPair(_1590941, _1590941), _1590943), _1590945)), _1590947)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590941, _1590941)), hAPP(hAPP(c_Product__Type_OPair(_1590941, _1590941), _1590945), _1590949)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590941, _1590941), tc_HOL_Obool), _1590951), _1590947))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590941, _1590941)), hAPP(hAPP(c_Product__Type_OPair(_1590941, _1590941), _1590943), _1590949)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590941, _1590941), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590951)), _1590947))))], (28117 ^ _776545) ^ [_1281519] : [class_Rings_Osemiring__1(_1281519), c_Int_Oiszero(_1281519, c_Groups_Oone__class_Oone(_1281519))], (47110 ^ _776545) ^ [_1723562, _1723564] : [-(_1723562 = c_List_Olist_ONil(_1723564)), -(c_List_Olast(_1723564, hAPP(c_List_Orev(_1723564), _1723562)) = hAPP(c_List_Ohd(_1723564), _1723562))], (51229 ^ _776545) ^ [_1813865, _1813867, _1813869, _1813871] : [class_Rings_Odvd(_1813865), _1813867 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813865), _1813869), _1813871), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813865), _1813869), _1813867)))], (15660 ^ _776545) ^ [_1060583, _1060585] : [class_Groups_Ozero(_1060583), 15663 ^ _776545 : [(15670 ^ _776545) ^ [] : [_1060585 = c_Groups_Ozero__class_Ozero(_1060583), -(c_Groups_Ozero__class_Ozero(_1060583) = _1060585)], (15664 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1060583) = _1060585, -(_1060585 = c_Groups_Ozero__class_Ozero(_1060583))]]], (34055 ^ _776545) ^ [_1408709, _1408711] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408709)), 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)), _1408709))), 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, _1408711))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35326 ^ _776545) ^ [_1435489, _1435491, _1435493] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435489), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435491)), _1435493)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435489, _1435491), hAPP(c_Divides_OnegateSnd, _1435493))))], (19428 ^ _776545) ^ [_1127292, _1127294, _1127296, _1127298] : [19429 ^ _776545 : [(19432 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1127296), _1127298)))], (19430 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1127292), _1127294)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1127292, _1127296)), c_Sum__Type_OPlus(_1127292, _1127296, _1127294, _1127298)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28835 ^ _776545) ^ [_1293493, _1293495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293493), _1293495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293493)), c_Int_OBit0(_1293495))))], (43675 ^ _776545) ^ [_1647635, _1647637, _1647639, _1647641, _1647643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647635), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647637)), _1647639))), -(hAPP(hAPP(c_List_Olist__update(_1647637, hAPP(hAPP(c_List_Oappend(_1647637), _1647639), _1647641)), _1647635), _1647643) = hAPP(hAPP(c_List_Oappend(_1647637), hAPP(hAPP(c_List_Olist__update(_1647637, _1647639), _1647635), _1647643)), _1647641))], (16596 ^ _776545) ^ [_1075069, _1075071] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1075069, _1075071)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1075069), hAPP(c_Nat_OSuc, _1075071)))], (9556 ^ _776545) ^ [_940472, _940474, _940476] : [class_Orderings_Oorder(_940472), -(_940474 = _940476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940472), _940476), _940474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940472), _940476), _940474)))], (47847 ^ _776545) ^ [_1739761, _1739763, _1739765, _1739767, _1739769] : [class_Orderings_Olinorder(_1739761), 47853 ^ _776545 : [(47856 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1739761), hAPP(_1739767, _1739769)), hAPP(_1739767, 47852 ^ [_1739761, _1739763, _1739765, _1739767, _1739769])))], (47854 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739763), 47852 ^ [_1739761, _1739763, _1739765, _1739767, _1739769]), hAPP(c_List_Oset(_1739763), _1739765))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739763, _1739761, _1739767), _1739769), _1739765) = hAPP(hAPP(c_List_Olist_OCons(_1739763), _1739769), _1739765))], (32839 ^ _776545) ^ [_1373674, _1373676, _1373678, _1373680, _1373682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373674, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373676, tc_fun(_1373674, tc_HOL_Obool)), _1373678), _1373680)), _1373682)), 32842 ^ _776545 : [(32843 ^ _776545) ^ [_1373807] : [hBOOL(hAPP(hAPP(c_member(_1373676), _1373807), _1373678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373674, tc_HOL_Obool)), hAPP(_1373680, _1373807)), _1373682)))]]], (28763 ^ _776545) ^ [_1292215, _1292217] : [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), _1292215))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1292217)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1292215))) = 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), _1292217), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292215)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30824 ^ _776545) ^ [_1329363, _1329365, _1329367] : [class_Orderings_Olinorder(_1329363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329363), _1329365)), -(c_Big__Operators_Olinorder__class_OMin(_1329363, hAPP(hAPP(c_Set_Oinsert(_1329363), _1329367), _1329365)) = hAPP(hAPP(c_Finite__Set_Ofold(_1329363, _1329363, c_Orderings_Oord__class_Omin(_1329363)), _1329367), _1329365))], (42593 ^ _776545) ^ [_1624588] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42596 ^ _776545 : [(42597 ^ _776545) ^ [_1624663] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1624663), hAPP(c_List_Oset(tc_Nat_Onat), _1624588))), -(_1624663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44705 ^ _776545) ^ [_1670226, _1670228, _1670230] : [c_Fun_Oinj__on(_1670226, _1670228, _1670230, c_Orderings_Otop__class_Otop(tc_fun(_1670226, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1670226), tc_List_Olist(_1670228), hAPP(c_List_Omap(_1670226, _1670228), _1670230), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670226), tc_HOL_Obool))))], (26354 ^ _776545) ^ [_1252297, _1252299] : [_1252297 = hAPP(c_Int_Onat, _1252299), 26357 ^ _776545 : [(26364 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252299))), -(_1252297 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26358 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252299)), -(_1252299 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252297))]]], (47026 ^ _776545) ^ [_1721727, _1721729, _1721731, _1721733] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721727)), _1721729) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721731)), _1721733), -(hAPP(hAPP(c_List_Ozip(_1721727, _1721731), hAPP(c_List_Orev(_1721727), _1721729)), hAPP(c_List_Orev(_1721731), _1721733)) = hAPP(c_List_Orev(tc_prod(_1721727, _1721731)), hAPP(hAPP(c_List_Ozip(_1721727, _1721731), _1721729), _1721733)))], (51137 ^ _776545) ^ [_1812111, _1812113, _1812115] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812111), _1812113)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812111), _1812115))), -(_1812111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812113), _1812115)))], (48454 ^ _776545) ^ [_1752650, _1752652, _1752654, _1752656, _1752658, _1752660, _1752662] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1752650, _1752652, _1752654, _1752656), _1752658), _1752660), _1752662) = c_New__DSequence_Opos__bind(_1752650, _1752652, hAPP(hAPP(hAPP(_1752654, _1752658), _1752660), _1752662), hAPP(hAPP(c_COMBC(_1752650, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752652))), hAPP(hAPP(c_COMBC(_1752650, 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(_1752652)))), hAPP(hAPP(c_COMBC(_1752650, 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(_1752652))))), _1752656), _1752658)), _1752660)), _1752662)))], (11505 ^ _776545) ^ [_977587, _977589, _977591, _977593] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977587), _977589)), 11508 ^ _776545 : [(11509 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977591), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_977587, tc_fun(_977591, tc_HOL_Obool)), _977589), _977593))), 11512 ^ _776545 : [(11513 ^ _776545) ^ [_977771] : [hBOOL(hAPP(hAPP(c_member(_977587), _977771), _977589)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977591), hAPP(_977593, _977771))))]]], (11519 ^ _776545) ^ [] : [11521 ^ _776545 : [(11524 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977591), hAPP(_977593, 11520 ^ [_977587, _977589, _977591, _977593])))], (11522 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977587), 11520 ^ [_977587, _977589, _977591, _977593]), _977589)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977591), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_977587, tc_fun(_977591, tc_HOL_Obool)), _977589), _977593))))]]], (27377 ^ _776545) ^ [_1268991, _1268993] : [class_Groups_Oordered__ab__group__add__abs(_1268991), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1268991), c_Groups_Ozero__class_Ozero(_1268991)), hAPP(c_Groups_Oabs__class_Oabs(_1268991), _1268993))))], (47261 ^ _776545) ^ [_1726794, _1726796] : [-(c_List_OtakeWhile(_1726794, _1726796, c_List_Olist_ONil(_1726794)) = c_List_Olist_ONil(_1726794))], (43561 ^ _776545) ^ [_1645540, _1645542, _1645544] : [-(hAPP(c_List_Oset(_1645540), hAPP(hAPP(c_List_Oappend(_1645540), _1645542), _1645544)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1645540, tc_HOL_Obool)), hAPP(c_List_Oset(_1645540), _1645542)), hAPP(c_List_Oset(_1645540), _1645544)))], (43234 ^ _776545) ^ [_1637908, _1637910, _1637912] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637908))), -(c_List_Osublist(_1637910, hAPP(hAPP(c_List_Olist_OCons(_1637910), _1637912), c_List_Olist_ONil(_1637910)), _1637908) = c_List_Olist_ONil(_1637910))], (11860 ^ _776545) ^ [_984669, _984671, _984673, _984675, _984677, _984679] : [hBOOL(hAPP(hAPP(c_member(_984669), _984671), _984673)), -(hAPP(c_Set_Oimage(_984669, _984675, c_Fun_Ofun__upd(_984669, _984675, _984677, _984671, _984679)), _984673) = hAPP(hAPP(c_Set_Oinsert(_984675), _984679), hAPP(c_Set_Oimage(_984669, _984675, _984677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984669, tc_HOL_Obool)), _984673), hAPP(hAPP(c_Set_Oinsert(_984669), _984671), c_Orderings_Obot__class_Obot(tc_fun(_984669, tc_HOL_Obool)))))))], (1844 ^ _776545) ^ [_802459, _802461] : [-(class_Groups_Ominus(_802459)), _802461 = _802459, class_Groups_Ominus(_802461)], (36422 ^ _776545) ^ [_1464462, _1464464, _1464466, _1464468] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464462), _1464468) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464466), _1464464), -(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), _1464462), _1464464)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464466), _1464468))), c_Int_Ointrel)))], (38894 ^ _776545) ^ [_1524871, _1524873, _1524875, _1524877] : [-(hAPP(c_Relation_ODomain(_1524871, _1524873), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524871, _1524873), tc_HOL_Obool)), _1524875), _1524877)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524871, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524871, _1524873), _1524875)), hAPP(c_Relation_ODomain(_1524871, _1524873), _1524877)))], (16664 ^ _776545) ^ [_1076292, _1076294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076292), _1076294)), -(_1076294 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076292), 16667 ^ [_1076292, _1076294])))], (14610 ^ _776545) ^ [_1039990, _1039992, _1039994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039992), _1039994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039990), _1039992)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039990), _1039994))))], (38945 ^ _776545) ^ [_1525875, _1525877, _1525879, _1525881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525875, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525875, _1525877), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1525875, _1525877), tc_HOL_Obool)), _1525879), _1525881))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525875, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525875, _1525877), _1525879)), hAPP(c_Relation_ODomain(_1525875, _1525877), _1525881)))))], (41168 ^ _776545) ^ [_1583850, _1583852, _1583854, _1583856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583850, _1583850)), hAPP(hAPP(c_Product__Type_OPair(_1583850, _1583850), _1583852), _1583854)), c_Transitive__Closure_Ortrancl(_1583850, _1583856))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583850, _1583850)), hAPP(hAPP(c_Product__Type_OPair(_1583850, _1583850), _1583854), _1583852)), c_Transitive__Closure_Ortrancl(_1583850, hAPP(c_Relation_Oconverse(_1583850, _1583850), _1583856)))))], (48069 ^ _776545) ^ [_1744738, _1744740, _1744742] : [48070 ^ _776545 : [(48071 ^ _776545) ^ [_1744815, _1744817] : [_1744742 = hAPP(hAPP(c_List_Oappend(_1744738), _1744817), hAPP(hAPP(c_List_Olist_OCons(_1744738), _1744740), _1744815))]], -(hBOOL(hAPP(hAPP(c_member(_1744738), _1744740), hAPP(c_List_Oset(_1744738), _1744742))))], (7638 ^ _776545) ^ [_903160, _903162, _903164, _903166] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903160, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903160, tc_HOL_Obool)), _903162), _903164)), _903166) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903160, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903160, tc_HOL_Obool)), _903162), _903166)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903160, tc_HOL_Obool)), _903164), _903166)))], (49869 ^ _776545) ^ [_1783720, _1783722] : [c_Equiv__Relations_Opart__equivp(_1783720, _1783722), 49873 ^ _776545 : [(49886 ^ _776545) ^ [_1784062, _1784064] : [-(hBOOL(hAPP(hAPP(_1783722, _1784064), _1784062))), hBOOL(hAPP(hAPP(_1783722, _1784064), _1784064)), hBOOL(hAPP(hAPP(_1783722, _1784062), _1784062)), hAPP(_1783722, _1784064) = hAPP(_1783722, _1784062)], (49876 ^ _776545) ^ [_1783893, _1783895] : [hBOOL(hAPP(hAPP(_1783722, _1783895), _1783893)), 49879 ^ _776545 : [(49884 ^ _776545) ^ [] : [-(hAPP(_1783722, _1783895) = hAPP(_1783722, _1783893))], (49882 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1783722, _1783893), _1783893)))], (49880 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1783722, _1783895), _1783895)))]]], (49874 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1783722, 49872 ^ [_1783720, _1783722]), 49872 ^ [_1783720, _1783722])))]]], (7071 ^ _776545) ^ [_891655, _891657, _891659] : [class_Orderings_Oorder(_891655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891655), _891657), _891659)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_891655, _891659, _891657) = c_Orderings_Obot__class_Obot(tc_fun(_891655, tc_HOL_Obool)))], (33419 ^ _776545) ^ [_1390388, _1390390, _1390392, _1390394, _1390396, _1390398] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390388, tc_fun(_1390390, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390392, tc_fun(_1390388, tc_HOL_Obool)), _1390394), _1390396)), _1390398) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390392, tc_fun(_1390390, tc_HOL_Obool)), _1390394), hAPP(hAPP(c_COMBC(_1390392, tc_fun(_1390388, tc_fun(_1390390, tc_HOL_Obool)), tc_fun(_1390390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390388, tc_HOL_Obool), tc_fun(tc_fun(_1390388, tc_fun(_1390390, tc_HOL_Obool)), tc_fun(_1390390, tc_HOL_Obool)), _1390392), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390388, tc_fun(_1390390, tc_HOL_Obool))), _1390396)), _1390398)))], (37576 ^ _776545) ^ [_1491815, _1491817, _1491819, _1491821, _1491823] : [c_Fun_Oinj__on(_1491815, _1491817, _1491819, c_Orderings_Otop__class_Otop(tc_fun(_1491815, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1491815, _1491817, _1491819), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491815, tc_HOL_Obool)), _1491821), _1491823)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491817, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491815, _1491817, _1491819), _1491821)), hAPP(c_Set_Oimage(_1491815, _1491817, _1491819), _1491823)))], (32518 ^ _776545) ^ [_1364159, _1364161, _1364163] : [-(hAPP(c_Set_OCollect(_1364159), hAPP(hAPP(c_COMBS(_1364159, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364159), c_fdisj), _1364161)), _1364163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364159, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1364159), _1364161)), hAPP(c_Set_OCollect(_1364159), _1364163)))], (12892 ^ _776545) ^ [_1004013, _1004015, _1004017, _1004019, _1004021] : [c_Finite__Set_Ofolding__one(_1004013, _1004015, _1004017), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004013), _1004019)), -(hBOOL(hAPP(hAPP(c_member(_1004013), _1004021), _1004019))), -(hAPP(_1004017, hAPP(hAPP(c_Set_Oinsert(_1004013), _1004021), _1004019)) = hAPP(hAPP(c_Finite__Set_Ofold(_1004013, _1004013, _1004015), _1004021), _1004019))], (42003 ^ _776545) ^ [_1607338, _1607340, _1607342, _1607344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607338), tc_List_Olist(_1607338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607338), tc_List_Olist(_1607338)), _1607340), _1607342)), c_List_Olistrel(_1607338, _1607344))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607338)), _1607340) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607338)), _1607342))], (41027 ^ _776545) ^ [_1580395, _1580397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580395), _1580397)), -(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), _1580395), _1580397)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (15462 ^ _776545) ^ [_1056164, _1056166, _1056168] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056164), _1056166)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056164), _1056168)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056164, tc_HOL_Obool)), _1056166), _1056168) = c_Orderings_Obot__class_Obot(tc_fun(_1056164, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1056164), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056164, tc_HOL_Obool)), _1056166), _1056168)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056164), _1056166)), hAPP(c_Finite__Set_Ocard(_1056164), _1056168)))], (32424 ^ _776545) ^ [_1360083, _1360085, _1360087] : [-(hAPP(hAPP(c_Set_Oinsert(_1360083), _1360085), _1360087) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360083, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1360083), hAPP(hAPP(c_COMBC(_1360083, _1360083, tc_HOL_Obool), c_fequal), _1360085))), _1360087))], (22327 ^ _776545) ^ [_1181212, _1181214, _1181216] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181214), _1181216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181214), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181212), _1181216)))], (39868 ^ _776545) ^ [_1552328, _1552330, _1552332, _1552334, _1552336, _1552338] : [c_Fun_Oinj__on(_1552328, _1552330, hAPP(c_Fun_Ocomp(_1552332, _1552330, _1552328, _1552334), _1552336), _1552338), -(c_Fun_Oinj__on(_1552328, _1552332, _1552336, _1552338))], (25269 ^ _776545) ^ [_1233955, _1233957] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1233955), _1233957), hAPP(c_Int_Onumber__class_Onumber__of(_1233955), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233955), _1233957)), class_Fields_Ofield__inverse__zero(_1233955), class_Int_Onumber__ring(_1233955)], (52131 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (45038 ^ _776545) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (36665 ^ _776545) ^ [_1471778, _1471780, _1471782, _1471784] : [hBOOL(hAPP(hAPP(c_member(_1471778), _1471780), _1471782)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1471778, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1471778, _1471778, _1471784), hAPP(hAPP(c_Set_Oinsert(_1471778), _1471780), c_Orderings_Obot__class_Obot(tc_fun(_1471778, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471778), _1471782), _1471784))))], (38917 ^ _776545) ^ [_1525440, _1525442, _1525444, _1525446, _1525448] : [-(hAPP(c_Relation_ODomain(_1525440, _1525442), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1525440, _1525442)), hAPP(hAPP(c_Product__Type_OPair(_1525440, _1525442), _1525444), _1525446)), _1525448)) = hAPP(hAPP(c_Set_Oinsert(_1525440), _1525444), hAPP(c_Relation_ODomain(_1525440, _1525442), _1525448)))], (13652 ^ _776545) ^ [_1019615, _1019617, _1019619, _1019621] : [class_Groups_Oordered__ab__semigroup__add(_1019615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019615), _1019617), _1019619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019615), _1019621), _1019617)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019615), _1019621), _1019619))))], (33897 ^ _776545) ^ [_1404738, _1404740, _1404742] : [class_Groups_Ocomm__monoid__add(_1404738), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404738), _1404740), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404742))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404738), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404738), _1404740), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1404742))), hAPP(_1404740, hAPP(c_Nat_OSuc, _1404742))))], (34007 ^ _776545) ^ [_1407881, _1407883] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1407881), _1407883))), -(hAPP(c_Finite__Set_Ocard(_1407881), _1407883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5376 ^ _776545) ^ [_858680, _858682, _858684, _858686] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_858686, _858682) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_858684, _858680)), _858686 = _858684, _858682 = _858680], (36472 ^ _776545) ^ [_1466401, _1466403, _1466405, _1466407, _1466409] : [-(hAPP(c_Relation_OImage(_1466401, _1466403, _1466405), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466401, tc_HOL_Obool)), _1466407), _1466409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466403, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466401, _1466403, _1466405), _1466407)), hAPP(c_Relation_OImage(_1466401, _1466403, _1466405), _1466409)))], (45373 ^ _776545) ^ [_1685831, _1685833, _1685835, _1685837] : [-(hBOOL(hAPP(c_List_Olistsp(_1685831, hAPP(hAPP(c_COMBS(_1685831, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1685831), c_fconj), _1685833)), _1685835)), _1685837))), hBOOL(hAPP(c_List_Olistsp(_1685831, _1685833), _1685837)), hBOOL(hAPP(c_List_Olistsp(_1685831, _1685835), _1685837))], (23069 ^ _776545) ^ [_1194511] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194511) = _1194511)], (50061 ^ _776545) ^ [_1787939, _1787941, _1787943, _1787945, _1787947] : [c_Fun_Oinj__on(_1787939, _1787941, _1787943, _1787945), hBOOL(hAPP(hAPP(c_member(_1787939), _1787947), _1787945)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787939, _1787941, _1787945, _1787943), hAPP(_1787943, _1787947)) = _1787947)], (50279 ^ _776545) ^ [_1792904, _1792906, _1792908] : [c_Fun_Obij__betw(_1792904, _1792906, _1792908, c_Orderings_Otop__class_Otop(tc_fun(_1792904, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792906, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1792906, _1792904, c_Hilbert__Choice_Oinv__into(_1792904, _1792906, c_Orderings_Otop__class_Otop(tc_fun(_1792904, tc_HOL_Obool)), _1792908), c_Orderings_Otop__class_Otop(tc_fun(_1792906, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792904, tc_HOL_Obool))))], (52491 ^ _776545) ^ [_1831393] : [hBOOL(hAPP(c_fNot, _1831393)), hBOOL(_1831393)], (42207 ^ _776545) ^ [_1613421, _1613423, _1613425] : [_1613421 = _1613423, 42210 ^ _776545 : [(42213 ^ _776545) ^ [_1613569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613569), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613425)), _1613421))), -(hAPP(hAPP(c_List_Onth(_1613425), _1613421), _1613569) = hAPP(hAPP(c_List_Onth(_1613425), _1613423), _1613569))], (42211 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613425)), _1613421) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613425)), _1613423))]]], (48942 ^ _776545) ^ [_1763285, _1763287, _1763289] : [-(c_List_Olist__ex1(_1763285, _1763287, _1763289)), 48943 ^ _776545 : [(48944 ^ _776545) ^ [_1763379] : [hBOOL(hAPP(hAPP(c_member(_1763285), _1763379), hAPP(c_List_Oset(_1763285), _1763289))), hBOOL(hAPP(_1763287, _1763379)), 48952 ^ _776545 : [(48957 ^ _776545) ^ [] : [48951 ^ [_1763285, _1763287, _1763289, _1763379] = _1763379], (48955 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1763287, 48951 ^ [_1763285, _1763287, _1763289, _1763379])))], (48953 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763285), 48951 ^ [_1763285, _1763287, _1763289, _1763379]), hAPP(c_List_Oset(_1763285), _1763289))))]]]]], (15324 ^ _776545) ^ [_1053083, _1053085, _1053087] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053083), _1053085)), hBOOL(hAPP(hAPP(c_member(_1053083), _1053087), _1053085)), -(hAPP(c_Finite__Set_Ocard(_1053083), _1053085) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1053083), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053083, tc_HOL_Obool)), _1053085), hAPP(hAPP(c_Set_Oinsert(_1053083), _1053087), c_Orderings_Obot__class_Obot(tc_fun(_1053083, tc_HOL_Obool)))))))], (18135 ^ _776545) ^ [_1102539, _1102541, _1102543] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102539), _1102541)), 18138 ^ _776545 : [(18139 ^ _776545) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102539, tc_Nat_Onat), _1102543), _1102541) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18142 ^ _776545 : [(18143 ^ _776545) ^ [_1102701] : [hBOOL(hAPP(hAPP(c_member(_1102539), _1102701), _1102541)), -(hAPP(_1102543, _1102701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18149 ^ _776545) ^ [] : [18151 ^ _776545 : [(18154 ^ _776545) ^ [] : [hAPP(_1102543, 18150 ^ [_1102539, _1102541, _1102543]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18152 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1102539), 18150 ^ [_1102539, _1102541, _1102543]), _1102541)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102539, tc_Nat_Onat), _1102543), _1102541) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (14422 ^ _776545) ^ [_1036929, _1036931, _1036933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036929), _1036931)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036931), _1036929)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036933), _1036931)), _1036929))], (29609 ^ _776545) ^ [_1307237, _1307239] : [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), _1307237))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1307239))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1307237))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307239)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1307237)))], (45922 ^ _776545) ^ [_1697692] : [-(c_List_Oconcat(_1697692, c_List_Olist_ONil(tc_List_Olist(_1697692))) = c_List_Olist_ONil(_1697692))], (46411 ^ _776545) ^ [_1709857] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1709857) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1709857))))], (48718 ^ _776545) ^ [_1758431, _1758433, _1758435, _1758437, _1758439] : [-(hAPP(hAPP(c_List_Omap(_1758431, _1758433), _1758435), c_List_Oreplicate(_1758431, _1758437, _1758439)) = c_List_Oreplicate(_1758433, _1758437, hAPP(_1758435, _1758439)))], (28635 ^ _776545) ^ [] : [-(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)))))], (14604 ^ _776545) ^ [_1039871, _1039873, _1039875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039871), _1039873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039871), _1039875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039873), _1039875)))], (47530 ^ _776545) ^ [_1732497, _1732499] : [class_Orderings_Olinorder(_1732497), 47533 ^ _776545 : [(47554 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732497, _1732499)), 47555 ^ _776545 : [(47558 ^ _776545) ^ [_1733057, _1733059] : [_1732499 = hAPP(hAPP(c_List_Olist_OCons(_1732497), _1733057), _1733059), 47564 ^ _776545 : [(47567 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732497), _1733057), 47563 ^ [_1732497, _1732499, _1733057, _1733059]))], (47565 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732497), 47563 ^ [_1732497, _1732499, _1733057, _1733059]), hAPP(c_List_Oset(_1732497), _1733059))))]], c_List_Olinorder__class_Osorted(_1732497, _1733059)], (47556 ^ _776545) ^ [] : [_1732499 = c_List_Olist_ONil(_1732497)]]], (47534 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1732497, _1732499), -(_1732499 = c_List_Olist_ONil(_1732497)), 47543 ^ _776545 : [(47546 ^ _776545) ^ [_1732831] : [hBOOL(hAPP(hAPP(c_member(_1732497), _1732831), hAPP(c_List_Oset(_1732497), 47541 ^ [_1732497, _1732499]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732497), 47542 ^ [_1732497, _1732499]), _1732831)))], (47552 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732497, 47541 ^ [_1732497, _1732499]))], (47544 ^ _776545) ^ [] : [-(_1732499 = hAPP(hAPP(c_List_Olist_OCons(_1732497), 47542 ^ [_1732497, _1732499]), 47541 ^ [_1732497, _1732499]))]]]]], (32624 ^ _776545) ^ [_1368178, _1368180, _1368182] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368178, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1368178, tc_HOL_Obool), _1368180)), _1368182) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1368178, tc_HOL_Obool), tc_fun(_1368178, tc_HOL_Obool)), _1368180), hAPP(hAPP(c_COMBC(tc_fun(_1368178, tc_HOL_Obool), tc_fun(_1368178, tc_HOL_Obool), tc_fun(_1368178, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368178, tc_HOL_Obool))), _1368182)))], (32520 ^ _776545) ^ [_1364232, _1364234, _1364236, _1364238, _1364240] : [class_Lattices_Olattice(_1364232), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364234, _1364232)), _1364236), _1364238), _1364240) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1364232), hAPP(_1364236, _1364240)), hAPP(_1364238, _1364240)))], (27048 ^ _776545) ^ [_1263658, _1263660] : [c_Nat__Transfer_Onat__set(_1263658), c_Nat__Transfer_Onat__set(_1263660), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1263658), _1263660) = 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), _1263658)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1263660))))], (52189 ^ _776545) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (44850 ^ _776545) ^ [_1673844, _1673846, _1673848, _1673850] : [hAPP(hAPP(c_List_Omap(_1673844, _1673846), _1673848), _1673850) = c_List_Olist_ONil(_1673846), -(_1673850 = c_List_Olist_ONil(_1673844))], (42238 ^ _776545) ^ [_1614192, _1614194, _1614196, _1614198] : [_1614192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1614194), hAPP(hAPP(c_List_Olist_OCons(_1614194), _1614196), _1614198)), _1614192) = _1614196)], (48592 ^ _776545) ^ [_1756148, _1756150, _1756152, _1756154, _1756156, _1756158] : [-(hAPP(hAPP(c_List_Ozip(_1756148, _1756150), c_List_Oreplicate(_1756148, _1756152, _1756154)), c_List_Oreplicate(_1756150, _1756156, _1756158)) = c_List_Oreplicate(tc_prod(_1756148, _1756150), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1756152), _1756156), hAPP(hAPP(c_Product__Type_OPair(_1756148, _1756150), _1756154), _1756158)))], (1274 ^ _776545) ^ [_795334, _795336] : [-(class_Int_Onumber__ring(_795334)), _795336 = _795334, class_Int_Onumber__ring(_795336)], (33119 ^ _776545) ^ [_1382123, _1382125, _1382127, _1382129, _1382131] : [hBOOL(hAPP(hAPP(c_member(_1382123), _1382125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382127, tc_fun(_1382123, tc_HOL_Obool)), _1382129), _1382131))), 33122 ^ _776545 : [(33123 ^ _776545) ^ [_1382247] : [hBOOL(hAPP(hAPP(c_member(_1382127), _1382247), _1382129)), -(hBOOL(hAPP(hAPP(c_member(_1382123), _1382125), hAPP(_1382131, _1382247))))]]], (46620 ^ _776545) ^ [_1713601, _1713603, _1713605] : [class_Orderings_Olinorder(_1713601), c_List_Olinorder__class_Osorted(_1713601, _1713603), hBOOL(hAPP(c_List_Odistinct(_1713601), _1713603)), c_List_Olinorder__class_Osorted(_1713601, _1713605), hBOOL(hAPP(c_List_Odistinct(_1713601), _1713605)), hAPP(c_List_Oset(_1713601), _1713603) = hAPP(c_List_Oset(_1713601), _1713605), -(_1713603 = _1713605)], (1564 ^ _776545) ^ [_798959, _798961] : [-(class_Groups_Ocancel__ab__semigroup__add(_798959)), _798961 = _798959, class_Groups_Ocancel__ab__semigroup__add(_798961)], (26433 ^ _776545) ^ [_1253573, _1253575, _1253577] : [hBOOL(hAPP(_1253573, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1253575, _1253577))), 26436 ^ _776545 : [(26443 ^ _776545) ^ [] : [-(_1253577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26446 ^ _776545 : [(26447 ^ _776545) ^ [_1253821, _1253823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253821), _1253577)), _1253575 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1253577), _1253823)), _1253821), -(hBOOL(hAPP(_1253573, _1253821)))]]], (26437 ^ _776545) ^ [] : [_1253577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1253573, _1253575)))]]], (49560 ^ _776545) ^ [_1778123, _1778125, _1778127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778123, _1778123), tc_HOL_Obool)), _1778125), _1778127)), c_Relation_Oantisym(_1778123, _1778127), -(c_Relation_Oantisym(_1778123, _1778125))], (44352 ^ _776545) ^ [_1663620] : [class_Groups_Omonoid__add(_1663620), -(c_List_Omonoid__add__class_Olistsum(_1663620) = c_List_Ofoldl(_1663620, _1663620, c_Groups_Oplus__class_Oplus(_1663620), c_Groups_Ozero__class_Ozero(_1663620)))], (23179 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (36290 ^ _776545) ^ [_1461820, _1461822, _1461824, _1461826] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1461820, tc_HOL_Obool), tc_fun(_1461820, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1461820, tc_HOL_Obool), tc_fun(_1461820, tc_HOL_Obool)), _1461824), _1461826)), c_Wellfounded_Omax__ext(_1461820, _1461822))), -(c_Wellfounded_Omax__extp(_1461820, hAPP(hAPP(c_COMBC(_1461820, tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_fun(_1461820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461820, tc_fun(tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_fun(_1461820, tc_HOL_Obool)), _1461820), c_COMBC(_1461820, tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461820, tc_prod(_1461820, _1461820)), tc_fun(_1461820, tc_fun(tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_HOL_Obool)), _1461820), hAPP(c_COMBB(tc_prod(_1461820, _1461820), tc_fun(tc_fun(tc_prod(_1461820, _1461820), tc_HOL_Obool), tc_HOL_Obool), _1461820), c_member(tc_prod(_1461820, _1461820)))), c_Product__Type_OPair(_1461820, _1461820)))), _1461822), _1461824, _1461826))], (37502 ^ _776545) ^ [_1490323, _1490325, _1490327] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490323), _1490325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490323, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1490323, _1490323, _1490327), _1490325)), _1490325)), c_Fun_Oinj__on(_1490323, _1490323, _1490327, _1490325), -(hAPP(c_Set_Oimage(_1490323, _1490323, _1490327), _1490325) = _1490325)], (35953 ^ _776545) ^ [_1450629, _1450631, _1450633] : [class_Lattices_Odistrib__lattice(_1450629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450629), _1450631)), -(_1450631 = c_Orderings_Obot__class_Obot(tc_fun(_1450629, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450629), _1450633), c_Big__Operators_Olattice__class_OInf__fin(_1450629, _1450631)) = c_Big__Operators_Olattice__class_OInf__fin(_1450629, hAPP(c_Set_OCollect(_1450629), hAPP(hAPP(c_COMBB(tc_fun(_1450629, tc_HOL_Obool), tc_HOL_Obool, _1450629), c_HOL_OEx(_1450629)), hAPP(hAPP(c_COMBC(_1450629, tc_fun(_1450629, tc_HOL_Obool), tc_fun(_1450629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450629, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1450629, tc_HOL_Obool), tc_fun(_1450629, tc_HOL_Obool)), _1450629), c_COMBS(_1450629, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450629, tc_HOL_Obool), tc_fun(_1450629, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1450629), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1450629), c_fconj)), hAPP(hAPP(c_COMBC(_1450629, tc_fun(_1450629, _1450629), tc_fun(_1450629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450629, tc_HOL_Obool), tc_fun(tc_fun(_1450629, _1450629), tc_fun(_1450629, tc_HOL_Obool)), _1450629), c_COMBB(_1450629, tc_HOL_Obool, _1450629)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1450629), _1450633))))), hAPP(hAPP(c_COMBC(_1450629, tc_fun(_1450629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450629)), _1450631))))))], (12077 ^ _776545) ^ [_988785, _988787, _988789] : [class_Lattices_Olattice(_988785), hBOOL(hAPP(c_Finite__Set_Ofinite(_988785), _988787)), hBOOL(hAPP(hAPP(c_member(_988785), _988789), _988787)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_988785), _988789), c_Big__Operators_Olattice__class_OSup__fin(_988785, _988787)) = _988789)], (37368 ^ _776545) ^ [_1487740, _1487742, _1487744, _1487746, _1487748] : [c_Fun_Oinj__on(_1487740, _1487742, _1487744, c_Orderings_Otop__class_Otop(tc_fun(_1487740, tc_HOL_Obool))), 37371 ^ _776545 : [(37378 ^ _776545) ^ [] : [_1487746 = _1487748, -(hAPP(_1487744, _1487746) = hAPP(_1487744, _1487748))], (37372 ^ _776545) ^ [] : [hAPP(_1487744, _1487746) = hAPP(_1487744, _1487748), -(_1487746 = _1487748)]]], (38632 ^ _776545) ^ [_1518699, _1518701, _1518703, _1518705] : [-(hAPP(c_Set_Ovimage(_1518699, _1518701, _1518703), hAPP(c_Set_OCollect(_1518701), _1518705)) = hAPP(c_Set_OCollect(_1518699), hAPP(hAPP(c_COMBB(_1518701, tc_HOL_Obool, _1518699), _1518705), _1518703)))], (45046 ^ _776545) ^ [_1678670, _1678672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678670), _1678672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678670)), hAPP(c_Code__Numeral_Oof__nat, _1678672))))], (17898 ^ _776545) ^ [_1098539, _1098541, _1098543, _1098545] : [class_Rings_Ocomm__semiring__1(_1098539), class_Rings_Ono__zero__divisors(_1098539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098541), _1098543)), 17909 ^ _776545 : [(17919 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1098541, _1098539), _1098545), _1098543) = c_Groups_Ozero__class_Ozero(_1098539)), 17920 ^ _776545 : [(17921 ^ _776545) ^ [_1098917] : [hBOOL(hAPP(hAPP(c_member(_1098541), _1098917), _1098543)), hAPP(_1098545, _1098917) = c_Groups_Ozero__class_Ozero(_1098539)]]], (17910 ^ _776545) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1098541, _1098539), _1098545), _1098543) = c_Groups_Ozero__class_Ozero(_1098539), 17914 ^ _776545 : [(17917 ^ _776545) ^ [] : [-(hAPP(_1098545, 17913 ^ [_1098539, _1098541, _1098543, _1098545]) = c_Groups_Ozero__class_Ozero(_1098539))], (17915 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098541), 17913 ^ [_1098539, _1098541, _1098543, _1098545]), _1098543)))]]]]], (23848 ^ _776545) ^ [_1208533, _1208535] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208533)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208535)), _1208533 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1208535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33525 ^ _776545) ^ [_1393411, _1393413, _1393415, _1393417] : [_1393411 = c_Orderings_Obot__class_Obot(tc_fun(_1393413, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393413, tc_fun(_1393415, tc_HOL_Obool)), _1393411), hAPP(c_COMBK(tc_fun(_1393415, tc_HOL_Obool), _1393413), _1393417)) = c_Orderings_Otop__class_Otop(tc_fun(_1393415, tc_HOL_Obool)))], (720 ^ _776545) ^ [_787383, _787385, _787387, _787389, _787391, _787393, _787395, _787397] : [-(c_Wellfounded_Omax__extp(_787395, _787391, _787387, _787383)), c_Wellfounded_Omax__extp(_787397, _787393, _787389, _787385), _787397 = _787395, _787393 = _787391, _787389 = _787387, _787385 = _787383], (14198 ^ _776545) ^ [_1031934, _1031936] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1031934, _1031936))))], (51995 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (46401 ^ _776545) ^ [_1709647, _1709649, _1709651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709647), _1709649)), _1709651)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1709647, _1709651)), _1709649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709647), _1709649))], (4584 ^ _776545) ^ [_846156, _846158, _846160, _846162, _846164, _846166, _846168, _846170, _846172, _846174] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846174, _846170, _846166, _846162, _846158) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_846172, _846168, _846164, _846160, _846156)), _846174 = _846172, _846170 = _846168, _846166 = _846164, _846162 = _846160, _846158 = _846156], (10745 ^ _776545) ^ [_961655, _961657, _961659] : [class_Orderings_Oorder(_961655), 10748 ^ _776545 : [(10755 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961655), _961657), _961659))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961655, _961657), _961659) = c_Orderings_Obot__class_Obot(tc_fun(_961655, tc_HOL_Obool)))], (10749 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961655, _961657), _961659) = c_Orderings_Obot__class_Obot(tc_fun(_961655, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961655), _961657), _961659))]]], (41995 ^ _776545) ^ [_1607134, _1607136, _1607138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607134, _1607134), tc_HOL_Obool)), _1607136), _1607138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607134), tc_List_Olist(_1607134)), tc_HOL_Obool)), c_List_Olistrel(_1607134, _1607136)), c_List_Olistrel(_1607134, _1607138))))], (24154 ^ _776545) ^ [_1213521, _1213523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213523), 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), _1213521), _1213523)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20373 ^ _776545) ^ [_1144079, _1144081, _1144083] : [class_Fields_Olinordered__field(_1144079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144079), c_Groups_Ozero__class_Ozero(_1144079)), _1144081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144079), c_Groups_Ozero__class_Ozero(_1144079)), _1144083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144079), c_Groups_Ozero__class_Ozero(_1144079)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144079), _1144081), _1144083))))], (6597 ^ _776545) ^ [_883297, _883299, _883301] : [6599 ^ _776545 : [(6602 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883297, tc_HOL_Obool)), _883301), 6598 ^ [_883297, _883299, _883301]))], (6600 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_883297, tc_HOL_Obool)), 6598 ^ [_883297, _883299, _883301]), _883299)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883297, tc_HOL_Obool)), _883301), c_Complete__Lattice_OInf__class_OInf(tc_fun(_883297, tc_HOL_Obool), _883299))))], (40905 ^ _776545) ^ [_1577503, _1577505, _1577507, _1577509, _1577511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577503, _1577503)), hAPP(hAPP(c_Product__Type_OPair(_1577503, _1577503), _1577505), _1577507)), c_Transitive__Closure_Ortrancl(_1577503, _1577509))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577503, _1577503)), hAPP(hAPP(c_Product__Type_OPair(_1577503, _1577503), _1577507), _1577511)), _1577509)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577503, _1577503)), hAPP(hAPP(c_Product__Type_OPair(_1577503, _1577503), _1577505), _1577511)), c_Transitive__Closure_Otrancl(_1577503, _1577509))))], (22961 ^ _776545) ^ [_1192607, _1192609, _1192611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192607)), _1192607 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192607), _1192611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192609), _1192607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1192611)))], (23803 ^ _776545) ^ [_1207684, _1207686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207684), _1207686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207684)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207686))))], (24958 ^ _776545) ^ [_1228518, _1228520, _1228522] : [-(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, _1228518, _1228520)), _1228522), _1228520) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228518), _1228522), _1228520))], (24782 ^ _776545) ^ [_1224771, _1224773, _1224775] : [class_Divides_Osemiring__div(_1224771), -(c_Divides_Odiv__class_Omod(_1224771, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224771), _1224773), _1224775), _1224773) = c_Divides_Odiv__class_Omod(_1224771, _1224775, _1224773))], (36211 ^ _776545) ^ [_1459575, _1459577, _1459579, _1459581, _1459583, _1459585, _1459587] : [-(hAPP(c_Product__Type_Oapsnd(_1459575, _1459577, _1459579, _1459581), hAPP(c_Product__Type_Oapfst(_1459583, _1459579, _1459575, _1459585), _1459587)) = hAPP(hAPP(c_Product__Type_OPair(_1459579, _1459577), hAPP(_1459585, hAPP(c_Product__Type_Ofst(_1459583, _1459575), _1459587))), hAPP(_1459581, hAPP(c_Product__Type_Osnd(_1459583, _1459575), _1459587))))], (5428 ^ _776545) ^ [_859470, _859472, _859474, _859476, _859478, _859480] : [-(c_SetInterval_Oord_OlessThan(_859480, _859476, _859472) = c_SetInterval_Oord_OlessThan(_859478, _859474, _859470)), _859480 = _859478, _859476 = _859474, _859472 = _859470], (19372 ^ _776545) ^ [_1126307] : [class_Rings_Oring__1(_1126307), -(hBOOL(hAPP(hAPP(c_member(_1126307), c_Groups_Oone__class_Oone(_1126307)), c_Int_Oring__1__class_OInts(_1126307))))], (19543 ^ _776545) ^ [_1129579, _1129581] : [class_Rings_Odivision__ring(_1129579), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129579), c_Groups_Ozero__class_Ozero(_1129579)), _1129581) = c_Groups_Ozero__class_Ozero(_1129579))], (52411 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (25656 ^ _776545) ^ [_1240751, _1240753, _1240755] : [-(hBOOL(hAPP(_1240751, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1240753, _1240755)))), 25659 ^ _776545 : [(25662 ^ _776545) ^ [] : [hBOOL(hAPP(_1240751, _1240753))], (25660 ^ _776545) ^ [] : [-(_1240755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 25665 ^ _776545 : [(25666 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240755)))], (25672 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25668 ^ [_1240751, _1240753, _1240755]), _1240755)))], (25676 ^ _776545) ^ [] : [hBOOL(hAPP(_1240751, 25668 ^ [_1240751, _1240753, _1240755]))], (25674 ^ _776545) ^ [] : [-(_1240753 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240755), 25667 ^ [_1240751, _1240753, _1240755])), 25668 ^ [_1240751, _1240753, _1240755]))], (25670 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25668 ^ [_1240751, _1240753, _1240755])))]], 25677 ^ _776545 : [(25678 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240755), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25684 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25680 ^ [_1240751, _1240753, _1240755]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25688 ^ _776545) ^ [] : [hBOOL(hAPP(_1240751, 25680 ^ [_1240751, _1240753, _1240755]))], (25686 ^ _776545) ^ [] : [-(_1240753 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240755), 25679 ^ [_1240751, _1240753, _1240755])), 25680 ^ [_1240751, _1240753, _1240755]))], (25682 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240755), 25680 ^ [_1240751, _1240753, _1240755])))]]], (28603 ^ _776545) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (17892 ^ _776545) ^ [_1098406, _1098408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1098406), hAPP(c_Nat_OSuc, _1098408))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1098406, hAPP(c_Nat_OSuc, _1098408)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1098408)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1098406, _1098408)))], (26252 ^ _776545) ^ [_1250721] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250721))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28559 ^ _776545) ^ [_1288983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1288983)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1288983), c_Int_OPls)))], (18186 ^ _776545) ^ [_1103511, _1103513, _1103515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103511), _1103513)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103515), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103513), _1103511))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103515), _1103511)), hAPP(c_Nat_OSuc, _1103513)))], (46956 ^ _776545) ^ [_1720315, _1720317] : [hBOOL(hAPP(c_List_Odistinct(_1720315), hAPP(c_List_Orev(_1720315), _1720317))), -(hBOOL(hAPP(c_List_Odistinct(_1720315), _1720317)))], (29337 ^ _776545) ^ [_1302271, _1302273] : [class_Fields_Olinordered__field__inverse__zero(_1302271), class_Int_Onumber__ring(_1302271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302271), c_Groups_Ozero__class_Ozero(_1302271)), _1302273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302271), c_Groups_Ozero__class_Ozero(_1302271)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302271), _1302273), hAPP(c_Int_Onumber__class_Onumber__of(_1302271), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (39333 ^ _776545) ^ [_1538079, _1538081] : [-(c_Product__Type_Oapsnd(_1538079, _1538079, _1538081, c_Fun_Oid(_1538079)) = c_Fun_Oid(tc_prod(_1538081, _1538079)))], (52309 ^ _776545) ^ [_1829332] : [-(class_HOL_Oequal(tc_Option_Ooption(_1829332)))], (10279 ^ _776545) ^ [_953199, _953201] : [class_Groups_Ogroup__add(_953199), -(hAPP(c_Groups_Ouminus__class_Ouminus(_953199), hAPP(c_Groups_Ouminus__class_Ouminus(_953199), _953201)) = _953201)], (48923 ^ _776545) ^ [_1762852, _1762854, _1762856] : [c_List_Olist__ex1(_1762852, _1762854, _1762856), 48927 ^ _776545 : [(48932 ^ _776545) ^ [_1763098] : [-(_1763098 = 48926 ^ [_1762852, _1762854, _1762856]), hBOOL(hAPP(hAPP(c_member(_1762852), _1763098), hAPP(c_List_Oset(_1762852), _1762856))), hBOOL(hAPP(_1762854, _1763098))], (48930 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1762854, 48926 ^ [_1762852, _1762854, _1762856])))], (48928 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762852), 48926 ^ [_1762852, _1762854, _1762856]), hAPP(c_List_Oset(_1762852), _1762856))))]]], (35638 ^ _776545) ^ [_1441803, _1441805, _1441807, _1441809, _1441811] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441803, _1441805, _1441807), _1441809), _1441811) = hAPP(hAPP(_1441809, hAPP(c_Product__Type_Ofst(_1441803, _1441805), _1441811)), hAPP(c_Product__Type_Osnd(_1441803, _1441805), _1441811)))], (10813 ^ _776545) ^ [_962873, _962875, _962877, _962879] : [class_Orderings_Olinorder(_962873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962873), _962875), _962877)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_962873, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962873, _962875), _962879)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962873, _962875), _962877)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962873, _962877), _962879))], (3018 ^ _776545) ^ [_821343, _821345] : [_821345 = _821343, -(c_Nitpick_ORep__Frac(_821345) = c_Nitpick_ORep__Frac(_821343))], (3868 ^ _776545) ^ [_834646, _834648, _834650, _834652, _834654, _834656] : [-(c_List_Olinorder__class_Oinsort__key(_834656, _834652, _834648) = c_List_Olinorder__class_Oinsort__key(_834654, _834650, _834646)), _834656 = _834654, _834652 = _834650, _834648 = _834646], (816 ^ _776545) ^ [_788777, _788779, _788781, _788783] : [-(c_Predicate_Osymp(_788781, _788777)), c_Predicate_Osymp(_788783, _788779), _788783 = _788781, _788779 = _788777], (7118 ^ _776545) ^ [_892476, _892478, _892480, _892482] : [7119 ^ _776545 : [(7122 ^ _776545) ^ [] : [_892478 = _892482], (7120 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892476), _892478), _892480))]], -(hBOOL(hAPP(hAPP(c_member(_892476), _892478), hAPP(hAPP(c_Set_Oinsert(_892476), _892482), _892480))))], (29011 ^ _776545) ^ [_1296595, _1296597] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1296595)), c_Int_OBit0(_1296597)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296595), _1296597)))], (19004 ^ _776545) ^ [_1118869, _1118871] : [19006 ^ _776545 : [(19009 ^ _776545) ^ [] : [hBOOL(hAPP(_1118871, 19005 ^ [_1118869, _1118871]))], (19007 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19005 ^ [_1118869, _1118871]), _1118869)))]], 19010 ^ _776545 : [(19011 ^ _776545) ^ [_1119020] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1119020), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118869))), -(hBOOL(hAPP(_1118871, _1119020)))]]], (19561 ^ _776545) ^ [_1129936, _1129938, _1129940, _1129942] : [class_Rings_Odivision__ring(_1129936), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129936), _1129938), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129936), _1129940), _1129942)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129936), _1129938), _1129940)), _1129942))], (48444 ^ _776545) ^ [_1752317, _1752319, _1752321, _1752323] : [-(c_New__Random__Sequence_Opos__empty(_1752317, _1752319, _1752321, _1752323) = c_New__DSequence_Opos__empty(_1752317))], (41504 ^ _776545) ^ [_1592266] : [-(c_Nat_Ofunpow(_1592266) = c_Nat_Ocompow(_1592266, _1592266))], (48430 ^ _776545) ^ [_1751916, _1751918, _1751920, _1751922, _1751924] : [-(_1751916 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1751918, _1751920, _1751922, _1751924), _1751916) = hAPP(c_Lazy__Sequence_Obind(_1751918, _1751920, hAPP(_1751922, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1751916), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1751918, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1751920)), _1751924), _1751916)))], (44180 ^ _776545) ^ [_1659981, _1659983, _1659985] : [-(hAPP(c_List_Oset(_1659981), hAPP(c_List_Orotate(_1659981, _1659983), _1659985)) = hAPP(c_List_Oset(_1659981), _1659985))], (52219 ^ _776545) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (15081 ^ _776545) ^ [_1048866, _1048868] : [class_Rings_Ocomm__semiring__1(_1048866), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048866), c_Groups_Oone__class_Oone(_1048866)), _1048868) = _1048868)], (13606 ^ _776545) ^ [_1018686, _1018688, _1018690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1018686), _1018688)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1018686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018688), _1018690)) = 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, _1018686), _1018688)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1018688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1018688), _1018690))))], (37981 ^ _776545) ^ [_1502126, _1502128, _1502130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502126, _1502126), tc_HOL_Obool)), _1502128), _1502130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502126, tc_HOL_Obool)), c_Wellfounded_Oacc(_1502126, _1502130)), c_Wellfounded_Oacc(_1502126, _1502128))))], (35632 ^ _776545) ^ [_1441630, _1441632] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441630), _1441632) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1441630, _1441632)))], (41443 ^ _776545) ^ [_1590556, _1590558, _1590560] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590556, _1590556), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590558)), _1590560) = hAPP(hAPP(c_Relation_Orel__comp(_1590556, _1590556, _1590556), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590556, _1590556), tc_HOL_Obool), _1590558), _1590560)), _1590560))], (24930 ^ _776545) ^ [_1227967, _1227969] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227967), _1227969)), _1227967)))], (44801 ^ _776545) ^ [_1672625, _1672627, _1672629] : [class_Groups_Omonoid__add(_1672625), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672625), hAPP(hAPP(c_List_Omap(_1672627, _1672625), hAPP(c_COMBK(_1672625, _1672627), c_Groups_Ozero__class_Ozero(_1672625))), _1672629)) = c_Groups_Ozero__class_Ozero(_1672625))], (29551 ^ _776545) ^ [_1305940, _1305942, _1305944] : [class_Rings_Olinordered__idom(_1305940), 29554 ^ _776545 : [(29555 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305940), c_Groups_Ozero__class_Ozero(_1305940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305940), hAPP(hAPP(c_Power_Opower__class_Opower(_1305940), _1305942), 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(_1305940), _1305944), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1305942 = c_Groups_Ozero__class_Ozero(_1305940), _1305944 = c_Groups_Ozero__class_Ozero(_1305940)], (29565 ^ _776545) ^ [] : [29566 ^ _776545 : [(29569 ^ _776545) ^ [] : [-(_1305944 = c_Groups_Ozero__class_Ozero(_1305940))], (29567 ^ _776545) ^ [] : [-(_1305942 = c_Groups_Ozero__class_Ozero(_1305940))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305940), c_Groups_Ozero__class_Ozero(_1305940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305940), hAPP(hAPP(c_Power_Opower__class_Opower(_1305940), _1305942), 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(_1305940), _1305944), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (43565 ^ _776545) ^ [_1645654, _1645656, _1645658] : [c_List_Olist_ONil(_1645654) = hAPP(hAPP(c_List_Oappend(_1645654), _1645656), _1645658), 43568 ^ _776545 : [(43571 ^ _776545) ^ [] : [-(_1645658 = c_List_Olist_ONil(_1645654))], (43569 ^ _776545) ^ [] : [-(_1645656 = c_List_Olist_ONil(_1645654))]]], (15781 ^ _776545) ^ [_1062540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062540)), -(_1062540 = hAPP(c_Nat_OSuc, 15784 ^ [_1062540]))], (30028 ^ _776545) ^ [_1315044, _1315046] : [class_Orderings_Olinorder(_1315044), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315044), _1315046), _1315046) = _1315046)], (30620 ^ _776545) ^ [_1326001, _1326003, _1326005] : [class_Orderings_Olinorder(_1326001), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326001), _1326003)), hBOOL(hAPP(hAPP(c_member(_1326001), _1326005), _1326003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326001), c_Big__Operators_Olinorder__class_OMin(_1326001, _1326003)), _1326005)))], (42380 ^ _776545) ^ [_1617780, _1617782, _1617784] : [42382 ^ _776545 : [(42385 ^ _776545) ^ [] : [hBOOL(hAPP(_1617784, hAPP(hAPP(c_List_Onth(_1617780), _1617782), 42381 ^ [_1617780, _1617782, _1617784])))], (42383 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42381 ^ [_1617780, _1617782, _1617784]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617780)), _1617782))))]], 42386 ^ _776545 : [(42387 ^ _776545) ^ [_1617982] : [hBOOL(hAPP(hAPP(c_member(_1617780), _1617982), hAPP(c_List_Oset(_1617780), _1617782))), -(hBOOL(hAPP(_1617784, _1617982)))]]], (6388 ^ _776545) ^ [_879650, _879652, _879654] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_879650, tc_HOL_Obool)), _879652), _879654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879650, tc_HOL_Obool)), _879652), c_Complete__Lattice_OSup__class_OSup(tc_fun(_879650, tc_HOL_Obool), _879654))))], (49371 ^ _776545) ^ [_1773315, _1773317, _1773319, _1773321] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1773315, tc_fun(_1773317, tc_HOL_Obool)), _1773319), _1773321) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1773317, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1773317, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773315, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1773317, tc_HOL_Obool)), c_HOL_OEx(_1773315)), hAPP(hAPP(c_COMBB(tc_fun(_1773315, tc_HOL_Obool), tc_fun(_1773315, tc_HOL_Obool), tc_fun(_1773317, tc_HOL_Obool)), hAPP(c_COMBS(_1773315, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1773315), c_fconj), hAPP(hAPP(c_COMBC(_1773315, tc_fun(_1773315, tc_HOL_Obool), tc_HOL_Obool), c_member(_1773315)), _1773319)))), hAPP(hAPP(c_COMBC(tc_fun(_1773317, tc_HOL_Obool), tc_fun(_1773315, tc_fun(_1773317, tc_HOL_Obool)), tc_fun(_1773315, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773317, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1773315, tc_fun(_1773317, tc_HOL_Obool)), tc_fun(_1773315, tc_HOL_Obool)), tc_fun(_1773317, tc_HOL_Obool)), c_COMBB(tc_fun(_1773317, tc_HOL_Obool), tc_HOL_Obool, _1773315)), c_fequal)), _1773321))))))], (33398 ^ _776545) ^ [_1389857, _1389859, _1389861, _1389863, _1389865] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1389857, tc_fun(_1389859, tc_HOL_Obool)), _1389861), _1389863), _1389865)), 33402 ^ _776545 : [(33405 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1389863, 33401 ^ [_1389857, _1389859, _1389861, _1389863, _1389865]), _1389865)))], (33403 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389857), 33401 ^ [_1389857, _1389859, _1389861, _1389863, _1389865]), _1389861)))]]], (44240 ^ _776545) ^ [_1661203, _1661205] : [class_Lattices_Oab__semigroup__idem__mult(_1661203), -(_1661205 = c_List_Olist_ONil(_1661203)), -(hAPP(c_Finite__Set_Ofold1(_1661203, c_Groups_Otimes__class_Otimes(_1661203)), hAPP(c_List_Oset(_1661203), _1661205)) = hAPP(c_List_Ofoldl(_1661203, _1661203, c_Groups_Otimes__class_Otimes(_1661203), hAPP(c_List_Ohd(_1661203), _1661205)), hAPP(c_List_Otl(_1661203), _1661205)))], (43833 ^ _776545) ^ [_1651949, _1651951, _1651953, _1651955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651949), tc_List_Olist(_1651949))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651949), tc_List_Olist(_1651949)), _1651951), _1651953)), c_List_Olistrel1(_1651949, _1651955))), 43838 ^ _776545 : [(43845 ^ _776545) ^ [] : [-(_1651953 = hAPP(hAPP(c_List_Oappend(_1651949), 43840 ^ [_1651949, _1651951, _1651953, _1651955]), hAPP(hAPP(c_List_Olist_OCons(_1651949), 43837 ^ [_1651949, _1651951, _1651953, _1651955]), 43841 ^ [_1651949, _1651951, _1651953, _1651955])))], (43843 ^ _776545) ^ [] : [-(_1651951 = hAPP(hAPP(c_List_Oappend(_1651949), 43840 ^ [_1651949, _1651951, _1651953, _1651955]), hAPP(hAPP(c_List_Olist_OCons(_1651949), 43836 ^ [_1651949, _1651951, _1651953, _1651955]), 43841 ^ [_1651949, _1651951, _1651953, _1651955])))], (43839 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651949, _1651949)), hAPP(hAPP(c_Product__Type_OPair(_1651949, _1651949), 43836 ^ [_1651949, _1651951, _1651953, _1651955]), 43837 ^ [_1651949, _1651951, _1651953, _1651955])), _1651955)))]]], (31395 ^ _776545) ^ [_1340268] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1340268) = c_Orderings_Oord__class_Omax(_1340268)), class_Lattices_Osemilattice__sup(_1340268), class_Orderings_Olinorder(_1340268)], (33807 ^ _776545) ^ [_1402515, _1402517, _1402519, _1402521, _1402523, _1402525] : [-(hAPP(c_Set_Oimage(_1402515, _1402517, hAPP(hAPP(c_COMBS(_1402515, _1402517, _1402517), hAPP(hAPP(c_COMBS(_1402515, _1402517, tc_fun(_1402517, _1402517)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1402517, tc_fun(_1402517, _1402517)), _1402515), c_If(_1402517)), _1402519)), _1402521)), _1402523)), _1402525) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402517, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1402515, _1402517, _1402521), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402515, tc_HOL_Obool)), _1402525), hAPP(c_Set_OCollect(_1402515), _1402519)))), hAPP(c_Set_Oimage(_1402515, _1402517, _1402523), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402515, tc_HOL_Obool)), _1402525), hAPP(c_Set_OCollect(_1402515), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1402515), c_fNot), _1402519))))))], (39267 ^ _776545) ^ [_1534913, _1534915, _1534917, _1534919] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534913), _1534915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534913, _1534913), tc_HOL_Obool)), _1534917), hAPP(hAPP(c_Product__Type_OSigma(_1534913, _1534913), _1534915), hAPP(c_COMBK(tc_fun(_1534913, tc_HOL_Obool), _1534913), _1534915)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1534913, tc_HOL_Obool)), _1534919), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1534913), _1534915), _1534917))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1534913), _1534919)))], (31032 ^ _776545) ^ [_1333354, _1333356] : [class_Orderings_Olinorder(_1333354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333354), _1333356)), -(_1333356 = c_Orderings_Obot__class_Obot(tc_fun(_1333354, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1333354), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333354), 31045 ^ [_1333354, _1333356]), 31046 ^ [_1333354, _1333356])), hAPP(hAPP(c_Set_Oinsert(_1333354), 31045 ^ [_1333354, _1333356]), hAPP(hAPP(c_Set_Oinsert(_1333354), 31046 ^ [_1333354, _1333356]), c_Orderings_Obot__class_Obot(tc_fun(_1333354, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1333354), c_Big__Operators_Olinorder__class_OMin(_1333354, _1333356)), _1333356)))], (42603 ^ _776545) ^ [_1624756] : [42605 ^ _776545 : [(42608 ^ _776545) ^ [] : [42604 ^ [_1624756] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42606 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42604 ^ [_1624756]), hAPP(c_List_Oset(tc_Nat_Onat), _1624756))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48748 ^ _776545) ^ [_1758998, _1759000, _1759002] : [_1758998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1759000), c_List_Oreplicate(_1759000, _1758998, _1759002)) = c_Orderings_Obot__class_Obot(tc_fun(_1759000, tc_HOL_Obool)))], (7362 ^ _776545) ^ [_897187, _897189] : [class_Orderings_Oorder(_897187), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_897187, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_897187), _897189)), hAPP(c_SetInterval_Oord__class_OatLeast(_897187), _897189)) = hAPP(hAPP(c_Set_Oinsert(_897187), _897189), c_Orderings_Obot__class_Obot(tc_fun(_897187, tc_HOL_Obool))))], (29795 ^ _776545) ^ [_1310763, _1310765, _1310767] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1310763, _1310765, _1310767, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1310765)], (4840 ^ _776545) ^ [_850218, _850220, _850222, _850224] : [-(c_Complete__Lattice_OInf__class_OInf(_850224, _850220) = c_Complete__Lattice_OInf__class_OInf(_850222, _850218)), _850224 = _850222, _850220 = _850218], (9088 ^ _776545) ^ [_933634, _933636, _933638, _933640] : [class_Orderings_Oorder(_933634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933634), _933636), _933638)), _933636 = _933640, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933634), _933640), _933638)))], (17497 ^ _776545) ^ [_1091675, _1091677, _1091679, _1091681] : [class_Rings_Olinordered__ring__strict(_1091675), 17500 ^ _776545 : [(17515 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091675), _1091677), _1091679)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091675), _1091677), _1091681)))), 17516 ^ _776545 : [(17523 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091677), c_Groups_Ozero__class_Ozero(_1091675))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091681), _1091679))], (17517 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), c_Groups_Ozero__class_Ozero(_1091675)), _1091677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091679), _1091681))]]], (17501 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091675), _1091677), _1091679)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091675), _1091677), _1091681))), 17506 ^ _776545 : [(17509 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091679), _1091681)))], (17507 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), c_Groups_Ozero__class_Ozero(_1091675)), _1091677)))]], 17510 ^ _776545 : [(17513 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091681), _1091679)))], (17511 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091675), _1091677), c_Groups_Ozero__class_Ozero(_1091675))))]]]]], (8044 ^ _776545) ^ [_913176, _913178, _913180, _913182] : [-(hBOOL(hAPP(hAPP(c_member(_913176), _913178), _913180))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913176, tc_HOL_Obool)), _913180), hAPP(hAPP(c_Set_Oinsert(_913176), _913178), _913182)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913176, tc_HOL_Obool)), _913180), _913182))], (29027 ^ _776545) ^ [_1296907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296907), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1296907)), c_Int_OMin)))], (36452 ^ _776545) ^ [_1465610] : [-(c_Wellfounded_Omeasure(_1465610) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1465610), c_Wellfounded_Oless__than))], (14939 ^ _776545) ^ [_1046040, _1046042, _1046044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046040), _1046044)), _1046042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046042), _1046044))))], (36681 ^ _776545) ^ [_1472165, _1472167, _1472169, _1472171] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1472165, _1472165)), hAPP(hAPP(c_Product__Type_OPair(_1472165, _1472165), _1472167), _1472169)), c_Relation_OId__on(_1472165, _1472171))), 36684 ^ _776545 : [(36687 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472165), _1472167), _1472171)))], (36685 ^ _776545) ^ [] : [-(_1472167 = _1472169)]]], (7678 ^ _776545) ^ [_904630, _904632, _904634] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904630, tc_HOL_Obool)), _904632), _904634) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904630, tc_HOL_Obool)), _904634), _904632))], (34047 ^ _776545) ^ [_1408595] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1408595) = 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), _1408595), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (48911 ^ _776545) ^ [_1762602, _1762604, _1762606] : [hBOOL(hAPP(hAPP(c_member(_1762602), _1762604), hAPP(c_List_Oset(_1762602), _1762606))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762602), _1762606), _1762604)))], (31210 ^ _776545) ^ [_1336572, _1336574, _1336576] : [class_Orderings_Olinorder(_1336572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336572), _1336574)), hBOOL(hAPP(hAPP(c_member(_1336572), _1336576), _1336574)), 31221 ^ _776545 : [(31228 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336572, tc_HOL_Obool)), _1336574), hAPP(hAPP(c_Set_Oinsert(_1336572), _1336576), c_Orderings_Obot__class_Obot(tc_fun(_1336572, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336572, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1336572, _1336574) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336572), _1336576), c_Big__Operators_Olinorder__class_OMax(_1336572, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336572, tc_HOL_Obool)), _1336574), hAPP(hAPP(c_Set_Oinsert(_1336572), _1336576), c_Orderings_Obot__class_Obot(tc_fun(_1336572, tc_HOL_Obool)))))))], (31222 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336572, tc_HOL_Obool)), _1336574), hAPP(hAPP(c_Set_Oinsert(_1336572), _1336576), c_Orderings_Obot__class_Obot(tc_fun(_1336572, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1336572, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1336572, _1336574) = _1336576)]]], (11710 ^ _776545) ^ [_981491, _981493, _981495, _981497] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981491, tc_HOL_Obool)), _981493), _981497))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981491, tc_HOL_Obool)), _981493), hAPP(hAPP(c_Set_Oinsert(_981491), _981495), _981497)))))], (37792 ^ _776545) ^ [_1496921, _1496923, _1496925, _1496927, _1496929, _1496931] : [c_Fun_Oinj__on(_1496921, _1496923, _1496925, _1496927), hBOOL(hAPP(hAPP(c_member(_1496923), _1496929), hAPP(c_Set_Oimage(_1496921, _1496923, _1496925), _1496927))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496921, tc_HOL_Obool)), _1496927), _1496931)), -(hBOOL(hAPP(hAPP(c_member(_1496921), hAPP(c_Fun_Othe__inv__into(_1496921, _1496923, _1496927, _1496925), _1496929)), _1496931)))], (7025 ^ _776545) ^ [_890782, _890784, _890786] : [class_Orderings_Olinorder(_890782), 7028 ^ _776545 : [(7035 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890782), _890784), _890786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890782, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_890782), _890784)), hAPP(c_SetInterval_Oord__class_OlessThan(_890782), _890786))))], (7029 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890782, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_890782), _890784)), hAPP(c_SetInterval_Oord__class_OlessThan(_890782), _890786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890782), _890784), _890786)))]]], (35785 ^ _776545) ^ [_1444785, _1444787, _1444789] : [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), _1444785), _1444787))), -(hBOOL(hAPP(hAPP(_1444789, _1444785), _1444787))), 35792 ^ _776545 : [(35795 ^ _776545) ^ [] : [-(35791 ^ [_1444785, _1444787, _1444789] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1444789, 35791 ^ [_1444785, _1444787, _1444789]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 35790 ^ [_1444785, _1444787, _1444789], 35791 ^ [_1444785, _1444787, _1444789]))))], (35801 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1444789, 35790 ^ [_1444785, _1444787, _1444789]), 35791 ^ [_1444785, _1444787, _1444789]))], (35793 ^ _776545) ^ [] : [-(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), 35790 ^ [_1444785, _1444787, _1444789]), 35791 ^ [_1444785, _1444787, _1444789]))))]]], (9652 ^ _776545) ^ [_941783, _941785, _941787, _941789] : [class_Orderings_Opreorder(_941783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941783), _941785), _941787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941783), _941787), _941789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941783), _941785), _941789)))], (35473 ^ _776545) ^ [_1438252, _1438254, _1438256, _1438258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1438258, _1438254)), hAPP(_1438258, _1438256))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1438252, _1438252)), hAPP(hAPP(c_Product__Type_OPair(_1438252, _1438252), _1438254), _1438256)), hAPP(c_Wellfounded_Omeasure(_1438252), _1438258))))], (41389 ^ _776545) ^ [_1589283, _1589285, _1589287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589283, _1589283)), _1589285), c_Transitive__Closure_Ortrancl(_1589283, _1589287))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589283, _1589283)), _1589285), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1589283, _1589283), 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(_1589283, _1589283), tc_HOL_Obool), tc_fun(tc_prod(_1589283, _1589283), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1589283, _1589283), tc_HOL_Obool)), _1589287)))))], (2 ^ _776545) ^ [_776572] : [-(_776572 = _776572)], (7476 ^ _776545) ^ [_899643, _899645, _899647, _899649] : [hBOOL(hAPP(hAPP(c_member(_899643), _899645), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899643, tc_HOL_Obool)), _899647), _899649))), -(hBOOL(hAPP(hAPP(c_member(_899643), _899645), _899647))), -(hBOOL(hAPP(hAPP(c_member(_899643), _899645), _899649)))], (25921 ^ _776545) ^ [_1245332, _1245334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245334, _1245332)), _1245332)))], (15584 ^ _776545) ^ [_1058963, _1058965, _1058967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058963), _1058965)), hBOOL(hAPP(hAPP(c_member(_1058963), _1058967), _1058965)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1058963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058963, tc_HOL_Obool)), _1058965), hAPP(hAPP(c_Set_Oinsert(_1058963), _1058967), c_Orderings_Obot__class_Obot(tc_fun(_1058963, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1058963), _1058965))], (8084 ^ _776545) ^ [_913997, _913999, _914001] : [class_Complete__Lattice_Ocomplete__lattice(_913997), -(c_Complete__Lattice_OInf__class_OInf(_913997, hAPP(hAPP(c_Set_Oinsert(_913997), _913999), _914001)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_913997), _913999), c_Complete__Lattice_OInf__class_OInf(_913997, _914001)))], (26559 ^ _776545) ^ [_1255931, _1255933] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1255931, _1255933)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255933), _1255931)))], (6287 ^ _776545) ^ [_877676, _877678, _877680] : [class_Complete__Lattice_Ocomplete__lattice(_877676), 6290 ^ _776545 : [(6291 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877676), c_Complete__Lattice_OSup__class_OSup(_877676, _877678)), _877680)), 6294 ^ _776545 : [(6295 ^ _776545) ^ [_877834] : [hBOOL(hAPP(hAPP(c_member(_877676), _877834), _877678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877676), _877834), _877680)))]]], (6301 ^ _776545) ^ [] : [6303 ^ _776545 : [(6306 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877676), 6302 ^ [_877676, _877678, _877680]), _877680))], (6304 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877676), 6302 ^ [_877676, _877678, _877680]), _877678)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877676), c_Complete__Lattice_OSup__class_OSup(_877676, _877678)), _877680)))]]], (9770 ^ _776545) ^ [_943865, _943867, _943869, _943871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943865, tc_HOL_Obool)), _943867), _943869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943865, tc_HOL_Obool)), _943869), _943871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943865, tc_HOL_Obool)), _943867), _943871)))], (52459 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (18304 ^ _776545) ^ [_1105724, _1105726, _1105728, _1105730] : [class_Rings_Olinordered__semiring__strict(_1105724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105724), _1105726), _1105728)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105724), _1105726), _1105730))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105724), c_Groups_Ozero__class_Ozero(_1105724)), _1105726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105724), _1105728), _1105730)))], (9938 ^ _776545) ^ [_946722, _946724, _946726] : [class_Orderings_Oord(_946722), 9941 ^ _776545 : [(9948 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946722), _946726), _946724)), -(hBOOL(hAPP(hAPP(c_member(_946722), _946724), hAPP(c_SetInterval_Oord__class_OgreaterThan(_946722), _946726))))], (9942 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_946722), _946724), hAPP(c_SetInterval_Oord__class_OgreaterThan(_946722), _946726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946722), _946726), _946724)))]]], (46365 ^ _776545) ^ [_1709012, _1709014, _1709016, _1709018] : [c_List_Oupt(_1709012, _1709014) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1709016), _1709018), 46368 ^ _776545 : [(46373 ^ _776545) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709012), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1709014) = _1709018)], (46371 ^ _776545) ^ [] : [-(_1709012 = _1709016)], (46369 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709012), _1709014)))]]], (38665 ^ _776545) ^ [_1519430, _1519432, _1519434, _1519436, _1519438, _1519440] : [-(hAPP(c_Set_Ovimage(_1519430, _1519432, _1519434), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1519436, tc_fun(_1519432, tc_HOL_Obool)), _1519438), _1519440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1519436, tc_fun(_1519430, tc_HOL_Obool)), _1519438), hAPP(hAPP(c_COMBB(tc_fun(_1519432, tc_HOL_Obool), tc_fun(_1519430, tc_HOL_Obool), _1519436), c_Set_Ovimage(_1519430, _1519432, _1519434)), _1519440)))], (13628 ^ _776545) ^ [_1019149, _1019151, _1019153, _1019155] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1019149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019149), _1019151), _1019153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019149), _1019155), _1019153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019149), _1019151), _1019155)))], (28605 ^ _776545) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (34325 ^ _776545) ^ [_1415303, _1415305] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415305)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415305))), 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), _1415303)), c_Int_Onat)))))], (51805 ^ _776545) ^ [_1823829, _1823831] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823829), _1823831)), 51810 ^ _776545 : [(51813 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823831), _1823829))], (51811 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823829), _1823831)))]], -(_1823829 = _1823831)], (27064 ^ _776545) ^ [_1263910, _1263912] : [c_Nat__Transfer_Onat__set(_1263910), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1263912), _1263910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263912)))], (15105 ^ _776545) ^ [_1049246, _1049248] : [class_Groups_Omonoid__mult(_1049246), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049246), c_Groups_Oone__class_Oone(_1049246)), _1049248) = _1049248)], (42317 ^ _776545) ^ [_1616323, _1616325, _1616327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616323, tc_HOL_Obool)), hAPP(c_List_Oset(_1616323), hAPP(hAPP(c_List_Otake(_1616323), _1616325), _1616327))), hAPP(c_List_Oset(_1616323), _1616327))))], (26052 ^ _776545) ^ [_1247466] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247466)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247466))], (45806 ^ _776545) ^ [_1695571] : [-(c_List_Oremdups(_1695571, c_List_Olist_ONil(_1695571)) = c_List_Olist_ONil(_1695571))], (36436 ^ _776545) ^ [_1464732, _1464734, _1464736] : [-(c_Wellfounded_Omlex__prod(_1464732, _1464734, _1464736) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1464732), _1464732), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1464732, c_Wellfounded_Oless__than, _1464736)), hAPP(hAPP(c_COMBS(_1464732, _1464732, tc_prod(tc_Nat_Onat, _1464732)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1464732, tc_prod(tc_Nat_Onat, _1464732)), _1464732), c_Product__Type_OPair(tc_Nat_Onat, _1464732)), _1464734)), c_COMBI(_1464732))))], (25073 ^ _776545) ^ [_1230487, _1230489] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230487, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230489)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230487, _1230489) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (44196 ^ _776545) ^ [_1660270, _1660272, _1660274] : [-(hAPP(c_List_Orotate1(_1660270), hAPP(c_List_Orotate(_1660270, _1660272), _1660274)) = hAPP(c_List_Orotate(_1660270, _1660272), hAPP(c_List_Orotate1(_1660270), _1660274)))], (45211 ^ _776545) ^ [_1682117, _1682119] : [_1682117 = _1682119, -(hAPP(c_Code__Numeral_Onat__of, _1682117) = hAPP(c_Code__Numeral_Onat__of, _1682119))], (4272 ^ _776545) ^ [_841262, _841264] : [_841264 = _841262, -(c_Orderings_Oord__class_Omin(_841264) = c_Orderings_Oord__class_Omin(_841262))], (48317 ^ _776545) ^ [_1749655, _1749657, _1749659] : [c_List_Olist__all(_1749655, _1749657, _1749659), 48320 ^ _776545 : [(48321 ^ _776545) ^ [_1749736] : [hBOOL(hAPP(hAPP(c_member(_1749655), _1749736), hAPP(c_List_Oset(_1749655), _1749659))), -(hBOOL(hAPP(_1749657, _1749736)))]]], (7668 ^ _776545) ^ [_904328, _904330, _904332, _904334] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904328, tc_HOL_Obool)), _904330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904328, tc_HOL_Obool)), _904332), _904334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904328, tc_HOL_Obool)), _904332), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904328, tc_HOL_Obool)), _904330), _904334)))], (19981 ^ _776545) ^ [_1137158, _1137160, _1137162, _1137164] : [class_Fields_Olinordered__field(_1137158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1137158), c_Groups_Ozero__class_Ozero(_1137158)), _1137160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137158), _1137162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137158), _1137164), _1137160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137158), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137158), _1137162), _1137160)), _1137164)))], (26591 ^ _776545) ^ [_1256512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256512)), -(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, _1256512))))], (23571 ^ _776545) ^ [_1203782, _1203784] : [-(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, _1203782)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203784))))], (3242 ^ _776545) ^ [_824835, _824837, _824839, _824841, _824843, _824845, _824847, _824849, _824851, _824853] : [-(c_Fun_Ofun__upd(_824853, _824849, _824845, _824841, _824837) = c_Fun_Ofun__upd(_824851, _824847, _824843, _824839, _824835)), _824853 = _824851, _824849 = _824847, _824845 = _824843, _824841 = _824839, _824837 = _824835], (39890 ^ _776545) ^ [_1552798, _1552800, _1552802, _1552804] : [c_Finite__Set_Ofun__left__comm__idem(_1552798, _1552800, _1552802), -(hAPP(c_Fun_Ocomp(_1552800, _1552800, _1552800, hAPP(_1552802, _1552804)), hAPP(_1552802, _1552804)) = hAPP(_1552802, _1552804))], (32676 ^ _776545) ^ [_1370003, _1370005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1370003, 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(_1370003, tc_HOL_Obool)), tc_fun(_1370003, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1370003, tc_HOL_Obool)), tc_fun(_1370003, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1370003, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1370005)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1370003, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1370005))], (22203 ^ _776545) ^ [_1179244, _1179246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179244), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179244), _1179246)))], (20773 ^ _776545) ^ [_1151588, _1151590, _1151592, _1151594] : [class_Fields_Ofield(_1151588), -(_1151590 = c_Groups_Ozero__class_Ozero(_1151588)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151588), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151588), _1151592), _1151590)), _1151594) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151588), _1151592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151588), _1151590), _1151594))), _1151590))], (25085 ^ _776545) ^ [_1230666] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230666), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50224 ^ _776545) ^ [_1791914] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1791914), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1791914 = hAPP(c_Code__Numeral_Onat__of, 50227 ^ [_1791914]))], (33174 ^ _776545) ^ [_1384265, _1384267, _1384269] : [hBOOL(hAPP(hAPP(c_member(_1384265), _1384267), hAPP(c_Set_OCollect(_1384265), _1384269))), -(hBOOL(hAPP(_1384269, _1384267)))], (24968 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (22167 ^ _776545) ^ [_1178556] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178556)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178556)))], (14720 ^ _776545) ^ [_1041841, _1041843, _1041845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041841), _1041843)), _1041845)), 14723 ^ _776545 : [(14726 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041843), _1041845)))], (14724 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041841), _1041845)))]]], (16030 ^ _776545) ^ [_1066529, _1066531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066529), _1066531)), -(hAPP(c_Nat_OSuc, _1066529) = _1066531), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066529)), _1066531)))], (11562 ^ _776545) ^ [_978686, _978688] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_978686, _978688)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_978686, _978688), tc_HOL_Obool)))), 11565 ^ _776545 : [(11568 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978688), c_Orderings_Otop__class_Otop(tc_fun(_978688, tc_HOL_Obool)))))], (11566 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_978686), c_Orderings_Otop__class_Otop(tc_fun(_978686, tc_HOL_Obool)))))]]], (27383 ^ _776545) ^ [_1269094, _1269096] : [class_Groups_Oordered__ab__group__add__abs(_1269094), 27386 ^ _776545 : [(27393 ^ _776545) ^ [] : [_1269096 = c_Groups_Ozero__class_Ozero(_1269094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269094), hAPP(c_Groups_Oabs__class_Oabs(_1269094), _1269096)), c_Groups_Ozero__class_Ozero(_1269094))))], (27387 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269094), hAPP(c_Groups_Oabs__class_Oabs(_1269094), _1269096)), c_Groups_Ozero__class_Ozero(_1269094))), -(_1269096 = c_Groups_Ozero__class_Ozero(_1269094))]]], (28377 ^ _776545) ^ [_1285956, _1285958] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1285956)), c_Int_OBit1(_1285958))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1285956), _1285958)))], (28823 ^ _776545) ^ [_1293270, _1293272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293270), _1293272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293270)), c_Int_OBit0(_1293272))))], (7980 ^ _776545) ^ [_911626, _911628, _911630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911626, tc_HOL_Obool)), _911628), _911630)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911626, tc_HOL_Obool)), _911630), _911628) = _911628)], (48607 ^ _776545) ^ [_1756448, _1756450, _1756452, _1756454] : [48608 ^ _776545 : [(48611 ^ _776545) ^ [] : [_1756450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48609 ^ _776545) ^ [] : [hBOOL(hAPP(_1756454, _1756452))]], 48612 ^ _776545 : [(48613 ^ _776545) ^ [_1756573] : [hBOOL(hAPP(hAPP(c_member(_1756448), _1756573), hAPP(c_List_Oset(_1756448), c_List_Oreplicate(_1756448, _1756450, _1756452)))), -(hBOOL(hAPP(_1756454, _1756573)))]]], (45335 ^ _776545) ^ [_1685066, _1685068, _1685070, _1685072] : [hBOOL(hAPP(c_List_Olistsp(_1685066, _1685068), hAPP(hAPP(c_List_Olist_OCons(_1685066), _1685070), _1685072))), 45338 ^ _776545 : [(45341 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685066, _1685068), _1685072)))], (45339 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1685068, _1685070)))]]], (38655 ^ _776545) ^ [_1519179, _1519181, _1519183, _1519185] : [38656 ^ _776545 : [(38657 ^ _776545) ^ [_1519233] : [hBOOL(hAPP(hAPP(_1519183, _1519233), _1519185))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1519179, _1519181, _1519183), _1519185)))], (24862 ^ _776545) ^ [_1226545, _1226547, _1226549, _1226551] : [class_Divides_Osemiring__div(_1226545), -(c_Divides_Odiv__class_Omod(_1226545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226545), c_Divides_Odiv__class_Omod(_1226545, _1226547, _1226549)), _1226551), _1226549) = c_Divides_Odiv__class_Omod(_1226545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226545), _1226547), _1226551), _1226549))], (45265 ^ _776545) ^ [_1683058, _1683060] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1683058), _1683060) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1683058)), hAPP(c_Code__Numeral_Onat__of, _1683060))))], (23992 ^ _776545) ^ [_1210996, _1210998, _1211000, _1211002] : [class_Divides_Osemiring__div(_1210996), -(_1210998 = c_Groups_Ozero__class_Ozero(_1210996)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210996), _1210998), _1211000)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210996), _1210998), _1211002)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210996), _1211000), _1211002))], (50723 ^ _776545) ^ [_1801825, _1801827, _1801829] : [hBOOL(hAPP(hAPP(c_member(_1801825), _1801827), c_Quotient_ORespects(_1801825, _1801829))), -(hBOOL(hAPP(hAPP(_1801829, _1801827), _1801827)))], (32946 ^ _776545) ^ [_1377363, _1377365, _1377367, _1377369, _1377371] : [-(_1377363 = c_Orderings_Obot__class_Obot(tc_fun(_1377365, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377367, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377365, tc_fun(_1377367, tc_HOL_Obool)), _1377363), _1377369)), _1377371) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377365, tc_fun(_1377367, tc_HOL_Obool)), _1377363), hAPP(hAPP(c_COMBC(_1377365, tc_fun(_1377367, tc_HOL_Obool), tc_fun(_1377367, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377367, tc_HOL_Obool), tc_fun(tc_fun(_1377367, tc_HOL_Obool), tc_fun(_1377367, tc_HOL_Obool)), _1377365), c_Groups_Ominus__class_Ominus(tc_fun(_1377367, tc_HOL_Obool))), _1377369)), _1377371)))], (27122 ^ _776545) ^ [_1264819, _1264821] : [class_Rings_Olinordered__idom(_1264819), 27125 ^ _776545 : [(27132 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264821), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264819), hAPP(c_Int_Oring__1__class_Oof__int(_1264819), _1264821)), c_Groups_Ozero__class_Ozero(_1264819))))], (27126 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264819), hAPP(c_Int_Oring__1__class_Oof__int(_1264819), _1264821)), c_Groups_Ozero__class_Ozero(_1264819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1264821), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (33062 ^ _776545) ^ [_1380583, _1380585] : [-(hAPP(c_Set_Oimage(_1380583, _1380583, c_COMBI(_1380583)), _1380585) = _1380585)], (50000 ^ _776545) ^ [_1786477, _1786479, _1786481, _1786483, _1786485, _1786487] : [hAPP(c_Set_Oimage(_1786477, _1786479, _1786481), _1786483) = _1786485, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1786479, tc_HOL_Obool)), _1786487), _1786485)), -(hAPP(c_Set_Oimage(_1786477, _1786479, _1786481), hAPP(c_Set_Oimage(_1786479, _1786477, c_Hilbert__Choice_Oinv__into(_1786477, _1786479, _1786483, _1786481)), _1786487)) = _1786487)], (39956 ^ _776545) ^ [_1554386, _1554388, _1554390, _1554392, _1554394, _1554396] : [class_Groups_Ocomm__monoid__mult(_1554386), c_Fun_Oinj__on(_1554388, _1554390, _1554392, _1554394), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554390, _1554386), _1554396), hAPP(c_Set_Oimage(_1554388, _1554390, _1554392), _1554394)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554388, _1554386), hAPP(c_Fun_Ocomp(_1554390, _1554386, _1554388, _1554396), _1554392)), _1554394))], (44789 ^ _776545) ^ [_1672239, _1672241, _1672243, _1672245, _1672247] : [class_Rings_Osemiring__0(_1672239), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672239), hAPP(hAPP(c_List_Omap(_1672241, _1672239), hAPP(hAPP(c_COMBB(_1672239, _1672239, _1672241), hAPP(c_Groups_Otimes__class_Otimes(_1672239), _1672243)), _1672245)), _1672247)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672239), _1672243), hAPP(c_List_Omonoid__add__class_Olistsum(_1672239), hAPP(hAPP(c_List_Omap(_1672241, _1672239), _1672245), _1672247))))], (24896 ^ _776545) ^ [_1227246, _1227248, _1227250, _1227252] : [class_Divides_Oring__div(_1227246), -(c_Divides_Odiv__class_Omod(_1227246, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227246), _1227248), _1227250), _1227252) = c_Divides_Odiv__class_Omod(_1227246, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227246), c_Divides_Odiv__class_Omod(_1227246, _1227248, _1227252)), c_Divides_Odiv__class_Omod(_1227246, _1227250, _1227252)), _1227252))], (8197 ^ _776545) ^ [_916601, _916603, _916605, _916607] : [class_Lattices_Olattice(_916601), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916601), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916601), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916601), _916603), _916605)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916601), _916603), _916607))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916601), _916603), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916601), _916605), _916607)))))], (27745 ^ _776545) ^ [_1275596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275596)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1275596 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26026 ^ _776545) ^ [_1246990, _1246992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246990), _1246992)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246990, _1246992) = _1246990)], (14813 ^ _776545) ^ [_1043618, _1043620, _1043622] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043618), _1043620)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043622), _1043620)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043618), _1043622))], (45096 ^ _776545) ^ [_1679642, _1679644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679642), _1679644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679642)), hAPP(c_Code__Numeral_Oof__nat, _1679644))))], (20821 ^ _776545) ^ [_1152438, _1152440, _1152442, _1152444] : [class_Fields_Ofield(_1152438), -(_1152440 = c_Groups_Ozero__class_Ozero(_1152438)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152438), _1152442), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152438), _1152444), _1152440)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152438), _1152440), _1152442)), _1152444)), _1152440))], (36396 ^ _776545) ^ [] : [-(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)))))], (43791 ^ _776545) ^ [_1650602, _1650604, _1650606, _1650608, _1650610, _1650612, _1650614] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650602, _1650602)), hAPP(hAPP(c_Product__Type_OPair(_1650602, _1650602), _1650604), _1650606)), _1650608)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650602), tc_List_Olist(_1650602))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650602), tc_List_Olist(_1650602)), hAPP(hAPP(c_List_Oappend(_1650602), _1650610), hAPP(hAPP(c_List_Olist_OCons(_1650602), _1650604), _1650612))), hAPP(hAPP(c_List_Oappend(_1650602), _1650610), hAPP(hAPP(c_List_Olist_OCons(_1650602), _1650606), _1650614)))), c_List_Olexord(_1650602, _1650608))))], (2982 ^ _776545) ^ [_820803, _820805, _820807, _820809, _820811, _820813] : [-(c_Nitpick_Oplus__frac(_820813, _820809, _820805) = c_Nitpick_Oplus__frac(_820811, _820807, _820803)), _820813 = _820811, _820809 = _820807, _820805 = _820803], (14660 ^ _776545) ^ [_1040943, _1040945] : [14661 ^ _776545 : [(14664 ^ _776545) ^ [] : [_1040943 = _1040945], (14662 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040943), _1040945))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040943), _1040945)))], (33537 ^ _776545) ^ [_1393616, _1393618, _1393620] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393616, tc_fun(_1393618, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1393616, tc_HOL_Obool))), _1393620) = c_Orderings_Otop__class_Otop(tc_fun(_1393618, tc_HOL_Obool)))], (33451 ^ _776545) ^ [_1391522, _1391524, _1391526, _1391528] : [-(hAPP(c_Finite__Set_Ofold__image(_1391522, _1391524, _1391526), _1391528) = c_Finite__Set_Ofold(_1391524, _1391522, hAPP(hAPP(c_COMBB(_1391522, tc_fun(_1391522, _1391522), _1391524), _1391526), _1391528)))], (23017 ^ _776545) ^ [_1193537, _1193539, _1193541, _1193543, _1193545] : [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), _1193537), _1193539)), _1193541)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193537), _1193543)), _1193545))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193541), _1193537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193545), _1193537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193539), _1193543)))], (22209 ^ _776545) ^ [_1179349, _1179351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179349), _1179351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179349), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179351)))], (24722 ^ _776545) ^ [_1223807, _1223809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1223807), _1223809)), -(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)), _1223807)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223809))))], (37340 ^ _776545) ^ [_1487256, _1487258, _1487260, _1487262, _1487264, _1487266] : [c_Fun_Oinj__on(_1487256, _1487258, _1487260, _1487262), -(_1487264 = _1487266), hBOOL(hAPP(hAPP(c_member(_1487256), _1487264), _1487262)), hBOOL(hAPP(hAPP(c_member(_1487256), _1487266), _1487262)), hAPP(_1487260, _1487264) = hAPP(_1487260, _1487266)], (14580 ^ _776545) ^ [_1039461, _1039463] : [_1039461 = _1039463, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039461), _1039463)))], (50243 ^ _776545) ^ [_1792214] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50239 ^ [_1792214]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45383 ^ _776545) ^ [_1686058, _1686060, _1686062] : [hBOOL(hAPP(c_List_Olistsp(_1686058, _1686060), _1686062)), 45386 ^ _776545 : [(45387 ^ _776545) ^ [_1686147] : [hBOOL(hAPP(hAPP(c_member(_1686058), _1686147), hAPP(c_List_Oset(_1686058), _1686062))), -(hBOOL(hAPP(_1686060, _1686147)))]]], (6796 ^ _776545) ^ [_886443, _886445, _886447] : [6798 ^ _776545 : [(6801 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886443, tc_HOL_Obool)), 6797 ^ [_886443, _886445, _886447]), _886447))], (6799 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_886443, tc_HOL_Obool)), 6797 ^ [_886443, _886445, _886447]), _886445)))]], -(_886445 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_886443, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886443, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_886443, tc_HOL_Obool), _886445)), _886447)))], (50953 ^ _776545) ^ [_1808466, _1808468, _1808470, _1808472, _1808474] : [-(c_Lazy__Sequence_Omap(_1808466, _1808468, _1808470, c_Lazy__Sequence_Olazy__sequence_OInsert(_1808466, _1808472, _1808474)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1808468, hAPP(_1808470, _1808472), c_Lazy__Sequence_Omap(_1808466, _1808468, _1808470, _1808474)))], (52269 ^ _776545) ^ [_1828822] : [class_Lazy__Sequence_Osmall__lazy(_1828822), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1828822)))], (38456 ^ _776545) ^ [_1513819, _1513821] : [c_Wellfounded_Owf(_1513819, hAPP(c_Set_OCollect(tc_prod(_1513819, _1513819)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513819, _1513819, tc_HOL_Obool), _1513821))), -(c_Wellfounded_OwfP(_1513819, _1513821))], (47611 ^ _776545) ^ [_1733998, _1734000, _1734002, _1734004] : [-(c_List_Omaps(_1733998, _1734000, _1734002, _1734004) = c_List_Oconcat(_1734000, hAPP(hAPP(c_List_Omap(_1733998, tc_List_Olist(_1734000)), _1734002), _1734004)))], (30022 ^ _776545) ^ [_1314953, _1314955] : [class_Orderings_Olinorder(_1314953), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314953), _1314955), _1314955) = _1314955)], (39834 ^ _776545) ^ [_1551664, _1551666, _1551668, _1551670, _1551672, _1551674] : [-(hAPP(c_Set_Oimage(_1551664, _1551666, hAPP(c_Fun_Ocomp(_1551668, _1551666, _1551664, _1551670), _1551672)), _1551674) = hAPP(c_Set_Oimage(_1551668, _1551666, _1551670), hAPP(c_Set_Oimage(_1551664, _1551668, _1551672), _1551674)))], (31092 ^ _776545) ^ [_1334616, _1334618] : [class_Groups_Olinordered__ab__group__add(_1334616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334616), _1334618)), -(_1334618 = c_Orderings_Obot__class_Obot(tc_fun(_1334616, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334616), c_Big__Operators_Olinorder__class_OMax(_1334616, _1334618)) = c_Big__Operators_Olinorder__class_OMin(_1334616, hAPP(c_Set_Oimage(_1334616, _1334616, c_Groups_Ouminus__class_Ouminus(_1334616)), _1334618)))], (13904 ^ _776545) ^ [_1024825, _1024827, _1024829] : [class_Groups_Oab__group__add(_1024825), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024825), _1024827), _1024829) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024825), _1024827), hAPP(c_Groups_Ouminus__class_Ouminus(_1024825), _1024829)))], (28143 ^ _776545) ^ [_1281920] : [class_Int_Onumber__ring(_1281920), -(c_Int_Oiszero(_1281920, hAPP(c_Int_Onumber__class_Onumber__of(_1281920), c_Int_OPls)))], (32894 ^ _776545) ^ [_1376092, _1376094, _1376096, _1376098, _1376100] : [class_Groups_Ocomm__monoid__add(_1376092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376094), _1376096)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376094, _1376092), hAPP(hAPP(c_COMBS(_1376094, _1376092, _1376092), hAPP(hAPP(c_COMBB(_1376092, tc_fun(_1376092, _1376092), _1376094), c_Groups_Oplus__class_Oplus(_1376092)), _1376098)), _1376100)), _1376096) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376092), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376094, _1376092), _1376098), _1376096)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1376094, _1376092), _1376100), _1376096)))], (13474 ^ _776545) ^ [_1016202, _1016204, _1016206, _1016208, _1016210, _1016212, _1016214, _1016216] : [c_Finite__Set_Ofolding__image__simple__idem(_1016202, _1016204, _1016206, _1016208, _1016210, _1016212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016204), _1016214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016204), _1016216)), -(hAPP(_1016212, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016204, tc_HOL_Obool)), _1016214), _1016216)) = hAPP(hAPP(_1016206, hAPP(_1016212, _1016214)), hAPP(_1016212, _1016216)))], (41118 ^ _776545) ^ [_1582889, _1582891] : [c_Wellfounded_Oacyclic(_1582889, hAPP(c_Relation_Oconverse(_1582889, _1582889), _1582891)), -(c_Wellfounded_Oacyclic(_1582889, _1582891))], (33188 ^ _776545) ^ [_1384540, _1384542, _1384544] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384540), hAPP(c_Set_OCollect(_1384540), hAPP(hAPP(c_COMBS(_1384540, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1384540), c_fdisj), _1384542)), _1384544)))), 33191 ^ _776545 : [(33194 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384540), hAPP(c_Set_OCollect(_1384540), _1384544))))], (33192 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384540), hAPP(c_Set_OCollect(_1384540), _1384542))))]]], (16713 ^ _776545) ^ [_1077182, _1077184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077182), _1077184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077182), hAPP(c_Nat_OSuc, _1077184))))], (44641 ^ _776545) ^ [_1669135, _1669137, _1669139, _1669141] : [-(hAPP(hAPP(c_List_Oappend(_1669135), _1669137), hAPP(hAPP(c_List_Olist_OCons(_1669135), _1669139), c_List_Olist_ONil(_1669135))) = _1669141), -(_1669141 = c_List_Olist_ONil(_1669135)), c_List_Obutlast(_1669135, _1669141) = _1669137, c_List_Olast(_1669135, _1669141) = _1669139], (27773 ^ _776545) ^ [_1276008, _1276010] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276008), _1276010), hAPP(c_Int_Onumber__class_Onumber__of(_1276008), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1276008)), class_Fields_Ofield__inverse__zero(_1276008), class_Int_Onumber__ring(_1276008)], (37698 ^ _776545) ^ [_1494539, _1494541, _1494543, _1494545, _1494547] : [c_Fun_Oinj__on(_1494539, _1494541, _1494543, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494539, tc_HOL_Obool)), _1494545), _1494547)), 37701 ^ _776545 : [(37706 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494541, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494539, _1494541, _1494543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494539, tc_HOL_Obool)), _1494545), _1494547))), hAPP(c_Set_Oimage(_1494539, _1494541, _1494543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494539, tc_HOL_Obool)), _1494547), _1494545))) = c_Orderings_Obot__class_Obot(tc_fun(_1494541, tc_HOL_Obool)))], (37704 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1494539, _1494541, _1494543, _1494547))], (37702 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1494539, _1494541, _1494543, _1494545))]]], (12646 ^ _776545) ^ [_999423, _999425, _999427, _999429] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_999423, _999425, _999427), _999429), c_Orderings_Obot__class_Obot(tc_fun(_999423, tc_HOL_Obool))) = _999429)], (47607 ^ _776545) ^ [_1733909, _1733911] : [-(c_List_Oinsert(_1733909, _1733911, c_List_Olist_ONil(_1733909)) = hAPP(hAPP(c_List_Olist_OCons(_1733909), _1733911), c_List_Olist_ONil(_1733909)))], (104 ^ _776545) ^ [_778157, _778159, _778161, _778163, _778165, _778167, _778169, _778171, _778173, _778175, _778177, _778179] : [-(c_Finite__Set_Ofolding__image__simple__idem(_778177, _778173, _778169, _778165, _778161, _778157)), c_Finite__Set_Ofolding__image__simple__idem(_778179, _778175, _778171, _778167, _778163, _778159), _778179 = _778177, _778175 = _778173, _778171 = _778169, _778167 = _778165, _778163 = _778161, _778159 = _778157], (17359 ^ _776545) ^ [_1089128, _1089130, _1089132] : [class_Rings_Olinordered__ring__strict(_1089128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089128), _1089130), c_Groups_Ozero__class_Ozero(_1089128))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089128), _1089132), c_Groups_Ozero__class_Ozero(_1089128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089128), c_Groups_Ozero__class_Ozero(_1089128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089128), _1089130), _1089132))))], (8369 ^ _776545) ^ [_920037, _920039, _920041, _920043] : [class_Lattices_Osemilattice__inf(_920037), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920037), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920037), _920039), _920041)), _920043) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920037), _920039), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920037), _920041), _920043)))], (9638 ^ _776545) ^ [_941609, _941611, _941613] : [class_Orderings_Oorder(_941609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941609), _941611), _941613)), -(_941613 = _941611), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941609), _941611), _941613)))], (44998 ^ _776545) ^ [_1677698, _1677700, _1677702, _1677704] : [class_Groups_Ocomm__monoid__add(_1677698), 45001 ^ _776545 : [(45008 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1677700), _1677702))), -(c_Nitpick_Osetsum_H(_1677700, _1677698, _1677704, _1677702) = c_Groups_Ozero__class_Ozero(_1677698))], (45002 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1677700), _1677702)), -(c_Nitpick_Osetsum_H(_1677700, _1677698, _1677704, _1677702) = hAPP(c_List_Omonoid__add__class_Olistsum(_1677698), hAPP(hAPP(c_List_Omap(_1677700, _1677698), _1677704), c_Hilbert__Choice_OEps(tc_List_Olist(_1677700), hAPP(hAPP(c_COMBS(tc_List_Olist(_1677700), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1677700)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677700), tc_fun(_1677700, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1677700, tc_HOL_Obool), tc_fun(tc_fun(_1677700, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1677700)), c_fequal), c_List_Oset(_1677700))), _1677702))), c_List_Odistinct(_1677700))))))]]], (14768 ^ _776545) ^ [_1042768, _1042770, _1042772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042768), _1042770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042768), _1042772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042770), _1042772)))], (48836 ^ _776545) ^ [_1760756] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1760756) = c_Lazy__Sequence_Osmall__lazy_H(_1760756, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1760756)))], (8972 ^ _776545) ^ [_931508, _931510, _931512] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931508, tc_HOL_Obool)), _931510), _931512))), 8978 ^ _776545 : [(8982 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931508, tc_HOL_Obool)), 8980 ^ [_931508, _931510, _931512]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_931508, tc_HOL_Obool)), _931510), _931512))))], (8984 ^ _776545) ^ [] : [8977 ^ [_931508, _931510, _931512] = 8980 ^ [_931508, _931510, _931512]], (8986 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931508, tc_HOL_Obool)), 8977 ^ [_931508, _931510, _931512]), 8980 ^ [_931508, _931510, _931512]) = c_Orderings_Obot__class_Obot(tc_fun(_931508, tc_HOL_Obool))], (8979 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_931508, tc_HOL_Obool)), 8977 ^ [_931508, _931510, _931512]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_931508, tc_HOL_Obool)), _931510), _931512))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931508, tc_HOL_Obool)), _931510), c_Complete__Lattice_OSup__class_OSup(tc_fun(_931508, tc_HOL_Obool), _931512)) = c_Orderings_Obot__class_Obot(tc_fun(_931508, tc_HOL_Obool)))], (49350 ^ _776545) ^ [_1772781, _1772783, _1772785] : [-(c_List_Olist__ex(_1772781, _1772785, _1772783)), 49351 ^ _776545 : [(49352 ^ _776545) ^ [_1772838] : [hBOOL(hAPP(hAPP(c_member(_1772781), _1772838), hAPP(c_List_Oset(_1772781), _1772783))), hBOOL(hAPP(_1772785, _1772838))]]], (32820 ^ _776545) ^ [_1373129, _1373131, _1373133, _1373135, _1373137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373129, tc_HOL_Obool)), _1373131), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373133, tc_fun(_1373129, tc_HOL_Obool)), _1373135), _1373137))), 32823 ^ _776545 : [(32824 ^ _776545) ^ [_1373262] : [hBOOL(hAPP(hAPP(c_member(_1373133), _1373262), _1373135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373129, tc_HOL_Obool)), _1373131), hAPP(_1373137, _1373262))))]]], (45353 ^ _776545) ^ [_1685388, _1685390, _1685392, _1685394] : [hBOOL(hAPP(c_List_Olistsp(_1685388, _1685390), _1685392)), hBOOL(hAPP(c_List_Olistsp(_1685388, _1685394), _1685392)), -(hBOOL(hAPP(c_List_Olistsp(_1685388, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1685388, tc_HOL_Obool)), _1685390), _1685394)), _1685392)))], (30668 ^ _776545) ^ [_1326756, _1326758] : [class_Orderings_Olinorder(_1326756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326756), _1326758)), -(c_Big__Operators_Olattice_OInf__fin(_1326756, c_Orderings_Oord__class_Omin(_1326756), _1326758) = hAPP(c_Finite__Set_Ofold1(_1326756, c_Orderings_Oord__class_Omin(_1326756)), _1326758))], (19613 ^ _776545) ^ [_1130902, _1130904, _1130906, _1130908] : [class_Rings_Odivision__ring(_1130902), -(_1130904 = c_Groups_Ozero__class_Ozero(_1130902)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130902), _1130906), _1130904) = _1130908, -(_1130906 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130902), _1130908), _1130904))], (32149 ^ _776545) ^ [_1354271, _1354273, _1354275] : [class_Orderings_Olinorder(_1354271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354271), _1354273)), -(_1354273 = c_Orderings_Obot__class_Obot(tc_fun(_1354271, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354271), _1354275)), -(_1354275 = c_Orderings_Obot__class_Obot(tc_fun(_1354271, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354271, tc_HOL_Obool)), _1354273), _1354275) = c_Orderings_Obot__class_Obot(tc_fun(_1354271, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1354271, c_Orderings_Oord__class_Omax(_1354271), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354271, tc_HOL_Obool)), _1354273), _1354275)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354271), c_Big__Operators_Olattice_OSup__fin(_1354271, c_Orderings_Oord__class_Omax(_1354271), _1354273)), c_Big__Operators_Olattice_OSup__fin(_1354271, c_Orderings_Oord__class_Omax(_1354271), _1354275)))], (36221 ^ _776545) ^ [_1459883, _1459885, _1459887, _1459889, _1459891, _1459893] : [hAPP(_1459889, hAPP(c_Product__Type_Ofst(_1459883, _1459887), _1459891)) = hAPP(_1459893, hAPP(c_Product__Type_Ofst(_1459883, _1459887), _1459891)), -(hAPP(c_Product__Type_Oapfst(_1459883, _1459885, _1459887, _1459889), _1459891) = hAPP(c_Product__Type_Oapfst(_1459883, _1459885, _1459887, _1459893), _1459891))], (38761 ^ _776545) ^ [_1521805, _1521807, _1521809, _1521811] : [c_Fun_Oinj__on(_1521805, _1521807, _1521809, c_Orderings_Otop__class_Otop(tc_fun(_1521805, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1521805, _1521807, _1521809), hAPP(c_Set_Oimage(_1521805, _1521807, _1521809), _1521811)) = _1521811)], (42575 ^ _776545) ^ [_1624117, _1624119, _1624121, _1624123, _1624125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624117), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624119)), _1624121))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624117), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624123)), _1624125))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1624119, _1624123)), hAPP(hAPP(c_List_Ozip(_1624119, _1624123), _1624121), _1624125)), _1624117) = hAPP(hAPP(c_Product__Type_OPair(_1624119, _1624123), hAPP(hAPP(c_List_Onth(_1624119), _1624121), _1624117)), hAPP(hAPP(c_List_Onth(_1624123), _1624125), _1624117)))], (34576 ^ _776545) ^ [_1420500, _1420502, _1420504, _1420506, _1420508, _1420510] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420500, tc_fun(_1420502, tc_HOL_Obool))), _1420504), _1420506), _1420508), _1420510)), -(hBOOL(hAPP(hAPP(_1420504, _1420508), _1420510)))], (43609 ^ _776545) ^ [_1646427, _1646429, _1646431] : [hAPP(hAPP(c_List_Oappend(_1646427), _1646429), _1646431) = c_List_Olist_ONil(_1646427), 43612 ^ _776545 : [(43615 ^ _776545) ^ [] : [-(_1646431 = c_List_Olist_ONil(_1646427))], (43613 ^ _776545) ^ [] : [-(_1646429 = c_List_Olist_ONil(_1646427))]]], (48692 ^ _776545) ^ [_1758022, _1758024, _1758026] : [c_List_Oreplicate(_1758022, _1758024, _1758026) = c_List_Olist_ONil(_1758022), -(_1758024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8729 ^ _776545) ^ [_926537, _926539, _926541] : [class_Lattices_Osemilattice__inf(_926537), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926537), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926537), _926539), _926541)), _926541)))], (18180 ^ _776545) ^ [_1103362, _1103364, _1103366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1103362), _1103364)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103364), _1103362))), _1103366) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1103364)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1103362), _1103366)))], (6553 ^ _776545) ^ [_882426, _882428, _882430, _882432, _882434] : [class_Orderings_Oord(_882426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882428, _882426)), _882430), _882432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882426), hAPP(_882430, _882434)), hAPP(_882432, _882434))))], (51539 ^ _776545) ^ [_1819441, _1819443, _1819445] : [class_Divides_Osemiring__div(_1819441), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819441), _1819443), _1819445)), -(c_Divides_Odiv__class_Omod(_1819441, _1819445, _1819443) = c_Groups_Ozero__class_Ozero(_1819441))], (39874 ^ _776545) ^ [_1552437, _1552439, _1552441, _1552443, _1552445] : [c_Fun_Oinj__on(_1552437, _1552439, _1552441, c_Orderings_Otop__class_Otop(tc_fun(_1552437, tc_HOL_Obool))), c_Fun_Oinj__on(_1552443, _1552437, _1552445, c_Orderings_Otop__class_Otop(tc_fun(_1552443, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1552443, _1552439, hAPP(c_Fun_Ocomp(_1552437, _1552439, _1552443, _1552441), _1552445), c_Orderings_Otop__class_Otop(tc_fun(_1552443, tc_HOL_Obool))))], (7946 ^ _776545) ^ [_910851, _910853, _910855] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910851, tc_HOL_Obool)), _910853), _910855) = _910855, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910851, tc_HOL_Obool)), _910853), _910855)))], (8637 ^ _776545) ^ [_924972, _924974, _924976, _924978] : [class_Lattices_Osemilattice__inf(_924972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), _924974), _924976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), _924974), _924978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924972), _924974), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924972), _924976), _924978))))], (6430 ^ _776545) ^ [_880427, _880429, _880431, _880433] : [hBOOL(hAPP(hAPP(c_member(_880427), _880429), _880431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880427, tc_HOL_Obool)), _880431), _880433)), -(hBOOL(hAPP(hAPP(c_member(_880427), _880429), _880433)))], (7786 ^ _776545) ^ [_907350, _907352, _907354, _907356] : [hBOOL(hAPP(hAPP(c_member(_907350), _907352), _907354)), -(hBOOL(hAPP(hAPP(c_member(_907350), _907352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907350, tc_HOL_Obool)), _907356), _907354))))], (43890 ^ _776545) ^ [_1653466, _1653468] : [hBOOL(hAPP(c_List_Odistinct(_1653466), _1653468)), -(hBOOL(hAPP(c_List_Odistinct(_1653466), hAPP(c_List_Orotate1(_1653466), _1653468))))], (11987 ^ _776545) ^ [_987132, _987134, _987136, _987138, _987140] : [11989 ^ _776545 : [(11995 ^ _776545) ^ [] : [hBOOL(hAPP(_987140, 11991 ^ [_987132, _987134, _987136, _987138, _987140]))], (11993 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987132), 11991 ^ [_987132, _987134, _987136, _987138, _987140]), hAPP(_987138, 11988 ^ [_987132, _987134, _987136, _987138, _987140]))))], (11990 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987134), 11988 ^ [_987132, _987134, _987136, _987138, _987140]), _987136)))]], 11996 ^ _776545 : [(11997 ^ _776545) ^ [_987442] : [hBOOL(hAPP(hAPP(c_member(_987132), _987442), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987134, tc_fun(_987132, tc_HOL_Obool)), _987136), _987138))), -(hBOOL(hAPP(_987140, _987442)))]]], (5016 ^ _776545) ^ [_853002, _853004, _853006, _853008, _853010, _853012, _853014, _853016] : [-(c_Fun_Othe__inv__into(_853016, _853012, _853008, _853004) = c_Fun_Othe__inv__into(_853014, _853010, _853006, _853002)), _853016 = _853014, _853012 = _853010, _853008 = _853006, _853004 = _853002], (41714 ^ _776545) ^ [_1597953] : [-(c_Nitpick_Onum(_1597953) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1597953, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1597953)))], (14823 ^ _776545) ^ [_1043845, _1043847, _1043849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043845), _1043847)), _1043849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043845), _1043849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043847), _1043849)))], (4252 ^ _776545) ^ [_840964, _840966, _840968, _840970] : [-(c_List_Olast(_840970, _840966) = c_List_Olast(_840968, _840964)), _840970 = _840968, _840966 = _840964], (22351 ^ _776545) ^ [_1181778, _1181780] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181778), _1181780) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1181778), _1181780)))], (22291 ^ _776545) ^ [_1180694, _1180696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180694), _1180696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180696), _1180694)), -(_1180694 = _1180696)], (33257 ^ _776545) ^ [_1386177, _1386179, _1386181, _1386183] : [-(_1386177 = c_Orderings_Obot__class_Obot(tc_fun(_1386179, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386179, tc_fun(_1386181, tc_HOL_Obool)), _1386177), hAPP(c_COMBK(tc_fun(_1386181, tc_HOL_Obool), _1386179), _1386183)) = _1386183)], (46095 ^ _776545) ^ [_1702358, _1702360, _1702362] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1702358), tc_List_Olist(_1702358)), c_List_Opartition(_1702358, _1702360, _1702362)) = hAPP(c_List_Ofilter(_1702358, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1702358, c_fNot), _1702360)), _1702362))], (34185 ^ _776545) ^ [_1411967, _1411969] : [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(_1411969))), 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), _1411967)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411967)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411969))))], (48136 ^ _776545) ^ [_1745919, _1745921, _1745923, _1745925] : [48137 ^ _776545 : [(48140 ^ _776545) ^ [] : [c_List_Olist__ex(_1745919, _1745921, _1745925)], (48138 ^ _776545) ^ [] : [hBOOL(hAPP(_1745921, _1745923))]], -(c_List_Olist__ex(_1745919, _1745921, hAPP(hAPP(c_List_Olist_OCons(_1745919), _1745923), _1745925)))], (26487 ^ _776545) ^ [_1254620, _1254622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254622)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254620), _1254622)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254620)), hAPP(c_Int_Onat, _1254622)))], (41672 ^ _776545) ^ [_1597066, _1597068, _1597070] : [-(c_Nitpick_Otimes__frac(_1597066, _1597068, _1597070) = hAPP(hAPP(c_Nitpick_Ofrac(_1597066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597066), _1597068)), hAPP(c_Nitpick_Onum(_1597066), _1597070))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1597066), _1597068)), hAPP(c_Nitpick_Odenom(_1597066), _1597070))))], (18814 ^ _776545) ^ [_1115488, _1115490, _1115492, _1115494] : [class_Groups_Ocomm__monoid__mult(_1115488), 18817 ^ _776545 : [(18824 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115490), _1115492))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115490, _1115488), _1115494), _1115492) = c_Groups_Oone__class_Oone(_1115488))], (18818 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1115490), _1115492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115490, _1115488), _1115494), _1115492) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115488, _1115490, c_Groups_Otimes__class_Otimes(_1115488)), _1115494), c_Groups_Oone__class_Oone(_1115488)), _1115492))]]], (43114 ^ _776545) ^ [_1635556, _1635558] : [c_Orderings_Obot__class_Obot(tc_fun(_1635556, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635556), _1635558), -(_1635558 = c_List_Olist_ONil(_1635556))], (23145 ^ _776545) ^ [_1195869, _1195871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195869)), -(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), _1195869), _1195871))))], (42403 ^ _776545) ^ [_1618298, _1618300, _1618302, _1618304, _1618306] : [hBOOL(hAPP(hAPP(c_member(_1618298), _1618300), hAPP(c_List_Oset(_1618298), _1618302))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1618304), hAPP(_1618306, _1618300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1618304), c_List_Olist_Olist__size(_1618298, _1618306, _1618302))))], (46327 ^ _776545) ^ [_1708257, _1708259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708257), _1708259)), -(c_List_Oupt(_1708257, hAPP(c_Nat_OSuc, _1708259)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1708257, _1708259)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1708259), c_List_Olist_ONil(tc_Nat_Onat))))], (32338 ^ _776545) ^ [_1358158, _1358160, _1358162, _1358164, _1358166, _1358168] : [hBOOL(hAPP(hAPP(c_member(_1358158), _1358160), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358162, tc_fun(_1358158, tc_HOL_Obool)), _1358164), _1358166))), -(hBOOL(hAPP(hAPP(c_member(_1358158), _1358160), hAPP(_1358166, _1358168)))), hBOOL(hAPP(hAPP(c_member(_1358162), _1358168), _1358164))], (45030 ^ _776545) ^ [_1678423, _1678425] : [_1678423 = _1678425, -(hAPP(c_Code__Numeral_Oof__nat, _1678423) = hAPP(c_Code__Numeral_Oof__nat, _1678425))], (37830 ^ _776545) ^ [] : [-(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))))], (38509 ^ _776545) ^ [_1514834, _1514836] : [-(hAPP(c_Relation_ORange(_1514834, _1514836), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514834, _1514836), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1514836, tc_HOL_Obool)))], (27633 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (32630 ^ _776545) ^ [_1368460, _1368462, _1368464, _1368466, _1368468] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368460, tc_HOL_Obool)), _1368462), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368464, tc_fun(_1368460, tc_HOL_Obool)), _1368466), _1368468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368464, tc_fun(_1368460, tc_HOL_Obool)), _1368466), hAPP(hAPP(c_COMBB(tc_fun(_1368460, tc_HOL_Obool), tc_fun(_1368460, tc_HOL_Obool), _1368464), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368460, tc_HOL_Obool)), _1368462)), _1368468)))], (39285 ^ _776545) ^ [_1535774, _1535776, _1535778] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535774), _1535776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535774, _1535774), tc_HOL_Obool)), _1535778), hAPP(hAPP(c_Product__Type_OSigma(_1535774, _1535774), _1535776), hAPP(c_COMBK(tc_fun(_1535774, tc_HOL_Obool), _1535774), _1535776)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1535774, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1535774), _1535776), _1535778))))], (42947 ^ _776545) ^ [_1632523, _1632525] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1632523), _1632525))), -(c_Nitpick_Ocard_H(_1632523, _1632525) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9906 ^ _776545) ^ [_946284, _946286, _946288] : [class_Orderings_Oorder(_946284), 9909 ^ _776545 : [(9916 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946284), _946286), _946288))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_946284, _946286, _946288) = c_Orderings_Obot__class_Obot(tc_fun(_946284, tc_HOL_Obool)))], (9910 ^ _776545) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_946284, _946286, _946288) = c_Orderings_Obot__class_Obot(tc_fun(_946284, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946284), _946286), _946288))]]], (50343 ^ _776545) ^ [_1794389, _1794391, _1794393, _1794395, _1794397] : [c_Fun_Obij__betw(_1794389, _1794391, _1794393, c_Orderings_Otop__class_Otop(tc_fun(_1794389, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794391, tc_HOL_Obool))), c_Fun_Obij__betw(_1794391, _1794395, _1794397, c_Orderings_Otop__class_Otop(tc_fun(_1794391, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794395, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1794389, _1794395, hAPP(c_Fun_Ocomp(_1794391, _1794395, _1794389, _1794397), _1794393), c_Orderings_Otop__class_Otop(tc_fun(_1794389, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794395, tc_HOL_Obool))))], (26877 ^ _776545) ^ [_1260828, _1260830] : [class_Int_Oring__char__0(_1260828), 26880 ^ _776545 : [(26887 ^ _776545) ^ [] : [_1260830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1260828), _1260830) = c_Groups_Ozero__class_Ozero(_1260828))], (26881 ^ _776545) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1260828), _1260830) = c_Groups_Ozero__class_Ozero(_1260828), -(_1260830 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25187 ^ _776545) ^ [_1232588, _1232590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1232588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232590), _1232588)), _1232590)))], (24954 ^ _776545) ^ [_1228416, _1228418, _1228420] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228416), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228418, _1228420)), _1228420) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228416), _1228418), _1228420))], (29897 ^ _776545) ^ [_1312587, _1312589, _1312591] : [class_Divides_Osemiring__div(_1312587), -(_1312589 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312587), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1312587), _1312589), _1312591)), _1312591)), c_Divides_Odiv__class_Omod(_1312587, _1312589, _1312591)))], (34135 ^ _776545) ^ [_1410822] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410822))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1410822)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32610 ^ _776545) ^ [_1367851, _1367853, _1367855, _1367857, _1367859] : [_1367851 = c_Orderings_Obot__class_Obot(tc_fun(_1367853, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367855, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367853, tc_fun(_1367855, tc_HOL_Obool)), _1367851), _1367857)), _1367859) = _1367859)], (46199 ^ _776545) ^ [_1704745, _1704747] : [-(c_List_Oconcat(tc_List_Olist(_1704745), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704745), tc_List_Olist(tc_List_Olist(_1704745))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704745)), _1704745, c_List_Olist_ONil(tc_List_Olist(_1704745)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704745), tc_List_Olist(tc_List_Olist(_1704745))), _1704745), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704745), tc_List_Olist(tc_List_Olist(_1704745)), tc_List_Olist(tc_List_Olist(_1704745))), c_List_Olist_OCons(tc_List_Olist(_1704745))), c_List_Olist_ONil(tc_List_Olist(_1704745)))))), _1704747)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704745), tc_List_Olist(_1704745)), c_List_Otl(_1704745)), hAPP(c_List_Ofilter(tc_List_Olist(_1704745), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1704745)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704745), tc_List_Olist(_1704745), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1704745)))), _1704747)))], (33701 ^ _776545) ^ [_1399412, _1399414, _1399416] : [-(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)), _1399412)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1399414, _1399416)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399414), _1399412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399416), _1399412)))], (41062 ^ _776545) ^ [_1581302] : [-(hAPP(c_Relation_Oconverse(_1581302, _1581302), c_Relation_OId(_1581302)) = c_Relation_OId(_1581302))], (27581 ^ _776545) ^ [_1272685] : [class_Int_Onumber__ring(_1272685), -(c_Groups_Ozero__class_Ozero(_1272685) = hAPP(c_Int_Onumber__class_Onumber__of(_1272685), c_Int_OPls))], (44314 ^ _776545) ^ [_1662715, _1662717, _1662719, _1662721, _1662723] : [class_Orderings_Olinorder(_1662715), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662717)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662717, _1662715, _1662719), _1662721), _1662723)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662717)), _1662723)))], (43184 ^ _776545) ^ [_1636788, _1636790] : [-(c_List_Osublist(_1636788, _1636790, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1636788))], (7792 ^ _776545) ^ [_907502, _907504, _907506, _907508] : [hBOOL(hAPP(hAPP(c_member(_907502), _907504), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907502, tc_HOL_Obool)), _907506), _907508))), 7795 ^ _776545 : [(7798 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907502), _907504), _907508)))], (7796 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907502), _907504), _907506)))]]], (37971 ^ _776545) ^ [_1501853, _1501855, _1501857, _1501859] : [hAPP(hAPP(c_Relation_Orel__comp(_1501853, _1501853, _1501853), _1501855), _1501857) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501853, _1501853), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501853, _1501853, _1501853), _1501859), _1501857) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501853, _1501853), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1501853, _1501853, _1501853), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501853, _1501853), tc_HOL_Obool)), _1501855), _1501859)), _1501857) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501853, _1501853), tc_HOL_Obool)))], (35282 ^ _776545) ^ [_1434926] : [-(_1434926 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1434926), 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)))))], (40847 ^ _776545) ^ [_1576189, _1576191, _1576193] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576189, _1576189)), hAPP(hAPP(c_Product__Type_OPair(_1576189, _1576189), _1576191), _1576193)), c_Relation_OId(_1576189))), -(_1576191 = _1576193)], (5004 ^ _776545) ^ [_852832, _852834] : [_852834 = _852832, -(c_Groups_Ouminus__class_Ouminus(_852834) = c_Groups_Ouminus__class_Ouminus(_852832))], (24800 ^ _776545) ^ [_1225150, _1225152, _1225154, _1225156] : [class_Divides_Osemiring__div(_1225150), -(c_Divides_Odiv__class_Omod(_1225150, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225150), _1225152), _1225154), _1225156) = c_Divides_Odiv__class_Omod(_1225150, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225150), c_Divides_Odiv__class_Omod(_1225150, _1225152, _1225156)), c_Divides_Odiv__class_Omod(_1225150, _1225154, _1225156)), _1225156))], (13294 ^ _776545) ^ [_1012197, _1012199, _1012201, _1012203] : [-(hBOOL(hAPP(hAPP(c_member(_1012197), _1012199), _1012201))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012197, tc_Nat_Onat), _1012203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012197, tc_HOL_Obool)), _1012201), hAPP(hAPP(c_Set_Oinsert(_1012197), _1012199), c_Orderings_Obot__class_Obot(tc_fun(_1012197, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012197, tc_Nat_Onat), _1012203), _1012201))], (10505 ^ _776545) ^ [_957075, _957077, _957079] : [hBOOL(hAPP(hAPP(c_member(_957075), _957077), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957075, tc_HOL_Obool)), _957079))), hBOOL(hAPP(hAPP(c_member(_957075), _957077), _957079))], (39538 ^ _776545) ^ [_1543341, _1543343, _1543345, _1543347, _1543349, _1543351] : [-(_1543341 = c_Orderings_Obot__class_Obot(tc_fun(_1543343, tc_HOL_Obool))), 39544 ^ _776545 : [(39547 ^ _776545) ^ [] : [c_Fun_Oinj__on(_1543345, _1543347, _1543349, hAPP(_1543351, 39543 ^ [_1543341, _1543343, _1543345, _1543347, _1543349, _1543351]))], (39545 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543343), 39543 ^ [_1543341, _1543343, _1543345, _1543347, _1543349, _1543351]), _1543341)))]], -(c_Fun_Oinj__on(_1543345, _1543347, _1543349, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1543343, tc_fun(_1543345, tc_HOL_Obool)), _1543341), _1543351)))], (36502 ^ _776545) ^ [_1467366, _1467368, _1467370, _1467372, _1467374, _1467376] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467366, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1467368, _1467366, _1467370), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1467372, tc_fun(_1467368, tc_HOL_Obool)), _1467374), _1467376))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1467372, tc_fun(_1467366, tc_HOL_Obool)), _1467374), hAPP(hAPP(c_COMBB(tc_fun(_1467368, tc_HOL_Obool), tc_fun(_1467366, tc_HOL_Obool), _1467372), c_Relation_OImage(_1467368, _1467366, _1467370)), _1467376)))))], (18570 ^ _776545) ^ [_1110730, _1110732, _1110734] : [-(hBOOL(hAPP(_1110730, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110732), _1110734)))), 18573 ^ _776545 : [(18576 ^ _776545) ^ [] : [hBOOL(hAPP(_1110730, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18574 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110732), _1110734)))]], 18578 ^ _776545 : [(18581 ^ _776545) ^ [] : [hBOOL(hAPP(_1110730, 18577 ^ [_1110730, _1110732, _1110734]))], (18579 ^ _776545) ^ [] : [-(_1110732 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110734), 18577 ^ [_1110730, _1110732, _1110734]))]]], (33457 ^ _776545) ^ [_1391755, _1391757, _1391759] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391755, tc_Nat_Onat), _1391757), _1391759)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391755, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1391755), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1391757)), _1391759))], (24914 ^ _776545) ^ [_1227659, _1227661, _1227663, _1227665] : [class_Divides_Oring__div(_1227659), c_Divides_Odiv__class_Omod(_1227659, _1227661, _1227663) = c_Divides_Odiv__class_Omod(_1227659, _1227665, _1227663), -(c_Divides_Odiv__class_Omod(_1227659, hAPP(c_Groups_Ouminus__class_Ouminus(_1227659), _1227661), _1227663) = c_Divides_Odiv__class_Omod(_1227659, hAPP(c_Groups_Ouminus__class_Ouminus(_1227659), _1227665), _1227663))], (5945 ^ _776545) ^ [_871121, _871123, _871125, _871127, _871129, _871131] : [c_Typedef_Otype__definition(_871121, _871123, _871125, _871127, _871129), 5949 ^ _776545 : [(5952 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871123), 5948 ^ [_871121, _871123, _871125, _871127, _871129, _871131]), _871129)))], (5950 ^ _776545) ^ [] : [-(_871131 = hAPP(_871127, 5948 ^ [_871121, _871123, _871125, _871127, _871129, _871131]))]]], (18105 ^ _776545) ^ [_1102089, _1102091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102089), _1102091)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102089), _1102091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36535 ^ _776545) ^ [_1468282, _1468284, _1468286] : [class_Rings_Oring__1(_1468282), -(hAPP(c_Int_Oring__1__class_Oof__int(_1468282), 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), _1468284), _1468286)), 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(_1468282), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468282), _1468284)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1468282), _1468286)))], (38146 ^ _776545) ^ [_1507072, _1507074, _1507076, _1507078, _1507080, _1507082, _1507084] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1507072, _1507074, _1507076, _1507078, _1507080), _1507082), _1507084)), 38150 ^ _776545 : [(38153 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1507080, 38149 ^ [_1507072, _1507074, _1507076, _1507078, _1507080, _1507082, _1507084]), _1507084)))], (38151 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1507078, _1507082), 38149 ^ [_1507072, _1507074, _1507076, _1507078, _1507080, _1507082, _1507084])))]]], (15788 ^ _776545) ^ [_1062631] : [15789 ^ _776545 : [(15790 ^ _776545) ^ [_1062673] : [_1062631 = hAPP(c_Nat_OSuc, _1062673)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062631)))], (47460 ^ _776545) ^ [_1730902, _1730904, _1730906, _1730908, _1730910] : [class_Groups_Omonoid__add(_1730902), 47466 ^ _776545 : [(47471 ^ _776545) ^ [] : [hAPP(_1730910, 47465 ^ [_1730902, _1730904, _1730906, _1730908, _1730910]) = c_Groups_Ozero__class_Ozero(_1730902)], (47469 ^ _776545) ^ [] : [hBOOL(hAPP(_1730908, 47465 ^ [_1730902, _1730904, _1730906, _1730908, _1730910]))], (47467 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730904), 47465 ^ [_1730902, _1730904, _1730906, _1730908, _1730910]), hAPP(c_List_Oset(_1730904), _1730906))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1730902), hAPP(hAPP(c_List_Omap(_1730904, _1730902), _1730910), hAPP(c_List_Ofilter(_1730904, _1730908), _1730906))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1730902), hAPP(hAPP(c_List_Omap(_1730904, _1730902), _1730910), _1730906)))], (1992 ^ _776545) ^ [_805200, _805202] : [_805202 = _805200, -(c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_805202) = c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_805200))], (43012 ^ _776545) ^ [_1633858, _1633860, _1633862] : [hBOOL(hAPP(c_List_Odistinct(_1633858), _1633860)), -(hBOOL(hAPP(c_List_Odistinct(_1633858), c_List_Oremove1(_1633858, _1633862, _1633860))))], (14710 ^ _776545) ^ [_1041687, _1041689] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041687), _1041689))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041687), _1041689)), -(_1041687 = _1041689)], (48961 ^ _776545) ^ [_1763714, _1763716, _1763718, _1763720] : [class_Groups_Ocomm__monoid__add(_1763714), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1763716, tc_HOL_Obool)), _1763718)), 48971 ^ _776545 : [(48974 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1763716), 48970 ^ [_1763714, _1763716, _1763718, _1763720]))], (48972 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763716, tc_HOL_Obool)), 48970 ^ [_1763714, _1763716, _1763718, _1763720]), _1763718)))]], 48978 ^ _776545 : [(48982 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763716, tc_HOL_Obool)), 48980 ^ [_1763714, _1763716, _1763718, _1763720]), _1763718)))], (48979 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1763716, tc_HOL_Obool)), 48977 ^ [_1763714, _1763716, _1763718, _1763720]), _1763718)))], (48991 ^ _776545) ^ [] : [hAPP(_1763720, 48985 ^ [_1763714, _1763716, _1763718, _1763720]) = c_Groups_Ozero__class_Ozero(_1763714)], (48987 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763716), 48985 ^ [_1763714, _1763716, _1763718, _1763720]), 48977 ^ [_1763714, _1763716, _1763718, _1763720])))], (48989 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1763716), 48985 ^ [_1763714, _1763716, _1763718, _1763720]), 48980 ^ [_1763714, _1763716, _1763718, _1763720])))], (48984 ^ _776545) ^ [] : [48977 ^ [_1763714, _1763716, _1763718, _1763720] = 48980 ^ [_1763714, _1763716, _1763718, _1763720]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1763716, _1763714), _1763720), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1763716, tc_HOL_Obool), _1763718)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1763716, tc_HOL_Obool), _1763714), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1763716, _1763714), _1763720)), _1763718))], (46117 ^ _776545) ^ [_1702846, _1702848, _1702850] : [hAPP(c_List_Ofilter(_1702846, _1702848), _1702850) = c_List_Olist_ONil(_1702846), 46120 ^ _776545 : [(46121 ^ _776545) ^ [_1702943] : [hBOOL(hAPP(hAPP(c_member(_1702846), _1702943), hAPP(c_List_Oset(_1702846), _1702850))), hBOOL(hAPP(_1702848, _1702943))]]], (37688 ^ _776545) ^ [_1494263, _1494265, _1494267, _1494269, _1494271] : [-(c_Fun_Oinj__on(_1494263, _1494265, _1494267, hAPP(hAPP(c_Set_Oinsert(_1494263), _1494269), _1494271))), c_Fun_Oinj__on(_1494263, _1494265, _1494267, _1494271), -(hBOOL(hAPP(hAPP(c_member(_1494265), hAPP(_1494267, _1494269)), hAPP(c_Set_Oimage(_1494263, _1494265, _1494267), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494263, tc_HOL_Obool)), _1494271), hAPP(hAPP(c_Set_Oinsert(_1494263), _1494269), c_Orderings_Obot__class_Obot(tc_fun(_1494263, tc_HOL_Obool))))))))], (48288 ^ _776545) ^ [_1749084, _1749086, _1749088, _1749090] : [-(c_List_Olist__all(_1749084, _1749086, hAPP(hAPP(c_List_Olist_OCons(_1749084), _1749088), _1749090))), hBOOL(hAPP(_1749086, _1749088)), c_List_Olist__all(_1749084, _1749086, _1749090)], (14290 ^ _776545) ^ [_1033924, _1033926, _1033928, _1033930] : [class_Rings_Ocomm__semiring__1(_1033924), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033924), _1033926), _1033928)), _1033930) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033924), _1033926), _1033930)), _1033928))], (25285 ^ _776545) ^ [_1234218, _1234220] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234218, _1234220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234218, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234220)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234218, _1234220)), _1234220))], (38705 ^ _776545) ^ [_1520446, _1520448, _1520450, _1520452] : [hAPP(c_Set_Oimage(_1520446, _1520448, _1520450), c_Orderings_Otop__class_Otop(tc_fun(_1520446, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1520448, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1520446, _1520448, _1520450), hAPP(c_Set_Ovimage(_1520446, _1520448, _1520450), _1520452)) = _1520452)], (35594 ^ _776545) ^ [_1440849, _1440851, _1440853, _1440855] : [-(_1440849 = _1440851), hAPP(c_Product__Type_Ofst(_1440853, _1440855), _1440849) = hAPP(c_Product__Type_Ofst(_1440853, _1440855), _1440851), hAPP(c_Product__Type_Osnd(_1440853, _1440855), _1440849) = hAPP(c_Product__Type_Osnd(_1440853, _1440855), _1440851)], (6536 ^ _776545) ^ [_882080, _882082, _882084, _882086] : [class_Orderings_Oord(_882080), 6539 ^ _776545 : [(6546 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882080), hAPP(_882084, 6547 ^ [_882080, _882082, _882084, _882086])), hAPP(_882086, 6547 ^ [_882080, _882082, _882084, _882086]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882082, _882080)), _882084), _882086)))], (6540 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882082, _882080)), _882084), _882086)), 6543 ^ _776545 : [(6544 ^ _776545) ^ [_882237] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882080), hAPP(_882084, _882237)), hAPP(_882086, _882237))))]]]]], (20763 ^ _776545) ^ [_1151410, _1151412, _1151414, _1151416] : [class_Fields_Ofield__inverse__zero(_1151410), -(_1151412 = c_Groups_Ozero__class_Ozero(_1151410)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151410), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151410), _1151414), _1151412)), _1151416) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151410), _1151414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151410), _1151416), _1151412))), _1151412))], (50971 ^ _776545) ^ [_1808808, _1808810] : [class_Rings_Ocomm__semiring__1(_1808808), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808808), _1808810), c_Groups_Ozero__class_Ozero(_1808808))))], (29377 ^ _776545) ^ [_1302971, _1302973, _1302975] : [class_Rings_Olinordered__semidom(_1302971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302971), hAPP(hAPP(c_Power_Opower__class_Opower(_1302971), _1302973), 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(_1302971), _1302975), 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(_1302971), c_Groups_Ozero__class_Ozero(_1302971)), _1302975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302971), _1302973), _1302975)))], (15648 ^ _776545) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18892 ^ _776545) ^ [_1116811, _1116813, _1116815] : [class_Rings_Olinordered__ring__strict(_1116811), 18895 ^ _776545 : [(18896 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116811), c_Groups_Ozero__class_Ozero(_1116811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116811), _1116813), _1116813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116811), _1116815), _1116815)))), _1116813 = c_Groups_Ozero__class_Ozero(_1116811), _1116815 = c_Groups_Ozero__class_Ozero(_1116811)], (18906 ^ _776545) ^ [] : [18907 ^ _776545 : [(18910 ^ _776545) ^ [] : [-(_1116815 = c_Groups_Ozero__class_Ozero(_1116811))], (18908 ^ _776545) ^ [] : [-(_1116813 = c_Groups_Ozero__class_Ozero(_1116811))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116811), c_Groups_Ozero__class_Ozero(_1116811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116811), _1116813), _1116813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116811), _1116815), _1116815)))))]]], (44807 ^ _776545) ^ [_1672750, _1672752, _1672754, _1672756, _1672758, _1672760, _1672762] : [hAPP(hAPP(c_List_Omap(_1672750, _1672752), _1672754), _1672756) = hAPP(hAPP(c_List_Omap(_1672758, _1672752), _1672760), _1672762), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672750)), _1672756) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672758)), _1672762))], (38404 ^ _776545) ^ [_1512771, _1512773, _1512775] : [c_Wellfounded_Owf(_1512771, _1512773), -(c_Wellfounded_Owf(tc_List_Olist(_1512771), hAPP(c_List_Olexn(_1512771, _1512773), _1512775)))], (22149 ^ _776545) ^ [_1178184, _1178186] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178186)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178184), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178186))))], (22413 ^ _776545) ^ [_1182853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1182853)))], (25840 ^ _776545) ^ [_1244011] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244011))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244011)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28219 ^ _776545) ^ [_1283219, _1283221, _1283223] : [class_Int_Onumber__ring(_1283219), 28222 ^ _776545 : [(28229 ^ _776545) ^ [] : [c_Int_Oiszero(_1283219, hAPP(c_Int_Onumber__class_Onumber__of(_1283219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283221), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1283223)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1283219), _1283221) = hAPP(c_Int_Onumber__class_Onumber__of(_1283219), _1283223))], (28223 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283219), _1283221) = hAPP(c_Int_Onumber__class_Onumber__of(_1283219), _1283223), -(c_Int_Oiszero(_1283219, hAPP(c_Int_Onumber__class_Onumber__of(_1283219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283221), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1283223)))))]]], (28037 ^ _776545) ^ [_1280323, _1280325] : [class_Int_Onumber__ring(_1280323), 28040 ^ _776545 : [(28047 ^ _776545) ^ [] : [c_Int_Oiszero(_1280323, hAPP(c_Int_Onumber__class_Onumber__of(_1280323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280325), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1280323), _1280325) = c_Groups_Ozero__class_Ozero(_1280323))], (28041 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1280323), _1280325) = c_Groups_Ozero__class_Ozero(_1280323), -(c_Int_Oiszero(_1280323, hAPP(c_Int_Onumber__class_Onumber__of(_1280323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1280325), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (37608 ^ _776545) ^ [_1492465, _1492467, _1492469, _1492471, _1492473, _1492475] : [c_Fun_Oinj__on(_1492465, _1492467, _1492469, _1492471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492465, tc_HOL_Obool)), _1492473), _1492471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492465, tc_HOL_Obool)), _1492475), _1492471)), -(hAPP(c_Set_Oimage(_1492465, _1492467, _1492469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492465, tc_HOL_Obool)), _1492473), _1492475)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492467, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492465, _1492467, _1492469), _1492473)), hAPP(c_Set_Oimage(_1492465, _1492467, _1492469), _1492475)))], (48524 ^ _776545) ^ [_1754294, _1754296, _1754298, _1754300, _1754302] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754294, _1754296, _1754298), _1754300), _1754302)), -(hBOOL(hAPP(hAPP(_1754298, _1754302), _1754300)))], (48566 ^ _776545) ^ [_1755714, _1755716, _1755718] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755714)), c_List_Oreplicate(_1755714, _1755716, _1755718)) = _1755716)], (13814 ^ _776545) ^ [_1022854, _1022856, _1022858] : [class_Groups_Oab__group__add(_1022854), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1022854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022854), _1022856), _1022858)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022854), hAPP(c_Groups_Ouminus__class_Ouminus(_1022854), _1022856)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022854), _1022858)))], (38237 ^ _776545) ^ [_1508756] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1508756)))], (37078 ^ _776545) ^ [_1481177, _1481179, _1481181, _1481183, _1481185, _1481187] : [c_Equiv__Relations_Ocongruent(_1481177, _1481179, _1481181, _1481183), hBOOL(hAPP(hAPP(c_member(tc_prod(_1481177, _1481177)), hAPP(hAPP(c_Product__Type_OPair(_1481177, _1481177), _1481185), _1481187)), _1481181)), -(hAPP(_1481183, _1481185) = hAPP(_1481183, _1481187))], (32374 ^ _776545) ^ [_1358937, _1358939, _1358941] : [32375 ^ _776545 : [(32378 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358937), hAPP(c_Set_OCollect(_1358937), _1358941)))], (32376 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358937), hAPP(c_Set_OCollect(_1358937), _1358939)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1358937), hAPP(c_Set_OCollect(_1358937), hAPP(hAPP(c_COMBS(_1358937, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1358937), c_fconj), _1358939)), _1358941)))))], (41236 ^ _776545) ^ [_1585722, _1585724, _1585726] : [c_Relation_Ototal__on(_1585722, _1585724, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1585722, _1585722), tc_HOL_Obool)), _1585726), c_Relation_OId(_1585722))), -(c_Relation_Ototal__on(_1585722, _1585724, _1585726))], (2166 ^ _776545) ^ [_807971, _807973] : [_807973 = _807971, -(c_Int_Osucc(_807973) = c_Int_Osucc(_807971))], (25865 ^ _776545) ^ [_1244370, _1244372] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244370), _1244372) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244370, _1244372)), _1244372))], (26655 ^ _776545) ^ [_1257667, _1257669] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257667)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257667)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257669)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257667)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257669))))], (37016 ^ _776545) ^ [_1479939, _1479941] : [c_Equiv__Relations_Oequivp(_1479939, _1479941), 37019 ^ _776545 : [(37026 ^ _776545) ^ [_1480132, _1480134] : [hAPP(_1479941, _1480134) = hAPP(_1479941, _1480132), -(hBOOL(hAPP(hAPP(_1479941, _1480134), _1480132)))], (37020 ^ _776545) ^ [_1480033, _1480035] : [hBOOL(hAPP(hAPP(_1479941, _1480035), _1480033)), -(hAPP(_1479941, _1480035) = hAPP(_1479941, _1480033))]]], (26014 ^ _776545) ^ [_1246818, _1246820] : [26015 ^ _776545 : [(26016 ^ _776545) ^ [_1246867] : [_1246818 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246820), _1246867)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246818, _1246820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52205 ^ _776545) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (21217 ^ _776545) ^ [_1160242, _1160244, _1160246] : [class_Int_Onumber__ring(_1160242), class_Rings_Olinordered__idom(_1160242), 21224 ^ _776545 : [(21231 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160244), _1160246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160242), hAPP(c_Int_Onumber__class_Onumber__of(_1160242), _1160244)), hAPP(c_Int_Onumber__class_Onumber__of(_1160242), _1160246))))], (21225 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160242), hAPP(c_Int_Onumber__class_Onumber__of(_1160242), _1160244)), hAPP(c_Int_Onumber__class_Onumber__of(_1160242), _1160246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160244), _1160246)))]]], (43050 ^ _776545) ^ [_1634483, _1634485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634483), _1634485)), -(c_List_Oupto(_1634485, _1634483) = c_List_Olist_ONil(tc_Int_Oint))], (8467 ^ _776545) ^ [_921987, _921989, _921991, _921993] : [class_Lattices_Osemilattice__sup(_921987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921987), _921989), _921991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921987), _921993), _921991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921987), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921987), _921989), _921993)), _921991)))], (42869 ^ _776545) ^ [_1630639, _1630641] : [hAPP(c_Finite__Set_Ocard(_1630639), hAPP(c_List_Oset(_1630639), _1630641)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630639)), _1630641), -(hBOOL(hAPP(c_List_Odistinct(_1630639), _1630641)))], (52199 ^ _776545) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (28921 ^ _776545) ^ [_1295014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1295014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1295014))))], (11467 ^ _776545) ^ [_976845] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_976845), c_Orderings_Obot__class_Obot(tc_fun(_976845, tc_HOL_Obool)))))], (32456 ^ _776545) ^ [_1360906, _1360908, _1360910, _1360912, _1360914] : [-(_1360906 = c_Orderings_Obot__class_Obot(tc_fun(_1360908, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360908, tc_fun(_1360910, tc_HOL_Obool)), _1360906), hAPP(hAPP(c_COMBC(_1360908, tc_fun(_1360910, tc_HOL_Obool), tc_fun(_1360910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360910, tc_HOL_Obool), tc_fun(tc_fun(_1360910, tc_HOL_Obool), tc_fun(_1360910, tc_HOL_Obool)), _1360908), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360910, tc_HOL_Obool))), _1360912)), _1360914)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360910, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360908, tc_fun(_1360910, tc_HOL_Obool)), _1360906), _1360912)), _1360914))], (27939 ^ _776545) ^ [_1278735, _1278737] : [class_Int_Onumber__ring(_1278735), class_Rings_Olinordered__idom(_1278735), 27946 ^ _776545 : [(27953 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1278737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278735), c_Groups_Ozero__class_Ozero(_1278735)), hAPP(c_Int_Onumber__class_Onumber__of(_1278735), _1278737))))], (27947 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278735), c_Groups_Ozero__class_Ozero(_1278735)), hAPP(c_Int_Onumber__class_Onumber__of(_1278735), _1278737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1278737)))]]], (18862 ^ _776545) ^ [_1116418, _1116420] : [_1116418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116418), _1116420) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29391 ^ _776545) ^ [_1303234, _1303236, _1303238] : [class_Rings_Olinordered__semidom(_1303234), hAPP(hAPP(c_Power_Opower__class_Opower(_1303234), _1303236), 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(_1303234), _1303238), 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(_1303234), c_Groups_Ozero__class_Ozero(_1303234)), _1303236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303234), c_Groups_Ozero__class_Ozero(_1303234)), _1303238)), -(_1303236 = _1303238)], (25046 ^ _776545) ^ [_1230034, _1230036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230034), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230034), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230036, _1230034))))], (8747 ^ _776545) ^ [_926858, _926860, _926862] : [class_Lattices_Olattice(_926858), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926858), _926860), _926862)), _926860)))], (33346 ^ _776545) ^ [_1388562, _1388564, _1388566, _1388568, _1388570] : [c_Finite__Set_Ofun__left__comm__idem(_1388562, _1388564, _1388566), -(c_Finite__Set_Ofun__left__comm__idem(_1388568, _1388564, hAPP(hAPP(c_COMBB(_1388562, tc_fun(_1388564, _1388564), _1388568), _1388566), _1388570)))], (45521 ^ _776545) ^ [_1689307, _1689309, _1689311, _1689313, _1689315, _1689317, _1689319] : [c_List_Olist__all2(_1689307, _1689309, _1689311, hAPP(hAPP(c_List_Olist_OCons(_1689307), _1689313), _1689315), hAPP(hAPP(c_List_Olist_OCons(_1689309), _1689317), _1689319)), 45524 ^ _776545 : [(45527 ^ _776545) ^ [] : [-(c_List_Olist__all2(_1689307, _1689309, _1689311, _1689315, _1689319))], (45525 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1689311, _1689313), _1689317)))]]], (23667 ^ _776545) ^ [_1205419, _1205421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205419), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23670 ^ _776545 : [(23677 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205421), _1205419)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23671 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205421), _1205419)), 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)), _1205421)))]]], (39239 ^ _776545) ^ [_1534135, _1534137, _1534139, _1534141] : [-(hAPP(c_Set_OCollect(tc_prod(_1534135, _1534137)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534135, _1534137, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1534135, tc_fun(_1534137, tc_HOL_Obool), tc_fun(_1534137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534137, tc_HOL_Obool), tc_fun(_1534137, tc_HOL_Obool)), _1534135), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534137)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534135), c_fconj), _1534139))), _1534141))) = hAPP(hAPP(c_Product__Type_OSigma(_1534135, _1534137), hAPP(c_Set_OCollect(_1534135), _1534139)), hAPP(hAPP(c_COMBB(tc_fun(_1534137, tc_HOL_Obool), tc_fun(_1534137, tc_HOL_Obool), _1534135), c_Set_OCollect(_1534137)), _1534141)))], (46672 ^ _776545) ^ [_1714461, _1714463, _1714465, _1714467, _1714469] : [class_Orderings_Olinorder(_1714461), 46675 ^ _776545 : [(46682 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1714461, hAPP(hAPP(c_List_Omap(_1714463, _1714461), _1714465), _1714469)), -(c_List_Olinorder__class_Osorted(_1714461, hAPP(hAPP(c_List_Omap(_1714463, _1714461), _1714465), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714463, _1714461, _1714465), _1714467), _1714469))))], (46676 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1714461, hAPP(hAPP(c_List_Omap(_1714463, _1714461), _1714465), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714463, _1714461, _1714465), _1714467), _1714469))), -(c_List_Olinorder__class_Osorted(_1714461, hAPP(hAPP(c_List_Omap(_1714463, _1714461), _1714465), _1714469)))]]], (8351 ^ _776545) ^ [_919660, _919662] : [class_Lattices_Osemilattice__sup(_919660), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919660), _919662), _919662) = _919662)], (25071 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12465 ^ _776545) ^ [_995534, _995536] : [class_Lattices_Olattice(_995534), hBOOL(hAPP(c_Finite__Set_Ofinite(_995534), _995536)), -(_995536 = c_Orderings_Obot__class_Obot(tc_fun(_995534, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_995534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_995534), 12478 ^ [_995534, _995536]), 12479 ^ [_995534, _995536])), hAPP(hAPP(c_Set_Oinsert(_995534), 12478 ^ [_995534, _995536]), hAPP(hAPP(c_Set_Oinsert(_995534), 12479 ^ [_995534, _995536]), c_Orderings_Obot__class_Obot(tc_fun(_995534, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_995534), c_Big__Operators_Olattice__class_OInf__fin(_995534, _995536)), _995536)))], (11060 ^ _776545) ^ [_967765, _967767, _967769] : [class_Rings_Oring(_967765), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967765), _967767), _967769)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967765), _967767), hAPP(c_Groups_Ouminus__class_Ouminus(_967765), _967769)))], (47198 ^ _776545) ^ [_1725303, _1725305, _1725307] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725303), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1725303))), _1725305))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725307), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1725303))), _1725305))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1725303))), hAPP(c_List_Ofilter(tc_List_Olist(_1725303), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1725303)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725307)), c_Nat_Osize__class_Osize(tc_List_Olist(_1725303)))), c_List_Otranspose(_1725303, _1725305))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725303)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1725303)), _1725305), _1725307)))], (41033 ^ _776545) ^ [_1580506, _1580508, _1580510, _1580512, _1580514] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580506, _1580506)), hAPP(hAPP(c_Product__Type_OPair(_1580506, _1580506), _1580508), _1580510)), c_Transitive__Closure_Ortrancl(_1580506, _1580512))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580506, _1580506), tc_HOL_Obool)), _1580512), hAPP(hAPP(c_Product__Type_OSigma(_1580506, _1580506), _1580514), hAPP(c_COMBK(tc_fun(_1580506, tc_HOL_Obool), _1580506), _1580514)))), -(_1580508 = _1580510), -(hBOOL(hAPP(hAPP(c_member(_1580506), _1580508), _1580514)))], (41610 ^ _776545) ^ [_1595488, _1595490, _1595492, _1595494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595488, _1595488)), hAPP(hAPP(c_Product__Type_OPair(_1595488, _1595488), _1595490), _1595492)), c_Transitive__Closure_Otrancl(_1595488, _1595494))), 41614 ^ _776545 : [(41617 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595488, _1595488)), hAPP(hAPP(c_Product__Type_OPair(_1595488, _1595488), 41613 ^ [_1595488, _1595490, _1595492, _1595494]), _1595492)), _1595494)))], (41615 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595488, _1595488)), hAPP(hAPP(c_Product__Type_OPair(_1595488, _1595488), _1595490), 41613 ^ [_1595488, _1595490, _1595492, _1595494])), c_Transitive__Closure_Ortrancl(_1595488, _1595494))))]]], (21285 ^ _776545) ^ [_1161751, _1161753, _1161755] : [class_Int_Onumber__ring(_1161751), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161751), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1161753), _1161755)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161751), hAPP(c_Int_Onumber__class_Onumber__of(_1161751), _1161753)), hAPP(c_Int_Onumber__class_Onumber__of(_1161751), _1161755)))], (17621 ^ _776545) ^ [_1093901] : [class_Rings_Olinordered__semidom(_1093901), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093901), c_Groups_Ozero__class_Ozero(_1093901)), c_Groups_Oone__class_Oone(_1093901))))], (6254 ^ _776545) ^ [_877065] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_877065, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_877065, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_877065, tc_HOL_Obool)))], (7486 ^ _776545) ^ [_899803, _899805, _899807, _899809] : [7487 ^ _776545 : [(7490 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899803), _899805), _899809))], (7488 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899803), _899805), _899807))]], -(hBOOL(hAPP(hAPP(c_member(_899803), _899805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899803, tc_HOL_Obool)), _899809), _899807))))], (4818 ^ _776545) ^ [_849899, _849901] : [_849901 = _849899, -(c_Set_OBex(_849901) = c_Set_OBex(_849899))], (40040 ^ _776545) ^ [_1556172, _1556174, _1556176, _1556178, _1556180, _1556182] : [c_Finite__Set_Ofolding(_1556172, _1556174, _1556176, _1556178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556172), _1556180)), hBOOL(hAPP(hAPP(c_member(_1556172), _1556182), _1556180)), -(hAPP(_1556178, _1556180) = hAPP(c_Fun_Ocomp(_1556174, _1556174, _1556174, hAPP(_1556178, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556172, tc_HOL_Obool)), _1556180), hAPP(hAPP(c_Set_Oinsert(_1556172), _1556182), c_Orderings_Obot__class_Obot(tc_fun(_1556172, tc_HOL_Obool)))))), hAPP(_1556176, _1556182)))], (6510 ^ _776545) ^ [_881667, _881669] : [class_Orderings_Opreorder(_881667), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881667), _881669), _881669)))], (35616 ^ _776545) ^ [_1441267, _1441269, _1441271, _1441273, _1441275] : [hAPP(c_Product__Type_Ofst(_1441267, _1441269), hAPP(hAPP(c_Product__Type_OPair(_1441267, _1441269), _1441271), _1441273)) = _1441275, -(_1441271 = _1441275)], (25303 ^ _776545) ^ [_1234438, _1234440] : [-(_1234438 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234440), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234438), _1234440))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234438, _1234440)))], (43210 ^ _776545) ^ [_1637377, _1637379, _1637381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637377), tc_List_Olist(_1637377))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637377), tc_List_Olist(_1637377)), _1637379), c_List_Olist_ONil(_1637377))), c_List_Olex(_1637377, _1637381)))], (24042 ^ _776545) ^ [_1211813] : [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)), _1211813))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1211813)))], (224 ^ _776545) ^ [_780135, _780137] : [-(class_Fields_Olinordered__field__inverse__zero(_780135)), _780137 = _780135, class_Fields_Olinordered__field__inverse__zero(_780137)], (8585 ^ _776545) ^ [_924015, _924017, _924019] : [class_Lattices_Osemilattice__sup(_924015), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924015), _924017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924015), _924017), _924019))))], (4098 ^ _776545) ^ [_838577, _838579] : [_838579 = _838577, -(c_New__Random__Sequence_Oneg__single(_838579) = c_New__Random__Sequence_Oneg__single(_838577))], (8233 ^ _776545) ^ [_917375, _917377, _917379] : [class_Lattices_Obounded__lattice__top(_917375), 8236 ^ _776545 : [(8245 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917375), _917377), _917379) = c_Orderings_Otop__class_Otop(_917375)), _917377 = c_Orderings_Otop__class_Otop(_917375), _917379 = c_Orderings_Otop__class_Otop(_917375)], (8237 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917375), _917377), _917379) = c_Orderings_Otop__class_Otop(_917375), 8240 ^ _776545 : [(8243 ^ _776545) ^ [] : [-(_917379 = c_Orderings_Otop__class_Otop(_917375))], (8241 ^ _776545) ^ [] : [-(_917377 = c_Orderings_Otop__class_Otop(_917375))]]]]], (45164 ^ _776545) ^ [_1681097, _1681099] : [-(c_Random_Oselect__weight(_1681097, _1681099) = 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(_1681097, 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, _1681097), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1681097)), _1681099)))), hAPP(hAPP(c_COMBB(_1681097, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1681097, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1681097, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1681097, _1681099))))], (7316 ^ _776545) ^ [_896307, _896309, _896311, _896313] : [-(hBOOL(hAPP(hAPP(c_member(_896307), _896309), _896311))), 7319 ^ _776545 : [(7326 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896307, tc_HOL_Obool)), _896311), _896313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896307, tc_HOL_Obool)), _896311), hAPP(hAPP(c_Set_Oinsert(_896307), _896309), _896313))))], (7320 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896307, tc_HOL_Obool)), _896311), hAPP(hAPP(c_Set_Oinsert(_896307), _896309), _896313))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896307, tc_HOL_Obool)), _896311), _896313)))]]], (32270 ^ _776545) ^ [_1356767] : [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), _1356767))), 32273 ^ _776545 : [(32280 ^ _776545) ^ [] : [-(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), _1356767))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356767)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356767)), 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), _1356767)))))], (32274 ^ _776545) ^ [] : [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), _1356767)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1356767)) = 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), _1356767))))]]], (28775 ^ _776545) ^ [_1292444, _1292446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1292444), 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)))), _1292446)), 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)))), _1292444)) = 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), _1292446), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1292444))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15302 ^ _776545) ^ [_1052588, _1052590, _1052592, _1052594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052588), _1052590)), hBOOL(hAPP(hAPP(c_member(_1052588), _1052592), _1052590)), -(hBOOL(hAPP(hAPP(c_member(_1052588), _1052592), _1052594))), -(hAPP(c_Finite__Set_Ocard(_1052588), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052588, tc_HOL_Obool)), _1052590), hAPP(hAPP(c_Set_Oinsert(_1052588), _1052592), _1052594))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1052588), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052588, tc_HOL_Obool)), _1052590), _1052594))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4458 ^ _776545) ^ [_844219, _844221, _844223, _844225] : [-(c_Wellfounded_Oaccp(_844225, _844221) = c_Wellfounded_Oaccp(_844223, _844219)), _844225 = _844223, _844221 = _844219], (36565 ^ _776545) ^ [_1469144, _1469146, _1469148, _1469150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469144), _1469150)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469148), _1469146))), -(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), _1469144), _1469146)), 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), _1469148), _1469150)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (40687 ^ _776545) ^ [_1571485, _1571487, _1571489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571485, _1571485), tc_HOL_Obool)), _1571487), _1571489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571485, _1571485), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1571485, _1571485, _1571485), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1571485, _1571485), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571485, _1571487)), _1571489)), _1571487)), _1571489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571485, _1571485), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571485, _1571487)), _1571489)))], (28869 ^ _776545) ^ [_1294135, _1294137] : [c_Int_OBit0(_1294135) = c_Int_OBit0(_1294137), -(_1294135 = _1294137)], (17257 ^ _776545) ^ [_1087217, _1087219] : [class_Groups_Olinordered__ab__group__add(_1087217), 17260 ^ _776545 : [(17267 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087217), _1087219), c_Groups_Ozero__class_Ozero(_1087217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087217), _1087219), _1087219)), c_Groups_Ozero__class_Ozero(_1087217))))], (17261 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087217), _1087219), _1087219)), c_Groups_Ozero__class_Ozero(_1087217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087217), _1087219), c_Groups_Ozero__class_Ozero(_1087217))))]]], (35634 ^ _776545) ^ [_1441667, _1441669] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441667, _1441669) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1441667, _1441669)))], (23701 ^ _776545) ^ [_1205906] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205906) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1205906 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10923 ^ _776545) ^ [_965137, _965139, _965141, _965143] : [_965141 = _965143, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_965137, _965139, hAPP(hAPP(c_Set_Oinsert(_965137), _965141), c_Orderings_Obot__class_Obot(tc_fun(_965137, tc_HOL_Obool)))), _965143)))], (25566 ^ _776545) ^ [_1238980, _1238982] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238980) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238982)), 25569 ^ _776545 : [(25572 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238982)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25570 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238980))))]], 25573 ^ _776545 : [(25576 ^ _776545) ^ [] : [25577 ^ _776545 : [(25580 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238980) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25578 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238982))))]], 25581 ^ _776545 : [(25584 ^ _776545) ^ [] : [_1238980 = _1238982], (25582 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238982)))]]], (25574 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238980)))]]], (32940 ^ _776545) ^ [_1377198, _1377200, _1377202, _1377204, _1377206] : [_1377198 = c_Orderings_Obot__class_Obot(tc_fun(_1377200, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377202, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377200, tc_fun(_1377202, tc_HOL_Obool)), _1377198), _1377204)), _1377206) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377202, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1377202, tc_HOL_Obool))), _1377206))], (33591 ^ _776545) ^ [] : [-(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)))], (37422 ^ _776545) ^ [_1488711, _1488713, _1488715, _1488717, _1488719] : [c_Fun_Oinj__on(_1488711, _1488713, _1488715, _1488717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1488711, tc_HOL_Obool)), _1488719), _1488717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1488713, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1488711, _1488713, _1488715), _1488719)), hAPP(c_Set_Oimage(_1488711, _1488713, _1488715), _1488717))))], (39888 ^ _776545) ^ [_1552748, _1552750, _1552752, _1552754, _1552756, _1552758] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552748, _1552750, _1552752, hAPP(c_COMBK(_1552750, _1552748), _1552754)), _1552756), _1552758) = _1552754)], (49992 ^ _776545) ^ [_1786291, _1786293, _1786295, _1786297, _1786299] : [c_Fun_Oinj__on(_1786291, _1786293, _1786295, c_Orderings_Otop__class_Otop(tc_fun(_1786291, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1786293, _1786297, _1786291, hAPP(c_Fun_Ocomp(_1786291, _1786297, _1786293, _1786299), c_Hilbert__Choice_Oinv__into(_1786291, _1786293, c_Orderings_Otop__class_Otop(tc_fun(_1786291, tc_HOL_Obool)), _1786295))), _1786295) = _1786299)], (41712 ^ _776545) ^ [_1597918] : [-(c_Nitpick_Odenom(_1597918) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1597918, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1597918)))], (14398 ^ _776545) ^ [_1036451, _1036453, _1036455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036451), _1036453)), _1036455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036455), _1036453))))], (22407 ^ _776545) ^ [_1182774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1182774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182774)))], (39722 ^ _776545) ^ [_1547849, _1547851, _1547853, _1547855] : [-(hAPP(c_Set_OCollect(_1547849), hAPP(hAPP(c_COMBB(tc_fun(_1547851, tc_HOL_Obool), tc_HOL_Obool, _1547849), c_HOL_OAll(_1547851)), hAPP(hAPP(c_COMBB(tc_fun(_1547851, tc_HOL_Obool), tc_fun(_1547851, tc_HOL_Obool), _1547849), hAPP(c_COMBS(_1547851, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547851), c_fimplies), hAPP(hAPP(c_COMBC(_1547851, tc_fun(_1547851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547851)), _1547853)))), _1547855))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547851, tc_fun(_1547849, tc_HOL_Obool)), _1547853), hAPP(hAPP(c_COMBB(tc_fun(_1547849, tc_HOL_Obool), tc_fun(_1547849, tc_HOL_Obool), _1547851), c_Set_OCollect(_1547849)), hAPP(c_COMBC(_1547849, _1547851, tc_HOL_Obool), _1547855))))], (32714 ^ _776545) ^ [_1370880, _1370882, _1370884, _1370886, _1370888] : [class_Complete__Lattice_Ocomplete__lattice(_1370880), class_Orderings_Olinorder(_1370880), 32721 ^ _776545 : [(32731 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370880), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370882, _1370880), _1370884), _1370886)), _1370888))), 32732 ^ _776545 : [(32733 ^ _776545) ^ [_1371228] : [hBOOL(hAPP(hAPP(c_member(_1370882), _1371228), _1370884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370880), hAPP(_1370886, _1371228)), _1370888))]]], (32722 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370880), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1370882, _1370880), _1370884), _1370886)), _1370888)), 32726 ^ _776545 : [(32729 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370880), hAPP(_1370886, 32725 ^ [_1370880, _1370882, _1370884, _1370886, _1370888])), _1370888)))], (32727 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370882), 32725 ^ [_1370880, _1370882, _1370884, _1370886, _1370888]), _1370884)))]]]]], (7384 ^ _776545) ^ [_897749, _897751, _897753, _897755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897749, tc_HOL_Obool)), _897751), hAPP(hAPP(c_Set_Oinsert(_897749), _897753), _897755))), 7387 ^ _776545 : [(7394 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897749), _897753), _897751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897749, tc_HOL_Obool)), _897751), _897755)))], (7388 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897749), _897753), _897751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897749, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897749, tc_HOL_Obool)), _897751), hAPP(hAPP(c_Set_Oinsert(_897749), _897753), c_Orderings_Obot__class_Obot(tc_fun(_897749, tc_HOL_Obool))))), _897755)))]]], (288 ^ _776545) ^ [_780953, _780955, _780957, _780959] : [-(c_FunDef_Oreduction__pair(_780957, _780953)), c_FunDef_Oreduction__pair(_780959, _780955), _780959 = _780957, _780955 = _780953], (38450 ^ _776545) ^ [_1513716, _1513718] : [c_Wellfounded_OwfP(_1513716, _1513718), -(c_Wellfounded_Owf(_1513716, hAPP(c_Set_OCollect(tc_prod(_1513716, _1513716)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513716, _1513716, tc_HOL_Obool), _1513718))))], (48891 ^ _776545) ^ [_1762237] : [-(c_List_Omember(_1762237) = c_List_Oset(_1762237))], (12586 ^ _776545) ^ [_998152, _998154, _998156, _998158, _998160, _998162] : [c_Finite__Set_Ofun__left__comm(_998152, _998154, _998156), hBOOL(hAPP(c_Finite__Set_Ofinite(_998152), _998158)), hBOOL(hAPP(hAPP(c_member(_998152), _998160), _998158)), -(hAPP(hAPP(c_Finite__Set_Ofold(_998152, _998154, _998156), _998162), _998158) = hAPP(hAPP(_998156, _998160), hAPP(hAPP(c_Finite__Set_Ofold(_998152, _998154, _998156), _998162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998152, tc_HOL_Obool)), _998158), hAPP(hAPP(c_Set_Oinsert(_998152), _998160), c_Orderings_Obot__class_Obot(tc_fun(_998152, tc_HOL_Obool)))))))], (7690 ^ _776545) ^ [_904884, _904886, _904888] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904884, tc_HOL_Obool)), _904886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904884, tc_HOL_Obool)), _904888), _904886)) = c_Orderings_Obot__class_Obot(tc_fun(_904884, tc_HOL_Obool)))], (40871 ^ _776545) ^ [_1576708, _1576710, _1576712, _1576714] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576708, _1576708)), hAPP(hAPP(c_Product__Type_OPair(_1576708, _1576708), _1576710), _1576712)), c_Transitive__Closure_Ortrancl(_1576708, _1576714)))), 40872 ^ _776545 : [(40875 ^ _776545) ^ [] : [-(_1576710 = _1576712), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576708, _1576708)), hAPP(hAPP(c_Product__Type_OPair(_1576708, _1576708), _1576710), _1576712)), c_Transitive__Closure_Otrancl(_1576708, _1576714)))], (40873 ^ _776545) ^ [] : [_1576710 = _1576712]]], (48231 ^ _776545) ^ [_1748035, _1748037] : [-(c_FunDef_Ois__measure(_1748035, _1748037))], (37266 ^ _776545) ^ [_1485769, _1485771, _1485773, _1485775] : [c_Fun_Oinj__on(_1485769, _1485771, _1485773, _1485775), 37269 ^ _776545 : [(37270 ^ _776545) ^ [_1485877] : [hBOOL(hAPP(hAPP(c_member(_1485769), _1485877), _1485775)), 37273 ^ _776545 : [(37274 ^ _776545) ^ [_1485979] : [hBOOL(hAPP(hAPP(c_member(_1485769), _1485979), _1485775)), hAPP(_1485773, _1485877) = hAPP(_1485773, _1485979), -(_1485877 = _1485979)]]]]], (18796 ^ _776545) ^ [_1115181, _1115183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1115181), _1115183))), 18799 ^ _776545 : [(18802 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1115181), _1115183)))], (18800 ^ _776545) ^ [] : [_1115183 = c_Orderings_Obot__class_Obot(tc_fun(_1115181, tc_HOL_Obool))]]], (45263 ^ _776545) ^ [_1683012, _1683014] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1683012), _1683014) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1683012)), hAPP(c_Code__Numeral_Onat__of, _1683014))))], (9522 ^ _776545) ^ [_939953, _939955, _939957] : [class_Orderings_Olinorder(_939953), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939953), _939955), _939957))), 9529 ^ _776545 : [(9536 ^ _776545) ^ [] : [_939955 = _939957, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939953), _939955), _939957)))], (9530 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939953), _939955), _939957)), -(_939955 = _939957)]]], (38888 ^ _776545) ^ [_1524720, _1524722, _1524724, _1524726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524720, _1524722), tc_HOL_Obool)), _1524724), _1524726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524720, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524720, _1524722), _1524724)), hAPP(c_Relation_ODomain(_1524720, _1524722), _1524726))))], (8775 ^ _776545) ^ [_927292, _927294] : [class_Lattices_Obounded__lattice__bot(_927292), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927292), _927294), c_Orderings_Obot__class_Obot(_927292)) = _927294)], (45529 ^ _776545) ^ [_1689470, _1689472, _1689474, _1689476, _1689478, _1689480, _1689482] : [-(c_List_Olist__all2(_1689470, _1689472, _1689474, hAPP(hAPP(c_List_Olist_OCons(_1689470), _1689476), _1689478), hAPP(hAPP(c_List_Olist_OCons(_1689472), _1689480), _1689482))), hBOOL(hAPP(hAPP(_1689474, _1689476), _1689480)), c_List_Olist__all2(_1689470, _1689472, _1689474, _1689478, _1689482)], (34616 ^ _776545) ^ [_1421344, _1421346] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421344), _1421346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421344)), _1421346)))], (29639 ^ _776545) ^ [_1307746, _1307748, _1307750] : [class_Int_Onumber__ring(_1307746), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307746), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1307746), _1307748), _1307750)), 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(_1307746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1307746), hAPP(hAPP(c_Power_Opower__class_Opower(_1307746), _1307748), 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(_1307746), _1307750), 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(_1307746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307746), hAPP(c_Int_Onumber__class_Onumber__of(_1307746), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1307748)), _1307750)))], (29975 ^ _776545) ^ [_1314114, _1314116, _1314118] : [class_Orderings_Olinorder(_1314114), -(_1314116 = c_Orderings_Obot__class_Obot(tc_fun(_1314114, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314114, tc_HOL_Obool)), _1314116), _1314118)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314114), _1314118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314114), hAPP(c_Finite__Set_Ofold1(_1314114, c_Orderings_Oord__class_Omin(_1314114)), _1314118)), hAPP(c_Finite__Set_Ofold1(_1314114, c_Orderings_Oord__class_Omin(_1314114)), _1314116))))], (14542 ^ _776545) ^ [_1038822, _1038824, _1038826] : [_1038824 = _1038826, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038822), _1038824) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038822), _1038826))], (14004 ^ _776545) ^ [_1027362, _1027364, _1027366, _1027368, _1027370] : [class_Groups_Ocomm__monoid__add(_1027362), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027364), _1027366)), -(hBOOL(hAPP(hAPP(c_member(_1027364), _1027368), _1027366))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027364, _1027362), _1027370), hAPP(hAPP(c_Set_Oinsert(_1027364), _1027368), _1027366)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027362), hAPP(_1027370, _1027368)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027364, _1027362), _1027370), _1027366)))], (45404 ^ _776545) ^ [_1686478, _1686480, _1686482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1686478, tc_HOL_Obool)), _1686480), _1686482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1686478), tc_HOL_Obool)), c_List_Olistsp(_1686478, _1686480)), c_List_Olistsp(_1686478, _1686482))))], (46146 ^ _776545) ^ [_1703342, _1703344, _1703346] : [-(c_List_Oremdups(_1703342, hAPP(c_List_Ofilter(_1703342, _1703344), _1703346)) = hAPP(c_List_Ofilter(_1703342, _1703344), c_List_Oremdups(_1703342, _1703346)))], (22503 ^ _776545) ^ [_1184329, _1184331] : [class_Groups_Omonoid__mult(_1184329), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184329), c_Groups_Oone__class_Oone(_1184329)), _1184331) = c_Groups_Oone__class_Oone(_1184329))], (31723 ^ _776545) ^ [_1346349, _1346351, _1346353, _1346355, _1346357] : [class_Orderings_Olinorder(_1346349), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346349, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346349, _1346351), _1346353)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346349, _1346355), _1346357)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346349, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346349), _1346351), _1346355)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346349), _1346353), _1346357)))], (10829 ^ _776545) ^ [_963233, _963235, _963237] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963233, tc_HOL_Obool)), _963235), _963237) = c_Orderings_Obot__class_Obot(tc_fun(_963233, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963233, tc_HOL_Obool)), _963235), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963233, tc_HOL_Obool)), _963237))))], (43306 ^ _776545) ^ [_1639191, _1639193, _1639195, _1639197, _1639199] : [-(hAPP(hAPP(c_List_Ozip(_1639191, _1639193), hAPP(hAPP(c_List_Olist_OCons(_1639191), _1639195), _1639197)), _1639199) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1639191, _1639193)), _1639193, c_List_Olist_ONil(tc_prod(_1639191, _1639193)), hAPP(hAPP(c_COMBC(_1639193, tc_fun(tc_List_Olist(_1639193), tc_List_Olist(tc_prod(_1639191, _1639193))), tc_fun(tc_List_Olist(_1639193), tc_List_Olist(tc_prod(_1639191, _1639193)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1639191, _1639193)), tc_List_Olist(tc_prod(_1639191, _1639193))), tc_fun(tc_fun(tc_List_Olist(_1639193), tc_List_Olist(tc_prod(_1639191, _1639193))), tc_fun(tc_List_Olist(_1639193), tc_List_Olist(tc_prod(_1639191, _1639193)))), _1639193), c_COMBB(tc_List_Olist(tc_prod(_1639191, _1639193)), tc_List_Olist(tc_prod(_1639191, _1639193)), tc_List_Olist(_1639193))), hAPP(hAPP(c_COMBB(tc_prod(_1639191, _1639193), tc_fun(tc_List_Olist(tc_prod(_1639191, _1639193)), tc_List_Olist(tc_prod(_1639191, _1639193))), _1639193), c_List_Olist_OCons(tc_prod(_1639191, _1639193))), hAPP(c_Product__Type_OPair(_1639191, _1639193), _1639195)))), hAPP(c_List_Ozip(_1639191, _1639193), _1639197))), _1639199))], (18846 ^ _776545) ^ [_1116072, _1116074, _1116076] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1116072), _1116074)), -(hAPP(c_Finite__Set_Ocard(_1116072), hAPP(hAPP(c_Set_Oinsert(_1116072), _1116076), _1116074)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1116072), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1116072, tc_HOL_Obool)), _1116074), hAPP(hAPP(c_Set_Oinsert(_1116072), _1116076), c_Orderings_Obot__class_Obot(tc_fun(_1116072, tc_HOL_Obool)))))))], (39693 ^ _776545) ^ [_1547298] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39689 ^ [_1547298]), c_Int_OInteg)))], (13232 ^ _776545) ^ [_1010769, _1010771, _1010773, _1010775, _1010777] : [class_Groups_Ocomm__monoid__mult(_1010769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010771), _1010773)), -(hBOOL(hAPP(hAPP(c_member(_1010771), _1010775), _1010773))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010771, _1010769), _1010777), hAPP(hAPP(c_Set_Oinsert(_1010771), _1010775), _1010773)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010769), hAPP(_1010777, _1010775)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1010771, _1010769), _1010777), _1010773)))], (27363 ^ _776545) ^ [_1268826] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1268826) = _1268826)], (38040 ^ _776545) ^ [_1505037, _1505039, _1505041] : [c_Wellfounded_Owf(_1505037, _1505039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1505037, _1505037), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1505037, _1505037, _1505037), _1505039), _1505041)), _1505039)), -(c_FunDef_Oreduction__pair(_1505037, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1505037, _1505037), tc_HOL_Obool), tc_fun(tc_prod(_1505037, _1505037), tc_HOL_Obool)), _1505039), _1505041)))], (52165 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (19711 ^ _776545) ^ [_1132434, _1132436] : [class_Rings_Odivision__ring__inverse__zero(_1132434), 19714 ^ _776545 : [(19721 ^ _776545) ^ [] : [-(_1132436 = c_Groups_Ozero__class_Ozero(_1132434)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132434), _1132436), _1132436) = c_Groups_Oone__class_Oone(_1132434))], (19715 ^ _776545) ^ [] : [_1132436 = c_Groups_Ozero__class_Ozero(_1132434), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132434), _1132436), _1132436) = c_Groups_Ozero__class_Ozero(_1132434))]]], (47333 ^ _776545) ^ [_1728194] : [c_List_Onat__list(_1728194), -(c_List_Oembed__list(c_List_Oreturn__list(_1728194)) = _1728194)], (47214 ^ _776545) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (24818 ^ _776545) ^ [_1225563, _1225565, _1225567, _1225569, _1225571, _1225573] : [class_Divides_Osemiring__div(_1225563), c_Divides_Odiv__class_Omod(_1225563, _1225565, _1225567) = c_Divides_Odiv__class_Omod(_1225563, _1225569, _1225567), c_Divides_Odiv__class_Omod(_1225563, _1225571, _1225567) = c_Divides_Odiv__class_Omod(_1225563, _1225573, _1225567), -(c_Divides_Odiv__class_Omod(_1225563, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225563), _1225565), _1225571), _1225567) = c_Divides_Odiv__class_Omod(_1225563, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225563), _1225569), _1225573), _1225567))], (41837 ^ _776545) ^ [_1602195, _1602197, _1602199, _1602201, _1602203, _1602205] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602195), tc_List_Olist(_1602195))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602195), tc_List_Olist(_1602195)), hAPP(hAPP(c_List_Olist_OCons(_1602195), _1602197), _1602199)), hAPP(hAPP(c_List_Olist_OCons(_1602195), _1602201), _1602203))), c_List_Olexord(_1602195, _1602205)))), 41838 ^ _776545 : [(41841 ^ _776545) ^ [] : [_1602197 = _1602201, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602195), tc_List_Olist(_1602195))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602195), tc_List_Olist(_1602195)), _1602199), _1602203)), c_List_Olexord(_1602195, _1602205)))], (41839 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602195, _1602195)), hAPP(hAPP(c_Product__Type_OPair(_1602195, _1602195), _1602197), _1602201)), _1602205))]]], (30654 ^ _776545) ^ [_1326521, _1326523, _1326525] : [class_Orderings_Olinorder(_1326521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326521), _1326523)), hBOOL(hAPP(hAPP(c_member(_1326521), _1326525), _1326523)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326521), _1326525), c_Big__Operators_Olinorder__class_OMin(_1326521, _1326523)) = c_Big__Operators_Olinorder__class_OMin(_1326521, _1326523))], (45363 ^ _776545) ^ [_1685577, _1685579, _1685581] : [-(c_List_Olistsp(_1685577, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1685577, tc_HOL_Obool)), _1685579), _1685581)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1685577), tc_HOL_Obool)), c_List_Olistsp(_1685577, _1685579)), c_List_Olistsp(_1685577, _1685581)))], (15057 ^ _776545) ^ [] : [-(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))], (15174 ^ _776545) ^ [_1050354] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1050354)) = _1050354)], (40751 ^ _776545) ^ [_1573827, _1573829] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573827, _1573827, _1573827), _1573829), c_Transitive__Closure_Ortrancl(_1573827, _1573829)) = hAPP(hAPP(c_Relation_Orel__comp(_1573827, _1573827, _1573827), c_Transitive__Closure_Ortrancl(_1573827, _1573829)), _1573829))], (40611 ^ _776545) ^ [_1569581] : [-(c_Transitive__Closure_Otrancl(_1569581, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569581, _1569581), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569581, _1569581), tc_HOL_Obool)))], (8597 ^ _776545) ^ [_924229, _924231, _924233, _924235] : [class_Lattices_Osemilattice__inf(_924229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924229), _924231), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924229), _924233), _924235))), 8604 ^ _776545 : [(8607 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924229), _924231), _924235)))], (8605 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924229), _924231), _924233)))]]], (19787 ^ _776545) ^ [_1133652, _1133654, _1133656, _1133658] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133652, _1133654)), c_Sum__Type_OPlus(_1133652, _1133654, _1133656, _1133658)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133652), _1133656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133654), _1133658))], (4412 ^ _776545) ^ [_843530, _843532, _843534, _843536, _843538, _843540] : [-(c_New__DSequence_Opos__union(_843540, _843536, _843532) = c_New__DSequence_Opos__union(_843538, _843534, _843530)), _843540 = _843538, _843536 = _843534, _843532 = _843530], (6700 ^ _776545) ^ [_884978, _884980, _884982, _884984] : [class_Orderings_Oorder(_884978), _884980 = _884982, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884978), _884984), _884982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884978), _884984), _884980)))], (9786 ^ _776545) ^ [_944199, _944201, _944203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944199, tc_HOL_Obool)), _944201), _944203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944199, tc_HOL_Obool)), _944201), _944203))), -(_944201 = _944203)], (23275 ^ _776545) ^ [_1198308, _1198310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198308)), 23284 ^ _776545 : [(23287 ^ _776545) ^ [] : [hBOOL(hAPP(_1198310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23280 ^ [_1198308, _1198310]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 23281 ^ [_1198308, _1198310]), _1198308))))], (23285 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1198310, 23280 ^ [_1198308, _1198310])))]], 23288 ^ _776545 : [(23291 ^ _776545) ^ [] : [hBOOL(hAPP(_1198310, 23280 ^ [_1198308, _1198310]))], (23289 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1198310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23280 ^ [_1198308, _1198310]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 23281 ^ [_1198308, _1198310]), _1198308)))))]], 23292 ^ _776545 : [(23302 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1198310, 23309 ^ [_1198308, _1198310]))), 23303 ^ _776545 : [(23304 ^ _776545) ^ [_1198855] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1198855), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1198308))), hBOOL(hAPP(_1198310, _1198855))]]], (23293 ^ _776545) ^ [] : [23294 ^ _776545 : [(23295 ^ _776545) ^ [_1198740] : [hBOOL(hAPP(_1198310, _1198740))]], 23297 ^ _776545 : [(23300 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1198310, 23296 ^ [_1198308, _1198310])))], (23298 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23296 ^ [_1198308, _1198310]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1198308))))]]]]], (3906 ^ _776545) ^ [_835207, _835209, _835211, _835213, _835215, _835217, _835219, _835221, _835223, _835225, _835227, _835229, _835231, _835233] : [-(c_New__Random__Sequence_Oneg__decr__bind(_835233, _835229, _835225, _835221, _835217, _835213, _835209) = c_New__Random__Sequence_Oneg__decr__bind(_835231, _835227, _835223, _835219, _835215, _835211, _835207)), _835233 = _835231, _835229 = _835227, _835225 = _835223, _835221 = _835219, _835217 = _835215, _835213 = _835211, _835209 = _835207], (44268 ^ _776545) ^ [_1661747, _1661749, _1661751] : [class_Orderings_Olinorder(_1661747), -(c_List_Oremove1(_1661747, _1661749, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661747, _1661747, c_COMBI(_1661747)), _1661749), _1661751)) = _1661751)], (21345 ^ _776545) ^ [_1162908, _1162910, _1162912, _1162914] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162908), hAPP(c_Int_Onumber__class_Onumber__of(_1162908), _1162910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162908), _1162912), _1162914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162908), hAPP(c_Int_Onumber__class_Onumber__of(_1162908), _1162910)), _1162912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162908), hAPP(c_Int_Onumber__class_Onumber__of(_1162908), _1162910)), _1162914))), class_Int_Onumber(_1162908), class_Rings_Osemiring(_1162908)], (11036 ^ _776545) ^ [_967317, _967319] : [class_Lattices_Oab__semigroup__idem__mult(_967317), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967317), _967319), _967319) = _967319)], (6069 ^ _776545) ^ [_873604, _873606, _873608, _873610, _873612] : [-(hBOOL(hAPP(hAPP(c_member(_873604), _873606), c_SetInterval_Oord_OgreaterThanLessThan(_873604, _873608, _873610, _873612)))), hBOOL(hAPP(hAPP(_873608, _873610), _873606)), hBOOL(hAPP(hAPP(_873608, _873606), _873612))], (39455 ^ _776545) ^ [_1541083, _1541085, _1541087, _1541089, _1541091, _1541093, _1541095] : [-(hAPP(c_Product__Type_Ofst(_1541083, _1541085), hAPP(c_Product__Type_Omap__pair(_1541087, _1541083, _1541089, _1541085, _1541091, _1541093), _1541095)) = hAPP(_1541091, hAPP(c_Product__Type_Ofst(_1541087, _1541089), _1541095)))], (22329 ^ _776545) ^ [_1181263, _1181265, _1181267] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181263), _1181265)), _1181267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181263), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181265), _1181267)))], (18290 ^ _776545) ^ [_1105455, _1105457, _1105459, _1105461] : [class_Rings_Olinordered__semiring__strict(_1105455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105455), _1105457), _1105459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105455), _1105461), _1105459))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105455), c_Groups_Ozero__class_Ozero(_1105455)), _1105459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105455), _1105457), _1105461)))], (38493 ^ _776545) ^ [_1514496, _1514498] : [-(hAPP(c_Relation_ORange(_1514496, _1514496), c_Relation_OId__on(_1514496, _1514498)) = _1514498)], (45275 ^ _776545) ^ [_1683193, _1683195] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1683193), _1683195) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1683193, 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)))), _1683195))))], (52263 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (38181 ^ _776545) ^ [_1507748, _1507750, _1507752] : [c_Wellfounded_Owf(_1507748, _1507750), -(c_Wellfounded_Owf(_1507748, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507748, _1507748), tc_HOL_Obool)), _1507750), _1507752)))], (39896 ^ _776545) ^ [_1552915, _1552917, _1552919, _1552921, _1552923] : [c_Finite__Set_Ofun__left__comm(_1552915, _1552917, _1552919), -(hAPP(c_Fun_Ocomp(_1552917, _1552917, _1552917, hAPP(_1552919, _1552921)), hAPP(_1552919, _1552923)) = hAPP(c_Fun_Ocomp(_1552917, _1552917, _1552917, hAPP(_1552919, _1552923)), hAPP(_1552919, _1552921)))], (1774 ^ _776545) ^ [_801584, _801586] : [-(class_Groups_Omonoid__add(_801584)), _801586 = _801584, class_Groups_Omonoid__add(_801586)], (10823 ^ _776545) ^ [_963080, _963082, _963084, _963086] : [class_Orderings_Oorder(_963080), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963080, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963080, _963082), _963084)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963080, _963084), _963086)) = c_Orderings_Obot__class_Obot(tc_fun(_963080, tc_HOL_Obool)))], (49658 ^ _776545) ^ [_1780216, _1780218] : [c_Relation_Osym(_1780216, _1780218), 49661 ^ _776545 : [(49662 ^ _776545) ^ [_1780322, _1780324] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780216, _1780216)), hAPP(hAPP(c_Product__Type_OPair(_1780216, _1780216), _1780324), _1780322)), _1780218)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780216, _1780216)), hAPP(hAPP(c_Product__Type_OPair(_1780216, _1780216), _1780322), _1780324)), _1780218)))]]], (44052 ^ _776545) ^ [_1657389, _1657391, _1657393, _1657395] : [-(hAPP(c_List_Orotate1(_1657391), hAPP(hAPP(c_List_Olist_OCons(_1657391), _1657393), _1657395)) = hAPP(hAPP(c_List_Oappend(_1657391), _1657395), hAPP(hAPP(c_List_Olist_OCons(_1657391), _1657393), c_List_Olist_ONil(_1657391))))], (5749 ^ _776545) ^ [_867342, _867344, _867346] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867342, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867342)), tc_HOL_Obool)), _867344), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867342, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867342)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867342)))), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867342, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867342)), tc_HOL_Obool)), _867346), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867342, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867342)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867342)))), 5756 ^ _776545 : [(5763 ^ _776545) ^ [] : [_867344 = _867346, -(hAPP(c_Hoare__Mirabelle_OAbs__triple(_867342), _867344) = hAPP(c_Hoare__Mirabelle_OAbs__triple(_867342), _867346))], (5757 ^ _776545) ^ [] : [hAPP(c_Hoare__Mirabelle_OAbs__triple(_867342), _867344) = hAPP(c_Hoare__Mirabelle_OAbs__triple(_867342), _867346), -(_867344 = _867346)]]], (5398 ^ _776545) ^ [_858999, _859001, _859003, _859005, _859007, _859009, _859011, _859013] : [-(c_SetInterval_Oord_OatLeastAtMost(_859013, _859009, _859005, _859001) = c_SetInterval_Oord_OatLeastAtMost(_859011, _859007, _859003, _858999)), _859013 = _859011, _859009 = _859007, _859005 = _859003, _859001 = _858999], (26643 ^ _776545) ^ [_1257409, _1257411] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1257409, _1257411)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257411), _1257409)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (14190 ^ _776545) ^ [_1031705, _1031707, _1031709, _1031711, _1031713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031705), _1031707)), -(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), _1031707), _1031709)), _1031711)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031705), _1031709)), _1031713)) = 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), _1031707), _1031705)), _1031709)), _1031711)), _1031713))], (35505 ^ _776545) ^ [_1439036, _1439038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439036), 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)), _1439038)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439036, _1439038) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1439036, _1439038)))], (13704 ^ _776545) ^ [_1020619, _1020621, _1020623, _1020625] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020619), _1020621), _1020623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020619), _1020621), _1020625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020619), _1020623), _1020625)))], (50957 ^ _776545) ^ [_1808554, _1808556, _1808558, _1808560, _1808562] : [-(c_New__DSequence_Opos__map(_1808554, _1808556, _1808558, _1808560, _1808562) = c_Lazy__Sequence_Omap(_1808554, _1808556, _1808558, hAPP(_1808560, _1808562)))], (22273 ^ _776545) ^ [_1180461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180461), _1180461)))], (22319 ^ _776545) ^ [_1181052, _1181054, _1181056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181052), _1181054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181052), _1181056)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181054), _1181056))))], (52445 ^ _776545) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (29463 ^ _776545) ^ [_1304437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1304437), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1304437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1304437 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17331 ^ _776545) ^ [_1088590, _1088592, _1088594, _1088596] : [class_Rings_Olinordered__semiring__strict(_1088590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088590), _1088592), _1088594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088590), c_Groups_Ozero__class_Ozero(_1088590)), _1088596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088590), _1088596), _1088592)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088590), _1088596), _1088594))))], (670 ^ _776545) ^ [_786652, _786654, _786656, _786658, _786660, _786662] : [-(c_List_Olist__ex1(_786660, _786656, _786652)), c_List_Olist__ex1(_786662, _786658, _786654), _786662 = _786660, _786658 = _786656, _786654 = _786652], (46694 ^ _776545) ^ [_1714931, _1714933, _1714935, _1714937, _1714939] : [class_Orderings_Olinorder(_1714931), c_List_Olinorder__class_Osorted(_1714931, hAPP(hAPP(c_List_Omap(_1714933, _1714931), _1714935), _1714937)), -(c_List_Olinorder__class_Osorted(_1714931, hAPP(hAPP(c_List_Omap(_1714933, _1714931), _1714935), hAPP(c_List_Ofilter(_1714933, _1714939), _1714937))))], (32526 ^ _776545) ^ [_1364369, _1364371, _1364373] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364369, tc_HOL_Obool)), _1364371), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1364369, tc_HOL_Obool), _1364373)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1364369, tc_HOL_Obool), tc_fun(_1364369, tc_HOL_Obool)), _1364373), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364369, tc_HOL_Obool)), _1364371)))], (27525 ^ _776545) ^ [_1271713, _1271715] : [class_Groups_Oordered__ab__group__add__abs(_1271713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271713), hAPP(c_Groups_Ouminus__class_Ouminus(_1271713), _1271715)), hAPP(c_Groups_Oabs__class_Oabs(_1271713), _1271715))))], (15144 ^ _776545) ^ [_1049913, _1049915] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049913), _1049915)), _1049913 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1049915 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (23495 ^ _776545) ^ [_1202448, _1202450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202448), _1202450))), -(c_Nat__Transfer_Otsub(_1202450, _1202448) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38201 ^ _776545) ^ [] : [-(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)))))], (41437 ^ _776545) ^ [_1590405, _1590407, _1590409, _1590411] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590405, _1590405)), _1590407), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590405, _1590405), tc_HOL_Obool), _1590409), _1590411))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590405, _1590405)), _1590407), c_Transitive__Closure_Ortrancl(_1590405, _1590411))))], (49293 ^ _776545) ^ [_1771806, _1771808] : [-(c_Relation_Otrans(_1771806, c_Relation_OId__on(_1771806, _1771808)))], (40699 ^ _776545) ^ [_1572024, _1572026, _1572028, _1572030] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572024, tc_fun(_1572024, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1572024, tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_fun(_1572024, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572024, tc_fun(tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_fun(_1572024, tc_HOL_Obool)), _1572024), c_COMBC(_1572024, tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572024, tc_prod(_1572024, _1572024)), tc_fun(_1572024, tc_fun(tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_HOL_Obool)), _1572024), hAPP(c_COMBB(tc_prod(_1572024, _1572024), tc_fun(tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool), tc_HOL_Obool), _1572024), c_member(tc_prod(_1572024, _1572024)))), c_Product__Type_OPair(_1572024, _1572024)))), _1572026)), c_fequal), _1572028), _1572030)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572024, _1572024)), hAPP(hAPP(c_Product__Type_OPair(_1572024, _1572024), _1572028), _1572030)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572024, _1572024), tc_HOL_Obool)), _1572026), c_Relation_OId(_1572024)))))], (32648 ^ _776545) ^ [_1369304, _1369306, _1369308, _1369310] : [hBOOL(hAPP(hAPP(c_member(_1369304), _1369306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369304, tc_HOL_Obool)), _1369308), hAPP(c_Set_OCollect(_1369304), _1369310)))), 32651 ^ _776545 : [(32654 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1369310, _1369306)))], (32652 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369304), _1369306), _1369308)))]]], (46739 ^ _776545) ^ [_1715758, _1715760, _1715762] : [class_Orderings_Olinorder(_1715758), 46742 ^ _776545 : [(46761 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715758, hAPP(hAPP(c_List_Oappend(_1715758), _1715760), _1715762))), c_List_Olinorder__class_Osorted(_1715758, _1715760), c_List_Olinorder__class_Osorted(_1715758, _1715762), 46771 ^ _776545 : [(46777 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715758), 46770 ^ [_1715758, _1715760, _1715762]), 46773 ^ [_1715758, _1715760, _1715762]))], (46775 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715758), 46773 ^ [_1715758, _1715760, _1715762]), hAPP(c_List_Oset(_1715758), _1715762))))], (46772 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715758), 46770 ^ [_1715758, _1715760, _1715762]), hAPP(c_List_Oset(_1715758), _1715760))))]]], (46743 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1715758, hAPP(hAPP(c_List_Oappend(_1715758), _1715760), _1715762)), 46746 ^ _776545 : [(46751 ^ _776545) ^ [_1715994] : [hBOOL(hAPP(hAPP(c_member(_1715758), _1715994), hAPP(c_List_Oset(_1715758), _1715760))), 46754 ^ _776545 : [(46755 ^ _776545) ^ [_1716104] : [hBOOL(hAPP(hAPP(c_member(_1715758), _1716104), hAPP(c_List_Oset(_1715758), _1715762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715758), _1715994), _1716104)))]]], (46749 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715758, _1715762))], (46747 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715758, _1715760))]]]]], (16364 ^ _776545) ^ [_1071735, _1071737] : [class_Groups_Ogroup__add(_1071735), 16367 ^ _776545 : [(16374 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1071735) = _1071737, -(c_Groups_Ozero__class_Ozero(_1071735) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071735), _1071737))], (16368 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1071735) = hAPP(c_Groups_Ouminus__class_Ouminus(_1071735), _1071737), -(c_Groups_Ozero__class_Ozero(_1071735) = _1071737)]]], (20193 ^ _776545) ^ [_1141138, _1141140, _1141142] : [class_Fields_Olinordered__field__inverse__zero(_1141138), 20196 ^ _776545 : [(20211 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141138), _1141140), _1141142)), c_Groups_Ozero__class_Ozero(_1141138)))), 20212 ^ _776545 : [(20219 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), _1141140), c_Groups_Ozero__class_Ozero(_1141138))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), c_Groups_Ozero__class_Ozero(_1141138)), _1141142))], (20213 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), c_Groups_Ozero__class_Ozero(_1141138)), _1141140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), _1141142), c_Groups_Ozero__class_Ozero(_1141138)))]]], (20197 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141138), _1141140), _1141142)), c_Groups_Ozero__class_Ozero(_1141138))), 20202 ^ _776545 : [(20205 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), _1141142), c_Groups_Ozero__class_Ozero(_1141138))))], (20203 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), c_Groups_Ozero__class_Ozero(_1141138)), _1141140)))]], 20206 ^ _776545 : [(20209 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), c_Groups_Ozero__class_Ozero(_1141138)), _1141142)))], (20207 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141138), _1141140), c_Groups_Ozero__class_Ozero(_1141138))))]]]]], (18524 ^ _776545) ^ [_1109900] : [class_Rings_Olinordered__semidom(_1109900), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109900), c_Groups_Ozero__class_Ozero(_1109900)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109900), c_Groups_Oone__class_Oone(_1109900)), c_Groups_Oone__class_Oone(_1109900)))))], (49159 ^ _776545) ^ [_1768625, _1768627, _1768629, _1768631] : [c_Relation_Otrans(_1768625, _1768627), c_Relation_Otrans(_1768629, _1768631), -(c_Relation_Otrans(tc_prod(_1768625, _1768629), c_Wellfounded_Olex__prod(_1768625, _1768629, _1768627, _1768631)))], (45820 ^ _776545) ^ [_1695796, _1695798] : [-(hAPP(c_List_OremoveAll(_1695796, _1695798), c_List_Olist_ONil(_1695796)) = c_List_Olist_ONil(_1695796))], (36394 ^ _776545) ^ [] : [-(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)))))], (17775 ^ _776545) ^ [_1096483, _1096485] : [class_Groups_Ogroup__add(_1096483), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096483), _1096485), hAPP(c_Groups_Ouminus__class_Ouminus(_1096483), _1096485)) = c_Groups_Ozero__class_Ozero(_1096483))], (42899 ^ _776545) ^ [_1631208, _1631210] : [hBOOL(hAPP(c_List_Odistinct(_1631208), _1631210)), 42902 ^ _776545 : [(42903 ^ _776545) ^ [_1631340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631340), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631208)), _1631210))), 42906 ^ _776545 : [(42907 ^ _776545) ^ [_1631467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631467), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631208)), _1631210))), -(_1631340 = _1631467), hAPP(hAPP(c_List_Onth(_1631208), _1631210), _1631340) = hAPP(hAPP(c_List_Onth(_1631208), _1631210), _1631467)]]]]], (4468 ^ _776545) ^ [_844368, _844370, _844372, _844374, _844376, _844378, _844380, _844382, _844384, _844386] : [-(c_Option_Ooption_Ooption__case(_844386, _844382, _844378, _844374, _844370) = c_Option_Ooption_Ooption__case(_844384, _844380, _844376, _844372, _844368)), _844386 = _844384, _844382 = _844380, _844378 = _844376, _844374 = _844372, _844370 = _844368], (44513 ^ _776545) ^ [_1666887, _1666889, _1666891] : [class_Orderings_Olinorder(_1666887), -(hAPP(c_List_Oset(_1666887), c_List_Olinorder__class_Oinsort__insert__key(_1666887, _1666887, c_COMBI(_1666887), _1666889, _1666891)) = hAPP(hAPP(c_Set_Oinsert(_1666887), _1666889), hAPP(c_List_Oset(_1666887), _1666891)))], (52135 ^ _776545) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (49570 ^ _776545) ^ [_1778282, _1778284] : [-(c_Relation_Oantisym(_1778282, c_Relation_OId__on(_1778282, _1778284)))], (52417 ^ _776545) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52407 ^ _776545) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (28487 ^ _776545) ^ [_1287799] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1287799)))], (48087 ^ _776545) ^ [_1745071, _1745073, _1745075, _1745077] : [48088 ^ _776545 : [(48091 ^ _776545) ^ [] : [c_List_Olist__ex(_1745071, _1745073, _1745077)], (48089 ^ _776545) ^ [] : [c_List_Olist__ex(_1745071, _1745073, _1745075)]], -(c_List_Olist__ex(_1745071, _1745073, hAPP(hAPP(c_List_Oappend(_1745071), _1745075), _1745077)))], (35408 ^ _776545) ^ [_1436693, _1436695, _1436697, _1436699] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436693, _1436695), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436697), _1436699))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436693), _1436695), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1436699), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436697)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1436697)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, 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_1365985))], (35778 ^ _776545) ^ [_1444455, _1444457, _1444459, _1444461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444455, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35779 ^ [_1444455, _1444457, _1444459, _1444461])), _1444457)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444455, 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), 35779 ^ [_1444455, _1444457, _1444459, _1444461]), _1444459))), _1444461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444455, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1444457)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1444455, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1444461))))], (41666 ^ _776545) ^ [_1596842, _1596844, _1596846] : [-(c_Nitpick_Oplus__frac(_1596842, _1596844, _1596846) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1596842), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1596842), _1596844), hAPP(c_Nitpick_Odenom(_1596842), _1596846))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1596842), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1596842), tc_Int_Oint), c_Nitpick_Ofrac(_1596842)), 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(_1596842), _1596844))), 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(_1596842), _1596844))))), 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(_1596842), _1596846))), 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(_1596842), _1596846)))))), c_COMBI(tc_Int_Oint))))], (19157 ^ _776545) ^ [_1121643, _1121645, _1121647, _1121649, _1121651] : [class_Groups_Oordered__comm__monoid__add(_1121643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121645), _1121647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1121645, tc_HOL_Obool)), _1121649), _1121647)), 19171 ^ _776545 : [(19174 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121643), c_Groups_Ozero__class_Ozero(_1121643)), hAPP(_1121651, 19170 ^ [_1121643, _1121645, _1121647, _1121649, _1121651])))], (19172 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1121645), 19170 ^ [_1121643, _1121645, _1121647, _1121649, _1121651]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1121645, tc_HOL_Obool)), _1121647), _1121649))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121643), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1121645, _1121643), _1121651), _1121649)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1121645, _1121643), _1121651), _1121647))))], (45704 ^ _776545) ^ [_1693417, _1693419, _1693421, _1693423] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693417)), _1693419), hAPP(c_List_Oset(tc_List_Olist(_1693417)), c_Enum_On__lists(_1693417, _1693421, _1693423)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693417)), _1693419) = _1693421)], (49331 ^ _776545) ^ [_1772413, _1772415, _1772417] : [c_List_Olist__ex(_1772413, _1772415, _1772417), 49335 ^ _776545 : [(49338 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1772415, 49334 ^ [_1772413, _1772415, _1772417])))], (49336 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772413), 49334 ^ [_1772413, _1772415, _1772417]), hAPP(c_List_Oset(_1772413), _1772417))))]]], (8441 ^ _776545) ^ [_921493, _921495, _921497, _921499] : [class_Lattices_Osemilattice__sup(_921493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921493), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921493), _921495), _921497)), _921499)), 8448 ^ _776545 : [(8451 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921493), _921497), _921499)))], (8449 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921493), _921495), _921499)))]]], (34656 ^ _776545) ^ [_1422105, _1422107] : [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), _1422105))), 34659 ^ _776545 : [(34666 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422107)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422105)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422107), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422105)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422105)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422107), 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), _1422105)))))], (34660 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422107)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422105))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422107), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422105)) = 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), _1422107)))]]], (46389 ^ _776545) ^ [_1709426, _1709428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709426), _1709428)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1709426, _1709428)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1709428), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (28769 ^ _776545) ^ [_1292362, _1292364] : [-(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), _1292362)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1292364)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1292362))) = 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), _1292364)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1292362)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (39493 ^ _776545) ^ [_1542098, _1542100, _1542102, _1542104, _1542106, _1542108, _1542110, _1542112] : [c_Fun_Oinj__on(_1542098, _1542100, _1542102, _1542104), c_Fun_Oinj__on(_1542106, _1542108, _1542110, _1542112), -(c_Fun_Oinj__on(tc_prod(_1542098, _1542106), tc_prod(_1542100, _1542108), c_Product__Type_Omap__pair(_1542098, _1542100, _1542106, _1542108, _1542102, _1542110), hAPP(hAPP(c_Product__Type_OSigma(_1542098, _1542106), _1542104), hAPP(c_COMBK(tc_fun(_1542106, tc_HOL_Obool), _1542098), _1542112))))], (38661 ^ _776545) ^ [_1519297, _1519299, _1519301, _1519303] : [-(hAPP(c_Set_Ovimage(_1519297, _1519299, _1519301), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1519299, tc_HOL_Obool)), _1519303)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1519297, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519297, _1519299, _1519301), _1519303)))], (27569 ^ _776545) ^ [_1272497, _1272499] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1272497), _1272499)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1272497) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33273 ^ _776545) ^ [_1386495, _1386497, _1386499, _1386501] : [33275 ^ _776545 : [(33278 ^ _776545) ^ [] : [hAPP(_1386501, 33274 ^ [_1386495, _1386497, _1386499, _1386501]) = c_Orderings_Obot__class_Obot(tc_fun(_1386497, tc_HOL_Obool))], (33276 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386495), 33274 ^ [_1386495, _1386497, _1386499, _1386501]), _1386499)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386495, tc_fun(_1386497, tc_HOL_Obool)), _1386499), _1386501) = c_Orderings_Obot__class_Obot(tc_fun(_1386497, tc_HOL_Obool)))], (50969 ^ _776545) ^ [_1808780] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808780), _1808780)))], (2596 ^ _776545) ^ [_814804, _814806, _814808, _814810, _814812, _814814, _814816, _814818] : [-(c_Recdef_Osame__fst(_814818, _814814, _814810, _814806) = c_Recdef_Osame__fst(_814816, _814812, _814808, _814804)), _814818 = _814816, _814814 = _814812, _814810 = _814808, _814806 = _814804], (16875 ^ _776545) ^ [_1080186, _1080188, _1080190, _1080192] : [class_Groups_Oordered__comm__monoid__add(_1080186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080186), c_Groups_Ozero__class_Ozero(_1080186)), _1080188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080186), _1080190), _1080192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080186), _1080190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080186), _1080188), _1080192))))], (7274 ^ _776545) ^ [_895379, _895381, _895383, _895385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895379, tc_HOL_Obool)), _895381), _895383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895379, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_895379), _895385), _895381)), hAPP(hAPP(c_Set_Oinsert(_895379), _895385), _895383))))], (23235 ^ _776545) ^ [_1197492, _1197494, _1197496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197492)), 23238 ^ _776545 : [(23239 ^ _776545) ^ [_1197626] : [23241 ^ _776545 : [(23247 ^ _776545) ^ [] : [-(_1197626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23243 ^ [_1197492, _1197494, _1197496, _1197626]), 23240 ^ [_1197492, _1197494, _1197496, _1197626]))], (23245 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23243 ^ [_1197492, _1197494, _1197496, _1197626]), _1197494)))], (23242 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23240 ^ [_1197492, _1197494, _1197496, _1197626]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1197492))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197626), _1197496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197626), _1197492)), _1197496)))]]], (8579 ^ _776545) ^ [_923908, _923910, _923912] : [class_Lattices_Olattice(_923908), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923908), _923910), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923908), _923912), _923910))))], (27058 ^ _776545) ^ [_1263825] : [c_Nat__Transfer_Onat__set(_1263825), -(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), _1263825)) = _1263825)], (2626 ^ _776545) ^ [_815275, _815277, _815279, _815281] : [-(c_Nitpick_Onumber__of__frac(_815281, _815277) = c_Nitpick_Onumber__of__frac(_815279, _815275)), _815281 = _815279, _815277 = _815275], (10705 ^ _776545) ^ [_960984, _960986, _960988] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960984, tc_HOL_Obool)), _960986), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960984, tc_HOL_Obool)), _960988)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960984, tc_HOL_Obool)), _960986), _960988))], (28915 ^ _776545) ^ [_1294931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1294931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1294931)))], (23878 ^ _776545) ^ [_1209062, _1209064, _1209066] : [class_Rings_Olinordered__semidom(_1209062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209062), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209062), _1209064)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209062), _1209066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209064), _1209066)))], (52013 ^ _776545) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (44625 ^ _776545) ^ [_1668794, _1668796, _1668798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668794), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668796)), _1668798))), -(c_List_Olast(_1668796, hAPP(hAPP(c_List_Odrop(_1668796), _1668794), _1668798)) = c_List_Olast(_1668796, _1668798))], (38483 ^ _776545) ^ [_1514338, _1514340, _1514342] : [c_Wellfounded_OwfP(_1514338, _1514340), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1514338, _1514340), _1514342)))], (46233 ^ _776545) ^ [_1706369, _1706371, _1706373, _1706375] : [-(c_List_Ofoldr(_1706369, _1706371, _1706373, c_List_Olist_ONil(_1706369), _1706375) = _1706375)], (3312 ^ _776545) ^ [_825980, _825982, _825984, _825986] : [-(c_Code__Numeral_Onat__of__aux(_825986, _825982) = c_Code__Numeral_Onat__of__aux(_825984, _825980)), _825986 = _825984, _825982 = _825980], (3306 ^ _776545) ^ [_825895, _825897] : [_825897 = _825895, -(c_Random_Orange(_825897) = c_Random_Orange(_825895))], (26847 ^ _776545) ^ [_1260396, _1260398] : [c_Nat__Transfer_Ois__nat(_1260396), c_Nat__Transfer_Ois__nat(_1260398), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1260396, _1260398)))], (48644 ^ _776545) ^ [_1757222, _1757224, _1757226, _1757228, _1757230] : [c_List_Oreplicate(_1757222, _1757224, _1757226) = c_List_Oreplicate(_1757222, _1757228, _1757230), 48647 ^ _776545 : [(48650 ^ _776545) ^ [] : [-(_1757224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1757226 = _1757230)], (48648 ^ _776545) ^ [] : [-(_1757224 = _1757228)]]], (22357 ^ _776545) ^ [] : [-(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))], (43112 ^ _776545) ^ [_1635506] : [-(hAPP(c_List_Oset(_1635506), c_List_Olist_ONil(_1635506)) = c_Orderings_Obot__class_Obot(tc_fun(_1635506, tc_HOL_Obool)))], (29851 ^ _776545) ^ [_1311747, _1311749, _1311751, _1311753] : [29853 ^ _776545 : [(29858 ^ _776545) ^ [] : [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(_1311751, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29852 ^ [_1311747, _1311749, _1311751, _1311753]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1311751, 29852 ^ [_1311747, _1311749, _1311751, _1311753])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29856 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29852 ^ [_1311747, _1311749, _1311751, _1311753]), _1311749)))], (29854 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311747), 29852 ^ [_1311747, _1311749, _1311751, _1311753])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1311747), _1311749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1311751, _1311747)), _1311753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1311753), hAPP(_1311751, _1311749))), 29872 ^ _776545 : [(29877 ^ _776545) ^ [] : [-(hAPP(_1311751, 29871 ^ [_1311747, _1311749, _1311751, _1311753]) = _1311753)], (29875 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29871 ^ [_1311747, _1311749, _1311751, _1311753]), _1311749)))], (29873 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311747), 29871 ^ [_1311747, _1311749, _1311751, _1311753])))]]], (5534 ^ _776545) ^ [_861085, _861087] : [_861087 = _861085, -(c_Rings_Odvd__class_Odvd(_861087) = c_Rings_Odvd__class_Odvd(_861085))], (35298 ^ _776545) ^ [_1435081, _1435083, _1435085, _1435087, _1435089, _1435091] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435081, _1435083), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435085), _1435087))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435081, _1435083), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435089), _1435091))), -(_1435083 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435085 = _1435089)], (49812 ^ _776545) ^ [_1782839, _1782841] : [c_Predicate_Osymp(_1782839, _1782841), -(c_Relation_Osym(_1782839, hAPP(c_Set_OCollect(tc_prod(_1782839, _1782839)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782839, _1782839, tc_HOL_Obool), _1782841))))], (40649 ^ _776545) ^ [_1570466, _1570468, _1570470, _1570472, _1570474] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570466, _1570466)), hAPP(hAPP(c_Product__Type_OPair(_1570466, _1570466), _1570468), _1570470)), c_Transitive__Closure_Otrancl(_1570466, _1570472))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570466, _1570466)), hAPP(hAPP(c_Product__Type_OPair(_1570466, _1570466), _1570470), _1570474)), _1570472)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570466, _1570466)), hAPP(hAPP(c_Product__Type_OPair(_1570466, _1570466), _1570468), _1570474)), c_Transitive__Closure_Otrancl(_1570466, _1570472))))], (38239 ^ _776545) ^ [_1508781, _1508783, _1508785] : [c_Wellfounded_Owf(_1508781, _1508783), -(hBOOL(hAPP(hAPP(c_member(_1508781), _1508785), c_Wellfounded_Oacc(_1508781, _1508783))))], (49824 ^ _776545) ^ [_1783066, _1783068] : [c_Equiv__Relations_Opart__equivp(_1783066, _1783068), 49828 ^ _776545 : [(49833 ^ _776545) ^ [] : [-(c_Predicate_Otransp(_1783066, _1783068))], (49831 ^ _776545) ^ [] : [-(c_Predicate_Osymp(_1783066, _1783068))], (49829 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1783068, 49827 ^ [_1783066, _1783068]), 49827 ^ [_1783066, _1783068])))]]], (28887 ^ _776545) ^ [_1294404, _1294406] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1294404)), c_Int_OBit0(_1294406)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1294404), _1294406)))], (52361 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (24962 ^ _776545) ^ [_1228611, _1228613] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228611), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228613)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228611, _1228613)))], (29069 ^ _776545) ^ [_1297620] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1297620), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297620)), c_Int_OPls)))], (46480 ^ _776545) ^ [_1711479, _1711481] : [class_Orderings_Olinorder(_1711479), -(c_List_Olinorder__class_Osorted(_1711479, c_List_Olinorder__class_Osort__key(_1711479, _1711479, c_COMBI(_1711479), _1711481)))], (45906 ^ _776545) ^ [_1697436, _1697438, _1697440, _1697442] : [class_Orderings_Olinorder(_1697436), 45909 ^ _776545 : [(45916 ^ _776545) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1697438), _1697442)), -(hBOOL(hAPP(c_List_Odistinct(_1697438), c_List_Olinorder__class_Osort__key(_1697438, _1697436, _1697440, _1697442))))], (45910 ^ _776545) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1697438), c_List_Olinorder__class_Osort__key(_1697438, _1697436, _1697440, _1697442))), -(hBOOL(hAPP(c_List_Odistinct(_1697438), _1697442)))]]], (28433 ^ _776545) ^ [_1286893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1286893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1286893))))], (11534 ^ _776545) ^ [_978145, _978147] : [class_Finite__Set_Ofinite(_978145), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978145), _978147)))], (29283 ^ _776545) ^ [] : [-(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))))))], (12241 ^ _776545) ^ [_991347, _991349, _991351, _991353, _991355, _991357, _991359, _991361] : [c_Finite__Set_Ofolding__image__simple(_991347, _991349, _991351, _991353, _991355, _991357), hBOOL(hAPP(c_Finite__Set_Ofinite(_991349), _991359)), -(hBOOL(hAPP(hAPP(c_member(_991349), _991361), _991359))), -(hAPP(_991357, hAPP(hAPP(c_Set_Oinsert(_991349), _991361), _991359)) = hAPP(hAPP(_991351, hAPP(_991355, _991361)), hAPP(_991357, _991359)))], (38245 ^ _776545) ^ [_1508895, _1508897] : [c_Wellfounded_Owf(_1508895, _1508897), 38248 ^ _776545 : [(38249 ^ _776545) ^ [_1508964] : [-(hBOOL(hAPP(hAPP(c_member(_1508895), _1508964), c_Wellfounded_Oacc(_1508895, _1508897))))]]], (24964 ^ _776545) ^ [_1228653, _1228655] : [-(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, _1228653, _1228655)), _1228655) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228653), _1228655))], (10116 ^ _776545) ^ [_949762, _949764, _949766, _949768] : [class_Orderings_Olinorder(_949762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949762), _949764), _949766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949762), _949766), _949768)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_949762, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949762, _949764, _949766)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949762, _949766, _949768)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_949762, _949764, _949768))], (3328 ^ _776545) ^ [_826214, _826216] : [_826216 = _826214, -(c_Int_OBit1(_826216) = c_Int_OBit1(_826214))], (31549 ^ _776545) ^ [_1342971, _1342973, _1342975] : [class_Orderings_Olinorder(_1342971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342971), _1342973), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342971), _1342973), _1342975))))], (5442 ^ _776545) ^ [_859691, _859693, _859695, _859697, _859699, _859701] : [-(c_SetInterval_Oord_OgreaterThan(_859701, _859697, _859693) = c_SetInterval_Oord_OgreaterThan(_859699, _859695, _859691)), _859701 = _859699, _859697 = _859695, _859693 = _859691], (49648 ^ _776545) ^ [_1780014, _1780016] : [c_Relation_Osym(_1780014, _1780016), c_Relation_Otrans(_1780014, _1780016), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1780014, _1780014), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1780014, _1780014, _1780014), hAPP(c_Relation_Oconverse(_1780014, _1780014), _1780016)), _1780016)), _1780016)))], (18880 ^ _776545) ^ [_1116655, _1116657] : [-(_1116655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116655), _1116657) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116655), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1116657)))], (22309 ^ _776545) ^ [_1180999, _1181001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180999), _1181001))), -(_1180999 = _1181001), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181001), _1180999)))], (51999 ^ _776545) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (32972 ^ _776545) ^ [_1378147, _1378149, _1378151, _1378153, _1378155] : [class_Groups_Ominus(_1378147), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378149, _1378147)), _1378151), _1378153), _1378155) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1378147), hAPP(_1378151, _1378155)), hAPP(_1378153, _1378155)))], (16488 ^ _776545) ^ [_1073465, _1073467] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1073465), _1073467)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1073465)), hAPP(c_Nat_OSuc, _1073467)))], (28201 ^ _776545) ^ [_1282890, _1282892] : [class_Int_Onumber__ring(_1282890), -(hAPP(c_Int_Onumber__class_Onumber__of(_1282890), c_Int_Opred(_1282892)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282890), hAPP(c_Groups_Ouminus__class_Ouminus(_1282890), c_Groups_Oone__class_Oone(_1282890))), hAPP(c_Int_Onumber__class_Onumber__of(_1282890), _1282892)))], (40837 ^ _776545) ^ [_1575986, _1575988] : [-(hAPP(c_Relation_ODomain(_1575986, _1575986), c_Transitive__Closure_Ortrancl(_1575986, _1575988)) = c_Orderings_Otop__class_Otop(tc_fun(_1575986, tc_HOL_Obool)))], (45736 ^ _776545) ^ [_1694187, _1694189, _1694191, _1694193, _1694195] : [c_Finite__Set_Ofun__left__comm(_1694187, _1694189, _1694191), -(hAPP(hAPP(c_Finite__Set_Ofold(_1694187, _1694189, _1694191), _1694193), hAPP(c_List_Oset(_1694187), _1694195)) = hAPP(c_List_Ofoldl(_1694189, _1694187, hAPP(c_COMBC(_1694187, _1694189, _1694189), _1694191), _1694193), c_List_Oremdups(_1694187, _1694195)))], (40522 ^ _776545) ^ [_1567357, _1567359, _1567361, _1567363, _1567365, _1567367, _1567369, _1567371, _1567373] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567357, _1567359, _1567361, _1567363), hAPP(hAPP(c_Product__Type_Oscomp(_1567357, _1567365, _1567367, tc_prod(_1567359, _1567361)), _1567369), _1567371)), _1567373) = hAPP(hAPP(c_Product__Type_Oscomp(_1567357, _1567365, _1567367, _1567363), _1567369), hAPP(hAPP(c_COMBC(_1567365, tc_fun(_1567359, tc_fun(_1567361, _1567363)), tc_fun(_1567367, _1567363)), hAPP(hAPP(c_COMBB(tc_fun(_1567367, tc_prod(_1567359, _1567361)), tc_fun(tc_fun(_1567359, tc_fun(_1567361, _1567363)), tc_fun(_1567367, _1567363)), _1567365), c_Product__Type_Oscomp(_1567367, _1567359, _1567361, _1567363)), _1567371)), _1567373)))], (34445 ^ _776545) ^ [_1417648, _1417650] : [-(c_Divides_OposDivAlg(_1417648, _1417650) = hAPP(c_Divides_Oadjust(_1417650), c_Divides_OposDivAlg(_1417648, 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)))), _1417650)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417648), _1417650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1417650), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36476 ^ _776545) ^ [_1466559, _1466561, _1466563, _1466565, _1466567] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466559, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466561, _1466559, _1466563), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466561, tc_HOL_Obool)), _1466565), _1466567))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466559, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466561, _1466559, _1466563), _1466565)), hAPP(c_Relation_OImage(_1466561, _1466559, _1466563), _1466567)))))], (30266 ^ _776545) ^ [_1319391, _1319393, _1319395, _1319397] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1319391), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319391), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319391), _1319393), _1319395)), _1319397) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319391), _1319393), _1319397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319391), _1319395), _1319397)))], (14756 ^ _776545) ^ [_1042528, _1042530, _1042532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042528), _1042530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042532), _1042530))))], (25103 ^ _776545) ^ [_1230991] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1230991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230991)))], (51881 ^ _776545) ^ [_1824938, _1824940] : [class_Lattices_Olattice(_1824938), -(class_Lattices_Osemilattice__inf(tc_fun(_1824940, _1824938)))], (10713 ^ _776545) ^ [_961152, _961154] : [class_Orderings_Olinorder(_961152), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961152, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_961152), _961154)) = hAPP(c_SetInterval_Oord__class_OatLeast(_961152), _961154))], (51685 ^ _776545) ^ [_1821908, _1821910] : [class_Rings_Ocomm__semiring__1(_1821908), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821908), _1821910), _1821910)))], (25369 ^ _776545) ^ [_1235521] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235521)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235521)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235521))], (18710 ^ _776545) ^ [_1113449, _1113451, _1113453] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113449), _1113451)), 18713 ^ _776545 : [(18720 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1113449), _1113453), _1113451))), -(hAPP(c_Finite__Set_Ocard(_1113449), hAPP(hAPP(c_Set_Oinsert(_1113449), _1113453), _1113451)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1113449), _1113451)))], (18714 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1113449), _1113453), _1113451)), -(hAPP(c_Finite__Set_Ocard(_1113449), hAPP(hAPP(c_Set_Oinsert(_1113449), _1113453), _1113451)) = hAPP(c_Finite__Set_Ocard(_1113449), _1113451))]]], (52159 ^ _776545) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (42970 ^ _776545) ^ [_1632985, _1632987, _1632989] : [hBOOL(hAPP(c_List_Odistinct(_1632985), _1632987)), -(hAPP(c_List_Oset(_1632985), c_List_Oremove1(_1632985, _1632989, _1632987)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632985, tc_HOL_Obool)), hAPP(c_List_Oset(_1632985), _1632987)), hAPP(hAPP(c_Set_Oinsert(_1632985), _1632989), c_Orderings_Obot__class_Obot(tc_fun(_1632985, tc_HOL_Obool)))))], (52049 ^ _776545) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (47860 ^ _776545) ^ [_1740104, _1740106, _1740108, _1740110, _1740112] : [hAPP(c_List_Ofilter(_1740104, _1740106), _1740108) = hAPP(hAPP(c_List_Olist_OCons(_1740104), _1740110), _1740112), 47865 ^ _776545 : [(47874 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1740106, _1740110)))], (47876 ^ _776545) ^ [] : [-(_1740112 = hAPP(c_List_Ofilter(_1740104, _1740106), 47864 ^ [_1740104, _1740106, _1740108, _1740110, _1740112]))], (47868 ^ _776545) ^ [_1740418] : [hBOOL(hAPP(hAPP(c_member(_1740104), _1740418), hAPP(c_List_Oset(_1740104), 47863 ^ [_1740104, _1740106, _1740108, _1740110, _1740112]))), hBOOL(hAPP(_1740106, _1740418))], (47866 ^ _776545) ^ [] : [-(_1740108 = hAPP(hAPP(c_List_Oappend(_1740104), 47863 ^ [_1740104, _1740106, _1740108, _1740110, _1740112]), hAPP(hAPP(c_List_Olist_OCons(_1740104), _1740110), 47864 ^ [_1740104, _1740106, _1740108, _1740110, _1740112])))]]], (24295 ^ _776545) ^ [_1215938, _1215940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215938)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215940))))), _1215938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1215940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (14598 ^ _776545) ^ [_1039706, _1039708, _1039710] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039706), _1039708)), _1039710) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039708), _1039710)))], (7756 ^ _776545) ^ [_906727, _906729, _906731, _906733] : [hBOOL(hAPP(hAPP(c_member(_906727), _906729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906727, tc_HOL_Obool)), _906731), _906733))), hBOOL(hAPP(hAPP(c_member(_906727), _906729), _906733))], (11238 ^ _776545) ^ [_971701, _971703, _971705, _971707, _971709, _971711, _971713] : [c_Finite__Set_Ofun__left__comm(_971701, _971703, _971705), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_971701, _971703, _971705, _971707, _971709), _971711)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_971701, _971703, _971705, _971707, _971709), _971713)), -(_971713 = _971711)], (18071 ^ _776545) ^ [_1101516, _1101518, _1101520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101516)), 18074 ^ _776545 : [(18081 ^ _776545) ^ [] : [_1101518 = _1101520, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101516), _1101518) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101516), _1101520))], (18075 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101516), _1101518) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101516), _1101520), -(_1101518 = _1101520)]]], (52191 ^ _776545) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (29175 ^ _776545) ^ [] : [-(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))))], (48760 ^ _776545) ^ [_1759161, _1759163, _1759165] : [-(hAPP(c_List_Oset(_1759161), c_List_Oreplicate(_1759161, hAPP(c_Nat_OSuc, _1759163), _1759165)) = hAPP(hAPP(c_Set_Oinsert(_1759161), _1759165), c_Orderings_Obot__class_Obot(tc_fun(_1759161, tc_HOL_Obool))))], (50023 ^ _776545) ^ [_1787062, _1787064, _1787066, _1787068] : [hAPP(c_Set_Oimage(_1787062, _1787064, _1787066), c_Orderings_Otop__class_Otop(tc_fun(_1787062, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1787064, tc_HOL_Obool)), -(hAPP(_1787066, hAPP(c_Hilbert__Choice_Oinv__into(_1787062, _1787064, c_Orderings_Otop__class_Otop(tc_fun(_1787062, tc_HOL_Obool)), _1787066), _1787068)) = _1787068)], (38495 ^ _776545) ^ [_1514530, _1514532, _1514534] : [c_Wellfounded_OwfP(_1514530, _1514532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514530, tc_fun(_1514530, tc_HOL_Obool))), _1514534), _1514532)), -(c_Wellfounded_OwfP(_1514530, _1514534))], (51169 ^ _776545) ^ [_1812727, _1812729, _1812731, _1812733] : [class_Divides_Osemiring__div(_1812727), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812727), _1812729), _1812731)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812727), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812727), _1812731), _1812729)), _1812733) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812727), _1812731), _1812733)), _1812729))], (33427 ^ _776545) ^ [_1390864, _1390866, _1390868, _1390870, _1390872, _1390874] : [class_Complete__Lattice_Ocomplete__lattice(_1390864), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390866, _1390864), _1390868), hAPP(hAPP(c_COMBB(tc_fun(_1390870, _1390864), _1390864, _1390866), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390870, _1390864), _1390872)), _1390874)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390870, _1390864), _1390872), hAPP(hAPP(c_COMBB(tc_fun(_1390866, _1390864), _1390864, _1390870), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390866, _1390864), _1390868)), hAPP(c_COMBC(_1390866, _1390870, _1390864), _1390874))))], (3334 ^ _776545) ^ [_826299, _826301, _826303, _826305] : [-(c_List_Olistsp(_826305, _826301) = c_List_Olistsp(_826303, _826299)), _826305 = _826303, _826301 = _826299], (24716 ^ _776545) ^ [_1223701, _1223703] : [_1223701 = _1223703, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223701) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223703))], (44912 ^ _776545) ^ [_1675788, _1675790, _1675792, _1675794, _1675796, _1675798] : [-(hBOOL(hAPP(hAPP(c_member(_1675788), _1675790), hAPP(c_List_Oset(_1675788), _1675792)))), -(hAPP(hAPP(c_List_Omap(_1675788, _1675794), c_Fun_Ofun__upd(_1675788, _1675794, _1675796, _1675790, _1675798)), _1675792) = hAPP(hAPP(c_List_Omap(_1675788, _1675794), _1675796), _1675792))], (52053 ^ _776545) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (16578 ^ _776545) ^ [_1074814, _1074816, _1074818] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074814), _1074816) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074814), _1074818), -(_1074814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1074816 = _1074818)], (8962 ^ _776545) ^ [_931314, _931316, _931318] : [class_Orderings_Olinorder(_931314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931314), _931316), _931318)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931314, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_931314, _931316, _931318)), hAPP(c_SetInterval_Oord__class_OatLeast(_931314), _931318)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_931314), _931316))], (24281 ^ _776545) ^ [_1215670, _1215672] : [24282 ^ _776545 : [(24283 ^ _776545) ^ [_1215726] : [_1215672 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215670), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1215726)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215670), _1215672)))], (13324 ^ _776545) ^ [_1012874, _1012876, _1012878, _1012880, _1012882] : [class_Groups_Ocomm__monoid__mult(_1012874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012876), _1012878)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012876), _1012880)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012876, tc_HOL_Obool)), _1012878), _1012880) = c_Orderings_Obot__class_Obot(tc_fun(_1012876, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012876, _1012874), _1012882), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012876, tc_HOL_Obool)), _1012878), _1012880)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012874), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012876, _1012874), _1012882), _1012878)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012876, _1012874), _1012882), _1012880)))], (18920 ^ _776545) ^ [_1117330, _1117332, _1117334] : [class_Rings_Olinordered__ring__strict(_1117330), 18923 ^ _776545 : [(18932 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117330), _1117332), _1117332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117330), _1117334), _1117334))), c_Groups_Ozero__class_Ozero(_1117330)))), _1117332 = c_Groups_Ozero__class_Ozero(_1117330), _1117334 = c_Groups_Ozero__class_Ozero(_1117330)], (18924 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117330), _1117332), _1117332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117330), _1117334), _1117334))), c_Groups_Ozero__class_Ozero(_1117330))), 18927 ^ _776545 : [(18930 ^ _776545) ^ [] : [-(_1117334 = c_Groups_Ozero__class_Ozero(_1117330))], (18928 ^ _776545) ^ [] : [-(_1117332 = c_Groups_Ozero__class_Ozero(_1117330))]]]]], (25471 ^ _776545) ^ [_1237291, _1237293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1237291), _1237293)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237293), _1237291) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237293), _1237291)), _1237291)))], (26893 ^ _776545) ^ [_1261054, _1261056] : [class_Int_Oring__char__0(_1261054), 26896 ^ _776545 : [(26903 ^ _776545) ^ [] : [_1261056 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1261054) = hAPP(c_Int_Oring__1__class_Oof__int(_1261054), _1261056))], (26897 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1261054) = hAPP(c_Int_Oring__1__class_Oof__int(_1261054), _1261056), -(_1261056 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (48184 ^ _776545) ^ [_1747183, _1747185, _1747187] : [c_List_Olist__all(_1747183, _1747185, _1747187), 48187 ^ _776545 : [(48188 ^ _776545) ^ [_1747272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747272), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747183)), _1747187))), -(hBOOL(hAPP(_1747185, hAPP(hAPP(c_List_Onth(_1747183), _1747187), _1747272))))]]], (48619 ^ _776545) ^ [_1756721, _1756723, _1756725, _1756727] : [48626 ^ _776545 : [(48629 ^ _776545) ^ [] : [_1756723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48627 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1756727, _1756725)))]], 48620 ^ _776545 : [(48621 ^ _776545) ^ [_1756793] : [hBOOL(hAPP(hAPP(c_member(_1756721), _1756793), hAPP(c_List_Oset(_1756721), c_List_Oreplicate(_1756721, _1756723, _1756725)))), hBOOL(hAPP(_1756727, _1756793))]]], (20027 ^ _776545) ^ [_1138131, _1138133, _1138135, _1138137] : [class_Fields_Olinordered__field__inverse__zero(_1138131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138131), _1138133), _1138135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138131), c_Groups_Ozero__class_Ozero(_1138131)), _1138137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138131), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138131), _1138133), _1138137)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138131), _1138135), _1138137))))], (40343 ^ _776545) ^ [_1563121, _1563123, _1563125] : [-(c_Hilbert__Choice_OEps(tc_prod(_1563121, _1563123), hAPP(c_Product__Type_Oprod_Oprod__case(_1563121, _1563123, tc_HOL_Obool), _1563125)) = c_Hilbert__Choice_OEps(tc_prod(_1563121, _1563123), hAPP(hAPP(c_COMBS(tc_prod(_1563121, _1563123), _1563123, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1563121, tc_fun(_1563123, tc_HOL_Obool), tc_prod(_1563121, _1563123)), _1563125), c_Product__Type_Ofst(_1563121, _1563123))), c_Product__Type_Osnd(_1563121, _1563123))))], (14883 ^ _776545) ^ [_1044947, _1044949, _1044951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044947), _1044949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044947), _1044951)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044949), _1044951))))], (48720 ^ _776545) ^ [_1758503, _1758505, _1758507, _1758509] : [hBOOL(hAPP(hAPP(c_member(_1758503), _1758505), hAPP(c_List_Oset(_1758503), c_List_Oreplicate(_1758503, _1758507, _1758509)))), 48723 ^ _776545 : [(48726 ^ _776545) ^ [] : [_1758507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48724 ^ _776545) ^ [] : [-(_1758505 = _1758509)]]], (29045 ^ _776545) ^ [_1297192, _1297194] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297192))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297194))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297192)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297194)))], (37736 ^ _776545) ^ [_1495420, _1495422, _1495424, _1495426] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495420), _1495422)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495424), _1495426)), 37743 ^ _776545 : [(37744 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495420), _1495422)), hAPP(c_Finite__Set_Ocard(_1495424), _1495426)))), 37745 ^ _776545 : [(37746 ^ _776545) ^ [_1495631] : [c_Fun_Oinj__on(_1495420, _1495424, _1495631, _1495422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495424, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495420, _1495424, _1495631), _1495422)), _1495426))]]], (37754 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495420), _1495422)), hAPP(c_Finite__Set_Ocard(_1495424), _1495426))), 37758 ^ _776545 : [(37761 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495424, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495420, _1495424, 37757 ^ [_1495420, _1495422, _1495424, _1495426]), _1495422)), _1495426)))], (37759 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1495420, _1495424, 37757 ^ [_1495420, _1495422, _1495424, _1495426], _1495422))]]]]], (3554 ^ _776545) ^ [_829687, _829689, _829691, _829693, _829695, _829697] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_829697, _829693, _829689) = c_SetInterval_Oord__class_OgreaterThanLessThan(_829695, _829691, _829687)), _829697 = _829695, _829693 = _829691, _829689 = _829687], (5136 ^ _776545) ^ [_854908, _854910, _854912, _854914, _854916, _854918] : [-(c_Set_Oimage(_854918, _854914, _854910) = c_Set_Oimage(_854916, _854912, _854908)), _854918 = _854916, _854914 = _854912, _854910 = _854908], (29191 ^ _776545) ^ [_1299741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1299741)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299741), c_Int_OMin)))], (43904 ^ _776545) ^ [_1653803, _1653805, _1653807, _1653809] : [-(hAPP(hAPP(c_List_Odrop(_1653803), _1653805), hAPP(hAPP(c_List_Odrop(_1653803), _1653807), _1653809)) = hAPP(hAPP(c_List_Odrop(_1653803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653805), _1653807)), _1653809))], (30244 ^ _776545) ^ [_1319042, _1319044, _1319046, _1319048] : [class_Orderings_Olinorder(_1319042), 30247 ^ _776545 : [(30248 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319042), _1319044), _1319046)), _1319048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), _1319044), _1319048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), _1319046), _1319048)))], (30258 ^ _776545) ^ [] : [30259 ^ _776545 : [(30262 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), _1319046), _1319048))], (30260 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), _1319044), _1319048))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319042), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319042), _1319044), _1319046)), _1319048)))]]], (50767 ^ _776545) ^ [_1802629, _1802631, _1802633] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802629, _1802629)), hAPP(hAPP(c_Product__Type_OPair(_1802629, _1802629), hAPP(_1802631, hAPP(c_Nat_OSuc, 50768 ^ [_1802629, _1802631, _1802633]))), hAPP(_1802631, 50768 ^ [_1802629, _1802631, _1802633]))), c_Transitive__Closure_Ortrancl(_1802629, _1802633))), c_Wellfounded_Owf(_1802629, c_Transitive__Closure_Otrancl(_1802629, _1802633)), 50776 ^ _776545 : [(50777 ^ _776545) ^ [_1802895] : [-(hAPP(_1802631, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50775 ^ [_1802629, _1802631, _1802633]), _1802895)) = hAPP(_1802631, 50775 ^ [_1802629, _1802631, _1802633]))]]], (28413 ^ _776545) ^ [_1286568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286568)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286568), c_Int_OPls)))], (9410 ^ _776545) ^ [_938395, _938397, _938399] : [class_Orderings_Olinorder(_938395), 9413 ^ _776545 : [(9420 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938395), _938399), _938397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938395), _938397), _938399))], (9414 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938395), _938397), _938399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938395), _938399), _938397)))]]], (8505 ^ _776545) ^ [_922646, _922648, _922650] : [class_Lattices_Osemilattice__sup(_922646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922646), _922648), _922650)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922646), _922648), _922650) = _922650)], (44080 ^ _776545) ^ [_1658109, _1658111, _1658113, _1658115, _1658117] : [-(hAPP(hAPP(c_List_Ozip(_1658109, _1658111), _1658113), hAPP(hAPP(c_List_Oappend(_1658111), _1658115), _1658117)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1658109, _1658111)), hAPP(hAPP(c_List_Ozip(_1658109, _1658111), hAPP(hAPP(c_List_Otake(_1658109), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658111)), _1658115)), _1658113)), _1658115)), hAPP(hAPP(c_List_Ozip(_1658109, _1658111), hAPP(hAPP(c_List_Odrop(_1658109), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658111)), _1658115)), _1658113)), _1658117)))], (16050 ^ _776545) ^ [_1066822, _1066824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066822), hAPP(c_Nat_OSuc, _1066824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066822), _1066824))), -(_1066822 = _1066824)], (1040 ^ _776545) ^ [_792245, _792247, _792249, _792251, _792253, _792255] : [-(c_List_Oall__interval__nat(_792253, _792249, _792245)), c_List_Oall__interval__nat(_792255, _792251, _792247), _792255 = _792253, _792251 = _792249, _792247 = _792245], (52559 ^ _776545) ^ [_1832212, _1832214] : [hBOOL(hAPP(hAPP(c_fimplies, _1832212), _1832214)), hBOOL(_1832212), -(hBOOL(_1832214))], (18616 ^ _776545) ^ [_1111636, _1111638, _1111640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111636), _1111638)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111636), _1111640))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111638), _1111640)))], (41270 ^ _776545) ^ [_1586310, _1586312] : [-(c_Relation_Osingle__valued(_1586310, _1586310, c_Relation_OId__on(_1586310, _1586312)))], (254 ^ _776545) ^ [_780510, _780512] : [-(class_Fields_Ofield(_780510)), _780512 = _780510, class_Fields_Ofield(_780512)], (47034 ^ _776545) ^ [_1721972, _1721974, _1721976, _1721978, _1721980] : [c_List_Olist__all2(_1721972, _1721974, _1721976, hAPP(c_List_Orev(_1721972), _1721978), _1721980), -(c_List_Olist__all2(_1721972, _1721974, _1721976, _1721978, hAPP(c_List_Orev(_1721974), _1721980)))], (50507 ^ _776545) ^ [_1797516, _1797518, _1797520, _1797522] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797516), _1797518)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797520), _1797522)), 50514 ^ _776545 : [(50521 ^ _776545) ^ [] : [hAPP(c_Finite__Set_Ocard(_1797516), _1797518) = hAPP(c_Finite__Set_Ocard(_1797520), _1797522), -(c_Fun_Obij__betw(_1797516, _1797520, 50524 ^ [_1797516, _1797518, _1797520, _1797522], _1797518, _1797522))], (50515 ^ _776545) ^ [] : [50516 ^ _776545 : [(50517 ^ _776545) ^ [_1797705] : [c_Fun_Obij__betw(_1797516, _1797520, _1797705, _1797518, _1797522)]], -(hAPP(c_Finite__Set_Ocard(_1797516), _1797518) = hAPP(c_Finite__Set_Ocard(_1797520), _1797522))]]], (44862 ^ _776545) ^ [_1674056, _1674058] : [-(hAPP(hAPP(c_List_Ozip(_1674056, _1674056), _1674058), _1674058) = hAPP(hAPP(c_List_Omap(_1674056, tc_prod(_1674056, _1674056)), hAPP(hAPP(c_COMBS(_1674056, _1674056, tc_prod(_1674056, _1674056)), c_Product__Type_OPair(_1674056, _1674056)), c_COMBI(_1674056))), _1674058))], (5496 ^ _776545) ^ [_860524, _860526, _860528, _860530, _860532, _860534] : [-(c_Divides_Odiv__class_Omod(_860534, _860530, _860526) = c_Divides_Odiv__class_Omod(_860532, _860528, _860524)), _860534 = _860532, _860530 = _860528, _860526 = _860524], (15262 ^ _776545) ^ [_1051935, _1051937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1051935), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1051937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051937), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1051935))))), -(_1051935 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1051937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051937), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1051935))))], (34437 ^ _776545) ^ [_1417507, _1417509] : [34438 ^ _776545 : [(34441 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1417509), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34439 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417507), _1417509))]], -(c_Divides_OposDivAlg(_1417507, _1417509) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1417507))], (12987 ^ _776545) ^ [_1005699, _1005701, _1005703] : [class_Lattices_Olattice(_1005699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005699), _1005701)), -(hBOOL(hAPP(hAPP(c_member(_1005699), _1005703), _1005701))), -(c_Big__Operators_Olattice__class_OSup__fin(_1005699, hAPP(hAPP(c_Set_Oinsert(_1005699), _1005703), _1005701)) = hAPP(hAPP(c_Finite__Set_Ofold(_1005699, _1005699, c_Lattices_Osemilattice__sup__class_Osup(_1005699)), _1005703), _1005701))], (23739 ^ _776545) ^ [_1206483] : [23741 ^ _776545 : [(23744 ^ _776545) ^ [] : [hBOOL(hAPP(_1206483, 23740 ^ [_1206483]))], (23742 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23740 ^ [_1206483])))]], 23745 ^ _776545 : [(23746 ^ _776545) ^ [_1206610] : [-(hBOOL(hAPP(_1206483, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206610))))]]], (15866 ^ _776545) ^ [_1063787, _1063789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063789), _1063787))))], (44358 ^ _776545) ^ [_1663730, _1663732] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663730), _1663732) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44361 ^ _776545 : [(44364 ^ _776545) ^ [_1663844] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1663844), hAPP(c_List_Oset(tc_Nat_Onat), _1663732))), -(_1663844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44362 ^ _776545) ^ [] : [-(_1663730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36736 ^ _776545) ^ [_1473510, _1473512, _1473514] : [c_Equiv__Relations_Oequiv(_1473510, _1473512, _1473514), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1473510, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473510), _1473512), _1473514)) = _1473512)], (22383 ^ _776545) ^ [_1182335] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1182335), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1182335)], (7342 ^ _776545) ^ [_896789, _896791] : [class_Complete__Lattice_Ocomplete__lattice(_896789), -(c_Complete__Lattice_OSup__class_OSup(_896789, hAPP(hAPP(c_Set_Oinsert(_896789), _896791), c_Orderings_Obot__class_Obot(tc_fun(_896789, tc_HOL_Obool)))) = _896791)], (7642 ^ _776545) ^ [_903328, _903330, _903332, _903334] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903328, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903328, tc_HOL_Obool)), _903330), _903332)), _903334) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903328, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903328, tc_HOL_Obool)), _903330), _903334)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903328, tc_HOL_Obool)), _903332), _903334)))], (49212 ^ _776545) ^ [_1770096, _1770098] : [c_Relation_Otrans(_1770096, _1770098), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1770096, _1770096), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1770096, _1770096, _1770096), _1770098), _1770098)), _1770098)))], (2570 ^ _776545) ^ [_814413, _814415, _814417, _814419, _814421, _814423] : [-(c_Wellfounded_Omlex__prod(_814423, _814419, _814415) = c_Wellfounded_Omlex__prod(_814421, _814417, _814413)), _814423 = _814421, _814419 = _814417, _814415 = _814413], (45455 ^ _776545) ^ [_1687852, _1687854, _1687856, _1687858, _1687860, _1687862, _1687864] : [c_List_Olist__all2(_1687858, _1687854, hAPP(hAPP(c_COMBB(_1687852, tc_fun(_1687854, tc_HOL_Obool), _1687858), _1687856), _1687860), _1687862, _1687864), -(c_List_Olist__all2(_1687852, _1687854, _1687856, hAPP(hAPP(c_List_Omap(_1687858, _1687852), _1687860), _1687862), _1687864))], (11372 ^ _776545) ^ [_974819, _974821, _974823, _974825, _974827] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974819, _974821, hAPP(hAPP(c_Set_Oinsert(_974819), _974823), _974825)), _974827))), 11373 ^ _776545 : [(11374 ^ _776545) ^ [_974923, _974925] : [hAPP(hAPP(c_Set_Oinsert(_974819), _974823), _974825) = hAPP(hAPP(c_Set_Oinsert(_974819), _974925), _974923), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974819, _974819, _974821, _974925, _974923), _974827)), -(hBOOL(hAPP(hAPP(c_member(_974819), _974925), _974923)))]]], (3834 ^ _776545) ^ [_834119, _834121, _834123, _834125, _834127, _834129] : [-(c_List_OdropWhile(_834129, _834125, _834121) = c_List_OdropWhile(_834127, _834123, _834119)), _834129 = _834127, _834125 = _834123, _834121 = _834119], (26118 ^ _776545) ^ [_1248531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248531), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1248531) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11550 ^ _776545) ^ [_978435] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_978435)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_978435), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978435), c_Orderings_Otop__class_Otop(tc_fun(_978435, tc_HOL_Obool)))))], (37844 ^ _776545) ^ [_1497883, _1497885, _1497887, _1497889, _1497891, _1497893] : [c_Fun_Oinj__on(_1497883, _1497885, _1497887, _1497889), hAPP(_1497887, _1497891) = _1497893, hBOOL(hAPP(hAPP(c_member(_1497883), _1497891), _1497889)), -(hAPP(c_Fun_Othe__inv__into(_1497883, _1497885, _1497889, _1497887), _1497893) = _1497891)], (48412 ^ _776545) ^ [_1751624, _1751626, _1751628, _1751630, _1751632] : [_1751624 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1751626, _1751628, _1751630, _1751632), _1751624) = c_Lazy__Sequence_Ohit__bound(_1751628))], (32484 ^ _776545) ^ [_1361706, _1361708, _1361710, _1361712] : [hBOOL(hAPP(hAPP(c_member(_1361706), _1361712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361706, tc_HOL_Obool)), _1361708), _1361710))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361706, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1361706, tc_fun(_1361706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361706)), _1361708)), hAPP(hAPP(c_COMBC(_1361706, tc_fun(_1361706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361706)), _1361710)), _1361712)))], (23635 ^ _776545) ^ [_1204896, _1204898] : [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)), _1204896)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1204896), _1204898)))], (40833 ^ _776545) ^ [_1575911] : [-(c_Transitive__Closure_Ortrancl(_1575911, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575911, _1575911), tc_HOL_Obool))) = c_Relation_OId(_1575911))], (46359 ^ _776545) ^ [_1708933, _1708935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708933)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708935)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708933), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708935)) = c_List_Olist_ONil(tc_Nat_Onat))], (2160 ^ _776545) ^ [_807886, _807888] : [_807888 = _807886, -(c_HOL_Oequal__class_Oequal(_807888) = c_HOL_Oequal__class_Oequal(_807886))], (43156 ^ _776545) ^ [_1636314, _1636316, _1636318, _1636320] : [-(_1636314 = _1636316), 43159 ^ _776545 : [(43166 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1636318), _1636314), hAPP(c_List_Oset(_1636318), _1636320))), -(hBOOL(hAPP(hAPP(c_member(_1636318), _1636314), hAPP(c_List_Oset(_1636318), c_List_Oremove1(_1636318, _1636316, _1636320)))))], (43160 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1636318), _1636314), hAPP(c_List_Oset(_1636318), c_List_Oremove1(_1636318, _1636316, _1636320)))), -(hBOOL(hAPP(hAPP(c_member(_1636318), _1636314), hAPP(c_List_Oset(_1636318), _1636320))))]]], (43757 ^ _776545) ^ [_1649763, _1649765, _1649767, _1649769] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649763), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649765)), _1649767)))), -(hAPP(hAPP(c_List_Onth(_1649765), hAPP(hAPP(c_List_Oappend(_1649765), _1649767), _1649769)), _1649763) = hAPP(hAPP(c_List_Onth(_1649765), _1649769), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649763), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649765)), _1649767))))], (4664 ^ _776545) ^ [_847466, _847468, _847470, _847472, _847474, _847476, _847478, _847480] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_847480, _847476, _847472, _847468) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_847478, _847474, _847470, _847466)), _847480 = _847478, _847476 = _847474, _847472 = _847470, _847468 = _847466], (41092 ^ _776545) ^ [_1582225, _1582227, _1582229, _1582231, _1582233] : [-(hAPP(c_Relation_Oconverse(_1582225, _1582227), hAPP(hAPP(c_Relation_Orel__comp(_1582225, _1582229, _1582227), _1582231), _1582233)) = hAPP(hAPP(c_Relation_Orel__comp(_1582227, _1582229, _1582225), hAPP(c_Relation_Oconverse(_1582229, _1582227), _1582233)), hAPP(c_Relation_Oconverse(_1582225, _1582229), _1582231)))], (45664 ^ _776545) ^ [_1692443, _1692445] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1692443), tc_fun(_1692443, tc_HOL_Obool), c_List_Oset(_1692443)), hAPP(c_List_Oset(tc_List_Olist(_1692443)), c_Enum_Osublists(_1692443, _1692445))) = hAPP(c_Set_OPow(_1692443), hAPP(c_List_Oset(_1692443), _1692445)))], (52151 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (46781 ^ _776545) ^ [_1716606, _1716608, _1716610, _1716612, _1716614, _1716616] : [class_Orderings_Olinorder(_1716606), c_List_Olinorder__class_Osorted(_1716606, hAPP(hAPP(c_List_Omap(_1716608, _1716606), _1716610), _1716612)), hBOOL(hAPP(_1716614, _1716616)), -(hAPP(c_List_Ofilter(_1716608, _1716614), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716608, _1716606, _1716610), _1716616), _1716612)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716608, _1716606, _1716610), _1716616), hAPP(c_List_Ofilter(_1716608, _1716614), _1716612)))], (50664 ^ _776545) ^ [_1800689, _1800691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800689), _1800691)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1800689, 50667 ^ [_1800689, _1800691], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1800689), _1800691)), _1800691))], (21267 ^ _776545) ^ [_1161306, _1161308, _1161310] : [class_Int_Onumber__ring(_1161306), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161306), hAPP(c_Int_Onumber__class_Onumber__of(_1161306), _1161308)), hAPP(c_Int_Onumber__class_Onumber__of(_1161306), _1161310)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161308), _1161310)))], (23840 ^ _776545) ^ [_1208416, _1208418] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208416)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208418), 23843 ^ _776545 : [(23846 ^ _776545) ^ [] : [-(_1208418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23844 ^ _776545) ^ [] : [-(_1208416 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6154 ^ _776545) ^ [_875265, _875267, _875269, _875271] : [hBOOL(hAPP(hAPP(c_member(_875265), _875267), c_Complete__Lattice_OInf__class_OInf(tc_fun(_875265, tc_HOL_Obool), _875269))), hBOOL(hAPP(hAPP(c_member(tc_fun(_875265, tc_HOL_Obool)), _875271), _875269)), -(hBOOL(hAPP(hAPP(c_member(_875265), _875267), _875271)))], (6497 ^ _776545) ^ [_881502, _881504] : [hAPP(c_Set_OCollect(_881502), _881504) = c_Orderings_Obot__class_Obot(tc_fun(_881502, tc_HOL_Obool)), 6500 ^ _776545 : [(6501 ^ _776545) ^ [_881587] : [hBOOL(hAPP(_881504, _881587))]]], (45702 ^ _776545) ^ [_1693364, _1693366, _1693368] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693364))), c_Enum_On__lists(_1693364, _1693366, _1693368)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693364)), _1693368)), _1693366))], (7750 ^ _776545) ^ [_906596, _906598, _906600, _906602] : [hBOOL(hAPP(hAPP(c_member(_906596), _906598), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906596, tc_HOL_Obool)), _906600), _906602))), -(hBOOL(hAPP(hAPP(c_member(_906596), _906598), _906600)))], (49472 ^ _776545) ^ [_1776559, _1776561] : [c_Predicate_Oreflp(_1776559, _1776561), c_Predicate_Osymp(_1776559, _1776561), c_Predicate_Otransp(_1776559, _1776561), -(c_Equiv__Relations_Oequivp(_1776559, _1776561))], (39337 ^ _776545) ^ [_1538146, _1538148] : [-(hAPP(c_Fun_Oid(_1538146), _1538148) = _1538148)], (1784 ^ _776545) ^ [_801709, _801711] : [-(class_Rings_Osemiring__1(_801709)), _801711 = _801709, class_Rings_Osemiring__1(_801711)], (39822 ^ _776545) ^ [_1551316, _1551318, _1551320, _1551322, _1551324, _1551326, _1551328, _1551330, _1551332, _1551334, _1551336] : [-(hAPP(c_Product__Type_Omap__pair(_1551316, _1551318, _1551320, _1551322, _1551324, _1551326), hAPP(c_Product__Type_Omap__pair(_1551328, _1551316, _1551330, _1551320, _1551332, _1551334), _1551336)) = hAPP(c_Product__Type_Omap__pair(_1551328, _1551318, _1551330, _1551322, hAPP(c_Fun_Ocomp(_1551316, _1551318, _1551328, _1551324), _1551332), hAPP(c_Fun_Ocomp(_1551320, _1551322, _1551330, _1551326), _1551334)), _1551336))], (44216 ^ _776545) ^ [_1660714, _1660716, _1660718] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1660714, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660716)), _1660718)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1660716, _1660714), _1660718) = _1660718)], (42123 ^ _776545) ^ [_1611235] : [-(c_List_Olists(_1611235, c_Orderings_Otop__class_Otop(tc_fun(_1611235, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1611235), tc_HOL_Obool)))], (25919 ^ _776545) ^ [_1245305] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245305, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49678 ^ _776545) ^ [_1780744, _1780746, _1780748, _1780750] : [c_Relation_Osym(_1780744, _1780746), hBOOL(hAPP(hAPP(c_member(tc_prod(_1780744, _1780744)), hAPP(hAPP(c_Product__Type_OPair(_1780744, _1780744), _1780748), _1780750)), _1780746)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780744, _1780744)), hAPP(hAPP(c_Product__Type_OPair(_1780744, _1780744), _1780750), _1780748)), _1780746)))], (5386 ^ _776545) ^ [_858829, _858831] : [_858831 = _858829, -(c_Groups_Otimes__class_Otimes(_858831) = c_Groups_Otimes__class_Otimes(_858829))], (10317 ^ _776545) ^ [_953776, _953778, _953780] : [class_Groups_Ogroup__add(_953776), 10320 ^ _776545 : [(10327 ^ _776545) ^ [] : [_953778 = _953780, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953776), _953778) = hAPP(c_Groups_Ouminus__class_Ouminus(_953776), _953780))], (10321 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953776), _953778) = hAPP(c_Groups_Ouminus__class_Ouminus(_953776), _953780), -(_953778 = _953780)]]], (18448 ^ _776545) ^ [_1108492, _1108494, _1108496, _1108498] : [class_Rings_Olinordered__ring__strict(_1108492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108492), _1108494), c_Groups_Ozero__class_Ozero(_1108492))), 18455 ^ _776545 : [(18462 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108492), _1108498), _1108496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108492), _1108494), _1108496)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108492), _1108494), _1108498))))], (18456 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108492), _1108494), _1108496)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108492), _1108494), _1108498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108492), _1108498), _1108496)))]]], (15087 ^ _776545) ^ [_1048961, _1048963] : [class_Groups_Ocomm__monoid__mult(_1048961), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048961), _1048963), c_Groups_Oone__class_Oone(_1048961)) = _1048963)], (5040 ^ _776545) ^ [_853388, _853390] : [_853390 = _853388, -(c_Orderings_Obot__class_Obot(_853390) = c_Orderings_Obot__class_Obot(_853388))], (32496 ^ _776545) ^ [_1362595, _1362597, _1362599, _1362601, _1362603, _1362605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362595, _1362597)), hAPP(hAPP(c_Product__Type_OPair(_1362595, _1362597), _1362603), _1362605)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool)), _1362599), _1362601))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362595, tc_fun(_1362597, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1362595, tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_fun(_1362597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362597, tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_fun(_1362597, tc_HOL_Obool)), _1362595), c_COMBC(_1362597, tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362597, tc_prod(_1362595, _1362597)), tc_fun(_1362597, tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), _1362595), hAPP(c_COMBB(tc_prod(_1362595, _1362597), tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool), _1362597), c_member(tc_prod(_1362595, _1362597)))), c_Product__Type_OPair(_1362595, _1362597)))), _1362599)), hAPP(hAPP(c_COMBC(_1362595, tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_fun(_1362597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362597, tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_fun(_1362597, tc_HOL_Obool)), _1362595), c_COMBC(_1362597, tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1362597, tc_prod(_1362595, _1362597)), tc_fun(_1362597, tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool)), _1362595), hAPP(c_COMBB(tc_prod(_1362595, _1362597), tc_fun(tc_fun(tc_prod(_1362595, _1362597), tc_HOL_Obool), tc_HOL_Obool), _1362597), c_member(tc_prod(_1362595, _1362597)))), c_Product__Type_OPair(_1362595, _1362597)))), _1362601)), _1362603), _1362605)))], (28091 ^ _776545) ^ [_1281158, _1281160] : [-(c_Nitpick_Oint__lcm(_1281158, _1281160) = 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), _1281158)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1281160)))))], (31809 ^ _776545) ^ [_1348070, _1348072, _1348074] : [class_Orderings_Olinorder(_1348070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348070), _1348072)), hBOOL(hAPP(hAPP(c_member(_1348070), _1348074), _1348072)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348070), _1348074), c_Big__Operators_Olattice_OInf__fin(_1348070, c_Orderings_Oord__class_Omin(_1348070), _1348072)) = _1348074)], (6360 ^ _776545) ^ [_879111, _879113, _879115] : [-(_879111 = _879113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879115, tc_HOL_Obool)), _879111), _879113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879115, tc_HOL_Obool)), _879113), _879111))], (15176 ^ _776545) ^ [_1050383, _1050385, _1050387] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050383), _1050385)), -(hBOOL(hAPP(hAPP(c_member(_1050383), _1050387), _1050385))), -(hAPP(c_Finite__Set_Ocard(_1050383), hAPP(hAPP(c_Set_Oinsert(_1050383), _1050387), _1050385)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1050383), _1050385)))], (50678 ^ _776545) ^ [_1800927, _1800929, _1800931, _1800933, _1800935] : [50680 ^ _776545 : [(50683 ^ _776545) ^ [] : [c_Relation_Orefl__on(_1800931, hAPP(_1800933, 50679 ^ [_1800927, _1800929, _1800931, _1800933, _1800935]), hAPP(_1800935, 50679 ^ [_1800927, _1800929, _1800931, _1800933, _1800935]))], (50681 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800927), 50679 ^ [_1800927, _1800929, _1800931, _1800933, _1800935]), _1800929)))]], -(c_Relation_Orefl__on(_1800931, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800927, tc_fun(_1800931, tc_HOL_Obool)), _1800929), _1800933), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800927, tc_fun(tc_prod(_1800931, _1800931), tc_HOL_Obool)), _1800929), _1800935)))], (4696 ^ _776545) ^ [_847988, _847990] : [_847990 = _847988, -(c_DSequence_Oempty(_847990) = c_DSequence_Oempty(_847988))], (19330 ^ _776545) ^ [_1125542, _1125544, _1125546] : [class_Rings_Oring__1(_1125542), hBOOL(hAPP(hAPP(c_member(_1125542), _1125544), c_Int_Oring__1__class_OInts(_1125542))), hBOOL(hAPP(hAPP(c_member(_1125542), _1125546), c_Int_Oring__1__class_OInts(_1125542))), -(hBOOL(hAPP(hAPP(c_member(_1125542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125542), _1125544), _1125546)), c_Int_Oring__1__class_OInts(_1125542))))], (3388 ^ _776545) ^ [_827132, _827134, _827136, _827138] : [-(c_HOL_OLet(_827138, _827134) = c_HOL_OLet(_827136, _827132)), _827138 = _827136, _827134 = _827132], (30174 ^ _776545) ^ [_1317834, _1317836, _1317838, _1317840] : [class_Orderings_Olinorder(_1317834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317834), _1317836), _1317838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317834), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317834), _1317840), _1317836)), _1317838)))], (8405 ^ _776545) ^ [_920859, _920861, _920863] : [class_Lattices_Osemilattice__inf(_920859), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920859), _920861), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920859), _920861), _920863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920859), _920861), _920863))], (29327 ^ _776545) ^ [] : [-(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))))], (29801 ^ _776545) ^ [_1310867, _1310869, _1310871] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1310867, _1310869) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1310871, _1310869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1310871), _1310867)), -(_1310867 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1310869), 29808 ^ [_1310867, _1310869, _1310871])))], (17627 ^ _776545) ^ [_1093996] : [class_Rings_Olinordered__semidom(_1093996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093996), c_Groups_Oone__class_Oone(_1093996)), c_Groups_Ozero__class_Ozero(_1093996)))], (33292 ^ _776545) ^ [_1386859, _1386861, _1386863, _1386865] : [class_Groups_Oab__group__add(_1386859), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1386861, _1386859), hAPP(hAPP(c_COMBB(_1386859, _1386859, _1386861), c_Groups_Ouminus__class_Ouminus(_1386859)), _1386863)), _1386865) = hAPP(c_Groups_Ouminus__class_Ouminus(_1386859), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1386861, _1386859), _1386863), _1386865)))], (15136 ^ _776545) ^ [_1049802, _1049804] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049802), _1049804), 15139 ^ _776545 : [(15142 ^ _776545) ^ [] : [-(_1049804 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15140 ^ _776545) ^ [] : [-(_1049802 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (20467 ^ _776545) ^ [_1145858, _1145860, _1145862] : [class_Fields_Olinordered__field(_1145858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145858), _1145860), c_Groups_Ozero__class_Ozero(_1145858))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145858), c_Groups_Ozero__class_Ozero(_1145858)), _1145862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145858), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145858), _1145860), _1145862)), c_Groups_Ozero__class_Ozero(_1145858))))], (52037 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (34550 ^ _776545) ^ [_1419997, _1419999, _1420001, _1420003, _1420005, _1420007] : [hBOOL(hAPP(hAPP(_1419997, _1419999), _1420001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420003, tc_fun(_1420005, tc_HOL_Obool))), _1419997), _1420007)), -(hBOOL(hAPP(hAPP(_1420007, _1419999), _1420001)))], (42351 ^ _776545) ^ [_1617071, _1617073, _1617075, _1617077] : [-(hBOOL(hAPP(hAPP(c_member(_1617071), _1617073), hAPP(c_List_Oset(_1617071), _1617075)))), hBOOL(hAPP(hAPP(c_member(_1617071), _1617073), hAPP(c_List_Oset(_1617071), c_List_Osublist(_1617071, _1617075, _1617077))))], (35630 ^ _776545) ^ [_1441571, _1441573, _1441575, _1441577, _1441579] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441571, _1441573, _1441575), _1441577), _1441579) = hAPP(hAPP(_1441577, hAPP(c_Product__Type_Ofst(_1441571, _1441573), _1441579)), hAPP(c_Product__Type_Osnd(_1441571, _1441573), _1441579)))], (16662 ^ _776545) ^ [_1076238, _1076240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076238), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076240), _1076238)))))], (50231 ^ _776545) ^ [_1792019, _1792021] : [50233 ^ _776545 : [(50236 ^ _776545) ^ [] : [hBOOL(hAPP(_1792019, hAPP(c_Code__Numeral_Oof__nat, 50232 ^ [_1792019, _1792021])))], (50234 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50232 ^ [_1792019, _1792021]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1792019, _1792021)))], (52009 ^ _776545) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (46215 ^ _776545) ^ [_1705732, _1705734] : [-(c_Random_Opick(_1705732, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1705732), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1705732, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1705732, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1705732)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1705734)) = c_Random_Opick(_1705732, _1705734))], (39099 ^ _776545) ^ [_1529933, _1529935, _1529937, _1529939, _1529941, _1529943] : [class_Groups_Ocomm__monoid__mult(_1529933), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529935, _1529933), hAPP(hAPP(c_COMBC(_1529935, tc_fun(_1529937, tc_HOL_Obool), _1529933), hAPP(hAPP(c_COMBB(tc_fun(_1529937, _1529933), tc_fun(tc_fun(_1529937, tc_HOL_Obool), _1529933), _1529935), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529937, _1529933)), _1529939)), _1529941)), _1529943) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1529935, _1529937), _1529933), hAPP(c_Product__Type_Oprod_Oprod__case(_1529935, _1529937, _1529933), _1529939)), hAPP(hAPP(c_Product__Type_OSigma(_1529935, _1529937), _1529943), hAPP(c_COMBK(tc_fun(_1529937, tc_HOL_Obool), _1529935), _1529941))))], (42234 ^ _776545) ^ [_1614079, _1614081, _1614083] : [-(hAPP(hAPP(c_List_Onth(_1614079), hAPP(hAPP(c_List_Olist_OCons(_1614079), _1614081), _1614083)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1614081)], (28463 ^ _776545) ^ [_1287410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1287410)))], (43310 ^ _776545) ^ [_1639447, _1639449, _1639451, _1639453] : [-(hAPP(c_List_Olist_Olist__case(_1639447, _1639449, _1639451, _1639453), c_List_Olist_ONil(_1639449)) = _1639451)], (1204 ^ _776545) ^ [_794459, _794461] : [-(class_Groups_Oab__group__add(_794459)), _794461 = _794459, class_Groups_Oab__group__add(_794461)], (45539 ^ _776545) ^ [_1689675, _1689677, _1689679, _1689681, _1689683, _1689685, _1689687] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689675)), _1689677) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689679)), _1689681), 45542 ^ _776545 : [(45551 ^ _776545) ^ [] : [-(c_List_Olist__all2(_1689675, _1689679, _1689683, hAPP(hAPP(c_List_Oappend(_1689675), _1689677), _1689685), hAPP(hAPP(c_List_Oappend(_1689679), _1689681), _1689687))), c_List_Olist__all2(_1689675, _1689679, _1689683, _1689677, _1689681), c_List_Olist__all2(_1689675, _1689679, _1689683, _1689685, _1689687)], (45543 ^ _776545) ^ [] : [c_List_Olist__all2(_1689675, _1689679, _1689683, hAPP(hAPP(c_List_Oappend(_1689675), _1689677), _1689685), hAPP(hAPP(c_List_Oappend(_1689679), _1689681), _1689687)), 45546 ^ _776545 : [(45549 ^ _776545) ^ [] : [-(c_List_Olist__all2(_1689675, _1689679, _1689683, _1689685, _1689687))], (45547 ^ _776545) ^ [] : [-(c_List_Olist__all2(_1689675, _1689679, _1689683, _1689677, _1689681))]]]]], (12147 ^ _776545) ^ [_989813, _989815, _989817] : [class_Lattices_Olattice(_989813), hBOOL(hAPP(c_Finite__Set_Ofinite(_989813), _989815)), -(_989815 = c_Orderings_Obot__class_Obot(tc_fun(_989813, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_989813, hAPP(hAPP(c_Set_Oinsert(_989813), _989817), _989815)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_989813), _989817), c_Big__Operators_Olattice__class_OInf__fin(_989813, _989815)))], (46140 ^ _776545) ^ [_1703282, _1703284, _1703286, _1703288] : [-(hBOOL(hAPP(_1703282, _1703284))), -(hAPP(c_List_OremoveAll(_1703286, _1703284), hAPP(c_List_Ofilter(_1703286, _1703282), _1703288)) = hAPP(c_List_Ofilter(_1703286, _1703282), _1703288))], (43912 ^ _776545) ^ [_1654015, _1654017, _1654019] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654015)), hAPP(hAPP(c_List_Odrop(_1654015), _1654017), _1654019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654015)), _1654019)), _1654017))], (18840 ^ _776545) ^ [_1115955] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1115955), c_Orderings_Otop__class_Otop(tc_fun(_1115955, 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(_1115955), c_Orderings_Otop__class_Otop(tc_fun(_1115955, tc_HOL_Obool))))))], (46710 ^ _776545) ^ [_1715233, _1715235, _1715237] : [class_Orderings_Olinorder(_1715233), 46713 ^ _776545 : [(46726 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715233, hAPP(hAPP(c_List_Olist_OCons(_1715233), _1715235), _1715237))), c_List_Olinorder__class_Osorted(_1715233, _1715237), 46732 ^ _776545 : [(46735 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715233), _1715235), 46731 ^ [_1715233, _1715235, _1715237]))], (46733 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1715233), 46731 ^ [_1715233, _1715235, _1715237]), hAPP(c_List_Oset(_1715233), _1715237))))]]], (46714 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1715233, hAPP(hAPP(c_List_Olist_OCons(_1715233), _1715235), _1715237)), 46717 ^ _776545 : [(46720 ^ _776545) ^ [_1715419] : [hBOOL(hAPP(hAPP(c_member(_1715233), _1715419), hAPP(c_List_Oset(_1715233), _1715237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1715233), _1715235), _1715419)))], (46718 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1715233, _1715237))]]]]], (27833 ^ _776545) ^ [_1277008, _1277010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277008)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277008), _1277010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277008), c_Int_OPls)))], (41096 ^ _776545) ^ [_1582369, _1582371] : [-(hAPP(c_Relation_OField(_1582369), hAPP(c_Relation_Oconverse(_1582369, _1582369), _1582371)) = hAPP(c_Relation_OField(_1582369), _1582371))], (16701 ^ _776545) ^ [_1076978, _1076980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076978)), _1076980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076978), _1076980)))], (14702 ^ _776545) ^ [_1041560, _1041562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041560), _1041562)), 14705 ^ _776545 : [(14708 ^ _776545) ^ [] : [_1041560 = _1041562], (14706 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041560), _1041562)))]]], (12305 ^ _776545) ^ [_992398, _992400, _992402] : [class_Lattices_Olattice(_992398), hBOOL(hAPP(c_Finite__Set_Ofinite(_992398), _992400)), 12312 ^ _776545 : [(12319 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992398, tc_HOL_Obool)), _992400), hAPP(hAPP(c_Set_Oinsert(_992398), _992402), c_Orderings_Obot__class_Obot(tc_fun(_992398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992398, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_992398, hAPP(hAPP(c_Set_Oinsert(_992398), _992402), _992400)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_992398), _992402), c_Big__Operators_Olattice__class_OSup__fin(_992398, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992398, tc_HOL_Obool)), _992400), hAPP(hAPP(c_Set_Oinsert(_992398), _992402), c_Orderings_Obot__class_Obot(tc_fun(_992398, tc_HOL_Obool)))))))], (12313 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992398, tc_HOL_Obool)), _992400), hAPP(hAPP(c_Set_Oinsert(_992398), _992402), c_Orderings_Obot__class_Obot(tc_fun(_992398, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992398, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_992398, hAPP(hAPP(c_Set_Oinsert(_992398), _992402), _992400)) = _992402)]]], (41327 ^ _776545) ^ [_1587639, _1587641, _1587643] : [c_Relation_Ototal__on(_1587639, _1587641, _1587643), 41330 ^ _776545 : [(41331 ^ _776545) ^ [_1587783] : [hBOOL(hAPP(hAPP(c_member(_1587639), _1587783), _1587641)), 41334 ^ _776545 : [(41335 ^ _776545) ^ [_1587923] : [hBOOL(hAPP(hAPP(c_member(_1587639), _1587923), _1587641)), -(_1587783 = _1587923), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587639, _1587639)), hAPP(hAPP(c_Product__Type_OPair(_1587639, _1587639), _1587783), _1587923)), _1587643))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587639, _1587639)), hAPP(hAPP(c_Product__Type_OPair(_1587639, _1587639), _1587923), _1587783)), _1587643)))]]]]], (4890 ^ _776545) ^ [_851073, _851075, _851077, _851079] : [-(c_List_Olistrel(_851079, _851075) = c_List_Olistrel(_851077, _851073)), _851079 = _851077, _851075 = _851073], (5835 ^ _776545) ^ [_869073, _869075] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869075, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869075)), tc_HOL_Obool)), 5831 ^ [_869073, _869075]), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869075, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869075)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869075)))))], (12690 ^ _776545) ^ [_1000270, _1000272, _1000274, _1000276, _1000278, _1000280] : [c_Finite__Set_Ofun__left__comm(_1000270, _1000272, _1000274), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1000270, _1000272, _1000274, _1000276, _1000278), _1000280)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000270, _1000272, _1000274), _1000276), _1000278) = _1000280)], (31365 ^ _776545) ^ [_1339571, _1339573, _1339575] : [class_Orderings_Olinorder(_1339571), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339571), _1339573), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339571), _1339573), _1339575)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339571), _1339573), _1339575))], (28141 ^ _776545) ^ [_1281892] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1281892) = c_Int_Opred(_1281892))], (31685 ^ _776545) ^ [_1345550, _1345552, _1345554] : [class_Groups_Olinordered__ab__group__add(_1345550), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1345550), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345550), _1345552), _1345554)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345550), hAPP(c_Groups_Ouminus__class_Ouminus(_1345550), _1345552)), hAPP(c_Groups_Ouminus__class_Ouminus(_1345550), _1345554)))], (44795 ^ _776545) ^ [_1672422, _1672424, _1672426, _1672428, _1672430] : [class_Rings_Osemiring__0(_1672422), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672422), hAPP(hAPP(c_List_Omap(_1672424, _1672422), hAPP(hAPP(c_COMBC(_1672424, _1672422, _1672422), hAPP(hAPP(c_COMBB(_1672422, tc_fun(_1672422, _1672422), _1672424), c_Groups_Otimes__class_Otimes(_1672422)), _1672426)), _1672428)), _1672430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672422), hAPP(c_List_Omonoid__add__class_Olistsum(_1672422), hAPP(hAPP(c_List_Omap(_1672424, _1672422), _1672426), _1672430))), _1672428))], (45672 ^ _776545) ^ [_1692727, _1692729] : [hBOOL(hAPP(c_List_Odistinct(_1692727), _1692729)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1692727, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692727), tc_fun(_1692727, tc_HOL_Obool)), c_List_Oset(_1692727)), c_Enum_Osublists(_1692727, _1692729)))))], (49050 ^ _776545) ^ [_1765966] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765966)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1765966)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30852 ^ _776545) ^ [_1329797, _1329799, _1329801] : [class_Orderings_Olinorder(_1329797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329797), _1329799)), 30859 ^ _776545 : [(30866 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329797, tc_HOL_Obool)), _1329799), hAPP(hAPP(c_Set_Oinsert(_1329797), _1329801), c_Orderings_Obot__class_Obot(tc_fun(_1329797, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1329797, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1329797, c_Orderings_Oord__class_Omin(_1329797), hAPP(hAPP(c_Set_Oinsert(_1329797), _1329801), _1329799)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329797), _1329801), c_Big__Operators_Olattice_OInf__fin(_1329797, c_Orderings_Oord__class_Omin(_1329797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329797, tc_HOL_Obool)), _1329799), hAPP(hAPP(c_Set_Oinsert(_1329797), _1329801), c_Orderings_Obot__class_Obot(tc_fun(_1329797, tc_HOL_Obool)))))))], (30860 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329797, tc_HOL_Obool)), _1329799), hAPP(hAPP(c_Set_Oinsert(_1329797), _1329801), c_Orderings_Obot__class_Obot(tc_fun(_1329797, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1329797, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1329797, c_Orderings_Oord__class_Omin(_1329797), hAPP(hAPP(c_Set_Oinsert(_1329797), _1329801), _1329799)) = _1329801)]]], (48486 ^ _776545) ^ [_1753495, _1753497, _1753499, _1753501] : [-(c_Predicate_Oconversep(_1753495, _1753497, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753495, tc_fun(_1753497, tc_HOL_Obool))), _1753499), _1753501)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753497, tc_fun(_1753495, tc_HOL_Obool))), c_Predicate_Oconversep(_1753495, _1753497, _1753499)), c_Predicate_Oconversep(_1753495, _1753497, _1753501)))], (29039 ^ _776545) ^ [_1297103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1297103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1297103))))], (36440 ^ _776545) ^ [_1465342, _1465344] : [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)), _1465342), 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)), _1465344), 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)), _1465342), _1465344)), c_Int_Ointrel)))], (4490 ^ _776545) ^ [_844757, _844759] : [_844759 = _844757, -(c_Lazy__Sequence_Oyieldn(_844759) = c_Lazy__Sequence_Oyieldn(_844757))], (32988 ^ _776545) ^ [_1378673, _1378675, _1378677] : [-(hAPP(hAPP(c_Set_Oinsert(_1378673), _1378675), _1378677) = hAPP(c_Set_OCollect(_1378673), hAPP(hAPP(c_COMBS(_1378673, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378673), c_fdisj), hAPP(hAPP(c_COMBC(_1378673, _1378673, tc_HOL_Obool), c_fequal), _1378675))), hAPP(hAPP(c_COMBC(_1378673, tc_fun(_1378673, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378673)), _1378677))))], (31959 ^ _776545) ^ [_1350752, _1350754, _1350756] : [class_Orderings_Olinorder(_1350752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350752), _1350754)), hBOOL(hAPP(hAPP(c_member(_1350752), _1350756), _1350754)), 31970 ^ _776545 : [(31977 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350752, tc_HOL_Obool)), _1350754), hAPP(hAPP(c_Set_Oinsert(_1350752), _1350756), c_Orderings_Obot__class_Obot(tc_fun(_1350752, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350752, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1350752, c_Orderings_Oord__class_Omax(_1350752), _1350754) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350752), _1350756), c_Big__Operators_Olattice_OSup__fin(_1350752, c_Orderings_Oord__class_Omax(_1350752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350752, tc_HOL_Obool)), _1350754), hAPP(hAPP(c_Set_Oinsert(_1350752), _1350756), c_Orderings_Obot__class_Obot(tc_fun(_1350752, tc_HOL_Obool)))))))], (31971 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350752, tc_HOL_Obool)), _1350754), hAPP(hAPP(c_Set_Oinsert(_1350752), _1350756), c_Orderings_Obot__class_Obot(tc_fun(_1350752, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350752, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1350752, c_Orderings_Oord__class_Omax(_1350752), _1350754) = _1350756)]]], (29665 ^ _776545) ^ [_1308351, _1308353] : [class_Rings_Oring__1(_1308351), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308351), hAPP(c_Groups_Ouminus__class_Ouminus(_1308351), c_Groups_Oone__class_Oone(_1308351))), 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)))), _1308353))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1308351), c_Groups_Oone__class_Oone(_1308351)))], (45305 ^ _776545) ^ [_1684381, _1684383, _1684385, _1684387] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684381)), _1684383), c_List_Olists(_1684381, _1684385))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684381)), _1684383), c_List_Olists(_1684381, _1684387))), -(hBOOL(hAPP(c_List_Olistsp(_1684381, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684381, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1684381, tc_fun(_1684381, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684381)), _1684385)), hAPP(hAPP(c_COMBC(_1684381, tc_fun(_1684381, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684381)), _1684387))), _1684383)))], (46107 ^ _776545) ^ [_1702695, _1702697, _1702699, _1702701] : [-(hBOOL(hAPP(_1702695, _1702697))), -(hAPP(c_List_Ofilter(_1702699, _1702695), hAPP(hAPP(c_List_Olist_OCons(_1702699), _1702697), _1702701)) = hAPP(c_List_Ofilter(_1702699, _1702695), _1702701))], (44423 ^ _776545) ^ [_1664944, _1664946, _1664948] : [class_Lattices_Olattice(_1664944), -(c_Big__Operators_Olattice__class_OSup__fin(_1664944, hAPP(c_List_Oset(_1664944), hAPP(hAPP(c_List_Olist_OCons(_1664944), _1664946), _1664948))) = hAPP(c_List_Ofoldl(_1664944, _1664944, c_Lattices_Osemilattice__sup__class_Osup(_1664944), _1664946), _1664948))], (32924 ^ _776545) ^ [_1376741] : [-(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)))), _1376741))))], (28625 ^ _776545) ^ [_1289908, _1289910] : [class_Groups_Omonoid__mult(_1289908), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1289908), _1289910), 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(_1289908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289908), _1289910), _1289910)), _1289910))], (12658 ^ _776545) ^ [_999662, _999664, _999666] : [class_Groups_Oab__semigroup__mult(_999662), hBOOL(hAPP(c_Finite__Set_Ofinite(_999662), _999664)), -(hBOOL(hAPP(hAPP(c_member(_999662), _999666), _999664))), -(hAPP(c_Finite__Set_Ofold1(_999662, c_Groups_Otimes__class_Otimes(_999662)), hAPP(hAPP(c_Set_Oinsert(_999662), _999666), _999664)) = hAPP(hAPP(c_Finite__Set_Ofold(_999662, _999662, c_Groups_Otimes__class_Otimes(_999662)), _999666), _999664))], (22461 ^ _776545) ^ [_1183570] : [-(_1183570 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22464 ^ _776545 : [(22471 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183570))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183570) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22465 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183570)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183570) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (47052 ^ _776545) ^ [_1722335, _1722337, _1722339, _1722341, _1722343] : [c_List_Olist__all2(_1722335, _1722337, _1722339, _1722341, _1722343), -(c_List_Olist__all2(_1722335, _1722337, _1722339, hAPP(c_List_Orev(_1722335), _1722341), hAPP(c_List_Orev(_1722337), _1722343)))], (31411 ^ _776545) ^ [_1340556, _1340558, _1340560, _1340562] : [class_Orderings_Olinorder(_1340556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340556), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340556), _1340558), _1340560)), _1340562)), 31418 ^ _776545 : [(31421 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340556), _1340560), _1340562)))], (31419 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340556), _1340558), _1340562)))]]], (41449 ^ _776545) ^ [_1590740, _1590742, _1590744, _1590746] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590740, _1590740)), hAPP(hAPP(c_Product__Type_OPair(_1590740, _1590740), _1590742), _1590744)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590740, _1590740), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590746))), -(_1590742 = _1590744)], (28301 ^ _776545) ^ [_1284642] : [c_Int_OBit1(_1284642) = c_Int_OMin, -(_1284642 = c_Int_OMin)], (29119 ^ _776545) ^ [_1298414] : [-(c_Int_Osucc(c_Int_OBit0(_1298414)) = c_Int_OBit1(_1298414))], (10641 ^ _776545) ^ [_959551] : [class_Lattices_Oboolean__algebra(_959551), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959551), c_Orderings_Obot__class_Obot(_959551)) = c_Orderings_Otop__class_Otop(_959551))], (38203 ^ _776545) ^ [_1508067, _1508069, _1508071] : [c_Wellfounded_Owf(_1508067, _1508069), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508067, _1508067)), hAPP(hAPP(c_Product__Type_OPair(_1508067, _1508067), _1508071), _1508071)), _1508069))], (29289 ^ _776545) ^ [_1301403] : [class_Rings_Osemiring__1(_1301403), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301403), c_Groups_Oone__class_Oone(_1301403)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1301403))], (14965 ^ _776545) ^ [_1046518, _1046520, _1046522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046518), _1046520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046522), _1046518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046518), _1046522)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046520), _1046522))))], (15794 ^ _776545) ^ [_1062746, _1062748] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062746), _1062748), 15799 ^ _776545 : [(15802 ^ _776545) ^ [] : [-(_1062748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15800 ^ _776545) ^ [] : [-(_1062746 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 15803 ^ _776545 : [(15806 ^ _776545) ^ [] : [-(_1062748 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15804 ^ _776545) ^ [] : [-(_1062746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15896 ^ _776545) ^ [_1064273, _1064275] : [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), _1064273), _1064275))), 15899 ^ _776545 : [(15902 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064275)))], (15900 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064273)))]]], (41124 ^ _776545) ^ [_1582974, _1582976] : [c_Wellfounded_Oacyclic(_1582974, _1582976), -(c_Wellfounded_Oacyclic(_1582974, hAPP(c_Relation_Oconverse(_1582974, _1582974), _1582976)))], (32083 ^ _776545) ^ [_1352971, _1352973, _1352975] : [class_Orderings_Olinorder(_1352971), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352971), _1352973)), -(c_Big__Operators_Olattice_OSup__fin(_1352971, c_Orderings_Oord__class_Omax(_1352971), hAPP(hAPP(c_Set_Oinsert(_1352971), _1352975), _1352973)) = hAPP(hAPP(c_Finite__Set_Ofold(_1352971, _1352971, c_Orderings_Oord__class_Omax(_1352971)), _1352975), _1352973))], (4640 ^ _776545) ^ [_847080, _847082, _847084, _847086, _847088, _847090, _847092, _847094] : [-(c_Random__Sequence_ORandom(_847094, _847090, _847086, _847082) = c_Random__Sequence_ORandom(_847092, _847088, _847084, _847080)), _847094 = _847092, _847090 = _847088, _847086 = _847084, _847082 = _847080], (33517 ^ _776545) ^ [_1393276, _1393278, _1393280, _1393282, _1393284] : [-(_1393276 = c_Orderings_Obot__class_Obot(tc_fun(_1393278, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393278, tc_fun(_1393280, tc_HOL_Obool)), _1393276), hAPP(hAPP(c_COMBB(tc_fun(_1393280, tc_HOL_Obool), tc_fun(_1393280, tc_HOL_Obool), _1393278), hAPP(c_Set_Oinsert(_1393280), _1393282)), _1393284)) = hAPP(hAPP(c_Set_Oinsert(_1393280), _1393282), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393278, tc_fun(_1393280, tc_HOL_Obool)), _1393276), _1393284)))], (29209 ^ _776545) ^ [_1300048, _1300050] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1300048)), c_Int_OBit1(_1300050)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300048), c_Int_Osucc(_1300050))))], (52055 ^ _776545) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (35580 ^ _776545) ^ [_1440544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1440544)), 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), _1440544)) = 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), _1440544))))))], (28547 ^ _776545) ^ [_1288797] : [class_Int_Onumber__ring(_1288797), -(c_Groups_Oone__class_Oone(_1288797) = hAPP(c_Int_Onumber__class_Onumber__of(_1288797), c_Int_OBit1(c_Int_OPls)))], (23603 ^ _776545) ^ [_1204319, _1204321] : [class_Divides_Osemiring__div(_1204319), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204319), _1204321), c_Groups_Ozero__class_Ozero(_1204319)) = c_Groups_Ozero__class_Ozero(_1204319))], (13910 ^ _776545) ^ [_1024944, _1024946, _1024948] : [class_Groups_Ogroup__add(_1024944), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024944), _1024946), hAPP(c_Groups_Ouminus__class_Ouminus(_1024944), _1024948)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024944), _1024946), _1024948))], (43549 ^ _776545) ^ [_1645169, _1645171, _1645173] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645169)), hAPP(hAPP(c_List_Oappend(_1645169), _1645171), _1645173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645169)), _1645171)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645169)), _1645173)))], (49986 ^ _776545) ^ [_1786158, _1786160, _1786162] : [c_Fun_Oinj__on(_1786158, _1786160, _1786162, c_Orderings_Otop__class_Otop(tc_fun(_1786158, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1786160, _1786158, _1786158, c_Hilbert__Choice_Oinv__into(_1786158, _1786160, c_Orderings_Otop__class_Otop(tc_fun(_1786158, tc_HOL_Obool)), _1786162)), _1786162) = c_Fun_Oid(_1786158))], (20339 ^ _776545) ^ [_1143468, _1143470, _1143472, _1143474] : [class_Fields_Ofield__inverse__zero(_1143468), -(_1143470 = c_Groups_Ozero__class_Ozero(_1143468)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143468), _1143470), _1143472)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143468), _1143470), _1143474)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143468), _1143472), _1143474))], (28373 ^ _776545) ^ [_1285882] : [c_Int_OPls = c_Int_OBit1(_1285882)], (48656 ^ _776545) ^ [_1757358, _1757360, _1757362, _1757364, _1757366] : [-(c_List_Oreplicate(_1757358, _1757360, _1757362) = c_List_Oreplicate(_1757358, _1757364, _1757366)), _1757360 = _1757364, 48661 ^ _776545 : [(48664 ^ _776545) ^ [] : [_1757362 = _1757366], (48662 ^ _776545) ^ [] : [_1757360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (39908 ^ _776545) ^ [_1553210, _1553212, _1553214, _1553216, _1553218, _1553220, _1553222, _1553224, _1553226] : [hAPP(c_Fun_Ocomp(_1553210, _1553212, _1553214, _1553216), _1553218) = hAPP(c_Fun_Ocomp(_1553220, _1553212, _1553214, _1553222), _1553224), -(hAPP(_1553216, hAPP(_1553218, _1553226)) = hAPP(_1553222, hAPP(_1553224, _1553226)))], (18948 ^ _776545) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26997 ^ _776545) ^ [_1262847, _1262849, _1262851] : [class_Rings_Oring__1(_1262847), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262847), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1262849), _1262851)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1262847), hAPP(c_Int_Oring__1__class_Oof__int(_1262847), _1262849)), _1262851))], (52421 ^ _776545) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (43254 ^ _776545) ^ [_1638231, _1638233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638231)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638233))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638233)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638231)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638231)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638233))))], (8623 ^ _776545) ^ [_924723, _924725, _924727, _924729] : [class_Lattices_Osemilattice__inf(_924723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924723), _924725), _924727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924723), _924725), _924729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924723), _924725), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924723), _924727), _924729))))], (39019 ^ _776545) ^ [_1527985] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1527985), c_Int_OInteg)), -(_1527985 = hAPP(c_Int_ORep__Integ, 39022 ^ [_1527985]))], (52103 ^ _776545) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (36838 ^ _776545) ^ [_1475586, _1475588, _1475590, _1475592, _1475594] : [c_Equiv__Relations_Oequiv(_1475586, _1475588, _1475590), 36841 ^ _776545 : [(36852 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475586, _1475586)), hAPP(hAPP(c_Product__Type_OPair(_1475586, _1475586), _1475592), _1475594)), _1475590))), hAPP(c_Relation_OImage(_1475586, _1475586, _1475590), hAPP(hAPP(c_Set_Oinsert(_1475586), _1475592), c_Orderings_Obot__class_Obot(tc_fun(_1475586, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475586, _1475586, _1475590), hAPP(hAPP(c_Set_Oinsert(_1475586), _1475594), c_Orderings_Obot__class_Obot(tc_fun(_1475586, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1475586), _1475592), _1475588)), hBOOL(hAPP(hAPP(c_member(_1475586), _1475594), _1475588))], (36842 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1475586, _1475586)), hAPP(hAPP(c_Product__Type_OPair(_1475586, _1475586), _1475592), _1475594)), _1475590)), 36845 ^ _776545 : [(36850 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475586), _1475594), _1475588)))], (36848 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475586), _1475592), _1475588)))], (36846 ^ _776545) ^ [] : [-(hAPP(c_Relation_OImage(_1475586, _1475586, _1475590), hAPP(hAPP(c_Set_Oinsert(_1475586), _1475592), c_Orderings_Obot__class_Obot(tc_fun(_1475586, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1475586, _1475586, _1475590), hAPP(hAPP(c_Set_Oinsert(_1475586), _1475594), c_Orderings_Obot__class_Obot(tc_fun(_1475586, tc_HOL_Obool)))))]]]]], (9680 ^ _776545) ^ [_942249, _942251, _942253, _942255] : [class_Orderings_Opreorder(_942249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942249), _942251), _942253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942249), _942253), _942255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942249), _942251), _942255)))], (33362 ^ _776545) ^ [_1389017, _1389019, _1389021, _1389023, _1389025, _1389027] : [class_Complete__Lattice_Ocomplete__lattice(_1389017), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389019, tc_fun(_1389021, _1389017)), _1389023), _1389025), _1389027) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389019, _1389017), _1389023), hAPP(hAPP(c_COMBC(_1389019, _1389021, _1389017), _1389025), _1389027)))], (37222 ^ _776545) ^ [_1484969, _1484971, _1484973, _1484975, _1484977] : [c_Fun_Oinj__on(_1484969, _1484971, _1484973, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484969, tc_HOL_Obool)), _1484975), _1484977)), 37225 ^ _776545 : [(37232 ^ _776545) ^ [] : [_1484975 = _1484977, -(hAPP(c_Set_Oimage(_1484969, _1484971, _1484973), _1484975) = hAPP(c_Set_Oimage(_1484969, _1484971, _1484973), _1484977))], (37226 ^ _776545) ^ [] : [hAPP(c_Set_Oimage(_1484969, _1484971, _1484973), _1484975) = hAPP(c_Set_Oimage(_1484969, _1484971, _1484973), _1484977), -(_1484975 = _1484977)]]], (35805 ^ _776545) ^ [_1445222, _1445224] : [hAPP(c_Int_ORep__Integ, _1445222) = hAPP(c_Int_ORep__Integ, _1445224), -(_1445222 = _1445224)], (38836 ^ _776545) ^ [_1523738, _1523740, _1523742] : [c_Wellfounded_Owf(_1523738, _1523740), c_Wellfounded_Owf(_1523738, _1523742), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523738, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1523738, _1523738), _1523740)), hAPP(c_Relation_ORange(_1523738, _1523738), _1523742)) = c_Orderings_Obot__class_Obot(tc_fun(_1523738, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1523738, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523738, _1523738), tc_HOL_Obool)), _1523740), _1523742)))], (49068 ^ _776545) ^ [_1766298, _1766300, _1766302] : [c_List_Oall__interval__int(_1766298, _1766300, _1766302), -(c_List_Olist__all(tc_Int_Oint, _1766298, c_List_Oupto(_1766300, _1766302)))], (37939 ^ _776545) ^ [_1500814, _1500816, _1500818, _1500820, _1500822, _1500824, _1500826] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500814, _1500816, _1500818), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500820, tc_fun(tc_prod(_1500814, _1500816), tc_HOL_Obool)), _1500822), _1500824)), _1500826) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500820, tc_fun(tc_prod(_1500814, _1500818), tc_HOL_Obool)), _1500822), hAPP(hAPP(c_COMBC(_1500820, tc_fun(tc_prod(_1500816, _1500818), tc_HOL_Obool), tc_fun(tc_prod(_1500814, _1500818), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500814, _1500816), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1500816, _1500818), tc_HOL_Obool), tc_fun(tc_prod(_1500814, _1500818), tc_HOL_Obool)), _1500820), c_Relation_Orel__comp(_1500814, _1500816, _1500818)), _1500824)), _1500826)))], (46207 ^ _776545) ^ [_1705430, _1705432] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705430)), c_List_Otranspose__rel(_1705430)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705430)), c_List_Olist_ONil(_1705430)), _1705432))), -(c_List_Otranspose(_1705430, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1705430)), c_List_Olist_ONil(_1705430)), _1705432)) = c_List_Otranspose(_1705430, _1705432))], (10499 ^ _776545) ^ [_956933, _956935, _956937] : [hBOOL(hAPP(hAPP(c_member(_956933), _956935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_956933, tc_HOL_Obool)), _956937))), hBOOL(hAPP(hAPP(c_member(_956933), _956935), _956937))], (36130 ^ _776545) ^ [_1457566, _1457568, _1457570, _1457572, _1457574, _1457576, _1457578, _1457580] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457566, _1457568), tc_prod(_1457566, _1457568))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457566, _1457568), tc_prod(_1457566, _1457568)), hAPP(hAPP(c_Product__Type_OPair(_1457566, _1457568), _1457570), _1457572)), hAPP(hAPP(c_Product__Type_OPair(_1457566, _1457568), _1457574), _1457576))), c_Wellfounded_Olex__prod(_1457566, _1457568, _1457578, _1457580)))), 36131 ^ _776545 : [(36134 ^ _776545) ^ [] : [_1457570 = _1457574, hBOOL(hAPP(hAPP(c_member(tc_prod(_1457568, _1457568)), hAPP(hAPP(c_Product__Type_OPair(_1457568, _1457568), _1457572), _1457576)), _1457580))], (36132 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457566, _1457566)), hAPP(hAPP(c_Product__Type_OPair(_1457566, _1457566), _1457570), _1457574)), _1457578))]]], (25425 ^ _776545) ^ [_1236428, _1236430, _1236432] : [-(hBOOL(hAPP(_1236428, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1236430), _1236432)))), 25428 ^ _776545 : [(25431 ^ _776545) ^ [] : [hBOOL(hAPP(_1236428, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25429 ^ _776545) ^ [] : [-(_1236432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25432 ^ _776545 : [(25437 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25435 ^ [_1236428, _1236430, _1236432]), _1236432)))], (25439 ^ _776545) ^ [] : [-(_1236430 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1236432), 25434 ^ [_1236428, _1236430, _1236432])), 25435 ^ [_1236428, _1236430, _1236432]))], (25441 ^ _776545) ^ [] : [hBOOL(hAPP(_1236428, 25434 ^ [_1236428, _1236430, _1236432]))], (25433 ^ _776545) ^ [] : [_1236432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (34880 ^ _776545) ^ [_1427351, _1427353, _1427355, _1427357] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1427351, _1427353, _1427355), hAPP(hAPP(c_COMBB(tc_fun(_1427353, tc_prod(_1427351, _1427353)), tc_fun(_1427353, _1427355), _1427351), hAPP(c_COMBB(tc_prod(_1427351, _1427353), _1427355, _1427353), _1427357)), c_Product__Type_OPair(_1427351, _1427353))) = _1427357)], (41823 ^ _776545) ^ [_1601788, _1601790, _1601792] : [-(c_Random_Oselect__weight(_1601788, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601788)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1601788), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1601790)), _1601792)) = c_Random_Oselect__weight(_1601788, _1601792))], (10617 ^ _776545) ^ [_959131, _959133] : [class_Lattices_Oboolean__algebra(_959131), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959131), hAPP(c_Groups_Ouminus__class_Ouminus(_959131), _959133)), _959133) = c_Orderings_Obot__class_Obot(_959131))], (8990 ^ _776545) ^ [_932102, _932104, _932106, _932108, _932110] : [class_Orderings_Oorder(_932102), 8993 ^ _776545 : [(9014 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_932102, _932104, _932106)), c_SetInterval_Oord__class_OatLeastAtMost(_932102, _932108, _932110)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932108), _932110)), 9017 ^ _776545 : [(9020 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932108), _932104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932106), _932110)), 9027 ^ _776545 : [(9030 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932102), _932106), _932110))], (9028 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932102), _932108), _932104))]]], (9018 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932104), _932106)))]]], (8994 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932102, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_932102, _932104, _932106)), c_SetInterval_Oord__class_OatLeastAtMost(_932102, _932108, _932110))), 8997 ^ _776545 : [(8998 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932104), _932106)), 9001 ^ _776545 : [(9006 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932102), _932108), _932104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932102), _932106), _932110)))], (9004 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932106), _932110)))], (9002 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932108), _932104)))]]], (9012 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932102), _932108), _932110)))]]]]], (16486 ^ _776545) ^ [_1073427] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1073427), hAPP(c_Nat_OSuc, _1073427)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1073427), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (25987 ^ _776545) ^ [_1246413, _1246415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246415)), 25994 ^ _776545 : [(26001 ^ _776545) ^ [] : [_1246413 = _1246415, -(hAPP(c_Int_Onat, _1246413) = hAPP(c_Int_Onat, _1246415))], (25995 ^ _776545) ^ [] : [hAPP(c_Int_Onat, _1246413) = hAPP(c_Int_Onat, _1246415), -(_1246413 = _1246415)]]], (25141 ^ _776545) ^ [_1231667, _1231669, _1231671] : [class_Divides_Osemiring__div(_1231667), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231667), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231667), _1231669), _1231671)), _1231671)), c_Divides_Odiv__class_Omod(_1231667, _1231669, _1231671)) = _1231669)], (7644 ^ _776545) ^ [_903412, _903414, _903416, _903418] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903412, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903412, tc_HOL_Obool)), _903414), _903416)), _903418) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903412, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903412, tc_HOL_Obool)), _903414), _903418)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903412, tc_HOL_Obool)), _903416), _903418)))], (51483 ^ _776545) ^ [_1818447, _1818449] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818447), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818449))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818449), _1818447)))], (18852 ^ _776545) ^ [_1116249, _1116251] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1116249, _1116251)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1116249, _1116251), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1116251), c_Orderings_Otop__class_Otop(tc_fun(_1116251, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1116249), c_Orderings_Otop__class_Otop(tc_fun(_1116249, tc_HOL_Obool)))))], (27323 ^ _776545) ^ [_1268136, _1268138] : [class_Groups_Oordered__ab__group__add__abs(_1268136), 27326 ^ _776545 : [(27333 ^ _776545) ^ [] : [_1268138 = c_Groups_Ozero__class_Ozero(_1268136), -(hAPP(c_Groups_Oabs__class_Oabs(_1268136), _1268138) = c_Groups_Ozero__class_Ozero(_1268136))], (27327 ^ _776545) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1268136), _1268138) = c_Groups_Ozero__class_Ozero(_1268136), -(_1268138 = c_Groups_Ozero__class_Ozero(_1268136))]]], (25219 ^ _776545) ^ [_1233126, _1233128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233126), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25222 ^ _776545 : [(25225 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233126), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233128, _1233126))))], (25223 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233128, _1233126)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5582 ^ _776545) ^ [_861787, _861789, _861791, _861793] : [-(tc_prod(_861793, _861789) = tc_prod(_861791, _861787)), _861793 = _861791, _861789 = _861787], (5516 ^ _776545) ^ [_860830, _860832] : [_860832 = _860830, -(c_Divides_Odiv__class_Odiv(_860832) = c_Divides_Odiv__class_Odiv(_860830))], (36392 ^ _776545) ^ [_1463939] : [-(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)), _1463939), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (49295 ^ _776545) ^ [_1771834, _1771836] : [-(c_Relation_Otrans(_1771834, c_Transitive__Closure_Otrancl(_1771834, _1771836)))], (47777 ^ _776545) ^ [_1737937, _1737939, _1737941, _1737943, _1737945] : [47778 ^ _776545 : [(47781 ^ _776545) ^ [] : [hBOOL(hAPP(_1737945, hAPP(hAPP(c_List_Ozip(_1737937, _1737941), hAPP(hAPP(c_List_Otake(_1737937), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737941)), _1737943))), _1737939)), hAPP(hAPP(c_List_Otake(_1737941), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737941)), _1737943))), _1737943))))], (47779 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), hAPP(hAPP(c_List_Otake(_1737937), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737941)), _1737943))), _1737939)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737941)), hAPP(hAPP(c_List_Otake(_1737941), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737937)), _1737939)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737941)), _1737943))), _1737943)))]], -(hBOOL(hAPP(_1737945, hAPP(hAPP(c_List_Ozip(_1737937, _1737941), _1737939), _1737943))))], (40298 ^ _776545) ^ [_1562141, _1562143, _1562145, _1562147, _1562149, _1562151] : [c_Finite__Set_Ofolding__idem(_1562141, _1562143, _1562145, _1562147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562141), _1562149)), hBOOL(hAPP(hAPP(c_member(_1562141), _1562151), _1562149)), -(hAPP(c_Fun_Ocomp(_1562143, _1562143, _1562143, hAPP(_1562147, _1562149)), hAPP(_1562145, _1562151)) = hAPP(_1562147, _1562149))], (41110 ^ _776545) ^ [_1582716, _1582718, _1582720] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582718, _1582716)), _1582720)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582716, _1582718)), hAPP(c_Relation_Oconverse(_1582718, _1582716), _1582720))))], (50263 ^ _776545) ^ [_1792512, _1792514, _1792516, _1792518] : [c_Fun_Obij__betw(_1792512, _1792514, _1792516, c_Orderings_Otop__class_Otop(tc_fun(_1792512, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792514, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1792512, _1792514, _1792516), hAPP(c_Set_OCollect(_1792512), _1792518)) = hAPP(c_Set_OCollect(_1792514), hAPP(hAPP(c_COMBB(_1792512, tc_HOL_Obool, _1792514), _1792518), c_Hilbert__Choice_Oinv__into(_1792512, _1792514, c_Orderings_Otop__class_Otop(tc_fun(_1792512, tc_HOL_Obool)), _1792516))))], (31347 ^ _776545) ^ [_1339228, _1339230, _1339232] : [class_Orderings_Olinorder(_1339228), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339228), _1339230), _1339232) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339228), _1339232), _1339230))], (39836 ^ _776545) ^ [_1551726, _1551728, _1551730, _1551732, _1551734, _1551736] : [c_Fun_Oinj__on(_1551726, _1551728, _1551730, _1551732), 39839 ^ _776545 : [(39846 ^ _776545) ^ [] : [c_Fun_Oinj__on(_1551726, _1551734, hAPP(c_Fun_Ocomp(_1551728, _1551734, _1551726, _1551736), _1551730), _1551732), -(c_Fun_Oinj__on(_1551728, _1551734, _1551736, hAPP(c_Set_Oimage(_1551726, _1551728, _1551730), _1551732)))], (39840 ^ _776545) ^ [] : [c_Fun_Oinj__on(_1551728, _1551734, _1551736, hAPP(c_Set_Oimage(_1551726, _1551728, _1551730), _1551732)), -(c_Fun_Oinj__on(_1551726, _1551734, hAPP(c_Fun_Ocomp(_1551728, _1551734, _1551726, _1551736), _1551730), _1551732))]]], (45243 ^ _776545) ^ [_1682658, _1682660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682658)), hAPP(c_Code__Numeral_Onat__of, _1682660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1682658), _1682660)))], (7266 ^ _776545) ^ [_895197, _895199, _895201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895197, tc_HOL_Obool)), _895199), hAPP(hAPP(c_Set_Oinsert(_895197), _895201), _895199))))], (31747 ^ _776545) ^ [_1346981, _1346983, _1346985, _1346987] : [class_Orderings_Olinorder(_1346981), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346981, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1346981), _1346983)), c_SetInterval_Oord__class_OatLeastAtMost(_1346981, _1346985, _1346987)) = c_SetInterval_Oord__class_OatLeastAtMost(_1346981, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346981), _1346983), _1346985), _1346987))], (23797 ^ _776545) ^ [_1207579, _1207581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207579)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207579), _1207581)))], (38767 ^ _776545) ^ [_1521943, _1521945, _1521947, _1521949] : [hBOOL(hAPP(hAPP(c_member(_1521943), _1521945), _1521947)), -(hAPP(c_Set_Ovimage(_1521949, _1521943, hAPP(c_COMBK(_1521943, _1521949), _1521945)), _1521947) = c_Orderings_Otop__class_Otop(tc_fun(_1521949, tc_HOL_Obool)))], (40160 ^ _776545) ^ [_1559050, _1559052, _1559054, _1559056, _1559058, _1559060] : [c_Finite__Set_Ofolding(_1559050, _1559052, _1559054, _1559056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559050), _1559058)), -(hAPP(c_Fun_Ocomp(_1559052, _1559052, _1559052, hAPP(_1559054, _1559060)), hAPP(_1559056, _1559058)) = hAPP(c_Fun_Ocomp(_1559052, _1559052, _1559052, hAPP(_1559056, _1559058)), hAPP(_1559054, _1559060)))], (51981 ^ _776545) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (29497 ^ _776545) ^ [_1304860, _1304862, _1304864] : [class_Rings_Ocomm__semiring__1(_1304860), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1304860), _1304862), 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)))), _1304864)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304860), hAPP(hAPP(c_Power_Opower__class_Opower(_1304860), _1304862), _1304864)), hAPP(hAPP(c_Power_Opower__class_Opower(_1304860), _1304862), _1304864)))], (26477 ^ _776545) ^ [_1254415, _1254417, _1254419, _1254421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254417), _1254419)), -(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), _1254419), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254421, _1254415))), _1254417)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254419), _1254415))))], (17695 ^ _776545) ^ [_1095131, _1095133] : [class_Groups_Olinordered__ab__group__add(_1095131), 17698 ^ _776545 : [(17705 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095131), c_Groups_Ozero__class_Ozero(_1095131)), _1095133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095131), hAPP(c_Groups_Ouminus__class_Ouminus(_1095131), _1095133)), _1095133)))], (17699 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095131), hAPP(c_Groups_Ouminus__class_Ouminus(_1095131), _1095133)), _1095133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095131), c_Groups_Ozero__class_Ozero(_1095131)), _1095133)))]]], (29127 ^ _776545) ^ [_1298603, _1298605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298603)), c_Int_OBit1(_1298605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298603), _1298605)))], (24234 ^ _776545) ^ [_1214849, _1214851, _1214853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214849), _1214851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214853), 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), _1214851), _1214853)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214849), _1214853))))], (3712 ^ _776545) ^ [_832208, _832210] : [_832210 = _832208, -(c_List_Oembed__list(_832210) = c_List_Oembed__list(_832208))], (12834 ^ _776545) ^ [_1002970, _1002972] : [class_Complete__Lattice_Ocomplete__lattice(_1002970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002970), _1002972)), -(c_Complete__Lattice_OInf__class_OInf(_1002970, _1002972) = hAPP(hAPP(c_Finite__Set_Ofold(_1002970, _1002970, c_Lattices_Osemilattice__inf__class_Oinf(_1002970)), c_Orderings_Otop__class_Otop(_1002970)), _1002972))], (29013 ^ _776545) ^ [_1296638, _1296640] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1296638)), c_Int_OBit1(_1296640)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296638), _1296640)))], (22189 ^ _776545) ^ [_1178969] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178969), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1178969)], (32849 ^ _776545) ^ [_1373932, _1373934, _1373936, _1373938, _1373940] : [32851 ^ _776545 : [(32854 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373932, tc_HOL_Obool)), hAPP(_1373938, 32850 ^ [_1373932, _1373934, _1373936, _1373938, _1373940])), _1373940))], (32852 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373934), 32850 ^ [_1373932, _1373934, _1373936, _1373938, _1373940]), _1373936)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373932, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1373934, tc_fun(_1373932, tc_HOL_Obool)), _1373936), _1373938)), _1373940)))], (7670 ^ _776545) ^ [_904401, _904403, _904405] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904401, tc_HOL_Obool)), _904403), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904401, tc_HOL_Obool)), _904403), _904405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904401, tc_HOL_Obool)), _904403), _904405))], (28889 ^ _776545) ^ [_1294447, _1294449] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1294447)), _1294449) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1294447), _1294449)))], (44176 ^ _776545) ^ [_1659878, _1659880, _1659882] : [-(c_List_Orotate(_1659878, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659880), _1659882)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1659878), tc_List_Olist(_1659878), tc_List_Olist(_1659878), c_List_Orotate(_1659878, _1659880)), c_List_Orotate(_1659878, _1659882)))], (15099 ^ _776545) ^ [_1049151, _1049153] : [class_Groups_Ocomm__monoid__mult(_1049151), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049151), c_Groups_Oone__class_Oone(_1049151)), _1049153) = _1049153)], (47743 ^ _776545) ^ [_1737451, _1737453] : [class_Enum_Oenum(_1737451), 47746 ^ _776545 : [(47753 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737451), _1737453)), -(hBOOL(hAPP(_1737453, 47756 ^ [_1737451, _1737453])))], (47747 ^ _776545) ^ [] : [47748 ^ _776545 : [(47749 ^ _776545) ^ [_1737553] : [hBOOL(hAPP(_1737453, _1737553))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737451), _1737453)))]]], (49506 ^ _776545) ^ [_1777049, _1777051, _1777053, _1777055] : [c_Wellfounded_Omax__extp(_1777049, _1777051, _1777053, _1777055), 49509 ^ _776545 : [(49512 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777049), _1777055)))], (49514 ^ _776545) ^ [] : [_1777055 = c_Orderings_Obot__class_Obot(tc_fun(_1777049, tc_HOL_Obool))], (49516 ^ _776545) ^ [_1777265] : [hBOOL(hAPP(hAPP(c_member(_1777049), _1777265), _1777053)), 49520 ^ _776545 : [(49523 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1777051, _1777265), 49519 ^ [_1777049, _1777051, _1777053, _1777055, _1777265])))], (49521 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777049), 49519 ^ [_1777049, _1777051, _1777053, _1777055, _1777265]), _1777055)))]]], (49510 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1777049), _1777053)))]]], (1594 ^ _776545) ^ [_799334, _799336] : [-(class_Groups_Ocancel__semigroup__add(_799334)), _799336 = _799334, class_Groups_Ocancel__semigroup__add(_799336)], (35054 ^ _776545) ^ [_1430672, _1430674] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430672, _1430674), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1430672), _1430674)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1430672, _1430674)))))], (25175 ^ _776545) ^ [_1232378, _1232380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232378)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232378), _1232380)), _1232378) = _1232380)], (49319 ^ _776545) ^ [_1772187, _1772189] : [c_Relation_Otrans(_1772187, _1772189), -(c_Relation_Otrans(_1772187, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1772187, _1772187), tc_HOL_Obool)), _1772189), c_Relation_OId(_1772187))))], (2460 ^ _776545) ^ [_812656, _812658, _812660, _812662] : [-(c_Divides_Odivmod__int__rel(_812662, _812658) = c_Divides_Odivmod__int__rel(_812660, _812656)), _812662 = _812660, _812658 = _812656], (7230 ^ _776545) ^ [_894488, _894490, _894492, _894494, _894496] : [hAPP(hAPP(c_Set_Oinsert(_894488), _894490), hAPP(hAPP(c_Set_Oinsert(_894488), _894492), c_Orderings_Obot__class_Obot(tc_fun(_894488, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_894488), _894494), hAPP(hAPP(c_Set_Oinsert(_894488), _894496), c_Orderings_Obot__class_Obot(tc_fun(_894488, tc_HOL_Obool)))), 7235 ^ _776545 : [(7238 ^ _776545) ^ [] : [-(_894492 = _894496)], (7236 ^ _776545) ^ [] : [-(_894490 = _894494)]], 7239 ^ _776545 : [(7242 ^ _776545) ^ [] : [-(_894492 = _894494)], (7240 ^ _776545) ^ [] : [-(_894490 = _894496)]]], (45253 ^ _776545) ^ [_1682835] : [-(c_Code__Numeral_OSuc__code__numeral(_1682835) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1682835))))], (44078 ^ _776545) ^ [_1658002, _1658004, _1658006, _1658008, _1658010] : [-(hAPP(hAPP(c_List_Ozip(_1658002, _1658004), hAPP(hAPP(c_List_Oappend(_1658002), _1658006), _1658008)), _1658010) = hAPP(hAPP(c_List_Oappend(tc_prod(_1658002, _1658004)), hAPP(hAPP(c_List_Ozip(_1658002, _1658004), _1658006), hAPP(hAPP(c_List_Otake(_1658004), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658002)), _1658006)), _1658010))), hAPP(hAPP(c_List_Ozip(_1658002, _1658004), _1658008), hAPP(hAPP(c_List_Odrop(_1658004), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658002)), _1658006)), _1658010))))], (34638 ^ _776545) ^ [_1421763, _1421765, _1421767, _1421769] : [-(c_Nat_Onat_Onat__case(_1421763, _1421765, _1421767, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421769)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1421763), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421769))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1421763, _1421763), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1421763, tc_fun(_1421763, _1421763)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1421763, tc_fun(_1421763, _1421763)), tc_Int_Oint), c_If(_1421763)), c_Nat__Numeral_Oneg)), _1421765)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1421763, tc_Int_Oint), _1421767), c_Int_Onat))))], (46032 ^ _776545) ^ [_1701053, _1701055, _1701057] : [-(hAPP(c_List_Ofilter(_1701053, _1701055), c_List_Oconcat(_1701053, _1701057)) = c_List_Oconcat(_1701053, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1701053), tc_List_Olist(_1701053)), c_List_Ofilter(_1701053, _1701055)), _1701057)))], (49932 ^ _776545) ^ [_1784969, _1784971, _1784973, _1784975] : [c_Equiv__Relations_Opart__equivp(_1784969, _1784971), hBOOL(hAPP(hAPP(_1784971, _1784973), _1784975)), -(hBOOL(hAPP(hAPP(_1784971, _1784975), _1784973)))], (42087 ^ _776545) ^ [_1610247, _1610249, _1610251, _1610253, _1610255, _1610257] : [c_List_Olistrelp(_1610247, _1610249, hAPP(hAPP(c_List_Olist_OCons(_1610247), _1610251), _1610253), hAPP(hAPP(c_List_Olist_OCons(_1610247), _1610255), _1610257)), 42090 ^ _776545 : [(42093 ^ _776545) ^ [] : [-(c_List_Olistrelp(_1610247, _1610249, _1610253, _1610257))], (42091 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1610249, _1610251), _1610255)))]]], (36213 ^ _776545) ^ [_1459653, _1459655, _1459657, _1459659, _1459661] : [-(hAPP(c_Product__Type_Ofst(_1459653, _1459655), hAPP(c_Product__Type_Oapfst(_1459657, _1459653, _1459655, _1459659), _1459661)) = hAPP(_1459659, hAPP(c_Product__Type_Ofst(_1459657, _1459655), _1459661)))], (38462 ^ _776545) ^ [_1513928] : [-(c_Wellfounded_OwfP(_1513928, hAPP(c_COMBK(tc_fun(_1513928, tc_HOL_Obool), _1513928), hAPP(c_COMBK(tc_HOL_Obool, _1513928), c_fFalse))))], (37462 ^ _776545) ^ [_1489555, _1489557, _1489559, _1489561, _1489563] : [c_Fun_Oinj__on(_1489555, _1489557, _1489559, c_Orderings_Otop__class_Otop(tc_fun(_1489555, tc_HOL_Obool))), 37465 ^ _776545 : [(37472 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1489555), _1489561), _1489563)), -(hBOOL(hAPP(hAPP(c_member(_1489557), hAPP(_1489559, _1489561)), hAPP(c_Set_Oimage(_1489555, _1489557, _1489559), _1489563))))], (37466 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1489557), hAPP(_1489559, _1489561)), hAPP(c_Set_Oimage(_1489555, _1489557, _1489559), _1489563))), -(hBOOL(hAPP(hAPP(c_member(_1489555), _1489561), _1489563)))]]], (19579 ^ _776545) ^ [_1130333, _1130335, _1130337] : [class_Rings_Odivision__ring(_1130333), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130333), _1130335), _1130337)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130333), hAPP(c_Groups_Ouminus__class_Ouminus(_1130333), _1130335)), _1130337))], (43492 ^ _776545) ^ [_1643866, _1643868, _1643870, _1643872] : [_1643868 = _1643872, -(hAPP(hAPP(c_List_Oappend(_1643866), _1643868), _1643870) = hAPP(hAPP(c_List_Oappend(_1643866), _1643872), _1643870))], (35856 ^ _776545) ^ [_1446593] : [-(c_Wellfounded_Ofinite__psubset(_1446593) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1446593, tc_HOL_Obool), tc_fun(_1446593, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1446593, tc_HOL_Obool), tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1446593, tc_HOL_Obool), tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1446593, tc_HOL_Obool)), c_COMBS(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446593, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1446593, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1446593, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1446593, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1446593)))))], (6909 ^ _776545) ^ [_888698, _888700, _888702] : [class_Orderings_Olinorder(_888698), 6912 ^ _776545 : [(6919 ^ _776545) ^ [] : [_888700 = _888702, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_888698), _888700) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888698), _888702))], (6913 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_888698), _888700) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888698), _888702), -(_888700 = _888702)]]], (33352 ^ _776545) ^ [_1388675, _1388677, _1388679, _1388681] : [-(hAPP(c_Set_OPow(_1388675), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388677, tc_fun(_1388675, tc_HOL_Obool)), _1388679), _1388681)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388677, tc_fun(tc_fun(_1388675, tc_HOL_Obool), tc_HOL_Obool)), _1388679), hAPP(hAPP(c_COMBB(tc_fun(_1388675, tc_HOL_Obool), tc_fun(tc_fun(_1388675, tc_HOL_Obool), tc_HOL_Obool), _1388677), c_Set_OPow(_1388675)), _1388681)))], (8681 ^ _776545) ^ [_925722, _925724, _925726, _925728] : [class_Lattices_Osemilattice__inf(_925722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925722), _925724), _925726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925722), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925722), _925724), _925728)), _925726)))], (6310 ^ _776545) ^ [_878110, _878112, _878114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878110, tc_HOL_Obool), tc_HOL_Obool)), _878112), _878114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878110, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_878110, tc_HOL_Obool), _878112)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_878110, tc_HOL_Obool), _878114))))], (4234 ^ _776545) ^ [_840709, _840711] : [_840711 = _840709, -(c_List_Otake(_840711) = c_List_Otake(_840709))], (52435 ^ _776545) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (4942 ^ _776545) ^ [_851839, _851841, _851843, _851845] : [-(c_Hilbert__Choice_OEps(_851845, _851841) = c_Hilbert__Choice_OEps(_851843, _851839)), _851845 = _851843, _851841 = _851839], (42367 ^ _776545) ^ [_1617469, _1617471, _1617473] : [42369 ^ _776545 : [(42372 ^ _776545) ^ [] : [hBOOL(hAPP(_1617473, 42368 ^ [_1617469, _1617471, _1617473]))], (42370 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617469), 42368 ^ [_1617469, _1617471, _1617473]), hAPP(c_List_Oset(_1617469), _1617471))))]], 42373 ^ _776545 : [(42374 ^ _776545) ^ [_1617653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617653), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617469)), _1617471))), -(hBOOL(hAPP(_1617473, hAPP(hAPP(c_List_Onth(_1617469), _1617471), _1617653))))]]], (32528 ^ _776545) ^ [_1364436, _1364438, _1364440, _1364442, _1364444] : [hBOOL(hAPP(hAPP(c_member(_1364436), _1364438), _1364440)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364442, tc_HOL_Obool)), hAPP(_1364444, _1364438)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364436, tc_fun(_1364442, tc_HOL_Obool)), _1364440), _1364444)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364436, tc_fun(_1364442, tc_HOL_Obool)), _1364440), _1364444))], (7666 ^ _776545) ^ [_904255, _904257, _904259, _904261] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904255, tc_HOL_Obool)), _904257), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904255, tc_HOL_Obool)), _904259), _904261)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904255, tc_HOL_Obool)), _904259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904255, tc_HOL_Obool)), _904257), _904261)))], (32986 ^ _776545) ^ [_1378588, _1378590, _1378592] : [-(hAPP(hAPP(c_Set_Oinsert(_1378588), _1378590), _1378592) = hAPP(c_Set_OCollect(_1378588), hAPP(hAPP(c_COMBS(_1378588, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378588), c_fdisj), hAPP(hAPP(c_COMBC(_1378588, _1378588, tc_HOL_Obool), c_fequal), _1378590))), hAPP(hAPP(c_COMBC(_1378588, tc_fun(_1378588, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378588)), _1378592))))], (46197 ^ _776545) ^ [_1704665, _1704667, _1704669] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704665)), hAPP(c_List_Ofilter(_1704665, _1704667), _1704669)) = 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(_1704665)), _1704669)))), hAPP(hAPP(c_COMBB(_1704665, tc_HOL_Obool, tc_Nat_Onat), _1704667), hAPP(c_List_Onth(_1704665), _1704669))))))], (12049 ^ _776545) ^ [_988321, _988323, _988325] : [class_Lattices_Olattice(_988321), hBOOL(hAPP(c_Finite__Set_Ofinite(_988321), _988323)), hBOOL(hAPP(hAPP(c_member(_988321), _988325), _988323)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_988321), _988325), c_Big__Operators_Olattice__class_OInf__fin(_988321, _988323)) = _988325)], (22345 ^ _776545) ^ [_1181683, _1181685] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1181683), _1181685)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181683), _1181685) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24525 ^ _776545) ^ [_1220174, _1220176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1220174, _1220176))))], (16574 ^ _776545) ^ [_1074741] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074741), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22375 ^ _776545) ^ [_1182198, _1182200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182198), _1182200)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182198), _1182200)))], (22069 ^ _776545) ^ [_1176680, _1176682, _1176684, _1176686] : [class_Fields_Ofield(_1176680), -(_1176682 = c_Groups_Ozero__class_Ozero(_1176680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1176684), _1176686)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1176680), _1176682), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1176686), _1176684)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1176680), hAPP(hAPP(c_Power_Opower__class_Opower(_1176680), _1176682), _1176686)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176680), _1176682), _1176684)))], (52225 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (26186 ^ _776545) ^ [_1249632, _1249634, _1249636] : [-(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), _1249632), _1249634)), _1249636)), _1249634) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1249636), _1249634))], (34952 ^ _776545) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (32502 ^ _776545) ^ [_1363258, _1363260, _1363262, _1363264, _1363266] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363258, tc_fun(_1363260, tc_HOL_Obool)), _1363262), hAPP(hAPP(c_COMBS(_1363258, tc_fun(_1363260, tc_HOL_Obool), tc_fun(_1363260, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363260, tc_HOL_Obool), tc_fun(tc_fun(_1363260, tc_HOL_Obool), tc_fun(_1363260, tc_HOL_Obool)), _1363258), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363260, tc_HOL_Obool))), _1363264)), _1363266)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363260, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363258, tc_fun(_1363260, tc_HOL_Obool)), _1363262), _1363264)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363258, tc_fun(_1363260, tc_HOL_Obool)), _1363262), _1363266)))], (22737 ^ _776545) ^ [_1188436, _1188438, _1188440, _1188442] : [class_Rings_Olinordered__semidom(_1188436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188436), hAPP(hAPP(c_Power_Opower__class_Opower(_1188436), _1188438), hAPP(c_Nat_OSuc, _1188440))), hAPP(hAPP(c_Power_Opower__class_Opower(_1188436), _1188442), hAPP(c_Nat_OSuc, _1188440)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188436), c_Groups_Ozero__class_Ozero(_1188436)), _1188442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188436), _1188438), _1188442)))], (34856 ^ _776545) ^ [_1426986, _1426988] : [-(c_Divides_Odivmod__int(_1426986, _1426988) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1426986), _1426988)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1426986, _1426988)))], (18772 ^ _776545) ^ [_1114663, _1114665, _1114667, _1114669, _1114671, _1114673] : [class_Groups_Oab__semigroup__mult(_1114663), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114665), _1114667)), -(hBOOL(hAPP(hAPP(c_member(_1114665), _1114669), _1114667))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1114663, _1114665, c_Groups_Otimes__class_Otimes(_1114663)), _1114671), _1114673), hAPP(hAPP(c_Set_Oinsert(_1114665), _1114669), _1114667)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114663), hAPP(_1114671, _1114669)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1114663, _1114665, c_Groups_Otimes__class_Otimes(_1114663)), _1114671), _1114673), _1114667)))], (37814 ^ _776545) ^ [_1497354, _1497356] : [37815 ^ _776545 : [(37816 ^ _776545) ^ [_1497418, _1497420] : [_1497356 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1497354, _1497418), 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)), _1497420)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497354), _1497356)))], (39816 ^ _776545) ^ [_1551012, _1551014, _1551016, _1551018, _1551020, _1551022] : [-(hAPP(c_Set_Ovimage(_1551012, tc_prod(_1551014, _1551016), _1551018), hAPP(hAPP(c_Product__Type_OSigma(_1551014, _1551016), _1551020), hAPP(c_COMBK(tc_fun(_1551016, tc_HOL_Obool), _1551014), _1551022))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551012, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1551012, _1551014, hAPP(c_Fun_Ocomp(tc_prod(_1551014, _1551016), _1551014, _1551012, c_Product__Type_Ofst(_1551014, _1551016)), _1551018)), _1551020)), hAPP(c_Set_Ovimage(_1551012, _1551016, hAPP(c_Fun_Ocomp(tc_prod(_1551014, _1551016), _1551016, _1551012, c_Product__Type_Osnd(_1551014, _1551016)), _1551018)), _1551022)))], (2944 ^ _776545) ^ [_820250, _820252] : [_820252 = _820250, -(c_Rings_Oinverse__class_Odivide(_820252) = c_Rings_Oinverse__class_Odivide(_820250))], (28527 ^ _776545) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (43314 ^ _776545) ^ [_1639534, _1639536, _1639538, _1639540, _1639542] : [-(hAPP(hAPP(c_List_Ozip(_1639534, _1639536), _1639538), hAPP(hAPP(c_List_Olist_OCons(_1639536), _1639540), _1639542)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1639534, _1639536)), _1639534, c_List_Olist_ONil(tc_prod(_1639534, _1639536)), hAPP(hAPP(c_COMBC(_1639534, tc_fun(tc_List_Olist(_1639534), tc_List_Olist(tc_prod(_1639534, _1639536))), tc_fun(tc_List_Olist(_1639534), tc_List_Olist(tc_prod(_1639534, _1639536)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1639534, _1639536)), tc_List_Olist(tc_prod(_1639534, _1639536))), tc_fun(tc_fun(tc_List_Olist(_1639534), tc_List_Olist(tc_prod(_1639534, _1639536))), tc_fun(tc_List_Olist(_1639534), tc_List_Olist(tc_prod(_1639534, _1639536)))), _1639534), c_COMBB(tc_List_Olist(tc_prod(_1639534, _1639536)), tc_List_Olist(tc_prod(_1639534, _1639536)), tc_List_Olist(_1639534))), hAPP(hAPP(c_COMBB(tc_prod(_1639534, _1639536), tc_fun(tc_List_Olist(tc_prod(_1639534, _1639536)), tc_List_Olist(tc_prod(_1639534, _1639536))), _1639534), c_List_Olist_OCons(tc_prod(_1639534, _1639536))), hAPP(hAPP(c_COMBC(_1639534, _1639536, tc_prod(_1639534, _1639536)), c_Product__Type_OPair(_1639534, _1639536)), _1639540)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639534), tc_List_Olist(_1639536), tc_List_Olist(tc_prod(_1639534, _1639536))), c_List_Ozip(_1639534, _1639536)), _1639542))), _1639538))], (10855 ^ _776545) ^ [_963794, _963796, _963798, _963800] : [class_Orderings_Oorder(_963794), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963794, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963794, _963796), _963798)), c_SetInterval_Oord__class_OatLeastAtMost(_963794, _963798, _963800)) = c_Orderings_Obot__class_Obot(tc_fun(_963794, tc_HOL_Obool)))], (31106 ^ _776545) ^ [_1334816, _1334818] : [class_Groups_Olinordered__ab__group__add(_1334816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334816), _1334818)), -(_1334818 = c_Orderings_Obot__class_Obot(tc_fun(_1334816, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1334816), c_Big__Operators_Olinorder__class_OMin(_1334816, _1334818)) = c_Big__Operators_Olinorder__class_OMax(_1334816, hAPP(c_Set_Oimage(_1334816, _1334816, c_Groups_Ouminus__class_Ouminus(_1334816)), _1334818)))], (7878 ^ _776545) ^ [_909241, _909243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909241, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_909241, tc_HOL_Obool))), _909243) = c_Orderings_Obot__class_Obot(tc_fun(_909241, tc_HOL_Obool)))], (29311 ^ _776545) ^ [] : [-(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)))))], (52223 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (27317 ^ _776545) ^ [_1268045] : [class_Groups_Oordered__ab__group__add__abs(_1268045), -(hAPP(c_Groups_Oabs__class_Oabs(_1268045), c_Groups_Ozero__class_Ozero(_1268045)) = c_Groups_Ozero__class_Ozero(_1268045))], (37858 ^ _776545) ^ [_1498128, _1498130, _1498132, _1498134] : [c_Fun_Oinj__on(_1498128, _1498130, _1498132, c_Orderings_Otop__class_Otop(tc_fun(_1498128, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1498128, _1498130, c_Orderings_Otop__class_Otop(tc_fun(_1498128, tc_HOL_Obool)), _1498132), hAPP(_1498132, _1498134)) = _1498134)], (32584 ^ _776545) ^ [_1366177, _1366179, _1366181, _1366183, _1366185, _1366187] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366177, tc_fun(_1366179, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1366177, tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_fun(_1366179, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366179, tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_fun(_1366179, tc_HOL_Obool)), _1366177), c_COMBC(_1366179, tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366179, tc_prod(_1366177, _1366179)), tc_fun(_1366179, tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), _1366177), hAPP(c_COMBB(tc_prod(_1366177, _1366179), tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool), _1366179), c_member(tc_prod(_1366177, _1366179)))), c_Product__Type_OPair(_1366177, _1366179)))), _1366181)), hAPP(hAPP(c_COMBC(_1366177, tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_fun(_1366179, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366179, tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_fun(_1366179, tc_HOL_Obool)), _1366177), c_COMBC(_1366179, tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366179, tc_prod(_1366177, _1366179)), tc_fun(_1366179, tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool)), _1366177), hAPP(c_COMBB(tc_prod(_1366177, _1366179), tc_fun(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool), tc_HOL_Obool), _1366179), c_member(tc_prod(_1366177, _1366179)))), c_Product__Type_OPair(_1366177, _1366179)))), _1366183)), _1366185), _1366187)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1366177, _1366179)), hAPP(hAPP(c_Product__Type_OPair(_1366177, _1366179), _1366185), _1366187)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1366177, _1366179), tc_HOL_Obool)), _1366181), _1366183))))], (35034 ^ _776545) ^ [_1430318, _1430320] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430318, _1430320), c_Divides_Odivmod__nat(_1430318, _1430320))))], (5098 ^ _776545) ^ [_854301, _854303, _854305, _854307, _854309, _854311, _854313, _854315] : [-(c_Hilbert__Choice_Oinv__into(_854315, _854311, _854307, _854303) = c_Hilbert__Choice_Oinv__into(_854313, _854309, _854305, _854301)), _854315 = _854313, _854311 = _854309, _854307 = _854305, _854303 = _854301], (1324 ^ _776545) ^ [_795959, _795961] : [-(class_Rings_Oidom(_795959)), _795961 = _795959, class_Rings_Oidom(_795961)], (17797 ^ _776545) ^ [_1096844, _1096846] : [class_Groups_Ogroup__add(_1096844), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096844), hAPP(c_Groups_Ouminus__class_Ouminus(_1096844), _1096846)), _1096846) = c_Groups_Ozero__class_Ozero(_1096844))], (28633 ^ _776545) ^ [_1290049] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1290049))) = 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)))), _1290049))], (34886 ^ _776545) ^ [_1427552, _1427554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427552)), 34889 ^ _776545 : [(34896 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427554))), 34899 ^ _776545 : [(34906 ^ _776545) ^ [] : [-(_1427552 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1427552, _1427554) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427552), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427554))))], (34900 ^ _776545) ^ [] : [_1427552 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1427552, _1427554) = 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)))]]], (34890 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427554)), -(c_Divides_Odivmod__int(_1427552, _1427554) = c_Divides_OposDivAlg(_1427552, _1427554))]]], (19727 ^ _776545) ^ [_1132656, _1132658, _1132660] : [class_Rings_Odivision__ring(_1132656), -(_1132658 = c_Groups_Ozero__class_Ozero(_1132656)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132656), hAPP(c_Groups_Ouminus__class_Ouminus(_1132656), _1132660)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132656), _1132658)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132656), _1132660), _1132658))], (21051 ^ _776545) ^ [_1156962, _1156964, _1156966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1156962), _1156964)), 21057 ^ _776545 : [(21060 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1156966, 21056 ^ [_1156962, _1156964, _1156966])))], (21058 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1156962), 21056 ^ [_1156962, _1156964, _1156966]), _1156964)))]], -(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(_1156962, tc_Nat_Onat), _1156966), _1156964))))], (48768 ^ _776545) ^ [_1759574, _1759576] : [-(c_Predicate_Opred__comp(_1759574, _1759574, _1759574, c_fequal, c_Predicate_Opred__comp(_1759574, _1759574, _1759574, _1759576, c_fequal)) = _1759576)], (48740 ^ _776545) ^ [_1758881, _1758883, _1758885] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1758881), hAPP(c_COMBK(_1758881, tc_Nat_Onat), _1758883)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1758885)) = c_List_Oreplicate(_1758881, _1758885, _1758883))], (50645 ^ _776545) ^ [_1800322, _1800324, _1800326, _1800328, _1800330, _1800332] : [c_Fun_Oinj__on(_1800322, _1800324, _1800326, _1800328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800324, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800322, _1800324, _1800326), _1800328)), _1800330)), c_Fun_Oinj__on(_1800324, _1800322, _1800332, _1800330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800322, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800324, _1800322, _1800332), _1800330)), _1800328)), -(c_Fun_Obij__betw(_1800322, _1800324, 50660 ^ [_1800322, _1800324, _1800326, _1800328, _1800330, _1800332], _1800328, _1800330))], (4222 ^ _776545) ^ [_840539, _840541] : [_840541 = _840539, -(c_List_Otl(_840541) = c_List_Otl(_840539))], (40801 ^ _776545) ^ [_1575070, _1575072, _1575074, _1575076, _1575078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575070, _1575070)), hAPP(hAPP(c_Product__Type_OPair(_1575070, _1575070), _1575072), _1575074)), _1575076)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575070, _1575070)), hAPP(hAPP(c_Product__Type_OPair(_1575070, _1575070), _1575074), _1575078)), c_Transitive__Closure_Ortrancl(_1575070, _1575076))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575070, _1575070)), hAPP(hAPP(c_Product__Type_OPair(_1575070, _1575070), _1575072), _1575078)), c_Transitive__Closure_Ortrancl(_1575070, _1575076))))], (27807 ^ _776545) ^ [] : [-(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))))], (42117 ^ _776545) ^ [_1610990, _1610992, _1610994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610990, _1610990), tc_HOL_Obool)), _1610992), hAPP(hAPP(c_Product__Type_OSigma(_1610990, _1610990), _1610994), hAPP(c_COMBK(tc_fun(_1610990, tc_HOL_Obool), _1610990), _1610994)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610990), tc_List_Olist(_1610990)), tc_HOL_Obool)), c_List_Olistrel(_1610990, _1610992)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1610990), tc_List_Olist(_1610990)), c_List_Olists(_1610990, _1610994)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1610990), tc_HOL_Obool), tc_List_Olist(_1610990)), c_List_Olists(_1610990, _1610994))))))], (15824 ^ _776545) ^ [_1063171, _1063173] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063171), _1063173) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15829 ^ _776545 : [(15832 ^ _776545) ^ [] : [-(_1063173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15830 ^ _776545) ^ [] : [-(_1063171 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 15833 ^ _776545 : [(15836 ^ _776545) ^ [] : [-(_1063173 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15834 ^ _776545) ^ [] : [-(_1063171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (51179 ^ _776545) ^ [_1812940, _1812942, _1812944] : [class_Divides_Osemiring__div(_1812940), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812940), _1812942), _1812944)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812940), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812940), _1812944), _1812942)), _1812942) = _1812944)], (40518 ^ _776545) ^ [_1567244, _1567246, _1567248, _1567250, _1567252, _1567254, _1567256] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567244, _1567246, _1567248, _1567250), _1567252), _1567254), _1567256) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1567246, _1567248, _1567250), _1567254), hAPP(_1567252, _1567256)))], (52489 ^ _776545) ^ [] : [-(hBOOL(c_fTrue))], (52393 ^ _776545) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (30986 ^ _776545) ^ [_1332427, _1332429, _1332431] : [class_Orderings_Olinorder(_1332427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332427), 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hAPP(hAPP(c_COMBC(tc_fun(_1774830, _1774828), _1774830, _1774828), c_COMBI(tc_fun(_1774830, _1774828))), _1774834)))))))], (52043 ^ _776545) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (37193 ^ _776545) ^ [] : [-(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))], (11153 ^ _776545) ^ [_969599, _969601, _969603] : [-(hAPP(c_Set_Oimage(_969599, _969601, _969603), c_Orderings_Obot__class_Obot(tc_fun(_969599, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_969601, tc_HOL_Obool)))], (52093 ^ _776545) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (9570 ^ _776545) ^ [_940688, _940690, _940692] : [class_Orderings_Olinorder(_940688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940688), _940690), _940692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940688), _940692), _940690))], (24315 ^ _776545) ^ [_1216295, _1216297] : [class_Rings_Osemiring__1(_1216295), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216295), hAPP(c_Nat_OSuc, _1216297)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216295), c_Groups_Oone__class_Oone(_1216295)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216295), _1216297)))], (6164 ^ _776545) ^ [_875462, _875464, _875466, _875468] : [hBOOL(hAPP(hAPP(c_member(_875462), _875464), c_Complete__Lattice_OInf__class_OInf(tc_fun(_875462, tc_HOL_Obool), _875466))), hBOOL(hAPP(hAPP(c_member(tc_fun(_875462, tc_HOL_Obool)), _875468), _875466)), -(hBOOL(hAPP(hAPP(c_member(_875462), _875464), _875468)))], (28781 ^ _776545) ^ [_1292595, _1292597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292595)), -(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)))), _1292597))), 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)))), _1292595)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1292597), _1292595))], (36549 ^ _776545) ^ [] : [-(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))))))], (47046 ^ _776545) ^ [_1722224, _1722226, _1722228, _1722230, _1722232] : [c_List_Olist__all2(_1722224, _1722226, _1722228, hAPP(c_List_Orev(_1722224), _1722230), hAPP(c_List_Orev(_1722226), _1722232)), -(c_List_Olist__all2(_1722224, _1722226, _1722228, _1722230, _1722232))], (594 ^ _776545) ^ [_785468, _785470, _785472, _785474, _785476, _785478, _785480, _785482, _785484, _785486] : [-(c_List_Olist__all2(_785484, _785480, _785476, _785472, _785468)), c_List_Olist__all2(_785486, _785482, _785478, _785474, _785470), _785486 = _785484, _785482 = _785480, _785478 = _785476, _785474 = _785472, _785470 = _785468], (46940 ^ _776545) ^ [_1719844, _1719846, _1719848, _1719850] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719844), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719844))), _1719846))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719844))), c_List_Otranspose(_1719844, _1719846)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719850), 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c_List_Omeasures(_1735332, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735332, tc_Nat_Onat)), _1735326), _1735334)))))], (34289 ^ _776545) ^ [_1414529, _1414531] : [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), _1414529))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414529))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414529))), 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), _1414531))), c_COMBI(tc_Int_Oint))))], (16781 ^ _776545) ^ [_1078485, _1078487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078485), _1078487)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078487)), _1078485) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078487), _1078485)))], (29775 ^ _776545) ^ [] : [-(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))], (6728 ^ _776545) ^ [_885416, _885418, _885420] : [class_Orderings_Oorder(_885416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885416), _885418), _885420)), 6735 ^ _776545 : [(6742 ^ _776545) ^ [] : [_885420 = _885418, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885416), _885420), _885418)))], (6736 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885416), _885420), _885418)), -(_885420 = _885418)]]], (13182 ^ _776545) ^ [_1009806, _1009808, _1009810, _1009812, _1009814] : [c_Finite__Set_Ofun__left__comm__idem(_1009806, _1009808, _1009810), -(hAPP(hAPP(_1009810, _1009812), hAPP(hAPP(_1009810, _1009812), _1009814)) = hAPP(hAPP(_1009810, _1009812), _1009814))], (28325 ^ _776545) ^ [_1284996, _1284998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1284996)), c_Int_OBit1(_1284998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1284996), _1284998)))], (7228 ^ _776545) ^ [_894424, _894426, _894428] : [hAPP(hAPP(c_Set_Oinsert(_894424), _894426), _894428) = c_Orderings_Obot__class_Obot(tc_fun(_894424, tc_HOL_Obool))], (2762 ^ _776545) ^ [_817391, _817393, _817395, _817397, _817399, _817401] : [-(c_Predicate_ODomainP(_817401, _817397, _817393) = c_Predicate_ODomainP(_817399, _817395, _817391)), _817401 = _817399, _817397 = _817395, _817393 = _817391], (29755 ^ _776545) ^ [_1310102, _1310104, _1310106] : [29757 ^ _776545 : [(29760 ^ _776545) ^ [] : [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(_1310104, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29756 ^ [_1310102, _1310104, _1310106]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1310104, 29756 ^ [_1310102, _1310104, _1310106])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29758 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29756 ^ [_1310102, _1310104, _1310106]), _1310102)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1310104, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1310106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1310106), hAPP(_1310104, _1310102))), 29770 ^ _776545 : [(29773 ^ _776545) ^ [] : [-(hAPP(_1310104, 29769 ^ [_1310102, _1310104, _1310106]) = _1310106)], (29771 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29769 ^ [_1310102, _1310104, _1310106]), _1310102)))]]], (26066 ^ _776545) ^ [_1247741] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1247741)), -(hAPP(c_Int_Onat, _1247741) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16078 ^ _776545) ^ [_1067290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067290)), _1067290))], (44232 ^ _776545) ^ [_1661047, _1661049, _1661051] : [-(_1661047 = c_List_Olist_ONil(_1661049)), -(hAPP(hAPP(c_List_Otake(_1661049), hAPP(c_Nat_OSuc, _1661051)), _1661047) = hAPP(hAPP(c_List_Olist_OCons(_1661049), hAPP(c_List_Ohd(_1661049), _1661047)), hAPP(hAPP(c_List_Otake(_1661049), _1661051), hAPP(c_List_Otl(_1661049), _1661047))))], (32538 ^ _776545) ^ [_1364791, _1364793, _1364795, _1364797] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1364791, tc_HOL_Obool), hAPP(c_Set_Oimage(_1364793, tc_fun(_1364791, tc_HOL_Obool), _1364795), _1364797)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364793, tc_fun(_1364791, tc_HOL_Obool)), _1364797), _1364795))], (16538 ^ _776545) ^ [_1074244, _1074246, _1074248] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074244), _1074246) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074244), _1074248), -(_1074246 = _1074248), -(_1074244 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39463 ^ _776545) ^ [_1541315, _1541317] : [-(c_Product__Type_Omap__pair(_1541315, _1541315, _1541317, _1541317, c_COMBI(_1541315), c_COMBI(_1541317)) = c_Fun_Oid(tc_prod(_1541315, _1541317)))], (15650 ^ _776545) ^ [_1060394, _1060396, _1060398] : [class_Groups_Ocomm__monoid__add(_1060394), hAPP(_1060396, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1060394), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1060394), _1060396), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1060398)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1060394), _1060396), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060398)))], (38935 ^ _776545) ^ [_1525732, _1525734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525732, _1525732)), _1525734)), c_Wellfounded_Oacyclic(_1525732, _1525734), -(c_Wellfounded_Owf(_1525732, _1525734))], (28755 ^ _776545) ^ [_1292004, _1292006] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292004)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1292006)) = 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)))), _1292004)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1292006)))], (20387 ^ _776545) ^ [_1144334, _1144336, _1144338] : [class_Fields_Olinordered__field(_1144334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144334), c_Groups_Ozero__class_Ozero(_1144334)), _1144336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144334), _1144338), c_Groups_Ozero__class_Ozero(_1144334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144334), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144334), _1144336), _1144338)), c_Groups_Ozero__class_Ozero(_1144334))))], (37598 ^ _776545) ^ [_1492282, _1492284, _1492286, _1492288] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492282), _1492284)), hAPP(c_Finite__Set_Ocard(_1492286), hAPP(c_Set_Oimage(_1492282, _1492286, _1492288), _1492284)) = hAPP(c_Finite__Set_Ocard(_1492282), _1492284), -(c_Fun_Oinj__on(_1492282, _1492286, _1492288, _1492284))], (45788 ^ _776545) ^ [_1695236, _1695238] : [-(hAPP(c_List_Oset(_1695236), c_List_Oremdups(_1695236, _1695238)) = hAPP(c_List_Oset(_1695236), _1695238))], (38606 ^ _776545) ^ [_1518040, _1518042, _1518044, _1518046] : [c_Fun_Oinj__on(_1518040, _1518042, _1518044, c_Orderings_Otop__class_Otop(tc_fun(_1518040, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518040, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1518040, _1518042, _1518044), hAPP(hAPP(c_Set_Oinsert(_1518042), _1518046), c_Orderings_Obot__class_Obot(tc_fun(_1518042, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1518040), c_HOL_OThe(_1518040, hAPP(hAPP(c_COMBC(_1518040, _1518042, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1518042, tc_fun(_1518042, tc_HOL_Obool), _1518040), c_fequal), _1518044)), _1518046))), c_Orderings_Obot__class_Obot(tc_fun(_1518040, tc_HOL_Obool))))))], (52035 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (28337 ^ _776545) ^ [_1285219, _1285221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285219)), c_Int_OBit1(_1285221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285219), _1285221)))], (15023 ^ _776545) ^ [_1047657, _1047659, _1047661, _1047663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047657), _1047659)), hBOOL(hAPP(hAPP(c_member(_1047657), _1047661), _1047659)), hBOOL(hAPP(hAPP(c_member(_1047657), _1047663), _1047659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1047657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047657, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047657, tc_HOL_Obool)), _1047659), hAPP(hAPP(c_Set_Oinsert(_1047657), _1047661), c_Orderings_Obot__class_Obot(tc_fun(_1047657, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1047657), _1047663), c_Orderings_Obot__class_Obot(tc_fun(_1047657, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1047657), _1047659))))], (42019 ^ _776545) ^ [_1607846, _1607848] : [-(c_List_Olistrel(_1607846, c_Transitive__Closure_Ortrancl(_1607846, _1607848)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607846), c_List_Olistrel1(_1607846, _1607848)))], (50717 ^ _776545) ^ [_1801706, _1801708, _1801710] : [hBOOL(hAPP(hAPP(_1801708, _1801710), _1801710)), -(hBOOL(hAPP(c_Quotient_ORespects(_1801706, _1801708), _1801710)))], (43847 ^ _776545) ^ [_1652354, _1652356, _1652358, _1652360, _1652362] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652354), tc_List_Olist(_1652354))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652354), tc_List_Olist(_1652354)), hAPP(hAPP(c_List_Oappend(_1652354), _1652356), _1652358)), hAPP(hAPP(c_List_Oappend(_1652354), _1652356), _1652360))), c_List_Olexord(_1652354, _1652362))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652354, _1652354)), hAPP(hAPP(c_Product__Type_OPair(_1652354, _1652354), 43852 ^ [_1652354, _1652356, _1652358, _1652360, _1652362]), 43852 ^ [_1652354, _1652356, _1652358, _1652360, _1652362])), _1652362))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652354), tc_List_Olist(_1652354))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652354), tc_List_Olist(_1652354)), _1652358), _1652360)), c_List_Olexord(_1652354, _1652362))))], (7958 ^ _776545) ^ [_911116, _911118] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911116, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_911116, tc_HOL_Obool))), _911118) = c_Orderings_Otop__class_Otop(tc_fun(_911116, tc_HOL_Obool)))], (48716 ^ _776545) ^ [_1758400, _1758402] : [-(c_List_Oreplicate(_1758400, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1758402) = c_List_Olist_ONil(_1758400))], (32968 ^ _776545) ^ [_1377948, _1377950, _1377952, _1377954, _1377956] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377948, tc_HOL_Obool)), _1377950), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377952, tc_fun(_1377948, tc_HOL_Obool)), _1377954), _1377956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377952, tc_fun(_1377948, tc_HOL_Obool)), _1377954), hAPP(hAPP(c_COMBB(tc_fun(_1377948, tc_HOL_Obool), tc_fun(_1377948, tc_HOL_Obool), _1377952), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377948, tc_HOL_Obool)), _1377950)), _1377956)))], (19601 ^ _776545) ^ [_1130688] : [class_Groups_Osgn__if(_1130688), -(c_Groups_Osgn__class_Osgn(_1130688, c_Groups_Ozero__class_Ozero(_1130688)) = c_Groups_Ozero__class_Ozero(_1130688))], (52089 ^ _776545) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (46466 ^ _776545) ^ [_1711279] : [class_Orderings_Olinorder(_1711279), -(c_List_Olinorder__class_Osorted(_1711279, c_List_Olist_ONil(_1711279)))], (44148 ^ _776545) ^ [_1659316, _1659318, _1659320] : [-(hAPP(hAPP(c_List_Odrop(_1659316), _1659318), hAPP(c_List_Otl(_1659316), _1659320)) = hAPP(c_List_Otl(_1659316), hAPP(hAPP(c_List_Odrop(_1659316), _1659318), _1659320)))], (42167 ^ _776545) ^ [_1612168, _1612170, _1612172] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612168)), _1612170), c_Wellfounded_Oacc(tc_List_Olist(_1612168), c_List_Olistrel1(_1612168, _1612172)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612168)), _1612170), c_List_Olists(_1612168, c_Wellfounded_Oacc(_1612168, _1612172)))))], (46136 ^ _776545) ^ [_1703168, _1703170, _1703172, _1703174, _1703176] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703168)), hAPP(c_List_Ofilter(_1703168, _1703170), hAPP(hAPP(c_List_Omap(_1703172, _1703168), _1703174), _1703176))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703172)), hAPP(c_List_Ofilter(_1703172, hAPP(c_Fun_Ocomp(_1703168, tc_HOL_Obool, _1703172, _1703170), _1703174)), _1703176)))], (50928 ^ _776545) ^ [_1807967, _1807969, _1807971] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1807967), _1807969, _1807971)), -(c_List_Olist__ex(tc_Nat_Onat, _1807967, c_List_Oupt(_1807969, _1807971)))], (33827 ^ _776545) ^ [_1403103, _1403105, _1403107] : [class_Int_Onumber__ring(_1403103), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1403103), _1403105), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1403107))) = hAPP(hAPP(c_HOL_OLet(_1403103, _1403103), hAPP(hAPP(c_Power_Opower__class_Opower(_1403103), _1403105), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403107))), hAPP(hAPP(c_COMBS(_1403103, _1403103, _1403103), c_Groups_Otimes__class_Otimes(_1403103)), c_COMBI(_1403103))))], (41506 ^ _776545) ^ [_1592294, _1592296, _1592298, _1592300, _1592302] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592294, _1592294)), hAPP(hAPP(c_Product__Type_OPair(_1592294, _1592294), _1592296), _1592298)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592294, _1592294), tc_HOL_Obool), _1592300), _1592302))), 41511 ^ _776545 : [(41514 ^ _776545) ^ [] : [-(_1592296 = _1592298)], (41512 ^ _776545) ^ [] : [-(_1592300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41517 ^ _776545 : [(41522 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592294, _1592294)), hAPP(hAPP(c_Product__Type_OPair(_1592294, _1592294), 41515 ^ [_1592294, _1592296, _1592298, _1592300, _1592302]), _1592298)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592294, _1592294), tc_HOL_Obool), 41516 ^ [_1592294, _1592296, _1592298, _1592300, _1592302]), _1592302))))], (41520 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592294, _1592294)), hAPP(hAPP(c_Product__Type_OPair(_1592294, _1592294), _1592296), 41515 ^ [_1592294, _1592296, _1592298, _1592300, _1592302])), _1592302)))], (41518 ^ _776545) ^ [] : [-(_1592300 = hAPP(c_Nat_OSuc, 41516 ^ [_1592294, _1592296, _1592298, _1592300, _1592302]))]]], (36545 ^ _776545) ^ [_1468584] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1468584)) = _1468584)], (32462 ^ _776545) ^ [_1361051, _1361053, _1361055, _1361057, _1361059] : [_1361051 = c_Orderings_Obot__class_Obot(tc_fun(_1361053, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361053, tc_fun(_1361055, tc_HOL_Obool)), _1361051), hAPP(hAPP(c_COMBB(tc_fun(_1361055, tc_HOL_Obool), tc_fun(_1361055, tc_HOL_Obool), _1361053), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361055, tc_HOL_Obool)), _1361057)), _1361059)) = c_Orderings_Obot__class_Obot(tc_fun(_1361055, tc_HOL_Obool)))], (18176 ^ _776545) ^ [_1103288, _1103290] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1103288), _1103290) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1103288, _1103290))], (16396 ^ _776545) ^ [_1072193, _1072195] : [class_Groups_Ogroup__add(_1072193), 16399 ^ _776545 : [(16406 ^ _776545) ^ [] : [_1072195 = c_Groups_Ozero__class_Ozero(_1072193), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072193), _1072195) = c_Groups_Ozero__class_Ozero(_1072193))], (16400 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1072193), _1072195) = c_Groups_Ozero__class_Ozero(_1072193), -(_1072195 = c_Groups_Ozero__class_Ozero(_1072193))]]], (29591 ^ _776545) ^ [_1306791, _1306793, _1306795] : [class_Groups_Omonoid__mult(_1306791), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306791), _1306793), 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)))), _1306795))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306791), _1306793), hAPP(hAPP(c_Power_Opower__class_Opower(_1306791), hAPP(hAPP(c_Power_Opower__class_Opower(_1306791), _1306793), _1306795)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (30437 ^ _776545) ^ [_1322620, _1322622, _1322624] : [class_Orderings_Olinorder(_1322620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322620), _1322622)), -(_1322622 = c_Orderings_Obot__class_Obot(tc_fun(_1322620, tc_HOL_Obool))), 30448 ^ _776545 : [(30458 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322620), hAPP(c_Finite__Set_Ofold1(_1322620, c_Orderings_Oord__class_Omin(_1322620)), _1322622)), _1322624))), 30459 ^ _776545 : [(30460 ^ _776545) ^ [_1323009] : [hBOOL(hAPP(hAPP(c_member(_1322620), _1323009), _1322622)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322620), _1323009), _1322624))]]], (30449 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322620), hAPP(c_Finite__Set_Ofold1(_1322620, c_Orderings_Oord__class_Omin(_1322620)), _1322622)), _1322624)), 30453 ^ _776545 : [(30456 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322620), 30452 ^ [_1322620, _1322622, _1322624]), _1322624)))], (30454 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322620), 30452 ^ [_1322620, _1322622, _1322624]), _1322622)))]]]]], (36866 ^ _776545) ^ [_1476186, _1476188, _1476190, _1476192, _1476194] : [c_Equiv__Relations_Oequiv(_1476186, _1476188, _1476190), hBOOL(hAPP(hAPP(c_member(_1476186), _1476192), _1476188)), hBOOL(hAPP(hAPP(c_member(_1476186), _1476194), _1476188)), 36877 ^ _776545 : [(36884 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476186, _1476186)), hAPP(hAPP(c_Product__Type_OPair(_1476186, _1476186), _1476192), _1476194)), _1476190)), -(hAPP(c_Relation_OImage(_1476186, _1476186, _1476190), hAPP(hAPP(c_Set_Oinsert(_1476186), _1476192), c_Orderings_Obot__class_Obot(tc_fun(_1476186, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476186, _1476186, _1476190), hAPP(hAPP(c_Set_Oinsert(_1476186), _1476194), c_Orderings_Obot__class_Obot(tc_fun(_1476186, tc_HOL_Obool)))))], (36878 ^ _776545) ^ [] : [hAPP(c_Relation_OImage(_1476186, _1476186, _1476190), hAPP(hAPP(c_Set_Oinsert(_1476186), _1476192), c_Orderings_Obot__class_Obot(tc_fun(_1476186, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476186, _1476186, _1476190), hAPP(hAPP(c_Set_Oinsert(_1476186), _1476194), c_Orderings_Obot__class_Obot(tc_fun(_1476186, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476186, _1476186)), hAPP(hAPP(c_Product__Type_OPair(_1476186, _1476186), _1476192), _1476194)), _1476190)))]]], (29545 ^ _776545) ^ [_1305797, _1305799, _1305801] : [class_Rings_Olinordered__idom(_1305797), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305797), c_Groups_Ozero__class_Ozero(_1305797)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305797), hAPP(hAPP(c_Power_Opower__class_Opower(_1305797), _1305799), 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(_1305797), _1305801), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (44022 ^ _776545) ^ [_1656595, _1656597, _1656599, _1656601, _1656603] : [-(hAPP(hAPP(c_List_Oappend(_1656595), _1656597), _1656599) = hAPP(hAPP(c_List_Oappend(_1656595), _1656601), _1656603)), 44025 ^ _776545 : [(44028 ^ _776545) ^ [] : [_1656597 = hAPP(hAPP(c_List_Otake(_1656595), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656597)), _1656601), _1656599 = hAPP(hAPP(c_List_Oappend(_1656595), hAPP(hAPP(c_List_Odrop(_1656595), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656597)), _1656601)), _1656603)], (44026 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656597)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656601))))]], 44033 ^ _776545 : [(44036 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Otake(_1656595), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656601)), _1656597) = _1656601, hAPP(hAPP(c_List_Oappend(_1656595), hAPP(hAPP(c_List_Odrop(_1656595), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656601)), _1656597)), _1656599) = _1656603], (44034 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656597)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656595)), _1656601)))]]], (12105 ^ _776545) ^ [_989186, _989188] : [class_Complete__Lattice_Ocomplete__lattice(_989186), hBOOL(hAPP(c_Finite__Set_Ofinite(_989186), _989188)), -(_989188 = c_Orderings_Obot__class_Obot(tc_fun(_989186, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_989186, _989188) = c_Complete__Lattice_OInf__class_OInf(_989186, _989188))], (4448 ^ _776545) ^ [_844070, _844072, _844074, _844076] : [-(c_Lazy__Sequence_Osmall__lazy_H(_844076, _844072) = c_Lazy__Sequence_Osmall__lazy_H(_844074, _844070)), _844076 = _844074, _844072 = _844070], (37943 ^ _776545) ^ [_1501001, _1501003, _1501005, _1501007] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501001, _1501003, _1501005), _1501007), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501003, _1501005), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501001, _1501005), tc_HOL_Obool)))], (19661 ^ _776545) ^ [_1131690, _1131692, _1131694, _1131696] : [class_Rings_Odivision__ring(_1131690), -(_1131692 = c_Groups_Ozero__class_Ozero(_1131690)), 19668 ^ _776545 : [(19675 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131690), _1131694), _1131692) = _1131696, -(_1131694 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131690), _1131696), _1131692))], (19669 ^ _776545) ^ [] : [_1131694 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131690), _1131696), _1131692), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131690), _1131694), _1131692) = _1131696)]]], (43188 ^ _776545) ^ [_1636885, _1636887] : [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(_1636885)), _1636887))), _1636887 = c_List_Olist_ONil(_1636885)], (31405 ^ _776545) ^ [_1340397, _1340399, _1340401, _1340403] : [class_Groups_Oordered__ab__group__add(_1340397), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340397), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340397), _1340399), _1340401)), _1340403) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340397), _1340399), _1340403)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1340397), _1340401), _1340403)))], (16278 ^ 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tc_HOL_Obool)), _1390513), hAPP(hAPP(c_COMBC(_1390511, tc_fun(_1390507, tc_fun(_1390509, tc_HOL_Obool)), tc_fun(_1390509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390507, tc_HOL_Obool), tc_fun(tc_fun(_1390507, tc_fun(_1390509, tc_HOL_Obool)), tc_fun(_1390509, tc_HOL_Obool)), _1390511), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390507, tc_fun(_1390509, tc_HOL_Obool))), _1390515)), _1390517)))], (29928 ^ _776545) ^ [_1313207, _1313209] : [_1313207 = _1313209, -(c_Random_Oinc__shift(_1313207, _1313209) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (39211 ^ _776545) ^ [_1533505, _1533507, _1533509, _1533511, _1533513, _1533515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533505, _1533507), tc_HOL_Obool)), _1533509), hAPP(hAPP(c_Product__Type_OSigma(_1533505, _1533507), _1533511), hAPP(c_COMBK(tc_fun(_1533507, tc_HOL_Obool), _1533505), _1533513)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533507, tc_HOL_Obool)), 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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)), _1412981)))))], (43603 ^ _776545) ^ [_1646308, _1646310, _1646312] : [_1646312 = c_List_Olist_ONil(_1646310), -(_1646308 = hAPP(hAPP(c_List_Oappend(_1646310), _1646312), _1646308))], (29211 ^ _776545) ^ [_1300093, _1300095] : [class_Int_Onumber__ring(_1300093), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300093), c_Groups_Oone__class_Oone(_1300093)), c_Groups_Oone__class_Oone(_1300093))), hAPP(c_Int_Onumber__class_Onumber__of(_1300093), _1300095)) = hAPP(c_Int_Onumber__class_Onumber__of(_1300093), c_Int_OBit0(_1300095)))], (39283 ^ _776545) ^ [_1535494, _1535496, _1535498, _1535500] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535494, _1535496), _1535498), _1535500) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535494, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), _1535498), hAPP(hAPP(c_COMBS(_1535494, tc_fun(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535496, tc_HOL_Obool), tc_fun(tc_fun(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), _1535494), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), _1535500)), hAPP(hAPP(c_COMBC(_1535494, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535496, tc_fun(tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), _1535494), c_COMBC(_1535496, tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1535496, tc_prod(_1535494, _1535496)), tc_fun(_1535496, tc_fun(tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))), _1535494), hAPP(c_COMBB(tc_prod(_1535494, _1535496), tc_fun(tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool), tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool)), _1535496), c_Set_Oinsert(tc_prod(_1535494, _1535496)))), c_Product__Type_OPair(_1535494, _1535496)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1535494, _1535496), tc_HOL_Obool))))))], (11600 ^ _776545) ^ [_979440, _979442, _979444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979440), hAPP(hAPP(c_Set_Oinsert(_979440), _979442), _979444))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979440), _979444)))], (7662 ^ _776545) ^ [_904087, _904089, _904091, _904093] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904087, tc_HOL_Obool)), _904089), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904087, tc_HOL_Obool)), _904091), _904093)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904087, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904087, tc_HOL_Obool)), _904089), _904091)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904087, tc_HOL_Obool)), _904089), _904093)))], (21026 ^ _776545) ^ [_1156428, _1156430, _1156432, _1156434] : [-(c_Sum__Type_OPlus(_1156428, _1156430, _1156432, _1156434) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1156428, _1156430), tc_HOL_Obool))), _1156432 = c_Orderings_Obot__class_Obot(tc_fun(_1156428, tc_HOL_Obool)), _1156434 = c_Orderings_Obot__class_Obot(tc_fun(_1156430, tc_HOL_Obool))], (43248 ^ _776545) ^ [_1638142, _1638144, _1638146, _1638148] : [-(_1638142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1638144), _1638142), hAPP(hAPP(c_List_Olist_OCons(_1638144), _1638146), _1638148)) = hAPP(hAPP(c_List_Olist_OCons(_1638144), _1638146), hAPP(hAPP(c_List_Otake(_1638144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1638142), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1638148)))], (43228 ^ _776545) ^ [_1637783, _1637785, _1637787] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637783)), -(c_List_Osublist(_1637785, hAPP(hAPP(c_List_Olist_OCons(_1637785), _1637787), c_List_Olist_ONil(_1637785)), _1637783) = hAPP(hAPP(c_List_Olist_OCons(_1637785), _1637787), c_List_Olist_ONil(_1637785)))], (16608 ^ _776545) ^ [] : [-(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)))], (17639 ^ _776545) ^ [_1094187] : [class_Rings_Olinordered__semidom(_1094187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094187), c_Groups_Oone__class_Oone(_1094187)), c_Groups_Ozero__class_Ozero(_1094187)))], (36428 ^ _776545) ^ [_1464615, _1464617, _1464619, _1464621] : [c_FunDef_Oreduction__pair(_1464615, _1464617), -(c_FunDef_Oreduction__pair(_1464619, hAPP(hAPP(c_FunDef_Orp__inv__image(_1464615, _1464619), _1464617), _1464621)))], (14370 ^ _776545) ^ [_1035746, _1035748, _1035750, _1035752] : [class_Rings_Ocomm__semiring__1(_1035746), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035746), _1035748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035746), _1035750), _1035752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035746), _1035748), _1035750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035746), _1035748), _1035752)))], (742 ^ _776545) ^ [_787736, _787738, _787740, _787742] : [-(c_Wellfounded_Oacyclic(_787740, _787736)), c_Wellfounded_Oacyclic(_787742, _787738), _787742 = _787740, _787738 = _787736], (4142 ^ _776545) ^ [_839261, _839263, _839265, _839267, _839269, _839271, _839273, _839275] : [-(c_New__Random__Sequence_Opos__map(_839275, _839271, _839267, _839263) = c_New__Random__Sequence_Opos__map(_839273, _839269, _839265, _839261)), _839275 = _839273, _839271 = _839269, _839267 = _839265, _839263 = _839261], (11930 ^ _776545) ^ [_986016, _986018, _986020, _986022, _986024, _986026, _986028] : [-(_986016 = _986018), -(c_Fun_Ofun__upd(_986020, _986022, c_Fun_Ofun__upd(_986020, _986022, _986024, _986016, _986026), _986018, _986028) = c_Fun_Ofun__upd(_986020, _986022, c_Fun_Ofun__upd(_986020, _986022, _986024, _986018, _986028), _986016, _986026))], (33316 ^ _776545) ^ [_1387731, _1387733, _1387735, _1387737, _1387739] : [class_Rings_Osemiring__0(_1387731), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387731), _1387733), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387735, _1387731), _1387737), _1387739)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387735, _1387731), hAPP(hAPP(c_COMBB(_1387731, _1387731, _1387735), hAPP(c_Groups_Otimes__class_Otimes(_1387731), _1387733)), _1387737)), _1387739))], (12063 ^ _776545) ^ [_988550, _988552, _988554] : [class_Lattices_Olattice(_988550), hBOOL(hAPP(c_Finite__Set_Ofinite(_988550), _988552)), hBOOL(hAPP(hAPP(c_member(_988550), _988554), _988552)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_988550), _988554), c_Big__Operators_Olattice__class_OInf__fin(_988550, _988552)) = c_Big__Operators_Olattice__class_OInf__fin(_988550, _988552))], (41743 ^ _776545) ^ [_1598586, _1598588] : [-(c_List_Olenlex(_1598586, _1598588) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1598586), tc_List_Olist(_1598586), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598586), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), tc_List_Olist(_1598586)), c_COMBS(tc_List_Olist(_1598586), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1598586)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1598586)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598586), tc_fun(tc_List_Olist(_1598586), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1598586), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), tc_List_Olist(_1598586)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1598586))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1598586)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1598586))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598586)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598586), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), tc_List_Olist(_1598586)), c_COMBS(tc_List_Olist(_1598586), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1598586)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1598586)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598586), tc_fun(tc_List_Olist(_1598586), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1598586), tc_Nat_Onat), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), tc_List_Olist(_1598586)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1598586))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1598586)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1598586))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598586)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1598586), tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1598586), tc_HOL_Obool)), tc_List_Olist(_1598586)), c_COMBC(tc_List_Olist(_1598586), tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1598586), tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586))), tc_fun(tc_List_Olist(_1598586), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1598586)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1598586)), c_member(tc_prod(tc_List_Olist(_1598586), tc_List_Olist(_1598586))))), c_Product__Type_OPair(tc_List_Olist(_1598586), tc_List_Olist(_1598586))))), c_List_Olex(_1598586, _1598588)))))))], (14594 ^ _776545) ^ [_1039618, _1039620, _1039622] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039618), _1039620)), _1039622) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039618), _1039622)), _1039620))], (40491 ^ _776545) ^ [_1566672, _1566674, _1566676, _1566678, _1566680] : [-(_1566672 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1566674, _1566676, _1566672, _1566678), _1566680) = hAPP(hAPP(c_Product__Type_Oscomp(_1566676, _1566674, _1566676, tc_prod(_1566674, _1566676)), hAPP(_1566678, _1566680)), c_Random_Oiterate(_1566674, _1566676, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1566672), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1566678)))], (38560 ^ _776545) ^ [_1516218, _1516220, _1516222] : [-(hAPP(c_Finite__Set_Ofold1(_1516218, _1516220), _1516222) = c_HOL_OThe(_1516218, c_Finite__Set_Ofold1Set(_1516218, _1516220, _1516222)))], (48806 ^ _776545) ^ [_1760282, _1760284, _1760286, _1760288] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760282, _1760284), c_Lazy__Sequence_Olazy__sequence_OInsert(_1760282, _1760286, _1760288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1760284, _1760286)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760282, _1760284), _1760288))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23163 ^ _776545) ^ [_1196137, _1196139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196139)), -(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), _1196137), _1196139))))], (3488 ^ _776545) ^ [_828692, _828694, _828696, _828698] : [-(c_Random_Opick(_828698, _828694) = c_Random_Opick(_828696, _828692)), _828698 = _828696, _828694 = _828692], (49229 ^ _776545) ^ [_1770434, _1770436] : [49230 ^ _776545 : [(49231 ^ _776545) ^ [_1770500] : [hBOOL(hAPP(_1770436, _1770500))]], 49233 ^ _776545 : [(49236 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1770436, 49232 ^ [_1770434, _1770436])))], (49234 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770434), 49232 ^ [_1770434, _1770436]), c_Orderings_Otop__class_Otop(tc_fun(_1770434, tc_HOL_Obool)))))]]], (34992 ^ _776545) ^ [_1429323, _1429325, _1429327, _1429329] : [-(c_Nitpick_Oprod(_1429323, _1429325, _1429327, _1429329) = hAPP(c_Set_OCollect(tc_prod(_1429323, _1429325)), hAPP(c_Product__Type_Oprod_Oprod__case(_1429323, _1429325, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1429323, tc_fun(_1429325, tc_HOL_Obool), tc_fun(_1429325, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1429325, tc_HOL_Obool), tc_fun(_1429325, tc_HOL_Obool)), _1429323), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1429325)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1429323), c_fconj), hAPP(hAPP(c_COMBC(_1429323, tc_fun(_1429323, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429323)), _1429327)))), hAPP(hAPP(c_COMBC(_1429325, tc_fun(_1429325, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429325)), _1429329)))))], (36296 ^ _776545) ^ [_1462211, _1462213, _1462215, _1462217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462211), _1462213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462215), _1462217)), -(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), _1462211), _1462215)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1462213), _1462217))), c_FunDef_Opair__leq)))], (39147 ^ _776545) ^ [_1531659, _1531661, _1531663, _1531665, _1531667] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531659, _1531661), _1531663), hAPP(hAPP(c_COMBS(_1531659, tc_fun(_1531661, tc_HOL_Obool), tc_fun(_1531661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531661, tc_HOL_Obool), tc_fun(tc_fun(_1531661, tc_HOL_Obool), tc_fun(_1531661, tc_HOL_Obool)), _1531659), c_Groups_Ominus__class_Ominus(tc_fun(_1531661, tc_HOL_Obool))), _1531665)), _1531667)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531659, _1531661), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531659, _1531661), _1531663), _1531665)), hAPP(hAPP(c_Product__Type_OSigma(_1531659, _1531661), _1531663), _1531667)))], (39163 ^ _776545) ^ [_1532252, _1532254, _1532256, _1532258, _1532260, _1532262] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532252, _1532254)), hAPP(hAPP(c_Product__Type_OPair(_1532252, _1532254), _1532256), _1532258)), hAPP(hAPP(c_Product__Type_OSigma(_1532252, _1532254), _1532260), _1532262)))), hBOOL(hAPP(hAPP(c_member(_1532252), _1532256), _1532260)), hBOOL(hAPP(hAPP(c_member(_1532254), _1532258), hAPP(_1532262, _1532256)))], (52111 ^ _776545) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (23077 ^ _776545) ^ [_1194657, _1194659] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194657), _1194659)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194657)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194659))))], (35106 ^ _776545) ^ [_1431711, _1431713, _1431715] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431711, _1431713), _1431715)), 35109 ^ _776545 : [(35110 ^ _776545) ^ [_1431796] : [hBOOL(hAPP(hAPP(_1431713, _1431796), _1431715)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431711, _1431713), _1431796)))]]], (40536 ^ _776545) ^ [_1567785, _1567787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567785), _1567787)), -(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), _1567785), _1567787)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (14208 ^ _776545) ^ [_1032138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1032138)), 14212 ^ _776545 : [(14213 ^ _776545) ^ [_1032218] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1032218), _1032138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032218), 14211 ^ [_1032138])))]]], (33617 ^ _776545) ^ [_1396403, _1396405, _1396407, _1396409, _1396411, _1396413] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396403, tc_fun(_1396405, tc_fun(_1396407, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1396403, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_fun(_1396405, tc_fun(_1396407, tc_HOL_Obool)), _1396403), hAPP(c_COMBC(_1396405, tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_fun(_1396407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396407, tc_fun(tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_fun(_1396407, tc_HOL_Obool)), _1396405), c_COMBC(_1396407, tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396407, tc_prod(_1396405, _1396407)), tc_fun(_1396407, tc_fun(tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_HOL_Obool)), _1396405), hAPP(c_COMBB(tc_prod(_1396405, _1396407), tc_fun(tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool), tc_HOL_Obool), _1396407), c_member(tc_prod(_1396405, _1396407)))), c_Product__Type_OPair(_1396405, _1396407))))), _1396409)), _1396411), _1396413)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396405, _1396407)), hAPP(hAPP(c_Product__Type_OPair(_1396405, _1396407), _1396411), _1396413)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396403, tc_fun(tc_prod(_1396405, _1396407), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396403, tc_HOL_Obool))), _1396409))))], (19641 ^ _776545) ^ [_1131362, _1131364, _1131366, _1131368] : [class_Rings_Odivision__ring(_1131362), -(_1131364 = c_Groups_Ozero__class_Ozero(_1131362)), 19648 ^ _776545 : [(19655 ^ _776545) ^ [] : [_1131366 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131362), _1131368), _1131364), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131362), _1131366), _1131364) = _1131368)], (19649 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131362), _1131366), _1131364) = _1131368, -(_1131366 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131362), _1131368), _1131364))]]], (27997 ^ _776545) ^ [_1279663, _1279665] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279663), c_Int_OPls))), 28000 ^ _776545 : [(28007 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279665), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279665)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1279663), _1279665)))], (28001 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279665), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279665)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279663))]]], (12485 ^ _776545) ^ [_995978, _995980] : [class_Lattices_Olattice(_995978), hBOOL(hAPP(c_Finite__Set_Ofinite(_995978), _995980)), -(_995980 = c_Orderings_Obot__class_Obot(tc_fun(_995978, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_995978), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_995978), 12498 ^ [_995978, _995980]), 12499 ^ [_995978, _995980])), hAPP(hAPP(c_Set_Oinsert(_995978), 12498 ^ [_995978, _995980]), hAPP(hAPP(c_Set_Oinsert(_995978), 12499 ^ [_995978, _995980]), c_Orderings_Obot__class_Obot(tc_fun(_995978, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_995978), c_Big__Operators_Olattice__class_OSup__fin(_995978, _995980)), _995980)))], (12672 ^ _776545) ^ [_999886, _999888, _999890, _999892, _999894, _999896] : [c_Finite__Set_Ofun__left__comm(_999886, _999888, _999890), hBOOL(hAPP(c_Finite__Set_Ofinite(_999886), _999892)), -(hAPP(hAPP(_999890, _999894), hAPP(hAPP(c_Finite__Set_Ofold(_999886, _999888, _999890), _999896), _999892)) = hAPP(hAPP(c_Finite__Set_Ofold(_999886, _999888, _999890), hAPP(hAPP(_999890, _999894), _999896)), _999892))], (33390 ^ _776545) ^ [_1389669, _1389671, _1389673, _1389675, _1389677] : [c_Finite__Set_Ofun__left__comm(_1389669, _1389671, _1389673), -(c_Finite__Set_Ofun__left__comm(_1389675, _1389671, hAPP(hAPP(c_COMBB(_1389669, tc_fun(_1389671, _1389671), _1389675), _1389673), _1389677)))], (20329 ^ _776545) ^ [_1143306, _1143308, _1143310, _1143312] : [class_Fields_Ofield__inverse__zero(_1143306), -(_1143308 = c_Groups_Ozero__class_Ozero(_1143306)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143306), _1143310), _1143308)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143306), _1143312), _1143308)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143306), _1143310), _1143312))], (5470 ^ _776545) ^ [_860133, _860135] : [_860135 = _860133, -(c_member(_860135) = c_member(_860133))], (17975 ^ _776545) ^ [_1099783, _1099785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1099785), _1099783)), _1099785)))], (38517 ^ _776545) ^ [_1515009, _1515011, _1515013] : [_1515013 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1515009, _1515011), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1515009, _1515011), _1515013) = c_Orderings_Obot__class_Obot(tc_fun(_1515011, tc_HOL_Obool)))], (45485 ^ _776545) ^ [_1688657, _1688659, _1688661, _1688663] : [c_List_Olist__all2(_1688657, _1688659, _1688661, c_List_Olist_ONil(_1688657), _1688663), -(_1688663 = c_List_Olist_ONil(_1688659))], (39308 ^ _776545) ^ [_1537336, _1537338, _1537340, _1537342] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537338, _1537336), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1537336, tc_prod(_1537338, _1537336), 39304 ^ [_1537336, _1537338, _1537340, _1537342]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537338, tc_fun(_1537336, tc_HOL_Obool)), _1537340), _1537342))), hAPP(hAPP(c_Product__Type_OSigma(_1537338, _1537336), _1537340), _1537342))))], (13758 ^ _776545) ^ [_1021670, _1021672, _1021674, _1021676] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1021670), 13761 ^ _776545 : [(13768 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021670), _1021674), _1021676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021670), _1021672), _1021674)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021670), _1021672), _1021676))))], (13762 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021670), _1021672), _1021674)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021670), _1021672), _1021676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021670), _1021674), _1021676)))]]], (25852 ^ _776545) ^ [_1244154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244154)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244154) = 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, _1244154))))], (46060 ^ _776545) ^ [_1701686, _1701688, _1701690] : [46062 ^ _776545 : [(46065 ^ _776545) ^ [] : [hBOOL(hAPP(_1701688, 46061 ^ [_1701686, _1701688, _1701690]))], (46063 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1701686), 46061 ^ [_1701686, _1701688, _1701690]), hAPP(c_List_Oset(_1701686), _1701690))))]], -(hAPP(c_List_Ofilter(_1701686, _1701688), _1701690) = _1701690)], (16144 ^ _776545) ^ [_1068324, _1068326] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068324)), hAPP(c_Nat_OSuc, _1068326)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1068324), _1068326))], (2470 ^ _776545) ^ [_812805, _812807, _812809, _812811] : [-(c_Divides_Odivmod__int(_812811, _812807) = c_Divides_Odivmod__int(_812809, _812805)), _812811 = _812809, _812807 = _812805], (27795 ^ _776545) ^ [_1276367] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276367), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276367), c_Int_OPls)))], (50955 ^ _776545) ^ [_1808518, _1808520, _1808522] : [-(c_Lazy__Sequence_Omap(_1808518, _1808520, _1808522, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1808518)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1808520))], (39139 ^ _776545) ^ [_1531292, _1531294, _1531296, _1531298, _1531300] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531292, _1531294), _1531296), hAPP(hAPP(c_COMBS(_1531292, tc_fun(_1531294, tc_HOL_Obool), tc_fun(_1531294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531294, tc_HOL_Obool), tc_fun(tc_fun(_1531294, tc_HOL_Obool), tc_fun(_1531294, tc_HOL_Obool)), _1531292), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531294, tc_HOL_Obool))), _1531298)), _1531300)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531292, _1531294), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531292, _1531294), _1531296), _1531298)), hAPP(hAPP(c_Product__Type_OSigma(_1531292, _1531294), _1531296), _1531300)))], (47281 ^ _776545) ^ [_1727091, _1727093, _1727095] : [-(c_List_OtakeWhile(_1727091, _1727093, _1727095) = hAPP(hAPP(c_List_Otake(_1727091), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727091)), c_List_OtakeWhile(_1727091, _1727093, _1727095))), _1727095))], (40345 ^ _776545) ^ [_1563202, _1563204] : [40347 ^ _776545 : [(40350 ^ _776545) ^ [] : [40346 ^ [_1563202, _1563204] = c_Orderings_Obot__class_Obot(tc_fun(_1563202, tc_HOL_Obool))], (40348 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563202, tc_HOL_Obool)), 40346 ^ [_1563202, _1563204]), hAPP(c_Relation_OImage(_1563202, _1563202, _1563204), 40346 ^ [_1563202, _1563204]))))]], -(c_Wellfounded_Owf(_1563202, _1563204))], (34797 ^ _776545) ^ [_1425816, _1425818, _1425820] : [class_Rings_Osemiring__1(_1425816), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1425816, _1425818, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1425820) = _1425820)], (52369 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (5871 ^ _776545) ^ [_869877, _869879, _869881, _869883, _869885, _869887] : [c_Typedef_Otype__definition(_869877, _869879, _869881, _869883, _869885), -(hAPP(_869883, hAPP(_869881, _869887)) = _869887)], (522 ^ _776545) ^ [_784360, _784362, _784364, _784366, _784368, _784370] : [-(c_Finite__Set_Ofun__left__comm__idem(_784368, _784364, _784360)), c_Finite__Set_Ofun__left__comm__idem(_784370, _784366, _784362), _784370 = _784368, _784366 = _784364, _784362 = _784360], (13073 ^ _776545) ^ [_1007316, _1007318, _1007320] : [class_Lattices_Oab__semigroup__idem__mult(_1007316), hAPP(_1007318, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007316), 13078 ^ [_1007316, _1007318, _1007320]), 13079 ^ [_1007316, _1007318, _1007320])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007316), hAPP(_1007318, 13078 ^ [_1007316, _1007318, _1007320])), hAPP(_1007318, 13079 ^ [_1007316, _1007318, _1007320])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007316), _1007320)), -(_1007320 = c_Orderings_Obot__class_Obot(tc_fun(_1007316, tc_HOL_Obool))), -(hAPP(_1007318, hAPP(c_Finite__Set_Ofold1(_1007316, c_Groups_Otimes__class_Otimes(_1007316)), _1007320)) = hAPP(c_Finite__Set_Ofold1(_1007316, c_Groups_Otimes__class_Otimes(_1007316)), hAPP(c_Set_Oimage(_1007316, _1007316, _1007318), _1007320)))], (43926 ^ _776545) ^ [_1654362, _1654364] : [hAPP(c_List_Orotate1(_1654362), _1654364) = c_List_Olist_ONil(_1654362), -(_1654364 = c_List_Olist_ONil(_1654362))], (8020 ^ _776545) ^ [_912532, _912534, _912536] : [-(hAPP(hAPP(c_Set_Oinsert(_912532), _912534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912532, tc_HOL_Obool)), _912536), hAPP(hAPP(c_Set_Oinsert(_912532), _912534), c_Orderings_Obot__class_Obot(tc_fun(_912532, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_912532), _912534), _912536))], (51147 ^ _776545) ^ [_1812243, _1812245, _1812247] : [51148 ^ _776545 : [(51151 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812245), _1812247))], (51149 ^ _776545) ^ [] : [_1812243 = 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), _1812243), _1812245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1812243), _1812247))))], (50213 ^ _776545) ^ [_1791732, _1791734] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1791732), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1791734, hAPP(c_Code__Numeral_Onat__of, 50218 ^ [_1791732, _1791734]))), -(hBOOL(hAPP(_1791734, _1791732)))], (24850 ^ _776545) ^ [_1226259, _1226261, _1226263, _1226265] : [class_Divides_Osemiring__div(_1226259), -(c_Divides_Odiv__class_Omod(_1226259, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226259), _1226261), _1226263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226259), _1226261), _1226265)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226259), _1226261), c_Divides_Odiv__class_Omod(_1226259, _1226263, _1226265)))], (30140 ^ _776545) ^ [_1317263, _1317265, _1317267, _1317269] : [class_Orderings_Olinorder(_1317263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317263), _1317265), _1317267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317263), _1317265), _1317269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317263), _1317265), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317263), _1317267), _1317269))))], (15708 ^ _776545) ^ [_1061394, _1061396] : [_1061394 = _1061396, -(hAPP(c_Nat_OSuc, _1061394) = hAPP(c_Nat_OSuc, _1061396))], (1144 ^ _776545) ^ [_793709, _793711] : [-(class_Rings_Oring__no__zero__divisors(_793709)), _793711 = _793709, class_Rings_Oring__no__zero__divisors(_793711)], (51629 ^ _776545) ^ [_1820937, _1820939] : [class_Rings_Ocomm__semiring__1(_1820937), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820937), c_Groups_Ozero__class_Ozero(_1820937)), _1820939)), -(_1820939 = c_Groups_Ozero__class_Ozero(_1820937))], (50632 ^ _776545) ^ [_1800046, _1800048, _1800050, _1800052] : [c_Fun_Obij__betw(_1800046, _1800048, _1800050, c_Orderings_Otop__class_Otop(tc_fun(_1800046, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800048, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1800046, _1800048, _1800050), _1800052) = hAPP(c_Set_Oimage(_1800048, _1800046, c_Hilbert__Choice_Oinv__into(_1800046, _1800048, c_Orderings_Otop__class_Otop(tc_fun(_1800046, tc_HOL_Obool)), _1800050)), _1800052))], (27763 ^ _776545) ^ [_1275873] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275873), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275873) = _1275873)], (38535 ^ _776545) ^ [_1515437, _1515439, _1515441, _1515443] : [-(c_HOL_OThe(tc_prod(_1515437, _1515439), hAPP(c_Product__Type_Oprod_Oprod__case(_1515437, _1515439, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1515437, tc_fun(_1515439, tc_HOL_Obool), tc_fun(_1515439, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1515439, tc_HOL_Obool), tc_fun(_1515439, tc_HOL_Obool)), _1515437), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1515439)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515437), c_fconj), hAPP(c_fequal, _1515441)))), hAPP(c_fequal, _1515443)))) = hAPP(hAPP(c_Product__Type_OPair(_1515437, _1515439), _1515441), _1515443))], (41447 ^ _776545) ^ [_1590701, _1590703] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590701, _1590701), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590703) = c_Relation_OId(_1590701))], (33749 ^ _776545) ^ [_1400666, _1400668, _1400670, _1400672, _1400674, _1400676, _1400678] : [class_Groups_Ocomm__monoid__add(_1400666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400668), _1400670)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400672), _1400674)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400668, _1400666), hAPP(hAPP(c_COMBS(_1400668, tc_fun(_1400672, tc_HOL_Obool), _1400666), hAPP(hAPP(c_COMBB(tc_fun(_1400672, _1400666), tc_fun(tc_fun(_1400672, tc_HOL_Obool), _1400666), _1400668), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400672, _1400666)), _1400676)), hAPP(hAPP(c_COMBB(tc_fun(_1400672, tc_HOL_Obool), tc_fun(_1400672, tc_HOL_Obool), _1400668), c_Set_OCollect(_1400672)), hAPP(hAPP(c_COMBB(tc_fun(_1400672, tc_HOL_Obool), tc_fun(_1400672, tc_HOL_Obool), _1400668), hAPP(c_COMBS(_1400672, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1400672), c_fconj), hAPP(hAPP(c_COMBC(_1400672, tc_fun(_1400672, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400672)), _1400674)))), _1400678)))), _1400670) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400672, _1400666), hAPP(hAPP(c_COMBS(_1400672, tc_fun(_1400668, tc_HOL_Obool), _1400666), hAPP(hAPP(c_COMBB(tc_fun(_1400668, _1400666), tc_fun(tc_fun(_1400668, tc_HOL_Obool), _1400666), _1400672), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1400668, _1400666)), hAPP(c_COMBC(_1400668, _1400672, _1400666), _1400676))), hAPP(hAPP(c_COMBB(tc_fun(_1400668, tc_HOL_Obool), tc_fun(_1400668, tc_HOL_Obool), _1400672), c_Set_OCollect(_1400668)), hAPP(hAPP(c_COMBB(tc_fun(_1400668, tc_HOL_Obool), tc_fun(_1400668, tc_HOL_Obool), _1400672), hAPP(c_COMBS(_1400668, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1400668), c_fconj), hAPP(hAPP(c_COMBC(_1400668, tc_fun(_1400668, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400668)), _1400670)))), hAPP(c_COMBC(_1400668, _1400672, tc_HOL_Obool), _1400678))))), _1400674))], (47032 ^ _776545) ^ [_1721908, _1721910] : [-(hAPP(c_List_Oset(_1721908), hAPP(c_List_Orev(_1721908), _1721910)) = hAPP(c_List_Oset(_1721908), _1721910))], (40234 ^ _776545) ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584] : [class_Groups_Ocomm__monoid__add(_1560574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560576), _1560578)), 40244 ^ _776545 : [(40245 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560576), 40243 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584]), _1560578)))], (40250 ^ _776545) ^ [] : [40243 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584] = 40246 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584]], (40254 ^ _776545) ^ [] : [hAPP(_1560582, hAPP(_1560580, 40243 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584])) = c_Groups_Ozero__class_Ozero(_1560574)], (40252 ^ _776545) ^ [] : [-(hAPP(_1560580, 40243 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584]) = hAPP(_1560580, 40246 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584]))], (40248 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560576), 40246 ^ [_1560574, _1560576, _1560578, _1560580, _1560582, _1560584]), _1560578)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560584, _1560574), _1560582), hAPP(c_Set_Oimage(_1560576, _1560584, _1560580), _1560578)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560576, _1560574), hAPP(c_Fun_Ocomp(_1560584, _1560574, _1560576, _1560582), _1560580)), _1560578))], (39459 ^ _776545) ^ [_1541203, _1541205, _1541207, _1541209, _1541211, _1541213, _1541215, _1541217] : [-(hAPP(c_Product__Type_Omap__pair(_1541203, _1541205, _1541207, _1541209, _1541211, _1541213), hAPP(hAPP(c_Product__Type_OPair(_1541203, _1541207), _1541215), _1541217)) = hAPP(hAPP(c_Product__Type_OPair(_1541205, _1541209), hAPP(_1541211, _1541215)), hAPP(_1541213, _1541217)))], (31583 ^ _776545) ^ [_1343586, _1343588, _1343590, _1343592] : [class_Orderings_Olinorder(_1343586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343586), _1343588), _1343590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343586), _1343588), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343586), _1343592), _1343590))))], (36470 ^ _776545) ^ [_1466357, _1466359, _1466361] : [-(hAPP(c_Relation_OImage(_1466357, _1466359, _1466361), c_Orderings_Obot__class_Obot(tc_fun(_1466357, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1466359, tc_HOL_Obool)))], (23918 ^ _776545) ^ [_1209725, _1209727, _1209729] : [class_Rings_Olinordered__semidom(_1209725), 23921 ^ _776545 : [(23928 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209727), _1209729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209725), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209725), _1209727)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209725), _1209729))))], (23922 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209725), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209725), _1209727)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209725), _1209729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209727), _1209729)))]]], (29831 ^ _776545) ^ [_1311441, _1311443] : [c_Code__Numeral_OSuc__code__numeral(_1311441) = c_Code__Numeral_OSuc__code__numeral(_1311443), -(_1311441 = _1311443)], (35967 ^ _776545) ^ [_1451115, _1451117, _1451119] : [class_Lattices_Odistrib__lattice(_1451115), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451115), _1451117)), -(_1451117 = c_Orderings_Obot__class_Obot(tc_fun(_1451115, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451115), _1451119)), -(_1451119 = c_Orderings_Obot__class_Obot(tc_fun(_1451115, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1451115), c_Big__Operators_Olattice__class_OInf__fin(_1451115, _1451117)), c_Big__Operators_Olattice__class_OInf__fin(_1451115, _1451119)) = c_Big__Operators_Olattice__class_OInf__fin(_1451115, hAPP(c_Set_OCollect(_1451115), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_HOL_Obool), tc_HOL_Obool, _1451115), c_HOL_OEx(_1451115)), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool)), tc_fun(_1451115, tc_HOL_Obool), _1451115), hAPP(c_COMBB(tc_fun(_1451115, tc_HOL_Obool), tc_HOL_Obool, _1451115), c_HOL_OEx(_1451115))), hAPP(hAPP(c_COMBC(_1451115, tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool)), tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_fun(tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool))), tc_fun(tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool)), tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool))), _1451115), c_COMBS(_1451115, tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_fun(_1451115, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1451115, tc_fun(tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool))), _1451115), hAPP(c_COMBB(tc_fun(_1451115, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool)), _1451115), c_COMBS(_1451115, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool)), tc_fun(_1451115, tc_fun(_1451115, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1451115), hAPP(c_COMBB(tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1451115), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1451115), c_fconj))), hAPP(hAPP(c_COMBC(_1451115, tc_fun(_1451115, tc_fun(_1451115, _1451115)), tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1451115, _1451115), tc_fun(_1451115, tc_HOL_Obool)), tc_fun(tc_fun(_1451115, tc_fun(_1451115, _1451115)), tc_fun(_1451115, tc_fun(_1451115, tc_HOL_Obool))), _1451115), c_COMBB(tc_fun(_1451115, _1451115), tc_fun(_1451115, tc_HOL_Obool), _1451115)), hAPP(hAPP(c_COMBB(tc_fun(_1451115, tc_HOL_Obool), tc_fun(tc_fun(_1451115, _1451115), tc_fun(_1451115, tc_HOL_Obool)), _1451115), c_COMBB(_1451115, tc_HOL_Obool, _1451115)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1451115)))))), hAPP(hAPP(c_COMBC(_1451115, tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1451115, tc_HOL_Obool), tc_fun(_1451115, tc_HOL_Obool)), _1451115), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1451115)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1451115), c_fconj), hAPP(hAPP(c_COMBC(_1451115, tc_fun(_1451115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451115)), _1451117)))), hAPP(hAPP(c_COMBC(_1451115, tc_fun(_1451115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1451115)), _1451119))))))))], (49744 ^ _776545) ^ [_1781806, _1781808, _1781810] : [c_Relation_Osym(_1781806, _1781808), c_Relation_Osym(_1781806, _1781810), -(c_Relation_Osym(_1781806, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1781806, _1781806), tc_HOL_Obool)), _1781808), _1781810)))], (30100 ^ _776545) ^ [_1316520, _1316522, _1316524, _1316526] : [class_Orderings_Olinorder(_1316520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316520), _1316522), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316520), _1316524), _1316526))), 30107 ^ _776545 : [(30110 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316520), _1316522), _1316526)))], (30108 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316520), _1316522), _1316524)))]]], (10339 ^ _776545) ^ [_954112, _954114, _954116, _954118] : [class_Groups_Ouminus(_954112), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_954114, _954112)), _954116), _954118) = hAPP(c_Groups_Ouminus__class_Ouminus(_954112), hAPP(_954116, _954118)))], (21249 ^ _776545) ^ [_1160867, _1160869, _1160871] : [class_Int_Onumber__ring(_1160867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160867), hAPP(c_Int_Onumber__class_Onumber__of(_1160867), _1160869)), hAPP(c_Int_Onumber__class_Onumber__of(_1160867), _1160871)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160869), _1160871)))], (15678 ^ _776545) ^ [_1060832] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060832)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1060832)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060832)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (52395 ^ _776545) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (48820 ^ _776545) ^ [_1760500, _1760502] : [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), _1760500), _1760502))), 48823 ^ _776545 : [(48830 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760500), _1760502))), -(c_Lazy__Sequence_Osmall__lazy_H(_1760500, _1760502) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1760502), c_Lazy__Sequence_Osmall__lazy_H(_1760500, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1760502), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48824 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760500), _1760502)), -(c_Lazy__Sequence_Osmall__lazy_H(_1760500, _1760502) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (15734 ^ _776545) ^ [_1061788, _1061790] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061788), _1061790) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1061788 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1061790 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35894 ^ _776545) ^ [_1448368, _1448370, _1448372, _1448374] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448368), hAPP(c_Set_OCollect(_1448368), _1448370))), 35897 ^ _776545 : [(35898 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448372), hAPP(c_Set_OCollect(_1448372), hAPP(hAPP(c_COMBB(tc_fun(_1448368, tc_HOL_Obool), tc_HOL_Obool, _1448372), c_HOL_OEx(_1448368)), hAPP(hAPP(c_COMBB(tc_fun(_1448368, tc_HOL_Obool), tc_fun(_1448368, tc_HOL_Obool), _1448372), hAPP(c_COMBS(_1448368, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1448368), c_fconj), _1448370))), _1448374))))), 35901 ^ _776545 : [(35902 ^ _776545) ^ [_1448651] : [hBOOL(hAPP(_1448370, _1448651)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448372), hAPP(c_Set_OCollect(_1448372), hAPP(hAPP(c_COMBC(_1448372, _1448368, tc_HOL_Obool), _1448374), _1448651)))))]]], (35908 ^ _776545) ^ [] : [35910 ^ _776545 : [(35913 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448372), hAPP(c_Set_OCollect(_1448372), hAPP(hAPP(c_COMBC(_1448372, _1448368, tc_HOL_Obool), _1448374), 35909 ^ [_1448368, _1448370, _1448372, _1448374]))))], (35911 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1448370, 35909 ^ [_1448368, _1448370, _1448372, _1448374])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448372), hAPP(c_Set_OCollect(_1448372), hAPP(hAPP(c_COMBB(tc_fun(_1448368, tc_HOL_Obool), tc_HOL_Obool, _1448372), c_HOL_OEx(_1448368)), hAPP(hAPP(c_COMBB(tc_fun(_1448368, tc_HOL_Obool), tc_fun(_1448368, tc_HOL_Obool), _1448372), hAPP(c_COMBS(_1448368, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1448368), c_fconj), _1448370))), _1448374))))))]]], (32490 ^ _776545) ^ [_1361938, _1361940, _1361942, _1361944, _1361946, _1361948] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361938, tc_fun(_1361940, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1361938, tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_fun(_1361940, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361940, tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_fun(_1361940, tc_HOL_Obool)), _1361938), c_COMBC(_1361940, tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361940, tc_prod(_1361938, _1361940)), tc_fun(_1361940, tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), _1361938), hAPP(c_COMBB(tc_prod(_1361938, _1361940), tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool), _1361940), c_member(tc_prod(_1361938, _1361940)))), c_Product__Type_OPair(_1361938, _1361940)))), _1361942)), hAPP(hAPP(c_COMBC(_1361938, tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_fun(_1361940, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361940, tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_fun(_1361940, tc_HOL_Obool)), _1361938), c_COMBC(_1361940, tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1361940, tc_prod(_1361938, _1361940)), tc_fun(_1361940, tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool)), _1361938), hAPP(c_COMBB(tc_prod(_1361938, _1361940), tc_fun(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool), tc_HOL_Obool), _1361940), c_member(tc_prod(_1361938, _1361940)))), c_Product__Type_OPair(_1361938, _1361940)))), _1361944)), _1361946), _1361948)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361938, _1361940)), hAPP(hAPP(c_Product__Type_OPair(_1361938, _1361940), _1361946), _1361948)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1361938, _1361940), tc_HOL_Obool)), _1361942), _1361944))))], (46343 ^ _776545) ^ [_1708567, _1708569, _1708571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708567), _1708569)), _1708571)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1708569), c_List_Oupt(_1708567, _1708571)) = c_List_Oupt(_1708567, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708567), _1708569)))], (41314 ^ _776545) ^ [_1587251, _1587253, _1587255] : [41317 ^ _776545 : [(41323 ^ _776545) ^ [] : [41316 ^ [_1587251, _1587253, _1587255] = 41319 ^ [_1587251, _1587253, _1587255]], (41321 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587251, _1587253)), hAPP(hAPP(c_Product__Type_OPair(_1587251, _1587253), 41315 ^ [_1587251, _1587253, _1587255]), 41319 ^ [_1587251, _1587253, _1587255])), _1587255)))], (41318 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587251, _1587253)), hAPP(hAPP(c_Product__Type_OPair(_1587251, _1587253), 41315 ^ [_1587251, _1587253, _1587255]), 41316 ^ [_1587251, _1587253, _1587255])), _1587255)))]], -(c_Relation_Osingle__valued(_1587251, _1587253, _1587255))], (50421 ^ _776545) ^ [_1795984, _1795986, _1795988, _1795990, _1795992] : [c_Fun_Obij__betw(_1795984, _1795986, _1795988, _1795990, _1795992), -(c_Fun_Oinj__on(_1795984, _1795986, _1795988, _1795990))], (33048 ^ _776545) ^ [_1380106, _1380108, _1380110, _1380112] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380106, tc_fun(_1380108, tc_HOL_Obool)), _1380110), _1380112) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1380108, tc_HOL_Obool), hAPP(c_Set_Oimage(_1380106, tc_fun(_1380108, tc_HOL_Obool), _1380112), _1380110)))], (52275 ^ _776545) ^ [_1828897] : [-(class_HOL_Oequal(tc_List_Olist(_1828897)))], (40987 ^ _776545) ^ [_1579390, _1579392, _1579394, _1579396] : [-(c_Wellfounded_Owf(_1579390, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579390, _1579390)), hAPP(hAPP(c_Product__Type_OPair(_1579390, _1579390), _1579392), _1579394)), _1579396))), c_Wellfounded_Owf(_1579390, _1579396), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579390, _1579390)), hAPP(hAPP(c_Product__Type_OPair(_1579390, _1579390), _1579394), _1579392)), c_Transitive__Closure_Ortrancl(_1579390, _1579396))))], (22181 ^ _776545) ^ [_1178822, _1178824] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1178822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178824), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1178822, _1178824))], (33016 ^ _776545) ^ [_1379324, _1379326] : [-(hAPP(c_Set_OCollect(_1379324), hAPP(c_fequal, _1379326)) = hAPP(hAPP(c_Set_Oinsert(_1379324), _1379326), c_Orderings_Obot__class_Obot(tc_fun(_1379324, tc_HOL_Obool))))], (36081 ^ _776545) ^ [_1455894, _1455896, _1455898, _1455900, _1455902, _1455904] : [-(c_Product__Type_Oprod_Oprod__rec(_1455894, _1455896, _1455898, _1455900, hAPP(hAPP(c_Product__Type_OPair(_1455894, _1455896), _1455902), _1455904)) = hAPP(hAPP(_1455900, _1455902), _1455904))], (24760 ^ _776545) ^ [_1224429, _1224431] : [class_Divides_Osemiring__div(_1224429), -(c_Divides_Odiv__class_Omod(_1224429, _1224431, _1224431) = c_Groups_Ozero__class_Ozero(_1224429))], (42659 ^ _776545) ^ [_1625891, _1625893, _1625895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1625891), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625893)), _1625895))), -(c_List_Obutlast(_1625893, hAPP(hAPP(c_List_Otake(_1625893), _1625891), _1625895)) = hAPP(hAPP(c_List_Otake(_1625893), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1625891), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1625895))], (40224 ^ _776545) ^ [_1560319, _1560321, _1560323, _1560325, _1560327, _1560329] : [c_Finite__Set_Ofolding(_1560319, _1560321, _1560323, _1560325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560319), _1560327)), -(hAPP(_1560325, hAPP(hAPP(c_Set_Oinsert(_1560319), _1560329), _1560327)) = hAPP(c_Fun_Ocomp(_1560321, _1560321, _1560321, hAPP(_1560325, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1560319, tc_HOL_Obool)), _1560327), hAPP(hAPP(c_Set_Oinsert(_1560319), _1560329), c_Orderings_Obot__class_Obot(tc_fun(_1560319, tc_HOL_Obool)))))), hAPP(_1560323, _1560329)))], (28355 ^ _776545) ^ [_1285543, _1285545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285543), _1285545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285543)), c_Int_OBit1(_1285545))))], (2084 ^ _776545) ^ [_806750, _806752, _806754, _806756, _806758, _806760] : [-(c_Power_Opower_Opower(_806760, _806756, _806752) = c_Power_Opower_Opower(_806758, _806754, _806750)), _806760 = _806758, _806756 = _806754, _806752 = _806750], (17819 ^ _776545) ^ [_1097215, _1097217] : [class_Groups_Ogroup__add(_1097215), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097215), c_Groups_Ozero__class_Ozero(_1097215)), _1097217) = hAPP(c_Groups_Ouminus__class_Ouminus(_1097215), _1097217))], (34163 ^ _776545) ^ [_1411369, _1411371, _1411373, _1411375] : [class_Groups_Oab__group__add(_1411369), 34166 ^ _776545 : [(34173 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411371), _1411373))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411369), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1411369, _1411369), hAPP(hAPP(c_COMBB(_1411369, tc_fun(_1411369, _1411369), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1411369)), _1411375)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411369, tc_Nat_Onat), _1411375), 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, _1411371, _1411373)) = c_Groups_Ozero__class_Ozero(_1411369))], (34167 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411371), _1411373)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411369), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1411369, _1411369), hAPP(hAPP(c_COMBB(_1411369, tc_fun(_1411369, _1411369), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1411369)), _1411375)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411369, tc_Nat_Onat), _1411375), 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, _1411371, _1411373)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1411369), hAPP(_1411375, _1411371)), hAPP(_1411375, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411373), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (6780 ^ _776545) ^ [_886188, _886190, _886192] : [class_Orderings_Olinorder(_886188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886188), _886190), _886192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886188), _886192), _886190)))], (37775 ^ _776545) ^ [_1496432, _1496434, _1496436, _1496438, _1496440, _1496442, _1496444, _1496446] : [c_Fun_Oinj__on(_1496432, _1496434, _1496436, _1496438), 37781 ^ _776545 : [(37784 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496432, tc_HOL_Obool)), hAPP(_1496444, 37780 ^ [_1496432, _1496434, _1496436, _1496438, _1496440, _1496442, _1496444, _1496446])), _1496438))], (37782 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496440), 37780 ^ [_1496432, _1496434, _1496436, _1496438, _1496440, _1496442, _1496444, _1496446]), _1496442)))]], hBOOL(hAPP(hAPP(c_member(_1496440), _1496446), _1496442)), -(hAPP(c_Set_Oimage(_1496432, _1496434, _1496436), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496440, tc_fun(_1496432, tc_HOL_Obool)), _1496442), _1496444)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1496440, tc_fun(_1496434, tc_HOL_Obool)), _1496442), hAPP(hAPP(c_COMBB(tc_fun(_1496432, tc_HOL_Obool), tc_fun(_1496434, tc_HOL_Obool), _1496440), c_Set_Oimage(_1496432, _1496434, _1496436)), _1496444)))], (33070 ^ _776545) ^ [_1380829, _1380831, _1380833, _1380835, _1380837, _1380839] : [hBOOL(hAPP(hAPP(c_member(_1380829), _1380831), _1380833)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380829, tc_fun(_1380835, tc_HOL_Obool)), _1380833), hAPP(hAPP(c_COMBB(tc_fun(_1380835, tc_HOL_Obool), tc_fun(_1380835, tc_HOL_Obool), _1380829), hAPP(c_Set_Oinsert(_1380835), _1380837)), _1380839)) = hAPP(hAPP(c_Set_Oinsert(_1380835), _1380837), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380829, tc_fun(_1380835, tc_HOL_Obool)), _1380833), _1380839)))], (48203 ^ _776545) ^ [] : [-(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))))], (14530 ^ _776545) ^ [_1038566, _1038568] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038566), _1038568) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038568), _1038566))], (2698 ^ _776545) ^ [_816409, _816411, _816413, _816415, _816417, _816419] : [-(c_Finite__Set_Ofold1Set(_816419, _816415, _816411) = c_Finite__Set_Ofold1Set(_816417, _816413, _816409)), _816419 = _816417, _816415 = _816413, _816411 = _816409], (6616 ^ _776545) ^ [_883648, _883650, _883652, _883654] : [class_Orderings_Oorder(_883648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883648), _883650), _883652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883648), _883654), _883650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883648), _883654), _883652)))], (26276 ^ _776545) ^ [_1251101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1251101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251101)))], (38114 ^ _776545) ^ [_1506535, _1506537, _1506539, _1506541] : [c_Wellfounded_Owf(_1506535, _1506537), c_Wellfounded_Owf(_1506539, _1506541), -(c_Wellfounded_Owf(tc_prod(_1506535, _1506539), c_Wellfounded_Olex__prod(_1506535, _1506539, _1506537, _1506541)))], (7512 ^ _776545) ^ [_900364, _900366, _900368, _900370] : [hBOOL(hAPP(hAPP(c_member(_900364), _900366), _900368)), -(hBOOL(hAPP(hAPP(c_member(_900364), _900366), _900370))), -(hBOOL(hAPP(hAPP(c_member(_900364), _900366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900364, tc_HOL_Obool)), _900368), _900370))))], (31012 ^ _776545) ^ [_1332904, _1332906] : [class_Orderings_Olinorder(_1332904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332904), _1332906)), -(_1332906 = c_Orderings_Obot__class_Obot(tc_fun(_1332904, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1332904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332904), 31025 ^ [_1332904, _1332906]), 31026 ^ [_1332904, _1332906])), hAPP(hAPP(c_Set_Oinsert(_1332904), 31025 ^ [_1332904, _1332906]), hAPP(hAPP(c_Set_Oinsert(_1332904), 31026 ^ [_1332904, _1332906]), c_Orderings_Obot__class_Obot(tc_fun(_1332904, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1332904), c_Big__Operators_Olattice_OInf__fin(_1332904, c_Orderings_Oord__class_Omin(_1332904), _1332906)), _1332906)))], (44274 ^ _776545) ^ [_1661856, _1661858, _1661860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1661856), _1661858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1661856), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661858), _1661860))))], (36547 ^ _776545) ^ [_1468613, _1468615] : [-(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), _1468613), _1468615)), 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), _1468615), _1468613)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (16683 ^ _776545) ^ [_1076639, _1076641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076639)), _1076641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076639), _1076641)))], (22331 ^ _776545) ^ [_1181314, _1181316, _1181318] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181314), _1181316)), _1181318) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181314), _1181318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181316), _1181318)))], (52259 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (1794 ^ _776545) ^ [_801834, _801836] : [-(class_Rings_Osemiring__0(_801834)), _801836 = _801834, class_Rings_Osemiring__0(_801836)], (48154 ^ _776545) ^ [_1746337, _1746339, _1746341] : [-(hBOOL(hAPP(hAPP(c_member(_1746337), _1746339), hAPP(c_List_Oset(_1746337), _1746341)))), 48155 ^ _776545 : [(48156 ^ _776545) ^ [_1746426] : [48157 ^ _776545 : [(48158 ^ _776545) ^ [_1746499] : [_1746341 = hAPP(hAPP(c_List_Oappend(_1746337), _1746426), hAPP(hAPP(c_List_Olist_OCons(_1746337), _1746339), _1746499))]], -(hBOOL(hAPP(hAPP(c_member(_1746337), _1746339), hAPP(c_List_Oset(_1746337), _1746426))))]]], (17571 ^ _776545) ^ [_1092997, _1092999, _1093001] : [class_Groups_Oordered__ab__group__add(_1092997), 17574 ^ _776545 : [(17581 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092997), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092997), _1092999), _1093001)), c_Groups_Ozero__class_Ozero(_1092997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092997), _1092999), _1093001)))], (17575 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092997), _1092999), _1093001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092997), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092997), _1092999), _1093001)), c_Groups_Ozero__class_Ozero(_1092997))))]]], (1754 ^ _776545) ^ [_801334, _801336] : [-(class_Orderings_Olinorder(_801334)), _801336 = _801334, class_Orderings_Olinorder(_801336)], (3024 ^ _776545) ^ [_821428, _821430] : [_821430 = _821428, -(c_HOL_Obool_Obool__size(_821430) = c_HOL_Obool_Obool__size(_821428))], (34954 ^ _776545) ^ [_1428677, _1428679] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1428677), _1428679)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1428677), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428679)))], (11489 ^ _776545) ^ [_977262, _977264, _977266] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977262), _977264)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977262), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977262, tc_HOL_Obool)), _977264), _977266))))], (36416 ^ _776545) ^ [_1464315, _1464317, _1464319, _1464321] : [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), _1464315), _1464317)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464319), _1464321))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464315), _1464321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1464319), _1464317))], (31667 ^ _776545) ^ [_1345065, _1345067, _1345069, _1345071] : [class_Orderings_Olinorder(_1345065), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345065), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345065), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345065), _1345067), _1345069)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345065), _1345067), _1345071))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345065), _1345067), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345065), _1345069), _1345071)))))], (40679 ^ _776545) ^ [_1571221, _1571223] : [-(c_Transitive__Closure_Otrancl(_1571221, _1571223) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571221, _1571221), tc_HOL_Obool)), _1571223), hAPP(hAPP(c_Relation_Orel__comp(_1571221, _1571221, _1571221), c_Transitive__Closure_Otrancl(_1571221, _1571223)), _1571223)))], (23151 ^ _776545) ^ [_1195966, _1195968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195968)), -(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), _1195966), _1195968))))], (11792 ^ _776545) ^ [_983150, _983152, _983154] : [class_Lattices_Olattice(_983150), hBOOL(hAPP(c_Finite__Set_Ofinite(_983150), _983152)), hBOOL(hAPP(hAPP(c_member(_983150), _983154), _983152)), 11803 ^ _776545 : [(11810 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983150, tc_HOL_Obool)), _983152), hAPP(hAPP(c_Set_Oinsert(_983150), _983154), c_Orderings_Obot__class_Obot(tc_fun(_983150, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983150, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_983150, _983152) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983150), _983154), c_Big__Operators_Olattice__class_OInf__fin(_983150, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983150, tc_HOL_Obool)), _983152), hAPP(hAPP(c_Set_Oinsert(_983150), _983154), c_Orderings_Obot__class_Obot(tc_fun(_983150, tc_HOL_Obool)))))))], (11804 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983150, tc_HOL_Obool)), _983152), hAPP(hAPP(c_Set_Oinsert(_983150), _983154), c_Orderings_Obot__class_Obot(tc_fun(_983150, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983150, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_983150, _983152) = _983154)]]], (43172 ^ _776545) ^ [_1636614, _1636616, _1636618, _1636620] : [-(hBOOL(hAPP(hAPP(c_member(_1636614), _1636616), hAPP(c_List_Oset(_1636614), _1636618)))), hBOOL(hAPP(hAPP(c_member(_1636614), _1636616), hAPP(c_List_Oset(_1636614), c_List_Oremove1(_1636614, _1636620, _1636618))))], (30034 ^ _776545) ^ [_1315135, _1315137, _1315139] : [class_Orderings_Olinorder(_1315135), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315135), _1315137), _1315139) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315135), _1315139), _1315137))], (28123 ^ _776545) ^ [_1281612, _1281614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281612), _1281614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1281612)), _1281614)))], (41015 ^ _776545) ^ [_1580058, _1580060] : [-(c_Relation_Orefl__on(_1580058, c_Orderings_Otop__class_Otop(tc_fun(_1580058, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580058, _1580058), tc_HOL_Obool)), _1580060), c_Relation_OId(_1580058))))], (39347 ^ _776545) ^ [_1538313, _1538315, _1538317, _1538319] : [class_Groups_Ocomm__monoid__add(_1538313), c_Fun_Oinj__on(_1538315, _1538313, _1538317, _1538319), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538315, _1538313), _1538317), _1538319) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538313, _1538313), c_Fun_Oid(_1538313)), hAPP(c_Set_Oimage(_1538315, _1538313, _1538317), _1538319)))], (4830 ^ _776545) ^ [_850069, _850071, _850073, _850075] : [-(c_Complete__Lattice_OSup__class_OSup(_850075, _850071) = c_Complete__Lattice_OSup__class_OSup(_850073, _850069)), _850075 = _850073, _850071 = _850069], (26831 ^ _776545) ^ [_1260176, _1260178] : [c_Nat__Transfer_Ois__nat(_1260176), c_Nat__Transfer_Ois__nat(_1260178), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1260176), _1260178)))], (10226 ^ _776545) ^ [_952174, _952176, _952178, _952180, _952182, _952184, _952186] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_952174, _952176, _952178, _952180, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952174, tc_HOL_Obool)), _952182), hAPP(hAPP(c_Set_Oinsert(_952174), _952184), c_Orderings_Obot__class_Obot(tc_fun(_952174, tc_HOL_Obool))))), _952186)), hBOOL(hAPP(hAPP(c_member(_952174), _952184), _952182)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_952174, _952176, _952178, _952180, _952182), hAPP(hAPP(_952178, _952184), _952186))))], (4 ^ _776545) ^ [_776595, _776597] : [_776597 = _776595, -(_776595 = _776597)], (18041 ^ _776545) ^ [_1100971, _1100973, _1100975] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100971), _1100973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100975), _1100973)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100971), _1100975))], (36404 ^ _776545) ^ [_1464078, _1464080] : [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), _1464078), _1464080)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1464078), _1464080)))], (7728 ^ _776545) ^ [_906034, _906036, _906038] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906034, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906034, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_906034, tc_HOL_Obool), tc_HOL_Obool)), _906036), _906038))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_906034, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906034, tc_HOL_Obool), _906036)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_906034, tc_HOL_Obool), _906038)))))], (11218 ^ _776545) ^ [_971260, _971262, _971264, _971266, _971268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971260, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971260, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971262, _971260, _971264), _971266)), hAPP(c_Set_Oimage(_971262, _971260, _971264), _971268))), hAPP(c_Set_Oimage(_971262, _971260, _971264), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971262, tc_HOL_Obool)), _971266), _971268)))))], (16620 ^ _776545) ^ [_1075482, _1075484, _1075486, _1075488] : [class_Groups_Ocomm__monoid__add(_1075482), 16623 ^ _776545 : [(16630 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075484), _1075486))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075484, _1075482), _1075488), _1075486) = c_Groups_Ozero__class_Ozero(_1075482))], (16624 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075484), _1075486)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075484, _1075482), _1075488), _1075486) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075482, _1075484, c_Groups_Oplus__class_Oplus(_1075482)), _1075488), c_Groups_Ozero__class_Ozero(_1075482)), _1075486))]]], (47573 ^ _776545) ^ [_1733378, _1733380, _1733382] : [hBOOL(hAPP(hAPP(c_member(_1733378), _1733380), hAPP(c_List_Oset(_1733378), _1733382))), -(c_List_Oinsert(_1733378, _1733380, _1733382) = _1733382)], (38600 ^ _776545) ^ [_1517931, _1517933, _1517935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517931, tc_HOL_Obool)), _1517933), hAPP(hAPP(c_Set_Oinsert(_1517931), _1517935), c_Orderings_Obot__class_Obot(tc_fun(_1517931, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1517931, _1517935, _1517933) = c_HOL_OThe(_1517931, hAPP(hAPP(c_COMBC(_1517931, tc_fun(_1517931, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517931)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1517931, tc_HOL_Obool)), _1517933), hAPP(hAPP(c_Set_Oinsert(_1517931), _1517935), c_Orderings_Obot__class_Obot(tc_fun(_1517931, tc_HOL_Obool)))))))], (42432 ^ _776545) ^ [_1618962, _1618964, _1618966] : [hBOOL(hAPP(hAPP(c_member(_1618962), _1618964), hAPP(c_List_Oset(_1618962), _1618966))), -(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(_1618962)), _1618966))))], (51609 ^ _776545) ^ [_1820603, _1820605, _1820607, _1820609] : [class_Divides_Osemiring__div(_1820603), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820603), _1820605), c_Divides_Odiv__class_Omod(_1820603, _1820607, _1820609))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820603), _1820605), _1820609)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820603), _1820605), _1820607)))], (15059 ^ _776545) ^ [_1048554, _1048556] : [class_Groups_Oone(_1048554), 15062 ^ _776545 : [(15069 ^ _776545) ^ [] : [_1048556 = c_Groups_Oone__class_Oone(_1048554), -(c_Groups_Oone__class_Oone(_1048554) = _1048556)], (15063 ^ _776545) ^ [] : [c_Groups_Oone__class_Oone(_1048554) = _1048556, -(_1048556 = c_Groups_Oone__class_Oone(_1048554))]]], (5691 ^ _776545) ^ [_866308, _866310, _866312] : [hAPP(c_Hoare__Mirabelle_ORep__triple(_866308), _866310) = hAPP(c_Hoare__Mirabelle_ORep__triple(_866308), _866312), -(_866310 = _866312)], (416 ^ _776545) ^ [_782825, _782827, _782829, _782831, _782833, _782835] : [-(c_Relation_Osingle__valued(_782833, _782829, _782825)), c_Relation_Osingle__valued(_782835, _782831, _782827), _782835 = _782833, _782831 = _782829, _782827 = _782825], (27531 ^ _776545) ^ [_1271822, _1271824, _1271826] : [class_Rings_Olinordered__idom(_1271822), 27534 ^ _776545 : [(27543 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), hAPP(c_Groups_Oabs__class_Oabs(_1271822), _1271824)), _1271826))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), _1271824), _1271826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), hAPP(c_Groups_Ouminus__class_Ouminus(_1271822), _1271824)), _1271826))], (27535 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), hAPP(c_Groups_Oabs__class_Oabs(_1271822), _1271824)), _1271826)), 27538 ^ _776545 : [(27541 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), hAPP(c_Groups_Ouminus__class_Ouminus(_1271822), _1271824)), _1271826)))], (27539 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271822), _1271824), _1271826)))]]]]], (44719 ^ _776545) ^ [_1670469, _1670471, _1670473, _1670475, _1670477, _1670479] : [-(hAPP(hAPP(c_List_Omap(_1670469, _1670471), _1670473), hAPP(hAPP(c_List_Omap(_1670475, _1670469), _1670477), _1670479)) = hAPP(hAPP(c_List_Omap(_1670475, _1670471), hAPP(c_Fun_Ocomp(_1670469, _1670471, _1670475, _1670473), _1670477)), _1670479))], (15860 ^ _776545) ^ [_1063678, _1063680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063678), hAPP(c_Nat_OSuc, _1063680))), _1063678)))], (22477 ^ _776545) ^ [_1183762, _1183764, _1183766] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1183764), _1183766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183762), _1183764)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183762), _1183766)))], (2300 ^ _776545) ^ [_810052, _810054] : [_810054 = _810052, -(c_Int_Opred(_810054) = c_Int_Opred(_810052))], (24048 ^ _776545) ^ [] : [-(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))))], (11030 ^ _776545) ^ [_967226, _967228] : [class_Lattices_Oab__semigroup__idem__mult(_967226), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967226), _967228), _967228) = _967228)], (13210 ^ _776545) ^ [_1010358] : [class_Lattices_Osemilattice__sup(_1010358), -(c_Finite__Set_Ofun__left__comm__idem(_1010358, _1010358, c_Lattices_Osemilattice__sup__class_Osup(_1010358)))], (11750 ^ _776545) ^ [_982173, _982175, _982177, _982179, _982181, _982183, _982185, _982187] : [c_Finite__Set_Ofolding__image__simple(_982173, _982175, _982177, _982179, _982181, _982183), hBOOL(hAPP(c_Finite__Set_Ofinite(_982175), _982185)), hBOOL(hAPP(hAPP(c_member(_982175), _982187), _982185)), -(hAPP(_982183, _982185) = hAPP(hAPP(_982177, hAPP(_982181, _982187)), hAPP(_982183, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982175, tc_HOL_Obool)), _982185), hAPP(hAPP(c_Set_Oinsert(_982175), _982187), c_Orderings_Obot__class_Obot(tc_fun(_982175, tc_HOL_Obool)))))))], (22083 ^ _776545) ^ [_1176964, _1176966, _1176968] : [class_Rings_Olinordered__semidom(_1176964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176964), c_Groups_Oone__class_Oone(_1176964)), _1176966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176964), c_Groups_Oone__class_Oone(_1176964)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176964), _1176966), _1176968))))], (38264 ^ _776545) ^ [_1509261, _1509263, _1509265] : [c_Wellfounded_Owf(_1509261, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509261, _1509261), tc_HOL_Obool)), _1509263), _1509265)), -(c_Wellfounded_Owf(_1509261, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509261, _1509261), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509261, _1509261), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509261, _1509261, _1509261), _1509263), _1509263)), hAPP(hAPP(c_Relation_Orel__comp(_1509261, _1509261, _1509261), _1509265), _1509263))), _1509265)))], (24086 ^ _776545) ^ [_1212463, _1212465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212463)), 24089 ^ _776545 : [(24096 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212465)), -(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), _1212465), _1212463))))], (24090 ^ _776545) ^ [] : [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), _1212465), _1212463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212465)))]]], (46101 ^ _776545) ^ [_1702560, _1702562, _1702564, _1702566] : [hBOOL(hAPP(_1702560, _1702562)), -(hAPP(c_List_Ofilter(_1702564, _1702560), hAPP(hAPP(c_List_Olist_OCons(_1702564), _1702562), _1702566)) = hAPP(hAPP(c_List_Olist_OCons(_1702564), _1702562), hAPP(c_List_Ofilter(_1702564, _1702560), _1702566)))], (48307 ^ _776545) ^ [_1749441, _1749443, _1749445] : [c_List_Olist__all(_1749441, _1749445, _1749443), 48310 ^ _776545 : [(48311 ^ _776545) ^ [_1749522] : [hBOOL(hAPP(hAPP(c_member(_1749441), _1749522), hAPP(c_List_Oset(_1749441), _1749443))), -(hBOOL(hAPP(_1749445, _1749522)))]]], (12878 ^ _776545) ^ [_1003761, _1003763, _1003765, _1003767, _1003769, _1003771] : [c_Finite__Set_Ofun__left__comm(_1003761, _1003763, _1003765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003761), _1003767)), -(hBOOL(hAPP(hAPP(c_member(_1003761), _1003769), _1003767))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1003761, _1003763, _1003765), _1003771), hAPP(hAPP(c_Set_Oinsert(_1003761), _1003769), _1003767)) = hAPP(hAPP(_1003765, _1003769), hAPP(hAPP(c_Finite__Set_Ofold(_1003761, _1003763, _1003765), _1003771), _1003767)))], (23898 ^ _776545) ^ [_1209412, _1209414, _1209416] : [class_Rings_Olinordered__semidom(_1209412), 23901 ^ _776545 : [(23908 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209414), _1209416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209412), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209412), _1209414)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209412), _1209416))))], (23902 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209412), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209412), _1209414)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209412), _1209416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209414), _1209416)))]]], (42037 ^ _776545) ^ [_1608309, _1608311, _1608313, _1608315] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608309), tc_List_Olist(_1608309))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608309), tc_List_Olist(_1608309)), _1608311), _1608313)), c_List_Olistrel(_1608309, _1608315))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608309), tc_List_Olist(_1608309))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608309), tc_List_Olist(_1608309)), _1608311), _1608313)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608309), c_List_Olistrel1(_1608309, _1608315)))))], (17317 ^ _776545) ^ [_1088321, _1088323, _1088325, _1088327] : [class_Rings_Olinordered__comm__semiring__strict(_1088321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088321), _1088323), _1088325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088321), c_Groups_Ozero__class_Ozero(_1088321)), _1088327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088321), _1088327), _1088323)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088321), _1088327), _1088325))))], (21102 ^ _776545) ^ [_1158187, _1158189, _1158191, _1158193] : [class_Groups_Ocomm__monoid__mult(_1158187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158189), _1158191)), 21112 ^ _776545 : [(21115 ^ _776545) ^ [] : [hAPP(_1158193, 21111 ^ [_1158187, _1158189, _1158191, _1158193]) = c_Groups_Oone__class_Oone(_1158187)], (21113 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158189), 21111 ^ [_1158187, _1158189, _1158191, _1158193]), _1158191)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158187, _1158189, c_Groups_Otimes__class_Otimes(_1158187)), _1158193), c_Groups_Oone__class_Oone(_1158187)), _1158191) = c_Groups_Oone__class_Oone(_1158187))], (50552 ^ _776545) ^ [_1798298, _1798300, _1798302, _1798304, _1798306, _1798308, _1798310] : [c_Fun_Obij__betw(_1798298, _1798300, _1798302, _1798304, _1798306), c_Fun_Obij__betw(_1798298, _1798300, _1798302, _1798308, _1798310), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798300, tc_HOL_Obool)), _1798306), _1798310) = c_Orderings_Obot__class_Obot(tc_fun(_1798300, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1798298, _1798300, _1798302, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798298, tc_HOL_Obool)), _1798304), _1798308), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798300, tc_HOL_Obool)), _1798306), _1798310)))], (29940 ^ _776545) ^ [_1313331, _1313333, _1313335, _1313337] : [class_Rings_Olinordered__semidom(_1313331), 29946 ^ _776545 : [(29949 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313331), c_Groups_Ozero__class_Ozero(_1313331)), hAPP(_1313337, 29945 ^ [_1313331, _1313333, _1313335, _1313337])))], (29947 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313333), 29945 ^ [_1313331, _1313333, _1313335, _1313337]), _1313335)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313331), c_Groups_Ozero__class_Ozero(_1313331)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1313333, _1313331), _1313337), _1313335))))], (25010 ^ _776545) ^ [_1229473] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229473), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1229473)], (45233 ^ _776545) ^ [_1682488] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1682488)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1682488))], (14560 ^ _776545) ^ [_1039149, _1039151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039149), _1039151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039151), _1039149)), -(_1039149 = _1039151)], (12029 ^ _776545) ^ [_987979, _987981] : [class_Lattices_Olattice(_987979), -(c_Big__Operators_Olattice__class_OSup__fin(_987979, hAPP(hAPP(c_Set_Oinsert(_987979), _987981), c_Orderings_Obot__class_Obot(tc_fun(_987979, tc_HOL_Obool)))) = _987981)], (2220 ^ _776545) ^ [_808812, _808814, _808816, _808818] : [-(c_Random_Oinc__shift(_808818, _808814) = c_Random_Oinc__shift(_808816, _808812)), _808818 = _808816, _808814 = _808812], (880 ^ _776545) ^ [_789709, _789711, _789713, _789715, _789717, _789719, _789721, _789723, _789725, _789727] : [-(c_Fun_Obij__betw(_789725, _789721, _789717, _789713, _789709)), c_Fun_Obij__betw(_789727, _789723, _789719, _789715, _789711), _789727 = _789725, _789723 = _789721, _789719 = _789717, _789715 = _789713, _789711 = _789709], (23139 ^ _776545) ^ [_1195806, _1195808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195806), _1195808))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1195808, _1195806) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1195808), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1195808), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1195806)))], (32741 ^ _776545) ^ [_1371398, _1371400, _1371402, _1371404, _1371406] : [class_Complete__Lattice_Ocomplete__lattice(_1371398), class_Orderings_Olinorder(_1371398), 32748 ^ _776545 : [(32758 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371398), _1371400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1371402, _1371398), _1371404), _1371406)))), 32759 ^ _776545 : [(32760 ^ _776545) ^ [_1371746] : [hBOOL(hAPP(hAPP(c_member(_1371402), _1371746), _1371404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371398), _1371400), hAPP(_1371406, _1371746)))]]], (32749 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371398), _1371400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1371402, _1371398), _1371404), _1371406))), 32753 ^ _776545 : [(32756 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371398), _1371400), hAPP(_1371406, 32752 ^ [_1371398, _1371400, _1371402, _1371404, _1371406]))))], (32754 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1371402), 32752 ^ [_1371398, _1371400, _1371402, _1371404, _1371406]), _1371404)))]]]]], (44082 ^ _776545) ^ [_1658216, _1658218, _1658220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658218)), _1658220))), -(_1658220 = hAPP(hAPP(c_List_Oappend(_1658218), hAPP(hAPP(c_List_Otake(_1658218), _1658216), _1658220)), hAPP(hAPP(c_List_Olist_OCons(_1658218), hAPP(hAPP(c_List_Onth(_1658218), _1658220), _1658216)), hAPP(hAPP(c_List_Odrop(_1658218), hAPP(c_Nat_OSuc, _1658216)), _1658220))))], (16446 ^ _776545) ^ [_1072894, _1072896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072894), _1072896)), _1072896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47917 ^ _776545) ^ [_1741690, _1741692, _1741694, _1741696, _1741698] : [-(hAPP(hAPP(c_List_Olist_OCons(_1741690), _1741692), _1741694) = hAPP(c_List_Ofilter(_1741690, _1741696), _1741698)), 47918 ^ _776545 : [(47919 ^ _776545) ^ [_1741818, _1741820] : [_1741698 = hAPP(hAPP(c_List_Oappend(_1741690), _1741820), hAPP(hAPP(c_List_Olist_OCons(_1741690), _1741692), _1741818)), 47925 ^ _776545 : [(47928 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1741696, 47924 ^ [_1741690, _1741692, _1741694, _1741696, _1741698, _1741818, _1741820])))], (47926 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741690), 47924 ^ [_1741690, _1741692, _1741694, _1741696, _1741698, _1741818, _1741820]), hAPP(c_List_Oset(_1741690), _1741820))))]], hBOOL(hAPP(_1741696, _1741692)), _1741694 = hAPP(c_List_Ofilter(_1741690, _1741696), _1741818)]]], (32964 ^ _776545) ^ [_1377749, _1377751, _1377753, _1377755, _1377757] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377749, tc_fun(_1377751, tc_HOL_Obool)), _1377753), hAPP(hAPP(c_COMBB(tc_fun(_1377751, tc_HOL_Obool), tc_fun(_1377751, tc_HOL_Obool), _1377749), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377751, tc_HOL_Obool)), _1377755)), _1377757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377751, tc_HOL_Obool)), _1377755), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377749, tc_fun(_1377751, tc_HOL_Obool)), _1377753), _1377757)))], (23870 ^ _776545) ^ [_1208929, _1208931] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208929)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208931)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208929), _1208931)))], (30164 ^ _776545) ^ [_1317673, _1317675, _1317677] : [class_Orderings_Olinorder(_1317673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317673), _1317675), _1317677)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317673), _1317675), _1317677) = _1317675)], (52081 ^ _776545) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (13990 ^ _776545) ^ [_1027112, _1027114, _1027116, _1027118, _1027120] : [class_Groups_Ocomm__monoid__add(_1027112), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027114), _1027116)), -(hBOOL(hAPP(hAPP(c_member(_1027114), _1027118), _1027116))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027114, _1027112), _1027120), hAPP(hAPP(c_Set_Oinsert(_1027114), _1027118), _1027116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027112), hAPP(_1027120, _1027118)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027114, _1027112), _1027120), _1027116)))], (50779 ^ _776545) ^ [_1802954, _1802956, _1802958, _1802960, _1802962, _1802964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802954, tc_HOL_Obool)), _1802956), _1802958)), 50785 ^ _776545 : [(50788 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802960, tc_HOL_Obool)), hAPP(_1802962, 50784 ^ [_1802954, _1802956, _1802958, _1802960, _1802962, _1802964])), hAPP(_1802964, 50784 ^ [_1802954, _1802956, _1802958, _1802960, _1802962, _1802964])))], (50786 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802954), 50784 ^ [_1802954, _1802956, _1802958, _1802960, _1802962, _1802964]), _1802958)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802960, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1802954, tc_fun(_1802960, tc_HOL_Obool)), _1802958), _1802962)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1802954, tc_fun(_1802960, tc_HOL_Obool)), _1802958), _1802964))))], (48690 ^ _776545) ^ [_1757966, _1757968] : [-(c_List_Oconcat(_1757966, c_List_Oreplicate(tc_List_Olist(_1757966), _1757968, c_List_Olist_ONil(_1757966))) = c_List_Olist_ONil(_1757966))], (25956 ^ _776545) ^ [_1245871] : [-(hBOOL(hAPP(_1245871, 25963 ^ [_1245871]))), 25957 ^ _776545 : [(25958 ^ _776545) ^ [_1245923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245923)), hBOOL(hAPP(_1245871, hAPP(c_Int_Onat, _1245923)))]]], (8109 ^ _776545) ^ [_914667, _914669, _914671, _914673] : [class_Orderings_Olinorder(_914667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914667), _914669), _914671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914667), _914671), _914673)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914667, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914667, _914669, _914671)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914667, _914671, _914673)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_914667, _914669, _914673))], (6877 ^ _776545) ^ [_888114, _888116, _888118] : [class_Orderings_Oorder(_888114), 6880 ^ _776545 : [(6887 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888114), _888116), _888118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888114, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888114), _888116)), hAPP(c_SetInterval_Oord__class_OatMost(_888114), _888118))))], (6881 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888114, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888114), _888116)), hAPP(c_SetInterval_Oord__class_OatMost(_888114), _888118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888114), _888116), _888118)))]]], (38165 ^ _776545) ^ [_1507482, _1507484, _1507486] : [c_Wellfounded_Owf(_1507482, _1507484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507482, _1507482), tc_HOL_Obool)), _1507486), _1507484)), -(c_Wellfounded_Owf(_1507482, _1507486))], (22779 ^ _776545) ^ [_1189255, _1189257, _1189259] : [class_Rings_Olinordered__semidom(_1189255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189255), c_Groups_Oone__class_Oone(_1189255)), _1189257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189255), c_Groups_Oone__class_Oone(_1189255)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189255), _1189257), hAPP(hAPP(c_Power_Opower__class_Opower(_1189255), _1189257), _1189259)))))], (49317 ^ _776545) ^ [_1772159] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1772159, tc_HOL_Obool) = c_Set_OBex(_1772159))], (23791 ^ _776545) ^ [_1207453, _1207455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207453), _1207455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207453)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207455))))], (11125 ^ _776545) ^ [_969026, _969028, _969030, _969032, _969034] : [hBOOL(hAPP(hAPP(c_member(_969026), _969028), _969030)), -(hBOOL(hAPP(hAPP(c_member(_969032), hAPP(_969034, _969028)), hAPP(c_Set_Oimage(_969026, _969032, _969034), _969030))))], (23815 ^ _776545) ^ [_1207962, _1207964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1207962), _1207964)), -(_1207964 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1207962), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23818 ^ [_1207962, _1207964])))], (23071 ^ _776545) ^ [_1194552, _1194554] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194552)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194554))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194552), _1194554)))], (35358 ^ _776545) ^ [_1435888, _1435890, _1435892, _1435894] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435888, _1435890), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435892), _1435894))), -(_1435890 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1435888), _1435890) = _1435892)], (38648 ^ _776545) ^ [_1519064, _1519066, _1519068, _1519070] : [hBOOL(hAPP(c_Predicate_ORangeP(_1519064, _1519066, _1519068), _1519070)), -(hBOOL(hAPP(hAPP(_1519068, 38651 ^ [_1519064, _1519066, _1519068, _1519070]), _1519070)))], (8525 ^ _776545) ^ [_922986, _922988, _922990, _922992] : [class_Lattices_Osemilattice__sup(_922986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922986), _922988), _922990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922986), _922988), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922986), _922990), _922992))))], (28319 ^ _776545) ^ [_1284894, _1284896] : [_1284894 = _1284896, -(c_Int_OBit1(_1284894) = c_Int_OBit1(_1284896))], (51921 ^ _776545) ^ [_1825462, _1825464] : [class_Orderings_Oorder(_1825462), -(class_Orderings_Oorder(tc_fun(_1825464, _1825462)))], (40354 ^ _776545) ^ [_1563399, _1563401] : [40355 ^ _776545 : [(40356 ^ _776545) ^ [_1563445] : [hBOOL(hAPP(_1563399, _1563445))]], -(hBOOL(hAPP(_1563399, c_Hilbert__Choice_OEps(_1563401, _1563399))))], (51501 ^ _776545) ^ [_1818771, _1818773] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818771), _1818773)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818771), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818773))))], (20445 ^ _776545) ^ [_1145435, _1145437, _1145439, _1145441, _1145443] : [class_Fields_Olinordered__field(_1145435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145435), c_Groups_Ozero__class_Ozero(_1145435)), _1145437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145435), _1145437), _1145439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145435), c_Groups_Ozero__class_Ozero(_1145435)), _1145441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145435), _1145441), _1145443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145435), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145435), _1145437), _1145443)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145435), _1145439), _1145441))))], (29245 ^ _776545) ^ [_1300730] : [class_Rings_Osemiring__1(_1300730), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300730), c_Groups_Ozero__class_Ozero(_1300730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300730))], (6714 ^ _776545) ^ [_885197, _885199, _885201, _885203] : [class_Orderings_Oord(_885197), _885199 = _885201, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885197), _885201), _885203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885197), _885199), _885203)))], (15366 ^ _776545) ^ [_1054044, _1054046, _1054048] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054044), _1054046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1054044, tc_HOL_Obool)), _1054048), _1054046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054044), _1054046)), hAPP(c_Finite__Set_Ocard(_1054044), _1054048))), -(_1054048 = _1054046)], (210 ^ _776545) ^ [_779942, _779944, _779946, _779948] : [-(c_Int_Oiszero(_779946, _779942)), c_Int_Oiszero(_779948, _779944), _779948 = _779946, _779944 = _779942], (28361 ^ _776545) ^ [_1285665, _1285667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285665)), c_Int_OBit1(_1285667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285665), _1285667)))], (18087 ^ _776545) ^ [_1101769, _1101771, _1101773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101769)), 18090 ^ _776545 : [(18097 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101771), _1101773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101769), _1101771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101769), _1101773))))], (18091 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101769), _1101771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101769), _1101773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101771), _1101773)))]]], (39017 ^ _776545) ^ [_1527788, _1527790, _1527792, _1527794, _1527796, _1527798] : [-(hAPP(c_Set_Oimage(_1527788, tc_prod(_1527790, _1527792), hAPP(hAPP(c_COMBS(_1527788, _1527792, tc_prod(_1527790, _1527792)), hAPP(hAPP(c_COMBB(_1527790, tc_fun(_1527792, tc_prod(_1527790, _1527792)), _1527788), c_Product__Type_OPair(_1527790, _1527792)), _1527794)), _1527796)), _1527798) = hAPP(hAPP(c_Product__Type_OSigma(_1527790, _1527792), hAPP(c_Set_Oimage(_1527788, _1527790, _1527794), _1527798)), hAPP(hAPP(c_COMBB(tc_fun(_1527788, tc_HOL_Obool), tc_fun(_1527792, tc_HOL_Obool), _1527790), c_Set_Oimage(_1527788, _1527792, _1527796)), hAPP(hAPP(c_COMBC(_1527790, tc_fun(_1527788, tc_HOL_Obool), tc_fun(_1527788, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1527788, tc_HOL_Obool), tc_fun(tc_fun(_1527788, tc_HOL_Obool), tc_fun(_1527788, tc_HOL_Obool)), _1527790), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527788, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527790, tc_HOL_Obool), tc_fun(_1527788, tc_HOL_Obool), _1527790), c_Set_Ovimage(_1527788, _1527790, _1527794)), hAPP(hAPP(c_COMBC(_1527790, tc_fun(_1527790, tc_HOL_Obool), tc_fun(_1527790, tc_HOL_Obool)), c_Set_Oinsert(_1527790)), c_Orderings_Obot__class_Obot(tc_fun(_1527790, tc_HOL_Obool)))))), _1527798))))], (28553 ^ _776545) ^ [_1288884] : [class_Int_Onumber__ring(_1288884), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288884), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1288884))], (16763 ^ _776545) ^ [_1078068, _1078070] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078068), _1078070)), hAPP(c_Nat_OSuc, _1078068))))], (25209 ^ _776545) ^ [_1232969, _1232971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232969), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232971), _1232969)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232969, _1232971) = _1232969)], (45571 ^ _776545) ^ [_1690296, _1690298, _1690300, _1690302, _1690304, _1690306] : [c_List_Olist__all2(_1690296, _1690298, _1690300, _1690302, _1690304), -(c_List_Olist__all2(_1690296, _1690298, _1690300, hAPP(hAPP(c_List_Odrop(_1690296), _1690306), _1690302), hAPP(hAPP(c_List_Odrop(_1690298), _1690306), _1690304)))], (15563 ^ _776545) ^ [_1058512, _1058514, _1058516, _1058518, _1058520] : [class_Groups_Ocomm__monoid__mult(_1058512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058514), _1058516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1058514, tc_HOL_Obool)), _1058518), _1058516)), 15577 ^ _776545 : [(15580 ^ _776545) ^ [] : [hAPP(_1058520, 15576 ^ [_1058512, _1058514, _1058516, _1058518, _1058520]) = c_Groups_Oone__class_Oone(_1058512)], (15578 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058514), 15576 ^ [_1058512, _1058514, _1058516, _1058518, _1058520]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058514, tc_HOL_Obool)), _1058516), _1058518))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058514, _1058512), _1058520), _1058518) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058514, _1058512), _1058520), _1058516))], (6450 ^ _776545) ^ [_880806, _880808] : [-(hBOOL(hAPP(hAPP(c_member(_880806), 6451 ^ [_880806, _880808]), _880808))), -(_880808 = c_Orderings_Obot__class_Obot(tc_fun(_880806, tc_HOL_Obool)))], (2522 ^ _776545) ^ [_813641, _813643, _813645, _813647, _813649, _813651, _813653, _813655, _813657, _813659] : [-(c_Product__Type_Oprod_Oprod__rec(_813659, _813655, _813651, _813647, _813643) = c_Product__Type_Oprod_Oprod__rec(_813657, _813653, _813649, _813645, _813641)), _813659 = _813657, _813655 = _813653, _813651 = _813649, _813647 = _813645, _813643 = _813641], (14018 ^ _776545) ^ [_1027612, _1027614, _1027616, _1027618, _1027620] : [class_Groups_Ocomm__monoid__add(_1027612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027614), _1027616)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027614), _1027618)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027612), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027614, _1027612), _1027620), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027614, tc_HOL_Obool)), _1027616), _1027618))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027614, _1027612), _1027620), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027614, tc_HOL_Obool)), _1027616), _1027618))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1027612), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027614, _1027612), _1027620), _1027616)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1027614, _1027612), _1027620), _1027618)))], (29843 ^ _776545) ^ [_1311618] : [c_Code__Numeral_OSuc__code__numeral(_1311618) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (42697 ^ _776545) ^ [_1626736, _1626738, _1626740, _1626742, _1626744] : [-(hAPP(hAPP(c_List_Olist__update(_1626736, hAPP(hAPP(c_List_Olist__update(_1626736, _1626738), _1626740), _1626742)), _1626740), _1626744) = hAPP(hAPP(c_List_Olist__update(_1626736, _1626738), _1626740), _1626744))], (30184 ^ _776545) ^ [_1318013, _1318015, _1318017, _1318019] : [class_Orderings_Olinorder(_1318013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318013), _1318015), _1318017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318013), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318013), _1318015), _1318019)), _1318017)))], (36402 ^ _776545) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17215 ^ _776545) ^ [_1086454, _1086456, _1086458, _1086460] : [class_Rings_Olinordered__semidom(_1086454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086454), c_Groups_Ozero__class_Ozero(_1086454)), _1086456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086454), _1086458), _1086460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086454), _1086458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086454), _1086456), _1086460))))], (40681 ^ _776545) ^ [_1571276, _1571278, _1571280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571276, _1571276), tc_HOL_Obool)), _1571278), hAPP(hAPP(c_Product__Type_OSigma(_1571276, _1571276), _1571280), hAPP(c_COMBK(tc_fun(_1571276, tc_HOL_Obool), _1571276), _1571280)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571276, _1571276), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571276, _1571278)), hAPP(hAPP(c_Product__Type_OSigma(_1571276, _1571276), _1571280), hAPP(c_COMBK(tc_fun(_1571276, tc_HOL_Obool), _1571276), _1571280)))))], (13385 ^ _776545) ^ [_1014195, _1014197, _1014199, _1014201, _1014203] : [class_Groups_Ocomm__monoid__add(_1014195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014197), _1014199)), hBOOL(hAPP(hAPP(c_member(_1014197), _1014201), _1014199)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014197, _1014195), _1014203), _1014199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014195), hAPP(_1014203, _1014201)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014197, _1014195), _1014203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014197, tc_HOL_Obool)), _1014199), hAPP(hAPP(c_Set_Oinsert(_1014197), _1014201), c_Orderings_Obot__class_Obot(tc_fun(_1014197, tc_HOL_Obool)))))))], (7660 ^ _776545) ^ [_904003, _904005, _904007, _904009] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904003, tc_HOL_Obool)), _904005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904003, tc_HOL_Obool)), _904007), _904009)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904003, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904003, tc_HOL_Obool)), _904005), _904007)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904003, tc_HOL_Obool)), _904005), _904009)))], (7710 ^ _776545) ^ [_905451, _905453, _905455, _905457] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905451, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905451, tc_HOL_Obool)), _905453), _905455)), _905457) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905451, tc_HOL_Obool)), _905453), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905451, tc_HOL_Obool)), _905455), _905457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905451, tc_HOL_Obool)), _905457), _905453)))], (10072 ^ _776545) ^ [_948862, _948864, _948866, _948868] : [class_Orderings_Olinorder(_948862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948862), _948864), _948866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948862), _948866), _948868)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948862, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_948862, _948864, _948866)), c_SetInterval_Oord__class_OgreaterThanAtMost(_948862, _948866, _948868)) = c_SetInterval_Oord__class_OatLeastAtMost(_948862, _948864, _948868))], (27769 ^ _776545) ^ [_1275917, _1275919] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1275917), _1275919))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275917))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275919))))], (35662 ^ _776545) ^ [_1442249] : [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), _1442249))), -(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), _1442249)) = 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), _1442249))))], (29233 ^ _776545) ^ [_1300506, _1300508] : [class_Int_Onumber__ring(_1300506), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300506), hAPP(c_Int_Onumber__class_Onumber__of(_1300506), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1300508) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300506), _1300508), _1300508))], (38689 ^ _776545) ^ [_1520037, _1520039, _1520041, _1520043, _1520045] : [hBOOL(hAPP(hAPP(c_member(_1520037), hAPP(_1520039, _1520041)), _1520043)), -(hBOOL(hAPP(hAPP(c_member(_1520045), _1520041), hAPP(c_Set_Ovimage(_1520045, _1520037, _1520039), _1520043))))], (8309 ^ _776545) ^ [_918867, _918869, _918871] : [class_Lattices_Osemilattice__sup(_918867), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918867), _918869), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918867), _918869), _918871)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918867), _918869), _918871))], (44683 ^ _776545) ^ [_1669802, _1669804, _1669806] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669802)), _1669804), c_List_Olists(_1669802, _1669806)))), 44684 ^ _776545 : [(44687 ^ _776545) ^ [_1669930, _1669932] : [_1669804 = hAPP(hAPP(c_List_Olist_OCons(_1669802), _1669932), _1669930), hBOOL(hAPP(hAPP(c_member(_1669802), _1669932), _1669806)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669802)), _1669930), c_List_Olists(_1669802, _1669806)))], (44685 ^ _776545) ^ [] : [_1669804 = c_List_Olist_ONil(_1669802)]]], (7356 ^ _776545) ^ [_897044, _897046] : [class_Orderings_Olinorder(_897044), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897044, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897044), _897046), c_Orderings_Obot__class_Obot(tc_fun(_897044, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_897044), _897046)) = hAPP(c_SetInterval_Oord__class_OatLeast(_897044), _897046))], (29793 ^ _776545) ^ [] : [-(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))], (3540 ^ _776545) ^ [_829466, _829468, _829470, _829472, _829474, _829476] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_829476, _829472, _829468) = c_SetInterval_Oord__class_OgreaterThanAtMost(_829474, _829470, _829466)), _829476 = _829474, _829472 = _829470, _829468 = _829466], (34267 ^ _776545) ^ [_1414099, _1414101, _1414103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414099), _1414101)), -(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)), _1414099)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414103), _1414101)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414103), _1414099)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414101), _1414099)))], (15542 ^ _776545) ^ [_1058061, _1058063, _1058065, _1058067, _1058069] : [class_Groups_Ocomm__monoid__mult(_1058061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058063), _1058065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1058063, tc_HOL_Obool)), _1058067), _1058065)), 15556 ^ _776545 : [(15559 ^ _776545) ^ [] : [hAPP(_1058069, 15555 ^ [_1058061, _1058063, _1058065, _1058067, _1058069]) = c_Groups_Oone__class_Oone(_1058061)], (15557 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1058063), 15555 ^ [_1058061, _1058063, _1058065, _1058067, _1058069]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058063, tc_HOL_Obool)), _1058065), _1058067))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058063, _1058061), _1058069), _1058065) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1058063, _1058061), _1058069), _1058067))], (23617 ^ _776545) ^ [_1204560, _1204562] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1204560), _1204562)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204560)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204562))))], (36571 ^ _776545) ^ [_1469364, _1469366, _1469368, _1469370] : [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), _1469364), _1469366)), 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), _1469368), _1469370)), 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), _1469364), _1469370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469368), _1469366))))], (52213 ^ _776545) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (46994 ^ _776545) ^ [_1721125] : [-(hAPP(c_List_Orev(_1721125), c_List_Olist_ONil(_1721125)) = c_List_Olist_ONil(_1721125))], (24960 ^ _776545) ^ [_1228569, _1228571] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228569, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228571)) = 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), _1228569), _1228571)))], (35378 ^ _776545) ^ [_1436173, _1436175] : [-(_1436173 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436175, _1436173), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1436175), _1436173)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1436175, _1436173)))))], (7414 ^ _776545) ^ [_898445, _898447, _898449] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898445, tc_HOL_Obool)), _898447), _898449) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_898445, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898445, tc_HOL_Obool)), _898447), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898445, tc_HOL_Obool)), _898449), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_898445, tc_HOL_Obool), tc_HOL_Obool))))))], (25357 ^ _776545) ^ [_1235333] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235333))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11115 ^ _776545) ^ [_968808, _968810, _968812, _968814, _968816] : [-(hBOOL(hAPP(hAPP(c_member(_968808), _968810), hAPP(c_Set_Oimage(_968812, _968808, _968814), _968816)))), 11116 ^ _776545 : [(11117 ^ _776545) ^ [_968878] : [hBOOL(hAPP(hAPP(c_member(_968812), _968878), _968816)), _968810 = hAPP(_968814, _968878)]]], (20075 ^ _776545) ^ [_1138990, _1138992, _1138994] : [class_Fields_Olinordered__field__inverse__zero(_1138990), 20078 ^ _776545 : [(20093 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138990), _1138992), _1138994)))), 20094 ^ _776545 : [(20101 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), _1138992), c_Groups_Ozero__class_Ozero(_1138990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), _1138994), c_Groups_Ozero__class_Ozero(_1138990)))], (20095 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), _1138992)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), _1138994))]]], (20079 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138990), _1138992), _1138994))), 20084 ^ _776545 : [(20087 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), _1138994)))], (20085 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), c_Groups_Ozero__class_Ozero(_1138990)), _1138992)))]], 20088 ^ _776545 : [(20091 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), _1138994), c_Groups_Ozero__class_Ozero(_1138990))))], (20089 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138990), _1138992), c_Groups_Ozero__class_Ozero(_1138990))))]]]]], (21553 ^ _776545) ^ [_1166855, _1166857, _1166859, _1166861] : [class_Fields_Ofield__inverse__zero(_1166855), class_Int_Onumber(_1166855), 21560 ^ _776545 : [(21561 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166855), _1166857), hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859)) = _1166861, 21564 ^ _776545 : [(21571 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859) = c_Groups_Ozero__class_Ozero(_1166855), -(_1166861 = c_Groups_Ozero__class_Ozero(_1166855))], (21565 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859) = c_Groups_Ozero__class_Ozero(_1166855)), -(_1166857 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166855), _1166861), hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859)))]]], (21577 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166855), _1166857), hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859)) = _1166861), 21580 ^ _776545 : [(21583 ^ _776545) ^ [] : [_1166857 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166855), _1166861), hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859))], (21581 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859) = c_Groups_Ozero__class_Ozero(_1166855)]], 21584 ^ _776545 : [(21587 ^ _776545) ^ [] : [_1166861 = c_Groups_Ozero__class_Ozero(_1166855)], (21585 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1166855), _1166859) = c_Groups_Ozero__class_Ozero(_1166855))]]]]], (49574 ^ _776545) ^ [_1778335] : [-(c_Relation_Oantisym(_1778335, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1778335, _1778335), tc_HOL_Obool))))], (3174 ^ _776545) ^ [_823797, _823799, _823801, _823803] : [-(c_Big__Operators_Olattice__class_OSup__fin(_823803, _823799) = c_Big__Operators_Olattice__class_OSup__fin(_823801, _823797)), _823803 = _823801, _823799 = _823797], (6983 ^ _776545) ^ [_889995, _889997, _889999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889995, tc_HOL_Obool)), _889997), _889999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889995, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_889995), _889997)), hAPP(c_Set_OPow(_889995), _889999))))], (28951 ^ _776545) ^ [_1295549, _1295551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295549)), c_Int_OBit1(_1295551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295549), _1295551)))], (14815 ^ _776545) ^ [_1043669, _1043671, _1043673] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043669), _1043671)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043669), _1043673)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043671), _1043673))], (45577 ^ _776545) ^ [_1690425, _1690427, _1690429] : [-(c_Enum_Oproduct(_1690425, _1690427, c_List_Olist_ONil(_1690425), _1690429) = c_List_Olist_ONil(tc_prod(_1690425, _1690427)))], (28809 ^ _776545) ^ [_1293055] : [c_Int_OPls = _1293055, -(c_Int_OPls = c_Int_OBit0(_1293055))], (39173 ^ _776545) ^ [_1532489, _1532491, _1532493, _1532495, _1532497, _1532499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532489, _1532491)), hAPP(hAPP(c_Product__Type_OPair(_1532489, _1532491), _1532493), _1532495)), hAPP(hAPP(c_Product__Type_OSigma(_1532489, _1532491), _1532497), _1532499))), -(hBOOL(hAPP(hAPP(c_member(_1532489), _1532493), _1532497)))], (15234 ^ _776545) ^ [_1051513, _1051515] : [class_Rings_Ocomm__ring__1(_1051513), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1051513), _1051515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051513), hAPP(c_Groups_Ouminus__class_Ouminus(_1051513), c_Groups_Oone__class_Oone(_1051513))), _1051515))], (28927 ^ _776545) ^ [_1295115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295115)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295115), c_Int_OPls)))], (33433 ^ _776545) ^ [_1391094, _1391096, _1391098, _1391100, _1391102, _1391104] : [_1391094 = _1391096, -(hAPP(c_Fun_Ofun__upd(_1391098, _1391100, _1391102, _1391096, _1391104), _1391094) = _1391104)], (52289 ^ _776545) ^ [_1829074, _1829076] : [-(class_HOL_Oequal(tc_sum(_1829074, _1829076)))], (36980 ^ _776545) ^ [_1479122, _1479124] : [c_Equiv__Relations_Oequivp(_1479122, hAPP(hAPP(c_COMBC(_1479122, tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_fun(_1479122, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479122, tc_fun(tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_fun(_1479122, tc_HOL_Obool)), _1479122), c_COMBC(_1479122, tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479122, tc_prod(_1479122, _1479122)), tc_fun(_1479122, tc_fun(tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_HOL_Obool)), _1479122), hAPP(c_COMBB(tc_prod(_1479122, _1479122), tc_fun(tc_fun(tc_prod(_1479122, _1479122), tc_HOL_Obool), tc_HOL_Obool), _1479122), c_member(tc_prod(_1479122, _1479122)))), c_Product__Type_OPair(_1479122, _1479122)))), _1479124)), -(c_Equiv__Relations_Oequiv(_1479122, c_Orderings_Otop__class_Otop(tc_fun(_1479122, tc_HOL_Obool)), _1479124))], (11952 ^ _776545) ^ [_986377, _986379, _986381, _986383, _986385] : [c_Fun_Ofun__upd(_986377, _986379, _986381, _986383, _986385) = _986381, -(hAPP(_986381, _986383) = _986385)], (48780 ^ _776545) ^ [_1759774, _1759776, _1759778, _1759780] : [-(hAPP(c_New__DSequence_Opos__union(_1759774, _1759776, _1759778), _1759780) = c_Lazy__Sequence_Oappend(_1759774, hAPP(_1759776, _1759780), hAPP(_1759778, _1759780)))], (34713 ^ _776545) ^ [_1423493, _1423495, _1423497] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423493, _1423495, _1423497), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1423495)], (10635 ^ _776545) ^ [_959460] : [class_Lattices_Oboolean__algebra(_959460), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959460), c_Orderings_Otop__class_Otop(_959460)) = c_Orderings_Obot__class_Obot(_959460))], (33687 ^ _776545) ^ [_1399090, _1399092, _1399094, _1399096] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1399090), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399092, tc_Nat_Onat), _1399094), _1399096)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399092, _1399090), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1399090, _1399092), c_Nat_Osemiring__1__class_Oof__nat(_1399090)), _1399094)), _1399096)), class_Groups_Ocomm__monoid__mult(_1399090), class_Rings_Osemiring__1(_1399090)], (46528 ^ _776545) ^ [_1712166, _1712168, _1712170] : [class_Orderings_Olinorder(_1712166), c_List_Olinorder__class_Osorted(_1712166, _1712168), -(c_List_Olinorder__class_Osorted(_1712166, hAPP(hAPP(c_List_Odrop(_1712166), _1712170), _1712168)))], (43466 ^ _776545) ^ [_1643300, _1643302, _1643304, _1643306] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643300)), hAPP(hAPP(c_List_Oappend(_1643300), _1643302), _1643304)), c_List_Olists(_1643300, _1643306)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643300)), _1643302), c_List_Olists(_1643300, _1643306))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643300)), _1643304), c_List_Olists(_1643300, _1643306)))], (22185 ^ _776545) ^ [_1178904, _1178906] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178904), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1178906) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1178904, _1178906))], (16799 ^ _776545) ^ [_1078894, _1078896] : [class_Groups_Olinordered__ab__group__add(_1078894), 16802 ^ _776545 : [(16809 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078894), c_Groups_Ozero__class_Ozero(_1078894)), _1078896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078894), c_Groups_Ozero__class_Ozero(_1078894)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078894), _1078896), _1078896))))], (16803 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078894), c_Groups_Ozero__class_Ozero(_1078894)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078894), _1078896), _1078896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078894), c_Groups_Ozero__class_Ozero(_1078894)), _1078896)))]]], (12854 ^ _776545) ^ [_1003324, _1003326, _1003328] : [class_Lattices_Olattice(_1003324), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003324), _1003326)), -(c_Big__Operators_Olattice__class_OInf__fin(_1003324, hAPP(hAPP(c_Set_Oinsert(_1003324), _1003328), _1003326)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003324, _1003324, c_Lattices_Osemilattice__inf__class_Oinf(_1003324)), _1003328), _1003326))], (41923 ^ _776545) ^ [_1604902, _1604904, _1604906, _1604908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604902), tc_List_Olist(_1604902))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604902), tc_List_Olist(_1604902)), _1604904), _1604906)), c_List_Olistrel1(_1604902, hAPP(c_Relation_Oconverse(_1604902, _1604902), _1604908)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604902), tc_List_Olist(_1604902))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604902), tc_List_Olist(_1604902)), _1604904), _1604906)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1604902), tc_List_Olist(_1604902)), c_List_Olistrel1(_1604902, _1604908)))))], (30092 ^ _776545) ^ [_1316304, _1316306, _1316308] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1316304), _1316306)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1316308), _1316306)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1316304), _1316308)), _1316306))], (31823 ^ _776545) ^ [_1348305, _1348307, _1348309] : [class_Orderings_Olinorder(_1348305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348305), _1348307)), -(_1348307 = c_Orderings_Obot__class_Obot(tc_fun(_1348305, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348305), _1348309)), -(_1348309 = c_Orderings_Obot__class_Obot(tc_fun(_1348305, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1348305, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1348305, tc_HOL_Obool)), _1348307), _1348309)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348305), c_Big__Operators_Olinorder__class_OMax(_1348305, _1348307)), c_Big__Operators_Olinorder__class_OMax(_1348305, _1348309)))], (42137 ^ _776545) ^ [_1611507, _1611509, _1611511] : [c_Relation_Orefl__on(_1611507, _1611509, _1611511), -(c_Relation_Orefl__on(tc_List_Olist(_1611507), c_List_Olists(_1611507, _1611509), c_List_Olistrel(_1611507, _1611511)))], (27287 ^ _776545) ^ [_1267476, _1267478, _1267480] : [class_Rings_Olinordered__idom(_1267476), -(hAPP(c_Groups_Oabs__class_Oabs(_1267476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267476), _1267478), _1267480)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267476), hAPP(c_Groups_Oabs__class_Oabs(_1267476), _1267478)), hAPP(c_Groups_Oabs__class_Oabs(_1267476), _1267480)))], (39695 ^ _776545) ^ [_1547333] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547333, tc_HOL_Obool) = c_Set_OBall(_1547333))], (6476 ^ _776545) ^ [_881166, _881168] : [hBOOL(hAPP(hAPP(c_member(_881166), _881168), c_Orderings_Obot__class_Obot(tc_fun(_881166, tc_HOL_Obool))))], (10773 ^ _776545) ^ [_962102, _962104, _962106, _962108, _962110] : [class_Orderings_Olinorder(_962102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962102, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962102, _962104), _962106)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962102, _962108), _962110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962102), _962106), _962104))), 10784 ^ _776545 : [(10787 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962102), _962106), _962110)))], (10785 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962102), _962108), _962104)))]]], (28093 ^ _776545) ^ [_1281204] : [-(c_Int_Osucc(c_Int_Opred(_1281204)) = _1281204)], (28439 ^ _776545) ^ [_1286994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1286994)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1286994), c_Int_OMin)))], (48233 ^ _776545) ^ [_1748060, _1748062] : [-(c_FunDef_Ois__measure(_1748060, _1748062))], (50584 ^ _776545) ^ [_1799020, _1799022, _1799024] : [c_Fun_Obij__betw(_1799020, _1799022, _1799024, c_Orderings_Otop__class_Otop(tc_fun(_1799020, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799022, tc_HOL_Obool))), 50587 ^ _776545 : [(50590 ^ _776545) ^ [] : [-(hAPP(c_Set_Oimage(_1799020, _1799022, _1799024), c_Orderings_Otop__class_Otop(tc_fun(_1799020, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799022, tc_HOL_Obool)))], (50588 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1799020, _1799022, _1799024, c_Orderings_Otop__class_Otop(tc_fun(_1799020, tc_HOL_Obool))))]]], (23085 ^ _776545) ^ [_1194792] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1194792), _1194792)))], (316 ^ _776545) ^ [_781339, _781341] : [-(c_Nitpick_Ounknown(_781339)), _781341 = _781339, c_Nitpick_Ounknown(_781341)], (22809 ^ _776545) ^ [_1189728, _1189730, _1189732] : [class_Rings_Olinordered__semidom(_1189728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189728), c_Groups_Oone__class_Oone(_1189728)), _1189730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189728), c_Groups_Oone__class_Oone(_1189728)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189728), _1189730), hAPP(c_Nat_OSuc, _1189732)))))], (22215 ^ _776545) ^ [_1179460, _1179462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179460), _1179462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179460), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1179462)))], (28135 ^ _776545) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (34560 ^ _776545) ^ [_1420188, _1420190, _1420192, _1420194, _1420196, _1420198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420188, tc_fun(_1420190, tc_HOL_Obool))), _1420192), _1420194)), hBOOL(hAPP(hAPP(_1420192, _1420196), _1420198)), -(hBOOL(hAPP(hAPP(_1420194, _1420196), _1420198)))], (9590 ^ _776545) ^ [_941007, _941009, _941011] : [class_Orderings_Olinorder(_941007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941007), _941009), _941011)), 9597 ^ _776545 : [(9604 ^ _776545) ^ [] : [_941009 = _941011, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941007), _941009), _941011))], (9598 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941007), _941009), _941011))), -(_941009 = _941011)]]], (49718 ^ _776545) ^ [_1781426, _1781428] : [-(c_Relation_Osym(_1781426, c_Relation_OId__on(_1781426, _1781428)))], (6232 ^ _776545) ^ [_876702] : [class_Complete__Lattice_Ocomplete__lattice(_876702), -(c_Complete__Lattice_OInf__class_OInf(_876702, c_Orderings_Obot__class_Obot(tc_fun(_876702, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_876702))], (16428 ^ _776545) ^ [_1072651, _1072653, _1072655, _1072657, _1072659] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1072651, _1072653, _1072655), _1072657), _1072659), c_Orderings_Obot__class_Obot(tc_fun(_1072653, tc_HOL_Obool))) = _1072659)], (52215 ^ _776545) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (6853 ^ _776545) ^ [_887652, _887654, _887656] : [class_Orderings_Olinorder(_887652), 6856 ^ _776545 : [(6863 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887652), _887656), _887654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887652, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887652), _887654)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887652), _887656))))], (6857 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887652, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887652), _887654)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_887652), _887656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887652), _887656), _887654)))]]], (32882 ^ _776545) ^ [_1375764, _1375766, _1375768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375764, tc_HOL_Obool)), _1375766), _1375768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375764, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1375764, tc_fun(_1375764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375764)), _1375766)), hAPP(hAPP(c_COMBC(_1375764, tc_fun(_1375764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375764)), _1375768))))], (3372 ^ _776545) ^ [_826898, _826900, _826902, _826904] : [-(c_Product__Type_OSigma(_826904, _826900) = c_Product__Type_OSigma(_826902, _826898)), _826904 = _826902, _826900 = _826898], (32626 ^ _776545) ^ [_1368261, _1368263, _1368265, _1368267, _1368269] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368261, tc_fun(_1368263, tc_HOL_Obool)), _1368265), hAPP(hAPP(c_COMBB(tc_fun(_1368263, tc_HOL_Obool), tc_fun(_1368263, tc_HOL_Obool), _1368261), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368263, tc_HOL_Obool)), _1368267)), _1368269)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368263, tc_HOL_Obool)), _1368267), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368261, tc_fun(_1368263, tc_HOL_Obool)), _1368265), _1368269)))], (26735 ^ _776545) ^ [_1258880, _1258882] : [c_Nat__Transfer_Onat__set(_1258880), c_Nat__Transfer_Onat__set(_1258882), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258880), _1258882)))], (3528 ^ _776545) ^ [_829296, _829298] : [_829298 = _829296, -(c_Int_Onumber__class_Onumber__of(_829298) = c_Int_Onumber__class_Onumber__of(_829296))], (26072 ^ _776545) ^ [_1247822] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1247822))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1247822)) = _1247822)], (39665 ^ _776545) ^ [_1546462, _1546464, _1546466] : [-(c_Relation_Orefl__on(_1546462, _1546464, _1546466)), 39669 ^ _776545 : [(39672 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546462, _1546462, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546462, tc_fun(_1546462, tc_HOL_Obool), tc_fun(_1546462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546462, tc_HOL_Obool), tc_fun(_1546462, tc_HOL_Obool)), _1546462), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546462)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546462), c_fconj), hAPP(hAPP(c_COMBC(_1546462, tc_fun(_1546462, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546462)), _1546464)))), hAPP(hAPP(c_COMBC(_1546462, tc_fun(_1546462, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546462)), _1546464))), 39668 ^ [_1546462, _1546464, _1546466]))], (39670 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546462, _1546462)), 39668 ^ [_1546462, _1546464, _1546466]), _1546466)))]], 39674 ^ _776545 : [(39677 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546462, _1546462)), hAPP(hAPP(c_Product__Type_OPair(_1546462, _1546462), 39673 ^ [_1546462, _1546464, _1546466]), 39673 ^ [_1546462, _1546464, _1546466])), _1546466))], (39675 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546462), 39673 ^ [_1546462, _1546464, _1546466]), _1546464)))]]], (28743 ^ _776545) ^ [_1291815, _1291817] : [-(_1291815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1291817, _1291815) = c_Nitpick_Onat__gcd(_1291815, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291817, _1291815)))], (23641 ^ _776545) ^ [_1205007, _1205009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205009)), -(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), _1205007), _1205009))))], (10789 ^ _776545) ^ [_962383, _962385, _962387, _962389] : [class_Orderings_Olinorder(_962383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962383), _962385), _962387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962383), _962387), _962389)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962383, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962383, _962385), _962387)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962383, _962387), _962389)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962383, _962385), _962389))], (30678 ^ _776545) ^ [_1326919, _1326921] : [class_Orderings_Olinorder(_1326919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326919), _1326921)), -(c_Big__Operators_Olinorder__class_OMin(_1326919, _1326921) = hAPP(c_Finite__Set_Ofold1(_1326919, c_Orderings_Oord__class_Omin(_1326919)), _1326921))], (27563 ^ _776545) ^ [_1272358, _1272360, _1272362] : [class_Rings_Olinordered__idom(_1272358), -(hAPP(c_Groups_Oabs__class_Oabs(_1272358), hAPP(hAPP(c_Power_Opower__class_Opower(_1272358), hAPP(c_Groups_Ouminus__class_Ouminus(_1272358), _1272360)), _1272362)) = hAPP(c_Groups_Oabs__class_Oabs(_1272358), hAPP(hAPP(c_Power_Opower__class_Opower(_1272358), _1272360), _1272362)))], (47353 ^ _776545) ^ [_1728637, _1728639, _1728641] : [hBOOL(hAPP(c_List_Odistinct(_1728637), _1728639)), hBOOL(hAPP(hAPP(c_member(_1728637), _1728641), hAPP(c_List_Oset(_1728637), _1728639))), -(c_List_OdropWhile(_1728637, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728637), c_fNot), hAPP(hAPP(c_COMBC(_1728637, _1728637, tc_HOL_Obool), c_fequal), _1728641)), hAPP(c_List_Orev(_1728637), _1728639)) = hAPP(hAPP(c_List_Olist_OCons(_1728637), _1728641), hAPP(c_List_Orev(_1728637), c_List_OtakeWhile(_1728637, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728637), c_fNot), hAPP(hAPP(c_COMBC(_1728637, _1728637, tc_HOL_Obool), c_fequal), _1728641)), _1728639))))], (36410 ^ _776545) ^ [_1464183, _1464185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1464183), _1464185)), -(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), _1464183), _1464185)), c_Wellfounded_Oless__than)))], (32029 ^ _776545) ^ [_1352037, _1352039, _1352041] : [class_Orderings_Olinorder(_1352037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352037), _1352039)), -(_1352041 = c_Orderings_Obot__class_Obot(tc_fun(_1352037, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352037, tc_HOL_Obool)), _1352041), _1352039)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352037), c_Big__Operators_Olattice_OSup__fin(_1352037, c_Orderings_Oord__class_Omax(_1352037), _1352041)), c_Big__Operators_Olattice_OSup__fin(_1352037, c_Orderings_Oord__class_Omax(_1352037), _1352039)) = c_Big__Operators_Olattice_OSup__fin(_1352037, c_Orderings_Oord__class_Omax(_1352037), _1352039))], (43142 ^ _776545) ^ [_1636042, _1636044, _1636046] : [-(hAPP(hAPP(c_List_Olist__update(_1636042, c_List_Olist_ONil(_1636042)), _1636044), _1636046) = c_List_Olist_ONil(_1636042))], (4334 ^ _776545) ^ [_842185, _842187] : [_842187 = _842185, -(c_Set_Oinsert(_842187) = c_Set_Oinsert(_842185))], (37432 ^ _776545) ^ [_1488924, _1488926, _1488928, _1488930] : [c_Fun_Oinj__on(_1488924, _1488926, _1488928, c_Orderings_Otop__class_Otop(tc_fun(_1488924, tc_HOL_Obool))), 37435 ^ _776545 : [(37449 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488926), _1488930), hAPP(c_Set_Oimage(_1488924, _1488926, _1488928), c_Orderings_Otop__class_Otop(tc_fun(_1488924, tc_HOL_Obool)))))), 37450 ^ _776545 : [(37451 ^ _776545) ^ [_1489327] : [_1488930 = hAPP(_1488928, _1489327), 37455 ^ _776545 : [(37458 ^ _776545) ^ [] : [37454 ^ [_1488924, _1488926, _1488928, _1488930, _1489327] = _1489327], (37456 ^ _776545) ^ [] : [-(_1488930 = hAPP(_1488928, 37454 ^ [_1488924, _1488926, _1488928, _1488930, _1489327]))]]]]], (37436 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1488926), _1488930), hAPP(c_Set_Oimage(_1488924, _1488926, _1488928), c_Orderings_Otop__class_Otop(tc_fun(_1488924, tc_HOL_Obool))))), 37440 ^ _776545 : [(37443 ^ _776545) ^ [_1489189] : [_1488930 = hAPP(_1488928, _1489189), -(_1489189 = 37439 ^ [_1488924, _1488926, _1488928, _1488930])], (37441 ^ _776545) ^ [] : [-(_1488930 = hAPP(_1488928, 37439 ^ [_1488924, _1488926, _1488928, _1488930]))]]]]], (44429 ^ _776545) ^ [_1665073, _1665075, _1665077] : [class_Lattices_Olattice(_1665073), -(c_Big__Operators_Olattice__class_OInf__fin(_1665073, hAPP(c_List_Oset(_1665073), hAPP(hAPP(c_List_Olist_OCons(_1665073), _1665075), _1665077))) = hAPP(c_List_Ofoldl(_1665073, _1665073, c_Lattices_Osemilattice__inf__class_Oinf(_1665073), _1665075), _1665077))], (37680 ^ _776545) ^ [_1494044, _1494046, _1494048, _1494050, _1494052] : [c_Fun_Oinj__on(_1494044, _1494046, _1494048, hAPP(hAPP(c_Set_Oinsert(_1494044), _1494050), _1494052)), 37683 ^ _776545 : [(37686 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1494046), hAPP(_1494048, _1494050)), hAPP(c_Set_Oimage(_1494044, _1494046, _1494048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494044, tc_HOL_Obool)), _1494052), hAPP(hAPP(c_Set_Oinsert(_1494044), _1494050), c_Orderings_Obot__class_Obot(tc_fun(_1494044, tc_HOL_Obool)))))))], (37684 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1494044, _1494046, _1494048, _1494052))]]], (6037 ^ _776545) ^ [_872956, _872958, _872960, _872962] : [hBOOL(hAPP(hAPP(_872960, _872962), _872958)), -(hBOOL(hAPP(hAPP(c_member(_872956), _872958), c_SetInterval_Oord_OgreaterThan(_872956, _872960, _872962))))], (11078 ^ _776545) ^ [_968152, _968154, _968156] : [class_Rings_Oring(_968152), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968152), hAPP(c_Groups_Ouminus__class_Ouminus(_968152), _968154)), hAPP(c_Groups_Ouminus__class_Ouminus(_968152), _968156)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968152), _968154), _968156))], (19436 ^ _776545) ^ [_1127392, _1127394, _1127396, _1127398, _1127400] : [class_Fields_Ofield(_1127392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127394), _1127396)), -(hAPP(_1127398, _1127400) = c_Groups_Ozero__class_Ozero(_1127392)), 19447 ^ _776545 : [(19454 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1127394), _1127400), _1127396))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127394, _1127392), _1127398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127394, tc_HOL_Obool)), _1127396), hAPP(hAPP(c_Set_Oinsert(_1127394), _1127400), c_Orderings_Obot__class_Obot(tc_fun(_1127394, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127394, _1127392), _1127398), _1127396))], (19448 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1127394), _1127400), _1127396)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127394, _1127392), _1127398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127394, tc_HOL_Obool)), _1127396), hAPP(hAPP(c_Set_Oinsert(_1127394), _1127400), c_Orderings_Obot__class_Obot(tc_fun(_1127394, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127392), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1127394, _1127392), _1127398), _1127396)), hAPP(_1127398, _1127400)))]]], (30126 ^ _776545) ^ [_1317014, _1317016, _1317018, _1317020] : [class_Orderings_Olinorder(_1317014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317014), _1317016), _1317018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317014), _1317016), _1317020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317014), _1317016), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317014), _1317018), _1317020))))], (33082 ^ _776545) ^ [_1381212, _1381214, _1381216, _1381218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1381212, _1381214)), hAPP(hAPP(c_Product__Type_OPair(_1381212, _1381214), _1381216), _1381218)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1381212, _1381214), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381212, tc_fun(_1381214, tc_HOL_Obool))), _1381216), _1381218)))], (30082 ^ _776545) ^ [_1316175] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1316175) = c_Orderings_Oord__class_Omin(_1316175)), class_Lattices_Osemilattice__inf(_1316175), class_Orderings_Olinorder(_1316175)], (40617 ^ _776545) ^ [_1569718, _1569720] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569718, _1569718)), c_Transitive__Closure_Otrancl(_1569718, _1569720))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569718, _1569718)), _1569720)))], (14104 ^ _776545) ^ [_1029609, _1029611, _1029613, _1029615, _1029617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029609), _1029611)), 14107 ^ _776545 : [(14114 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029615), 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), _1029611), _1029609)), _1029613)), _1029617))), -(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), _1029609), _1029613)), _1029615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029611), _1029613)), _1029617))))], (14108 ^ _776545) ^ [] : [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), _1029609), _1029613)), _1029615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029611), _1029613)), _1029617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029615), 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), _1029611), _1029609)), _1029613)), _1029617))))]]], (49458 ^ _776545) ^ [_1776376, _1776378] : [-(c_Equiv__Relations_Oequivp(_1776376, _1776378)), c_Predicate_Oreflp(_1776376, _1776378), c_Predicate_Osymp(_1776376, _1776378), c_Predicate_Otransp(_1776376, _1776378)], (7800 ^ _776545) ^ [_907669, _907671, _907673, _907675] : [-(hBOOL(hAPP(hAPP(c_member(_907669), _907671), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907669, tc_HOL_Obool)), _907673), _907675)))), hBOOL(hAPP(hAPP(c_member(_907669), _907671), _907673)), hBOOL(hAPP(hAPP(c_member(_907669), _907671), _907675))], (34301 ^ _776545) ^ [_1414740, _1414742, _1414744, _1414746] : [class_Rings_Ocomm__semiring__1(_1414740), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414740), c_Groups_Oone__class_Oone(_1414740)), c_Groups_Oone__class_Oone(_1414740))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1414740), hAPP(hAPP(c_COMBB(_1414740, _1414740, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1414740), _1414742)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1414740, _1414740), hAPP(hAPP(c_COMBB(_1414740, tc_fun(_1414740, _1414740), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1414740)), c_Nat_Osemiring__1__class_Oof__nat(_1414740))), _1414744))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1414746))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414740), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1414740), _1414746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414740), _1414742), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414740), _1414742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414740), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1414740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414746), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1414744)))))], (38773 ^ _776545) ^ [_1522068, _1522070, _1522072, _1522074] : [-(hBOOL(hAPP(hAPP(c_member(_1522068), _1522070), _1522072))), -(hAPP(c_Set_Ovimage(_1522074, _1522068, hAPP(c_COMBK(_1522068, _1522074), _1522070)), _1522072) = c_Orderings_Obot__class_Obot(tc_fun(_1522074, tc_HOL_Obool)))], (29799 ^ _776545) ^ [_1310832] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1310832)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1310832)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14616 ^ _776545) ^ [_1040115, _1040117, _1040119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040115), _1040117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040115), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040117), _1040119))))], (46265 ^ _776545) ^ [_1707281] : [-(c_List_Oupt(_1707281, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (18234 ^ _776545) ^ [_1104423, _1104425, _1104427, _1104429] : [class_Groups_Oordered__comm__monoid__add(_1104423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104423), c_Groups_Ozero__class_Ozero(_1104423)), _1104425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104423), _1104427), _1104429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104423), _1104427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104423), _1104425), _1104429))))], (47585 ^ _776545) ^ [_1733543, _1733545, _1733547] : [-(hBOOL(hAPP(hAPP(c_member(_1733543), _1733545), hAPP(c_List_Oset(_1733543), _1733547)))), -(c_List_Oinsert(_1733543, _1733545, _1733547) = hAPP(hAPP(c_List_Olist_OCons(_1733543), _1733545), _1733547))], (3882 ^ _776545) ^ [_834867, _834869] : [_834869 = _834867, -(c_Enum_Oenum__class_Oenum__all(_834869) = c_Enum_Oenum__class_Oenum__all(_834867))], (27843 ^ _776545) ^ [_1277138, _1277140] : [27844 ^ _776545 : [(27847 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277138), c_Int_OPls))], (27845 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1277138), _1277140))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277138)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1277140))))], (9780 ^ _776545) ^ [_944062, _944064, _944066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944062, tc_HOL_Obool)), _944064), _944066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944062, tc_HOL_Obool)), _944064), _944066)))], (46079 ^ _776545) ^ [_1702034, _1702036, _1702038, _1702040] : [-(hAPP(c_List_Ofilter(_1702034, _1702036), hAPP(c_List_Ofilter(_1702034, _1702038), _1702040)) = hAPP(c_List_Ofilter(_1702034, hAPP(hAPP(c_COMBS(_1702034, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1702034), c_fconj), _1702038)), _1702036)), _1702040))], (40401 ^ _776545) ^ [_1564227, _1564229, _1564231, _1564233] : [-(c_Hilbert__Choice_OEps(tc_prod(_1564227, _1564229), hAPP(c_Product__Type_Oprod_Oprod__case(_1564227, _1564229, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1564227, tc_fun(_1564229, tc_HOL_Obool), tc_fun(_1564229, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1564229, tc_HOL_Obool), tc_fun(_1564229, tc_HOL_Obool)), _1564227), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564229)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564227), c_fconj), hAPP(c_fequal, _1564231)))), hAPP(c_fequal, _1564233)))) = hAPP(hAPP(c_Product__Type_OPair(_1564227, _1564229), _1564231), _1564233))], (47613 ^ _776545) ^ [_1734046, _1734048, _1734050] : [-(c_List_Omaps(_1734046, _1734048, _1734050, c_List_Olist_ONil(_1734046)) = c_List_Olist_ONil(_1734048))], (9849 ^ _776545) ^ [_945291, _945293, _945295] : [class_Complete__Lattice_Ocomplete__lattice(_945291), class_Orderings_Olinorder(_945291), 9856 ^ _776545 : [(9866 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945291), c_Complete__Lattice_OInf__class_OInf(_945291, _945293)), _945295))), 9867 ^ _776545 : [(9868 ^ _776545) ^ [_945597] : [hBOOL(hAPP(hAPP(c_member(_945291), _945597), _945293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945291), _945597), _945295))]]], (9857 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945291), c_Complete__Lattice_OInf__class_OInf(_945291, _945293)), _945295)), 9861 ^ _776545 : [(9864 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945291), 9860 ^ [_945291, _945293, _945295]), _945295)))], (9862 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945291), 9860 ^ [_945291, _945293, _945295]), _945293)))]]]]], (27587 ^ _776545) ^ [_1272772, _1272774] : [class_Int_Onumber__ring(_1272772), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272772), hAPP(c_Int_Onumber__class_Onumber__of(_1272772), c_Int_OPls)), _1272774) = _1272774)], (32797 ^ _776545) ^ [_1372611, _1372613, _1372615, _1372617, _1372619] : [class_Complete__Lattice_Ocomplete__lattice(_1372611), 32800 ^ _776545 : [(32801 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372611), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372613, _1372611), _1372615), _1372617)), _1372619)), 32804 ^ _776545 : [(32805 ^ _776545) ^ [_1372792] : [hBOOL(hAPP(hAPP(c_member(_1372613), _1372792), _1372615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372611), hAPP(_1372617, _1372792)), _1372619)))]]], (32811 ^ _776545) ^ [] : [32813 ^ _776545 : [(32816 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372611), hAPP(_1372617, 32812 ^ [_1372611, _1372613, _1372615, _1372617, _1372619])), _1372619))], (32814 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372613), 32812 ^ [_1372611, _1372613, _1372615, _1372617, _1372619]), _1372615)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372611), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1372613, _1372611), _1372615), _1372617)), _1372619)))]]], (10571 ^ _776545) ^ [_958324, _958326, _958328, _958330, _958332] : [class_Orderings_Olinorder(_958324), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958324, _958326), _958328) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958324, _958330), _958332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958324), _958326), _958328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958324), _958330), _958332)), -(_958326 = _958330)], (7960 ^ _776545) ^ [_911162, _911164, _911166, _911168, _911170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911162, tc_HOL_Obool)), _911164), _911166)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911162, tc_HOL_Obool)), _911168), _911170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911162, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911162, tc_HOL_Obool)), _911164), _911168)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911162, tc_HOL_Obool)), _911166), _911170))))], (42833 ^ _776545) ^ [_1629899, _1629901, _1629903, _1629905] : [hBOOL(hAPP(c_List_Odistinct(_1629899), _1629901)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1629899, _1629903)), hAPP(hAPP(c_List_Ozip(_1629899, _1629903), _1629901), _1629905))))], (1224 ^ _776545) ^ [_794709, _794711] : [-(class_Rings_Ocomm__ring__1(_794709)), _794711 = _794709, class_Rings_Ocomm__ring__1(_794711)], (47760 ^ _776545) ^ [_1737694, _1737696] : [class_Enum_Oenum(_1737694), 47763 ^ _776545 : [(47771 ^ _776545) ^ [] : [47772 ^ _776545 : [(47773 ^ _776545) ^ [_1737874] : [hBOOL(hAPP(_1737696, _1737874))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737694), _1737696)))], (47764 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737694), _1737696)), -(hBOOL(hAPP(_1737696, 47767 ^ [_1737694, _1737696])))]]], (45790 ^ _776545) ^ [_1695274, _1695276] : [-(c_List_Oremdups(_1695274, c_List_Oremdups(_1695274, _1695276)) = c_List_Oremdups(_1695274, _1695276))], (6644 ^ _776545) ^ [_884094, _884096, _884098, _884100] : [class_Orderings_Opreorder(_884094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884094), _884096), _884098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884094), _884098), _884100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884094), _884096), _884100)))], (22491 ^ _776545) ^ [_1184029, _1184031, _1184033, _1184035] : [class_Groups_Ocomm__monoid__mult(_1184029), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184029), _1184031), _1184033)), _1184035) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184029), hAPP(hAPP(c_Power_Opower__class_Opower(_1184029), _1184031), _1184035)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184029), _1184033), _1184035)))], (42622 ^ _776545) ^ [_1625103, _1625105, _1625107] : [class_Groups_Omonoid__add(_1625103), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1625103), hAPP(hAPP(c_List_Olist_OCons(_1625103), _1625105), _1625107)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1625103), _1625105), hAPP(c_List_Omonoid__add__class_Olistsum(_1625103), _1625107)))], (39575 ^ _776545) ^ [_1544093, _1544095, _1544097, _1544099, _1544101] : [c_Relation_Orefl__on(_1544093, _1544095, _1544097), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544093, _1544093)), hAPP(hAPP(c_Product__Type_OPair(_1544093, _1544093), _1544099), _1544101)), _1544097)), -(hBOOL(hAPP(hAPP(c_member(_1544093), _1544101), _1544095)))], (11662 ^ _776545) ^ [_980558, _980560, _980562] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980558, tc_HOL_Obool)), _980560), _980562)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_980558), _980560)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980558), _980562))], (23629 ^ _776545) ^ [_1204791, _1204793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1204791), _1204793)), -(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)), _1204791)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204793))))], (27265 ^ _776545) ^ [_1267021, _1267023, _1267025] : [class_Groups_Oordered__ab__group__add__abs(_1267021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267021), hAPP(c_Groups_Oabs__class_Oabs(_1267021), _1267023)), _1267025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267021), _1267023), _1267025)))], (44238 ^ _776545) ^ [_1661124, _1661126, _1661128] : [-(hAPP(c_List_Orotate(_1661124, _1661126), _1661128) = hAPP(hAPP(c_List_Oappend(_1661124), hAPP(hAPP(c_List_Odrop(_1661124), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1661126, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661124)), _1661128))), _1661128)), hAPP(hAPP(c_List_Otake(_1661124), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1661126, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661124)), _1661128))), _1661128)))], (52029 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (32684 ^ _776545) ^ [_1370262, _1370264, _1370266] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1370262), _1370264), _1370266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1370262), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370262, tc_Int_Oint), _1370264), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1370266))), class_Groups_Ocomm__monoid__add(_1370262), class_Groups_Ocomm__monoid__mult(_1370262)], (45343 ^ _776545) ^ [_1685209, _1685211, _1685213, _1685215] : [-(hBOOL(hAPP(c_List_Olistsp(_1685209, _1685211), hAPP(hAPP(c_List_Olist_OCons(_1685209), _1685213), _1685215)))), hBOOL(hAPP(_1685211, _1685213)), hBOOL(hAPP(c_List_Olistsp(_1685209, _1685211), _1685215))], (14510 ^ _776545) ^ [_1038342, _1038344] : [-(_1038342 = _1038344), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038342), _1038344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038344), _1038342)))], (39553 ^ _776545) ^ [_1543662] : [-(c_Relation_Orefl__on(_1543662, c_Orderings_Obot__class_Obot(tc_fun(_1543662, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543662, _1543662), tc_HOL_Obool))))], (42053 ^ _776545) ^ [_1608876, _1608878, _1608880, _1608882] : [c_List_Olistrelp(_1608876, hAPP(hAPP(c_COMBC(_1608876, tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_fun(_1608876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608876, tc_fun(tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_fun(_1608876, tc_HOL_Obool)), _1608876), c_COMBC(_1608876, tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1608876, tc_prod(_1608876, _1608876)), tc_fun(_1608876, tc_fun(tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_HOL_Obool)), _1608876), hAPP(c_COMBB(tc_prod(_1608876, _1608876), tc_fun(tc_fun(tc_prod(_1608876, _1608876), tc_HOL_Obool), tc_HOL_Obool), _1608876), c_member(tc_prod(_1608876, _1608876)))), c_Product__Type_OPair(_1608876, _1608876)))), _1608878), _1608880, _1608882), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608876), tc_List_Olist(_1608876))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608876), tc_List_Olist(_1608876)), _1608880), _1608882)), c_List_Olistrel(_1608876, _1608878))))], (35503 ^ _776545) ^ [_1439001, _1439003] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439001, _1439003) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1439001, _1439003)))], (22723 ^ _776545) ^ [_1188167, _1188169, _1188171, _1188173] : [class_Rings_Olinordered__semidom(_1188167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188167), hAPP(hAPP(c_Power_Opower__class_Opower(_1188167), _1188169), _1188171)), hAPP(hAPP(c_Power_Opower__class_Opower(_1188167), _1188173), _1188171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188167), c_Groups_Ozero__class_Ozero(_1188167)), _1188173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188167), _1188169), _1188173)))], (26384 ^ _776545) ^ [_1252713, _1252715] : [26385 ^ _776545 : [(26388 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252715))], (26386 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252713))]], 26389 ^ _776545 : [(26396 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252713), _1252715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1252713)), hAPP(c_Int_Onat, _1252715))))], (26390 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1252713)), hAPP(c_Int_Onat, _1252715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252713), _1252715)))]]], (32638 ^ _776545) ^ [_1368952, _1368954, _1368956, _1368958, _1368960] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368952, tc_fun(_1368954, tc_HOL_Obool)), _1368956), hAPP(hAPP(c_COMBS(_1368952, tc_fun(_1368954, tc_HOL_Obool), tc_fun(_1368954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368954, tc_HOL_Obool), tc_fun(tc_fun(_1368954, tc_HOL_Obool), tc_fun(_1368954, tc_HOL_Obool)), _1368952), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368954, tc_HOL_Obool))), _1368958)), _1368960)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368954, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368952, tc_fun(_1368954, tc_HOL_Obool)), _1368956), _1368958)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1368952, tc_fun(_1368954, tc_HOL_Obool)), _1368956), _1368960)))], (33423 ^ _776545) ^ [_1390626, _1390628, _1390630, _1390632, _1390634, _1390636] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390626, tc_fun(_1390628, tc_HOL_Obool)), _1390630), hAPP(hAPP(c_COMBC(_1390626, tc_fun(_1390632, tc_fun(_1390628, tc_HOL_Obool)), tc_fun(_1390628, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390632, tc_HOL_Obool), tc_fun(tc_fun(_1390632, tc_fun(_1390628, tc_HOL_Obool)), tc_fun(_1390628, tc_HOL_Obool)), _1390626), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390632, tc_fun(_1390628, tc_HOL_Obool))), _1390634)), _1390636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390632, tc_fun(_1390628, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390626, tc_fun(_1390632, tc_HOL_Obool)), _1390630), _1390634)), _1390636))], (16695 ^ _776545) ^ [_1076858, _1076860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076858), _1076860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076858), hAPP(c_Nat_OSuc, _1076860))))], (27138 ^ _776545) ^ [_1265081, _1265083] : [class_Rings_Oring__1(_1265081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265083)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1265081), hAPP(c_Int_Onat, _1265083)) = hAPP(c_Int_Oring__1__class_Oof__int(_1265081), _1265083))], (31735 ^ _776545) ^ [_1346679, _1346681, _1346683, _1346685, _1346687] : [class_Orderings_Olinorder(_1346679), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346679, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1346679, _1346681, _1346683)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1346679, _1346685, _1346687)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1346679, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346679), _1346681), _1346685), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346679), _1346683), _1346687)))], (50435 ^ _776545) ^ [_1796230, _1796232, _1796234, _1796236, _1796238] : [-(c_Fun_Obij__betw(_1796230, _1796232, _1796234, _1796236, _1796238)), c_Fun_Oinj__on(_1796230, _1796232, _1796234, _1796236), hAPP(c_Set_Oimage(_1796230, _1796232, _1796234), _1796236) = _1796238], (4770 ^ _776545) ^ [_849143, _849145, _849147, _849149, _849151, _849153] : [-(c_Relation_OImage(_849153, _849149, _849145) = c_Relation_OImage(_849151, _849147, _849143)), _849153 = _849151, _849149 = _849147, _849145 = _849143], (24565 ^ _776545) ^ [_1220903, _1220905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220903), _1220905)), -(c_Nat__Transfer_Otsub(_1220905, _1220903) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220905), _1220903))], (28731 ^ _776545) ^ [_1291606, _1291608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1291606)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1291608)), _1291606) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1291608), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1291606), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (14817 ^ _776545) ^ [_1043720, _1043722, _1043724] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043720), _1043722)), _1043724) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043722), _1043724)))], (48061 ^ _776545) ^ [_1744579, _1744581, _1744583] : [hBOOL(hAPP(hAPP(c_member(_1744579), _1744581), hAPP(c_List_Oset(_1744579), _1744583))), -(_1744583 = hAPP(hAPP(c_List_Oappend(_1744579), 48064 ^ [_1744579, _1744581, _1744583]), hAPP(hAPP(c_List_Olist_OCons(_1744579), _1744581), 48065 ^ [_1744579, _1744581, _1744583])))], (50095 ^ _776545) ^ [_1788552, _1788554, _1788556, _1788558] : [c_Fun_Oinj__on(_1788552, _1788554, _1788556, c_Orderings_Otop__class_Otop(tc_fun(_1788552, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1788552, _1788554, c_Orderings_Otop__class_Otop(tc_fun(_1788552, tc_HOL_Obool)), _1788556), hAPP(_1788556, _1788558)) = _1788558)], (25279 ^ _776545) ^ [_1234125, _1234127] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234125, _1234127) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234125, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234127)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44954 ^ _776545) ^ [_1676682, _1676684, _1676686] : [c_Fun_Oinj__on(tc_List_Olist(_1676682), tc_List_Olist(_1676684), hAPP(c_List_Omap(_1676682, _1676684), _1676686), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676682), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1676682, _1676684, _1676686, c_Orderings_Otop__class_Otop(tc_fun(_1676682, tc_HOL_Obool))))], (31693 ^ _776545) ^ [_1345732, _1345734, _1345736, _1345738] : [class_Orderings_Olinorder(_1345732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345732), _1345734)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1345732, _1345732, c_Orderings_Oord__class_Omax(_1345732)), _1345736), hAPP(hAPP(c_Set_Oinsert(_1345732), _1345738), _1345734)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345732), _1345738), hAPP(hAPP(c_Finite__Set_Ofold(_1345732, _1345732, c_Orderings_Oord__class_Omax(_1345732)), _1345736), _1345734)))], (34998 ^ _776545) ^ [_1429543, _1429545, _1429547, _1429549, _1429551] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429543, _1429545), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1429547), _1429549))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429545)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429551), _1429543), _1429545), 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), _1429551), _1429547)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429551), _1429549)), _1429545))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429551), _1429549), _1429545)))))], (36633 ^ _776545) ^ [_1471053, _1471055, _1471057] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471053), _1471055), _1471057) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471053, tc_HOL_Obool), tc_HOL_Obool)), -(_1471055 = c_Orderings_Obot__class_Obot(tc_fun(_1471053, tc_HOL_Obool)))], (38007 ^ _776545) ^ [_1502749, _1502751, _1502753] : [38009 ^ _776545 : [(38012 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1502749), 38008 ^ [_1502749, _1502751, _1502753]), c_Wellfounded_Oacc(_1502749, _1502753)))], (38010 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1502749, _1502749)), hAPP(hAPP(c_Product__Type_OPair(_1502749, _1502749), 38008 ^ [_1502749, _1502751, _1502753]), _1502751)), _1502753)))]], -(hBOOL(hAPP(hAPP(c_member(_1502749), _1502751), c_Wellfounded_Oacc(_1502749, _1502753))))], (43972 ^ _776545) ^ [_1655380, _1655382, _1655384, _1655386] : [-(hAPP(hAPP(c_List_Oappend(_1655380), _1655382), _1655384) = _1655386), _1655382 = hAPP(hAPP(c_List_Otake(_1655380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655380)), _1655382)), _1655386), _1655384 = hAPP(hAPP(c_List_Odrop(_1655380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655380)), _1655382)), _1655386)], (51529 ^ _776545) ^ [_1819212, _1819214, _1819216, _1819218] : [class_Divides_Osemiring__div(_1819212), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819212), _1819214), _1819216)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1819212), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819212), _1819216), _1819214)), _1819218) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819212), hAPP(hAPP(c_Power_Opower__class_Opower(_1819212), _1819216), _1819218)), hAPP(hAPP(c_Power_Opower__class_Opower(_1819212), _1819214), _1819218)))], (40520 ^ _776545) ^ [_1567306, _1567308, _1567310, _1567312, _1567314] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567306, _1567308, _1567306, _1567310), hAPP(c_Product__Type_OPair(_1567308, _1567306), _1567312)), _1567314) = hAPP(_1567314, _1567312))], (38132 ^ _776545) ^ [_1506826, _1506828] : [c_Wellfounded_Owf(_1506826, hAPP(hAPP(c_Relation_Orel__comp(_1506826, _1506826, _1506826), _1506828), _1506828)), -(c_Wellfounded_Owf(_1506826, _1506828))], (46231 ^ _776545) ^ [_1706310, _1706312, _1706314, _1706316, _1706318, _1706320] : [-(c_List_Ofoldr(_1706310, _1706312, _1706314, hAPP(hAPP(c_List_Olist_OCons(_1706310), _1706316), _1706318), _1706320) = hAPP(hAPP(_1706314, _1706316), c_List_Ofoldr(_1706310, _1706312, _1706314, _1706318, _1706320)))], (10046 ^ _776545) ^ [_948440, _948442] : [class_Orderings_Oorder(_948440), -(c_SetInterval_Oord__class_OatLeastAtMost(_948440, _948442, _948442) = hAPP(hAPP(c_Set_Oinsert(_948440), _948442), c_Orderings_Obot__class_Obot(tc_fun(_948440, tc_HOL_Obool))))], (44302 ^ _776545) ^ [_1662449, _1662451, _1662453, _1662455] : [class_Orderings_Olinorder(_1662449), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662449, _1662449, c_COMBI(_1662449)), _1662451), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662449, _1662449, c_COMBI(_1662449)), _1662453), _1662455)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662449, _1662449, c_COMBI(_1662449)), _1662453), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662449, _1662449, c_COMBI(_1662449)), _1662451), _1662455)))], (39339 ^ _776545) ^ [_1538176, _1538178] : [-(hAPP(c_Set_Ovimage(_1538176, _1538176, c_Fun_Oid(_1538176)), _1538178) = _1538178)], (7023 ^ _776545) ^ [_890725] : [-(hAPP(c_Set_OPow(_890725), c_Orderings_Obot__class_Obot(tc_fun(_890725, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_890725, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_890725, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_890725, tc_HOL_Obool), tc_HOL_Obool))))], (52457 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (10387 ^ _776545) ^ [_954932, _954934, _954936] : [class_Groups_Oordered__ab__group__add(_954932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954932), _954934), _954936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954932), hAPP(c_Groups_Ouminus__class_Ouminus(_954932), _954936)), hAPP(c_Groups_Ouminus__class_Ouminus(_954932), _954934))))], (47609 ^ _776545) ^ [_1733950, _1733952, _1733954, _1733956] : [-(c_List_Oconcat(_1733950, hAPP(hAPP(c_List_Omap(_1733952, tc_List_Olist(_1733950)), _1733954), _1733956)) = c_List_Omaps(_1733952, _1733950, _1733954, _1733956))], (19747 ^ _776545) ^ [_1132952, _1132954] : [class_Rings_Olinordered__idom(_1132952), 19750 ^ _776545 : [(19757 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132952), _1132954), c_Groups_Ozero__class_Ozero(_1132952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132952), c_Groups_Osgn__class_Osgn(_1132952, _1132954)), c_Groups_Ozero__class_Ozero(_1132952))))], (19751 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132952), c_Groups_Osgn__class_Osgn(_1132952, _1132954)), c_Groups_Ozero__class_Ozero(_1132952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132952), _1132954), c_Groups_Ozero__class_Ozero(_1132952))))]]], (25881 ^ _776545) ^ [_1244731] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1244731)) = _1244731)], (42357 ^ _776545) ^ [_1617195, _1617197, _1617199] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617195)), hAPP(hAPP(c_List_Otake(_1617195), _1617197), _1617199)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617195)), _1617199)), _1617197))], (14847 ^ _776545) ^ [_1044312, _1044314, _1044316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044312), _1044314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044312), _1044316)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044314), _1044312)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044316), _1044312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044314), _1044316))], (43436 ^ _776545) ^ [_1642603, _1642605, _1642607, _1642609, _1642611] : [-(hAPP(hAPP(c_List_Oappend(_1642603), _1642605), hAPP(hAPP(c_List_Olist_OCons(_1642603), _1642607), c_List_Olist_ONil(_1642603))) = hAPP(hAPP(c_List_Oappend(_1642603), _1642609), hAPP(hAPP(c_List_Olist_OCons(_1642603), _1642611), c_List_Olist_ONil(_1642603)))), _1642605 = _1642609, _1642607 = _1642611], (33915 ^ _776545) ^ [_1405217, _1405219] : [-(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)), _1405217)), 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), _1405219), _1405217))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1405217), _1405219))], (26007 ^ _776545) ^ [_1246713, _1246715] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246713, _1246715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1246713 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246715), 26010 ^ [_1246713, _1246715]))], (29791 ^ _776545) ^ [] : [-(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))], (32478 ^ _776545) ^ [_1361507, _1361509, _1361511, _1361513] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361507, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1361507, tc_fun(_1361507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361507)), _1361509)), hAPP(hAPP(c_COMBC(_1361507, tc_fun(_1361507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361507)), _1361511)), _1361513)), -(hBOOL(hAPP(hAPP(c_member(_1361507), _1361513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361507, tc_HOL_Obool)), _1361509), _1361511))))], (16576 ^ _776545) ^ [_1074770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074770) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30560 ^ _776545) ^ [_1324891, _1324893, _1324895] : [class_Orderings_Olinorder(_1324891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324891), _1324893)), hBOOL(hAPP(hAPP(c_member(_1324891), _1324895), _1324893)), 30571 ^ _776545 : [(30578 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324891, tc_HOL_Obool)), _1324893), hAPP(hAPP(c_Set_Oinsert(_1324891), _1324895), c_Orderings_Obot__class_Obot(tc_fun(_1324891, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324891, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1324891, c_Orderings_Oord__class_Omin(_1324891), _1324893) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324891), _1324895), c_Big__Operators_Olattice_OInf__fin(_1324891, c_Orderings_Oord__class_Omin(_1324891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324891, tc_HOL_Obool)), _1324893), hAPP(hAPP(c_Set_Oinsert(_1324891), _1324895), c_Orderings_Obot__class_Obot(tc_fun(_1324891, tc_HOL_Obool)))))))], (30572 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324891, tc_HOL_Obool)), _1324893), hAPP(hAPP(c_Set_Oinsert(_1324891), _1324895), c_Orderings_Obot__class_Obot(tc_fun(_1324891, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324891, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1324891, c_Orderings_Oord__class_Omin(_1324891), _1324893) = _1324895)]]], (39327 ^ _776545) ^ [_1537979, _1537981] : [-(hAPP(c_Set_Oimage(_1537979, _1537979, c_Fun_Oid(_1537979)), _1537981) = _1537981)], (8435 ^ _776545) ^ [_921402, _921404] : [class_Lattices_Osemilattice__inf(_921402), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921402), _921404), _921404) = _921404)], (31741 ^ _776545) ^ [_1346838, _1346840, _1346842, _1346844] : [class_Orderings_Olinorder(_1346838), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346838, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1346838, _1346840, _1346842)), hAPP(c_SetInterval_Oord__class_OatLeast(_1346838), _1346844)) = c_SetInterval_Oord__class_OatLeastAtMost(_1346838, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346838), _1346840), _1346844), _1346842))], (45185 ^ _776545) ^ [_1681693, _1681695] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1681693), _1681695) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1681693)), hAPP(c_Code__Numeral_Onat__of, _1681695))))], (44094 ^ _776545) ^ [_1658607, _1658609, _1658611] : [-(_1658607 = c_List_Olist_ONil(_1658609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658611), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658609)), _1658607))), -(hAPP(c_List_Ohd(_1658609), hAPP(hAPP(c_List_Odrop(_1658609), _1658611), _1658607)) = hAPP(hAPP(c_List_Onth(_1658609), _1658607), _1658611))], (6941 ^ _776545) ^ [_889180, _889182, _889184] : [class_Orderings_Olinorder(_889180), 6944 ^ _776545 : [(6951 ^ _776545) ^ [] : [_889182 = _889184, -(hAPP(c_SetInterval_Oord__class_OatMost(_889180), _889182) = hAPP(c_SetInterval_Oord__class_OatMost(_889180), _889184))], (6945 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_889180), _889182) = hAPP(c_SetInterval_Oord__class_OatMost(_889180), _889184), -(_889182 = _889184)]]], (39253 ^ _776545) ^ [_1534525, _1534527, _1534529, _1534531] : [_1534525 = c_Orderings_Obot__class_Obot(tc_fun(_1534527, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1534527, _1534529), _1534529, c_Product__Type_Osnd(_1534527, _1534529)), hAPP(hAPP(c_Product__Type_OSigma(_1534527, _1534529), _1534525), hAPP(c_COMBK(tc_fun(_1534529, tc_HOL_Obool), _1534527), _1534531))) = c_Orderings_Obot__class_Obot(tc_fun(_1534529, tc_HOL_Obool)))], (43932 ^ _776545) ^ [_1654453, _1654455] : [_1654455 = c_List_Olist_ONil(_1654453), -(hAPP(c_List_Orotate1(_1654453), _1654455) = c_List_Olist_ONil(_1654453))], (18548 ^ _776545) ^ [_1110329, _1110331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1110329), _1110331))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110329), _1110331)))], (20841 ^ _776545) ^ [_1152831, _1152833, _1152835] : [class_Fields_Olinordered__field(_1152831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152831), _1152833), _1152835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152831), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152831), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152831), _1152833), _1152835)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152831), c_Groups_Oone__class_Oone(_1152831)), c_Groups_Oone__class_Oone(_1152831)))), _1152835)))], (8781 ^ _776545) ^ [_927387, _927389] : [class_Lattices_Obounded__lattice__bot(_927387), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927387), c_Orderings_Obot__class_Obot(_927387)), _927389) = _927389)], (6530 ^ _776545) ^ [_881987, _881989] : [class_Orderings_Otop(_881987), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881987), _881989), c_Orderings_Otop__class_Otop(_881987))))], (30742 ^ _776545) ^ [_1327995, _1327997, _1327999] : [class_Orderings_Olinorder(_1327995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327995, tc_HOL_Obool)), _1327997), _1327999)), -(_1327997 = c_Orderings_Obot__class_Obot(tc_fun(_1327995, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327995), _1327999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327995), c_Big__Operators_Olinorder__class_OMin(_1327995, _1327999)), c_Big__Operators_Olinorder__class_OMin(_1327995, _1327997))))], (26208 ^ _776545) ^ [_1249950, _1249952] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249950) = _1249952), _1249950 = hAPP(c_Int_Onat, _1249952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249952))], (39457 ^ _776545) ^ [_1541143, _1541145, _1541147, _1541149, _1541151, _1541153, _1541155] : [-(hAPP(c_Product__Type_Osnd(_1541143, _1541145), hAPP(c_Product__Type_Omap__pair(_1541147, _1541143, _1541149, _1541145, _1541151, _1541153), _1541155)) = hAPP(_1541153, hAPP(c_Product__Type_Osnd(_1541147, _1541149), _1541155)))], (47593 ^ _776545) ^ [_1733646, _1733648, _1733650] : [hBOOL(hAPP(c_List_Odistinct(_1733646), _1733648)), -(hBOOL(hAPP(c_List_Odistinct(_1733646), c_List_Oinsert(_1733646, _1733650, _1733648))))], (22677 ^ _776545) ^ [_1187501, _1187503] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187501), _1187503) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187503 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187501 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45604 ^ _776545) ^ [_1691164, _1691166, _1691168, _1691170, _1691172, _1691174] : [c_List_Olist__all2(_1691164, _1691166, _1691168, _1691170, _1691172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691164)), _1691170))), -(hBOOL(hAPP(hAPP(_1691168, hAPP(hAPP(c_List_Onth(_1691164), _1691170), _1691174)), hAPP(hAPP(c_List_Onth(_1691166), _1691172), _1691174))))], (12844 ^ _776545) ^ [_1003139, _1003141, _1003143] : [class_Lattices_Olattice(_1003139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003139), _1003141)), -(c_Big__Operators_Olattice__class_OSup__fin(_1003139, hAPP(hAPP(c_Set_Oinsert(_1003139), _1003143), _1003141)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003139, _1003139, c_Lattices_Osemilattice__sup__class_Osup(_1003139)), _1003143), _1003141))], (37708 ^ _776545) ^ [_1494806, _1494808, _1494810, _1494812, _1494814] : [-(c_Fun_Oinj__on(_1494806, _1494808, _1494810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494806, tc_HOL_Obool)), _1494812), _1494814))), c_Fun_Oinj__on(_1494806, _1494808, _1494810, _1494812), c_Fun_Oinj__on(_1494806, _1494808, _1494810, _1494814), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494808, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1494806, _1494808, _1494810), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494806, tc_HOL_Obool)), _1494812), _1494814))), hAPP(c_Set_Oimage(_1494806, _1494808, _1494810), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1494806, tc_HOL_Obool)), _1494814), _1494812))) = c_Orderings_Obot__class_Obot(tc_fun(_1494808, tc_HOL_Obool))], (3354 ^ _776545) ^ [_826597, _826599, _826601, _826603, _826605, _826607, _826609, _826611] : [-(c_Enum_Oproduct(_826611, _826607, _826603, _826599) = c_Enum_Oproduct(_826609, _826605, _826601, _826597)), _826611 = _826609, _826607 = _826605, _826603 = _826601, _826599 = _826597], (38630 ^ _776545) ^ [_1518615, _1518617, _1518619, _1518621, _1518623, _1518625] : [-(hAPP(c_Set_Ovimage(_1518615, _1518617, _1518619), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518621, tc_fun(_1518617, tc_HOL_Obool)), _1518623), _1518625)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1518621, tc_fun(_1518615, tc_HOL_Obool)), _1518623), hAPP(hAPP(c_COMBB(tc_fun(_1518617, tc_HOL_Obool), tc_fun(_1518615, tc_HOL_Obool), _1518621), c_Set_Ovimage(_1518615, _1518617, _1518619)), _1518625)))], (3322 ^ _776545) ^ [_826129, _826131] : [_826131 = _826129, -(c_Lazy__Sequence_Ohb__not__seq(_826131) = c_Lazy__Sequence_Ohb__not__seq(_826129))], (23337 ^ _776545) ^ [_1199452, _1199454, _1199456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199452)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199454), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199456)), 23347 ^ _776545 : [(23353 ^ _776545) ^ [] : [-(_1199454 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23349 ^ [_1199452, _1199454, _1199456]), 23346 ^ [_1199452, _1199454, _1199456]))], (23351 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23349 ^ [_1199452, _1199454, _1199456]), _1199456)))], (23348 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23346 ^ [_1199452, _1199454, _1199456]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1199452))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199454), _1199452) = _1199454)], (5901 ^ _776545) ^ [_870385, _870387, _870389, _870391] : [_870385 = _870387, 5904 ^ _776545 : [(5911 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870389), _870391), _870387)), -(hBOOL(hAPP(hAPP(c_member(_870389), _870391), _870385)))], (5905 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870389), _870391), _870385)), -(hBOOL(hAPP(hAPP(c_member(_870389), _870391), _870387)))]]], (39343 ^ _776545) ^ [_1538228] : [-(hAPP(c_Set_Oimage(_1538228, _1538228, c_Fun_Oid(_1538228)), c_Orderings_Otop__class_Otop(tc_fun(_1538228, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1538228, tc_HOL_Obool)))], (48866 ^ _776545) ^ [_1761624, _1761626, _1761628, _1761630, _1761632, _1761634] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1761624, _1761626, _1761628, _1761630, c_Lazy__Sequence_Olazy__sequence_OInsert(_1761626, _1761632, _1761634)) = hAPP(hAPP(_1761630, _1761632), _1761634))], (49668 ^ _776545) ^ [_1780479, _1780481] : [49671 ^ _776545 : [(49674 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780479, _1780479)), hAPP(hAPP(c_Product__Type_OPair(_1780479, _1780479), 49670 ^ [_1780479, _1780481]), 49669 ^ [_1780479, _1780481])), _1780481))], (49672 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780479, _1780479)), hAPP(hAPP(c_Product__Type_OPair(_1780479, _1780479), 49669 ^ [_1780479, _1780481]), 49670 ^ [_1780479, _1780481])), _1780481)))]], -(c_Relation_Osym(_1780479, _1780481))], (26543 ^ _776545) ^ [_1255639, _1255641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255639), _1255641)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255641), _1255639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1255641)), hAPP(c_Int_Onat, _1255639)))], (22341 ^ _776545) ^ [_1181554, _1181556, _1181558] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181554), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181556), _1181558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181554), _1181556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181554), _1181558)))], (16206 ^ _776545) ^ [_1069386, _1069388] : [class_Rings_Ocomm__semiring__1(_1069386), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069386), _1069388), c_Groups_Ozero__class_Ozero(_1069386)) = _1069388)], (35501 ^ _776545) ^ [_1438947, _1438949, _1438951] : [-(hAPP(c_Product__Type_Osnd(_1438947, _1438949), _1438951) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1438947, _1438949, _1438949), hAPP(c_COMBK(tc_fun(_1438949, _1438949), _1438947), c_COMBI(_1438949))), _1438951))], (48864 ^ _776545) ^ [_1761591] : [-(c_Lazy__Sequence_Oyieldn(_1761591) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1761591), _1761591, c_Lazy__Sequence_Oyield(_1761591)))], (40524 ^ _776545) ^ [_1567484, _1567486, _1567488, _1567490] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1567484, _1567486, _1567488, tc_prod(_1567486, _1567488)), _1567490), c_Product__Type_OPair(_1567486, _1567488)) = _1567490)], (756 ^ _776545) ^ [_787929, _787931, _787933, _787935] : [-(c_Relation_Oantisym(_787933, _787929)), c_Relation_Oantisym(_787935, _787931), _787935 = _787933, _787931 = _787929], (52161 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (16707 ^ _776545) ^ [_1077077, _1077079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077077), _1077079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077077)), _1077079)))], (36478 ^ _776545) ^ [_1466643, _1466645, _1466647, _1466649, _1466651, _1466653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1466643, _1466645), tc_HOL_Obool)), _1466647), _1466649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466643, tc_HOL_Obool)), _1466651), _1466653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466645, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466643, _1466645, _1466647), _1466651)), hAPP(c_Relation_OImage(_1466643, _1466645, _1466649), _1466653))))], (45086 ^ _776545) ^ [_1679410, _1679412, _1679414] : [-(hAPP(hAPP(c_List_Ozip(_1679410, _1679412), hAPP(hAPP(c_List_Omap(tc_prod(_1679410, _1679412), _1679410), c_Product__Type_Ofst(_1679410, _1679412)), _1679414)), hAPP(hAPP(c_List_Omap(tc_prod(_1679410, _1679412), _1679412), c_Product__Type_Osnd(_1679410, _1679412)), _1679414)) = _1679414)], (35495 ^ _776545) ^ [_1438834, _1438836, _1438838, _1438840, _1438842] : [hAPP(c_Product__Type_Osnd(_1438834, _1438836), hAPP(hAPP(c_Product__Type_OPair(_1438834, _1438836), _1438838), _1438840)) = _1438842, -(_1438840 = _1438842)], (25455 ^ _776545) ^ [_1237025, _1237027] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237025), hAPP(c_Int_Onumber__class_Onumber__of(_1237025), c_Int_OMin)), _1237027) = hAPP(c_Groups_Ouminus__class_Ouminus(_1237025), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237025), c_Groups_Oone__class_Oone(_1237025)), _1237027))), class_Fields_Ofield__inverse__zero(_1237025), class_Int_Onumber__ring(_1237025)], (10695 ^ _776545) ^ [_960667, _960669, _960671] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960667, tc_HOL_Obool)), _960669), _960671)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960667, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960667, tc_HOL_Obool)), _960669)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960667, tc_HOL_Obool)), _960671)))], (25913 ^ _776545) ^ [_1245246, _1245248] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245246, _1245248)) = _1245248), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245246), _1245248) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245246, _1245248)))], (38096 ^ _776545) ^ [_1506210, _1506212, _1506214, _1506216, _1506218, _1506220, _1506222, _1506224] : [hBOOL(hAPP(hAPP(_1506210, _1506212), _1506214)), hBOOL(hAPP(hAPP(_1506216, _1506214), _1506218)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1506220, _1506222, _1506224, _1506210, _1506216), _1506212), _1506218)))], (44874 ^ _776545) ^ [_1674861, _1674863, _1674865, _1674867] : [-(hAPP(hAPP(c_List_Omap(_1674861, _1674863), _1674865), hAPP(c_List_Otl(_1674861), _1674867)) = hAPP(c_List_Otl(_1674863), hAPP(hAPP(c_List_Omap(_1674861, _1674863), _1674865), _1674867)))], (40312 ^ _776545) ^ [_1562406, _1562408, _1562410, _1562412, _1562414, _1562416] : [c_Finite__Set_Ofolding__idem(_1562406, _1562408, _1562410, _1562412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562406), _1562414)), -(hAPP(_1562412, hAPP(hAPP(c_Set_Oinsert(_1562406), _1562416), _1562414)) = hAPP(c_Fun_Ocomp(_1562408, _1562408, _1562408, hAPP(_1562412, _1562414)), hAPP(_1562410, _1562416)))], (13838 ^ _776545) ^ [_1023370, _1023372, _1023374, _1023376, _1023378] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1023370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023370), _1023372), _1023374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023370), _1023376), _1023378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023370), _1023372), _1023376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023370), _1023374), _1023378))))], (51839 ^ _776545) ^ [_1824372, _1824374, _1824376] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824372), _1824374)), _1824374 = _1824376, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824372), _1824376)))], (42473 ^ _776545) ^ [_1620175, _1620177, _1620179] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1620175), _1620177)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1620175)), hAPP(c_Set_OCollect(tc_List_Olist(_1620175)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1620175), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1620175)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1620175), tc_fun(_1620175, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1620175, tc_HOL_Obool), tc_fun(tc_fun(_1620175, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1620175)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1620175, tc_HOL_Obool))), c_List_Oset(_1620175))), _1620177))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1620175), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1620175)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1620175)))), _1620179))))))], (22051 ^ _776545) ^ [_1176351, _1176353, _1176355, _1176357] : [class_Rings_Olinordered__semidom(_1176351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176351), _1176353), _1176355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176351), c_Groups_Ozero__class_Ozero(_1176351)), _1176353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176351), hAPP(hAPP(c_Power_Opower__class_Opower(_1176351), _1176353), _1176357)), hAPP(hAPP(c_Power_Opower__class_Opower(_1176351), _1176355), _1176357))))], (8082 ^ _776545) ^ [_913938, _913940, _913942] : [-(hAPP(hAPP(c_Set_Oinsert(_913938), _913940), _913942) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913938, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913938), _913940), c_Orderings_Obot__class_Obot(tc_fun(_913938, tc_HOL_Obool)))), _913942))], (39087 ^ _776545) ^ [_1529556, _1529558, _1529560, _1529562] : [39088 ^ _776545 : [(39091 ^ _776545) ^ [] : [_1529562 = c_Orderings_Obot__class_Obot(tc_fun(_1529558, tc_HOL_Obool))], (39089 ^ _776545) ^ [] : [_1529560 = c_Orderings_Obot__class_Obot(tc_fun(_1529556, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1529556, _1529558), _1529560), hAPP(c_COMBK(tc_fun(_1529558, tc_HOL_Obool), _1529556), _1529562)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529556, _1529558), tc_HOL_Obool)))], (40765 ^ _776545) ^ [_1574217, _1574219, _1574221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574217, _1574217), tc_HOL_Obool)), _1574219), c_Transitive__Closure_Ortrancl(_1574217, _1574221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574217, _1574217), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574217, _1574219)), c_Transitive__Closure_Ortrancl(_1574217, _1574221))))], (2480 ^ _776545) ^ [_812954, _812956, _812958, _812960] : [-(c_Divides_OnegDivAlg(_812960, _812956) = c_Divides_OnegDivAlg(_812958, _812954)), _812960 = _812958, _812956 = _812954], (17849 ^ _776545) ^ [_1097722, _1097724, _1097726, _1097728] : [class_Groups_Ocomm__monoid__add(_1097722), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097724), _1097726))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097724, _1097722), _1097728), _1097726) = c_Groups_Ozero__class_Ozero(_1097722))], (32047 ^ _776545) ^ [_1352369, _1352371, _1352373] : [class_Orderings_Olinorder(_1352369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352369), _1352371)), hBOOL(hAPP(hAPP(c_member(_1352369), _1352373), _1352371)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1352369), _1352373), c_Big__Operators_Olattice_OSup__fin(_1352369, c_Orderings_Oord__class_Omax(_1352369), _1352371)) = _1352373)], (20639 ^ _776545) ^ [_1149148, _1149150, _1149152, _1149154] : [class_Fields_Olinordered__field__inverse__zero(_1149148), 20642 ^ _776545 : [(20643 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149148), _1149150), _1149152)), _1149154)), 20646 ^ _776545 : [(20653 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149152))), 20656 ^ _776545 : [(20663 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149152), c_Groups_Ozero__class_Ozero(_1149148)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149154)))], (20657 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149152), c_Groups_Ozero__class_Ozero(_1149148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149148), _1149154), _1149152)), _1149150)))]]], (20647 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149148), _1149154), _1149152))))]]], (20669 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149148), _1149150), _1149152)), _1149154))), 20672 ^ _776545 : [(20675 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149148), _1149154), _1149152)))], (20673 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149152)))]], 20676 ^ _776545 : [(20679 ^ _776545) ^ [] : [20680 ^ _776545 : [(20683 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149148), _1149154), _1149152)), _1149150))], (20681 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149152), c_Groups_Ozero__class_Ozero(_1149148))))]], 20684 ^ _776545 : [(20687 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149154))], (20685 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), _1149152), c_Groups_Ozero__class_Ozero(_1149148)))]]], (20677 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149148), c_Groups_Ozero__class_Ozero(_1149148)), _1149152))]]]]], (3686 ^ _776545) ^ [_831825, _831827, _831829, _831831] : [-(c_List_Otranspose(_831831, _831827) = c_List_Otranspose(_831829, _831825)), _831831 = _831829, _831827 = _831825], (15757 ^ _776545) ^ [_1062126, _1062128] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062126), hAPP(c_Nat_OSuc, _1062128)))), 15758 ^ _776545 : [(15761 ^ _776545) ^ [_1062214] : [_1062126 = hAPP(c_Nat_OSuc, _1062214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062214), _1062128))], (15759 ^ _776545) ^ [] : [_1062126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (41160 ^ _776545) ^ [_1583624, _1583626, _1583628] : [-(hAPP(c_Relation_ORange(_1583624, _1583626), _1583628) = hAPP(c_Relation_ODomain(_1583626, _1583624), hAPP(c_Relation_Oconverse(_1583624, _1583626), _1583628)))], (15442 ^ _776545) ^ [_1055738, _1055740, _1055742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055738), _1055740)), -(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(_1055738), _1055742)), hAPP(c_Finite__Set_Ocard(_1055738), _1055740))), hAPP(c_Finite__Set_Ocard(_1055738), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055738, tc_HOL_Obool)), _1055742), _1055740)))))], (28213 ^ _776545) ^ [_1283122] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283122) = 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(_1283122)))))], (49640 ^ _776545) ^ [_1779718, _1779720] : [c_Wellfounded_Oacyclic(_1779718, _1779720), -(c_Relation_Oantisym(_1779718, c_Transitive__Closure_Ortrancl(_1779718, _1779720)))], (15726 ^ _776545) ^ [_1061677, _1061679] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061677), _1061679) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15729 ^ _776545 : [(15732 ^ _776545) ^ [] : [-(_1061679 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15730 ^ _776545) ^ [] : [-(_1061677 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (49279 ^ _776545) ^ [_1771604, _1771606] : [c_Relation_Otrans(_1771604, _1771606), -(c_Relation_Otrans(tc_List_Olist(_1771604), c_List_Olistrel(_1771604, _1771606)))], (52363 ^ _776545) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (3776 ^ _776545) ^ [_833198, _833200, _833202, _833204] : [-(c_List_Omeasures(_833204, _833200) = c_List_Omeasures(_833202, _833198)), _833204 = _833202, _833200 = _833198], (924 ^ _776545) ^ [_790423, _790425, _790427, _790429] : [-(c_Equiv__Relations_Oequivp(_790427, _790423)), c_Equiv__Relations_Oequivp(_790429, _790425), _790429 = _790427, _790425 = _790423], (36215 ^ _776545) ^ [_1459734, _1459736, _1459738, _1459740, _1459742, _1459744] : [hAPP(c_Product__Type_Oapfst(_1459734, _1459736, _1459738, _1459740), _1459742) = hAPP(c_Product__Type_Oapfst(_1459734, _1459736, _1459738, _1459744), _1459742), -(hAPP(_1459740, hAPP(c_Product__Type_Ofst(_1459734, _1459738), _1459742)) = hAPP(_1459744, hAPP(c_Product__Type_Ofst(_1459734, _1459738), _1459742)))], (8050 ^ _776545) ^ [_913268, _913270, _913272, _913274] : [hBOOL(hAPP(hAPP(c_member(_913268), _913270), _913272)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913268, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913268), _913270), _913274)), _913272) = hAPP(hAPP(c_Set_Oinsert(_913268), _913270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913268, tc_HOL_Obool)), _913274), _913272)))], (34608 ^ _776545) ^ [_1421178, _1421180] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1421178), hAPP(c_Nat_OSuc, _1421180)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1421180), 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)), _1421180)), _1421178))], (30020 ^ _776545) ^ [_1314907, _1314909] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1314907)), hAPP(c_Nat_OSuc, _1314909)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1314907), _1314909)))], (35172 ^ _776545) ^ [_1432933, _1432935] : [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), _1432933), _1432935))), 35175 ^ _776545 : [(35182 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432935), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35185 ^ _776545 : [(35194 ^ _776545) ^ [] : [-(c_Nitpick_Onorm__frac(_1432933, _1432935) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1432933), _1432935)), 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), _1432933))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1432935)))), -(_1432933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1432935 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35186 ^ _776545) ^ [] : [35187 ^ _776545 : [(35190 ^ _776545) ^ [] : [_1432935 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35188 ^ _776545) ^ [] : [_1432933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1432933, _1432935) = 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)))]]], (35176 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432935), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1432933, _1432935) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1432933), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1432935)))]]], (27919 ^ _776545) ^ [_1278421, _1278423] : [class_Int_Onumber__ring(_1278421), class_Rings_Olinordered__idom(_1278421), 27926 ^ _776545 : [(27933 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1278423), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278421), hAPP(c_Int_Onumber__class_Onumber__of(_1278421), _1278423)), c_Groups_Ozero__class_Ozero(_1278421))))], (27927 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278421), hAPP(c_Int_Onumber__class_Onumber__of(_1278421), _1278423)), c_Groups_Ozero__class_Ozero(_1278421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1278423), c_Int_OPls)))]]], (7556 ^ _776545) ^ [_901286, _901288, _901290, _901292] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901286, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901286, tc_HOL_Obool)), _901288), _901290)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901286, tc_HOL_Obool)), _901292), _901290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901286, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901286, tc_HOL_Obool)), _901288), _901290)), _901292))], (47938 ^ _776545) ^ [_1742216, _1742218, _1742220, _1742222] : [class_Orderings_Oorder(_1742216), class_Enum_Oenum(_1742218), 47945 ^ _776545 : [(47952 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742218), hAPP(hAPP(c_COMBS(_1742218, _1742216, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742216, tc_fun(_1742216, tc_HOL_Obool), _1742218), c_Orderings_Oord__class_Oless__eq(_1742216)), _1742220)), _1742222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742218, _1742216)), _1742220), _1742222)))], (47946 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1742218, _1742216)), _1742220), _1742222)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742218), hAPP(hAPP(c_COMBS(_1742218, _1742216, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742216, tc_fun(_1742216, tc_HOL_Obool), _1742218), c_Orderings_Oord__class_Oless__eq(_1742216)), _1742220)), _1742222))))]]], (32768 ^ _776545) ^ [_1371916, _1371918, _1371920, _1371922, _1371924] : [class_Groups_Ocomm__monoid__add(_1371916), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371918, _1371916), hAPP(hAPP(c_COMBS(_1371918, _1371916, _1371916), hAPP(hAPP(c_COMBB(_1371916, tc_fun(_1371916, _1371916), _1371918), c_Groups_Oplus__class_Oplus(_1371916)), _1371920)), _1371922)), _1371924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1371916), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371918, _1371916), _1371920), _1371924)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371918, _1371916), _1371922), _1371924)))], (35252 ^ _776545) ^ [_1434406, _1434408] : [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), _1434406), _1434408))), 35255 ^ _776545 : [(35262 ^ _776545) ^ [] : [-(_1434408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1434406, _1434408) = c_Nitpick_Onat__gcd(_1434408, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1434406, _1434408)))], (35256 ^ _776545) ^ [] : [_1434408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1434406, _1434408) = _1434406)]]], (40360 ^ _776545) ^ [_1563503, _1563505, _1563507] : [hBOOL(hAPP(_1563503, _1563505)), -(hBOOL(hAPP(_1563503, c_Hilbert__Choice_OEps(_1563507, _1563503))))], (45152 ^ _776545) ^ [_1680757, _1680759, _1680761, _1680763] : [class_Groups_Ocomm__monoid__add(_1680757), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1680757), _1680759), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1680761, _1680763))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1680757), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1680757), _1680759), c_List_Oupto(_1680761, _1680763))))], (5620 ^ _776545) ^ [_862340, _862342, _862344, _862346, _862348, _862350] : [-(c_COMBB(_862350, _862346, _862342) = c_COMBB(_862348, _862344, _862340)), _862350 = _862348, _862346 = _862344, _862342 = _862340], (27225 ^ _776545) ^ [_1266432, _1266434, _1266436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266434), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266436), 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), _1266436), _1266434))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1266432)))))], (23003 ^ _776545) ^ [_1193298, _1193300, _1193302] : [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), _1193298), _1193300)), _1193302)), 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)), _1193302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40843 ^ _776545) ^ [_1576093, _1576095, _1576097] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1576093, _1576093, _1576095), c_Relation_OId(_1576093)), _1576097) = _1576097)], (5194 ^ _776545) ^ [_855813, _855815, _855817, _855819] : [-(c_Transitive__Closure_Otrancl(_855819, _855815) = c_Transitive__Closure_Otrancl(_855817, _855813)), _855819 = _855817, _855815 = _855813], (11840 ^ _776545) ^ [_984162, _984164, _984166, _984168] : [c_Finite__Set_Ofolding__one(_984162, _984164, _984166), hBOOL(hAPP(c_Finite__Set_Ofinite(_984162), _984168)), -(_984168 = c_Orderings_Obot__class_Obot(tc_fun(_984162, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_984162), hAPP(hAPP(_984164, 11853 ^ [_984162, _984164, _984166, _984168]), 11854 ^ [_984162, _984164, _984166, _984168])), hAPP(hAPP(c_Set_Oinsert(_984162), 11853 ^ [_984162, _984164, _984166, _984168]), hAPP(hAPP(c_Set_Oinsert(_984162), 11854 ^ [_984162, _984164, _984166, _984168]), c_Orderings_Obot__class_Obot(tc_fun(_984162, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_984162), hAPP(_984166, _984168)), _984168)))], (19178 ^ _776545) ^ [_1122129, _1122131, _1122133, _1122135, _1122137] : [class_Groups_Ocomm__monoid__mult(_1122129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122131), _1122133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122131), _1122135)), 19192 ^ _776545 : [(19195 ^ _776545) ^ [] : [hAPP(_1122137, 19191 ^ [_1122129, _1122131, _1122133, _1122135, _1122137]) = c_Groups_Oone__class_Oone(_1122129)], (19193 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122131), 19191 ^ [_1122129, _1122131, _1122133, _1122135, _1122137]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122131, tc_HOL_Obool)), _1122133), _1122135))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122129, _1122131, c_Groups_Otimes__class_Otimes(_1122129)), _1122137), c_Groups_Oone__class_Oone(_1122129)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122131, tc_HOL_Obool)), _1122133), _1122135)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122129), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122129, _1122131, c_Groups_Otimes__class_Otimes(_1122129)), _1122137), c_Groups_Oone__class_Oone(_1122129)), _1122133)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1122129, _1122131, c_Groups_Otimes__class_Otimes(_1122129)), _1122137), c_Groups_Oone__class_Oone(_1122129)), _1122135)))], (29335 ^ _776545) ^ [_1302236] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1302236), _1302236)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1302236)], (46285 ^ _776545) ^ [_1707557, _1707559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707557), _1707559)), -(c_List_Oupt(_1707559, _1707557) = c_List_Olist_ONil(tc_Nat_Onat))], (12255 ^ _776545) ^ [_991591, _991593, _991595, _991597, _991599, _991601, _991603, _991605] : [c_Finite__Set_Ofolding__image__simple(_991591, _991593, _991595, _991597, _991599, _991601), hBOOL(hAPP(c_Finite__Set_Ofinite(_991593), _991603)), hBOOL(hAPP(c_Finite__Set_Ofinite(_991593), _991605)), -(hAPP(hAPP(_991595, hAPP(_991601, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991593, tc_HOL_Obool)), _991603), _991605))), hAPP(_991601, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_991593, tc_HOL_Obool)), _991603), _991605))) = hAPP(hAPP(_991595, hAPP(_991601, _991603)), hAPP(_991601, _991605)))], (41300 ^ _776545) ^ [_1586877, _1586879, _1586881] : [c_Relation_Osingle__valued(_1586877, _1586879, _1586881), 41303 ^ _776545 : [(41304 ^ _776545) ^ [_1586998, _1587000] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586877, _1586879)), hAPP(hAPP(c_Product__Type_OPair(_1586877, _1586879), _1587000), _1586998)), _1586881)), 41307 ^ _776545 : [(41308 ^ _776545) ^ [_1587124] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586877, _1586879)), hAPP(hAPP(c_Product__Type_OPair(_1586877, _1586879), _1587000), _1587124)), _1586881)), -(_1586998 = _1587124)]]]]], (4294 ^ _776545) ^ [_841581, _841583, _841585, _841587] : [-(c_List_Oconcat(_841587, _841583) = c_List_Oconcat(_841585, _841581)), _841587 = _841585, _841583 = _841581], (42781 ^ _776545) ^ [_1628586, _1628588] : [-(c_List_Obutlast(_1628586, _1628588) = hAPP(hAPP(c_List_Otake(_1628586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628586)), _1628588)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1628588))], (15334 ^ _776545) ^ [_1053312, _1053314, _1053316] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053312), _1053314)), hBOOL(hAPP(hAPP(c_member(_1053312), _1053316), _1053314)), -(hAPP(c_Finite__Set_Ocard(_1053312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053312, tc_HOL_Obool)), _1053314), hAPP(hAPP(c_Set_Oinsert(_1053312), _1053316), c_Orderings_Obot__class_Obot(tc_fun(_1053312, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053312), _1053314)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16086 ^ _776545) ^ [_1067375, _1067377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067377)), _1067375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067375), _1067377))], (46257 ^ _776545) ^ [_1706899, _1706901, _1706903] : [-(c_List_Osublist(_1706899, _1706901, _1706903) = hAPP(hAPP(c_List_Omap(tc_prod(_1706899, tc_Nat_Onat), _1706899), c_Product__Type_Ofst(_1706899, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1706899, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1706899, 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(_1706899, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1706899, tc_Nat_Onat))), _1706903)), hAPP(hAPP(c_List_Ozip(_1706899, tc_Nat_Onat), _1706901), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706899)), _1706901))))))], (49080 ^ _776545) ^ [_1766497, _1766499, _1766501] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1766497), _1766499, _1766501)), -(c_List_Olist__ex(tc_Int_Oint, _1766497, c_List_Oupto(_1766499, _1766501)))], (33445 ^ _776545) ^ [_1391249, _1391251, _1391253, _1391255, _1391257, _1391259] : [class_Groups_Ocomm__monoid__add(_1391249), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391251, _1391249), hAPP(hAPP(c_COMBC(_1391251, tc_fun(_1391253, tc_HOL_Obool), _1391249), hAPP(hAPP(c_COMBB(tc_fun(_1391253, _1391249), tc_fun(tc_fun(_1391253, tc_HOL_Obool), _1391249), _1391251), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391253, _1391249)), _1391255)), _1391257)), _1391259) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391253, _1391249), hAPP(hAPP(c_COMBC(_1391253, tc_fun(_1391251, tc_HOL_Obool), _1391249), hAPP(hAPP(c_COMBB(tc_fun(_1391251, _1391249), tc_fun(tc_fun(_1391251, tc_HOL_Obool), _1391249), _1391253), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391251, _1391249)), hAPP(c_COMBC(_1391251, _1391253, _1391249), _1391255))), _1391259)), _1391257))], (12716 ^ _776545) ^ [_1000757, _1000759, _1000761, _1000763] : [class_Lattices_Osemilattice__sup(_1000757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000757), _1000759)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000757, _1000757, c_Lattices_Osemilattice__sup__class_Osup(_1000757)), _1000761), hAPP(hAPP(c_Set_Oinsert(_1000757), _1000763), _1000759)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1000757), _1000763), hAPP(hAPP(c_Finite__Set_Ofold(_1000757, _1000757, c_Lattices_Osemilattice__sup__class_Osup(_1000757)), _1000761), _1000759)))], (52051 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (17711 ^ _776545) ^ [_1095399, _1095401] : [class_Groups_Oordered__ab__group__add(_1095399), 17714 ^ _776545 : [(17721 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095399), _1095401), c_Groups_Ozero__class_Ozero(_1095399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095399), c_Groups_Ozero__class_Ozero(_1095399)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095399), _1095401))))], (17715 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095399), c_Groups_Ozero__class_Ozero(_1095399)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095399), _1095401))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095399), _1095401), c_Groups_Ozero__class_Ozero(_1095399))))]]], (18346 ^ _776545) ^ [_1106531, _1106533, _1106535, _1106537] : [class_Rings_Olinordered__semiring(_1106531), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106531), _1106533), _1106535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106531), _1106537), _1106535))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106531), c_Groups_Ozero__class_Ozero(_1106531)), _1106535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106531), _1106533), _1106537)))], (48366 ^ _776545) ^ [] : [-(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)))], (29267 ^ _776545) ^ [] : [-(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))))], (32694 ^ _776545) ^ [_1370453, _1370455, _1370457, _1370459, _1370461] : [class_Groups_Ocomm__monoid__add(_1370453), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370453), _1370455), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370457), _1370459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1370461), _1370459))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370453), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370453, tc_Nat_Onat), _1370455), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1370459))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370457, _1370461)))], (22819 ^ _776545) ^ [_1189917, _1189919, _1189921, _1189923] : [class_Rings_Olinordered__semidom(_1189917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189917), c_Groups_Oone__class_Oone(_1189917)), _1189919)), 22826 ^ _776545 : [(22833 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189921), _1189923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189917), hAPP(hAPP(c_Power_Opower__class_Opower(_1189917), _1189919), _1189921)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189917), _1189919), _1189923))))], (22827 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189917), hAPP(hAPP(c_Power_Opower__class_Opower(_1189917), _1189919), _1189921)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189917), _1189919), _1189923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189921), _1189923)))]]], (23593 ^ _776545) ^ [_1204134, _1204136] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204134)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204136)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204134), _1204136))], (51691 ^ _776545) ^ [_1821997, _1821999, _1822001, _1822003] : [class_Rings_Ocomm__semiring__1(_1821997), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821997), _1821999), _1822001)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821997), _1822001), _1822003)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821997), _1821999), _1822003)))], (21335 ^ _776545) ^ [_1162665, _1162667, _1162669, _1162671] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162665), _1162667), _1162669)), hAPP(c_Int_Onumber__class_Onumber__of(_1162665), _1162671)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162665), _1162667), hAPP(c_Int_Onumber__class_Onumber__of(_1162665), _1162671))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162665), _1162669), hAPP(c_Int_Onumber__class_Onumber__of(_1162665), _1162671)))), class_Int_Onumber(_1162665), class_Rings_Osemiring(_1162665)], (5604 ^ _776545) ^ [_862106, _862108] : [_862108 = _862106, -(c_COMBI(_862108) = c_COMBI(_862106))], (26254 ^ _776545) ^ [_1250753, _1250755] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1250753, _1250755) = 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), _1250753), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250755))))], (31371 ^ _776545) ^ [_1339696, _1339698, _1339700, _1339702] : [class_Orderings_Olinorder(_1339696), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339696), _1339698), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339696), _1339700), _1339702)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339696), _1339700), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339696), _1339698), _1339702)))], (30606 ^ _776545) ^ [_1325754, _1325756, _1325758] : [class_Orderings_Olinorder(_1325754), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325754), _1325756)), hBOOL(hAPP(hAPP(c_member(_1325754), _1325758), _1325756)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325754), _1325758), c_Big__Operators_Olattice_OInf__fin(_1325754, c_Orderings_Oord__class_Omin(_1325754), _1325756)) = c_Big__Operators_Olattice_OInf__fin(_1325754, c_Orderings_Oord__class_Omin(_1325754), _1325756))], (49074 ^ _776545) ^ [_1766407, _1766409, _1766411] : [c_List_Olist__ex(tc_Int_Oint, _1766407, c_List_Oupto(_1766409, _1766411)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1766407), _1766409, _1766411)], (41467 ^ _776545) ^ [_1591254, _1591256, _1591258, _1591260, _1591262, _1591264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591254, _1591254)), hAPP(hAPP(c_Product__Type_OPair(_1591254, _1591254), _1591256), _1591258)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591254, _1591254), tc_HOL_Obool), _1591260), _1591262))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591254, _1591254)), hAPP(hAPP(c_Product__Type_OPair(_1591254, _1591254), _1591258), _1591264)), _1591262)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591254, _1591254)), hAPP(hAPP(c_Product__Type_OPair(_1591254, _1591254), _1591256), _1591264)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591254, _1591254), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591260)), _1591262))))], (326 ^ _776545) ^ [_781464, _781466, _781468, _781470] : [-(c_Wellfounded_OwfP(_781468, _781464)), c_Wellfounded_OwfP(_781470, _781466), _781470 = _781468, _781466 = _781464], (14302 ^ _776545) ^ [_1034244, _1034246, _1034248, _1034250, _1034252] : [class_Rings_Ocomm__semiring__1(_1034244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034246), _1034248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034250), _1034252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034246), _1034248)), _1034252)))], (2866 ^ _776545) ^ [_819055, _819057, _819059, _819061] : [-(c_Relation_ORange(_819061, _819057) = c_Relation_ORange(_819059, _819055)), _819061 = _819059, _819057 = _819055], (11495 ^ _776545) ^ [_977379, _977381] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_977379), c_Complete__Lattice_OInf__class_OInf(tc_fun(_977379, tc_HOL_Obool), _977381)))), 11496 ^ _776545 : [(11497 ^ _776545) ^ [_977443] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_977379, tc_HOL_Obool)), _977443), _977381)), hBOOL(hAPP(c_Finite__Set_Ofinite(_977379), _977443))]]], (6097 ^ _776545) ^ [_874191, _874193, _874195, _874197, _874199, _874201] : [hBOOL(hAPP(hAPP(c_member(_874191), _874193), c_SetInterval_Oord_OatLeastLessThan(_874191, _874195, _874197, _874199, _874201))), 6100 ^ _776545 : [(6103 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_874197, _874193), _874201)))], (6101 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_874195, _874199), _874193)))]]], (41204 ^ _776545) ^ [_1584968, _1584970, _1584972] : [hAPP(hAPP(c_Relation_Orel__comp(_1584968, _1584968, _1584968), hAPP(c_Relation_Oconverse(_1584968, _1584968), _1584970)), _1584970) = _1584970, hAPP(c_Relation_ODomain(_1584968, _1584968), _1584970) = _1584972, -(c_Equiv__Relations_Oequiv(_1584968, _1584972, _1584970))], (33631 ^ _776545) ^ [] : [-(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)))], (17001 ^ _776545) ^ [_1082545, _1082547, _1082549, _1082551] : [class_Rings_Oordered__ring(_1082545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082545), _1082547), _1082549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082545), _1082551), c_Groups_Ozero__class_Ozero(_1082545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082545), _1082551), _1082549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082545), _1082551), _1082547))))], (28307 ^ _776545) ^ [_1284717] : [_1284717 = c_Int_OMin, -(c_Int_OBit1(_1284717) = c_Int_OMin)], (4284 ^ _776545) ^ [_841432, _841434, _841436, _841438] : [-(c_List_Ofilter(_841438, _841434) = c_List_Ofilter(_841436, _841432)), _841438 = _841436, _841434 = _841432], (45219 ^ _776545) ^ [_1682241, _1682243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1682241), _1682243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682241)), hAPP(c_Code__Numeral_Onat__of, _1682243))))], (44699 ^ _776545) ^ [_1670164, _1670166] : [-(_1670164 = c_List_Olist_ONil(_1670166)), -(c_Random_Oselect__weight(_1670166, hAPP(hAPP(c_List_Omap(_1670166, tc_prod(tc_Code__Numeral_Ocode__numeral, _1670166)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1670166), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1670164)) = c_Random_Oselect(_1670166, _1670164))], (19627 ^ _776545) ^ [_1131132, _1131134, _1131136, _1131138] : [class_Rings_Odivision__ring(_1131132), -(_1131134 = c_Groups_Ozero__class_Ozero(_1131132)), _1131136 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131132), _1131138), _1131134), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131132), _1131136), _1131134) = _1131138)], (33611 ^ _776545) ^ [_1395887, _1395889, _1395891, _1395893, _1395895, _1395897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1395889, _1395891)), hAPP(hAPP(c_Product__Type_OPair(_1395889, _1395891), _1395895), _1395897)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395887, tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395887, tc_HOL_Obool))), _1395893))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395887, tc_fun(_1395889, tc_fun(_1395891, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395887, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_fun(_1395889, tc_fun(_1395891, tc_HOL_Obool)), _1395887), hAPP(c_COMBC(_1395889, tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_fun(_1395891, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395891, tc_fun(tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_fun(_1395891, tc_HOL_Obool)), _1395889), c_COMBC(_1395891, tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395891, tc_prod(_1395889, _1395891)), tc_fun(_1395891, tc_fun(tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_HOL_Obool)), _1395889), hAPP(c_COMBB(tc_prod(_1395889, _1395891), tc_fun(tc_fun(tc_prod(_1395889, _1395891), tc_HOL_Obool), tc_HOL_Obool), _1395891), c_member(tc_prod(_1395889, _1395891)))), c_Product__Type_OPair(_1395889, _1395891))))), _1395893)), _1395895), _1395897)))], (32404 ^ _776545) ^ [_1359593] : [-(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)), _1359593)))))], (32858 ^ _776545) ^ [_1374216, _1374218, _1374220, _1374222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374216, tc_fun(_1374218, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1374216, tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_fun(_1374218, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374218, tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_fun(_1374218, tc_HOL_Obool)), _1374216), c_COMBC(_1374218, tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374218, tc_prod(_1374216, _1374218)), tc_fun(_1374218, tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), _1374216), hAPP(c_COMBB(tc_prod(_1374216, _1374218), tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool), _1374218), c_member(tc_prod(_1374216, _1374218)))), c_Product__Type_OPair(_1374216, _1374218)))), _1374220)), hAPP(hAPP(c_COMBC(_1374216, tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_fun(_1374218, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374218, tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_fun(_1374218, tc_HOL_Obool)), _1374216), c_COMBC(_1374218, tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374218, tc_prod(_1374216, _1374218)), tc_fun(_1374218, tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool)), _1374216), hAPP(c_COMBB(tc_prod(_1374216, _1374218), tc_fun(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool), tc_HOL_Obool), _1374218), c_member(tc_prod(_1374216, _1374218)))), c_Product__Type_OPair(_1374216, _1374218)))), _1374222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374216, _1374218), tc_HOL_Obool)), _1374220), _1374222)))], (42329 ^ _776545) ^ [_1616632, _1616634, _1616636, _1616638] : [hBOOL(hAPP(hAPP(c_member(_1616632), _1616634), hAPP(c_List_Oset(_1616632), hAPP(hAPP(c_List_Olist_OCons(_1616632), _1616636), _1616638)))), -(_1616634 = _1616636), -(hBOOL(hAPP(hAPP(c_member(_1616632), _1616634), hAPP(c_List_Oset(_1616632), _1616638))))], (1804 ^ _776545) ^ [_801959, _801961] : [-(class_Rings_Omult__zero(_801959)), _801961 = _801959, class_Rings_Omult__zero(_801961)], (26573 ^ _776545) ^ [_1256206] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1256206) = 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), _1256206))))], (49303 ^ _776545) ^ [_1771945] : [-(c_Relation_Otrans(_1771945, c_Relation_OId(_1771945)))], (12119 ^ _776545) ^ [_989358, _989360, _989362, _989364, _989366] : [c_Finite__Set_Ofolding__one__idem(_989358, _989360, _989362), hBOOL(hAPP(c_Finite__Set_Ofinite(_989358), _989364)), hBOOL(hAPP(hAPP(c_member(_989358), _989366), _989364)), -(hAPP(hAPP(_989360, _989366), hAPP(_989362, _989364)) = hAPP(_989362, _989364))], (52409 ^ _776545) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (43090 ^ _776545) ^ [_1635137, _1635139, _1635141] : [-(hAPP(hAPP(c_List_Ozip(_1635137, _1635139), _1635141), c_List_Olist_ONil(_1635139)) = c_List_Olist_ONil(tc_prod(_1635137, _1635139)))], (38779 ^ _776545) ^ [_1522135, _1522137, _1522139, _1522141] : [-(hAPP(c_Set_Ovimage(_1522135, _1522137, _1522139), _1522141) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522137, tc_fun(_1522135, tc_HOL_Obool)), _1522141), hAPP(hAPP(c_COMBB(tc_fun(_1522137, tc_HOL_Obool), tc_fun(_1522135, tc_HOL_Obool), _1522137), c_Set_Ovimage(_1522135, _1522137, _1522139)), hAPP(hAPP(c_COMBC(_1522137, tc_fun(_1522137, tc_HOL_Obool), tc_fun(_1522137, tc_HOL_Obool)), c_Set_Oinsert(_1522137)), c_Orderings_Obot__class_Obot(tc_fun(_1522137, tc_HOL_Obool))))))], (4208 ^ _776545) ^ [_840318, _840320, _840322, _840324, _840326, _840328] : [-(c_Predicate_Oconversep(_840328, _840324, _840320) = c_Predicate_Oconversep(_840326, _840322, _840318)), _840328 = _840326, _840324 = _840322, _840320 = _840318], (1998 ^ _776545) ^ [_805285, _805287] : [_805287 = _805285, -(c_Hoare__Mirabelle_ORep__triple(_805287) = c_Hoare__Mirabelle_ORep__triple(_805285))], (48704 ^ _776545) ^ [_1758220, _1758222, _1758224] : [c_List_Olist_ONil(_1758220) = c_List_Oreplicate(_1758220, _1758222, _1758224), -(_1758222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32554 ^ _776545) ^ [_1365275, _1365277, _1365279, _1365281, _1365283] : [_1365275 = c_Orderings_Obot__class_Obot(tc_fun(_1365277, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365277, tc_fun(_1365279, tc_HOL_Obool)), _1365275), hAPP(hAPP(c_COMBB(tc_fun(_1365279, tc_HOL_Obool), tc_fun(_1365279, tc_HOL_Obool), _1365277), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365279, tc_HOL_Obool)), _1365281)), _1365283)) = c_Orderings_Otop__class_Otop(tc_fun(_1365279, tc_HOL_Obool)))], (44866 ^ _776545) ^ [_1674262, _1674264, _1674266, _1674268, _1674270, _1674272, _1674274, _1674276] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674262, _1674264), _1674266), _1674268), hAPP(hAPP(c_List_Ozip(_1674262, _1674264), _1674270), hAPP(hAPP(c_List_Omap(_1674272, _1674264), _1674274), _1674276))) = hAPP(hAPP(c_List_Omap(tc_prod(_1674262, _1674272), _1674266), hAPP(c_Product__Type_Oprod_Oprod__case(_1674262, _1674272, _1674266), hAPP(hAPP(c_COMBB(tc_fun(_1674272, tc_prod(_1674262, _1674264)), tc_fun(_1674272, _1674266), _1674262), hAPP(c_COMBB(tc_prod(_1674262, _1674264), _1674266, _1674272), _1674268)), hAPP(hAPP(c_COMBC(_1674262, tc_fun(_1674272, _1674264), tc_fun(_1674272, tc_prod(_1674262, _1674264))), hAPP(hAPP(c_COMBB(tc_fun(_1674264, tc_prod(_1674262, _1674264)), tc_fun(tc_fun(_1674272, _1674264), tc_fun(_1674272, tc_prod(_1674262, _1674264))), _1674262), c_COMBB(_1674264, tc_prod(_1674262, _1674264), _1674272)), c_Product__Type_OPair(_1674262, _1674264))), _1674274)))), hAPP(hAPP(c_List_Ozip(_1674262, _1674272), _1674270), _1674276)))], (22751 ^ _776545) ^ [_1188717, _1188719, _1188721, _1188723] : [class_Rings_Olinordered__semidom(_1188717), hAPP(hAPP(c_Power_Opower__class_Opower(_1188717), _1188719), hAPP(c_Nat_OSuc, _1188721)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1188717), _1188723), hAPP(c_Nat_OSuc, _1188721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188717), c_Groups_Ozero__class_Ozero(_1188717)), _1188719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188717), c_Groups_Ozero__class_Ozero(_1188717)), _1188723)), -(_1188719 = _1188723)], (47228 ^ _776545) ^ [_1726030, _1726032, _1726034] : [c_List_OtakeWhile(_1726030, _1726032, _1726034) = _1726034, 47231 ^ _776545 : [(47232 ^ _776545) ^ [_1726117] : [hBOOL(hAPP(hAPP(c_member(_1726030), _1726117), hAPP(c_List_Oset(_1726030), _1726034))), -(hBOOL(hAPP(_1726032, _1726117)))]]], (33056 ^ _776545) ^ [_1380358, _1380360, _1380362, _1380364, _1380366, _1380368] : [-(hAPP(c_Set_Oimage(_1380358, _1380360, _1380362), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380364, tc_fun(_1380358, tc_HOL_Obool)), _1380366), _1380368)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380364, tc_fun(_1380360, tc_HOL_Obool)), _1380366), hAPP(hAPP(c_COMBB(tc_fun(_1380358, tc_HOL_Obool), tc_fun(_1380360, tc_HOL_Obool), _1380364), c_Set_Oimage(_1380358, _1380360, _1380362)), _1380368)))], (12003 ^ _776545) ^ [_987577, _987579] : [class_Lattices_Olattice(_987577), hBOOL(hAPP(c_Finite__Set_Ofinite(_987577), _987579)), -(_987579 = c_Orderings_Obot__class_Obot(tc_fun(_987577, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987577), c_Big__Operators_Olattice__class_OInf__fin(_987577, _987579)), c_Big__Operators_Olattice__class_OSup__fin(_987577, _987579))))], (4876 ^ _776545) ^ [_850852, _850854, _850856, _850858, _850860, _850862] : [-(c_Relation_Orel__comp(_850862, _850858, _850854) = c_Relation_Orel__comp(_850860, _850856, _850852)), _850862 = _850860, _850858 = _850856, _850854 = _850852], (25846 ^ _776545) ^ [_1244102] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244102)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1244102)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1244102)))], (9812 ^ _776545) ^ [_944653, _944655, _944657] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944653, tc_HOL_Obool)), _944655), _944657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944653, tc_HOL_Obool)), _944655), _944657)), -(_944655 = _944657)], (22433 ^ _776545) ^ [_1183187, _1183189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183187)), 22436 ^ _776545 : [(22445 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183187), _1183189) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1183187 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1183189 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (22437 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1183187), _1183189) = c_Groups_Oone__class_Oone(tc_Int_Oint), 22440 ^ _776545 : [(22443 ^ _776545) ^ [] : [-(_1183189 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22441 ^ _776545) ^ [] : [-(_1183187 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (8417 ^ _776545) ^ [_921093, _921095, _921097] : [class_Lattices_Olattice(_921093), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921093), _921095), _921097) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921093), _921097), _921095))], (28111 ^ _776545) ^ [_1281442] : [class_Rings_Osemiring__1(_1281442), -(c_Int_Oiszero(_1281442, c_Groups_Ozero__class_Ozero(_1281442)))], (26088 ^ _776545) ^ [_1248050, _1248052] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248050)))), 26091 ^ _776545 : [(26098 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248052)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248052)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248052))))], (26092 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1248052))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248052)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1248050))]]], (52451 ^ _776545) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (31158 ^ _776545) ^ [_1335752, _1335754] : [class_Orderings_Olinorder(_1335752), -(c_Big__Operators_Olinorder__class_OMax(_1335752, hAPP(hAPP(c_Set_Oinsert(_1335752), _1335754), c_Orderings_Obot__class_Obot(tc_fun(_1335752, tc_HOL_Obool)))) = _1335754)], (19114 ^ _776545) ^ [_1120930, _1120932, _1120934] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1120930), _1120932)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120930), _1120934)), 19124 ^ _776545 : [(19127 ^ _776545) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19125 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120930), 19123 ^ [_1120930, _1120932, _1120934]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120930, tc_HOL_Obool)), _1120932), _1120934))))]], -(hAPP(c_Finite__Set_Ocard(_1120930), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120930, tc_HOL_Obool)), _1120932), _1120934)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1120930), _1120932)), hAPP(c_Finite__Set_Ocard(_1120930), _1120934)))], (28787 ^ _776545) ^ [_1292730, _1292732] : [c_Int_OBit1(_1292730) = c_Int_OBit0(_1292732)], (49369 ^ _776545) ^ [_1773131, _1773133, _1773135, _1773137] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1773131, tc_fun(_1773133, tc_HOL_Obool)), _1773135), _1773137) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773133, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1773133, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773131, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1773133, tc_HOL_Obool)), c_HOL_OEx(_1773131)), hAPP(hAPP(c_COMBB(tc_fun(_1773131, tc_HOL_Obool), tc_fun(_1773131, tc_HOL_Obool), tc_fun(_1773133, tc_HOL_Obool)), hAPP(c_COMBS(_1773131, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1773131), c_fconj), hAPP(hAPP(c_COMBC(_1773131, tc_fun(_1773131, tc_HOL_Obool), tc_HOL_Obool), c_member(_1773131)), _1773135)))), hAPP(hAPP(c_COMBC(tc_fun(_1773133, tc_HOL_Obool), tc_fun(_1773131, tc_fun(_1773133, tc_HOL_Obool)), tc_fun(_1773131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773133, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1773131, tc_fun(_1773133, tc_HOL_Obool)), tc_fun(_1773131, tc_HOL_Obool)), tc_fun(_1773133, tc_HOL_Obool)), c_COMBB(tc_fun(_1773133, tc_HOL_Obool), tc_HOL_Obool, _1773131)), c_fequal)), _1773137))))))], (16092 ^ _776545) ^ [_1067496, _1067498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067496), hAPP(c_Nat_OSuc, _1067498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067496), _1067498))), -(_1067496 = hAPP(c_Nat_OSuc, _1067498))], (10699 ^ _776545) ^ [_960813, _960815] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960813, tc_HOL_Obool)), _960815) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960813, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_960813, tc_HOL_Obool))), _960815))], (23864 ^ _776545) ^ [_1208798, _1208800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208798)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208800))))], (27619 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (22191 ^ _776545) ^ [_1179013, _1179015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179015), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179013), _1179015)))], (4184 ^ _776545) ^ [_839948, _839950, _839952, _839954, _839956, _839958] : [-(c_List_Osplice(_839958, _839954, _839950) = c_List_Osplice(_839956, _839952, _839948)), _839958 = _839956, _839954 = _839952, _839950 = _839948], (52383 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (27243 ^ _776545) ^ [_1266734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266734), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1266734)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24942 ^ _776545) ^ [_1228204] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1228204) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17969 ^ _776545) ^ [_1099738, _1099740] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1099738), _1099740))), -(hAPP(c_Finite__Set_Ocard(_1099738), _1099740) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46150 ^ _776545) ^ [_1703430, _1703432, _1703434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703430), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703432))), c_List_Otranspose(_1703432, _1703434)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1703432)), c_List_Otranspose(_1703432, _1703434)), _1703430) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703432), _1703432), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703432), tc_Nat_Onat, _1703432), c_List_Onth(_1703432)), _1703430)), hAPP(c_List_Ofilter(tc_List_Olist(_1703432), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1703432)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703430)), c_Nat_Osize__class_Osize(tc_List_Olist(_1703432)))), _1703434)))], (36770 ^ _776545) ^ [_1474144, _1474146, _1474148, _1474150, _1474152] : [c_Equiv__Relations_Oequiv(_1474144, _1474146, _1474148), hBOOL(hAPP(hAPP(c_member(tc_prod(_1474144, _1474144)), hAPP(hAPP(c_Product__Type_OPair(_1474144, _1474144), _1474150), _1474152)), _1474148)), -(hAPP(c_Relation_OImage(_1474144, _1474144, _1474148), hAPP(hAPP(c_Set_Oinsert(_1474144), _1474150), c_Orderings_Obot__class_Obot(tc_fun(_1474144, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1474144, _1474144, _1474148), hAPP(hAPP(c_Set_Oinsert(_1474144), _1474152), c_Orderings_Obot__class_Obot(tc_fun(_1474144, tc_HOL_Obool)))))], (13053 ^ _776545) ^ [_1006862, _1006864] : [class_Groups_Oab__semigroup__mult(_1006862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006862), _1006864)), -(_1006864 = c_Orderings_Obot__class_Obot(tc_fun(_1006862, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1006862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006862), 13066 ^ [_1006862, _1006864]), 13067 ^ [_1006862, _1006864])), hAPP(hAPP(c_Set_Oinsert(_1006862), 13066 ^ [_1006862, _1006864]), hAPP(hAPP(c_Set_Oinsert(_1006862), 13067 ^ [_1006862, _1006864]), c_Orderings_Obot__class_Obot(tc_fun(_1006862, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1006862), hAPP(c_Finite__Set_Ofold1(_1006862, c_Groups_Otimes__class_Otimes(_1006862)), _1006864)), _1006864)))], (27237 ^ _776545) ^ [_1266676] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266676), 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), _1266676)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1266676)))], (23173 ^ _776545) ^ [_1196290] : [class_Power_Opower(_1196290), -(c_Power_Opower__class_Opower(_1196290) = c_Power_Opower_Opower(_1196290, c_Groups_Oone__class_Oone(_1196290), c_Groups_Otimes__class_Otimes(_1196290)))], (31527 ^ _776545) ^ [_1342608, _1342610, _1342612] : [class_Orderings_Olinorder(_1342608), 31530 ^ _776545 : [(31537 ^ _776545) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342608), _1342610), _1342612) = _1342612, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342608), _1342610), _1342612)))], (31531 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342608), _1342610), _1342612)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342608), _1342610), _1342612) = _1342612)]]], (3120 ^ _776545) ^ [_822964, _822966, _822968, _822970] : [-(c_List_Olistrel1(_822970, _822966) = c_List_Olistrel1(_822968, _822964)), _822970 = _822968, _822966 = _822964], (31311 ^ _776545) ^ [_1338548, _1338550, _1338552, _1338554] : [class_Orderings_Olinorder(_1338548), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338548), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338548), _1338550), _1338552)), _1338554) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338548), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338548), _1338550), _1338554)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338548), _1338552), _1338554)))], (37238 ^ _776545) ^ [_1485262, _1485264] : [-(c_Fun_Oinj__on(_1485262, _1485262, c_COMBI(_1485262), _1485264))], (34117 ^ _776545) ^ [_1410420, _1410422] : [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(_1410422))), 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)), _1410420))))), -(hAPP(c_Nat_OSuc, _1410420) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410422))], (7111 ^ _776545) ^ [_892421, _892423] : [-(hBOOL(hAPP(hAPP(c_member(_892421), 7112 ^ [_892421, _892423]), _892423))), -(_892423 = c_Orderings_Obot__class_Obot(tc_fun(_892421, tc_HOL_Obool)))], (24393 ^ _776545) ^ [_1217689] : [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, _1217689)))))], (45146 ^ _776545) ^ [_1680614, _1680616, _1680618, _1680620] : [class_Groups_Ocomm__monoid__add(_1680614), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1680614), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1680614), _1680616), c_List_Oupto(_1680618, _1680620))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1680614), _1680616), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1680618, _1680620))))], (44222 ^ _776545) ^ [_1660827, _1660829, _1660831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660827)), _1660829)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1660827, _1660831), _1660829) = _1660829)], (25012 ^ _776545) ^ [_1229502, _1229504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229502), _1229504)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229502), _1229504) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49008 ^ _776545) ^ [_1764981, _1764983, _1764985] : [-(c_FunDef_OTHE__default(_1764983, _1764985, _1764981) = _1764985), 49010 ^ _776545 : [(49013 ^ _776545) ^ [_1765103] : [hBOOL(hAPP(_1764981, _1765103)), -(_1765103 = 49009 ^ [_1764981, _1764983, _1764985])], (49011 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1764981, 49009 ^ [_1764981, _1764983, _1764985])))]]], (28235 ^ _776545) ^ [_1283502, _1283504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1283502)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1283504)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1283504), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1283502))))], (37806 ^ _776545) ^ [_1497223, _1497225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497223), _1497225)), -(_1497225 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1497223, 37810 ^ [_1497223, _1497225]), 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)), 37809 ^ [_1497223, _1497225]))))], (41899 ^ _776545) ^ [_1604043, _1604045, _1604047, _1604049, _1604051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604043), tc_List_Olist(_1604043))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604043), tc_List_Olist(_1604043)), _1604045), _1604047)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604043), c_List_Olistrel1(_1604043, _1604049)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604043), tc_List_Olist(_1604043))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604043), tc_List_Olist(_1604043)), hAPP(hAPP(c_List_Olist_OCons(_1604043), _1604051), _1604045)), hAPP(hAPP(c_List_Olist_OCons(_1604043), _1604051), _1604047))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604043), c_List_Olistrel1(_1604043, _1604049)))))], (41694 ^ _776545) ^ [_1597555, _1597557, _1597559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597555), c_Nitpick_Oplus__frac(_1597555, _1597557, c_Nitpick_Ouminus__frac(_1597555, _1597559)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1597555, _1597557, _1597559))], (32508 ^ _776545) ^ [_1363558, _1363560, _1363562, _1363564, _1363566] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363558, tc_fun(_1363560, tc_HOL_Obool)), _1363562), hAPP(hAPP(c_COMBC(_1363558, tc_fun(_1363560, tc_HOL_Obool), tc_fun(_1363560, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363560, tc_HOL_Obool), tc_fun(tc_fun(_1363560, tc_HOL_Obool), tc_fun(_1363560, tc_HOL_Obool)), _1363558), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363560, tc_HOL_Obool))), _1363564)), _1363566)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363560, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363558, tc_fun(_1363560, tc_HOL_Obool)), _1363562), _1363564)), _1363566))], (20041 ^ _776545) ^ [_1138400, _1138402, _1138404] : [class_Fields_Olinordered__field__inverse__zero(_1138400), 20044 ^ _776545 : [(20059 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138400), _1138402), _1138404)), c_Groups_Ozero__class_Ozero(_1138400)))), 20060 ^ _776545 : [(20067 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), _1138402), c_Groups_Ozero__class_Ozero(_1138400))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), c_Groups_Ozero__class_Ozero(_1138400)), _1138404))], (20061 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), c_Groups_Ozero__class_Ozero(_1138400)), _1138402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), _1138404), c_Groups_Ozero__class_Ozero(_1138400)))]]], (20045 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138400), _1138402), _1138404)), c_Groups_Ozero__class_Ozero(_1138400))), 20050 ^ _776545 : [(20053 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), _1138404), c_Groups_Ozero__class_Ozero(_1138400))))], (20051 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), c_Groups_Ozero__class_Ozero(_1138400)), _1138402)))]], 20054 ^ _776545 : [(20057 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), c_Groups_Ozero__class_Ozero(_1138400)), _1138404)))], (20055 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138400), _1138402), c_Groups_Ozero__class_Ozero(_1138400))))]]]]], (48556 ^ _776545) ^ [_1755484, _1755486, _1755488, _1755490] : [-(c_Lazy__Sequence_Oproduct(_1755484, _1755486, _1755488, _1755490) = hAPP(c_Lazy__Sequence_Obind(_1755484, tc_prod(_1755484, _1755486), _1755488), hAPP(hAPP(c_COMBB(tc_fun(_1755486, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755484, _1755486))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755484, _1755486)), _1755484), c_Lazy__Sequence_Obind(_1755486, tc_prod(_1755484, _1755486), _1755490)), hAPP(hAPP(c_COMBB(tc_fun(_1755486, tc_prod(_1755484, _1755486)), tc_fun(_1755486, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755484, _1755486))), _1755484), hAPP(c_COMBB(tc_prod(_1755484, _1755486), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1755484, _1755486)), _1755486), c_Lazy__Sequence_Osingle(tc_prod(_1755484, _1755486)))), c_Product__Type_OPair(_1755484, _1755486)))))], (34824 ^ _776545) ^ [_1426384, _1426386, _1426388, _1426390, _1426392, _1426394] : [hAPP(hAPP(c_Product__Type_OPair(_1426384, _1426386), _1426388), _1426390) = hAPP(hAPP(c_Product__Type_OPair(_1426384, _1426386), _1426392), _1426394), 34827 ^ _776545 : [(34830 ^ _776545) ^ [] : [-(_1426390 = _1426394)], (34828 ^ _776545) ^ [] : [-(_1426388 = _1426392)]]], (25004 ^ _776545) ^ [_1229368, _1229370, _1229372] : [class_Divides_Osemiring__div(_1229368), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1229368), c_Divides_Odiv__class_Omod(_1229368, _1229370, _1229372)), _1229372) = c_Groups_Ozero__class_Ozero(_1229368))], (28427 ^ _776545) ^ [_1286810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1286810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1286810)))], (34626 ^ _776545) ^ [_1421543, _1421545] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421543)), _1421545) = 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), _1421543)), _1421545))], (48917 ^ _776545) ^ [_1762715, _1762717, _1762719] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762715), _1762719), _1762717)), -(hBOOL(hAPP(hAPP(c_member(_1762715), _1762717), hAPP(c_List_Oset(_1762715), _1762719))))], (24260 ^ _776545) ^ [_1215338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215338)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1215338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23065 ^ _776545) ^ [_1194449, _1194451] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1194449, _1194451))))], (31845 ^ _776545) ^ [_1348654, _1348656, _1348658] : [class_Orderings_Olinorder(_1348654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348654), _1348656)), -(c_Big__Operators_Olinorder__class_OMax(_1348654, hAPP(hAPP(c_Set_Oinsert(_1348654), _1348658), _1348656)) = hAPP(hAPP(c_Finite__Set_Ofold(_1348654, _1348654, c_Orderings_Oord__class_Omax(_1348654)), _1348658), _1348656))], (29207 ^ _776545) ^ [_1300003, _1300005] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1300003)), c_Int_OBit1(_1300005)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1300003)), _1300005)))], (52461 ^ _776545) ^ [_1830898] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1830898)))], (40603 ^ _776545) ^ [_1569387, _1569389] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569387, _1569387), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569387, _1569389)), hAPP(hAPP(c_Product__Type_OSigma(_1569387, _1569387), hAPP(c_Relation_OField(_1569387), _1569389)), hAPP(c_COMBK(tc_fun(_1569387, tc_HOL_Obool), _1569387), hAPP(c_Relation_OField(_1569387), _1569389))))))], (16548 ^ _776545) ^ [_1074356, _1074358, _1074360] : [16549 ^ _776545 : [(16552 ^ _776545) ^ [] : [_1074356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16550 ^ _776545) ^ [] : [_1074358 = _1074360]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074356), _1074358) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074356), _1074360))], (1584 ^ _776545) ^ [_799209, _799211] : [-(class_Rings_Oordered__comm__semiring(_799209)), _799211 = _799209, class_Rings_Oordered__comm__semiring(_799211)], (10968 ^ _776545) ^ [_966161, _966163] : [class_Lattices_Olattice(_966161), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_966161), _966163), _966163) = _966163)], (49123 ^ _776545) ^ [_1767573, _1767575, _1767577, _1767579] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1767573), _1767575), _1767577), _1767579) = 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(_1767573)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1767573), _1767575)))], (29017 ^ _776545) ^ [_1296714, _1296716] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1296714)), c_Int_OBit1(_1296716)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296714), _1296716)))], (11048 ^ _776545) ^ [_967543, _967545, _967547, _967549] : [class_Groups_Oab__semigroup__mult(_967543), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967543), _967545), _967547)), _967549) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967543), _967545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967543), _967547), _967549)))], (36152 ^ _776545) ^ [_1458246, _1458248, _1458250, _1458252, _1458254] : [class_Groups_Oordered__ab__group__add(_1458246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458248), _1458250)), 36162 ^ _776545 : [(36165 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458246), c_Groups_Ozero__class_Ozero(_1458246)), hAPP(_1458252, 36161 ^ [_1458246, _1458248, _1458250, _1458252, _1458254])))], (36163 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458248), 36161 ^ [_1458246, _1458248, _1458250, _1458252, _1458254]), _1458250)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458248, _1458246), _1458252), _1458250) = c_Groups_Ozero__class_Ozero(_1458246), hBOOL(hAPP(hAPP(c_member(_1458248), _1458254), _1458250)), -(hAPP(_1458252, _1458254) = c_Groups_Ozero__class_Ozero(_1458246))], (2776 ^ _776545) ^ [_817612, _817614, _817616, _817618, _817620, _817622] : [-(c_Predicate_ORangeP(_817622, _817618, _817614) = c_Predicate_ORangeP(_817620, _817616, _817612)), _817622 = _817620, _817618 = _817616, _817614 = _817612], (47122 ^ _776545) ^ [_1723660, _1723662] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723660), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723660))), c_List_Otranspose(_1723660, _1723662)))))], (38448 ^ _776545) ^ [_1513631, _1513633] : [-(c_Set_Othe__elem(_1513631, _1513633) = c_HOL_OThe(_1513631, hAPP(hAPP(c_COMBB(tc_fun(_1513631, tc_HOL_Obool), tc_HOL_Obool, _1513631), hAPP(c_fequal, _1513633)), hAPP(hAPP(c_COMBC(_1513631, tc_fun(_1513631, tc_HOL_Obool), tc_fun(_1513631, tc_HOL_Obool)), c_Set_Oinsert(_1513631)), c_Orderings_Obot__class_Obot(tc_fun(_1513631, tc_HOL_Obool))))))], (31983 ^ _776545) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (38523 ^ _776545) ^ [_1515128, _1515130, _1515132, _1515134] : [-(hAPP(c_Relation_ORange(_1515128, _1515130), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1515128, _1515130), tc_HOL_Obool)), _1515132), _1515134)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515130, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1515128, _1515130), _1515132)), hAPP(c_Relation_ORange(_1515128, _1515130), _1515134)))], (18162 ^ _776545) ^ [_1103020, _1103022, _1103024, _1103026, _1103028, _1103030, _1103032] : [c_Finite__Set_Ofolding__image__simple(_1103020, _1103022, _1103024, _1103026, _1103028, _1103030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103022), _1103032)), -(hAPP(_1103030, _1103032) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1103020, _1103022, _1103024), _1103028), _1103026), _1103032))], (52019 ^ _776545) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (22561 ^ _776545) ^ [_1185452, _1185454, _1185456] : [class_Power_Opower(_1185452), class_Rings_Omult__zero(_1185452), class_Rings_Ono__zero__divisors(_1185452), class_Rings_Ozero__neq__one(_1185452), 22576 ^ _776545 : [(22585 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1185452), _1185454), _1185456) = c_Groups_Ozero__class_Ozero(_1185452)), _1185454 = c_Groups_Ozero__class_Ozero(_1185452), -(_1185456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22577 ^ _776545) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1185452), _1185454), _1185456) = c_Groups_Ozero__class_Ozero(_1185452), 22580 ^ _776545 : [(22583 ^ _776545) ^ [] : [_1185456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22581 ^ _776545) ^ [] : [-(_1185454 = c_Groups_Ozero__class_Ozero(_1185452))]]]]], (34816 ^ _776545) ^ [_1426179, _1426181, _1426183] : [hBOOL(hAPP(_1426179, hAPP(hAPP(c_Product__Type_OPair(_1426181, _1426183), 34817 ^ [_1426179, _1426181, _1426183]), 34818 ^ [_1426179, _1426181, _1426183]))), 34821 ^ _776545 : [(34822 ^ _776545) ^ [_1426326] : [-(hBOOL(hAPP(_1426179, _1426326)))]]], (34111 ^ _776545) ^ [_1410297, _1410299] : [hAPP(c_Nat_OSuc, _1410297) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410299), -(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(_1410299))), 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)), _1410297))))))], (7952 ^ _776545) ^ [_910974, _910976, _910978] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910974, tc_HOL_Obool)), _910976), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910974, tc_HOL_Obool)), _910978), _910976))))], (15724 ^ _776545) ^ [] : [-(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))))], (8363 ^ _776545) ^ [_919894, _919896, _919898, _919900] : [class_Lattices_Olattice(_919894), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919894), _919896), _919898)), _919900) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919894), _919896), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_919894), _919898), _919900)))], (14336 ^ _776545) ^ [_1035010, _1035012, _1035014, _1035016] : [class_Rings_Ocomm__semiring__1(_1035010), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035010), _1035012), _1035014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035010), _1035016), _1035014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035010), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035010), _1035012), _1035016)), _1035014))], (48144 ^ _776545) ^ [_1746082, _1746084, _1746086] : [hBOOL(hAPP(hAPP(c_member(_1746082), _1746084), hAPP(c_List_Oset(_1746082), _1746086))), 48149 ^ _776545 : [(48152 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1746082), _1746084), hAPP(c_List_Oset(_1746082), 48147 ^ [_1746082, _1746084, _1746086])))], (48150 ^ _776545) ^ [] : [-(_1746086 = hAPP(hAPP(c_List_Oappend(_1746082), 48147 ^ [_1746082, _1746084, _1746086]), hAPP(hAPP(c_List_Olist_OCons(_1746082), _1746084), 48148 ^ [_1746082, _1746084, _1746086])))]]], (45315 ^ _776545) ^ [_1684658, _1684660] : [-(hBOOL(hAPP(c_List_Olistsp(_1684658, _1684660), c_List_Olist_ONil(_1684658))))], (29934 ^ _776545) ^ [_1313284, _1313286] : [-(_1313284 = _1313286), -(c_Random_Oinc__shift(_1313284, _1313286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1313286), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (36386 ^ _776545) ^ [_1463894] : [-(_1463894 = 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)), _1463894), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (51863 ^ _776545) ^ [_1824701, _1824703] : [class_Lattices_Obounded__lattice(_1824701), -(class_Lattices_Obounded__lattice__top(tc_fun(_1824703, _1824701)))], (11942 ^ _776545) ^ [_986204, _986206, _986208, _986210, _986212, _986214] : [-(_986204 = _986206), -(hAPP(c_Fun_Ofun__upd(_986208, _986210, _986212, _986206, _986214), _986204) = hAPP(_986212, _986204))], (14520 ^ _776545) ^ [_1038391, _1038393] : [14521 ^ _776545 : [(14524 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038393), _1038391))], (14522 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038391), _1038393))]], _1038391 = _1038393], (48336 ^ _776545) ^ [_1750048, _1750050, _1750052, _1750054] : [c_List_Olist__ex1(_1750048, _1750050, hAPP(hAPP(c_List_Olist_OCons(_1750048), _1750052), _1750054)), 48339 ^ _776545 : [(48346 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1750050, _1750052))), -(c_List_Olist__ex1(_1750048, _1750050, _1750054))], (48340 ^ _776545) ^ [] : [hBOOL(hAPP(_1750050, _1750052)), -(c_List_Olist__all(_1750048, hAPP(hAPP(c_COMBS(_1750048, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1750048), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1750048), c_fNot), _1750050))), hAPP(c_fequal, _1750052)), _1750054))]]], (17303 ^ _776545) ^ [_1088052, _1088054, _1088056, _1088058] : [class_Rings_Olinordered__ring__strict(_1088052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088052), _1088054), _1088056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088052), _1088058), c_Groups_Ozero__class_Ozero(_1088052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088052), _1088056), _1088058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088052), _1088054), _1088058))))], (46351 ^ _776545) ^ [_1708734, _1708736] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1708734, _1708736)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1708736), _1708734))], (11918 ^ _776545) ^ [_985867, _985869, _985871, _985873, _985875] : [hAPP(_985867, _985869) = _985871, -(c_Fun_Ofun__upd(_985873, _985875, _985867, _985869, _985871) = _985867)], (21036 ^ _776545) ^ [_1156613, _1156615, _1156617] : [class_Fields_Olinordered__field__inverse__zero(_1156613), 21042 ^ _776545 : [(21047 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156613), 21041 ^ [_1156613, _1156615, _1156617]), _1156615)), _1156617))], (21045 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156613), 21041 ^ [_1156613, _1156615, _1156617]), c_Groups_Oone__class_Oone(_1156613))))], (21043 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156613), c_Groups_Ozero__class_Ozero(_1156613)), 21041 ^ [_1156613, _1156615, _1156617])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156613), _1156615), _1156617)))], (50936 ^ _776545) ^ [_1808061, _1808063, _1808065, _1808067, _1808069, _1808071, _1808073, _1808075] : [c_Finite__Set_Ofolding__image(_1808061, _1808063, _1808065, _1808067, _1808069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1808063), _1808071)), 50946 ^ _776545 : [(50949 ^ _776545) ^ [] : [hAPP(_1808073, 50945 ^ [_1808061, _1808063, _1808065, _1808067, _1808069, _1808071, _1808073, _1808075]) = hAPP(_1808075, 50945 ^ [_1808061, _1808063, _1808065, _1808067, _1808069, _1808071, _1808073, _1808075])], (50947 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808063), 50945 ^ [_1808061, _1808063, _1808065, _1808067, _1808069, _1808071, _1808073, _1808075]), _1808071)))]], -(hAPP(hAPP(_1808069, _1808073), _1808071) = hAPP(hAPP(_1808069, _1808075), _1808071))], (45503 ^ _776545) ^ [_1688980, _1688982, _1688984] : [_1688980 = _1688982, -(c_List_Olist__all2(_1688984, _1688984, c_fequal, _1688980, _1688982))], (51987 ^ _776545) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (47255 ^ _776545) ^ [_1726581, _1726583, _1726585, _1726587, _1726589] : [-(hAPP(hAPP(c_List_Ozip(_1726581, _1726583), c_List_OtakeWhile(_1726581, _1726585, _1726587)), _1726589) = c_List_OtakeWhile(tc_prod(_1726581, _1726583), hAPP(c_Fun_Ocomp(_1726581, tc_HOL_Obool, tc_prod(_1726581, _1726583), _1726585), c_Product__Type_Ofst(_1726581, _1726583)), hAPP(hAPP(c_List_Ozip(_1726581, _1726583), _1726587), _1726589)))], (23357 ^ _776545) ^ [_1199791, _1199793, _1199795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199791)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199793), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199795)), 23367 ^ _776545 : [(23373 ^ _776545) ^ [] : [-(_1199793 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23369 ^ [_1199791, _1199793, _1199795]), 23366 ^ [_1199791, _1199793, _1199795]))], (23371 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23369 ^ [_1199791, _1199793, _1199795]), _1199795)))], (23368 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23366 ^ [_1199791, _1199793, _1199795]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1199791))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199793), _1199791) = _1199793)], (39469 ^ _776545) ^ [_1541442, _1541444] : [-(c_Product__Type_Omap__pair(_1541442, _1541442, _1541444, _1541444, c_Fun_Oid(_1541442), c_Fun_Oid(_1541444)) = c_Fun_Oid(tc_prod(_1541442, _1541444)))], (9174 ^ _776545) ^ [_934976, _934978, _934980] : [class_Orderings_Oorder(_934976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934976), _934978), _934980)), _934978 = _934980], (28957 ^ _776545) ^ [_1295650, _1295652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295650), _1295652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295650)), c_Int_OBit1(_1295652))))], (11131 ^ _776545) ^ [_969157, _969159, _969161, _969163, _969165, _969167] : [hBOOL(hAPP(hAPP(c_member(_969157), _969159), _969161)), _969163 = hAPP(_969165, _969159), -(hBOOL(hAPP(hAPP(c_member(_969167), _969163), hAPP(c_Set_Oimage(_969157, _969167, _969165), _969161))))], (24768 ^ _776545) ^ [_1224534] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1224534, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (49980 ^ _776545) ^ [_1786023, _1786025, _1786027] : [hAPP(c_Fun_Ocomp(_1786025, _1786023, _1786023, c_Hilbert__Choice_Oinv__into(_1786023, _1786025, c_Orderings_Otop__class_Otop(tc_fun(_1786023, tc_HOL_Obool)), _1786027)), _1786027) = c_Fun_Oid(_1786023), -(c_Fun_Oinj__on(_1786023, _1786025, _1786027, c_Orderings_Otop__class_Otop(tc_fun(_1786023, tc_HOL_Obool))))], (41418 ^ _776545) ^ [_1589893, _1589895, _1589897, _1589899] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1589893, _1589895), tc_fun(_1589893, _1589895)), _1589897), c_Fun_Ocomp(_1589895, _1589895, _1589893, _1589899)) = c_Fun_Ocomp(_1589895, _1589895, _1589893, hAPP(hAPP(c_Nat_Ocompow(_1589895, _1589895), _1589897), _1589899)))], (38531 ^ _776545) ^ [_1515313, _1515315, _1515317] : [-(hAPP(c_Set_Oimage(tc_prod(_1515313, _1515315), _1515315, c_Product__Type_Osnd(_1515313, _1515315)), _1515317) = hAPP(c_Relation_ORange(_1515313, _1515315), _1515317))], (16741 ^ _776545) ^ [_1077629, _1077631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077629)), _1077631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077629), _1077631)))], (31335 ^ _776545) ^ [_1339046, _1339048] : [class_Orderings_Olinorder(_1339046), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339046), _1339048), _1339048) = _1339048)], (41162 ^ _776545) ^ [_1583669, _1583671, _1583673, _1583675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583669, _1583669)), hAPP(hAPP(c_Product__Type_OPair(_1583669, _1583669), _1583671), _1583673)), c_Transitive__Closure_Ortrancl(_1583669, hAPP(c_Relation_Oconverse(_1583669, _1583669), _1583675)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583669, _1583669)), hAPP(hAPP(c_Product__Type_OPair(_1583669, _1583669), _1583673), _1583671)), c_Transitive__Closure_Ortrancl(_1583669, _1583675))))], (18160 ^ _776545) ^ [_1102991] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102991) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1102991))], (34531 ^ _776545) ^ [_1419526, _1419528, _1419530, _1419532, _1419534, _1419536, _1419538] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419526, tc_fun(_1419528, tc_fun(_1419530, tc_HOL_Obool))), _1419532), _1419534), _1419536), _1419538)), 34535 ^ _776545 : [(34538 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1419534, 34534 ^ [_1419526, _1419528, _1419530, _1419532, _1419534, _1419536, _1419538]), _1419536), _1419538)))], (34536 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419526), 34534 ^ [_1419526, _1419528, _1419530, _1419532, _1419534, _1419536, _1419538]), _1419532)))]]], (25169 ^ _776545) ^ [_1232247, _1232249, _1232251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232247)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232247), _1232249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232247), _1232251)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232249), _1232251))], (36462 ^ _776545) ^ [_1465939, _1465941, _1465943, _1465945, _1465947] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465943, _1465939)), hAPP(hAPP(c_Product__Type_OPair(_1465943, _1465939), _1465947), _1465941)), _1465945)), -(hBOOL(hAPP(hAPP(c_member(_1465939), _1465941), hAPP(c_Relation_OImage(_1465943, _1465939, _1465945), hAPP(hAPP(c_Set_Oinsert(_1465943), _1465947), c_Orderings_Obot__class_Obot(tc_fun(_1465943, tc_HOL_Obool)))))))], (22281 ^ _776545) ^ [_1180531, _1180533, _1180535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180531), _1180533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180533), _1180535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180531), _1180535)))], (51239 ^ _776545) ^ [_1814030, _1814032, _1814034, _1814036, _1814038] : [class_Rings_Ocomm__semiring__1(_1814030), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814030), _1814032), _1814034)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814030), _1814036), _1814038)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814030), _1814032), _1814036)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814030), _1814034), _1814038))))], (31323 ^ _776545) ^ [_1338866] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1338866), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1338866)], (33186 ^ _776545) ^ [_1384477, _1384479] : [-(hAPP(c_Set_OCollect(_1384477), hAPP(hAPP(c_COMBC(_1384477, tc_fun(_1384477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1384477)), _1384479)) = _1384479)], (34640 ^ _776545) ^ [_1421865, _1421867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421865)), 34643 ^ _776545 : [(34650 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421867), _1421865))), -(c_Divides_OposDivAlg(_1421867, _1421865) = hAPP(c_Divides_Oadjust(_1421865), c_Divides_OposDivAlg(_1421867, 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)))), _1421865))))], (34644 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421867), _1421865)), -(c_Divides_OposDivAlg(_1421867, _1421865) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421867))]]], (6184 ^ _776545) ^ [_875868, _875870] : [hBOOL(hAPP(hAPP(c_member(_875868), _875870), c_Orderings_Obot__class_Obot(tc_fun(_875868, tc_HOL_Obool))))], (10413 ^ _776545) ^ [_955394, _955396, _955398] : [class_Groups_Oordered__ab__group__add(_955394), 10416 ^ _776545 : [(10423 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955394), hAPP(c_Groups_Ouminus__class_Ouminus(_955394), _955398)), _955396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955394), hAPP(c_Groups_Ouminus__class_Ouminus(_955394), _955396)), _955398)))], (10417 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955394), hAPP(c_Groups_Ouminus__class_Ouminus(_955394), _955396)), _955398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955394), hAPP(c_Groups_Ouminus__class_Ouminus(_955394), _955398)), _955396)))]]], (39329 ^ _776545) ^ [_1538013, _1538015] : [-(c_Fun_Oinj__on(_1538013, _1538013, c_Fun_Oid(_1538013), _1538015))], (44982 ^ _776545) ^ [_1677290, _1677292, _1677294, _1677296] : [class_Rings_Osemiring__1(_1677290), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677290), hAPP(hAPP(c_List_Omap(_1677292, _1677290), hAPP(c_COMBK(_1677290, _1677292), _1677294)), _1677296)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1677290), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1677290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677292)), _1677296))), _1677294))], (50801 ^ _776545) ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614)), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), _1803616), _1803618)), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), _1803620), _1803622))), c_Transitive__Closure_Ortrancl(tc_prod(_1803612, _1803614), _1803624))), hBOOL(hAPP(hAPP(_1803626, _1803616), _1803618)), 50812 ^ _776545 : [(50817 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614)), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), 50810 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]), 50811 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626])), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), 50814 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]), 50815 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]))), _1803624)))], (50819 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1803626, 50810 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]), 50811 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626])))], (50821 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1803626, 50814 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]), 50815 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]))], (50813 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1803612, _1803614), tc_prod(_1803612, _1803614)), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), _1803616), _1803618)), hAPP(hAPP(c_Product__Type_OPair(_1803612, _1803614), 50810 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]), 50811 ^ [_1803612, _1803614, _1803616, _1803618, _1803620, _1803622, _1803624, _1803626]))), c_Transitive__Closure_Ortrancl(tc_prod(_1803612, _1803614), _1803624))))]], -(hBOOL(hAPP(hAPP(_1803626, _1803620), _1803622)))], (1554 ^ _776545) ^ [_798834, _798836] : [-(class_Groups_Oordered__comm__monoid__add(_798834)), _798836 = _798834, class_Groups_Oordered__comm__monoid__add(_798836)], (3574 ^ _776545) ^ [_829993, _829995, _829997, _829999, _830001, _830003, _830005, _830007] : [-(c_List_Olinorder__class_Osort__key(_830007, _830003, _829999, _829995) = c_List_Olinorder__class_Osort__key(_830005, _830001, _829997, _829993)), _830007 = _830005, _830003 = _830001, _829999 = _829997, _829995 = _829993], (33511 ^ _776545) ^ [_1393113, _1393115, _1393117, _1393119, _1393121] : [_1393113 = c_Orderings_Obot__class_Obot(tc_fun(_1393115, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393115, tc_fun(_1393117, tc_HOL_Obool)), _1393113), hAPP(hAPP(c_COMBB(tc_fun(_1393117, tc_HOL_Obool), tc_fun(_1393117, tc_HOL_Obool), _1393115), hAPP(c_Set_Oinsert(_1393117), _1393119)), _1393121)) = c_Orderings_Obot__class_Obot(tc_fun(_1393117, tc_HOL_Obool)))], (36624 ^ _776545) ^ [_1470811, _1470813, _1470815, _1470817, _1470819] : [hBOOL(hAPP(hAPP(c_member(_1470811), _1470813), hAPP(c_Relation_OImage(_1470815, _1470811, _1470817), _1470819))), 36628 ^ _776545 : [(36631 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470815), 36627 ^ [_1470811, _1470813, _1470815, _1470817, _1470819]), _1470819)))], (36629 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470815, _1470811)), hAPP(hAPP(c_Product__Type_OPair(_1470815, _1470811), 36627 ^ [_1470811, _1470813, _1470815, _1470817, _1470819]), _1470813)), _1470817)))]]], (12736 ^ _776545) ^ [_1001203, _1001205, _1001207] : [class_Complete__Lattice_Ocomplete__lattice(_1001203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001203), _1001205)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1001203), _1001207), c_Complete__Lattice_OSup__class_OSup(_1001203, _1001205)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001203, _1001203, c_Lattices_Osemilattice__sup__class_Osup(_1001203)), _1001207), _1001205))], (44815 ^ _776545) ^ [_1672977, _1672979, _1672981, _1672983, _1672985] : [hAPP(hAPP(c_List_Omap(_1672977, _1672979), _1672981), _1672983) = hAPP(hAPP(c_List_Omap(_1672977, _1672979), _1672985), _1672983), 44818 ^ _776545 : [(44819 ^ _776545) ^ [_1673100] : [hBOOL(hAPP(hAPP(c_member(_1672977), _1673100), hAPP(c_List_Oset(_1672977), _1672983))), -(hAPP(_1672981, _1673100) = hAPP(_1672985, _1673100))]]], (5122 ^ _776545) ^ [_854687, _854689, _854691, _854693, _854695, _854697] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_854697, _854693, _854689) = c_SetInterval_Oord__class_OatLeastAtMost(_854695, _854691, _854687)), _854697 = _854695, _854693 = _854691, _854689 = _854687], (9624 ^ _776545) ^ [_941435, _941437, _941439] : [class_Orderings_Oorder(_941435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941435), _941437), _941439)), -(_941437 = _941439), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941435), _941437), _941439)))], (29169 ^ _776545) ^ [_1299373, _1299375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299373), _1299375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299373)), c_Int_OBit0(_1299375))))], (5214 ^ _776545) ^ [_856111, _856113, _856115, _856117] : [-(c_Transitive__Closure_Ortrancl(_856117, _856113) = c_Transitive__Closure_Ortrancl(_856115, _856111)), _856117 = _856115, _856113 = _856111], (42463 ^ _776545) ^ [_1619668, _1619670] : [-(c_List_Olists(_1619668, _1619670) = hAPP(c_Set_OCollect(tc_List_Olist(_1619668)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619668), tc_fun(_1619668, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1619668, tc_HOL_Obool), tc_fun(tc_fun(_1619668, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1619668)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1619668, tc_HOL_Obool))), c_List_Oset(_1619668))), _1619670)))], (16506 ^ _776545) ^ [_1073742] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073742), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1073742)], (44066 ^ _776545) ^ [_1657682, _1657684, _1657686, _1657688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657682), _1657684)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657686)), _1657688))), -(hAPP(hAPP(c_List_Otake(_1657686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657682), _1657684)), _1657688) = hAPP(hAPP(c_List_Oappend(_1657686), hAPP(hAPP(c_List_Otake(_1657686), _1657682), _1657688)), hAPP(hAPP(c_List_Otake(_1657686), _1657684), hAPP(hAPP(c_List_Odrop(_1657686), _1657682), _1657688))))], (40969 ^ _776545) ^ [_1578953, _1578955, _1578957, _1578959] : [hBOOL(hAPP(hAPP(c_member(_1578953), _1578955), c_Wellfounded_Oacc(_1578953, _1578957))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578953, _1578953)), hAPP(hAPP(c_Product__Type_OPair(_1578953, _1578953), _1578959), _1578955)), c_Transitive__Closure_Ortrancl(_1578953, _1578957))), -(hBOOL(hAPP(hAPP(c_member(_1578953), _1578959), c_Wellfounded_Oacc(_1578953, _1578957))))], (37050 ^ _776545) ^ [_1480589, _1480591, _1480593, _1480595, _1480597, _1480599, _1480601, _1480603] : [c_Equiv__Relations_Oequiv(_1480589, _1480591, _1480593), c_Equiv__Relations_Ocongruent2(_1480589, _1480595, _1480597, _1480593, _1480599, _1480601), hBOOL(hAPP(hAPP(c_member(_1480589), _1480603), _1480591)), -(c_Equiv__Relations_Ocongruent(_1480595, _1480597, _1480599, hAPP(_1480601, _1480603)))], (5648 ^ _776545) ^ [_862782, _862784, _862786, _862788, _862790, _862792] : [-(c_COMBS(_862792, _862788, _862784) = c_COMBS(_862790, _862786, _862782)), _862792 = _862790, _862788 = _862786, _862784 = _862782], (33765 ^ _776545) ^ [_1401377, _1401379, _1401381, _1401383, _1401385] : [class_Groups_Ocomm__monoid__mult(_1401377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401379), _1401381)), 33772 ^ _776545 : [(33779 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401379), _1401383), _1401381))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401379, _1401377), hAPP(hAPP(c_COMBC(_1401379, _1401377, _1401377), hAPP(hAPP(c_COMBS(_1401379, _1401377, tc_fun(_1401377, _1401377)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401377, tc_fun(_1401377, _1401377)), _1401379), c_If(_1401377)), hAPP(c_fequal, _1401383))), _1401385)), c_Groups_Oone__class_Oone(_1401377))), _1401381) = c_Groups_Oone__class_Oone(_1401377))], (33773 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1401379), _1401383), _1401381)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401379, _1401377), hAPP(hAPP(c_COMBC(_1401379, _1401377, _1401377), hAPP(hAPP(c_COMBS(_1401379, _1401377, tc_fun(_1401377, _1401377)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401377, tc_fun(_1401377, _1401377)), _1401379), c_If(_1401377)), hAPP(c_fequal, _1401383))), _1401385)), c_Groups_Oone__class_Oone(_1401377))), _1401381) = hAPP(_1401385, _1401383))]]], (2270 ^ _776545) ^ [_809605, _809607, _809609, _809611] : [-(c_Orderings_Oord_Omax(_809611, _809607) = c_Orderings_Oord_Omax(_809609, _809605)), _809611 = _809609, _809607 = _809605], (10429 ^ _776545) ^ [_955677, _955679, _955681] : [class_Groups_Oordered__ab__group__add(_955677), 10432 ^ _776545 : [(10439 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955677), _955681), hAPP(c_Groups_Ouminus__class_Ouminus(_955677), _955679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955677), _955679), hAPP(c_Groups_Ouminus__class_Ouminus(_955677), _955681))))], (10433 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955677), _955679), hAPP(c_Groups_Ouminus__class_Ouminus(_955677), _955681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955677), _955681), hAPP(c_Groups_Ouminus__class_Ouminus(_955677), _955679))))]]], (15017 ^ _776545) ^ [_1047546, _1047548, _1047550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047546), _1047548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047550), _1047548))))], (39886 ^ _776545) ^ [_1552698, _1552700, _1552702, _1552704, _1552706, _1552708] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552698, _1552700, _1552702, _1552704), _1552706), _1552708) = hAPP(_1552704, hAPP(_1552706, _1552708)))], (43044 ^ _776545) ^ [_1634417, _1634419, _1634421, _1634423] : [-(_1634417 = _1634419), -(c_List_Oremove1(_1634421, _1634417, hAPP(hAPP(c_List_Olist_OCons(_1634421), _1634419), _1634423)) = hAPP(hAPP(c_List_Olist_OCons(_1634421), _1634419), c_List_Oremove1(_1634421, _1634417, _1634423)))], (23813 ^ _776545) ^ [_1207901, _1207903] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207901)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207903)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207901), _1207903)))], (45205 ^ _776545) ^ [_1682032, _1682034] : [hAPP(c_Code__Numeral_Onat__of, _1682032) = hAPP(c_Code__Numeral_Onat__of, _1682034), -(_1682032 = _1682034)], (29331 ^ _776545) ^ [_1302140] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1302140))), 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), _1302140), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (41483 ^ _776545) ^ [_1591747, _1591749, _1591751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591747, _1591747)), _1591749), c_Transitive__Closure_Otrancl(_1591747, _1591751))), 41487 ^ _776545 : [(41490 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591747, _1591747)), _1591749), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591747, _1591747), tc_HOL_Obool), 41486 ^ [_1591747, _1591749, _1591751]), _1591751))))], (41488 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41486 ^ [_1591747, _1591749, _1591751])))]]], (33008 ^ _776545) ^ [_1379196, _1379198, _1379200] : [-(hBOOL(hAPP(_1379196, _1379198))), -(hAPP(c_Set_OCollect(_1379200), hAPP(hAPP(c_COMBS(_1379200, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1379200), c_fconj), hAPP(c_fequal, _1379198))), _1379196)) = c_Orderings_Obot__class_Obot(tc_fun(_1379200, tc_HOL_Obool)))], (33094 ^ _776545) ^ [_1381501, _1381503] : [hBOOL(hAPP(hAPP(c_member(_1381501), _1381503), c_Orderings_Obot__class_Obot(tc_fun(_1381501, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381501, tc_HOL_Obool)), _1381503)))], (42691 ^ _776545) ^ [_1626499, _1626501, _1626503, _1626505] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626499)), hAPP(hAPP(c_List_Olist__update(_1626499, _1626501), _1626503), _1626505)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626499)), _1626501))], (45199 ^ _776545) ^ [_1681926, _1681928] : [_1681926 = _1681928, -(hAPP(c_Code__Numeral_Onat__of, _1681926) = hAPP(c_Code__Numeral_Onat__of, _1681928))], (7558 ^ _776545) ^ [_901370, _901372, _901374] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901370, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901370, tc_HOL_Obool)), _901372), _901374)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901370, tc_HOL_Obool)), _901372), _901374)) = _901372)], (40771 ^ _776545) ^ [_1574366, _1574368, _1574370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574366, _1574366), tc_HOL_Obool)), _1574368), _1574370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574366, _1574366), tc_HOL_Obool)), _1574370), c_Transitive__Closure_Ortrancl(_1574366, _1574368))), -(c_Transitive__Closure_Ortrancl(_1574366, _1574370) = c_Transitive__Closure_Ortrancl(_1574366, _1574368))], (24102 ^ _776545) ^ [_1212704, _1212706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212704)), 24105 ^ _776545 : [(24112 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212704), _1212706)), -(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), _1212706), _1212704))))], (24106 ^ _776545) ^ [] : [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), _1212706), _1212704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212704), _1212706)))]]], (3658 ^ _776545) ^ [_831351, _831353, _831355, _831357, _831359, _831361, _831363, _831365, _831367, _831369] : [-(c_List_Ofoldr(_831369, _831365, _831361, _831357, _831353) = c_List_Ofoldr(_831367, _831363, _831359, _831355, _831351)), _831369 = _831367, _831365 = _831363, _831361 = _831359, _831357 = _831355, _831353 = _831351], (20691 ^ _776545) ^ [_1150101, _1150103, _1150105, _1150107] : [class_Fields_Olinordered__field__inverse__zero(_1150101), 20694 ^ _776545 : [(20695 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150101), _1150105), _1150107))), 20698 ^ _776545 : [(20705 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), c_Groups_Ozero__class_Ozero(_1150101)), _1150107))), 20708 ^ _776545 : [(20715 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150107), c_Groups_Ozero__class_Ozero(_1150101)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150103), c_Groups_Ozero__class_Ozero(_1150101))))], (20709 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150107), c_Groups_Ozero__class_Ozero(_1150101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150101), _1150103), _1150107))))]]], (20699 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), c_Groups_Ozero__class_Ozero(_1150101)), _1150107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150101), _1150103), _1150107)), _1150105)))]]], (20721 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150101), _1150105), _1150107)))), 20724 ^ _776545 : [(20727 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150101), _1150103), _1150107)), _1150105))], (20725 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), c_Groups_Ozero__class_Ozero(_1150101)), _1150107)))]], 20728 ^ _776545 : [(20731 ^ _776545) ^ [] : [20732 ^ _776545 : [(20735 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150101), _1150103), _1150107)))], (20733 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150107), c_Groups_Ozero__class_Ozero(_1150101))))]], 20736 ^ _776545 : [(20739 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150103), c_Groups_Ozero__class_Ozero(_1150101)))], (20737 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), _1150107), c_Groups_Ozero__class_Ozero(_1150101)))]]], (20729 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150101), c_Groups_Ozero__class_Ozero(_1150101)), _1150107))]]]]], (49291 ^ _776545) ^ [_1771778] : [-(c_Relation_Otrans(tc_fun(_1771778, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1771778)))], (39449 ^ _776545) ^ [_1540864, _1540866, _1540868, _1540870, _1540872, _1540874, _1540876, _1540878, _1540880] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540864, _1540866)), hAPP(hAPP(c_Product__Type_OPair(_1540864, _1540866), _1540868), _1540870)), _1540872)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540874, _1540876)), hAPP(hAPP(c_Product__Type_OPair(_1540874, _1540876), hAPP(_1540878, _1540868)), hAPP(_1540880, _1540870))), hAPP(c_Set_Oimage(tc_prod(_1540864, _1540866), tc_prod(_1540874, _1540876), c_Product__Type_Omap__pair(_1540864, _1540874, _1540866, _1540876, _1540878, _1540880)), _1540872))))], (19279 ^ _776545) ^ [_1124520, _1124522, _1124524, _1124526, _1124528] : [class_Groups_Ocomm__monoid__add(_1124520), class_Groups_Oordered__ab__semigroup__add(_1124520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124522), _1124524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1124522, tc_HOL_Obool)), _1124526), _1124524)), 19297 ^ _776545 : [(19300 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124520), c_Groups_Ozero__class_Ozero(_1124520)), hAPP(_1124528, 19296 ^ [_1124520, _1124522, _1124524, _1124526, _1124528])))], (19298 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1124522), 19296 ^ [_1124520, _1124522, _1124524, _1124526, _1124528]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1124522, tc_HOL_Obool)), _1124524), _1124526))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124520), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1124522, _1124520), _1124528), _1124526)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1124522, _1124520), _1124528), _1124524))))], (52065 ^ _776545) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (47096 ^ _776545) ^ [_1723178, _1723180, _1723182] : [-(hAPP(c_List_Orev(_1723178), hAPP(hAPP(c_List_Olist_OCons(_1723178), _1723180), _1723182)) = hAPP(hAPP(c_List_Oappend(_1723178), hAPP(c_List_Orev(_1723178), _1723182)), hAPP(hAPP(c_List_Olist_OCons(_1723178), _1723180), c_List_Olist_ONil(_1723178))))], (45984 ^ _776545) ^ [_1699109, _1699111, _1699113] : [45986 ^ _776545 : [(45989 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1699109), tc_List_Olist(_1699109), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699109), tc_fun(tc_List_Olist(_1699109), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699109), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1699109), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699109), tc_HOL_Obool)), tc_List_Olist(_1699109)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699109))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699109)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1699109))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1699109)))), 45985 ^ [_1699109, _1699111, _1699113]))], (45987 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699109), tc_List_Olist(_1699109))), 45985 ^ [_1699109, _1699111, _1699113]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1699109), tc_List_Olist(_1699109))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1699109), tc_List_Olist(_1699109)), _1699111), _1699113)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699109))), _1699111) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699109))), _1699113), 45994 ^ _776545 : [(46001 ^ _776545) ^ [] : [_1699111 = _1699113, -(c_List_Oconcat(_1699109, _1699111) = c_List_Oconcat(_1699109, _1699113))], (45995 ^ _776545) ^ [] : [c_List_Oconcat(_1699109, _1699111) = c_List_Oconcat(_1699109, _1699113), -(_1699111 = _1699113)]]], (34421 ^ _776545) ^ [_1417238] : [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), _1417238))), 34424 ^ _776545 : [(34431 ^ _776545) ^ [] : [-(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), _1417238)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417238)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417238)), 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), _1417238)))))], (34425 ^ _776545) ^ [] : [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), _1417238))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417238)) = 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)))]]], (43657 ^ _776545) ^ [_1647258, _1647260, _1647262] : [_1647258 = c_List_Olist_ONil(_1647260), -(c_List_Obutlast(_1647260, hAPP(hAPP(c_List_Oappend(_1647260), _1647262), _1647258)) = c_List_Obutlast(_1647260, _1647262))], (41017 ^ _776545) ^ [_1580105] : [-(c_Relation_OId(_1580105) = hAPP(c_Set_OCollect(tc_prod(_1580105, _1580105)), hAPP(hAPP(c_COMBB(tc_fun(_1580105, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1580105, _1580105)), c_HOL_OEx(_1580105)), hAPP(hAPP(c_COMBC(tc_prod(_1580105, _1580105), tc_fun(_1580105, tc_prod(_1580105, _1580105)), tc_fun(_1580105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1580105, _1580105), tc_HOL_Obool), tc_fun(tc_fun(_1580105, tc_prod(_1580105, _1580105)), tc_fun(_1580105, tc_HOL_Obool)), tc_prod(_1580105, _1580105)), c_COMBB(tc_prod(_1580105, _1580105), tc_HOL_Obool, _1580105)), c_fequal)), hAPP(hAPP(c_COMBS(_1580105, _1580105, tc_prod(_1580105, _1580105)), c_Product__Type_OPair(_1580105, _1580105)), c_COMBI(_1580105))))))], (15998 ^ _776545) ^ [_1066045, _1066047] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066045), _1066047))), 16001 ^ _776545 : [(16008 ^ _776545) ^ [] : [_1066045 = _1066047, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066045), hAPP(c_Nat_OSuc, _1066047))))], (16002 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066045), hAPP(c_Nat_OSuc, _1066047))), -(_1066045 = _1066047)]]], (48298 ^ _776545) ^ [_1749265, _1749267, _1749269] : [48300 ^ _776545 : [(48303 ^ _776545) ^ [] : [hBOOL(hAPP(_1749269, 48299 ^ [_1749265, _1749267, _1749269]))], (48301 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749265), 48299 ^ [_1749265, _1749267, _1749269]), hAPP(c_List_Oset(_1749265), _1749267))))]], -(c_List_Olist__all(_1749265, _1749269, _1749267))], (36488 ^ _776545) ^ [_1466882, _1466884, _1466886, _1466888, _1466890] : [-(hAPP(c_Relation_OImage(_1466882, _1466884, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1466882, _1466884), tc_HOL_Obool)), _1466886), _1466888)), _1466890) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466884, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466882, _1466884, _1466886), _1466890)), hAPP(c_Relation_OImage(_1466882, _1466884, _1466888), _1466890)))], (11348 ^ _776545) ^ [_974011, _974013, _974015, _974017, _974019] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974011, _974013, hAPP(hAPP(c_Set_Oinsert(_974011), _974015), _974017)), _974019)), 11353 ^ _776545 : [(11358 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974011), 11351 ^ [_974011, _974013, _974015, _974017, _974019]), 11352 ^ [_974011, _974013, _974015, _974017, _974019]))], (11356 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974011, _974011, _974013, 11351 ^ [_974011, _974013, _974015, _974017, _974019], 11352 ^ [_974011, _974013, _974015, _974017, _974019]), _974019)))], (11354 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974011), _974015), _974017) = hAPP(hAPP(c_Set_Oinsert(_974011), 11351 ^ [_974011, _974013, _974015, _974017, _974019]), 11352 ^ [_974011, _974013, _974015, _974017, _974019]))]]], (46968 ^ _776545) ^ [_1720519, _1720521, _1720523] : [-(hAPP(c_List_Orev(_1720519), hAPP(hAPP(c_List_Oappend(_1720519), _1720521), _1720523)) = hAPP(hAPP(c_List_Oappend(_1720519), hAPP(c_List_Orev(_1720519), _1720523)), hAPP(c_List_Orev(_1720519), _1720521)))], (28981 ^ _776545) ^ [_1296060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1296060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1296060))))], (12219 ^ _776545) ^ [_990998, _991000, _991002] : [class_Lattices_Olattice(_990998), hBOOL(hAPP(c_Finite__Set_Ofinite(_990998), _991000)), -(_991000 = c_Orderings_Obot__class_Obot(tc_fun(_990998, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990998), _991002)), -(_991002 = c_Orderings_Obot__class_Obot(tc_fun(_990998, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_990998, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_990998, tc_HOL_Obool)), _991000), _991002)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_990998), c_Big__Operators_Olattice__class_OInf__fin(_990998, _991000)), c_Big__Operators_Olattice__class_OInf__fin(_990998, _991002)))], (7599 ^ _776545) ^ [_902358, _902360, _902362, _902364] : [7600 ^ _776545 : [(7601 ^ _776545) ^ [_902468] : [hBOOL(hAPP(hAPP(c_member(_902358), _902468), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902358, tc_HOL_Obool)), _902360), _902362))), hBOOL(hAPP(_902364, _902468))]], 7609 ^ _776545 : [(7612 ^ _776545) ^ [] : [-(hBOOL(hAPP(_902364, 7608 ^ [_902358, _902360, _902362, _902364])))], (7610 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902358), 7608 ^ [_902358, _902360, _902362, _902364]), _902360)))]], 7614 ^ _776545 : [(7617 ^ _776545) ^ [] : [-(hBOOL(hAPP(_902364, 7613 ^ [_902358, _902360, _902362, _902364])))], (7615 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902358), 7613 ^ [_902358, _902360, _902362, _902364]), _902362)))]]], (28031 ^ _776545) ^ [_1280259, _1280261] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280259), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280259)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280261)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1280259), _1280261)))], (45365 ^ _776545) ^ [_1685658, _1685660, _1685662, _1685664] : [hBOOL(hAPP(c_List_Olistsp(_1685658, hAPP(hAPP(c_COMBS(_1685658, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1685658), c_fconj), _1685660)), _1685662)), _1685664)), 45368 ^ _776545 : [(45371 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685658, _1685662), _1685664)))], (45369 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1685658, _1685660), _1685664)))]]], (45416 ^ _776545) ^ [_1686770, _1686772, _1686774] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1686770)), _1686774), c_List_Olists(_1686770, _1686772))), -(hBOOL(hAPP(c_List_Olistsp(_1686770, hAPP(hAPP(c_COMBC(_1686770, tc_fun(_1686770, tc_HOL_Obool), tc_HOL_Obool), c_member(_1686770)), _1686772)), _1686774)))], (1364 ^ _776545) ^ [_796459, _796461] : [-(class_Lattices_Obounded__lattice__top(_796459)), _796461 = _796459, class_Lattices_Obounded__lattice__top(_796461)], (14602 ^ _776545) ^ [_1039817, _1039819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039817), _1039819)), _1039819))], (40937 ^ _776545) ^ [_1578352] : [-(hAPP(c_Relation_ORange(_1578352, _1578352), c_Relation_OId(_1578352)) = c_Orderings_Otop__class_Otop(tc_fun(_1578352, tc_HOL_Obool)))], (43910 ^ _776545) ^ [_1653971, _1653973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653971)), hAPP(c_List_Orotate1(_1653971), _1653973)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653971)), _1653973))], (15270 ^ _776545) ^ [_1052122, _1052124, _1052126] : [class_Groups_Ocomm__monoid__mult(_1052122), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052124, _1052122), _1052126), c_Orderings_Obot__class_Obot(tc_fun(_1052124, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1052122))], (13618 ^ _776545) ^ [_1018954, _1018956, _1018958, _1018960] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1018954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018954), _1018956), _1018958)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018954), _1018956), _1018960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018954), _1018958), _1018960)))], (51915 ^ _776545) ^ [_1825383, _1825385] : [class_Lattices_Olattice(_1825383), -(class_Lattices_Olattice(tc_fun(_1825385, _1825383)))], (47226 ^ _776545) ^ [_1725962, _1725964, _1725966] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725962)), c_List_OtakeWhile(_1725962, _1725964, _1725966))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725962)), _1725966))))], (23211 ^ _776545) ^ [_1197008, _1197010, _1197012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197008)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197010), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1197012)), 23218 ^ _776545 : [(23219 ^ _776545) ^ [_1197216] : [23221 ^ _776545 : [(23227 ^ _776545) ^ [] : [-(_1197216 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23223 ^ [_1197008, _1197010, _1197012, _1197216]), 23220 ^ [_1197008, _1197010, _1197012, _1197216]))], (23225 ^ 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-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811102), _1811106), _1811104) = _1811108)], (51093 ^ _776545) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811102), _1811106), _1811104) = _1811108, -(_1811106 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811102), _1811108), _1811104))]]], (14342 ^ _776545) ^ [_1035169, _1035171, _1035173, _1035175] : [class_Rings_Ocomm__semiring__1(_1035169), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035169), _1035171), _1035173)), _1035175) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035169), _1035171), _1035175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035169), _1035173), _1035175)))], (32406 ^ _776545) ^ [_1359624, _1359626, _1359628, _1359630] : [class_Groups_Oordered__ab__group__add__abs(_1359624), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359624), hAPP(c_Groups_Oabs__class_Oabs(_1359624), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359626, _1359624), _1359628), _1359630))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359626, _1359624), hAPP(hAPP(c_COMBB(_1359624, _1359624, _1359626), c_Groups_Oabs__class_Oabs(_1359624)), _1359628)), _1359630))))], (3766 ^ _776545) ^ [_833049, _833051, _833053, _833055] : [-(c_List_Olex(_833055, _833051) = c_List_Olex(_833053, _833049)), _833055 = _833053, _833051 = _833049], (39617 ^ _776545) ^ [_1544925, _1544927, _1544929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544925, _1544925), tc_HOL_Obool)), _1544927), hAPP(hAPP(c_Product__Type_OSigma(_1544925, _1544925), _1544929), hAPP(c_COMBK(tc_fun(_1544925, tc_HOL_Obool), _1544925), _1544929)))), 39623 ^ _776545 : [(39626 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544925, _1544925)), hAPP(hAPP(c_Product__Type_OPair(_1544925, _1544925), 39622 ^ [_1544925, _1544927, _1544929]), 39622 ^ [_1544925, _1544927, 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c_Groups_Otimes__class_Otimes(_998481)), _998483)), hAPP(c_Finite__Set_Ofold1(_998481, c_Groups_Otimes__class_Otimes(_998481)), _998485)))], (19378 ^ _776545) ^ [_1126402, _1126404] : [class_Rings_Oring__1(_1126402), hBOOL(hAPP(hAPP(c_member(_1126402), _1126404), c_Int_Oring__1__class_OInts(_1126402))), -(hBOOL(hAPP(hAPP(c_member(_1126402), hAPP(c_Groups_Ouminus__class_Ouminus(_1126402), _1126404)), c_Int_Oring__1__class_OInts(_1126402))))], (1234 ^ _776545) ^ [_794834, _794836] : [-(class_Groups_Ogroup__add(_794834)), _794836 = _794834, class_Groups_Ogroup__add(_794836)], (32510 ^ _776545) ^ [_1363667, _1363669, _1363671, _1363673, _1363675] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363667, tc_HOL_Obool)), _1363669), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363671, tc_fun(_1363667, tc_HOL_Obool)), _1363673), _1363675)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363671, tc_fun(_1363667, tc_HOL_Obool)), _1363673), hAPP(hAPP(c_COMBB(tc_fun(_1363667, tc_HOL_Obool), tc_fun(_1363667, tc_HOL_Obool), _1363671), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363667, tc_HOL_Obool)), _1363669)), _1363675)))], (12756 ^ _776545) ^ [_1001573, _1001575, _1001577, _1001579, _1001581] : [c_Finite__Set_Ofun__left__comm(_1001573, _1001575, _1001577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001573), _1001579)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1001573, _1001575, _1001577, _1001581, _1001579), hAPP(hAPP(c_Finite__Set_Ofold(_1001573, _1001575, _1001577), _1001581), _1001579))))], (8481 ^ _776545) ^ [_922236, _922238, _922240, _922242] : [class_Lattices_Osemilattice__sup(_922236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922236), _922238), _922240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922236), _922242), _922240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922236), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922236), _922238), _922242)), _922240)))], (52137 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (24034 ^ _776545) ^ [_1211673, _1211675] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211673)), _1211675) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211673), _1211675)))], (44320 ^ _776545) ^ [_1662850, _1662852, _1662854, _1662856, _1662858] : [class_Orderings_Olinorder(_1662850), -(hAPP(c_List_Oset(_1662852), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662852, _1662850, _1662854), _1662856), _1662858)) = hAPP(hAPP(c_Set_Oinsert(_1662852), _1662856), hAPP(c_List_Oset(_1662852), _1662858)))], (2044 ^ _776545) ^ [_806060, _806062, _806064, _806066, _806068, _806070, _806072, _806074, _806076, _806078] : [-(c_SetInterval_Oord_OatLeastLessThan(_806078, _806074, _806070, _806066, _806062) = c_SetInterval_Oord_OatLeastLessThan(_806076, _806072, _806068, _806064, _806060)), _806078 = _806076, _806074 = _806072, _806070 = _806068, _806066 = _806064, _806062 = _806060], (36622 ^ _776545) ^ [_1470655, _1470657, _1470659] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1470655), _1470657), _1470659) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470655, tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool)), _1470657), hAPP(hAPP(c_COMBC(_1470655, tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470655, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool)), _1470655), c_Set_Oinsert(tc_fun(_1470655, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470655, tc_HOL_Obool), tc_fun(_1470655, tc_HOL_Obool), _1470655), c_Relation_OImage(_1470655, _1470655, _1470659)), hAPP(hAPP(c_COMBC(_1470655, tc_fun(_1470655, tc_HOL_Obool), tc_fun(_1470655, tc_HOL_Obool)), c_Set_Oinsert(_1470655)), c_Orderings_Obot__class_Obot(tc_fun(_1470655, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1470655, tc_HOL_Obool), tc_HOL_Obool)))))], (46496 ^ _776545) ^ [_1711715, _1711717] : [class_Orderings_Olinorder(_1711715), c_List_Olinorder__class_Osorted(_1711715, _1711717), -(c_List_Olinorder__class_Osorted(_1711715, hAPP(c_List_Otl(_1711715), _1711717)))], (38612 ^ _776545) ^ [_1518273, _1518275, _1518277, _1518279, _1518281] : [hBOOL(hAPP(hAPP(_1518273, _1518275), _1518277)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1518279, _1518281, _1518273), _1518277)))], (35332 ^ _776545) ^ [_1435602, _1435604] : [-(_1435602 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435604, _1435602), c_Divides_Odivmod__int(_1435604, _1435602))))], (22647 ^ _776545) ^ [_1186883, _1186885] : [class_Power_Opower(_1186883), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186883), _1186885), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1186883))], (18125 ^ _776545) ^ [_1102437, _1102439] : [_1102437 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102437), _1102439), -(_1102439 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1102437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22275 ^ _776545) ^ [_1180485, _1180487] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180485), _1180487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180487), _1180485)))], (33889 ^ _776545) ^ [_1404534, _1404536] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1404534), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1404536))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1404534), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404536))), 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))))], (33263 ^ _776545) ^ [_1386266, _1386268, _1386270, _1386272] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386266, tc_fun(_1386268, tc_HOL_Obool)), _1386270), _1386272) = c_Orderings_Obot__class_Obot(tc_fun(_1386268, tc_HOL_Obool)), 33266 ^ _776545 : [(33267 ^ _776545) ^ [_1386382] : [hBOOL(hAPP(hAPP(c_member(_1386266), _1386382), _1386270)), -(hAPP(_1386272, _1386382) = c_Orderings_Obot__class_Obot(tc_fun(_1386268, tc_HOL_Obool)))]]], (21591 ^ _776545) ^ [_1167465, _1167467, _1167469, _1167471] : [class_Fields_Olinordered__field__inverse__zero(_1167465), class_Int_Onumber(_1167465), 21598 ^ _776545 : [(21599 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167465), _1167469), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)))), 21602 ^ _776545 : [(21609 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), c_Groups_Ozero__class_Ozero(_1167465)), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)))), 21612 ^ _776545 : [(21619 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)), c_Groups_Ozero__class_Ozero(_1167465)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167467), c_Groups_Ozero__class_Ozero(_1167465))))], (21613 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)), c_Groups_Ozero__class_Ozero(_1167465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167465), _1167467), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)))))]]], (21603 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), c_Groups_Ozero__class_Ozero(_1167465)), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167465), _1167467), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))), _1167469)))]]], (21625 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167467), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1167465), _1167469), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))))), 21628 ^ _776545 : [(21631 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167465), _1167467), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))), _1167469))], (21629 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), c_Groups_Ozero__class_Ozero(_1167465)), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))))]], 21632 ^ _776545 : [(21635 ^ _776545) ^ [] : [21636 ^ _776545 : [(21639 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167465), _1167467), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471))))], (21637 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)), c_Groups_Ozero__class_Ozero(_1167465))))]], 21640 ^ _776545 : [(21643 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), _1167467), c_Groups_Ozero__class_Ozero(_1167465)))], (21641 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)), c_Groups_Ozero__class_Ozero(_1167465)))]]], (21633 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167465), c_Groups_Ozero__class_Ozero(_1167465)), hAPP(c_Int_Onumber__class_Onumber__of(_1167465), _1167471)))]]]]], (43082 ^ _776545) ^ [_1634999, _1635001] : [-(c_List_Oremove1(_1634999, _1635001, c_List_Olist_ONil(_1634999)) = c_List_Olist_ONil(_1634999))], (39237 ^ _776545) ^ [_1534014, _1534016, _1534018, _1534020] : [-(hAPP(c_Set_OCollect(tc_prod(_1534014, _1534016)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534014, _1534016, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1534014, tc_fun(_1534016, tc_HOL_Obool), tc_fun(_1534016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534016, tc_HOL_Obool), tc_fun(_1534016, tc_HOL_Obool)), _1534014), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534016)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534014), c_fconj), _1534018))), _1534020))) = hAPP(hAPP(c_Product__Type_OSigma(_1534014, _1534016), hAPP(c_Set_OCollect(_1534014), _1534018)), hAPP(c_COMBK(tc_fun(_1534016, tc_HOL_Obool), _1534014), hAPP(c_Set_OCollect(_1534016), _1534020))))], (44868 ^ _776545) ^ [_1674443, _1674445, _1674447, _1674449, _1674451, _1674453, _1674455, _1674457] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674443, _1674445), _1674447), _1674449), hAPP(hAPP(c_List_Ozip(_1674443, _1674445), hAPP(hAPP(c_List_Omap(_1674451, _1674443), _1674453), _1674455)), _1674457)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674451, _1674445), _1674447), hAPP(c_Product__Type_Oprod_Oprod__case(_1674451, _1674445, _1674447), hAPP(hAPP(c_COMBB(tc_fun(_1674445, tc_prod(_1674443, _1674445)), tc_fun(_1674445, _1674447), _1674451), hAPP(c_COMBB(tc_prod(_1674443, _1674445), _1674447, _1674445), _1674449)), hAPP(hAPP(c_COMBB(_1674443, tc_fun(_1674445, tc_prod(_1674443, _1674445)), _1674451), c_Product__Type_OPair(_1674443, _1674445)), _1674453)))), hAPP(hAPP(c_List_Ozip(_1674451, _1674445), _1674455), _1674457)))], (19069 ^ _776545) ^ [_1120125, _1120127] : [19071 ^ _776545 : [(19074 ^ _776545) ^ [] : [hBOOL(hAPP(_1120127, 19070 ^ [_1120125, _1120127]))], (19072 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19070 ^ [_1120125, _1120127]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1120125))))]], 19075 ^ _776545 : [(19076 ^ _776545) ^ [_1120278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120278), _1120125)), -(hBOOL(hAPP(_1120127, _1120278)))]]], (24844 ^ _776545) ^ [_1226116, _1226118, _1226120, _1226122] : [class_Divides_Osemiring__div(_1226116), -(c_Divides_Odiv__class_Omod(_1226116, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226116), _1226118), _1226120), _1226122) = c_Divides_Odiv__class_Omod(_1226116, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226116), c_Divides_Odiv__class_Omod(_1226116, _1226118, _1226122)), c_Divides_Odiv__class_Omod(_1226116, _1226120, _1226122)), _1226122))], (4516 ^ _776545) ^ [_845148, _845150] : [_845150 = _845148, -(c_List_Olist_ONil(_845150) = c_List_Olist_ONil(_845148))], (46900 ^ _776545) ^ [_1718934, _1718936, _1718938, _1718940, _1718942] : [class_Orderings_Olinorder(_1718934), c_Fun_Oinj__on(_1718936, _1718934, _1718938, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1718936, tc_HOL_Obool)), hAPP(c_List_Oset(_1718936), _1718940)), hAPP(c_List_Oset(_1718936), _1718942))), c_List_Olinorder__class_Osorted(_1718934, hAPP(hAPP(c_List_Omap(_1718936, _1718934), _1718938), _1718940)), hBOOL(hAPP(c_List_Odistinct(_1718934), hAPP(hAPP(c_List_Omap(_1718936, _1718934), _1718938), _1718940))), c_List_Olinorder__class_Osorted(_1718934, hAPP(hAPP(c_List_Omap(_1718936, _1718934), _1718938), _1718942)), hBOOL(hAPP(c_List_Odistinct(_1718934), hAPP(hAPP(c_List_Omap(_1718936, _1718934), _1718938), _1718942))), hAPP(c_List_Oset(_1718936), _1718940) = hAPP(c_List_Oset(_1718936), _1718942), -(_1718940 = _1718942)], (22907 ^ _776545) ^ [_1191632, _1191634, _1191636, _1191638] : [class_Rings_Olinordered__semidom(_1191632), hAPP(hAPP(c_Power_Opower__class_Opower(_1191632), _1191634), _1191636) = hAPP(hAPP(c_Power_Opower__class_Opower(_1191632), _1191638), _1191636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191632), c_Groups_Ozero__class_Ozero(_1191632)), _1191634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191632), c_Groups_Ozero__class_Ozero(_1191632)), _1191638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191636)), -(_1191634 = _1191638)], (29845 ^ _776545) ^ [_1311652] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1311652)], (6758 ^ _776545) ^ [_885861, _885863, _885865] : [class_Orderings_Oorder(_885861), 6761 ^ _776545 : [(6770 ^ _776545) ^ [] : [-(_885863 = _885865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885861), _885863), _885865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885861), _885865), _885863))], (6762 ^ _776545) ^ [] : [_885863 = _885865, 6765 ^ _776545 : [(6768 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885861), _885865), _885863)))], (6766 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885861), _885863), _885865)))]]]]], (28511 ^ _776545) ^ [_1288191] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1288191), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1288191)), c_Int_OMin)))], (7332 ^ _776545) ^ [_896615, _896617, _896619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896615, tc_HOL_Obool)), _896617), hAPP(hAPP(c_Set_Oinsert(_896615), _896619), c_Orderings_Obot__class_Obot(tc_fun(_896615, tc_HOL_Obool))))), -(_896617 = c_Orderings_Obot__class_Obot(tc_fun(_896615, tc_HOL_Obool))), -(_896617 = hAPP(hAPP(c_Set_Oinsert(_896615), _896619), c_Orderings_Obot__class_Obot(tc_fun(_896615, tc_HOL_Obool))))], (41100 ^ _776545) ^ [_1582469, _1582471, _1582473] : [-(hAPP(c_Relation_Oconverse(_1582469, _1582471), hAPP(c_Relation_Oconverse(_1582471, _1582469), _1582473)) = _1582473)], (11066 ^ _776545) ^ [_967894, _967896, _967898] : [class_Rings_Oring(_967894), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967894), _967896), _967898)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967894), hAPP(c_Groups_Ouminus__class_Ouminus(_967894), _967896)), _967898))], (29075 ^ _776545) ^ [_1297733] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1297733))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1297733)))], (20495 ^ _776545) ^ [_1146368, _1146370, _1146372, _1146374] : [class_Fields_Olinordered__field(_1146368), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146368), _1146370), _1146372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146368), _1146374), c_Groups_Ozero__class_Ozero(_1146368))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146368), c_Groups_Ozero__class_Ozero(_1146368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146368), _1146370), _1146372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146368), _1146374), _1146370)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146368), _1146374), _1146372))))], (37644 ^ _776545) ^ [_1493261] : [-(c_Fun_Oinj__on(_1493261, tc_fun(_1493261, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1493261, tc_fun(_1493261, tc_HOL_Obool), tc_fun(_1493261, tc_HOL_Obool)), c_Set_Oinsert(_1493261)), c_Orderings_Obot__class_Obot(tc_fun(_1493261, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1493261, tc_HOL_Obool))))], (31691 ^ _776545) ^ [_1345689, _1345691] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1345689), _1345691)), _1345691) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1345689), _1345691))], (27635 ^ _776545) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (40530 ^ _776545) ^ [_1567680, _1567682] : [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), _1567680), _1567682)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567680), _1567682)))], (28659 ^ _776545) ^ [_1290425, _1290427] : [class_Int_Onumber__ring(_1290425), class_Rings_Olinordered__idom(_1290425), 28666 ^ _776545 : [(28673 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290427), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290425), hAPP(c_Int_Onumber__class_Onumber__of(_1290425), _1290427)), c_Groups_Oone__class_Oone(_1290425))))], (28667 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290425), hAPP(c_Int_Onumber__class_Onumber__of(_1290425), _1290427)), c_Groups_Oone__class_Oone(_1290425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1290427), c_Int_OBit1(c_Int_OPls))))]]], (3296 ^ _776545) ^ [_825746, _825748, _825750, _825752] : [-(c_Random_Oselect(_825752, _825748) = c_Random_Oselect(_825750, _825746)), _825752 = _825750, _825748 = _825746], (24754 ^ _776545) ^ [_1224342, _1224344] : [class_Divides_Osemiring__div(_1224342), -(c_Divides_Odiv__class_Omod(_1224342, _1224344, c_Groups_Ozero__class_Ozero(_1224342)) = _1224344)], (770 ^ _776545) ^ [_788122, _788124, _788126, _788128, _788130, _788132] : [-(c_Equiv__Relations_Oequiv(_788130, _788126, _788122)), c_Equiv__Relations_Oequiv(_788132, _788128, _788124), _788132 = _788130, _788128 = _788126, _788124 = _788122], (19479 ^ _776545) ^ [_1128322, _1128324, _1128326, _1128328, _1128330] : [class_Groups_Ocomm__monoid__add(_1128322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128324), _1128326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128324, tc_HOL_Obool)), _1128328), _1128326)), 19493 ^ _776545 : [(19496 ^ _776545) ^ [] : [hAPP(_1128330, 19492 ^ [_1128322, _1128324, _1128326, _1128328, _1128330]) = c_Groups_Ozero__class_Ozero(_1128322)], (19494 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1128324), 19492 ^ [_1128322, _1128324, _1128326, _1128328, _1128330]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128324, tc_HOL_Obool)), _1128326), _1128328))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128324, _1128322), _1128330), _1128326) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128324, _1128322), _1128330), _1128328))], (16122 ^ _776545) ^ [_1067994, _1067996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067994), _1067996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067994), hAPP(c_Nat_OSuc, _1067996))))], (38126 ^ _776545) ^ [_1506733, _1506735] : [c_Wellfounded_Owf(_1506733, _1506735), -(c_Wellfounded_Owf(_1506733, hAPP(hAPP(c_Relation_Orel__comp(_1506733, _1506733, _1506733), _1506735), _1506735)))], (33645 ^ _776545) ^ [_1397872, _1397874, _1397876, _1397878] : [hBOOL(hAPP(hAPP(c_member(_1397874), _1397878), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397872, tc_fun(_1397874, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397872, tc_HOL_Obool))), _1397876))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397872, tc_fun(_1397874, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397872, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397874, tc_HOL_Obool), tc_fun(_1397874, tc_HOL_Obool), _1397872), hAPP(c_COMBC(_1397874, tc_fun(_1397874, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397874))), _1397876)), _1397878)))], (36118 ^ _776545) ^ [_1457241, _1457243, _1457245, _1457247, _1457249, _1457251, _1457253, _1457255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457241, _1457243), tc_prod(_1457241, _1457243))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457241, _1457243), tc_prod(_1457241, _1457243)), hAPP(hAPP(c_Product__Type_OPair(_1457241, _1457243), _1457245), _1457247)), hAPP(hAPP(c_Product__Type_OPair(_1457241, _1457243), _1457249), _1457251))), c_Wellfounded_Olex__prod(_1457241, _1457243, _1457253, _1457255))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457241, _1457241)), hAPP(hAPP(c_Product__Type_OPair(_1457241, _1457241), _1457245), _1457249)), _1457253))), 36125 ^ _776545 : [(36128 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457243, _1457243)), hAPP(hAPP(c_Product__Type_OPair(_1457243, _1457243), _1457247), _1457251)), _1457255)))], (36126 ^ _776545) ^ [] : [-(_1457245 = _1457249)]]], (7140 ^ _776545) ^ [_892914, _892916, _892918, _892920] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_892914), _892916), _892918), _892920)), -(_892916 = _892920), -(hBOOL(hAPP(_892918, _892920)))], (11540 ^ _776545) ^ [_978228, _978230] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_978228), c_Orderings_Otop__class_Otop(tc_fun(_978228, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978230), c_Orderings_Otop__class_Otop(tc_fun(_978230, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_978228, _978230)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_978228, _978230), tc_HOL_Obool)))))], (398 ^ _776545) ^ [_782556, _782558, _782560, _782562, _782564, _782566] : [-(c_Relation_Ototal__on(_782564, _782560, _782556)), c_Relation_Ototal__on(_782566, _782562, _782558), _782566 = _782564, _782562 = _782560, _782558 = _782556], (6957 ^ _776545) ^ [_889421, _889423] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_889421, tc_HOL_Obool)), _889423), hAPP(c_Set_OPow(_889421), _889423))))], (46433 ^ _776545) ^ [_1710390, _1710392, _1710394] : [46434 ^ _776545 : [(46437 ^ _776545) ^ [] : [_1710394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46435 ^ _776545) ^ [] : [-(_1710390 = c_List_Olist_ONil(tc_List_Olist(_1710392)))]], 46441 ^ _776545 : [(46444 ^ _776545) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710392)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1710392)), _1710390), 46440 ^ [_1710390, _1710392, _1710394])) = _1710394], (46442 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46440 ^ [_1710390, _1710392, _1710394]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710392))), _1710390))))]], -(c_List_Otranspose(_1710392, _1710390) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1710392)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1710392)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1710392), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1710392)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1710392)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1710392), hAPP(hAPP(c_COMBB(tc_List_Olist(_1710392), tc_fun(tc_Nat_Onat, _1710392), tc_Nat_Onat), c_List_Onth(_1710392)), hAPP(c_List_Onth(tc_List_Olist(_1710392)), _1710390))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710392))), _1710390)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1710394)))], (23866 ^ _776545) ^ [_1208837, _1208839] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208837), _1208839)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208837)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208839)))], (35048 ^ _776545) ^ [_1430557, _1430559, _1430561, _1430563] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430557, _1430559), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430561), _1430563))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1430557), _1430559) = _1430561)], (13274 ^ _776545) ^ [_1011630, _1011632, _1011634, _1011636, _1011638] : [class_Groups_Ocomm__monoid__mult(_1011630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011632), _1011634)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011632), _1011636)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011630), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011632, _1011630), _1011638), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011632, tc_HOL_Obool)), _1011634), _1011636))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011632, _1011630), _1011638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011632, tc_HOL_Obool)), _1011634), _1011636))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011630), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011632, _1011630), _1011638), _1011634)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011632, _1011630), _1011638), _1011636)))], (44166 ^ _776545) ^ [_1659686, _1659688, _1659690] : [hBOOL(hAPP(c_List_Odistinct(_1659686), _1659690)), -(hBOOL(hAPP(c_List_Odistinct(_1659686), hAPP(c_List_Orotate(_1659686, _1659688), _1659690))))], (50123 ^ _776545) ^ [_1789280, _1789282, _1789284] : [hAPP(c_Set_Oimage(_1789280, _1789282, _1789284), c_Orderings_Otop__class_Otop(tc_fun(_1789280, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1789282, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1789282, _1789280, c_Hilbert__Choice_Oinv__into(_1789280, _1789282, c_Orderings_Otop__class_Otop(tc_fun(_1789280, tc_HOL_Obool)), _1789284), c_Orderings_Otop__class_Otop(tc_fun(_1789282, tc_HOL_Obool))))], (48280 ^ _776545) ^ [_1748957, _1748959, _1748961, _1748963] : [c_List_Olist__all(_1748957, _1748959, hAPP(hAPP(c_List_Olist_OCons(_1748957), _1748961), _1748963)), 48283 ^ _776545 : [(48286 ^ _776545) ^ [] : [-(c_List_Olist__all(_1748957, _1748959, _1748963))], (48284 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1748959, _1748961)))]]], (11216 ^ _776545) ^ [_971176, _971178, _971180, _971182, _971184] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971176, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971178, _971176, _971180), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971178, tc_HOL_Obool)), _971182), _971184))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971176, tc_HOL_Obool)), hAPP(c_Set_Oimage(_971178, _971176, _971180), _971182)), hAPP(c_Set_Oimage(_971178, _971176, _971180), _971184)))))], (41643 ^ _776545) ^ [_1596211, _1596213, _1596215, _1596217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596211, _1596213)), _1596215), hAPP(c_Relation_Oconverse(_1596213, _1596211), _1596217))), 41648 ^ _776545 : [(41651 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596213, _1596211)), hAPP(hAPP(c_Product__Type_OPair(_1596213, _1596211), 41646 ^ [_1596211, _1596213, _1596215, _1596217]), 41647 ^ [_1596211, _1596213, _1596215, _1596217])), _1596217)))], (41649 ^ _776545) ^ [] : [-(_1596215 = hAPP(hAPP(c_Product__Type_OPair(_1596211, _1596213), 41647 ^ [_1596211, _1596213, _1596215, _1596217]), 41646 ^ [_1596211, _1596213, _1596215, _1596217]))]]], (7880 ^ _776545) ^ [_909287, _909289, _909291, _909293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909287, tc_HOL_Obool)), _909289), _909291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909287, tc_HOL_Obool)), _909291), _909293)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909287, tc_HOL_Obool)), _909291), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909287, tc_HOL_Obool)), _909293), _909289)) = _909289)], (43705 ^ _776545) ^ [_1648402, _1648404, _1648406, _1648408, _1648410, _1648412] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648402), tc_List_Olist(_1648402))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648402), tc_List_Olist(_1648402)), hAPP(hAPP(c_List_Oappend(_1648402), _1648404), _1648410)), hAPP(hAPP(c_List_Oappend(_1648402), _1648406), _1648412))), c_List_Olistrel1(_1648402, _1648408)))), 43706 ^ _776545 : [(43713 ^ _776545) ^ [] : [_1648404 = _1648406, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648402), tc_List_Olist(_1648402))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648402), tc_List_Olist(_1648402)), _1648410), _1648412)), c_List_Olistrel1(_1648402, _1648408)))], (43707 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648402), tc_List_Olist(_1648402))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648402), tc_List_Olist(_1648402)), _1648404), _1648406)), c_List_Olistrel1(_1648402, _1648408))), _1648410 = _1648412]]], (14807 ^ _776545) ^ [_1043507, _1043509, _1043511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043507), _1043509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043507), _1043511)), _1043509)))], (30784 ^ _776545) ^ [_1328700, _1328702, _1328704] : [class_Orderings_Olinorder(_1328700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328700), _1328702)), -(_1328704 = c_Orderings_Obot__class_Obot(tc_fun(_1328700, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328700, tc_HOL_Obool)), _1328704), _1328702)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328700), c_Big__Operators_Olinorder__class_OMin(_1328700, _1328704)), c_Big__Operators_Olinorder__class_OMin(_1328700, _1328702)) = c_Big__Operators_Olinorder__class_OMin(_1328700, _1328702))], (14797 ^ _776545) ^ [_1043320, _1043322, _1043324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043320), _1043322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043320), _1043324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043324), _1043322)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043324), _1043320))))], (44350 ^ _776545) ^ [_1663555, _1663557, _1663559, _1663561, _1663563, _1663565] : [-(hAPP(c_List_Ofoldl(_1663555, _1663557, _1663559, _1663561), hAPP(hAPP(c_List_Oappend(_1663557), _1663563), _1663565)) = hAPP(c_List_Ofoldl(_1663555, _1663557, _1663559, hAPP(c_List_Ofoldl(_1663555, _1663557, _1663559, _1663561), _1663563)), _1663565))], (30720 ^ _776545) ^ [_1327628, _1327630, _1327632] : [class_Orderings_Olinorder(_1327628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327628), _1327630)), -(_1327630 = c_Orderings_Obot__class_Obot(tc_fun(_1327628, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327628), _1327632)), -(_1327632 = c_Orderings_Obot__class_Obot(tc_fun(_1327628, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1327628, c_Orderings_Oord__class_Omin(_1327628), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327628, tc_HOL_Obool)), _1327630), _1327632)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327628), c_Big__Operators_Olattice_OInf__fin(_1327628, c_Orderings_Oord__class_Omin(_1327628), _1327630)), c_Big__Operators_Olattice_OInf__fin(_1327628, c_Orderings_Oord__class_Omin(_1327628), _1327632)))], (18540 ^ _776545) ^ [_1110185, _1110187] : [18541 ^ _776545 : [(18544 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110185), _1110187)))], (18542 ^ _776545) ^ [] : [_1110187 = c_Orderings_Obot__class_Obot(tc_fun(_1110185, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1110185), _1110187) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41086 ^ _776545) ^ [_1582054, _1582056, _1582058, _1582060, _1582062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582054, _1582056)), hAPP(hAPP(c_Product__Type_OPair(_1582054, _1582056), _1582058), _1582060)), hAPP(c_Relation_Oconverse(_1582056, _1582054), _1582062))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582056, _1582054)), hAPP(hAPP(c_Product__Type_OPair(_1582056, _1582054), _1582060), _1582058)), _1582062)))], (33485 ^ _776545) ^ [_1392432, _1392434] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1392432, tc_HOL_Obool)), _1392434) = hAPP(c_Set_OCollect(_1392432), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1392432), c_fNot), hAPP(hAPP(c_COMBC(_1392432, tc_fun(_1392432, tc_HOL_Obool), tc_HOL_Obool), c_member(_1392432)), _1392434))))], (15769 ^ _776545) ^ [_1062360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062360), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1062360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7908 ^ _776545) ^ [_910010, _910012, _910014, _910016, _910018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910010, tc_HOL_Obool)), _910012), _910014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910010, tc_HOL_Obool)), _910016), _910018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910010, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910010, tc_HOL_Obool)), _910012), _910016)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910010, tc_HOL_Obool)), _910014), _910018))))], (22337 ^ _776545) ^ [_1181474, _1181476] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181474), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181474), _1181476))], (45888 ^ _776545) ^ [_1697115, _1697117, _1697119] : [class_Orderings_Olinorder(_1697115), -(c_List_Olinorder__class_Osort__key(_1697117, _1697115, _1697119, c_List_Olist_ONil(_1697117)) = c_List_Olist_ONil(_1697117))], (11638 ^ _776545) ^ [_980123] : [class_Finite__Set_Ofinite(_980123), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980123), c_Orderings_Otop__class_Otop(tc_fun(_980123, tc_HOL_Obool)))))], (3828 ^ _776545) ^ [_834034, _834036] : [_834036 = _834034, -(c_New__DSequence_Opos__not__seq(_834036) = c_New__DSequence_Opos__not__seq(_834034))], (41186 ^ _776545) ^ [_1584441, _1584443, _1584445, _1584447, _1584449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584441, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584443, _1584441, _1584445), _1584447)), _1584449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584443, tc_HOL_Obool)), _1584447), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584443, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584441, _1584443, hAPP(c_Relation_Oconverse(_1584443, _1584441), _1584445)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584441, tc_HOL_Obool)), _1584449))))))], (52109 ^ _776545) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (47381 ^ _776545) ^ [_1729221, _1729223, _1729225] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729221)), c_List_OdropWhile(_1729221, _1729223, _1729225))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729221)), _1729225))))], (52113 ^ _776545) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (36284 ^ _776545) ^ [_1461435, _1461437, _1461439, _1461441] : [c_Wellfounded_Omax__extp(_1461435, hAPP(hAPP(c_COMBC(_1461435, tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_fun(_1461435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461435, tc_fun(tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_fun(_1461435, tc_HOL_Obool)), _1461435), c_COMBC(_1461435, tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461435, tc_prod(_1461435, _1461435)), tc_fun(_1461435, tc_fun(tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_HOL_Obool)), _1461435), hAPP(c_COMBB(tc_prod(_1461435, _1461435), tc_fun(tc_fun(tc_prod(_1461435, _1461435), tc_HOL_Obool), tc_HOL_Obool), _1461435), c_member(tc_prod(_1461435, _1461435)))), c_Product__Type_OPair(_1461435, _1461435)))), _1461437), _1461439, _1461441), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1461435, tc_HOL_Obool), tc_fun(_1461435, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1461435, tc_HOL_Obool), tc_fun(_1461435, tc_HOL_Obool)), _1461439), _1461441)), c_Wellfounded_Omax__ext(_1461435, _1461437))))], (33356 ^ _776545) ^ [_1388808, _1388810, _1388812, _1388814, _1388816, _1388818] : [class_Complete__Lattice_Ocomplete__lattice(_1388808), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388810, _1388808), _1388812), hAPP(hAPP(c_COMBB(tc_fun(_1388814, _1388808), _1388808, _1388810), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388814, _1388808), _1388816)), _1388818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388814, _1388808), _1388816), hAPP(hAPP(c_COMBB(tc_fun(_1388810, _1388808), _1388808, _1388814), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388810, _1388808), _1388812)), hAPP(c_COMBC(_1388810, _1388814, _1388808), _1388818))))], (34315 ^ _776545) ^ [_1415231, _1415233] : [-(c_Divides_OnegDivAlg(_1415231, _1415233) = hAPP(c_Divides_Oadjust(_1415233), c_Divides_OnegDivAlg(_1415231, 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)))), _1415233)))), -(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), _1415231), _1415233)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415233), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16444 ^ _776545) ^ [_1072866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1072866), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7836 ^ _776545) ^ [_908433, _908435, _908437] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908433, tc_HOL_Obool)), _908435), _908437) = c_Orderings_Obot__class_Obot(tc_fun(_908433, tc_HOL_Obool))), _908435 = c_Orderings_Obot__class_Obot(tc_fun(_908433, tc_HOL_Obool)), _908437 = c_Orderings_Obot__class_Obot(tc_fun(_908433, tc_HOL_Obool))], (51887 ^ _776545) ^ [_1825017, _1825019] : [class_Lattices_Odistrib__lattice(_1825017), -(class_Lattices_Odistrib__lattice(tc_fun(_1825019, _1825017)))], (17859 ^ _776545) ^ [_1097846, _1097848, _1097850, _1097852] : [class_Groups_Ocomm__monoid__add(_1097846), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097848), _1097850))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097848, _1097846), _1097852), _1097850) = c_Groups_Ozero__class_Ozero(_1097846))], (7676 ^ _776545) ^ [_904581, _904583, _904585] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904581, tc_HOL_Obool)), _904583), _904585) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904581, tc_HOL_Obool)), _904585), _904583))], (11475 ^ _776545) ^ [_976988, _976990, _976992, _976994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976988), _976990)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976992), hAPP(c_Set_Oimage(_976988, _976992, _976994), _976990))))], (10461 ^ _776545) ^ [_956243, _956245, _956247] : [class_Groups_Oordered__ab__group__add(_956243), 10464 ^ _776545 : [(10471 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956243), hAPP(c_Groups_Ouminus__class_Ouminus(_956243), _956247)), _956245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956243), hAPP(c_Groups_Ouminus__class_Ouminus(_956243), _956245)), _956247)))], (10465 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956243), hAPP(c_Groups_Ouminus__class_Ouminus(_956243), _956245)), _956247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956243), hAPP(c_Groups_Ouminus__class_Ouminus(_956243), _956247)), _956245)))]]], (6484 ^ _776545) ^ [_881322, _881324] : [c_Orderings_Obot__class_Obot(tc_fun(_881322, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_881322), _881324), 6487 ^ _776545 : [(6488 ^ _776545) ^ [_881407] : [hBOOL(hAPP(_881324, _881407))]]], (38823 ^ _776545) ^ [_1523466, _1523468, _1523470, _1523472] : [hBOOL(hAPP(hAPP(c_member(_1523466), _1523468), hAPP(c_Relation_ORange(_1523470, _1523466), _1523472))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523470, _1523466)), hAPP(hAPP(c_Product__Type_OPair(_1523470, _1523466), 38826 ^ [_1523466, _1523468, _1523470, _1523472]), _1523468)), _1523472)))], (19098 ^ _776545) ^ [_1120662, _1120664, _1120666, _1120668, _1120670, _1120672, _1120674] : [c_Big__Operators_Ocomm__monoid__big(_1120662, _1120664, _1120666, _1120668, _1120670), 19101 ^ _776545 : [(19108 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1120664), _1120672))), -(hAPP(hAPP(_1120670, _1120674), _1120672) = _1120668)], (19102 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1120664), _1120672)), -(hAPP(hAPP(_1120670, _1120674), _1120672) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1120662, _1120664, _1120666), _1120674), _1120668), _1120672))]]], (37947 ^ _776545) ^ [_1501147, _1501149, _1501151, _1501153, _1501155, _1501157] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501147, _1501149, _1501151), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501147, _1501149), tc_HOL_Obool)), _1501153), _1501155)), _1501157) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501147, _1501151), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501147, _1501149, _1501151), _1501153), _1501157)), hAPP(hAPP(c_Relation_Orel__comp(_1501147, _1501149, _1501151), _1501155), _1501157)))], (6522 ^ _776545) ^ [_881853, _881855, _881857] : [class_Orderings_Obot(_881853), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_881855, _881853)), _881857) = c_Orderings_Obot__class_Obot(_881853))], (25610 ^ _776545) ^ [_1239874, _1239876, _1239878] : [hBOOL(hAPP(_1239874, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1239876, _1239878))), 25613 ^ _776545 : [(25638 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239878), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25641 ^ _776545 : [(25642 ^ _776545) ^ [_1240496, _1240498] : [-(hBOOL(hAPP(_1239874, _1240496))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1239878), _1240496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1239876 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239878), _1240498)), _1240496)]]], (25620 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239878)), 25623 ^ _776545 : [(25624 ^ _776545) ^ [_1240204, _1240206] : [-(hBOOL(hAPP(_1239874, _1240204))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240204), _1239878)), _1239876 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1239878), _1240206)), _1240204)]]], (25614 ^ _776545) ^ [] : [_1239878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1239874, _1239876)))]]], (49849 ^ _776545) ^ [_1783424, _1783426] : [49850 ^ _776545 : [(49851 ^ _776545) ^ [_1783480] : [hBOOL(hAPP(hAPP(_1783424, _1783480), _1783480))]], c_Predicate_Osymp(_1783426, _1783424), c_Predicate_Otransp(_1783426, _1783424), -(c_Equiv__Relations_Opart__equivp(_1783426, _1783424))], (27148 ^ _776545) ^ [_1265238] : [c_Nat__Transfer_Onat__set(_1265238), 27151 ^ _776545 : [(27158 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265238))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1265238)))], (27152 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1265238)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265238))))]]], (16771 ^ _776545) ^ [_1078256, _1078258, _1078260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078258), _1078260)), -(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, _1078256)), _1078258)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078256)), _1078260))))], (41592 ^ _776545) ^ [_1594916, _1594918, _1594920, _1594922, _1594924] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594916, _1594916)), hAPP(hAPP(c_Product__Type_OPair(_1594916, _1594916), _1594918), _1594920)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594916, _1594916), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594922)), _1594924))), 41596 ^ _776545 : [(41599 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594916, _1594916)), hAPP(hAPP(c_Product__Type_OPair(_1594916, _1594916), 41595 ^ [_1594916, _1594918, _1594920, _1594922, _1594924]), _1594920)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594916, _1594916), tc_HOL_Obool), _1594922), _1594924))))], (41597 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594916, _1594916)), hAPP(hAPP(c_Product__Type_OPair(_1594916, _1594916), _1594918), 41595 ^ [_1594916, _1594918, _1594920, _1594922, _1594924])), _1594924)))]]], (4900 ^ _776545) ^ [_851222, _851224, _851226, _851228] : [-(c_Relation_OId__on(_851228, _851224) = c_Relation_OId__on(_851226, _851222)), _851228 = _851226, _851224 = _851222], (40959 ^ _776545) ^ [_1578732, _1578734, _1578736, _1578738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578732, _1578732)), hAPP(hAPP(c_Product__Type_OPair(_1578732, _1578732), _1578734), _1578736)), c_Transitive__Closure_Ortrancl(_1578732, _1578738))), hBOOL(hAPP(hAPP(c_member(_1578732), _1578736), c_Wellfounded_Oacc(_1578732, _1578738))), -(hBOOL(hAPP(hAPP(c_member(_1578732), _1578734), c_Wellfounded_Oacc(_1578732, _1578738))))], (21395 ^ _776545) ^ [_1164131, _1164133, _1164135, _1164137] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164131), _1164133), _1164135)), hAPP(c_Int_Onumber__class_Onumber__of(_1164131), _1164137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164131), _1164133), hAPP(c_Int_Onumber__class_Onumber__of(_1164131), _1164137))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164131), _1164135), hAPP(c_Int_Onumber__class_Onumber__of(_1164131), _1164137)))), class_Int_Onumber(_1164131), class_Rings_Oring(_1164131)], (48448 ^ _776545) ^ [_1752476, _1752478, _1752480, _1752482, _1752484] : [-(hAPP(c_New__DSequence_Opos__bind(_1752476, _1752478, _1752480, _1752482), _1752484) = hAPP(c_Lazy__Sequence_Obind(_1752476, _1752478, hAPP(_1752480, _1752484)), hAPP(hAPP(c_COMBC(_1752476, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752478)), _1752482), _1752484)))], (35742 ^ _776545) ^ [_1443808, _1443810, _1443812] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1443808, _1443810), _1443812))), _1443808 = 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), _1443812)), _1443810)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443812)), 35749 ^ _776545 : [(35752 ^ _776545) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1443812) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35750 ^ _776545) ^ [] : [-(_1443810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 35753 ^ _776545 : [(35756 ^ _776545) ^ [] : [35757 ^ _776545 : [(35760 ^ _776545) ^ [] : [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), _1443812))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443812)), _1443810))], (35758 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443810)))]], 35765 ^ _776545 : [(35768 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1443810), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443812))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443812)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35766 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443810))]]], (35754 ^ _776545) ^ [] : [_1443810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (52171 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (8609 ^ _776545) ^ [_924452, _924454, _924456, _924458, _924460] : [class_Lattices_Osemilattice__inf(_924452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924452), _924454), _924456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924452), _924458), _924460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924452), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924452), _924454), _924458)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924452), _924456), _924460))))], (38677 ^ _776545) ^ [_1519773, _1519775, _1519777, _1519779, _1519781] : [hBOOL(hAPP(hAPP(c_member(_1519777), hAPP(_1519779, _1519775)), _1519781)), -(hBOOL(hAPP(hAPP(c_member(_1519773), _1519775), hAPP(c_Set_Ovimage(_1519773, _1519777, _1519779), _1519781))))], (46115 ^ _776545) ^ [_1702793, _1702795] : [-(hAPP(c_List_Ofilter(_1702793, _1702795), c_List_Olist_ONil(_1702793)) = c_List_Olist_ONil(_1702793))], (25520 ^ _776545) ^ [_1238182, _1238184, _1238186] : [-(hBOOL(hAPP(_1238182, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1238184), _1238186)))), 25521 ^ _776545 : [(25528 ^ _776545) ^ [_1238350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238186), _1238350)), _1238184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1238184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238186), hAPP(c_Nat_OSuc, _1238350)))), hBOOL(hAPP(_1238182, _1238350))], (25522 ^ _776545) ^ [] : [_1238186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1238182, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (18991 ^ _776545) ^ [_1118614, _1118616] : [18999 ^ _776545 : [(19002 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1118616, 18998 ^ [_1118614, _1118616])))], (19000 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18998 ^ [_1118614, _1118616]), _1118614)))]], 18992 ^ _776545 : [(18993 ^ _776545) ^ [_1118683] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1118683), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118614))), hBOOL(hAPP(_1118616, _1118683))]]], (36043 ^ _776545) ^ [_1454241, _1454243, _1454245] : [class_Orderings_Olinorder(_1454241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454241), _1454243)), -(_1454243 = c_Orderings_Obot__class_Obot(tc_fun(_1454241, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454241), _1454245)), -(_1454245 = c_Orderings_Obot__class_Obot(tc_fun(_1454241, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1454241), c_Big__Operators_Olattice_OSup__fin(_1454241, c_Orderings_Oord__class_Omax(_1454241), _1454243)), c_Big__Operators_Olattice_OSup__fin(_1454241, c_Orderings_Oord__class_Omax(_1454241), _1454245)) = c_Big__Operators_Olattice_OSup__fin(_1454241, c_Orderings_Oord__class_Omax(_1454241), hAPP(c_Set_OCollect(_1454241), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_HOL_Obool), tc_HOL_Obool, _1454241), c_HOL_OEx(_1454241)), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool)), tc_fun(_1454241, tc_HOL_Obool), _1454241), hAPP(c_COMBB(tc_fun(_1454241, tc_HOL_Obool), tc_HOL_Obool, _1454241), c_HOL_OEx(_1454241))), hAPP(hAPP(c_COMBC(_1454241, tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool)), tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_fun(tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool))), tc_fun(tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool)), tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool))), _1454241), c_COMBS(_1454241, tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_fun(_1454241, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1454241, tc_fun(tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool))), _1454241), hAPP(c_COMBB(tc_fun(_1454241, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool)), _1454241), c_COMBS(_1454241, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool)), tc_fun(_1454241, tc_fun(_1454241, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1454241), hAPP(c_COMBB(tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1454241), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1454241), c_fconj))), hAPP(hAPP(c_COMBC(_1454241, tc_fun(_1454241, tc_fun(_1454241, _1454241)), tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1454241, _1454241), tc_fun(_1454241, tc_HOL_Obool)), tc_fun(tc_fun(_1454241, tc_fun(_1454241, _1454241)), tc_fun(_1454241, tc_fun(_1454241, tc_HOL_Obool))), _1454241), c_COMBB(tc_fun(_1454241, _1454241), tc_fun(_1454241, tc_HOL_Obool), _1454241)), hAPP(hAPP(c_COMBB(tc_fun(_1454241, tc_HOL_Obool), tc_fun(tc_fun(_1454241, _1454241), tc_fun(_1454241, tc_HOL_Obool)), _1454241), c_COMBB(_1454241, tc_HOL_Obool, _1454241)), c_fequal))), c_Orderings_Oord__class_Omin(_1454241)))))), hAPP(hAPP(c_COMBC(_1454241, tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1454241, tc_HOL_Obool), tc_fun(_1454241, tc_HOL_Obool)), _1454241), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1454241)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1454241), c_fconj), hAPP(hAPP(c_COMBC(_1454241, tc_fun(_1454241, tc_HOL_Obool), tc_HOL_Obool), c_member(_1454241)), _1454243)))), hAPP(hAPP(c_COMBC(_1454241, tc_fun(_1454241, tc_HOL_Obool), tc_HOL_Obool), c_member(_1454241)), _1454245))))))))], (29177 ^ _776545) ^ [_1299498, _1299500] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1299498)), _1299500) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299498), _1299500))), _1299500))], (37240 ^ _776545) ^ [_1485291, _1485293, _1485295, _1485297, _1485299] : [c_Fun_Oinj__on(_1485291, _1485293, _1485295, _1485297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485291, tc_HOL_Obool)), _1485299), _1485297)), -(c_Fun_Oinj__on(_1485291, _1485293, _1485295, _1485299))], (29371 ^ _776545) ^ [_1302862, _1302864] : [class_Rings_Olinordered__idom(_1302862), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302862), c_Groups_Ozero__class_Ozero(_1302862)), hAPP(hAPP(c_Power_Opower__class_Opower(_1302862), _1302864), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (52513 ^ _776545) ^ [_1831643, _1831645] : [hBOOL(hAPP(hAPP(c_fconj, _1831643), _1831645)), -(hBOOL(_1831643))], (38749 ^ _776545) ^ [_1521558, _1521560, _1521562, _1521564] : [-(hAPP(c_Set_Oimage(_1521558, _1521560, _1521562), hAPP(c_Set_Ovimage(_1521558, _1521560, _1521562), _1521564)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521560, tc_HOL_Obool)), _1521564), hAPP(c_Set_Oimage(_1521558, _1521560, _1521562), c_Orderings_Otop__class_Otop(tc_fun(_1521558, tc_HOL_Obool)))))], (52333 ^ _776545) ^ [_1829638, _1829640] : [-(class_Finite__Set_Ofinite(tc_prod(_1829638, _1829640))), class_Finite__Set_Ofinite(_1829638), class_Finite__Set_Ofinite(_1829640)], (7260 ^ _776545) ^ [_895066, _895068, _895070] : [hAPP(hAPP(c_Set_Oinsert(_895066), _895068), c_Orderings_Obot__class_Obot(tc_fun(_895066, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_895066), _895070), c_Orderings_Obot__class_Obot(tc_fun(_895066, tc_HOL_Obool))), -(_895068 = _895070)], (27210 ^ _776545) ^ [_1266155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266155)), 27214 ^ _776545 : [(27217 ^ _776545) ^ [] : [-(_1266155 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 27213 ^ [_1266155]))], (27215 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27213 ^ [_1266155])))]]], (11782 ^ _776545) ^ [_982887, _982889, _982891, _982893, _982895, _982897, _982899, _982901] : [c_Finite__Set_Ofolding__image__simple(_982887, _982889, _982891, _982893, _982895, _982897), hBOOL(hAPP(c_Finite__Set_Ofinite(_982889), _982899)), -(hAPP(_982897, hAPP(hAPP(c_Set_Oinsert(_982889), _982901), _982899)) = hAPP(hAPP(_982891, hAPP(_982895, _982901)), hAPP(_982897, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982889, tc_HOL_Obool)), _982899), hAPP(hAPP(c_Set_Oinsert(_982889), _982901), c_Orderings_Obot__class_Obot(tc_fun(_982889, tc_HOL_Obool)))))))], (37546 ^ _776545) ^ [_1491139, _1491141, _1491143, _1491145, _1491147] : [c_Fun_Oinj__on(_1491139, _1491141, _1491143, c_Orderings_Otop__class_Otop(tc_fun(_1491139, tc_HOL_Obool))), 37549 ^ _776545 : [(37556 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491139, tc_HOL_Obool)), _1491145), _1491147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491141, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491139, _1491141, _1491143), _1491145)), hAPP(c_Set_Oimage(_1491139, _1491141, _1491143), _1491147))))], (37550 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491141, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491139, _1491141, _1491143), _1491145)), hAPP(c_Set_Oimage(_1491139, _1491141, _1491143), _1491147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491139, tc_HOL_Obool)), _1491145), _1491147)))]]], (42205 ^ _776545) ^ [_1613367] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1613367)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1613367), tc_HOL_Obool))))], (44864 ^ _776545) ^ [_1674120, _1674122, _1674124, _1674126, _1674128, _1674130] : [-(hAPP(hAPP(c_List_Ozip(_1674120, _1674122), _1674124), hAPP(hAPP(c_List_Omap(_1674126, _1674122), _1674128), _1674130)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674120, _1674126), tc_prod(_1674120, _1674122)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674120, _1674126, tc_prod(_1674120, _1674122)), hAPP(hAPP(c_COMBC(_1674120, tc_fun(_1674126, _1674122), tc_fun(_1674126, tc_prod(_1674120, _1674122))), hAPP(hAPP(c_COMBB(tc_fun(_1674122, tc_prod(_1674120, _1674122)), tc_fun(tc_fun(_1674126, _1674122), tc_fun(_1674126, tc_prod(_1674120, _1674122))), _1674120), c_COMBB(_1674122, tc_prod(_1674120, _1674122), _1674126)), c_Product__Type_OPair(_1674120, _1674122))), _1674128))), hAPP(hAPP(c_List_Ozip(_1674120, _1674126), _1674124), _1674130)))], (45878 ^ _776545) ^ [_1696908, _1696910] : [class_Orderings_Olinorder(_1696908), -(c_List_Olinorder__class_Osorted__list__of__set(_1696908, hAPP(c_List_Oset(_1696908), _1696910)) = c_List_Olinorder__class_Osort__key(_1696908, _1696908, c_COMBI(_1696908), c_List_Oremdups(_1696908, _1696910)))], (38562 ^ _776545) ^ [_1516258, _1516260, _1516262] : [-(c_HOL_OThe(tc_prod(_1516258, _1516260), hAPP(c_Product__Type_Oprod_Oprod__case(_1516258, _1516260, tc_HOL_Obool), _1516262)) = c_HOL_OThe(tc_prod(_1516258, _1516260), hAPP(hAPP(c_COMBS(tc_prod(_1516258, _1516260), _1516260, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1516258, tc_fun(_1516260, tc_HOL_Obool), tc_prod(_1516258, _1516260)), _1516262), c_Product__Type_Ofst(_1516258, _1516260))), c_Product__Type_Osnd(_1516258, _1516260))))], (14204 ^ _776545) ^ [_1032024, _1032026] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1032024, _1032026))))], (42941 ^ _776545) ^ [_1632286, _1632288] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1632286), _1632288)), -(c_Nitpick_Ocard_H(_1632286, _1632288) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632286)), c_Hilbert__Choice_OEps(tc_List_Olist(_1632286), hAPP(hAPP(c_COMBS(tc_List_Olist(_1632286), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1632286)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1632286), tc_fun(_1632286, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1632286, tc_HOL_Obool), tc_fun(tc_fun(_1632286, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1632286)), c_fequal), c_List_Oset(_1632286))), _1632288))), c_List_Odistinct(_1632286)))))], (9512 ^ _776545) ^ [_939833, _939835, _939837] : [class_Orderings_Olinorder(_939833), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939833), _939835), _939837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939833), _939837), _939835)))], (18530 ^ _776545) ^ [_1110030, _1110032] : [hAPP(c_Finite__Set_Ocard(_1110030), _1110032) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1110032 = c_Orderings_Obot__class_Obot(tc_fun(_1110030, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110030), _1110032))], (16358 ^ _776545) ^ [_1071644] : [class_Groups_Ogroup__add(_1071644), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071644), c_Groups_Ozero__class_Ozero(_1071644)) = c_Groups_Ozero__class_Ozero(_1071644))], (33497 ^ _776545) ^ [_1392780, _1392782, _1392784, _1392786, _1392788] : [_1392780 = c_Orderings_Obot__class_Obot(tc_fun(_1392782, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1392784), _1392786), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392782, tc_fun(_1392784, tc_HOL_Obool)), _1392780), _1392788)) = hAPP(hAPP(c_Set_Oinsert(_1392784), _1392786), c_Orderings_Obot__class_Obot(tc_fun(_1392784, tc_HOL_Obool))))], (24443 ^ _776545) ^ [_1218500, _1218502, _1218504] : [hBOOL(hAPP(_1218500, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218502), _1218504))), 24446 ^ _776545 : [(24471 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218504), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24474 ^ _776545 : [(24475 ^ _776545) ^ [_1219164] : [-(hBOOL(hAPP(_1218500, _1219164))), 24476 ^ _776545 : [(24477 ^ _776545) ^ [_1219238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218504), _1219238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1219238), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1218502 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218504), _1219164)), _1219238)]]]]], (24453 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218504)), 24456 ^ _776545 : [(24457 ^ _776545) ^ [_1218834] : [-(hBOOL(hAPP(_1218500, _1218834))), 24458 ^ _776545 : [(24459 ^ _776545) ^ [_1218905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218905), _1218504)), _1218502 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218504), _1218834)), _1218905)]]]]], (24447 ^ _776545) ^ [] : [_1218504 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1218500, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (52453 ^ _776545) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (29227 ^ _776545) ^ [_1300389, _1300391] : [class_Int_Onumber__ring(_1300389), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300389), _1300391), hAPP(c_Int_Onumber__class_Onumber__of(_1300389), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300389), _1300391), _1300391))], (9372 ^ _776545) ^ [_937794, _937796, _937798, _937800] : [class_Orderings_Oord(_937794), 9375 ^ _776545 : [(9384 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937796, _937794)), _937798), _937800))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937796, _937794)), _937798), _937800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937796, _937794)), _937800), _937798)))], (9376 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937796, _937794)), _937798), _937800)), 9379 ^ _776545 : [(9382 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937796, _937794)), _937800), _937798))], (9380 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937796, _937794)), _937798), _937800)))]]]]], (43645 ^ _776545) ^ [_1647046, _1647048, _1647050] : [_1647048 = c_List_Olist_ONil(_1647046), -(hAPP(hAPP(c_List_Oappend(_1647046), _1647048), _1647050) = _1647050)], (13948 ^ _776545) ^ [_1025941, _1025943, _1025945, _1025947, _1025949, _1025951] : [class_Rings_Oordered__ring(_1025941), 13951 ^ _776545 : [(13958 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025941), _1025943), _1025949)), _1025945)), _1025947)), _1025951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), _1025943), _1025945)), _1025947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), _1025949), _1025945)), _1025951))))], (13952 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), _1025943), _1025945)), _1025947)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), _1025949), _1025945)), _1025951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025941), _1025943), _1025949)), _1025945)), _1025947)), _1025951)))]]], (51705 ^ _776545) ^ [_1822245, _1822247] : [_1822245 = _1822247, 51708 ^ _776545 : [(51711 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822247), _1822245)))], (51709 ^ 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c_Int_OBit0(_1293840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293838), _1293840)))], (7138 ^ _776545) ^ [_892832, _892834, _892836, _892838] : [-(hAPP(hAPP(c_Set_Oinsert(_892832), _892834), hAPP(hAPP(c_Set_Oinsert(_892832), _892836), _892838)) = hAPP(hAPP(c_Set_Oinsert(_892832), _892836), hAPP(hAPP(c_Set_Oinsert(_892832), _892834), _892838)))], (11208 ^ _776545) ^ [_970998, _971000, _971002, _971004, _971006] : [_970998 = hAPP(_971000, _971002), -(hBOOL(hAPP(hAPP(c_member(_971004), _970998), hAPP(c_Set_Oimage(_971006, _971004, _971000), c_Orderings_Otop__class_Otop(tc_fun(_971006, tc_HOL_Obool))))))], (7864 ^ _776545) ^ [_909034, _909036, _909038] : [7866 ^ _776545 : [(7872 ^ _776545) ^ [] : [-(7865 ^ [_909034, _909036, _909038] = 7868 ^ [_909034, _909036, _909038])], (7870 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909034), 7868 ^ [_909034, _909036, _909038]), _909038)))], (7867 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909034), 7865 ^ [_909034, _909036, _909038]), _909036)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909034, tc_HOL_Obool)), _909036), _909038) = c_Orderings_Obot__class_Obot(tc_fun(_909034, tc_HOL_Obool)))], (43683 ^ _776545) ^ [_1647904, _1647906, _1647908, _1647910] : [hBOOL(hAPP(hAPP(c_member(_1647904), _1647906), hAPP(c_List_Oset(_1647904), _1647908))), -(c_List_Oremove1(_1647904, _1647906, hAPP(hAPP(c_List_Oappend(_1647904), _1647908), _1647910)) = hAPP(hAPP(c_List_Oappend(_1647904), c_List_Oremove1(_1647904, _1647906, _1647908)), _1647910))], (18585 ^ _776545) ^ [_1111033, _1111035, _1111037] : [hBOOL(hAPP(_1111033, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111035), _1111037))), 18588 ^ _776545 : [(18595 ^ _776545) ^ [_1111224] : [_1111035 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111037), _1111224), -(hBOOL(hAPP(_1111033, _1111224)))], (18589 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111035), _1111037)), -(hBOOL(hAPP(_1111033, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (24940 ^ _776545) ^ [_1228177] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228177, _1228177) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39745 ^ _776545) ^ [_1548920, _1548922] : [class_Complete__Lattice_Ocomplete__lattice(_1548920), -(c_Complete__Lattice_OInf__class_OInf(_1548920, _1548922) = c_Complete__Lattice_OSup__class_OSup(_1548920, hAPP(c_Set_OCollect(_1548920), hAPP(hAPP(c_COMBB(tc_fun(_1548920, tc_HOL_Obool), tc_HOL_Obool, _1548920), c_HOL_OAll(_1548920)), hAPP(hAPP(c_COMBB(tc_fun(_1548920, tc_HOL_Obool), tc_fun(_1548920, tc_HOL_Obool), _1548920), hAPP(c_COMBS(_1548920, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548920), c_fimplies), hAPP(hAPP(c_COMBC(_1548920, tc_fun(_1548920, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548920)), _1548922)))), c_Orderings_Oord__class_Oless__eq(_1548920))))))], (42707 ^ _776545) ^ [_1626967, _1626969, _1626971, 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_980413), _980415))), 11657 ^ _776545 : [(11660 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980411), _980415)))], (11658 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_980411), _980413)))]]], (32634 ^ _776545) ^ [_1368640, _1368642, _1368644, _1368646, _1368648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368640, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368642, tc_fun(_1368640, tc_HOL_Obool)), _1368644), _1368646)), _1368648) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368642, tc_fun(_1368640, tc_HOL_Obool)), _1368644), hAPP(hAPP(c_COMBC(_1368642, tc_fun(_1368640, tc_HOL_Obool), tc_fun(_1368640, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368640, tc_HOL_Obool), tc_fun(tc_fun(_1368640, tc_HOL_Obool), tc_fun(_1368640, tc_HOL_Obool)), _1368642), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368640, tc_HOL_Obool))), _1368646)), _1368648)))], (23693 ^ _776545) ^ [_1205836] : [-(_1205836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205836), _1205836) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7724 ^ _776545) ^ [_905897, _905899, _905901] : [-(hAPP(c_Set_OPow(_905897), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905897, tc_HOL_Obool)), _905899), _905901)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_905897, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_905897), _905899)), hAPP(c_Set_OPow(_905897), _905901)))], (27028 ^ _776545) ^ [_1263374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263374)), -(c_Nat__Transfer_Ois__nat(_1263374))], (44002 ^ _776545) ^ [_1656082, _1656084, _1656086, _1656088, _1656090] : [hAPP(hAPP(c_List_Oappend(_1656082), _1656084), _1656086) = hAPP(hAPP(c_List_Oappend(_1656082), _1656088), _1656090), 44005 ^ _776545 : [(44014 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656084)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656088)))), 44017 ^ _776545 : [(44020 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1656082), hAPP(hAPP(c_List_Odrop(_1656082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656088)), _1656084)), _1656086) = _1656090)], (44018 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1656082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656088)), _1656084) = _1656088)]]], (44006 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656084)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656088))), 44009 ^ _776545 : [(44012 ^ _776545) ^ [] : [-(_1656086 = hAPP(hAPP(c_List_Oappend(_1656082), hAPP(hAPP(c_List_Odrop(_1656082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656084)), _1656088)), _1656090))], (44010 ^ _776545) ^ [] : [-(_1656084 = hAPP(hAPP(c_List_Otake(_1656082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656082)), _1656084)), _1656088))]]]]], (29313 ^ _776545) ^ [] : [-(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)))))], (13488 ^ _776545) ^ [_1016495, _1016497, _1016499, _1016501, _1016503, _1016505, _1016507, _1016509] : [c_Finite__Set_Ofolding__image__simple__idem(_1016495, _1016497, _1016499, _1016501, _1016503, _1016505), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016497), _1016507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016497, tc_HOL_Obool)), _1016509), _1016507)), -(hAPP(hAPP(_1016499, hAPP(_1016505, _1016509)), hAPP(_1016505, _1016507)) = hAPP(_1016505, _1016507))], (32774 ^ _776545) ^ [_1372117, _1372119, _1372121, _1372123, _1372125] : [class_Complete__Lattice_Ocomplete__lattice(_1372117), 32777 ^ _776545 : [(32778 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372117), _1372119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372121, _1372117), _1372123), _1372125))), 32781 ^ _776545 : [(32782 ^ _776545) ^ [_1372298] : [hBOOL(hAPP(hAPP(c_member(_1372121), _1372298), _1372123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372117), _1372119), hAPP(_1372125, _1372298))))]]], (32788 ^ _776545) ^ [] : [32790 ^ _776545 : [(32793 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372117), _1372119), hAPP(_1372125, 32789 ^ [_1372117, _1372119, _1372121, _1372123, _1372125])))], (32791 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372121), 32789 ^ [_1372117, _1372119, _1372121, _1372123, _1372125]), _1372123)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372117), _1372119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1372121, _1372117), _1372123), _1372125))))]]], (24140 ^ _776545) ^ [_1213282, _1213284, _1213286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213284), _1213286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213282), _1213286)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213282), _1213284))))], (33210 ^ _776545) ^ [_1385132, _1385134, _1385136] : [-(hAPP(hAPP(c_Set_Oinsert(_1385132), _1385134), hAPP(c_Set_OCollect(_1385132), _1385136)) = hAPP(c_Set_OCollect(_1385132), hAPP(hAPP(c_COMBS(_1385132, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1385132), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1385132), c_fNot), hAPP(hAPP(c_COMBC(_1385132, _1385132, tc_HOL_Obool), c_fequal), _1385134)))), _1385136)))], (28639 ^ _776545) ^ [_1290120, _1290122] : [class_Int_Onumber__ring(_1290120), class_Rings_Olinordered__idom(_1290120), 28646 ^ _776545 : [(28653 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290120), c_Groups_Oone__class_Oone(_1290120)), hAPP(c_Int_Onumber__class_Onumber__of(_1290120), _1290122))))], (28647 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290120), c_Groups_Oone__class_Oone(_1290120)), hAPP(c_Int_Onumber__class_Onumber__of(_1290120), _1290122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290122)))]]], (24200 ^ _776545) ^ [_1214262, _1214264, _1214266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214262), 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)), _1214264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214264), _1214266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214262), _1214264)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214262), _1214266))))], (37106 ^ _776545) ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815] : [c_Equiv__Relations_Oequiv(_1481803, _1481805, _1481807), c_Equiv__Relations_Ocongruent(_1481803, tc_fun(_1481809, tc_HOL_Obool), _1481807, _1481811), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481803, tc_fun(_1481809, tc_HOL_Obool)), _1481813), _1481811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481803, tc_fun(_1481809, tc_HOL_Obool)), _1481815), _1481811), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481803, tc_HOL_Obool)), _1481813), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481803), _1481805), _1481807))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1481803, tc_HOL_Obool)), _1481815), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1481803), _1481805), _1481807))), 37128 ^ _776545 : [(37132 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481803), 37130 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815]), _1481805)))], (37134 ^ _776545) ^ [] : [-(hAPP(_1481811, 37127 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815]) = hAPP(_1481811, 37130 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815]))], (37136 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481803, _1481803)), hAPP(hAPP(c_Product__Type_OPair(_1481803, _1481803), 37127 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815]), 37130 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815])), _1481807))], (37129 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481803), 37127 ^ [_1481803, _1481805, _1481807, _1481809, _1481811, _1481813, _1481815]), _1481805)))]], -(_1481813 = _1481815)], (25978 ^ _776545) ^ [_1246247] : [25980 ^ _776545 : [(25983 ^ _776545) ^ [] : [hBOOL(hAPP(_1246247, hAPP(c_Int_Onat, 25979 ^ [_1246247])))], (25981 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25979 ^ [_1246247])))]], 25984 ^ _776545 : [(25985 ^ _776545) ^ [_1246380] : [-(hBOOL(hAPP(_1246247, _1246380)))]]], (47454 ^ _776545) ^ [_1730715, _1730717, _1730719, _1730721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730715), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730717)), c_List_OdropWhile(_1730717, _1730719, _1730721)))), -(hAPP(hAPP(c_List_Onth(_1730717), c_List_OdropWhile(_1730717, _1730719, _1730721)), _1730715) = hAPP(hAPP(c_List_Onth(_1730717), _1730721), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1730715), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730717)), c_List_OtakeWhile(_1730717, _1730719, _1730721)))))], (43737 ^ _776545) ^ [_1649320, _1649322, _1649324] : [-(hBOOL(hAPP(c_List_Odistinct(_1649320), hAPP(hAPP(c_List_Oappend(_1649320), _1649322), _1649324)))), hBOOL(hAPP(c_List_Odistinct(_1649320), _1649322)), hBOOL(hAPP(c_List_Odistinct(_1649320), _1649324)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649320, tc_HOL_Obool)), hAPP(c_List_Oset(_1649320), _1649322)), hAPP(c_List_Oset(_1649320), _1649324)) = c_Orderings_Obot__class_Obot(tc_fun(_1649320, tc_HOL_Obool))], (51985 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (46538 ^ _776545) ^ [_1712313, _1712315, _1712317] : [class_Orderings_Olinorder(_1712313), 46541 ^ _776545 : [(46548 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1712313, _1712317), -(c_List_Olinorder__class_Osorted(_1712313, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712313, _1712313, c_COMBI(_1712313)), _1712315), _1712317)))], (46542 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1712313, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712313, _1712313, c_COMBI(_1712313)), _1712315), _1712317)), -(c_List_Olinorder__class_Osorted(_1712313, _1712317))]]], (39149 ^ _776545) ^ [_1531774, _1531776, _1531778, _1531780, _1531782] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531774, _1531776), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531774, tc_HOL_Obool)), _1531778), _1531780)), hAPP(c_COMBK(tc_fun(_1531776, tc_HOL_Obool), _1531774), _1531782)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531774, _1531776), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531774, _1531776), _1531778), hAPP(c_COMBK(tc_fun(_1531776, tc_HOL_Obool), _1531774), _1531782))), hAPP(hAPP(c_Product__Type_OSigma(_1531774, _1531776), _1531780), hAPP(c_COMBK(tc_fun(_1531776, tc_HOL_Obool), _1531774), _1531782))))], (36209 ^ _776545) ^ [_1459497, _1459499, _1459501, _1459503, _1459505, _1459507, _1459509] : [-(hAPP(c_Product__Type_Oapfst(_1459497, _1459499, _1459501, _1459503), hAPP(c_Product__Type_Oapsnd(_1459505, _1459501, _1459497, _1459507), _1459509)) = hAPP(hAPP(c_Product__Type_OPair(_1459499, _1459501), hAPP(_1459503, hAPP(c_Product__Type_Ofst(_1459497, _1459505), _1459509))), hAPP(_1459507, hAPP(c_Product__Type_Osnd(_1459497, _1459505), _1459509))))], (44721 ^ _776545) ^ [_1670537, _1670539, _1670541, _1670543, _1670545, _1670547] : [-(hAPP(hAPP(c_List_Omap(_1670537, _1670539), _1670541), hAPP(hAPP(c_List_Omap(_1670543, _1670537), _1670545), _1670547)) = hAPP(hAPP(c_List_Omap(_1670543, _1670539), hAPP(c_Fun_Ocomp(_1670537, _1670539, _1670543, _1670541), _1670545)), _1670547))], (43944 ^ _776545) ^ [_1654731, _1654733, _1654735] : [hAPP(hAPP(c_List_Odrop(_1654731), _1654733), _1654735) = c_List_Olist_ONil(_1654731), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654731)), _1654735)), _1654733)))], (50291 ^ _776545) ^ [_1793200, _1793202, _1793204, _1793206, _1793208, _1793210] : [c_Fun_Obij__betw(_1793200, _1793202, _1793204, _1793206, _1793208), hBOOL(hAPP(hAPP(c_member(_1793200), _1793210), _1793206)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1793202, _1793200, _1793208, c_Hilbert__Choice_Oinv__into(_1793200, _1793202, _1793206, _1793204)), _1793210) = hAPP(_1793204, _1793210))], (3408 ^ _776545) ^ [_827430, _827432, _827434, _827436] : [-(c_Enum_Oenum__the(_827436, _827432) = c_Enum_Oenum__the(_827434, _827430)), _827436 = _827434, _827432 = _827430], (1604 ^ _776545) ^ [_799459, _799461] : [-(class_Rings_Olinordered__semiring(_799459)), _799461 = _799459, class_Rings_Olinordered__semiring(_799461)], (1022 ^ _776545) ^ [_791976, _791978, _791980, _791982, _791984, _791986] : [-(c_List_Olist__ex(_791984, _791980, _791976)), c_List_Olist__ex(_791986, _791982, _791978), _791986 = _791984, _791982 = _791980, _791978 = _791976], (24748 ^ _776545) ^ [_1224251, _1224253] : [class_Divides_Osemiring__div(_1224251), -(c_Divides_Odiv__class_Omod(_1224251, c_Groups_Ozero__class_Ozero(_1224251), _1224253) = c_Groups_Ozero__class_Ozero(_1224251))], (15854 ^ _776545) ^ [_1063581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063581)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063581), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1063581)], (23834 ^ _776545) ^ [_1208298, _1208300] : [class_Rings_Olinordered__semidom(_1208298), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208298), c_Groups_Ozero__class_Ozero(_1208298)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208298), _1208300))))], (46127 ^ _776545) ^ [_1703051, _1703053, _1703055] : [46129 ^ _776545 : [(46132 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1703053, 46128 ^ [_1703051, _1703053, _1703055])))], (46130 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703051), 46128 ^ [_1703051, _1703053, _1703055]), hAPP(c_List_Oset(_1703051), _1703055))))]], -(hAPP(c_List_Ofilter(_1703051, _1703053), _1703055) = c_List_Olist_ONil(_1703051))], (6588 ^ _776545) ^ [_883105, _883107, _883109] : [hBOOL(hAPP(hAPP(c_member(_883105), _883107), c_Complete__Lattice_OSup__class_OSup(tc_fun(_883105, tc_HOL_Obool), _883109))), 6592 ^ _776545 : [(6595 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_883105, tc_HOL_Obool)), 6591 ^ [_883105, _883107, _883109]), _883109)))], (6593 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_883105), _883107), 6591 ^ [_883105, _883107, _883109])))]]], (31919 ^ _776545) ^ [_1350023] : [class_Orderings_Oord(_1350023), -(c_Orderings_Oord__class_Omax(_1350023) = c_Orderings_Oord_Omax(_1350023, c_Orderings_Oord__class_Oless__eq(_1350023)))], (39306 ^ _776545) ^ [_1537282, _1537284, _1537286, _1537288] : [-(c_Fun_Oinj__on(_1537282, tc_prod(_1537284, _1537282), 39304 ^ [_1537282, _1537284, _1537286, _1537288], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537284, tc_fun(_1537282, tc_HOL_Obool)), _1537286), _1537288)))], (41849 ^ _776545) ^ [_1602589, _1602591, _1602593, _1602595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602589), tc_List_Olist(_1602589))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602589), tc_List_Olist(_1602589)), _1602591), _1602593)), c_List_Olex(_1602589, _1602595))), 41852 ^ _776545 : [(41855 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602589)), _1602591) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602589)), _1602593))], (41853 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602589), tc_List_Olist(_1602589))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602589), tc_List_Olist(_1602589)), _1602591), _1602593)), c_List_Olexord(_1602589, _1602595))))]]], (5982 ^ _776545) ^ [_871872, _871874, _871876, _871878, _871880, _871882] : [c_Typedef_Otype__definition(_871872, _871874, _871876, _871878, _871880), hBOOL(hAPP(hAPP(c_member(_871874), _871882), _871880)), -(_871882 = hAPP(_871876, 5989 ^ [_871872, _871874, _871876, _871878, _871880, _871882]))], (35452 ^ _776545) ^ [_1437719, _1437721, _1437723] : [35454 ^ _776545 : [(35457 ^ _776545) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1437723, 35453 ^ [_1437719, _1437721, _1437723]))], (35455 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437719), 35453 ^ [_1437719, _1437721, _1437723]), _1437721)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1437719, tc_Int_Oint), _1437723), _1437721) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1437719, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1437719), c_Int_Onat), _1437723)), _1437721)))], (3470 ^ _776545) ^ [_828391, _828393, _828395, _828397, _828399, _828401, _828403, _828405] : [-(c_List_Olist_Olist__case(_828405, _828401, _828397, _828393) = c_List_Olist_Olist__case(_828403, _828399, _828395, _828391)), _828405 = _828403, _828401 = _828399, _828397 = _828395, _828393 = _828391], (36952 ^ _776545) ^ [_1478203, _1478205, _1478207, _1478209, _1478211, _1478213, _1478215, _1478217, _1478219, _1478221] : [c_Equiv__Relations_Oequiv(_1478203, _1478205, _1478207), c_Equiv__Relations_Oequiv(_1478209, _1478211, _1478213), c_Equiv__Relations_Ocongruent2(_1478203, _1478209, tc_fun(_1478215, tc_HOL_Obool), _1478207, _1478213, _1478217), hBOOL(hAPP(hAPP(c_member(_1478203), _1478219), _1478205)), hBOOL(hAPP(hAPP(c_member(_1478209), _1478221), _1478211)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478203, tc_fun(_1478215, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1478203, _1478203, _1478207), hAPP(hAPP(c_Set_Oinsert(_1478203), _1478219), c_Orderings_Obot__class_Obot(tc_fun(_1478203, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1478209, tc_fun(_1478215, tc_HOL_Obool)), tc_fun(_1478215, tc_HOL_Obool), _1478203), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478209, tc_fun(_1478215, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1478209, _1478209, _1478213), hAPP(hAPP(c_Set_Oinsert(_1478209), _1478221), c_Orderings_Obot__class_Obot(tc_fun(_1478209, tc_HOL_Obool)))))), _1478217)) = hAPP(hAPP(_1478217, _1478219), _1478221))], (43266 ^ _776545) ^ [_1638448, _1638450] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1638448), tc_List_Olist(_1638448), c_List_Olistrel(_1638448, _1638450)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638448)), c_List_Olist_ONil(_1638448)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638448), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638448)), c_List_Olist_ONil(_1638448)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638448), tc_HOL_Obool))))], (28815 ^ _776545) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (28817 ^ _776545) ^ [_1293169, _1293171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293169)), c_Int_OBit0(_1293171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293169), _1293171)))], (16472 ^ _776545) ^ [_1073229, _1073231] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073229), _1073231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1073231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9368 ^ _776545) ^ [_937718, _937720, _937722, _937724] : [-(c_Nitpick_Ofold__graph_H(_937718, _937720, _937722, _937724, c_Orderings_Obot__class_Obot(tc_fun(_937718, tc_HOL_Obool)), _937724))], (44783 ^ _776545) ^ [_1672008, _1672010, _1672012, _1672014, _1672016] : [class_Groups_Ocomm__monoid__add(_1672008), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672008), hAPP(hAPP(c_List_Omap(_1672010, _1672008), hAPP(hAPP(c_COMBS(_1672010, _1672008, _1672008), hAPP(hAPP(c_COMBB(_1672008, tc_fun(_1672008, _1672008), _1672010), c_Groups_Oplus__class_Oplus(_1672008)), _1672012)), _1672014)), _1672016)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672008), hAPP(c_List_Omonoid__add__class_Olistsum(_1672008), hAPP(hAPP(c_List_Omap(_1672010, _1672008), _1672012), _1672016))), hAPP(c_List_Omonoid__add__class_Olistsum(_1672008), hAPP(hAPP(c_List_Omap(_1672010, _1672008), _1672014), _1672016))))], (38525 ^ _776545) ^ [_1515200, _1515202, _1515204] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1515200, _1515202)), _1515204)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1515202), hAPP(c_Relation_ORange(_1515200, _1515202), _1515204))))], (47323 ^ _776545) ^ [_1727947, _1727949, _1727951, _1727953, _1727955] : [class_Orderings_Olinorder(_1727947), c_List_Olinorder__class_Osorted(_1727947, hAPP(c_List_Orev(_1727947), hAPP(hAPP(c_List_Omap(_1727949, _1727947), _1727951), _1727953))), -(hAPP(c_List_Ofilter(_1727949, hAPP(hAPP(c_COMBB(_1727947, tc_HOL_Obool, _1727949), hAPP(c_Orderings_Oord__class_Oless(_1727947), _1727955)), _1727951)), _1727953) = c_List_OtakeWhile(_1727949, hAPP(hAPP(c_COMBB(_1727947, tc_HOL_Obool, _1727949), hAPP(c_Orderings_Oord__class_Oless(_1727947), _1727955)), _1727951), _1727953))], (28183 ^ _776545) ^ [_1282608] : [class_Int_Onumber__ring(_1282608), c_Int_Oiszero(_1282608, hAPP(c_Int_Onumber__class_Onumber__of(_1282608), c_Int_OMin))], (7658 ^ _776545) ^ [_903919, _903921, _903923, _903925] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903919, tc_HOL_Obool)), _903921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903919, tc_HOL_Obool)), _903923), _903925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903919, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903919, tc_HOL_Obool)), _903921), _903923)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903919, tc_HOL_Obool)), _903921), _903925)))], (37824 ^ _776545) ^ [_1497545] : [class_Nat_Osemiring__char__0(_1497545), -(c_Fun_Oinj__on(tc_Nat_Onat, _1497545, c_Nat_Osemiring__1__class_Oof__nat(_1497545), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (24036 ^ _776545) ^ [_1211728] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1211728)), -(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)), _1211728))))], (6606 ^ _776545) ^ [_883528, _883530, _883532] : [class_Orderings_Olinorder(_883528), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883528), _883530), _883532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883528), _883532), _883530)))], (29777 ^ _776545) ^ [] : [-(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))], (26773 ^ _776545) ^ [_1259409] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259409)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259409))], (33322 ^ _776545) ^ [_1387894, _1387896] : [-(hAPP(c_Set_OCollect(_1387894), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1387894), c_fNot), _1387896)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1387894, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1387894), _1387896)))], (50989 ^ _776545) ^ [_1809079, _1809081, _1809083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1809079)), 50992 ^ _776545 : [(50999 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809081), _1809083)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809079), _1809081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809079), _1809083))))], (50993 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809079), _1809081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1809079), _1809083))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809081), _1809083)))]]], (41130 ^ _776545) ^ [_1583083, _1583085, _1583087] : [c_Relation_Orefl__on(_1583083, _1583085, hAPP(c_Relation_Oconverse(_1583083, _1583083), _1583087)), -(c_Relation_Orefl__on(_1583083, _1583085, _1583087))], (40893 ^ _776545) ^ [_1577241, _1577243, _1577245, _1577247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577241, _1577241)), hAPP(hAPP(c_Product__Type_OPair(_1577241, _1577241), _1577243), _1577245)), c_Transitive__Closure_Ortrancl(_1577241, _1577247))), -(_1577243 = _1577245), 40900 ^ _776545 : [(40903 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577241, _1577241)), hAPP(hAPP(c_Product__Type_OPair(_1577241, _1577241), _1577243), _1577245)), c_Transitive__Closure_Otrancl(_1577241, _1577247))))], (40901 ^ _776545) ^ [] : [_1577243 = _1577245]]], (36557 ^ _776545) ^ [_1468892] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468892) = 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, _1468892)), 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))))))))], (23761 ^ _776545) ^ [_1206886, _1206888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206886)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206886), _1206888)))], (28615 ^ _776545) ^ [_1289788] : [class_Int_Onumber__ring(_1289788), c_Int_Oiszero(_1289788, hAPP(c_Int_Onumber__class_Onumber__of(_1289788), c_Int_OBit1(c_Int_OPls)))], (41935 ^ _776545) ^ [_1605393, _1605395, _1605397, _1605399, _1605401, _1605403] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605393), tc_List_Olist(_1605393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605393), tc_List_Olist(_1605393)), hAPP(hAPP(c_List_Olist_OCons(_1605393), _1605395), _1605397)), hAPP(hAPP(c_List_Olist_OCons(_1605393), _1605399), _1605401))), c_List_Olistrel1(_1605393, _1605403))), 41940 ^ _776545 : [(41943 ^ _776545) ^ [] : [-(_1605397 = _1605401)], (41941 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605393, _1605393)), hAPP(hAPP(c_Product__Type_OPair(_1605393, _1605393), _1605395), _1605399)), _1605403)))]], 41944 ^ _776545 : [(41947 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605393), tc_List_Olist(_1605393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605393), tc_List_Olist(_1605393)), _1605397), _1605401)), c_List_Olistrel1(_1605393, _1605403))))], (41945 ^ _776545) ^ [] : [-(_1605395 = _1605399)]]], (40841 ^ _776545) ^ [_1576059, _1576061] : [-(hAPP(c_Relation_OImage(_1576059, _1576059, c_Relation_OId(_1576059)), _1576061) = _1576061)], (51771 ^ _776545) ^ [_1823319, _1823321] : [-(_1823319 = _1823321), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823319), _1823321)), 51778 ^ _776545 : [(51781 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823321), _1823319))], (51779 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823319), _1823321)))]]], (26032 ^ _776545) ^ [_1247079, _1247081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247079), _1247081))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247079, _1247081) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247079), _1247081), _1247081))], (24938 ^ _776545) ^ [_1228126, _1228128, _1228130] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228128), _1228130)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228126), _1228128)), _1228130))], (43962 ^ _776545) ^ [_1655098, _1655100, _1655102, _1655104] : [-(hAPP(hAPP(c_List_Odrop(_1655098), _1655100), hAPP(hAPP(c_List_Oappend(_1655098), _1655102), _1655104)) = hAPP(hAPP(c_List_Oappend(_1655098), hAPP(hAPP(c_List_Odrop(_1655098), _1655100), _1655102)), hAPP(hAPP(c_List_Odrop(_1655098), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655100), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655098)), _1655102))), _1655104)))], (50761 ^ _776545) ^ [_1802510, _1802512, _1802514, _1802516, _1802518] : [hBOOL(hAPP(hAPP(c_member(_1802510), _1802512), _1802514)), -(hAPP(c_Quotient_OBabs(_1802510, _1802516, _1802514, _1802518), _1802512) = hAPP(_1802518, _1802512))], (17843 ^ _776545) ^ [_1097613, _1097615, _1097617] : [class_Groups_Ocomm__monoid__add(_1097613), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097615, _1097613), _1097617), c_Orderings_Obot__class_Obot(tc_fun(_1097615, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1097613))], (28419 ^ _776545) ^ [_1286663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286663), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286663)), c_Int_OPls)))], (11612 ^ _776545) ^ [_979660, _979662] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979660, _979662)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_979660, _979662), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979662), c_Orderings_Otop__class_Otop(tc_fun(_979662, tc_HOL_Obool)))))], (32061 ^ _776545) ^ [_1352604, _1352606, _1352608] : [class_Orderings_Olinorder(_1352604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352604), _1352606)), -(_1352606 = c_Orderings_Obot__class_Obot(tc_fun(_1352604, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352604), _1352608)), -(_1352608 = c_Orderings_Obot__class_Obot(tc_fun(_1352604, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352604, tc_HOL_Obool)), _1352606), _1352608)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352604), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), _1352606)), c_Big__Operators_Olattice_OSup__fin(_1352604, c_Orderings_Oord__class_Omax(_1352604), _1352608)))], (42717 ^ _776545) ^ [_1627222, _1627224, _1627226, _1627228, _1627230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627222, tc_HOL_Obool)), hAPP(c_List_Oset(_1627222), _1627224)), _1627226)), hBOOL(hAPP(hAPP(c_member(_1627222), _1627228), _1627226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627222, tc_HOL_Obool)), hAPP(c_List_Oset(_1627222), hAPP(hAPP(c_List_Olist__update(_1627222, _1627224), _1627230), _1627228))), _1627226)))], (5807 ^ _776545) ^ [_868491, _868493, _868495, _868497, _868499, _868501] : [c_Typedef_Otype__definition(_868491, _868493, _868495, _868497, _868499), hBOOL(hAPP(hAPP(c_member(_868493), _868501), _868499)), -(hAPP(_868495, hAPP(_868497, 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hAPP(hAPP(c_Set_Oinsert(_983656), _983660), c_Orderings_Obot__class_Obot(tc_fun(_983656, tc_HOL_Obool)))))))], (11828 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983656, tc_HOL_Obool)), _983658), hAPP(hAPP(c_Set_Oinsert(_983656), _983660), c_Orderings_Obot__class_Obot(tc_fun(_983656, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_983656, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_983656, _983658) = _983660)]]], (35710 ^ _776545) ^ [_1443272, _1443274, _1443276] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1443272, _1443274), _1443276)), 35713 ^ _776545 : [(35722 ^ _776545) ^ [] : [-(_1443274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35725 ^ _776545 : [(35734 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443274))), 35737 ^ _776545 : [(35740 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443276)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35738 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1443274), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443276))))]]], (35726 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443274)), 35729 ^ _776545 : [(35732 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443276)), _1443274)))], (35730 ^ _776545) ^ [] : [-(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), _1443276))))]]]]], (35716 ^ _776545) ^ [] : [_1443274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1443276) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35714 ^ _776545) ^ [] : [-(_1443272 = 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), _1443276)), _1443274)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1443276)))]]], (49021 ^ _776545) ^ [_1765242, _1765244, _1765246, _1765248, _1765250, _1765252, _1765254] : [49023 ^ _776545 : [(49026 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1765246, 49022 ^ [_1765242, _1765244, _1765246, _1765248, _1765250, _1765252, _1765254]), _1765248), _1765250))], (49024 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765242), 49022 ^ [_1765242, _1765244, _1765246, _1765248, _1765250, _1765252, _1765254]), _1765244)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1765242, tc_fun(_1765252, tc_fun(_1765254, tc_HOL_Obool))), _1765244), _1765246), _1765248), _1765250)))], (48574 ^ _776545) ^ [_1755922, _1755924, _1755926] : [-(hAPP(c_List_Orev(_1755922), c_List_Oreplicate(_1755922, _1755924, _1755926)) = c_List_Oreplicate(_1755922, _1755924, _1755926))], (19763 ^ _776545) ^ [_1133220, _1133222] : [class_Rings_Olinordered__idom(_1133220), 19766 ^ _776545 : [(19773 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133220), c_Groups_Ozero__class_Ozero(_1133220)), _1133222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133220), c_Groups_Ozero__class_Ozero(_1133220)), c_Groups_Osgn__class_Osgn(_1133220, _1133222))))], (19767 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133220), c_Groups_Ozero__class_Ozero(_1133220)), c_Groups_Osgn__class_Osgn(_1133220, _1133222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133220), c_Groups_Ozero__class_Ozero(_1133220)), _1133222)))]]], (13093 ^ _776545) ^ [_1007739, _1007741, _1007743, _1007745, _1007747, _1007749, _1007751, _1007753] : [c_Finite__Set_Ofolding__image__simple(_1007739, _1007741, _1007743, _1007745, _1007747, _1007749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007741), _1007751)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007741), _1007753)), 13107 ^ _776545 : [(13110 ^ _776545) ^ [] : [hAPP(_1007747, 13106 ^ [_1007739, _1007741, _1007743, _1007745, _1007747, _1007749, _1007751, _1007753]) = _1007745], (13108 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007741), 13106 ^ [_1007739, _1007741, _1007743, _1007745, _1007747, _1007749, _1007751, _1007753]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1007741, tc_HOL_Obool)), _1007751), _1007753))))]], -(hAPP(_1007749, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007741, tc_HOL_Obool)), _1007751), _1007753)) = hAPP(hAPP(_1007743, hAPP(_1007749, _1007751)), hAPP(_1007749, _1007753)))], (29239 ^ _776545) ^ [_1300623] : [class_Int_Onumber__ring(_1300623), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300623), c_Groups_Oone__class_Oone(_1300623)), c_Groups_Oone__class_Oone(_1300623)) = 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[hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614607), tc_List_Olist(_1614607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614607), tc_List_Olist(_1614607)), _1614609), _1614611)), c_List_Olexord(_1614607, _1614613))), 42267 ^ _776545 : [(42270 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1614607), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614607)), _1614609)), _1614611) = _1614609)], (42268 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614607)), _1614609)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614607)), _1614611))))]], 42272 ^ _776545 : [(42277 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614607, _1614607)), hAPP(hAPP(c_Product__Type_OPair(_1614607, _1614607), hAPP(hAPP(c_List_Onth(_1614607), _1614609), 42271 ^ [_1614607, _1614609, _1614611, _1614613])), hAPP(hAPP(c_List_Onth(_1614607), _1614611), 42271 ^ [_1614607, _1614609, _1614611, _1614613]))), _1614613)))], (42275 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1614607), 42271 ^ [_1614607, _1614609, _1614611, _1614613]), _1614609) = hAPP(hAPP(c_List_Otake(_1614607), 42271 ^ [_1614607, _1614609, _1614611, _1614613]), _1614611))], (42273 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42271 ^ [_1614607, _1614609, _1614611, _1614613]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614607)), _1614609)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614607)), _1614611)))))]]], (33833 ^ _776545) ^ [_1403274, _1403276, _1403278, _1403280, _1403282] : [class_Groups_Ocomm__monoid__mult(_1403274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403276), _1403278)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403274, _1403276, c_Groups_Otimes__class_Otimes(_1403274)), hAPP(hAPP(c_COMBS(_1403276, _1403274, _1403274), hAPP(hAPP(c_COMBB(_1403274, tc_fun(_1403274, _1403274), _1403276), c_Groups_Otimes__class_Otimes(_1403274)), _1403280)), _1403282)), c_Groups_Oone__class_Oone(_1403274)), _1403278) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403274), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403274, _1403276, c_Groups_Otimes__class_Otimes(_1403274)), _1403280), c_Groups_Oone__class_Oone(_1403274)), _1403278)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403274, _1403276, c_Groups_Otimes__class_Otimes(_1403274)), _1403282), c_Groups_Oone__class_Oone(_1403274)), _1403278)))], (8022 ^ _776545) ^ [_912599, _912601, _912603, _912605] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912599, tc_HOL_Obool)), _912601), hAPP(hAPP(c_Set_Oinsert(_912599), _912603), _912605)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912599, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912599, tc_HOL_Obool)), _912601), hAPP(hAPP(c_Set_Oinsert(_912599), _912603), c_Orderings_Obot__class_Obot(tc_fun(_912599, tc_HOL_Obool))))), _912605))], (4368 ^ _776545) ^ [_842744, _842746, _842748, _842750, _842752, _842754, _842756, _842758] : [-(c_Lazy__Sequence_Oproduct(_842758, _842754, _842750, _842746) = c_Lazy__Sequence_Oproduct(_842756, _842752, _842748, _842744)), _842758 = _842756, _842754 = _842752, _842750 = _842748, _842746 = _842744], (6376 ^ _776545) ^ [_879414, _879416] : [_879416 = c_Orderings_Obot__class_Obot(tc_fun(_879414, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879414, tc_HOL_Obool)), _879416), c_Orderings_Obot__class_Obot(tc_fun(_879414, tc_HOL_Obool)))))], (6105 ^ _776545) ^ [_874344, _874346, _874348, _874350, _874352, _874354] : [-(hBOOL(hAPP(hAPP(c_member(_874344), _874346), c_SetInterval_Oord_OatLeastLessThan(_874344, _874348, _874350, _874352, _874354)))), hBOOL(hAPP(hAPP(_874348, _874352), _874346)), hBOOL(hAPP(hAPP(_874350, _874346), _874354))], (1654 ^ _776545) ^ [_800084, _800086] : [-(class_Rings_Oordered__semiring(_800084)), _800086 = _800084, class_Rings_Oordered__semiring(_800086)], (24704 ^ _776545) ^ [_1223510, _1223512] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223510) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223512), -(_1223510 = _1223512)], (52401 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (9036 ^ _776545) ^ [_932873, _932875, _932877] : [class_Orderings_Olinorder(_932873), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932873), _932875), _932877))), -(_932875 = _932877), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932873), _932877), _932875)))], (51263 ^ _776545) ^ [_1814480, _1814482, _1814484, _1814486] : [class_Rings_Ocomm__semiring__1(_1814480), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814480), _1814482), _1814484)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814480), _1814482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814480), _1814484), _1814486))))], (30070 ^ _776545) ^ [_1315889, _1315891, _1315893, _1315895] : [class_Orderings_Olinorder(_1315889), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315889), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315889), _1315891), _1315893)), _1315895) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315889), _1315891), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315889), _1315893), _1315895)))], (52243 ^ _776545) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (42059 ^ _776545) ^ [_1609253, _1609255, _1609257, _1609259] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609253), tc_List_Olist(_1609253))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609253), tc_List_Olist(_1609253)), _1609257), _1609259)), c_List_Olistrel(_1609253, _1609255))), -(c_List_Olistrelp(_1609253, hAPP(hAPP(c_COMBC(_1609253, tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_fun(_1609253, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609253, tc_fun(tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_fun(_1609253, tc_HOL_Obool)), _1609253), c_COMBC(_1609253, tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609253, tc_prod(_1609253, _1609253)), tc_fun(_1609253, tc_fun(tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_HOL_Obool)), _1609253), hAPP(c_COMBB(tc_prod(_1609253, _1609253), tc_fun(tc_fun(tc_prod(_1609253, _1609253), tc_HOL_Obool), tc_HOL_Obool), _1609253), c_member(tc_prod(_1609253, _1609253)))), c_Product__Type_OPair(_1609253, _1609253)))), _1609255), _1609257, _1609259))], (14498 ^ _776545) ^ [_1038256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038256), _1038256))], (34803 ^ _776545) ^ [_1425903, _1425905, _1425907, _1425909] : [class_Rings_Osemiring__1(_1425903), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1425903, _1425905, hAPP(c_Nat_OSuc, _1425907), _1425909) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1425903, _1425905, _1425907, hAPP(_1425905, _1425909)))], (7682 ^ _776545) ^ [_904715, _904717] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904715, tc_HOL_Obool)), _904717), _904717) = _904717)], (34958 ^ _776545) ^ [_1428785, _1428787] : [_1428785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1428787, _1428785) = 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), _1428787)))], (5010 ^ _776545) ^ [_852917, _852919] : [_852919 = _852917, -(c_Fun_Oid(_852919) = c_Fun_Oid(_852917))], (34191 ^ _776545) ^ [_1412133, _1412135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412133)), hAPP(c_Nat_OSuc, _1412135))), -(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(_1412133))), 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)), _1412135)))))], (15282 ^ _776545) ^ [_1052340, _1052342, _1052344, _1052346] : [class_Groups_Ocomm__monoid__mult(_1052340), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052342), _1052344))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052342, _1052340), _1052346), _1052344) = c_Groups_Oone__class_Oone(_1052340))], (6031 ^ _776545) ^ [_872847, _872849, _872851, _872853] : [hBOOL(hAPP(hAPP(c_member(_872847), _872849), c_SetInterval_Oord_OgreaterThan(_872847, _872851, _872853))), -(hBOOL(hAPP(hAPP(_872851, _872853), _872849)))], (35551 ^ _776545) ^ [_1439841, _1439843, _1439845] : [35553 ^ _776545 : [(35556 ^ _776545) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1439845, 35552 ^ [_1439841, _1439843, _1439845]))], (35554 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439841), 35552 ^ [_1439841, _1439843, _1439845]), _1439843)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439841, tc_Int_Oint), _1439845), _1439843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1439841, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1439841), c_Int_Onat), _1439845)), _1439843)))], (40853 ^ _776545) ^ [_1576306, _1576308, _1576310] : [_1576308 = _1576310, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576306, _1576306)), hAPP(hAPP(c_Product__Type_OPair(_1576306, _1576306), _1576308), _1576310)), c_Relation_OId(_1576306))))], (30112 ^ _776545) ^ [_1316743, _1316745, _1316747, _1316749, _1316751] : [class_Orderings_Olinorder(_1316743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316743), _1316745), _1316747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316743), _1316749), _1316751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316743), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316743), _1316745), _1316749)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316743), _1316747), _1316751))))], (25706 ^ _776545) ^ [_1241710, _1241712, _1241714, _1241716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241712), _1241714)), -(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), _1241714), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241716, _1241710))), _1241712)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241714), _1241710))))], (47291 ^ _776545) ^ [_1727272, _1727274, _1727276, _1727278, _1727280] : [hBOOL(hAPP(hAPP(c_member(_1727272), _1727274), hAPP(c_List_Oset(_1727272), _1727276))), -(hBOOL(hAPP(_1727278, _1727274))), -(c_List_OtakeWhile(_1727272, _1727278, hAPP(hAPP(c_List_Oappend(_1727272), _1727276), _1727280)) = c_List_OtakeWhile(_1727272, _1727278, _1727276))], (24224 ^ _776545) ^ [_1214668, _1214670, _1214672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214668), _1214670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214668), _1214672)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214670), _1214672))))], (45267 ^ _776545) ^ [_1683104, _1683106] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1683104, _1683106) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1683104), hAPP(c_Code__Numeral_Onat__of, _1683106))))], (51105 ^ _776545) ^ [_1811500, _1811502, _1811504, _1811506, _1811508] : [class_Divides_Osemiring__div(_1811500), -(_1811502 = c_Groups_Ozero__class_Ozero(_1811500)), -(_1811504 = c_Groups_Ozero__class_Ozero(_1811500)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811500), _1811502), _1811506)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811500), _1811504), _1811508)), 51124 ^ _776545 : [(51131 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811500), _1811506), _1811504) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811500), _1811502), _1811508), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811500), _1811506), _1811502) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811500), _1811508), _1811504))], (51125 ^ _776545) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811500), _1811506), _1811502) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1811500), _1811508), _1811504), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811500), _1811506), _1811504) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1811500), _1811502), _1811508))]]], (14230 ^ _776545) ^ [_1032528, _1032530, _1032532] : [class_Rings_Ocomm__semiring__1(_1032528), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032528), _1032530), _1032532) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032528), _1032532), _1032530))], (41250 ^ _776545) ^ [_1585976, _1585978, _1585980, _1585982, _1585984] : [c_Relation_Osingle__valued(_1585976, _1585978, _1585980), c_Relation_Osingle__valued(_1585978, _1585982, _1585984), -(c_Relation_Osingle__valued(_1585976, _1585982, hAPP(hAPP(c_Relation_Orel__comp(_1585976, _1585978, _1585982), _1585980), _1585984)))], (10517 ^ _776545) ^ [_957255, _957257, _957259] : [class_Groups_Oab__group__add(_957255), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957255), _957257), _957259)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_957255), _957259), _957257))], (23623 ^ _776545) ^ [_1204665, _1204667] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204665)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204667))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1204665), _1204667)))], (2280 ^ _776545) ^ [_809754, _809756, _809758, _809760] : [-(c_Orderings_Oord_Omin(_809760, _809756) = c_Orderings_Oord_Omin(_809758, _809754)), _809760 = _809758, _809756 = _809754], (8026 ^ _776545) ^ [_912765, _912767, _912769, _912771] : [hBOOL(hAPP(hAPP(c_member(_912765), _912767), _912769)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912765, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912765), _912767), _912771)), _912769) = hAPP(hAPP(c_Set_Oinsert(_912765), _912767), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912765, tc_HOL_Obool)), _912771), _912769)))], (25927 ^ _776545) ^ [_1245431, _1245433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245433)), 25934 ^ _776545 : [(25941 ^ _776545) ^ [] : [_1245431 = _1245433, -(hAPP(c_Int_Onat, _1245431) = hAPP(c_Int_Onat, _1245433))], (25935 ^ _776545) ^ [] : [hAPP(c_Int_Onat, _1245431) = hAPP(c_Int_Onat, _1245433), -(_1245431 = _1245433)]]], (43878 ^ _776545) ^ [_1653241, _1653243, _1653245] : [hBOOL(hAPP(c_List_Odistinct(_1653241), _1653243)), -(hBOOL(hAPP(c_List_Odistinct(_1653241), hAPP(hAPP(c_List_Odrop(_1653241), _1653245), _1653243))))], (2252 ^ _776545) ^ [_809350, _809352] : [_809352 = _809350, -(c_Nat_Onat_Onat__size(_809352) = c_Nat_Onat_Onat__size(_809350))], (28909 ^ _776545) ^ [_1294818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294818), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1294818)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52343 ^ _776545) ^ [_1829767, _1829769] : [-(class_HOL_Oequal(tc_prod(_1829767, _1829769)))], (30238 ^ _776545) ^ [_1318935, _1318937, _1318939] : [class_Orderings_Olinorder(_1318935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318935), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318935), _1318937), _1318939)), _1318937)))], (28137 ^ _776545) ^ [_1281830] : [-(c_Int_Opred(_1281830) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1281830), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28499 ^ _776545) ^ [_1287995] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1287995)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287995))))], (5566 ^ _776545) ^ [_861553, _861555] : [_861555 = _861553, -(tc_Option_Ooption(_861555) = tc_Option_Ooption(_861553))], (35144 ^ _776545) ^ [_1432473, _1432475, _1432477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432473, tc_fun(_1432473, tc_HOL_Obool))), _1432475), _1432477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432473, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1432473, _1432477)), c_Wellfounded_Oaccp(_1432473, _1432475))))], (10493 ^ _776545) ^ [_956809, _956811, _956813] : [hBOOL(hAPP(hAPP(c_member(_956809), _956811), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_956809, tc_HOL_Obool)), _956813))), hBOOL(hAPP(hAPP(c_member(_956809), _956811), _956813))], (4910 ^ _776545) ^ [_851371, _851373] : [_851373 = _851371, -(c_Relation_OId(_851373) = c_Relation_OId(_851371))], (45624 ^ _776545) ^ [_1691598, _1691600, _1691602, _1691604, _1691606, _1691608, _1691610, _1691612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691598), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691600)), _1691602))), c_List_Olist__all2(_1691600, _1691604, _1691606, _1691602, _1691608), hBOOL(hAPP(hAPP(_1691606, _1691610), _1691612)), -(c_List_Olist__all2(_1691600, _1691604, _1691606, hAPP(hAPP(c_List_Olist__update(_1691600, _1691602), _1691598), _1691610), hAPP(hAPP(c_List_Olist__update(_1691604, _1691608), _1691598), _1691612)))], (28155 ^ _776545) ^ [_1282098, _1282100, _1282102] : [class_Rings_Osemiring__1(_1282098), hBOOL(hAPP(hAPP(c_member(_1282098), _1282100), c_Nat_Osemiring__1__class_ONats(_1282098))), hBOOL(hAPP(hAPP(c_member(_1282098), _1282102), c_Nat_Osemiring__1__class_ONats(_1282098))), -(hBOOL(hAPP(hAPP(c_member(_1282098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1282098), _1282100), _1282102)), c_Nat_Osemiring__1__class_ONats(_1282098))))], (31679 ^ _776545) ^ [_1345411, _1345413, _1345415] : [class_Groups_Olinordered__ab__group__add(_1345411), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1345411), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345411), _1345413), _1345415)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345411), hAPP(c_Groups_Ouminus__class_Ouminus(_1345411), _1345413)), hAPP(c_Groups_Ouminus__class_Ouminus(_1345411), _1345415)))], (33439 ^ _776545) ^ [_1391191, _1391193, _1391195, _1391197, _1391199, _1391201] : [-(_1391191 = _1391193), -(hAPP(c_Fun_Ofun__upd(_1391195, _1391197, _1391199, _1391193, _1391201), _1391191) = hAPP(_1391199, _1391191))], (44988 ^ _776545) ^ [_1677449, _1677451, _1677453, _1677455, _1677457] : [class_Groups_Ocomm__monoid__add(_1677449), hBOOL(hAPP(hAPP(c_member(_1677451), _1677453), hAPP(c_List_Oset(_1677451), _1677455))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677449), hAPP(hAPP(c_List_Omap(_1677451, _1677449), _1677457), _1677455)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1677449), hAPP(_1677457, _1677453)), hAPP(c_List_Omonoid__add__class_Olistsum(_1677449), hAPP(hAPP(c_List_Omap(_1677451, _1677449), _1677457), c_List_Oremove1(_1677451, _1677453, _1677455)))))], (14678 ^ _776545) ^ [_1041190, _1041192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041190), _1041192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041190), _1041192)))], (15276 ^ _776545) ^ [_1052231, _1052233, _1052235] : [class_Groups_Ocomm__monoid__mult(_1052231), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052233, _1052231), _1052235), c_Orderings_Obot__class_Obot(tc_fun(_1052233, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1052231))], (11732 ^ _776545) ^ [_981928, _981930, _981932, _981934, _981936] : [c_Finite__Set_Ofolding__one(_981928, _981930, _981932), hBOOL(hAPP(c_Finite__Set_Ofinite(_981928), _981934)), -(hBOOL(hAPP(hAPP(c_member(_981928), _981936), _981934))), -(_981934 = c_Orderings_Obot__class_Obot(tc_fun(_981928, tc_HOL_Obool))), -(hAPP(_981932, hAPP(hAPP(c_Set_Oinsert(_981928), _981936), _981934)) = hAPP(hAPP(_981930, _981936), hAPP(_981932, _981934)))], (38251 ^ _776545) ^ [_1508997, _1508999] : [hBOOL(hAPP(hAPP(c_member(_1508997), 38252 ^ [_1508997, _1508999]), c_Wellfounded_Oacc(_1508997, _1508999))), -(c_Wellfounded_Owf(_1508997, _1508999))], (38667 ^ _776545) ^ [_1519514, _1519516] : [-(hAPP(c_Set_Ovimage(_1519514, _1519514, c_COMBI(_1519514)), _1519516) = _1519516)], (2230 ^ _776545) ^ [_808961, _808963, _808965, _808967, _808969, _808971, _808973, _808975, _808977, _808979] : [-(c_Nitpick_Opair__box_Opair__box__size(_808979, _808975, _808971, _808967, _808963) = c_Nitpick_Opair__box_Opair__box__size(_808977, _808973, _808969, _808965, _808961)), _808979 = _808977, _808975 = _808973, _808971 = _808969, _808967 = _808965, _808963 = _808961], (24734 ^ _776545) ^ [_1224038, _1224040] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224038) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224040), -(_1224038 = _1224040)], (45509 ^ _776545) ^ [_1689061, _1689063, _1689065] : [c_List_Olist__all2(_1689065, _1689065, c_fequal, _1689061, _1689063), -(_1689061 = _1689063)], (47182 ^ _776545) ^ [_1724993, _1724995] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1724993), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1724993))), _1724995))), 47185 ^ _776545 : [(47192 ^ _776545) ^ [] : [-(_1724995 = c_List_Olist_ONil(tc_List_Olist(_1724993))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724993))), c_List_Otranspose(_1724993, _1724995)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724993)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1724993)), _1724995), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47186 ^ _776545) ^ [] : [_1724995 = c_List_Olist_ONil(tc_List_Olist(_1724993)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1724993))), c_List_Otranspose(_1724993, _1724995)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42339 ^ _776545) ^ [_1616790, _1616792, _1616794, _1616796] : [hBOOL(hAPP(hAPP(c_member(_1616790), _1616792), hAPP(c_List_Oset(_1616790), c_List_Osublist(_1616790, _1616794, _1616796)))), -(hBOOL(hAPP(hAPP(c_member(_1616790), _1616792), hAPP(c_List_Oset(_1616790), _1616794))))], (46472 ^ _776545) ^ [_1711356, _1711358] : [class_Orderings_Olinorder(_1711356), -(c_List_Olinorder__class_Osorted(_1711356, hAPP(hAPP(c_List_Olist_OCons(_1711356), _1711358), c_List_Olist_ONil(_1711356))))], (25858 ^ _776545) ^ [_1244257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244257), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1244257 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 25861 ^ [_1244257]))))], (32598 ^ _776545) ^ [_1367592, _1367594, _1367596, _1367598, _1367600] : [_1367592 = c_Orderings_Obot__class_Obot(tc_fun(_1367594, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367596, tc_HOL_Obool)), _1367598), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367594, tc_fun(_1367596, tc_HOL_Obool)), _1367592), _1367600)) = _1367598)], (11316 ^ _776545) ^ [_973236, _973238, _973240, _973242] : [hAPP(c_Set_Oimage(_973236, _973238, _973240), c_Orderings_Otop__class_Otop(tc_fun(_973236, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_973238, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973238, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973238, tc_HOL_Obool)), hAPP(c_Set_Oimage(_973236, _973238, _973240), _973242))), hAPP(c_Set_Oimage(_973236, _973238, _973240), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973236, tc_HOL_Obool)), _973242)))))], (52553 ^ _776545) ^ [_1832125, _1832127] : [hBOOL(_1832125), -(hBOOL(hAPP(hAPP(c_fimplies, _1832127), _1832125)))], (52405 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (8129 ^ _776545) ^ [_915059, _915061, _915063] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_915059, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_915059, tc_HOL_Obool)), _915061), _915063)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915059, tc_HOL_Obool)), _915061), c_Complete__Lattice_OSup__class_OSup(tc_fun(_915059, tc_HOL_Obool), _915063)))], (34602 ^ _776545) ^ [_1421064, _1421066, _1421068, _1421070] : [-(c_Nat_Onat_Onat__case(_1421064, _1421066, _1421068, hAPP(c_Nat_OSuc, _1421070)) = hAPP(_1421068, _1421070))], (38683 ^ _776545) ^ [_1519906, _1519908, _1519910, _1519912, _1519914] : [hBOOL(hAPP(hAPP(c_member(_1519906), _1519908), hAPP(c_Set_Ovimage(_1519906, _1519910, _1519912), _1519914))), -(hBOOL(hAPP(hAPP(c_member(_1519910), hAPP(_1519912, _1519908)), _1519914)))], (28383 ^ _776545) ^ [_1286057, _1286059] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1286057), _1286059)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1286057)), c_Int_OBit1(_1286059))))], (32666 ^ _776545) ^ [_1369674, _1369676, _1369678] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369674, tc_HOL_Obool)), _1369676), _1369678) = hAPP(c_Set_OCollect(_1369674), hAPP(hAPP(c_COMBS(_1369674, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369674), c_fconj), hAPP(hAPP(c_COMBC(_1369674, tc_fun(_1369674, tc_HOL_Obool), tc_HOL_Obool), c_member(_1369674)), _1369676))), hAPP(hAPP(c_COMBC(_1369674, tc_fun(_1369674, tc_HOL_Obool), tc_HOL_Obool), c_member(_1369674)), _1369678))))], (18874 ^ _776545) ^ [_1116572, _1116574] : [_1116572 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116572), _1116574) = _1116574)], (40026 ^ _776545) ^ [_1555861, _1555863, _1555865, _1555867, _1555869, _1555871, _1555873] : [class_Groups_Oab__semigroup__mult(_1555861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555863), _1555865)), c_Fun_Oinj__on(_1555863, _1555867, _1555869, _1555865), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1555861, _1555867, c_Groups_Otimes__class_Otimes(_1555861)), _1555871), _1555873), hAPP(c_Set_Oimage(_1555863, _1555867, _1555869), _1555865)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1555861, _1555863, c_Groups_Otimes__class_Otimes(_1555861)), hAPP(c_Fun_Ocomp(_1555867, _1555861, _1555863, _1555871), _1555869)), _1555873), _1555865))], (41524 ^ _776545) ^ [_1592736, _1592738, _1592740, _1592742, _1592744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592736, _1592736)), hAPP(hAPP(c_Product__Type_OPair(_1592736, _1592736), _1592738), _1592740)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592736, _1592736), tc_HOL_Obool), _1592742), _1592744))), 41529 ^ _776545 : [(41532 ^ _776545) ^ [] : [-(_1592738 = _1592740)], (41530 ^ _776545) ^ [] : [-(_1592742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41535 ^ _776545 : [(41540 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592736, _1592736)), hAPP(hAPP(c_Product__Type_OPair(_1592736, _1592736), 41533 ^ [_1592736, _1592738, _1592740, _1592742, _1592744]), _1592740)), _1592744)))], (41538 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592736, _1592736)), hAPP(hAPP(c_Product__Type_OPair(_1592736, _1592736), _1592738), 41533 ^ [_1592736, _1592738, _1592740, _1592742, _1592744])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592736, _1592736), tc_HOL_Obool), 41534 ^ [_1592736, _1592738, _1592740, _1592742, _1592744]), _1592744))))], (41536 ^ _776545) ^ [] : [-(_1592742 = hAPP(c_Nat_OSuc, 41534 ^ [_1592736, _1592738, _1592740, _1592742, _1592744]))]]], (4104 ^ _776545) ^ [_838662, _838664, _838666, _838668, _838670, _838672, _838674, _838676] : [-(c_New__DSequence_Opos__bind(_838676, _838672, _838668, _838664) = c_New__DSequence_Opos__bind(_838674, _838670, _838666, _838662)), _838676 = _838674, _838672 = _838670, _838668 = _838666, _838664 = _838662], (7900 ^ _776545) ^ [_909753, _909755, _909757] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909753, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909753, tc_HOL_Obool)), _909755), _909757)), _909755)))], (14762 ^ _776545) ^ [_1042639, _1042641, _1042643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042639), _1042641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042641), _1042643))))], (37064 ^ _776545) ^ [_1480840, _1480842, _1480844, _1480846, _1480848, _1480850, _1480852, _1480854, _1480856, _1480858] : [c_Equiv__Relations_Ocongruent2(_1480840, _1480842, _1480844, _1480846, _1480848, _1480850), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480840, _1480840)), hAPP(hAPP(c_Product__Type_OPair(_1480840, _1480840), _1480852), _1480854)), _1480846)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480842, _1480842)), hAPP(hAPP(c_Product__Type_OPair(_1480842, _1480842), _1480856), _1480858)), _1480848)), -(hAPP(hAPP(_1480850, _1480852), _1480856) = hAPP(hAPP(_1480850, _1480854), _1480858))], (7652 ^ _776545) ^ [_903715, _903717, _903719] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903715, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903715, tc_HOL_Obool)), _903717), _903719)), _903719) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903715, tc_HOL_Obool)), _903717), _903719))], (41737 ^ _776545) ^ [_1598494, _1598496, _1598498] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598494)), _1598496) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598494)), _1598498)), _1598496 = _1598498], (33459 ^ _776545) ^ [_1391813, _1391815, _1391817, _1391819] : [class_Rings_Oring__1(_1391813), -(hAPP(c_Int_Oring__1__class_Oof__int(_1391813), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391815, tc_Int_Oint), _1391817), _1391819)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1391815, _1391813), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1391813, _1391815), c_Int_Oring__1__class_Oof__int(_1391813)), _1391817)), _1391819))], (33475 ^ _776545) ^ [_1392165, _1392167, _1392169, _1392171, _1392173] : [class_Fields_Ofield__inverse__zero(_1392165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392167), _1392169)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392167, _1392165), hAPP(hAPP(c_COMBS(_1392167, _1392165, _1392165), hAPP(hAPP(c_COMBB(_1392165, tc_fun(_1392165, _1392165), _1392167), c_Rings_Oinverse__class_Odivide(_1392165)), _1392171)), _1392173)), _1392169) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392165), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392167, _1392165), _1392171), _1392169)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392167, _1392165), _1392173), _1392169)))], (33903 ^ _776545) ^ [_1404897, _1404899, _1404901] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404897), _1404899), _1404901) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1404897), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1404897, tc_Int_Oint), _1404899), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1404901))), class_Groups_Ocomm__monoid__add(_1404897), class_Groups_Ocomm__monoid__mult(_1404897)], (22359 ^ _776545) ^ [_1181897, _1181899, _1181901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181897), _1181899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181901), _1181897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181901), _1181899))))], (46421 ^ _776545) ^ [_1710084, _1710086, _1710088, _1710090] : [class_Groups_Ocomm__monoid__add(_1710084), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1710084), _1710086), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1710088, _1710090))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1710084), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1710084), _1710086), c_List_Oupt(_1710088, _1710090))))], (40196 ^ _776545) ^ [_1559758, _1559760, _1559762, _1559764, _1559766, _1559768] : [c_Finite__Set_Ofolding(_1559758, _1559760, _1559762, _1559764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559758), _1559766)), -(hBOOL(hAPP(hAPP(c_member(_1559758), _1559768), _1559766))), -(hAPP(_1559764, hAPP(hAPP(c_Set_Oinsert(_1559758), _1559768), _1559766)) = hAPP(c_Fun_Ocomp(_1559760, _1559760, _1559760, hAPP(_1559764, _1559766)), hAPP(_1559762, _1559768)))], (44623 ^ _776545) ^ [_1668746, _1668748, _1668750] : [-(c_List_Olast(_1668746, hAPP(hAPP(c_List_Oappend(_1668746), _1668748), hAPP(hAPP(c_List_Olist_OCons(_1668746), _1668750), c_List_Olist_ONil(_1668746)))) = _1668750)], (42447 ^ _776545) ^ [_1619289, _1619291, _1619293] : [-(hBOOL(hAPP(hAPP(c_member(_1619289), _1619291), hAPP(c_List_Oset(_1619289), _1619293)))), 42448 ^ _776545 : [(42449 ^ _776545) ^ [_1619363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619363), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619289)), _1619293))), hAPP(hAPP(c_List_Onth(_1619289), _1619293), _1619363) = _1619291]]], (2966 ^ _776545) ^ [_820569, _820571] : [_820571 = _820569, -(c_Nitpick_Ofrac(_820571) = c_Nitpick_Ofrac(_820569))], (37832 ^ _776545) ^ [_1497644, _1497646, _1497648] : [-(c_Fun_Oinj__on(tc_prod(_1497644, _1497646), tc_prod(_1497646, _1497644), hAPP(c_Product__Type_Oprod_Oprod__case(_1497644, _1497646, tc_prod(_1497646, _1497644)), hAPP(c_COMBC(_1497646, _1497644, tc_prod(_1497646, _1497644)), c_Product__Type_OPair(_1497646, _1497644))), _1497648))], (4554 ^ _776545) ^ [_845701, _845703, _845705, _845707, _845709, _845711] : [-(c_FunDef_OTHE__default(_845711, _845707, _845703) = c_FunDef_OTHE__default(_845709, _845705, _845701)), _845711 = _845709, _845707 = _845705, _845703 = _845701], (40258 ^ _776545) ^ [_1561311, _1561313, _1561315, _1561317, _1561319, _1561321] : [c_Finite__Set_Ofolding__idem(_1561311, _1561313, _1561315, _1561317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561311), _1561319)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561311), _1561321)), -(hAPP(_1561317, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561311, tc_HOL_Obool)), _1561319), _1561321)) = hAPP(c_Fun_Ocomp(_1561313, _1561313, _1561313, hAPP(_1561317, _1561319)), hAPP(_1561317, _1561321)))], (32504 ^ _776545) ^ [_1363379, _1363381, _1363383, _1363385, _1363387] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363379, tc_fun(_1363381, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363379, tc_HOL_Obool)), _1363383), _1363385)), _1363387) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363381, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363379, tc_fun(_1363381, tc_HOL_Obool)), _1363383), _1363387)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363379, tc_fun(_1363381, tc_HOL_Obool)), _1363385), _1363387)))], (14927 ^ _776545) ^ [_1045850, _1045852] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045850), _1045852))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045852), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045850), _1045852)) = _1045850)], (35056 ^ _776545) ^ [_1430718, _1430720, _1430722, _1430724, _1430726, _1430728, _1430730] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430718, _1430720), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430722), _1430724))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430726, _1430720), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430728), _1430730))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1430720)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430718), _1430726), _1430720), 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), _1430722), _1430728)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430724), _1430730)), _1430720))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430724), _1430730), _1430720)))))], (6051 ^ _776545) ^ [_873244, _873246, _873248, _873250, _873252] : [-(hBOOL(hAPP(hAPP(c_member(_873244), _873246), c_SetInterval_Oord_OatLeastAtMost(_873244, _873248, _873250, _873252)))), hBOOL(hAPP(hAPP(_873248, _873250), _873246)), hBOOL(hAPP(hAPP(_873248, _873246), _873252))], (45269 ^ _776545) ^ [_1683142] : [-(_1683142 = 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, _1683142)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1683142))))], (41670 ^ _776545) ^ [_1597008, _1597010, _1597012, _1597014, _1597016, _1597018] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1597008, _1597010, _1597012), _1597014), hAPP(hAPP(c_Product__Type_OPair(_1597008, _1597010), _1597016), _1597018)) = hAPP(hAPP(_1597014, _1597016), _1597018))], (47500 ^ _776545) ^ [_1731785, _1731787, _1731789, _1731791] : [47502 ^ _776545 : [(47507 ^ _776545) ^ [] : [hBOOL(hAPP(_1731791, hAPP(hAPP(c_List_Onth(_1731787), _1731789), 47501 ^ [_1731785, _1731787, _1731789, _1731791])))], (47505 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47501 ^ [_1731785, _1731787, _1731789, _1731791]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731787)), _1731789))))], (47503 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47501 ^ [_1731785, _1731787, _1731789, _1731791]), _1731785)))]], 47510 ^ _776545 : [(47513 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1731791, hAPP(hAPP(c_List_Onth(_1731787), _1731789), _1731785))))], (47511 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731785), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731787)), _1731789))))]], -(c_List_OtakeWhile(_1731787, _1731791, _1731789) = hAPP(hAPP(c_List_Otake(_1731787), _1731785), _1731789))], (47008 ^ _776545) ^ [_1721375, _1721377] : [hAPP(c_List_Orev(_1721375), _1721377) = c_List_Olist_ONil(_1721375), -(_1721377 = c_List_Olist_ONil(_1721375))], (26200 ^ _776545) ^ [_1249835, _1249837] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249835) = _1249837, 26203 ^ _776545 : [(26206 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249837)))], (26204 ^ _776545) ^ [] : [-(_1249835 = hAPP(c_Int_Onat, _1249837))]]], (26124 ^ _776545) ^ [_1248624, _1248626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248624)), 26127 ^ _776545 : [(26134 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248626), _1248624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248626)), hAPP(c_Int_Onat, _1248624))))], (26128 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248626)), hAPP(c_Int_Onat, _1248624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248626), _1248624)))]]], (9306 ^ _776545) ^ [_936621, _936623] : [class_Orderings_Opreorder(_936621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936621), _936623), _936623))], (45614 ^ _776545) ^ [_1691381, _1691383, _1691385, _1691387, _1691389, _1691391] : [c_List_Olist__all2(_1691381, _1691383, _1691385, _1691387, _1691389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691383)), _1691389))), -(hBOOL(hAPP(hAPP(_1691385, hAPP(hAPP(c_List_Onth(_1691381), _1691387), _1691391)), hAPP(hAPP(c_List_Onth(_1691383), _1691389), _1691391))))], (27367 ^ _776545) ^ [_1268878] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1268878), c_Int_OPls) = _1268878)], (38425 ^ _776545) ^ [_1513162] : [-(c_Nitpick_Ozero__frac(_1513162) = c_Nitpick_OAbs__Frac(_1513162, 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))))], (40859 ^ _776545) ^ [_1576450, _1576452, _1576454, _1576456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576450, _1576450)), hAPP(hAPP(c_Product__Type_OPair(_1576450, _1576450), _1576452), _1576454)), c_Transitive__Closure_Ortrancl(_1576450, _1576456))), -(_1576452 = _1576454), 40866 ^ _776545 : [(40869 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576450, _1576450)), hAPP(hAPP(c_Product__Type_OPair(_1576450, _1576450), _1576452), _1576454)), c_Transitive__Closure_Otrancl(_1576450, _1576456))))], (40867 ^ _776545) ^ [] : [_1576452 = _1576454]]], (25147 ^ _776545) ^ [_1231800, _1231802, _1231804] : [class_Divides_Osemiring__div(_1231800), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231800), _1231802), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231800), _1231804), _1231802))), c_Divides_Odiv__class_Omod(_1231800, _1231804, _1231802)) = _1231804)], (38874 ^ _776545) ^ [_1524426, _1524428] : [-(hAPP(c_Relation_ODomain(_1524426, _1524428), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524426, _1524428), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1524426, tc_HOL_Obool)))], (19737 ^ _776545) ^ [_1132804, _1132806, _1132808] : [class_Rings_Odivision__ring(_1132804), -(_1132806 = c_Groups_Ozero__class_Ozero(_1132804)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132804), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132804), _1132808), _1132806)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132804), _1132808), hAPP(c_Groups_Ouminus__class_Ouminus(_1132804), _1132806)))], (6965 ^ _776545) ^ [_889592, _889594, _889596] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_889592, tc_HOL_Obool)), _889594), hAPP(c_Set_OPow(_889592), _889596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889592, tc_HOL_Obool)), _889594), _889596)))], (17345 ^ _776545) ^ [_1088859, _1088861, _1088863, _1088865] : [class_Rings_Olinordered__semiring__strict(_1088859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088859), _1088861), _1088863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088859), c_Groups_Ozero__class_Ozero(_1088859)), _1088865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088859), _1088861), _1088865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088859), _1088863), _1088865))))], (45166 ^ _776545) ^ [_1681181, _1681183] : [-(c_Random_Oselect(_1681181, _1681183) = 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(_1681181, 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(_1681181)), _1681183)))), hAPP(hAPP(c_COMBB(_1681181, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1681181, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1681181, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1681181, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1681181), _1681183)), c_Code__Numeral_Onat__of))))], (46213 ^ _776545) ^ [_1705589, _1705591, _1705593, _1705595] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1705589, tc_Nat_Onat), _1705589), c_Product__Type_Ofst(_1705589, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1705589, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1705589, tc_Nat_Onat)), _1705591), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1705589, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1705589, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1705589, tc_Nat_Onat), _1705593), _1705595))) = hAPP(hAPP(c_List_Omap(tc_prod(_1705589, tc_Nat_Onat), _1705589), c_Product__Type_Ofst(_1705589, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1705589, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1705589, tc_Nat_Onat)), _1705591), c_Product__Type_Osnd(_1705589, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1705589, tc_Nat_Onat), _1705593), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1705595)))))], (26256 ^ _776545) ^ [_1250801] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1250801))), -(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), _1250801)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20349 ^ _776545) ^ [_1143630, _1143632, _1143634, _1143636, _1143638] : [class_Fields_Ofield(_1143630), -(_1143632 = c_Groups_Ozero__class_Ozero(_1143630)), -(_1143634 = c_Groups_Ozero__class_Ozero(_1143630)), 20360 ^ _776545 : [(20367 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143630), _1143636), _1143634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143630), _1143638), _1143632), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143630), _1143636), _1143632) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143630), _1143638), _1143634))], (20361 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143630), _1143636), _1143632) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143630), _1143638), _1143634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143630), _1143636), _1143634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143630), _1143638), _1143632))]]], (10523 ^ _776545) ^ [_957392, _957394, _957396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957392, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957392, tc_HOL_Obool)), _957394)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957392, tc_HOL_Obool)), _957396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957392, tc_HOL_Obool)), _957396), _957394)))], (2500 ^ _776545) ^ [_813252, _813254, _813256, _813258, _813260, _813262, _813264, _813266, _813268, _813270] : [-(c_Product__Type_Oprod_Oprod__size(_813270, _813266, _813262, _813258, _813254) = c_Product__Type_Oprod_Oprod__size(_813268, _813264, _813260, _813256, _813252)), _813270 = _813268, _813266 = _813264, _813262 = _813260, _813258 = _813256, _813254 = _813252], (45022 ^ _776545) ^ [_1678277, _1678279] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678277)), hAPP(c_Code__Numeral_Oof__nat, _1678279)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1678277), _1678279)))], (8411 ^ _776545) ^ [_920984, _920986, _920988] : [class_Lattices_Osemilattice__inf(_920984), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920984), _920986), _920988) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920984), _920988), _920986))], (40639 ^ _776545) ^ [_1570199, _1570201, _1570203, _1570205, _1570207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570199, _1570199)), hAPP(hAPP(c_Product__Type_OPair(_1570199, _1570199), _1570201), _1570203)), _1570205)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570199, _1570199)), hAPP(hAPP(c_Product__Type_OPair(_1570199, _1570199), _1570203), _1570207)), c_Transitive__Closure_Otrancl(_1570199, _1570205))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570199, _1570199)), hAPP(hAPP(c_Product__Type_OPair(_1570199, _1570199), _1570201), _1570207)), c_Transitive__Closure_Otrancl(_1570199, _1570205))))], (52357 ^ _776545) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (24902 ^ _776545) ^ [_1227389, _1227391, _1227393, _1227395] : [class_Divides_Oring__div(_1227389), -(c_Divides_Odiv__class_Omod(_1227389, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227389), _1227391), _1227393), _1227395) = c_Divides_Odiv__class_Omod(_1227389, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227389), c_Divides_Odiv__class_Omod(_1227389, _1227391, _1227395)), _1227393), _1227395))], (14532 ^ _776545) ^ [_1038603, _1038605, _1038607] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038603), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038605), _1038607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038603), _1038607)))], (45752 ^ _776545) ^ [_1694611, _1694613] : [c_List_Oremdups(_1694611, _1694613) = _1694613, -(hBOOL(hAPP(c_List_Odistinct(_1694611), _1694613)))], (52119 ^ _776545) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (32540 ^ _776545) ^ [_1364848, _1364850, _1364852, _1364854] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1364848, tc_fun(_1364850, tc_HOL_Obool)), _1364852), _1364854) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1364850, tc_HOL_Obool), hAPP(c_Set_Oimage(_1364848, tc_fun(_1364850, tc_HOL_Obool), _1364854), _1364852)))], (14897 ^ _776545) ^ [_1045229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045229), _1045229))))], (43870 ^ _776545) ^ [_1653054, _1653056, _1653058, _1653060] : [-(hAPP(hAPP(c_List_Odrop(_1653054), hAPP(c_Nat_OSuc, _1653056)), hAPP(hAPP(c_List_Olist_OCons(_1653054), _1653058), _1653060)) = hAPP(hAPP(c_List_Odrop(_1653054), _1653056), _1653060))], (51433 ^ _776545) ^ [_1817529, _1817531, _1817533] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817531), _1817533))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817529), _1817533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1817533), _1817531)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817529), _1817531)))], (10098 ^ _776545) ^ [_949381, _949383, _949385, _949387] : [class_Orderings_Oorder(_949381), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949381, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949381, _949383, _949385)), c_SetInterval_Oord__class_OatLeastAtMost(_949381, _949385, _949387)) = c_Orderings_Obot__class_Obot(tc_fun(_949381, tc_HOL_Obool)))], (8056 ^ _776545) ^ [_913433, _913435, _913437, _913439] : [-(hBOOL(hAPP(hAPP(c_member(_913433), _913435), _913437))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913433, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913433), _913435), _913439)), _913437) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913433, tc_HOL_Obool)), _913439), _913437))], (46303 ^ _776545) ^ [_1707887, _1707889] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707887), _1707889))), -(c_List_Oupt(_1707887, _1707889) = c_List_Olist_ONil(tc_Nat_Onat))], (18726 ^ _776545) ^ [_1113743, _1113745, _1113747] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113743), _1113745)), -(hBOOL(hAPP(hAPP(c_member(_1113743), _1113747), _1113745))), -(hAPP(c_Finite__Set_Ocard(_1113743), hAPP(hAPP(c_Set_Oinsert(_1113743), _1113747), _1113745)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1113743), _1113745)))], (50165 ^ _776545) ^ [_1790291, _1790293, _1790295] : [hAPP(c_Fun_Ocomp(_1790291, _1790293, _1790293, _1790295), c_Hilbert__Choice_Oinv__into(_1790291, _1790293, c_Orderings_Otop__class_Otop(tc_fun(_1790291, tc_HOL_Obool)), _1790295)) = c_Fun_Oid(_1790293), -(hAPP(c_Set_Oimage(_1790291, _1790293, _1790295), c_Orderings_Otop__class_Otop(tc_fun(_1790291, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790293, tc_HOL_Obool)))], (50105 ^ _776545) ^ [_1788847, _1788849, _1788851] : [c_Fun_Oinj__on(_1788847, _1788849, _1788851, c_Orderings_Otop__class_Otop(tc_fun(_1788847, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1788849, _1788847, c_Hilbert__Choice_Oinv__into(_1788847, _1788849, c_Orderings_Otop__class_Otop(tc_fun(_1788847, tc_HOL_Obool)), _1788851)), c_Orderings_Otop__class_Otop(tc_fun(_1788849, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1788847, tc_HOL_Obool)))], (10158 ^ _776545) ^ [_950689, _950691, _950693, _950695, _950697, _950699, _950701] : [-(c_Nitpick_Ofold__graph_H(_950689, _950691, _950693, _950695, _950697, hAPP(hAPP(_950693, _950699), _950701))), 10159 ^ _776545 : [(10166 ^ _776545) ^ [_950918, _950920] : [hAPP(hAPP(_950693, _950699), _950701) = hAPP(hAPP(_950693, _950920), _950918), hBOOL(hAPP(hAPP(c_member(_950689), _950920), _950697)), c_Nitpick_Ofold__graph_H(_950689, _950691, _950693, _950695, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950689, tc_HOL_Obool)), _950697), hAPP(hAPP(c_Set_Oinsert(_950689), _950920), c_Orderings_Obot__class_Obot(tc_fun(_950689, tc_HOL_Obool)))), _950918)], (10160 ^ _776545) ^ [] : [_950697 = c_Orderings_Obot__class_Obot(tc_fun(_950689, tc_HOL_Obool)), hAPP(hAPP(_950693, _950699), _950701) = _950695]]], (26268 ^ _776545) ^ [_1250952] : [-(c_Int_Osucc(_1250952) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1250952), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29677 ^ _776545) ^ [_1308593, _1308595] : [class_Int_Onumber__ring(_1308593), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308593), hAPP(c_Int_Onumber__class_Onumber__of(_1308593), 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)))), _1308595))) = hAPP(c_Int_Onumber__class_Onumber__of(_1308593), c_Int_OMin))], (1694 ^ _776545) ^ [_800584, _800586] : [-(class_Groups_Osemigroup__add(_800584)), _800586 = _800584, class_Groups_Osemigroup__add(_800586)], (50055 ^ _776545) ^ [_1787806, _1787808, _1787810, _1787812, _1787814] : [hBOOL(hAPP(hAPP(c_member(_1787806), _1787808), hAPP(c_Set_Oimage(_1787810, _1787806, _1787812), _1787814))), -(hAPP(_1787812, hAPP(c_Hilbert__Choice_Oinv__into(_1787810, _1787806, _1787814, _1787812), _1787808)) = _1787808)], (32996 ^ _776545) ^ [_1378943, _1378945, _1378947] : [-(hBOOL(hAPP(_1378943, _1378945))), -(hAPP(c_Set_OCollect(_1378947), hAPP(hAPP(c_COMBS(_1378947, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378947), c_fconj), hAPP(hAPP(c_COMBC(_1378947, _1378947, tc_HOL_Obool), c_fequal), _1378945))), _1378943)) = c_Orderings_Obot__class_Obot(tc_fun(_1378947, tc_HOL_Obool)))], (15344 ^ _776545) ^ [_1053547, _1053549, _1053551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053547), _1053549)), 15347 ^ _776545 : [(15354 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1053547), _1053551), _1053549))), -(hAPP(c_Finite__Set_Ocard(_1053547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053547, tc_HOL_Obool)), _1053549), hAPP(hAPP(c_Set_Oinsert(_1053547), _1053551), c_Orderings_Obot__class_Obot(tc_fun(_1053547, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1053547), _1053549))], (15348 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1053547), _1053551), _1053549)), -(hAPP(c_Finite__Set_Ocard(_1053547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053547, tc_HOL_Obool)), _1053549), hAPP(hAPP(c_Set_Oinsert(_1053547), _1053551), c_Orderings_Obot__class_Obot(tc_fun(_1053547, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053547), _1053549)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (9284 ^ _776545) ^ [_936367, _936369, _936371] : [class_Orderings_Olinorder(_936367), 9287 ^ _776545 : [(9288 ^ _776545) ^ [] : [-(_936369 = _936371), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936367), _936369), _936371))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936367), _936371), _936369)))], (9298 ^ _776545) ^ [] : [9299 ^ _776545 : [(9302 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936367), _936371), _936369))], (9300 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936367), _936369), _936371))]], _936369 = _936371]]], (41779 ^ _776545) ^ [_1600153, _1600155, _1600157, _1600159, _1600161, _1600163] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600153), tc_List_Olist(_1600153))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600153), tc_List_Olist(_1600153)), hAPP(hAPP(c_List_Olist_OCons(_1600153), _1600155), _1600157)), hAPP(hAPP(c_List_Olist_OCons(_1600153), _1600159), _1600161))), c_List_Olex(_1600153, _1600163))), 41784 ^ _776545 : [(41787 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600153)), _1600157) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600153)), _1600161))], (41785 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600153, _1600153)), hAPP(hAPP(c_Product__Type_OPair(_1600153, _1600153), _1600155), _1600159)), _1600163)))]], 41788 ^ _776545 : [(41791 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600153), tc_List_Olist(_1600153))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600153), tc_List_Olist(_1600153)), _1600157), _1600161)), c_List_Olex(_1600153, _1600163))))], (41789 ^ _776545) ^ [] : [-(_1600155 = _1600159)]]], (36514 ^ _776545) ^ [_1467709, _1467711, _1467713, _1467715, _1467717] : [hBOOL(hAPP(hAPP(c_member(_1467709), _1467711), hAPP(c_Relation_OImage(_1467713, _1467709, _1467715), _1467717))), 36518 ^ _776545 : [(36521 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1467713, _1467709)), hAPP(hAPP(c_Product__Type_OPair(_1467713, _1467709), 36517 ^ [_1467709, _1467711, _1467713, _1467715, _1467717]), _1467711)), _1467715)))], (36519 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1467713), 36517 ^ [_1467709, _1467711, _1467713, _1467715, _1467717]), _1467717)))]]], (46046 ^ _776545) ^ [_1701340, _1701342, _1701344] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701340)), hAPP(c_List_Ofilter(_1701340, _1701342), _1701344))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701340)), _1701344))))], (45876 ^ _776545) ^ [_1696842, _1696844] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696842)), c_List_Oremdups(_1696842, c_List_Oconcat(_1696842, _1696844))) = hAPP(c_Finite__Set_Ocard(_1696842), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1696842), tc_fun(_1696842, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1696842)), _1696844)), c_List_Oset(_1696842))))], (42614 ^ _776545) ^ [_1624947, _1624949] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624947, _1624949)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1624947, _1624949))], (12325 ^ _776545) ^ [_992868, _992870, _992872] : [class_Lattices_Olattice(_992868), hBOOL(hAPP(c_Finite__Set_Ofinite(_992868), _992870)), 12332 ^ _776545 : [(12339 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992868, tc_HOL_Obool)), _992870), hAPP(hAPP(c_Set_Oinsert(_992868), _992872), c_Orderings_Obot__class_Obot(tc_fun(_992868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992868, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_992868, hAPP(hAPP(c_Set_Oinsert(_992868), _992872), _992870)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_992868), _992872), c_Big__Operators_Olattice__class_OInf__fin(_992868, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992868, tc_HOL_Obool)), _992870), hAPP(hAPP(c_Set_Oinsert(_992868), _992872), c_Orderings_Obot__class_Obot(tc_fun(_992868, tc_HOL_Obool)))))))], (12333 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992868, tc_HOL_Obool)), _992870), hAPP(hAPP(c_Set_Oinsert(_992868), _992872), c_Orderings_Obot__class_Obot(tc_fun(_992868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992868, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_992868, hAPP(hAPP(c_Set_Oinsert(_992868), _992872), _992870)) = _992872)]]], (21405 ^ _776545) ^ [_1164374, _1164376] : [class_Rings_Ocomm__semiring__1(_1164374), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1164374), _1164376), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1164374))], (52375 ^ _776545) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52547 ^ _776545) ^ [_1832085, _1832087] : [-(hBOOL(_1832085)), -(hBOOL(hAPP(hAPP(c_fimplies, _1832085), _1832087)))], (22301 ^ _776545) ^ [_1180843] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180843)) = _1180843)], (52419 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52129 ^ _776545) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11866 ^ _776545) ^ [_984866, _984868, _984870, _984872, _984874, _984876] : [-(hBOOL(hAPP(hAPP(c_member(_984866), _984868), _984870))), -(hAPP(c_Set_Oimage(_984866, _984872, c_Fun_Ofun__upd(_984866, _984872, _984874, _984868, _984876)), _984870) = hAPP(c_Set_Oimage(_984866, _984872, _984874), _984870))], (33060 ^ _776545) ^ [_1380519, _1380521, _1380523, _1380525, _1380527, _1380529] : [-(hAPP(c_Set_Oimage(_1380519, _1380521, _1380523), hAPP(c_Set_Oimage(_1380525, _1380519, _1380527), _1380529)) = hAPP(c_Set_Oimage(_1380525, _1380521, hAPP(hAPP(c_COMBB(_1380519, _1380521, _1380525), _1380523), _1380527)), _1380529))], (52181 ^ _776545) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (34809 ^ _776545) ^ [_1426032, _1426034, _1426036] : [hBOOL(hAPP(_1426032, 34810 ^ [_1426032, _1426034, _1426036])), 34813 ^ _776545 : [(34814 ^ _776545) ^ [_1426143, _1426145] : [-(hBOOL(hAPP(_1426032, hAPP(hAPP(c_Product__Type_OPair(_1426034, _1426036), _1426145), _1426143))))]]], (29655 ^ _776545) ^ [_1308156, _1308158, _1308160] : [class_Rings_Olinordered__idom(_1308156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308156), _1308158), c_Groups_Ozero__class_Ozero(_1308156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308156), hAPP(hAPP(c_Power_Opower__class_Opower(_1308156), _1308158), 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)))), _1308160)))), c_Groups_Ozero__class_Ozero(_1308156))))], (46427 ^ _776545) ^ [_1710227, _1710229, _1710231, _1710233, _1710235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710227), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1710229), _1710231))), -(hAPP(hAPP(c_List_Onth(_1710233), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1710233), _1710235), c_List_Oupt(_1710231, _1710229))), _1710227) = hAPP(_1710235, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710231), _1710227)))], (28375 ^ _776545) ^ [_1285916] : [c_Int_OBit1(_1285916) = c_Int_OPls], (40763 ^ _776545) ^ [_1574170, _1574172] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574170, _1574170), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574170, _1574172)), c_Relation_OId(_1574170)) = c_Transitive__Closure_Ortrancl(_1574170, _1574172))], (13025 ^ _776545) ^ [_1006398, _1006400, _1006402] : [class_Groups_Oab__semigroup__mult(_1006398), -(_1006400 = c_Orderings_Obot__class_Obot(tc_fun(_1006398, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006398), _1006400)), -(hBOOL(hAPP(hAPP(c_member(_1006398), _1006402), _1006400))), -(hAPP(c_Finite__Set_Ofold1(_1006398, c_Groups_Otimes__class_Otimes(_1006398)), hAPP(hAPP(c_Set_Oinsert(_1006398), _1006402), _1006400)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006398), _1006402), hAPP(c_Finite__Set_Ofold1(_1006398, c_Groups_Otimes__class_Otimes(_1006398)), _1006400)))], (44441 ^ _776545) ^ [_1665331, _1665333, _1665335] : [class_Orderings_Olinorder(_1665331), -(c_Big__Operators_Olinorder__class_OMax(_1665331, hAPP(c_List_Oset(_1665331), hAPP(hAPP(c_List_Olist_OCons(_1665331), _1665333), _1665335))) = hAPP(c_List_Ofoldl(_1665331, _1665331, c_Orderings_Oord__class_Omax(_1665331), _1665333), _1665335))], (24600 ^ _776545) ^ [_1221555, _1221557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1221555), _1221557)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221555), _1221557) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35560 ^ _776545) ^ [_1440071, _1440073, _1440075] : [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), _1440071), _1440073))), -(hBOOL(hAPP(hAPP(_1440075, _1440071), _1440073))), 35567 ^ _776545 : [(35570 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35566 ^ [_1440071, _1440073, _1440075]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1440075, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35565 ^ [_1440071, _1440073, _1440075])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 35566 ^ [_1440071, _1440073, _1440075]))))], (35576 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1440075, 35565 ^ [_1440071, _1440073, _1440075]), 35566 ^ [_1440071, _1440073, _1440075]))], (35568 ^ _776545) ^ [] : [-(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), 35565 ^ [_1440071, _1440073, _1440075]), 35566 ^ [_1440071, _1440073, _1440075]))))]]], (29621 ^ _776545) ^ [_1307463] : [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, _1307463, 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, _1307463, 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))], (27371 ^ _776545) ^ [] : [c_Int_OPls = c_Int_OMin], (25692 ^ _776545) ^ [_1241463, _1241465, _1241467, _1241469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241465), _1241467)), -(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), _1241467), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241469, _1241463))), _1241465))))], (25129 ^ _776545) ^ [_1231333, _1231335, _1231337, _1231339] : [class_Divides_Osemiring__div(_1231333), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231333), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231333), _1231335), _1231337)), _1231337)), c_Divides_Odiv__class_Omod(_1231333, _1231335, _1231337))), _1231339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231333), _1231335), _1231339))], (47289 ^ _776545) ^ [_1727244] : [-(c_List_Oreturn__list(_1727244) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1727244))], (47809 ^ _776545) ^ [_1738970, _1738972] : [class_Orderings_Olinorder(_1738970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1738970), _1738972)), 47817 ^ _776545 : [(47820 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1738970, 47816 ^ [_1738970, _1738972]))], (47822 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1738970), 47816 ^ [_1738970, _1738972])))], (47824 ^ _776545) ^ [_1739296] : [-(_1739296 = 47816 ^ [_1738970, _1738972]), hAPP(c_List_Oset(_1738970), _1739296) = _1738972, c_List_Olinorder__class_Osorted(_1738970, _1739296), hBOOL(hAPP(c_List_Odistinct(_1738970), _1739296))], (47818 ^ _776545) ^ [] : [-(hAPP(c_List_Oset(_1738970), 47816 ^ [_1738970, _1738972]) = _1738972)]]], (11084 ^ _776545) ^ [_968281, _968283, _968285] : [class_Rings_Oidom(_968281), 11087 ^ _776545 : [(11088 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968281), _968283), _968283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968281), _968285), _968285), -(_968283 = _968285), -(_968283 = hAPP(c_Groups_Ouminus__class_Ouminus(_968281), _968285))], (11098 ^ _776545) ^ [] : [11099 ^ _776545 : [(11102 ^ _776545) ^ [] : [_968283 = hAPP(c_Groups_Ouminus__class_Ouminus(_968281), _968285)], (11100 ^ _776545) ^ [] : [_968283 = _968285]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968281), _968283), _968283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968281), _968285), _968285))]]], (13852 ^ _776545) ^ [_1023641, _1023643, _1023645, _1023647, _1023649] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1023641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023641), _1023643), _1023645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023641), _1023647), _1023649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023641), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023641), _1023643), _1023647)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023641), _1023645), _1023649))))], (43982 ^ _776545) ^ [_1655595, _1655597, _1655599, _1655601] : [-(hAPP(hAPP(c_List_Odrop(_1655595), _1655597), hAPP(hAPP(c_List_Olist_OCons(_1655595), _1655599), _1655601)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1655595), hAPP(hAPP(c_List_Olist_OCons(_1655595), _1655599), _1655601), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1655595), tc_List_Olist(_1655595)), c_List_Odrop(_1655595)), _1655601), _1655597))], (44834 ^ _776545) ^ [_1673478, _1673480, _1673482, _1673484, _1673486, _1673488] : [-(hAPP(hAPP(c_List_Omap(_1673478, _1673480), _1673482), hAPP(hAPP(c_List_Olist__update(_1673478, _1673484), _1673486), _1673488)) = hAPP(hAPP(c_List_Olist__update(_1673480, hAPP(hAPP(c_List_Omap(_1673478, _1673480), _1673482), _1673484)), _1673486), hAPP(_1673482, _1673488)))], (38552 ^ _776545) ^ [_1515981, _1515983, _1515985, _1515987, _1515989] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1515981, _1515983, _1515985), _1515987), _1515989) = c_HOL_OThe(_1515983, c_Finite__Set_Ofold__graph(_1515981, _1515983, _1515985, _1515987, _1515989)))], (39703 ^ _776545) ^ [_1547486, _1547488, _1547490] : [hBOOL(hAPP(c_Predicate_OPowp(_1547486, _1547488), _1547490)), 39706 ^ _776545 : [(39707 ^ _776545) ^ [_1547570] : [hBOOL(hAPP(hAPP(c_member(_1547486), _1547570), _1547490)), -(hBOOL(hAPP(_1547488, _1547570)))]]], (41272 ^ _776545) ^ [_1586339, _1586341] : [-(c_Relation_Ototal__on(_1586339, c_Orderings_Obot__class_Obot(tc_fun(_1586339, tc_HOL_Obool)), _1586341))], (7780 ^ _776545) ^ [_907219, _907221, _907223, _907225] : [hBOOL(hAPP(hAPP(c_member(_907219), _907221), _907223)), -(hBOOL(hAPP(hAPP(c_member(_907219), _907221), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907219, tc_HOL_Obool)), _907223), _907225))))], (43902 ^ _776545) ^ [_1653736, _1653738, _1653740, _1653742] : [-(hAPP(hAPP(c_List_Otake(_1653736), _1653738), hAPP(hAPP(c_List_Odrop(_1653736), _1653740), _1653742)) = hAPP(hAPP(c_List_Odrop(_1653736), _1653740), hAPP(hAPP(c_List_Otake(_1653736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653738), _1653740)), _1653742)))], (45966 ^ _776545) ^ [_1698662, _1698664] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698662)), c_List_Oconcat(_1698662, _1698664)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698662), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1698662))), _1698664)))], (23597 ^ _776545) ^ [_1204220, _1204222] : [class_Divides_Osemiring__div(_1204220), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204220), c_Groups_Ozero__class_Ozero(_1204220)), _1204222) = c_Groups_Ozero__class_Ozero(_1204220))], (43222 ^ _776545) ^ [_1637725, _1637727] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1637725), _1637727))), -(c_List_Oupto(_1637725, _1637727) = c_List_Olist_ONil(tc_Int_Oint))], (51723 ^ _776545) ^ [_1822530, _1822532] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822530), _1822532)), 51728 ^ _776545 : [(51731 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822532), _1822530))], (51729 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822530), _1822532)))]], -(_1822530 = _1822532)], (17175 ^ _776545) ^ [_1085755, _1085757, _1085759] : [class_Rings_Olinordered__ring__strict(_1085755), 17178 ^ _776545 : [(17193 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085755), _1085757), _1085759)))), 17194 ^ _776545 : [(17201 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), _1085757), c_Groups_Ozero__class_Ozero(_1085755))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), _1085759), c_Groups_Ozero__class_Ozero(_1085755)))], (17195 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), _1085757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), _1085759))]]], (17179 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085755), _1085757), _1085759))), 17184 ^ _776545 : [(17187 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), _1085759)))], (17185 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), c_Groups_Ozero__class_Ozero(_1085755)), _1085757)))]], 17188 ^ _776545 : [(17191 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), _1085759), c_Groups_Ozero__class_Ozero(_1085755))))], (17189 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085755), _1085757), c_Groups_Ozero__class_Ozero(_1085755))))]]]]], (8399 ^ _776545) ^ [_920734, _920736, _920738] : [class_Lattices_Olattice(_920734), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920734), _920736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920734), _920736), _920738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920734), _920736), _920738))], (8869 ^ _776545) ^ [_929198, _929200, _929202] : [class_Orderings_Olinorder(_929198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929198), _929200), _929202)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929198, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_929198, _929200, _929202)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_929198), _929202)) = hAPP(c_SetInterval_Oord__class_OatLeast(_929198), _929200))], (20423 ^ _776545) ^ [_1145012, _1145014, _1145016, _1145018, _1145020] : [class_Fields_Olinordered__field(_1145012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145012), c_Groups_Ozero__class_Ozero(_1145012)), _1145014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145012), _1145014), _1145016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145012), c_Groups_Ozero__class_Ozero(_1145012)), _1145018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145012), _1145018), _1145020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145012), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145012), _1145014), _1145020)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145012), _1145016), _1145018))))], (19881 ^ _776545) ^ [_1135244, _1135246] : [class_Rings_Olinordered__idom(_1135244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135244), _1135246), c_Groups_Ozero__class_Ozero(_1135244))), -(c_Groups_Osgn__class_Osgn(_1135244, _1135246) = hAPP(c_Groups_Ouminus__class_Ouminus(_1135244), c_Groups_Oone__class_Oone(_1135244)))], (42363 ^ _776545) ^ [_1617362, _1617364, _1617366] : [-(c_List_Osublist(_1617362, _1617364, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1617366)) = hAPP(hAPP(c_List_Otake(_1617362), _1617366), _1617364))], (41242 ^ _776545) ^ [_1585833, _1585835, _1585837] : [c_Relation_Ototal__on(_1585833, _1585835, _1585837), -(c_Relation_Ototal__on(_1585833, _1585835, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1585833, _1585833), tc_HOL_Obool)), _1585837), c_Relation_OId(_1585833))))], (12023 ^ _776545) ^ [_987872, _987874] : [class_Lattices_Olattice(_987872), -(c_Big__Operators_Olattice__class_OInf__fin(_987872, hAPP(hAPP(c_Set_Oinsert(_987872), _987874), c_Orderings_Obot__class_Obot(tc_fun(_987872, tc_HOL_Obool)))) = _987874)], (14925 ^ _776545) ^ [_1045797, _1045799, _1045801] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045797), _1045799)), _1045801) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045797), _1045801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045799), _1045801)))], (41879 ^ _776545) ^ [_1603548, _1603550, _1603552, _1603554] : [hBOOL(hAPP(hAPP(c_member(_1603548), _1603550), c_Wellfounded_Oacc(_1603548, _1603552))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1603548)), _1603554), c_Wellfounded_Oacc(tc_List_Olist(_1603548), c_List_Olistrel1(_1603548, _1603552)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1603548)), hAPP(hAPP(c_List_Olist_OCons(_1603548), _1603550), _1603554)), c_Wellfounded_Oacc(tc_List_Olist(_1603548), c_List_Olistrel1(_1603548, _1603552)))))], (37888 ^ _776545) ^ [_1498806, _1498808, _1498810, _1498812, _1498814] : [class_Groups_Ocomm__monoid__add(_1498806), class_Groups_Ocomm__monoid__mult(_1498806), _1498808 = _1498810, c_Nat__Transfer_Onat__set(_1498810), 37906 ^ _776545 : [(37909 ^ _776545) ^ [] : [hAPP(_1498812, 37905 ^ [_1498806, _1498808, _1498810, _1498812, _1498814]) = hAPP(_1498814, 37905 ^ [_1498806, _1498808, _1498810, _1498812, _1498814])], (37907 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37905 ^ [_1498806, _1498808, _1498810, _1498812, _1498814])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1498806), _1498812), _1498808) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1498806), _1498814), _1498810))], (34247 ^ _776545) ^ [_1413475, _1413477, _1413479, _1413481, _1413483, _1413485] : [class_Groups_Ocomm__monoid__mult(_1413475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413477), _1413479)), 34254 ^ _776545 : [(34261 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413477), _1413481), _1413479))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413477, _1413475), hAPP(hAPP(c_COMBC(_1413477, _1413475, _1413475), hAPP(hAPP(c_COMBS(_1413477, _1413475, tc_fun(_1413475, _1413475)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413475, tc_fun(_1413475, _1413475)), _1413477), c_If(_1413475)), hAPP(hAPP(c_COMBC(_1413477, _1413477, tc_HOL_Obool), c_fequal), _1413481))), _1413483)), _1413485)), _1413479) = hAPP(hAPP(c_Power_Opower__class_Opower(_1413475), _1413485), hAPP(c_Finite__Set_Ocard(_1413477), _1413479)))], (34255 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1413477), _1413481), _1413479)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1413477, _1413475), hAPP(hAPP(c_COMBC(_1413477, _1413475, _1413475), hAPP(hAPP(c_COMBS(_1413477, _1413475, tc_fun(_1413475, _1413475)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413475, tc_fun(_1413475, _1413475)), _1413477), c_If(_1413475)), hAPP(hAPP(c_COMBC(_1413477, _1413477, tc_HOL_Obool), c_fequal), _1413481))), _1413483)), _1413485)), _1413479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413475), hAPP(_1413483, _1413481)), hAPP(hAPP(c_Power_Opower__class_Opower(_1413475), _1413485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1413477), _1413479)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (47410 ^ _776545) ^ [_1729840, _1729842, _1729844, _1729846] : [-(hBOOL(hAPP(_1729840, _1729842))), -(c_List_OdropWhile(_1729844, _1729840, hAPP(hAPP(c_List_Olist_OCons(_1729844), _1729842), _1729846)) = hAPP(hAPP(c_List_Olist_OCons(_1729844), _1729842), _1729846))], (31465 ^ _776545) ^ [_1341548, _1341550, _1341552] : [class_Orderings_Olinorder(_1341548), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341548), _1341550), _1341552)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341548), _1341552), _1341550) = _1341552)], (28019 ^ _776545) ^ [_1280067, _1280069, _1280071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1280067), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280069)), _1280071)) = 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), _1280067), _1280069))), _1280071))], (39414 ^ _776545) ^ [_1539990, _1539992, _1539994, _1539996] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539990), _1539992)), 39420 ^ _776545 : [(39423 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539994), hAPP(_1539996, 39419 ^ [_1539990, _1539992, _1539994, _1539996])))], (39421 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539990), 39419 ^ [_1539990, _1539992, _1539994, _1539996]), _1539992)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539990, _1539994)), hAPP(hAPP(c_Product__Type_OSigma(_1539990, _1539994), _1539992), _1539996))))], (25867 ^ _776545) ^ [_1244413, _1244415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1244413), _1244415)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244413, _1244415) = _1244413)], (7934 ^ _776545) ^ [_910595, _910597, _910599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910595, tc_HOL_Obool)), _910597), _910599)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910595, tc_HOL_Obool)), _910597), _910599) = _910599)], (13672 ^ _776545) ^ [_1020005, _1020007, _1020009, _1020011] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020005), 13675 ^ _776545 : [(13682 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020005), _1020009), _1020011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020005), _1020007), _1020009)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020005), _1020007), _1020011))))], (13676 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020005), _1020007), _1020009)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020005), _1020007), _1020011))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020005), _1020009), _1020011)))]]], (29993 ^ _776545) ^ [_1314440, _1314442, _1314444] : [class_Fields_Olinordered__field(_1314440), 29999 ^ _776545 : [(30002 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314440), _1314442), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1314440), _1314444), 29998 ^ [_1314440, _1314442, _1314444])))], (30000 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314440), c_Groups_Ozero__class_Ozero(_1314440)), 29998 ^ [_1314440, _1314442, _1314444])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314440), _1314442), _1314444)))], (50379 ^ _776545) ^ [_1795102, _1795104, _1795106, _1795108, _1795110] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1795102, _1795104, tc_HOL_Obool, _1795106), _1795108), _1795110)), -(hBOOL(hAPP(_1795106, hAPP(hAPP(c_Product__Type_OPair(_1795102, _1795104), _1795108), _1795110))))], (25089 ^ _776545) ^ [_1230721, _1230723] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230721, _1230723)), _1230723) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32474 ^ _776545) ^ [_1361328, _1361330, _1361332, _1361334, _1361336] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361328, tc_fun(_1361330, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1361328), _1361332), _1361334)), _1361336) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361330, tc_HOL_Obool)), hAPP(_1361336, _1361332)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1361328, tc_fun(_1361330, tc_HOL_Obool)), _1361334), _1361336)))], (36233 ^ _776545) ^ [_1460218, _1460220, _1460222, _1460224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460218), _1460220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1460222), _1460224)), -(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), _1460218), _1460222)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460220), _1460224))), c_FunDef_Opair__less)))], (22339 ^ _776545) ^ [_1181514, _1181516] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181514), _1181516) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181514), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181516)))], (39123 ^ _776545) ^ [_1530946, _1530948, _1530950, _1530952] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530946), _1530948)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530950), _1530952)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1530946, _1530950)), hAPP(hAPP(c_Product__Type_OSigma(_1530946, _1530950), _1530948), hAPP(c_COMBK(tc_fun(_1530950, tc_HOL_Obool), _1530946), _1530952)))))], (44547 ^ _776545) ^ [_1667568, _1667570, _1667572] : [44548 ^ _776545 : [(44549 ^ _776545) ^ [_1667657, _1667659] : [_1667570 = hAPP(hAPP(c_List_Olist_OCons(_1667568), _1667659), _1667657)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667568), tc_List_Olist(_1667568))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667568), tc_List_Olist(_1667568)), c_List_Olist_ONil(_1667568)), _1667570)), c_List_Olexord(_1667568, _1667572))))], (38663 ^ _776545) ^ [_1519356, _1519358, _1519360, _1519362, _1519364] : [-(hAPP(c_Set_Ovimage(_1519356, _1519358, _1519360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519358, tc_HOL_Obool)), _1519362), _1519364)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519356, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519356, _1519358, _1519360), _1519362)), hAPP(c_Set_Ovimage(_1519356, _1519358, _1519360), _1519364)))], (3900 ^ _776545) ^ [_835122, _835124] : [_835124 = _835122, -(c_Lazy__Sequence_Ohit__bound(_835124) = c_Lazy__Sequence_Ohit__bound(_835122))], (43036 ^ _776545) ^ [_1634266, _1634268, _1634270] : [hAPP(hAPP(c_List_Olist_OCons(_1634266), _1634268), _1634270) = c_List_Olist_ONil(_1634266)], (36352 ^ _776545) ^ [_1463241, _1463243, _1463245, _1463247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463241), _1463243)), 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)), _1463245), _1463241)), 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)), _1463247), _1463243)), 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)), _1463245), _1463247)), _1463243)), c_FunDef_Omax__weak)))], (40090 ^ _776545) ^ [_1557293, _1557295, _1557297, _1557299, _1557301, _1557303, _1557305, _1557307] : [c_Finite__Set_Ofolding(_1557293, _1557295, _1557297, _1557299), -(hAPP(c_Fun_Ocomp(_1557295, _1557295, _1557301, hAPP(_1557297, _1557303)), hAPP(c_Fun_Ocomp(_1557295, _1557295, _1557301, hAPP(_1557297, _1557305)), _1557307)) = hAPP(c_Fun_Ocomp(_1557295, _1557295, _1557301, hAPP(_1557297, _1557305)), hAPP(c_Fun_Ocomp(_1557295, _1557295, _1557301, hAPP(_1557297, _1557303)), _1557307)))], (9542 ^ _776545) ^ [_940256, _940258, _940260] : [class_Orderings_Oorder(_940256), -(_940258 = _940260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940256), _940258), _940260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940256), _940258), _940260)))], (52139 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (23553 ^ _776545) ^ [_1203503, _1203505] : [class_Int_Onumber__ring(_1203503), 23556 ^ _776545 : [(23563 ^ _776545) ^ [] : [-(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), _1203505)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203503), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203505)) = c_Groups_Ozero__class_Ozero(_1203503))], (23557 ^ _776545) ^ [] : [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), _1203505))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203503), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203505)) = hAPP(c_Int_Onumber__class_Onumber__of(_1203503), _1203505))]]], (1314 ^ _776545) ^ [_795834, _795836] : [-(class_Rings_Oring(_795834)), _795836 = _795834, class_Rings_Oring(_795836)], (6386 ^ _776545) ^ [_879617] : [c_Orderings_Otop__class_Otop(tc_fun(_879617, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_879617, tc_HOL_Obool))], (28891 ^ _776545) ^ [_1294503, _1294505] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1294503)), c_Int_OBit0(_1294505))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1294503), _1294505)))], (26370 ^ _776545) ^ [_1252489, _1252491] : [-(_1252489 = hAPP(c_Int_Onat, _1252491)), 26373 ^ _776545 : [(26376 ^ _776545) ^ [] : [_1252491 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1252489)], (26374 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252491)))]], 26377 ^ _776545 : [(26380 ^ _776545) ^ [] : [_1252489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26378 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252491))]]], (28013 ^ _776545) ^ [_1279948, _1279950, _1279952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279948), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279948)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279950)), _1279952)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36434 ^ _776545) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (10333 ^ _776545) ^ [_954017, _954019] : [class_Lattices_Oboolean__algebra(_954017), -(hAPP(c_Groups_Ouminus__class_Ouminus(_954017), hAPP(c_Groups_Ouminus__class_Ouminus(_954017), _954019)) = _954019)], (5330 ^ _776545) ^ [_857905, _857907, _857909, _857911, _857913, _857915, _857917, _857919, _857921, _857923] : [-(c_New__DSequence_Opos__map(_857923, _857919, _857915, _857911, _857907) = c_New__DSequence_Opos__map(_857921, _857917, _857913, _857909, _857905)), _857923 = _857921, _857919 = _857917, _857915 = _857913, _857911 = _857909, _857907 = _857905], (51381 ^ _776545) ^ [_1816549, _1816551, _1816553, _1816555, _1816557] : [class_Rings_Ocomm__semiring__1(_1816549), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816549), hAPP(hAPP(c_Power_Opower__class_Opower(_1816549), _1816551), _1816553)), _1816555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816557), _1816553)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816549), hAPP(hAPP(c_Power_Opower__class_Opower(_1816549), _1816551), _1816557)), _1816555)))], (6115 ^ _776545) ^ [_874537, _874539, _874541, _874543] : [6117 ^ _776545 : [(6120 ^ _776545) ^ [] : [hBOOL(hAPP(_874541, 6116 ^ [_874537, _874539, _874541, _874543]))], (6118 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874537), 6116 ^ [_874537, _874539, _874541, _874543]), _874539)))]], -(hBOOL(hAPP(_874541, _874543))), hBOOL(hAPP(hAPP(c_member(_874537), _874543), _874539))], (7680 ^ _776545) ^ [_904679, _904681] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904679, tc_HOL_Obool)), _904681), _904681) = _904681)], (5610 ^ _776545) ^ [_862191, _862193, _862195, _862197] : [-(c_COMBK(_862197, _862193) = c_COMBK(_862195, _862191)), _862197 = _862195, _862193 = _862191], (18830 ^ _776545) ^ [_1115760, _1115762, _1115764, _1115766] : [class_Groups_Ocomm__monoid__mult(_1115760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115762), _1115764)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1115762, _1115760), _1115766), _1115764) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115760, _1115762, c_Groups_Otimes__class_Otimes(_1115760)), _1115766), c_Groups_Oone__class_Oone(_1115760)), _1115764))], (8879 ^ _776545) ^ [_929414, _929416, _929418, _929420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929414, tc_HOL_Obool)), _929416), hAPP(hAPP(c_Set_Oinsert(_929414), _929418), _929420))), 8882 ^ _776545 : [(8889 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929414), _929418), _929420))), 8892 ^ _776545 : [(8899 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929414), _929418), _929416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929414, tc_HOL_Obool)), _929416), _929420)))], (8893 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929414), _929418), _929416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929414, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929414, tc_HOL_Obool)), _929416), hAPP(hAPP(c_Set_Oinsert(_929414), _929418), c_Orderings_Obot__class_Obot(tc_fun(_929414, tc_HOL_Obool))))), _929420)))]]], (8883 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929414), _929418), _929420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929414, tc_HOL_Obool)), _929416), _929420)))]]], (28517 ^ _776545) ^ [_1288292, _1288294] : [c_Int_Oiszero(_1288292, hAPP(c_Int_Onumber__class_Onumber__of(_1288292), c_Int_OBit1(_1288294))), class_Int_Onumber__ring(_1288292), class_Int_Oring__char__0(_1288292)], (14592 ^ _776545) ^ [_1039590] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039590), _1039590)))], (11447 ^ _776545) ^ [_976363, _976365, _976367, _976369, _976371] : [c_Finite__Set_Ofolding__one(_976363, _976365, _976367), hBOOL(hAPP(c_Finite__Set_Ofinite(_976363), _976369)), 11454 ^ _776545 : [(11461 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976363, tc_HOL_Obool)), _976369), hAPP(hAPP(c_Set_Oinsert(_976363), _976371), c_Orderings_Obot__class_Obot(tc_fun(_976363, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_976363, tc_HOL_Obool))), -(hAPP(_976367, hAPP(hAPP(c_Set_Oinsert(_976363), _976371), _976369)) = hAPP(hAPP(_976365, _976371), hAPP(_976367, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976363, tc_HOL_Obool)), _976369), hAPP(hAPP(c_Set_Oinsert(_976363), _976371), c_Orderings_Obot__class_Obot(tc_fun(_976363, tc_HOL_Obool)))))))], (11455 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976363, tc_HOL_Obool)), _976369), hAPP(hAPP(c_Set_Oinsert(_976363), _976371), c_Orderings_Obot__class_Obot(tc_fun(_976363, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_976363, tc_HOL_Obool)), -(hAPP(_976367, hAPP(hAPP(c_Set_Oinsert(_976363), _976371), _976369)) = _976371)]]], (1884 ^ _776545) ^ [_802959, _802961] : [-(class_Groups_Oone(_802959)), _802961 = _802959, class_Groups_Oone(_802961)], (10212 ^ _776545) ^ [_951905, _951907, _951909, _951911] : [class_Orderings_Olinorder(_951905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951905), _951907), _951909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951905), _951909), _951911)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951905, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_951905, _951907, _951909)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951905, _951909), _951911)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_951905, _951907, _951911))], (45251 ^ _776545) ^ [_1682798, _1682800] : [-(c_Code__Numeral_Onat__of__aux(_1682798, _1682800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682798)), _1682800))], (10541 ^ _776545) ^ [_957843, _957845, _957847, _957849, _957851] : [class_Orderings_Olinorder(_957843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957843), _957845), _957847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957843), _957849), _957851)), 10552 ^ _776545 : [(10561 ^ _776545) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957843, _957845), _957847) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957843, _957849), _957851)), _957845 = _957849, _957847 = _957851], (10553 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957843, _957845), _957847) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957843, _957849), _957851), 10556 ^ _776545 : [(10559 ^ _776545) ^ [] : [-(_957847 = _957851)], (10557 ^ _776545) ^ [] : [-(_957845 = _957849)]]]]], (7418 ^ _776545) ^ [_898593, _898595, _898597] : [class_Orderings_Oorder(_898593), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898593, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_898593, _898595, _898597)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_898593), _898597)) = c_Orderings_Obot__class_Obot(tc_fun(_898593, tc_HOL_Obool)))], (31855 ^ _776545) ^ [_1348839, _1348841, _1348843] : [class_Orderings_Olinorder(_1348839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348839), _1348841)), -(hBOOL(hAPP(hAPP(c_member(_1348839), _1348843), _1348841))), -(_1348841 = c_Orderings_Obot__class_Obot(tc_fun(_1348839, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1348839, hAPP(hAPP(c_Set_Oinsert(_1348839), _1348843), _1348841)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348839), _1348843), c_Big__Operators_Olinorder__class_OMax(_1348839, _1348841)))], (33681 ^ _776545) ^ [_1398784, _1398786, _1398788, _1398790, _1398792] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1398784, tc_fun(_1398786, tc_HOL_Obool)), _1398788), hAPP(hAPP(c_COMBS(_1398784, tc_fun(_1398786, tc_HOL_Obool), tc_fun(_1398786, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398786, tc_HOL_Obool), tc_fun(tc_fun(_1398786, tc_HOL_Obool), tc_fun(_1398786, tc_HOL_Obool)), _1398784), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398786, tc_HOL_Obool))), _1398790)), _1398792)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398786, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398786, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398784, tc_fun(_1398786, tc_HOL_Obool), _1398790), _1398788))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1398786, tc_HOL_Obool), hAPP(c_Set_Oimage(_1398784, tc_fun(_1398786, tc_HOL_Obool), _1398792), _1398788))))], (13246 ^ _776545) ^ [_1011019, _1011021, _1011023, _1011025, _1011027] : [class_Groups_Ocomm__monoid__mult(_1011019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011021), _1011023)), -(hBOOL(hAPP(hAPP(c_member(_1011021), _1011025), _1011023))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011021, _1011019), _1011027), hAPP(hAPP(c_Set_Oinsert(_1011021), _1011025), _1011023)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011019), hAPP(_1011027, _1011025)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011021, _1011019), _1011027), _1011023)))], (51595 ^ _776545) ^ [_1820362, _1820364, _1820366, _1820368] : [class_Divides_Osemiring__div(_1820362), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820362), _1820364), _1820366)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820362), _1820364), _1820368)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820362), _1820364), c_Divides_Odiv__class_Omod(_1820362, _1820366, _1820368))))], (41825 ^ _776545) ^ [_1601868, _1601870, _1601872, _1601874, _1601876, _1601878] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601868), tc_List_Olist(_1601868))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601868), tc_List_Olist(_1601868)), hAPP(hAPP(c_List_Olist_OCons(_1601868), _1601870), _1601872)), hAPP(hAPP(c_List_Olist_OCons(_1601868), _1601874), _1601876))), c_List_Olexord(_1601868, _1601878))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601868, _1601868)), hAPP(hAPP(c_Product__Type_OPair(_1601868, _1601868), _1601870), _1601874)), _1601878))), 41832 ^ _776545 : [(41835 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601868), tc_List_Olist(_1601868))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601868), tc_List_Olist(_1601868)), _1601872), _1601876)), c_List_Olexord(_1601868, _1601878))))], (41833 ^ _776545) ^ [] : [-(_1601870 = _1601874)]]], (3888 ^ _776545) ^ [_834952, _834954] : [_834954 = _834952, -(c_Groups_Oabs__class_Oabs(_834954) = c_Groups_Oabs__class_Oabs(_834952))], (51869 ^ _776545) ^ [_1824780, _1824782] : [class_Lattices_Obounded__lattice(_1824780), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1824782, _1824780)))], (51663 ^ _776545) ^ [_1821545] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821545), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1821545 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16747 ^ _776545) ^ [_1077732, _1077734, _1077736, _1077738] : [class_Groups_Ocomm__monoid__add(_1077732), 16750 ^ _776545 : [(16757 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077734)), _1077736))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077732), _1077738), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077736, hAPP(c_Nat_OSuc, _1077734))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077732), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077732), _1077738), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077736, _1077734))), hAPP(_1077738, hAPP(c_Nat_OSuc, _1077734))))], (16751 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077734)), _1077736)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1077732), _1077738), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1077736, hAPP(c_Nat_OSuc, _1077734))) = c_Groups_Ozero__class_Ozero(_1077732))]]], (44118 ^ _776545) ^ [_1659025, _1659027, _1659029] : [-(_1659025 = c_List_Olist_ONil(_1659027)), -(hAPP(c_List_Ohd(_1659027), hAPP(hAPP(c_List_Oappend(_1659027), _1659025), _1659029)) = hAPP(c_List_Ohd(_1659027), _1659025))], (48530 ^ _776545) ^ [_1754423, _1754425, _1754427] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754423, _1754423, hAPP(hAPP(c_COMBB(tc_fun(_1754423, tc_HOL_Obool), tc_fun(_1754423, tc_HOL_Obool), _1754423), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754423), c_fNot)), c_fequal)), _1754425), _1754427)), _1754425 = _1754427], (39691 ^ _776545) ^ [_1547270] : [-(_1547270 = hAPP(c_Int_OAbs__Integ, 39689 ^ [_1547270]))], (5879 ^ _776545) ^ [_870010, _870012, _870014, _870016] : [_870010 = _870012, hBOOL(hAPP(hAPP(c_member(_870014), _870012), _870016)), -(hBOOL(hAPP(hAPP(c_member(_870014), _870010), _870016)))], (7536 ^ _776545) ^ [_900814, _900816, _900818, _900820] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900814, tc_HOL_Obool)), _900816), _900818), _900820)), -(hBOOL(hAPP(_900816, _900820)))], (45084 ^ _776545) ^ [] : [-(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))], (34719 ^ _776545) ^ [_1423608, _1423610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1423608), _1423610)), -(c_Divides_Odivmod__nat(_1423608, _1423610) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1423608))], (41226 ^ _776545) ^ [_1585478, _1585480, _1585482, _1585484, _1585486, _1585488] : [c_Relation_Osingle__valued(_1585478, _1585480, hAPP(c_Relation_Oconverse(_1585480, _1585478), _1585482)), -(_1585484 = c_Orderings_Obot__class_Obot(tc_fun(_1585486, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1585480, _1585478, _1585482), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585486, tc_fun(_1585480, tc_HOL_Obool)), _1585484), _1585488)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585486, tc_fun(_1585478, tc_HOL_Obool)), _1585484), hAPP(hAPP(c_COMBB(tc_fun(_1585480, tc_HOL_Obool), tc_fun(_1585478, tc_HOL_Obool), _1585486), c_Relation_OImage(_1585480, _1585478, _1585482)), _1585488)))], (52229 ^ _776545) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (49218 ^ _776545) ^ [_1770234, _1770236] : [-(hBOOL(hAPP(_1770236, 49225 ^ [_1770234, _1770236]))), 49219 ^ _776545 : [(49220 ^ _776545) ^ [_1770295] : [hBOOL(hAPP(hAPP(c_member(_1770234), _1770295), c_Orderings_Otop__class_Otop(tc_fun(_1770234, tc_HOL_Obool)))), hBOOL(hAPP(_1770236, _1770295))]]], (11324 ^ _776545) ^ [_973489, _973491, _973493, _973495, _973497] : [c_Finite__Set_Ofolding__one(_973489, _973491, _973493), hBOOL(hAPP(c_Finite__Set_Ofinite(_973489), _973495)), hBOOL(hAPP(hAPP(c_member(_973489), _973497), _973495)), 11335 ^ _776545 : [(11342 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973489, tc_HOL_Obool)), _973495), hAPP(hAPP(c_Set_Oinsert(_973489), _973497), c_Orderings_Obot__class_Obot(tc_fun(_973489, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_973489, tc_HOL_Obool))), -(hAPP(_973493, _973495) = hAPP(hAPP(_973491, _973497), hAPP(_973493, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973489, tc_HOL_Obool)), _973495), hAPP(hAPP(c_Set_Oinsert(_973489), _973497), c_Orderings_Obot__class_Obot(tc_fun(_973489, tc_HOL_Obool)))))))], (11336 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973489, tc_HOL_Obool)), _973495), hAPP(hAPP(c_Set_Oinsert(_973489), _973497), c_Orderings_Obot__class_Obot(tc_fun(_973489, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_973489, tc_HOL_Obool)), -(hAPP(_973493, _973495) = _973497)]]], (27341 ^ _776545) ^ [_1268400, _1268402, _1268404] : [class_Fields_Olinordered__field__inverse__zero(_1268400), -(hAPP(c_Groups_Oabs__class_Oabs(_1268400), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268400), _1268402), _1268404)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268400), hAPP(c_Groups_Oabs__class_Oabs(_1268400), _1268402)), hAPP(c_Groups_Oabs__class_Oabs(_1268400), _1268404)))], (46071 ^ _776545) ^ [_1701927, _1701929, _1701931, _1701933] : [-(hBOOL(hAPP(_1701927, _1701929))), -(c_List_Oremove1(_1701931, _1701929, hAPP(c_List_Ofilter(_1701931, _1701927), _1701933)) = hAPP(c_List_Ofilter(_1701931, _1701927), _1701933))], (38876 ^ _776545) ^ [_1524488, _1524490, _1524492] : [hAPP(c_Relation_ODomain(_1524488, _1524490), _1524492) = c_Orderings_Obot__class_Obot(tc_fun(_1524488, tc_HOL_Obool)), -(_1524492 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524488, _1524490), tc_HOL_Obool)))], (17057 ^ _776545) ^ [_1083621, _1083623, _1083625, _1083627] : [class_Rings_Oordered__semiring(_1083621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083621), _1083623), _1083625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083621), c_Groups_Ozero__class_Ozero(_1083621)), _1083627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083621), _1083623), _1083627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083621), _1083625), _1083627))))], (42359 ^ _776545) ^ [_1617250, _1617252, _1617254, _1617256] : [-(hAPP(hAPP(c_List_Otake(_1617250), _1617252), hAPP(hAPP(c_List_Otake(_1617250), _1617254), _1617256)) = hAPP(hAPP(c_List_Otake(_1617250), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1617252), _1617254)), _1617256))], (36504 ^ _776545) ^ [_1467460, _1467462, _1467464, _1467466, _1467468, _1467470] : [hBOOL(hAPP(hAPP(c_member(_1467460), _1467462), _1467464)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1467460, _1467466)), hAPP(hAPP(c_Product__Type_OPair(_1467460, _1467466), _1467462), _1467468)), _1467470)), -(hBOOL(hAPP(hAPP(c_member(_1467466), _1467468), hAPP(c_Relation_OImage(_1467460, _1467466, _1467470), _1467464))))], (5416 ^ _776545) ^ [_859300, _859302] : [_859302 = _859300, -(c_Groups_Ominus__class_Ominus(_859302) = c_Groups_Ominus__class_Ominus(_859300))], (47785 ^ _776545) ^ [_1738349, _1738351, _1738353, _1738355] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1738349, _1738351, _1738353, _1738355) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1738349, _1738351), _1738353), _1738355)))], (17727 ^ _776545) ^ [_1095673, _1095675] : [class_Groups_Oordered__ab__group__add(_1095673), 17730 ^ _776545 : [(17737 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095673), c_Groups_Ozero__class_Ozero(_1095673)), _1095675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095673), hAPP(c_Groups_Ouminus__class_Ouminus(_1095673), _1095675)), c_Groups_Ozero__class_Ozero(_1095673))))], (17731 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095673), hAPP(c_Groups_Ouminus__class_Ouminus(_1095673), _1095675)), c_Groups_Ozero__class_Ozero(_1095673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095673), c_Groups_Ozero__class_Ozero(_1095673)), _1095675)))]]], (5741 ^ _776545) ^ [_867088] : [-(c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(_867088), tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867088, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867088)), tc_HOL_Obool), c_Hoare__Mirabelle_ORep__triple(_867088), c_Hoare__Mirabelle_OAbs__triple(_867088), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867088, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867088)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867088))))], (31475 ^ _776545) ^ [_1341709, _1341711, _1341713] : [class_Orderings_Olinorder(_1341709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341709), _1341711), _1341713)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341709), _1341711), _1341713) = _1341713)], (46930 ^ _776545) ^ [_1719517, _1719519, _1719521] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719517), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719517))), _1719519))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719517))), _1719519))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719517), _1719517), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719517), tc_Nat_Onat, _1719517), c_List_Onth(_1719517)), _1719521)), hAPP(c_List_Ofilter(tc_List_Olist(_1719517), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719517)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719521)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719517)))), c_List_Otranspose(_1719517, _1719519))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719517)), _1719519), _1719521))], (32934 ^ _776545) ^ [_1377053, _1377055, _1377057, _1377059, _1377061] : [-(_1377053 = c_Orderings_Obot__class_Obot(tc_fun(_1377055, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377055, tc_fun(_1377057, tc_HOL_Obool)), _1377053), hAPP(hAPP(c_COMBC(_1377055, tc_fun(_1377057, tc_HOL_Obool), tc_fun(_1377057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377057, tc_HOL_Obool), tc_fun(tc_fun(_1377057, tc_HOL_Obool), tc_fun(_1377057, tc_HOL_Obool)), _1377055), c_Groups_Ominus__class_Ominus(tc_fun(_1377057, tc_HOL_Obool))), _1377059)), _1377061)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377057, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377055, tc_fun(_1377057, tc_HOL_Obool)), _1377053), _1377059)), _1377061))], (15448 ^ _776545) ^ [_1055899, _1055901, _1055903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055899), _1055901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055899, tc_HOL_Obool)), _1055903), _1055901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055899), _1055903)), hAPP(c_Finite__Set_Ocard(_1055899), _1055901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1055899, tc_HOL_Obool)), _1055903), _1055901)))], (28331 ^ _776545) ^ [_1285097, _1285099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285097), _1285099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285097)), c_Int_OBit1(_1285099))))], (7850 ^ _776545) ^ [_908720, _908722, _908724] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908720, tc_HOL_Obool)), _908722), _908724) = c_Orderings_Obot__class_Obot(tc_fun(_908720, tc_HOL_Obool)), 7853 ^ _776545 : [(7854 ^ _776545) ^ [_908844] : [hBOOL(hAPP(hAPP(c_member(_908720), _908844), _908722)), 7857 ^ _776545 : [(7858 ^ _776545) ^ [_908934] : [hBOOL(hAPP(hAPP(c_member(_908720), _908934), _908724)), _908844 = _908934]]]]], (40210 ^ _776545) ^ [_1559994, _1559996, _1559998, _1560000, _1560002, _1560004] : [c_Finite__Set_Ofolding(_1559994, _1559996, _1559998, _1560000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559994), _1560002)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559994), _1560004)), -(hAPP(c_Fun_Ocomp(_1559996, _1559996, _1559996, hAPP(_1560000, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1559994, tc_HOL_Obool)), _1560002), _1560004))), hAPP(_1560000, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1559994, tc_HOL_Obool)), _1560002), _1560004))) = hAPP(c_Fun_Ocomp(_1559996, _1559996, _1559996, hAPP(_1560000, _1560002)), hAPP(_1560000, _1560004)))], (29699 ^ _776545) ^ [_1309024, _1309026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309024)), -(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)))), _1309026)), 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)))), _1309024)) = 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, _1309026, _1309024))))], (24583 ^ _776545) ^ [_1221165, _1221167, _1221169, _1221171, _1221173] : [class_Groups_Oordered__ab__semigroup__add(_1221165), class_Rings_Osemiring__1(_1221165), 24593 ^ _776545 : [(24596 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221165), hAPP(_1221171, 24592 ^ [_1221165, _1221167, _1221169, _1221171, _1221173])), _1221173))], (24594 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1221167), 24592 ^ [_1221165, _1221167, _1221169, _1221171, _1221173]), _1221169)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221165), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221167, _1221165), _1221171), _1221169)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221165), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1221165), hAPP(c_Finite__Set_Ocard(_1221167), _1221169))), _1221173))))], (46156 ^ _776545) ^ [_1703673, _1703675, _1703677, _1703679] : [-(c_List_Otranspose(_1703673, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703675), tc_List_Olist(_1703673)), hAPP(c_List_Omap(_1703675, _1703673), _1703677)), _1703679)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1703675), tc_List_Olist(_1703673)), hAPP(c_List_Omap(_1703675, _1703673), _1703677)), c_List_Otranspose(_1703675, _1703679)))], (43140 ^ _776545) ^ [_1636002, _1636004, _1636006] : [-(hAPP(hAPP(c_List_Olist__update(_1636002, c_List_Olist_ONil(_1636002)), _1636004), _1636006) = c_List_Olist_ONil(_1636002))], (26645 ^ _776545) ^ [_1257456] : [-(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), _1257456)) = 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), _1257456))))], (36177 ^ _776545) ^ [_1458744, _1458746, _1458748, _1458750, _1458752, _1458754] : [class_Groups_Oordered__ab__group__add(_1458744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458746), _1458748)), 36187 ^ _776545 : [(36190 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458744), c_Groups_Ozero__class_Ozero(_1458744)), hAPP(_1458750, 36186 ^ [_1458744, _1458746, _1458748, _1458750, _1458752, _1458754])))], (36188 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458746), 36186 ^ [_1458744, _1458746, _1458748, _1458750, _1458752, _1458754]), _1458748)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458746, _1458744), _1458750), _1458748) = _1458752, hBOOL(hAPP(hAPP(c_member(_1458746), _1458754), _1458748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458744), hAPP(_1458750, _1458754)), _1458752)))], (18978 ^ _776545) ^ [_1118384, _1118386] : [18986 ^ _776545 : [(18989 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1118386, 18985 ^ [_1118384, _1118386])))], (18987 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 18985 ^ [_1118384, _1118386]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1118384))))]], 18979 ^ _776545 : [(18980 ^ _776545) ^ [_1118453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118453), _1118384)), hBOOL(hAPP(_1118386, _1118453))]]], (52487 ^ _776545) ^ [] : [hBOOL(c_fFalse)], (23828 ^ _776545) ^ [_1208195, _1208197] : [class_Rings_Olinordered__semidom(_1208195), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1208195), c_Groups_Ozero__class_Ozero(_1208195)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208195), _1208197))))], (8823 ^ _776545) ^ [_928316, _928318, _928320] : [class_Lattices_Olattice(_928316), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928316), _928318), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928316), _928318), _928320)) = _928318)], (45955 ^ _776545) ^ [_1698408, _1698410] : [45957 ^ _776545 : [(45960 ^ _776545) ^ [] : [45956 ^ [_1698408, _1698410] = c_List_Olist_ONil(_1698408)], (45958 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698408)), 45956 ^ [_1698408, _1698410]), hAPP(c_List_Oset(tc_List_Olist(_1698408)), _1698410))))]], -(c_List_Oconcat(_1698408, _1698410) = c_List_Olist_ONil(_1698408))], (3894 ^ _776545) ^ [_835037, _835039] : [_835039 = _835037, -(c_Nat_Osemiring__1__class_Oof__nat(_835039) = c_Nat_Osemiring__1__class_Oof__nat(_835037))], (47238 ^ _776545) ^ [_1726226, _1726228, _1726230] : [47240 ^ _776545 : [(47243 ^ _776545) ^ [] : [hBOOL(hAPP(_1726228, 47239 ^ [_1726226, _1726228, _1726230]))], (47241 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726226), 47239 ^ [_1726226, _1726228, _1726230]), hAPP(c_List_Oset(_1726226), _1726230))))]], -(c_List_OtakeWhile(_1726226, _1726228, _1726230) = _1726230)], (2138 ^ _776545) ^ [_807567, _807569] : [_807569 = _807567, -(c_Int_Oring__1__class_OInts(_807569) = c_Int_Oring__1__class_OInts(_807567))], (40453 ^ _776545) ^ [_1565715, _1565717, _1565719, _1565721] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1565715, tc_HOL_Obool), tc_fun(_1565715, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565715, tc_HOL_Obool), tc_fun(_1565715, tc_HOL_Obool)), _1565717), _1565719)), c_Wellfounded_Omax__ext(_1565715, _1565721)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565715), _1565717)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1565715), _1565719)), -(_1565719 = c_Orderings_Obot__class_Obot(tc_fun(_1565715, tc_HOL_Obool))), 40467 ^ _776545 : [(40470 ^ _776545) ^ [_1566120] : [hBOOL(hAPP(hAPP(c_member(_1565715), _1566120), _1565719)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565715, _1565715)), hAPP(hAPP(c_Product__Type_OPair(_1565715, _1565715), 40466 ^ [_1565715, _1565717, _1565719, _1565721]), _1566120)), _1565721))], (40468 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565715), 40466 ^ [_1565715, _1565717, _1565719, _1565721]), _1565717)))]]], (15426 ^ _776545) ^ [_1055318, _1055320, _1055322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055318), _1055320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055318, tc_HOL_Obool)), _1055320), _1055322)), -(hAPP(c_Finite__Set_Ocard(_1055318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055318, tc_HOL_Obool)), _1055322), _1055320)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055318), _1055322)), hAPP(c_Finite__Set_Ocard(_1055318), _1055320)))], (19043 ^ _776545) ^ [_1119622, _1119624] : [19051 ^ _776545 : [(19054 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1119624, 19050 ^ [_1119622, _1119624])))], (19052 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19050 ^ [_1119622, _1119624]), _1119622)))]], 19044 ^ _776545 : [(19045 ^ _776545) ^ [_1119690] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1119690), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119622))), hBOOL(hAPP(_1119624, _1119690))]]], (34141 ^ _776545) ^ [_1410911] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410911)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1410911)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410911)), 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)))))], (27693 ^ _776545) ^ [_1274712, _1274714] : [class_Groups_Oordered__ab__group__add__abs(_1274712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274712), _1274714), c_Groups_Ozero__class_Ozero(_1274712))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274712), _1274714) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274712), _1274714))], (52075 ^ _776545) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (40068 ^ _776545) ^ [_1556774, _1556776, _1556778, _1556780, _1556782, _1556784] : [c_Finite__Set_Ofolding(_1556774, _1556776, _1556778, _1556780), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556774), _1556782)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556774), _1556784)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1556774, tc_HOL_Obool)), _1556782), _1556784) = c_Orderings_Obot__class_Obot(tc_fun(_1556774, tc_HOL_Obool)), -(hAPP(_1556780, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556774, tc_HOL_Obool)), _1556782), _1556784)) = hAPP(c_Fun_Ocomp(_1556776, _1556776, _1556776, hAPP(_1556780, _1556782)), hAPP(_1556780, _1556784)))], (46188 ^ _776545) ^ [_1704470, _1704472] : [46190 ^ _776545 : [(46193 ^ _776545) ^ [] : [46189 ^ [_1704470, _1704472] = c_List_Olist_ONil(_1704470)], (46191 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704470)), 46189 ^ [_1704470, _1704472]), hAPP(c_List_Oset(tc_List_Olist(_1704470)), _1704472))))]], -(c_List_Otranspose(_1704470, _1704472) = c_List_Olist_ONil(tc_List_Olist(_1704470)))], (26991 ^ _776545) ^ [_1262744, _1262746] : [class_Rings_Oring__1(_1262744), -(hBOOL(hAPP(hAPP(c_member(_1262744), hAPP(c_Int_Oring__1__class_Oof__int(_1262744), _1262746)), c_Int_Oring__1__class_OInts(_1262744))))], (1924 ^ _776545) ^ [_803459, _803461] : [-(hBOOL(_803459)), _803461 = _803459, hBOOL(_803461)], (45828 ^ _776545) ^ [_1695933, _1695935] : [_1695935 = c_List_Olist_ONil(_1695933), -(c_List_Oremdups(_1695933, _1695935) = c_List_Olist_ONil(_1695933))], (23115 ^ _776545) ^ [_1195353, _1195355, _1195357, _1195359, _1195361] : [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), _1195353), _1195355)), _1195357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195353), _1195359)), _1195361))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195361), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195353), _1195361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195353), _1195357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195359), _1195355)))], (8515 ^ _776545) ^ [_922807, _922809, _922811, _922813] : [class_Lattices_Osemilattice__sup(_922807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922807), _922809), _922811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922807), _922809), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922807), _922813), _922811))))], (29151 ^ _776545) ^ [_1299049, _1299051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299049)), c_Int_OBit0(_1299051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299049), _1299051)))], (2860 ^ _776545) ^ [_818970, _818972] : [_818972 = _818970, -(c_Relation_OField(_818972) = c_Relation_OField(_818970))], (7180 ^ _776545) ^ [_893523, _893525, _893527, _893529] : [hBOOL(hAPP(hAPP(c_member(_893523), _893525), _893527)), -(hBOOL(hAPP(hAPP(c_member(_893523), _893525), hAPP(hAPP(c_Set_Oinsert(_893523), _893529), _893527))))], (3344 ^ _776545) ^ [_826448, _826450, _826452, _826454] : [-(c_List_Olists(_826454, _826450) = c_List_Olists(_826452, _826448)), _826454 = _826452, _826450 = _826448], (3228 ^ _776545) ^ [_824614, _824616, _824618, _824620, _824622, _824624] : [-(c_Big__Operators_Olattice_OSup__fin(_824624, _824620, _824616) = c_Big__Operators_Olattice_OSup__fin(_824622, _824618, _824614)), _824624 = _824622, _824620 = _824618, _824616 = _824614], (41601 ^ _776545) ^ [_1595228, _1595230, _1595232, _1595234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595228, _1595228)), hAPP(hAPP(c_Product__Type_OPair(_1595228, _1595228), _1595230), _1595232)), c_Transitive__Closure_Otrancl(_1595228, _1595234))), 41605 ^ _776545 : [(41608 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595228, _1595228)), hAPP(hAPP(c_Product__Type_OPair(_1595228, _1595228), 41604 ^ [_1595228, _1595230, _1595232, _1595234]), _1595232)), c_Transitive__Closure_Ortrancl(_1595228, _1595234))))], (41606 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595228, _1595228)), hAPP(hAPP(c_Product__Type_OPair(_1595228, _1595228), _1595230), 41604 ^ [_1595228, _1595230, _1595232, _1595234])), _1595234)))]]], (16671 ^ _776545) ^ [_1076405, _1076407] : [16672 ^ _776545 : [(16673 ^ _776545) ^ [_1076458] : [_1076407 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076405), _1076458))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076405), _1076407)))], (25335 ^ _776545) ^ [_1234981, _1234983] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234981), _1234983) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 25336 ^ _776545 : [(25343 ^ _776545) ^ [] : [_1234981 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1234983 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (25337 ^ _776545) ^ [] : [_1234981 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1234983 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (38882 ^ _776545) ^ [_1524601, _1524603, _1524605] : [_1524605 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524601, _1524603), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1524601, _1524603), _1524605) = c_Orderings_Obot__class_Obot(tc_fun(_1524601, tc_HOL_Obool)))], (50 ^ _776545) ^ [_777350, _777352, _777354, _777356, _777358, _777360] : [-(c_Finite__Set_Ofolding__one__idem(_777358, _777354, _777350)), c_Finite__Set_Ofolding__one__idem(_777360, _777356, _777352), _777360 = _777358, _777356 = _777354, _777352 = _777350], (1184 ^ _776545) ^ [_794209, _794211] : [-(class_Rings_Olinordered__ring(_794209)), _794211 = _794209, class_Rings_Olinordered__ring(_794211)], (22401 ^ _776545) ^ [_1182673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182673)), -(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)), _1182673))))], (43144 ^ _776545) ^ [_1636103, _1636105, _1636107, _1636109] : [hAPP(hAPP(c_List_Olist__update(_1636103, _1636105), _1636107), _1636109) = c_List_Olist_ONil(_1636103), -(_1636105 = c_List_Olist_ONil(_1636103))], (40705 ^ _776545) ^ [_1572445, _1572447, _1572449, _1572451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572445, _1572445)), hAPP(hAPP(c_Product__Type_OPair(_1572445, _1572445), _1572449), _1572451)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool)), _1572447), c_Relation_OId(_1572445)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572445, tc_fun(_1572445, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1572445, tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_fun(_1572445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572445, tc_fun(tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_fun(_1572445, tc_HOL_Obool)), _1572445), c_COMBC(_1572445, tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572445, tc_prod(_1572445, _1572445)), tc_fun(_1572445, tc_fun(tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_HOL_Obool)), _1572445), hAPP(c_COMBB(tc_prod(_1572445, _1572445), tc_fun(tc_fun(tc_prod(_1572445, _1572445), tc_HOL_Obool), tc_HOL_Obool), _1572445), c_member(tc_prod(_1572445, _1572445)))), c_Product__Type_OPair(_1572445, _1572445)))), _1572447)), c_fequal), _1572449), _1572451)))], (25159 ^ _776545) ^ [_1232066, _1232068, _1232070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1232066), _1232068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232070), _1232068)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1232070), _1232066))))], (7996 ^ _776545) ^ [_911964, _911966] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911964, tc_HOL_Obool)), _911966), c_Orderings_Otop__class_Otop(tc_fun(_911964, tc_HOL_Obool))) = _911966)], (46309 ^ _776545) ^ [_1707933, _1707935, _1707937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707933), _1707935)), -(c_List_Oupt(_1707933, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707935), _1707937)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1707933, _1707935)), c_List_Oupt(_1707935, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707935), _1707937))))], (27613 ^ _776545) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (13001 ^ _776545) ^ [_1005913, _1005915, _1005917] : [class_Lattices_Olattice(_1005913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005913), _1005915)), -(hBOOL(hAPP(hAPP(c_member(_1005913), _1005917), _1005915))), -(c_Big__Operators_Olattice__class_OInf__fin(_1005913, hAPP(hAPP(c_Set_Oinsert(_1005913), _1005917), _1005915)) = hAPP(hAPP(c_Finite__Set_Ofold(_1005913, _1005913, c_Lattices_Osemilattice__inf__class_Oinf(_1005913)), _1005917), _1005915))], (36645 ^ _776545) ^ [_1471311, _1471313, _1471315] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471311, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471311), _1471313), _1471315), -(_1471313 = c_Orderings_Obot__class_Obot(tc_fun(_1471311, tc_HOL_Obool)))], (52001 ^ _776545) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (26585 ^ _776545) ^ [_1256427] : [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, _1256427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256427)))], (7298 ^ _776545) ^ [_895926, _895928, _895930, _895932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895926, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_895926), _895928), _895930)), _895932)), 7301 ^ _776545 : [(7304 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895926, tc_HOL_Obool)), _895930), _895932)))], (7302 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895926), _895928), _895932)))]]], (31593 ^ _776545) ^ [_1343765, _1343767, _1343769, _1343771] : [class_Orderings_Olinorder(_1343765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343765), _1343767), _1343769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343765), _1343767), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343765), _1343769), _1343771))))], (38807 ^ _776545) ^ [_1522961, _1522963, _1522965, _1522967, _1522969, _1522971] : [-(hBOOL(hAPP(hAPP(c_member(_1522961), _1522963), _1522965))), 38810 ^ _776545 : [(38817 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522961), _1522967), _1522965))), -(hAPP(c_Set_Ovimage(_1522969, _1522961, hAPP(hAPP(c_COMBC(_1522969, _1522961, _1522961), hAPP(hAPP(c_COMBC(_1522969, _1522961, tc_fun(_1522961, _1522961)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1522961, tc_fun(_1522961, 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hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368550, tc_HOL_Obool)), _1368552)), _1368558)))], (7554 ^ _776545) ^ [_901147, _901149, _901151, _901153] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901147, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901147, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901147, tc_HOL_Obool)), _901149), _901151)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901147, tc_HOL_Obool)), _901151), _901153))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901147, tc_HOL_Obool)), _901153), _901149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901147, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_901147, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901147, tc_HOL_Obool)), _901149), _901151)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901147, tc_HOL_Obool)), _901151), _901153))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901147, tc_HOL_Obool)), _901153), _901149)))], (16677 ^ _776545) ^ [_1076540, _1076542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076540), _1076542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076540)), _1076542)))], (39195 ^ _776545) ^ [_1533083, _1533085, _1533087, _1533089, _1533091, _1533093] : [hBOOL(hAPP(hAPP(c_member(_1533083), _1533085), _1533087)), 39198 ^ _776545 : [(39205 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533089, tc_HOL_Obool)), _1533091), _1533093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533089, _1533083), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533089, _1533083), _1533091), hAPP(c_COMBK(tc_fun(_1533083, tc_HOL_Obool), _1533089), _1533087))), hAPP(hAPP(c_Product__Type_OSigma(_1533089, _1533083), _1533093), hAPP(c_COMBK(tc_fun(_1533083, tc_HOL_Obool), _1533089), _1533087)))))], (39199 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533089, _1533083), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533089, _1533083), _1533091), hAPP(c_COMBK(tc_fun(_1533083, tc_HOL_Obool), _1533089), _1533087))), hAPP(hAPP(c_Product__Type_OSigma(_1533089, _1533083), _1533093), hAPP(c_COMBK(tc_fun(_1533083, tc_HOL_Obool), _1533089), _1533087)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533089, tc_HOL_Obool)), _1533091), _1533093)))]]], (12538 ^ _776545) ^ [_997084, _997086, _997088] : [class_Lattices_Olattice(_997084), hAPP(_997086, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997084), 12543 ^ [_997084, _997086, _997088]), 12544 ^ [_997084, _997086, _997088])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_997084), hAPP(_997086, 12543 ^ [_997084, _997086, _997088])), hAPP(_997086, 12544 ^ [_997084, _997086, _997088])), hBOOL(hAPP(c_Finite__Set_Ofinite(_997084), 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(44575 ^ _776545) ^ [_1668142, _1668144, _1668146] : [-(_1668142 = c_List_Olist_ONil(_1668144)), -(c_List_Olast(_1668144, hAPP(hAPP(c_List_Olist_OCons(_1668144), _1668146), _1668142)) = c_List_Olast(_1668144, _1668142))], (33168 ^ _776545) ^ [_1384140, _1384142, _1384144] : [hBOOL(hAPP(hAPP(c_member(_1384140), _1384142), hAPP(c_Set_OCollect(_1384140), _1384144))), -(hBOOL(hAPP(_1384144, _1384142)))], (52057 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (34123 ^ _776545) ^ [_1410564, _1410566] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410564) = hAPP(c_Nat_OSuc, _1410566), -(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(_1410564))), 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)), _1410566))))))], (38290 ^ _776545) ^ [_1509984, _1509986, _1509988] : [c_Wellfounded_Owf(_1509984, _1509986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509984, tc_HOL_Obool)), _1509988), hAPP(c_Relation_OImage(_1509984, _1509984, _1509986), _1509988))), -(_1509988 = c_Orderings_Obot__class_Obot(tc_fun(_1509984, tc_HOL_Obool)))], (47130 ^ _776545) ^ [_1723893, _1723895, _1723897] : [-(hAPP(c_List_Orotate(_1723893, _1723895), hAPP(c_List_Orev(_1723893), _1723897)) = hAPP(c_List_Orev(_1723893), hAPP(c_List_Orotate(_1723893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723893)), _1723897)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723895, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723893)), _1723897)))), _1723897)))], (33018 ^ _776545) ^ [_1379370, _1379372, _1379374, _1379376, _1379378, _1379380] : [hBOOL(hAPP(hAPP(c_member(_1379370), _1379372), _1379374)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379370, tc_fun(_1379376, tc_HOL_Obool)), _1379374), hAPP(hAPP(c_COMBB(tc_fun(_1379376, tc_HOL_Obool), tc_fun(_1379376, tc_HOL_Obool), _1379370), hAPP(c_Set_Oinsert(_1379376), _1379378)), _1379380)) = hAPP(hAPP(c_Set_Oinsert(_1379376), _1379378), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379370, tc_fun(_1379376, tc_HOL_Obool)), _1379374), _1379380)))], (29579 ^ _776545) ^ [_1306459, _1306461, _1306463] : [class_Int_Onumber__ring(_1306459), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306459), _1306461), _1306463)), 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(_1306459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306459), hAPP(hAPP(c_Power_Opower__class_Opower(_1306459), _1306461), 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(_1306459), _1306463), 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(_1306459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306459), hAPP(c_Int_Onumber__class_Onumber__of(_1306459), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1306461)), _1306463)))], (32636 ^ _776545) ^ [_1368749, _1368751, _1368753, _1368755, _1368757, _1368759, _1368761] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368749, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368751, tc_fun(_1368749, tc_HOL_Obool)), _1368753), _1368755)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368757, tc_fun(_1368749, tc_HOL_Obool)), _1368759), _1368761)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368751, tc_fun(_1368749, tc_HOL_Obool)), _1368753), hAPP(hAPP(c_COMBB(tc_fun(_1368757, tc_fun(_1368749, tc_HOL_Obool)), tc_fun(_1368749, tc_HOL_Obool), _1368751), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368757, tc_fun(_1368749, tc_HOL_Obool)), _1368759)), hAPP(hAPP(c_COMBC(_1368751, tc_fun(_1368757, tc_fun(_1368749, tc_HOL_Obool)), tc_fun(_1368757, tc_fun(_1368749, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368749, tc_HOL_Obool), tc_fun(_1368749, tc_HOL_Obool)), tc_fun(tc_fun(_1368757, tc_fun(_1368749, tc_HOL_Obool)), tc_fun(_1368757, tc_fun(_1368749, tc_HOL_Obool))), _1368751), c_COMBB(tc_fun(_1368749, tc_HOL_Obool), tc_fun(_1368749, tc_HOL_Obool), _1368757)), hAPP(hAPP(c_COMBB(tc_fun(_1368749, tc_HOL_Obool), tc_fun(tc_fun(_1368749, tc_HOL_Obool), tc_fun(_1368749, tc_HOL_Obool)), _1368751), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368749, tc_HOL_Obool))), _1368755))), _1368761))))], (46030 ^ _776545) ^ [_1700910, _1700912] : [-(c_List_Oconcat(_1700910, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700910), tc_List_Olist(_1700910)), c_List_Olist_Olist__case(tc_List_Olist(_1700910), _1700910, c_List_Olist_ONil(_1700910), hAPP(hAPP(c_COMBB(tc_List_Olist(_1700910), tc_fun(tc_List_Olist(_1700910), tc_List_Olist(_1700910)), _1700910), c_COMBK(tc_List_Olist(_1700910), tc_List_Olist(_1700910))), hAPP(hAPP(c_COMBC(_1700910, tc_List_Olist(_1700910), tc_List_Olist(_1700910)), c_List_Olist_OCons(_1700910)), c_List_Olist_ONil(_1700910))))), _1700912)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700910), _1700910), c_List_Ohd(_1700910)), hAPP(c_List_Ofilter(tc_List_Olist(_1700910), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700910)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700910), tc_List_Olist(_1700910), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700910)))), _1700912)))], (48903 ^ _776545) ^ [_1762419, _1762421, _1762423, _1762425] : [48904 ^ _776545 : [(48907 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762419), _1762423), _1762425))], (48905 ^ _776545) ^ [] : [_1762421 = _1762425]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1762419), hAPP(hAPP(c_List_Olist_OCons(_1762419), _1762421), _1762423)), _1762425)))], (22431 ^ _776545) ^ [] : [-(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))))], (36454 ^ _776545) ^ [_1465641, _1465643, _1465645, _1465647] : [-(hAPP(c_Relation_OImage(_1465641, _1465643, _1465645), hAPP(hAPP(c_Set_Oinsert(_1465641), _1465647), c_Orderings_Obot__class_Obot(tc_fun(_1465641, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1465643), hAPP(hAPP(c_COMBC(_1465643, tc_fun(tc_prod(_1465641, _1465643), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1465641, _1465643), tc_fun(tc_fun(tc_prod(_1465641, _1465643), tc_HOL_Obool), tc_HOL_Obool), _1465643), c_member(tc_prod(_1465641, _1465643))), hAPP(c_Product__Type_OPair(_1465641, _1465643), _1465647))), _1465645)))], (27259 ^ _776545) ^ [_1266922, _1266924] : [class_Groups_Oordered__ab__group__add__abs(_1266922), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266922), _1266924), hAPP(c_Groups_Oabs__class_Oabs(_1266922), _1266924))))], (44503 ^ _776545) ^ [_1666716, _1666718, _1666720] : [class_Orderings_Olinorder(_1666716), hBOOL(hAPP(hAPP(c_member(_1666716), _1666718), hAPP(c_List_Oset(_1666716), _1666720))), -(c_List_Olinorder__class_Oinsort__insert__key(_1666716, _1666716, c_COMBI(_1666716), _1666718, _1666720) = _1666720)], (6198 ^ _776545) ^ [_876127, _876129, _876131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876127, tc_HOL_Obool)), _876129), _876131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876127, tc_HOL_Obool)), _876131), _876129)), -(_876129 = _876131)], (26755 ^ _776545) ^ [_1259150, _1259152] : [c_Nat__Transfer_Onat__set(_1259150), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1259152), _1259150)), -(c_Nat__Transfer_Ois__nat(_1259152))], (2420 ^ _776545) ^ [_812036, _812038, _812040, _812042, _812044, _812046, _812048, _812050] : [-(c_Nitpick_Opair__box_OPairBox(_812050, _812046, _812042, _812038) = c_Nitpick_Opair__box_OPairBox(_812048, _812044, _812040, _812036)), _812050 = _812048, _812046 = _812044, _812042 = _812040, _812038 = _812036], (14889 ^ _776545) ^ [_1045070, _1045072, _1045074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045070), _1045072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045074), _1045072)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045074), _1045070))))], (27629 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (46704 ^ _776545) ^ [_1715118, _1715120, _1715122] : [class_Orderings_Olinorder(_1715118), -(c_List_Olinorder__class_Osorted(_1715118, hAPP(c_List_Ofilter(_1715118, hAPP(hAPP(c_COMBC(_1715118, _1715118, tc_HOL_Obool), c_fequal), hAPP(_1715120, _1715122))), _1715122)))], (35074 ^ _776545) ^ [_1431179, _1431181] : [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), _1431179), _1431181))), 35077 ^ _776545 : [(35086 ^ _776545) ^ [] : [-(c_Divides_OnegDivAlg(_1431179, _1431181) = hAPP(c_Divides_Oadjust(_1431181), c_Divides_OnegDivAlg(_1431179, 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)))), _1431181)))), -(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), _1431179), _1431181)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431181), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35078 ^ _776545) ^ [] : [35079 ^ _776545 : [(35082 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431181), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35080 ^ _776545) ^ [] : [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), _1431179), _1431181)))]], -(c_Divides_OnegDivAlg(_1431179, _1431181) = 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), _1431179), _1431181)))]]], (31052 ^ _776545) ^ [_1333798, _1333800, _1333802] : [class_Orderings_Olinorder(_1333798), hAPP(_1333800, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333798), 31057 ^ [_1333798, _1333800, _1333802]), 31058 ^ [_1333798, _1333800, _1333802])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1333798), hAPP(_1333800, 31057 ^ [_1333798, _1333800, _1333802])), hAPP(_1333800, 31058 ^ [_1333798, _1333800, _1333802])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333798), _1333802)), -(_1333802 = c_Orderings_Obot__class_Obot(tc_fun(_1333798, tc_HOL_Obool))), -(hAPP(_1333800, c_Big__Operators_Olattice_OInf__fin(_1333798, c_Orderings_Oord__class_Omin(_1333798), _1333802)) = c_Big__Operators_Olattice_OInf__fin(_1333798, c_Orderings_Oord__class_Omin(_1333798), hAPP(c_Set_Oimage(_1333798, _1333798, _1333800), _1333802)))], (27164 ^ _776545) ^ [_1265458] : [c_Nat__Transfer_Onat__set(_1265458), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1265458) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265458)))], (46097 ^ _776545) ^ [_1702413, _1702415, _1702417, _1702419, _1702421] : [-(hAPP(c_List_Ofilter(_1702413, _1702415), hAPP(hAPP(c_List_Omap(_1702417, _1702413), _1702419), _1702421)) = hAPP(hAPP(c_List_Omap(_1702417, _1702413), _1702419), hAPP(c_List_Ofilter(_1702417, hAPP(c_Fun_Ocomp(_1702413, tc_HOL_Obool, _1702417, _1702415), _1702419)), _1702421)))], (15075 ^ _776545) ^ [_1048771, _1048773] : [class_Rings_Ocomm__semiring__1(_1048771), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048771), _1048773), c_Groups_Oone__class_Oone(_1048771)) = _1048773)], (46297 ^ _776545) ^ [_1707776, _1707778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707776), _1707778)), -(c_List_Oupt(_1707776, _1707778) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1707776), c_List_Oupt(hAPP(c_Nat_OSuc, _1707776), _1707778)))], (40086 ^ _776545) ^ [_1557147, _1557149, _1557151, _1557153, _1557155, _1557157] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557147, _1557149), _1557147, tc_prod(_1557151, _1557153), c_Product__Type_Ofst(_1557147, _1557149)), c_Product__Type_Omap__pair(_1557151, _1557147, _1557153, _1557149, _1557155, _1557157)) = hAPP(c_Fun_Ocomp(_1557151, _1557147, tc_prod(_1557151, _1557153), _1557155), c_Product__Type_Ofst(_1557151, _1557153)))], (32870 ^ _776545) ^ [_1375424, _1375426, _1375428, _1375430, _1375432] : [hBOOL(hAPP(hAPP(c_member(_1375424), _1375426), _1375428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375430, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1375424, tc_fun(_1375430, tc_HOL_Obool)), _1375428), _1375432)), hAPP(_1375432, _1375426))))], (37878 ^ _776545) ^ [_1498611, _1498613, _1498615, _1498617, _1498619] : [c_Fun_Oinj__on(_1498611, _1498613, _1498615, _1498617), hBOOL(hAPP(hAPP(c_member(_1498613), _1498619), hAPP(c_Set_Oimage(_1498611, _1498613, _1498615), _1498617))), -(hAPP(_1498615, hAPP(c_Fun_Othe__inv__into(_1498611, _1498613, _1498617, _1498615), _1498619)) = _1498619)], (10236 ^ _776545) ^ [_952429, _952431, _952433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_952429, tc_HOL_Obool)), _952431), _952433)), -(hBOOL(hAPP(hAPP(c_member(_952429), 10239 ^ [_952429, _952431, _952433]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952429, tc_HOL_Obool)), _952433), _952431))))], (33699 ^ _776545) ^ [_1399351, _1399353, _1399355] : [-(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)), _1399351)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1399353), _1399355)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399353), _1399351)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399355), _1399351)))], (15216 ^ _776545) ^ [_1051092, _1051094, _1051096] : [class_Rings_Ocomm__semiring__1(_1051092), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051092), _1051094), _1051096)), _1051096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051092), _1051094), c_Groups_Oone__class_Oone(_1051092))), _1051096))], (33503 ^ _776545) ^ [_1392933, _1392935, _1392937, _1392939, _1392941] : [-(_1392933 = c_Orderings_Obot__class_Obot(tc_fun(_1392935, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1392937), _1392939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392935, tc_fun(_1392937, tc_HOL_Obool)), _1392933), _1392941)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392935, tc_fun(_1392937, tc_HOL_Obool)), _1392933), hAPP(hAPP(c_COMBB(tc_fun(_1392937, tc_HOL_Obool), tc_fun(_1392937, tc_HOL_Obool), _1392935), hAPP(c_Set_Oinsert(_1392937), _1392939)), _1392941)))], (33979 ^ _776545) ^ [_1407206, _1407208, _1407210] : [class_Int_Onumber__ring(_1407206), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1407206), hAPP(c_Int_Onumber__class_Onumber__of(_1407206), _1407208)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1407210))) = hAPP(hAPP(c_HOL_OLet(_1407206, _1407206), hAPP(hAPP(c_Power_Opower__class_Opower(_1407206), hAPP(c_Int_Onumber__class_Onumber__of(_1407206), _1407208)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407210))), hAPP(hAPP(c_COMBS(_1407206, _1407206, _1407206), c_Groups_Otimes__class_Otimes(_1407206)), c_COMBI(_1407206))))], (20797 ^ _776545) ^ [_1152013, _1152015, _1152017, _1152019, _1152021] : [class_Fields_Ofield(_1152013), -(_1152015 = c_Groups_Ozero__class_Ozero(_1152013)), -(_1152017 = c_Groups_Ozero__class_Ozero(_1152013)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152013), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152013), _1152019), _1152015)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152013), _1152021), _1152017)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152013), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152013), _1152019), _1152017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152013), _1152021), _1152015))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152013), _1152015), _1152017)))], (42065 ^ _776545) ^ [_1609636, _1609638, _1609640, _1609642, _1609644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609636), tc_List_Olist(_1609636))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609636), tc_List_Olist(_1609636)), hAPP(hAPP(c_List_Olist_OCons(_1609636), _1609638), _1609640)), _1609642)), c_List_Olistrel(_1609636, _1609644))), 42070 ^ _776545 : [(42075 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609636), tc_List_Olist(_1609636))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609636), tc_List_Olist(_1609636)), _1609640), 42069 ^ [_1609636, _1609638, _1609640, _1609642, _1609644])), c_List_Olistrel(_1609636, _1609644))))], (42073 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609636, _1609636)), hAPP(hAPP(c_Product__Type_OPair(_1609636, _1609636), _1609638), 42068 ^ [_1609636, _1609638, _1609640, _1609642, _1609644])), _1609644)))], (42071 ^ _776545) ^ [] : [-(_1609642 = hAPP(hAPP(c_List_Olist_OCons(_1609636), 42068 ^ [_1609636, _1609638, _1609640, _1609642, _1609644]), 42069 ^ [_1609636, _1609638, _1609640, _1609642, _1609644]))]]], (1058 ^ _776545) ^ [_792514, _792516, _792518, _792520, _792522, _792524, _792526, _792528, _792530, _792532] : [-(c_Finite__Set_Ofolding__image(_792530, _792526, _792522, _792518, _792514)), c_Finite__Set_Ofolding__image(_792532, _792528, _792524, _792520, _792516), _792532 = _792530, _792528 = _792526, _792524 = _792522, _792520 = _792518, _792516 = _792514], (41412 ^ _776545) ^ [_1589790, _1589792, _1589794] : [c_Wellfounded_Owf(_1589790, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589790, _1589790), tc_HOL_Obool), _1589792), _1589794)), -(c_Wellfounded_Owf(_1589790, _1589794))], (18123 ^ _776545) ^ [_1102399, _1102401] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1102399), hAPP(c_Nat_OSuc, _1102401)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1102399, _1102401))], (40088 ^ _776545) ^ [_1557218, _1557220, _1557222, _1557224, _1557226, _1557228] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557218, tc_fun(_1557220, tc_HOL_Obool)), _1557222), hAPP(c_Fun_Ocomp(_1557224, tc_fun(_1557220, tc_HOL_Obool), _1557218, _1557226), _1557228)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557224, tc_fun(_1557220, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1557218, _1557224, _1557228), _1557222)), _1557226))], (49720 ^ _776545) ^ [_1781454, _1781456] : [c_Relation_Osym(_1781454, _1781456), -(c_Relation_Osym(_1781454, c_Transitive__Closure_Otrancl(_1781454, _1781456)))], (15156 ^ _776545) ^ [_1050100, _1050102] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050100), _1050102) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15159 ^ _776545 : [(15162 ^ _776545) ^ [] : [-(_1050102 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15160 ^ _776545) ^ [] : [-(_1050100 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (33913 ^ _776545) ^ [_1405088, _1405090, _1405092, _1405094, _1405096] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405088, tc_fun(_1405090, tc_HOL_Obool)), _1405092), hAPP(hAPP(c_COMBS(_1405088, tc_fun(_1405090, tc_HOL_Obool), tc_fun(_1405090, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1405090, tc_HOL_Obool), tc_fun(tc_fun(_1405090, tc_HOL_Obool), tc_fun(_1405090, tc_HOL_Obool)), _1405088), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405090, tc_HOL_Obool))), _1405094)), _1405096)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405090, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1405090, tc_HOL_Obool), hAPP(c_Set_Oimage(_1405088, tc_fun(_1405090, tc_HOL_Obool), _1405094), _1405092))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1405090, tc_HOL_Obool), hAPP(c_Set_Oimage(_1405088, tc_fun(_1405090, tc_HOL_Obool), _1405096), _1405092))))], (5166 ^ _776545) ^ [_855363, _855365, _855367, _855369] : [-(c_Quotient_ORespects(_855369, _855365) = c_Quotient_ORespects(_855367, _855363)), _855369 = _855367, _855365 = _855363], (43458 ^ _776545) ^ [_1643109, _1643111, _1643113, _1643115] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643109)), hAPP(hAPP(c_List_Oappend(_1643109), _1643111), _1643113)), c_List_Olists(_1643109, _1643115))), 43461 ^ _776545 : [(43464 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643109)), _1643113), c_List_Olists(_1643109, _1643115))))], (43462 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1643109)), _1643111), c_List_Olists(_1643109, _1643115))))]]], (6925 ^ _776545) ^ [_888939, _888941, _888943] : [class_Orderings_Olinorder(_888939), 6928 ^ _776545 : [(6935 ^ _776545) ^ [] : [_888941 = _888943, -(hAPP(c_SetInterval_Oord__class_OatLeast(_888939), _888941) = hAPP(c_SetInterval_Oord__class_OatLeast(_888939), _888943))], (6929 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_888939), _888941) = hAPP(c_SetInterval_Oord__class_OatLeast(_888939), _888943), -(_888941 = _888943)]]], (52179 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (43673 ^ _776545) ^ [_1647553, _1647555, _1647557, _1647559] : [-(hAPP(hAPP(c_List_Otake(_1647553), _1647555), hAPP(hAPP(c_List_Oappend(_1647553), _1647557), _1647559)) = hAPP(hAPP(c_List_Oappend(_1647553), hAPP(hAPP(c_List_Otake(_1647553), _1647555), _1647557)), hAPP(hAPP(c_List_Otake(_1647553), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647555), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647553)), _1647557))), _1647559)))], (32642 ^ _776545) ^ [_1369146, _1369148, _1369150, _1369152, _1369154] : [class_Lattices_Olattice(_1369146), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369148, _1369146)), _1369150), _1369152), _1369154) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369146), hAPP(_1369150, _1369154)), hAPP(_1369152, _1369154)))], (7286 ^ _776545) ^ [_895665, _895667, _895669] : [_895667 = _895669, -(hBOOL(hAPP(hAPP(c_member(_895665), _895667), hAPP(hAPP(c_Set_Oinsert(_895665), _895669), c_Orderings_Obot__class_Obot(tc_fun(_895665, tc_HOL_Obool))))))], (43080 ^ _776545) ^ [_1634954, _1634956, _1634958, _1634960] : [-(c_List_Oremove1(_1634954, _1634956, c_List_Oremove1(_1634954, _1634958, _1634960)) = c_List_Oremove1(_1634954, _1634958, c_List_Oremove1(_1634954, _1634956, _1634960)))], (10697 ^ _776545) ^ [_960740, _960742, _960744] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960740, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960740, tc_HOL_Obool)), _960742), _960744)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960740, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960740, tc_HOL_Obool)), _960742)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960740, tc_HOL_Obool)), _960744)))], (40629 ^ _776545) ^ [_1569938, _1569940, _1569942, _1569944, _1569946] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569938, _1569938)), hAPP(hAPP(c_Product__Type_OPair(_1569938, _1569938), _1569940), _1569942)), _1569944)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569938, _1569938)), hAPP(hAPP(c_Product__Type_OPair(_1569938, _1569938), _1569942), _1569946)), _1569944)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569938, _1569938)), hAPP(hAPP(c_Product__Type_OPair(_1569938, _1569938), _1569940), _1569946)), c_Transitive__Closure_Otrancl(_1569938, _1569944))))], (42917 ^ _776545) ^ [_1631668, _1631670] : [42919 ^ _776545 : [(42923 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42921 ^ [_1631668, _1631670]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631668)), _1631670))))], (42925 ^ _776545) ^ [] : [42918 ^ [_1631668, _1631670] = 42921 ^ [_1631668, _1631670]], (42927 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1631668), _1631670), 42918 ^ [_1631668, _1631670]) = hAPP(hAPP(c_List_Onth(_1631668), _1631670), 42921 ^ [_1631668, _1631670]))], (42920 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42918 ^ [_1631668, _1631670]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631668)), _1631670))))]], -(hBOOL(hAPP(c_List_Odistinct(_1631668), _1631670)))], (8393 ^ _776545) ^ [_920609, _920611, _920613] : [class_Lattices_Osemilattice__inf(_920609), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920609), _920611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920609), _920611), _920613)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920609), _920611), _920613))], (6382 ^ _776545) ^ [_879533, _879535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879533, tc_HOL_Obool)), _879535), _879535)))], (45814 ^ _776545) ^ [_1695703, _1695705] : [_1695705 = c_List_Olist_ONil(_1695703), -(c_List_Olist_ONil(_1695703) = c_List_Oremdups(_1695703, _1695705))], (44926 ^ _776545) ^ [_1676040, _1676042, _1676044, _1676046] : [-(hBOOL(hAPP(c_List_Odistinct(_1676040), hAPP(hAPP(c_List_Omap(_1676042, _1676040), _1676044), _1676046)))), hBOOL(hAPP(c_List_Odistinct(_1676042), _1676046)), c_Fun_Oinj__on(_1676042, _1676040, _1676044, hAPP(c_List_Oset(_1676042), _1676046))], (25197 ^ _776545) ^ [_1232747, _1232749] : [class_Int_Onumber__ring(_1232747), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232747), _1232749), hAPP(c_Int_Onumber__class_Onumber__of(_1232747), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1232747), _1232749))], (42671 ^ _776545) ^ [_1626163, _1626165, _1626167, _1626169, _1626171] : [-(_1626163 = _1626165), -(hAPP(hAPP(c_List_Onth(_1626167), hAPP(hAPP(c_List_Olist__update(_1626167, _1626169), _1626163), _1626171)), _1626165) = hAPP(hAPP(c_List_Onth(_1626167), _1626169), _1626165))], (46291 ^ _776545) ^ [_1707650, _1707652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707650), _1707652)), -(c_List_Oupt(_1707650, _1707652) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1707650), c_List_Oupt(hAPP(c_Nat_OSuc, _1707650), _1707652)))], (5662 ^ _776545) ^ [_862999, _863001, _863003, _863005] : [-(hAPP(_863005, _863001) = hAPP(_863003, _862999)), _863005 = _863003, _863001 = _862999], (38998 ^ _776545) ^ [_1527429, _1527431, _1527433, _1527435, _1527437] : [hBOOL(hAPP(hAPP(_1527429, _1527431), _1527433)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1527435, _1527437, _1527429), _1527431)))], (50873 ^ _776545) ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651] : [50876 ^ _776545 : [(50883 ^ _776545) ^ [] : [hAPP(hAPP(_1806649, 50874 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651]), 50878 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651]) = hAPP(hAPP(_1806649, 50875 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651]), 50879 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651])], (50881 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806645, _1806645)), hAPP(hAPP(c_Product__Type_OPair(_1806645, _1806645), 50878 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651]), 50879 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651])), _1806647)))], (50877 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806641, _1806641)), hAPP(hAPP(c_Product__Type_OPair(_1806641, _1806641), 50874 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651]), 50875 ^ [_1806641, _1806643, _1806645, _1806647, _1806649, _1806651])), _1806643)))]], -(c_Equiv__Relations_Ocongruent2(_1806641, _1806645, _1806651, _1806643, _1806647, _1806649))], (42931 ^ _776545) ^ [_1632100, _1632102] : [class_Groups_Ocomm__monoid__add(_1632100), hBOOL(hAPP(c_List_Odistinct(_1632100), _1632102)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1632100), _1632102) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1632100, _1632100), c_COMBI(_1632100)), hAPP(c_List_Oset(_1632100), _1632102)))], (33723 ^ _776545) ^ [_1399979, _1399981, _1399983, _1399985, _1399987] : [class_Groups_Ocomm__monoid__add(_1399979), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399981), _1399983)), 33730 ^ _776545 : [(33737 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399981), _1399985), _1399983))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399981, _1399979), hAPP(hAPP(c_COMBC(_1399981, _1399979, _1399979), hAPP(hAPP(c_COMBS(_1399981, _1399979, tc_fun(_1399979, _1399979)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399979, tc_fun(_1399979, _1399979)), _1399981), c_If(_1399979)), hAPP(hAPP(c_COMBC(_1399981, _1399981, tc_HOL_Obool), c_fequal), _1399985))), _1399987)), c_Groups_Ozero__class_Ozero(_1399979))), _1399983) = c_Groups_Ozero__class_Ozero(_1399979))], (33731 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399981), _1399985), _1399983)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1399981, _1399979), hAPP(hAPP(c_COMBC(_1399981, _1399979, _1399979), hAPP(hAPP(c_COMBS(_1399981, _1399979, tc_fun(_1399979, _1399979)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1399979, tc_fun(_1399979, _1399979)), _1399981), c_If(_1399979)), hAPP(hAPP(c_COMBC(_1399981, _1399981, tc_HOL_Obool), c_fequal), _1399985))), _1399987)), c_Groups_Ozero__class_Ozero(_1399979))), _1399983) = hAPP(_1399987, _1399985))]]], (28389 ^ _776545) ^ [_1286176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286176)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286176), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21255 ^ _776545) ^ [_1161002, _1161004, _1161006, _1161008] : [class_Int_Onumber__ring(_1161002), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161002), hAPP(c_Int_Onumber__class_Onumber__of(_1161002), _1161004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161002), hAPP(c_Int_Onumber__class_Onumber__of(_1161002), _1161006)), _1161008)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161002), hAPP(c_Int_Onumber__class_Onumber__of(_1161002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161004), _1161006))), _1161008))], (49572 ^ _776545) ^ [_1778310] : [-(c_Relation_Oantisym(_1778310, c_Relation_OId(_1778310)))], (46962 ^ _776545) ^ [_1720414, _1720416] : [hBOOL(hAPP(c_List_Odistinct(_1720414), _1720416)), -(hBOOL(hAPP(c_List_Odistinct(_1720414), hAPP(c_List_Orev(_1720414), _1720416))))], (16602 ^ _776545) ^ [_1075178] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075178)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075178)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1075178)))], (52143 ^ _776545) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (47599 ^ _776545) ^ [_1733749, _1733751, _1733753] : [hBOOL(hAPP(hAPP(c_member(_1733749), _1733751), hAPP(c_List_Oset(_1733749), _1733753))), -(c_List_Oinsert(_1733749, _1733751, _1733753) = _1733753)], (23185 ^ _776545) ^ [] : [-(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))))], (11469 ^ _776545) ^ [_976877, _976879, _976881] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_976877), _976879)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_976877), hAPP(hAPP(c_Set_Oinsert(_976877), _976881), _976879))))], (24305 ^ _776545) ^ [_1216097] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1216097)) = 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), _1216097)))], (33220 ^ _776545) ^ [_1385353, _1385355, _1385357, _1385359] : [class_Complete__Lattice_Ocomplete__lattice(_1385353), -(_1385355 = c_Orderings_Obot__class_Obot(tc_fun(_1385357, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385357, _1385353), _1385355), hAPP(c_COMBK(_1385353, _1385357), _1385359)) = _1385359)], (36589 ^ _776545) ^ [_1469893, _1469895] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1469893, _1469893)), hAPP(hAPP(c_Product__Type_OPair(_1469893, _1469893), 36590 ^ [_1469893, _1469895]), 36590 ^ [_1469893, _1469895])), _1469895))), -(c_Relation_Oirrefl(_1469893, _1469895))], (47084 ^ _776545) ^ [_1722915, _1722917] : [class_Groups_Ocomm__monoid__add(_1722915), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722915), hAPP(c_List_Orev(_1722915), _1722917)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1722915), _1722917))], (50908 ^ _776545) ^ [_1807633] : [-(c_Lazy__Sequence_Oflat(_1807633, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1807633))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1807633))], (49127 ^ _776545) ^ [_1767705, _1767707, _1767709, _1767711, _1767713, _1767715, _1767717] : [hBOOL(hAPP(hAPP(_1767705, hAPP(c_Product__Type_Osnd(_1767707, _1767709), _1767711)), hAPP(c_Product__Type_Ofst(_1767707, _1767709), _1767711))), 49134 ^ _776545 : [(49137 ^ _776545) ^ [] : [hBOOL(hAPP(_1767713, hAPP(hAPP(_1767715, 49132 ^ [_1767705, _1767707, _1767709, _1767711, _1767713, _1767715, _1767717]), 49133 ^ [_1767705, _1767707, _1767709, _1767711, _1767713, _1767715, _1767717])))], (49135 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1767705, 49133 ^ [_1767705, _1767707, _1767709, _1767711, _1767713, _1767715, _1767717]), 49132 ^ [_1767705, _1767707, _1767709, _1767711, _1767713, _1767715, _1767717])))]], -(hBOOL(hAPP(_1767713, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1767707, _1767709, _1767717), _1767715), _1767711))))], (32712 ^ _776545) ^ [_1370838, _1370840] : [-(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), _1370838)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1370840))))))], (2172 ^ _776545) ^ [_808056, _808058] : [_808058 = _808056, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808058) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808056))], (15680 ^ _776545) ^ [_1060879] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060879)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1060879)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1060879), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (33549 ^ _776545) ^ [_1393915, _1393917, _1393919, _1393921] : [33551 ^ _776545 : [(33554 ^ _776545) ^ [] : [hAPP(_1393921, 33550 ^ [_1393915, _1393917, _1393919, _1393921]) = c_Orderings_Otop__class_Otop(tc_fun(_1393915, tc_HOL_Obool))], (33552 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1393917), 33550 ^ [_1393915, _1393917, _1393919, _1393921]), _1393919)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1393915, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393917, tc_fun(_1393915, tc_HOL_Obool)), _1393919), _1393921))], (33282 ^ _776545) ^ [_1386725, _1386727, _1386729, _1386731] : [class_Complete__Lattice_Ocomplete__lattice(_1386725), -(_1386727 = c_Orderings_Obot__class_Obot(tc_fun(_1386729, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386729, _1386725), _1386727), hAPP(c_COMBK(_1386725, _1386729), _1386731)) = _1386731)], (32358 ^ _776545) ^ [_1358602, _1358604, _1358606, _1358608] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1358606), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358602, tc_fun(_1358606, tc_HOL_Obool)), _1358604), _1358608)))), 32359 ^ _776545 : [(32360 ^ _776545) ^ [_1358676] : [hBOOL(hAPP(hAPP(c_member(_1358602), _1358676), _1358604)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358606), hAPP(_1358608, _1358676)))]]], (2902 ^ _776545) ^ [_819587, _819589, _819591, _819593, _819595, _819597] : [-(c_Product__Type_Ointernal__split(_819597, _819593, _819589) = c_Product__Type_Ointernal__split(_819595, _819591, _819587)), _819597 = _819595, _819593 = _819591, _819589 = _819587], (50385 ^ _776545) ^ [_1795227, _1795229, _1795231, _1795233, _1795235] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1795227, _1795229, tc_HOL_Obool, _1795231), _1795233), _1795235)), -(hBOOL(hAPP(_1795231, hAPP(hAPP(c_Product__Type_OPair(_1795227, _1795229), _1795233), _1795235))))], (35312 ^ _776545) ^ [_1435285, _1435287, _1435289, _1435291, _1435293, _1435295] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435285, _1435287), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435289), _1435291))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435285, _1435287), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435293), _1435295))), -(_1435287 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435291 = _1435295)], (40759 ^ _776545) ^ [_1574056, _1574058] : [-(c_Transitive__Closure_Ortrancl(_1574056, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574056, _1574056), tc_HOL_Obool)), _1574058), c_Relation_OId(_1574056))) = c_Transitive__Closure_Ortrancl(_1574056, _1574058))], (52467 ^ _776545) ^ [_1830976, _1830978, _1830980, _1830982] : [-(hAPP(hAPP(c_COMBK(_1830976, _1830978), _1830980), _1830982) = _1830980)], (40845 ^ _776545) ^ [_1576132, _1576134, _1576136] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1576132, _1576134, _1576134), _1576136), c_Relation_OId(_1576134)) = _1576136)], (51747 ^ _776545) ^ [_1822930, _1822932] : [51754 ^ _776545 : [(51757 ^ _776545) ^ [] : [_1822930 = _1822932], (51755 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822930), _1822932)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822930), _1822932)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822932), _1822930)))], (37214 ^ _776545) ^ [_1484852, _1484854, _1484856] : [-(c_Fun_Oinj__on(_1484852, _1484854, _1484856, c_Orderings_Obot__class_Obot(tc_fun(_1484852, tc_HOL_Obool))))], (4438 ^ _776545) ^ [_843921, _843923, _843925, _843927] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_843927, _843923) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_843925, _843921)), _843927 = _843925, _843923 = _843921], (44435 ^ _776545) ^ [_1665202, _1665204, _1665206] : [class_Orderings_Olinorder(_1665202), -(c_Big__Operators_Olinorder__class_OMin(_1665202, hAPP(c_List_Oset(_1665202), hAPP(hAPP(c_List_Olist_OCons(_1665202), _1665204), _1665206))) = hAPP(c_List_Ofoldl(_1665202, _1665202, c_Orderings_Oord__class_Omin(_1665202), _1665204), _1665206))], (52257 ^ _776545) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (22387 ^ _776545) ^ [_1182405] : [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)), _1182405)), _1182405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (18652 ^ _776545) ^ [_1112332, _1112334, _1112336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1112332)), 18655 ^ _776545 : [(18662 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112334), _1112336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112332), _1112334)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112332), _1112336))))], (18656 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112332), _1112334)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112332), _1112336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112334), _1112336)))]]], (43346 ^ _776545) ^ [_1640459] : [class_Orderings_Olinorder(_1640459), -(c_List_Olinorder__class_Osorted__list__of__set(_1640459, c_Orderings_Obot__class_Obot(tc_fun(_1640459, tc_HOL_Obool))) = c_List_Olist_ONil(_1640459))], (35008 ^ _776545) ^ [_1429812, _1429814, _1429816, _1429818, _1429820] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429812, _1429814), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1429816), _1429818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429820)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1429812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429814), _1429820)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1429816), _1429820)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1429814), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1429816, _1429820))), _1429818)))))], (33251 ^ _776545) ^ [_1386040, _1386042, _1386044, _1386046] : [_1386040 = c_Orderings_Obot__class_Obot(tc_fun(_1386042, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1386042, tc_fun(_1386044, tc_HOL_Obool)), _1386040), hAPP(c_COMBK(tc_fun(_1386044, tc_HOL_Obool), _1386042), _1386046)) = c_Orderings_Obot__class_Obot(tc_fun(_1386044, tc_HOL_Obool)))], (33368 ^ _776545) ^ [_1389168, _1389170, _1389172, _1389174] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389168, tc_fun(_1389170, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1389168, tc_HOL_Obool), _1389172)), _1389174) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1389168, tc_HOL_Obool), tc_fun(_1389170, tc_HOL_Obool)), _1389172), hAPP(hAPP(c_COMBC(tc_fun(_1389168, tc_HOL_Obool), tc_fun(_1389168, tc_fun(_1389170, tc_HOL_Obool)), tc_fun(_1389170, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389168, tc_fun(_1389170, tc_HOL_Obool))), _1389174)))], (51549 ^ _776545) ^ [_1819598, _1819600, _1819602] : [class_Divides_Osemiring__div(_1819598), 51552 ^ _776545 : [(51559 ^ _776545) ^ [] : [c_Divides_Odiv__class_Omod(_1819598, _1819602, _1819600) = c_Groups_Ozero__class_Ozero(_1819598), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819598), _1819600), _1819602)))], (51553 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819598), _1819600), _1819602)), -(c_Divides_Odiv__class_Omod(_1819598, _1819602, _1819600) = c_Groups_Ozero__class_Ozero(_1819598))]]], (13714 ^ _776545) ^ [_1020814, _1020816, _1020818, _1020820] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020814), _1020816), _1020818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020814), _1020820), _1020818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020814), _1020816), _1020820)))], (24321 ^ _776545) ^ [_1216416, _1216418, _1216420] : [class_Rings_Oring__1(_1216416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216418), _1216420)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216420), _1216418)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216416), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216416), _1216420)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216416), _1216418)))], (16979 ^ _776545) ^ [_1082122, _1082124, _1082126, _1082128, _1082130] : [class_Rings_Oordered__semiring(_1082122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082122), _1082124), _1082126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082122), _1082128), _1082130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082122), c_Groups_Ozero__class_Ozero(_1082122)), _1082124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082122), c_Groups_Ozero__class_Ozero(_1082122)), _1082128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082122), _1082124), _1082128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082122), _1082126), _1082130))))], (34870 ^ _776545) ^ [_1427286, _1427288] : [-(c_Divides_Odivmod__nat(_1427288, _1427286) = 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), _1427288), _1427286), _1427286))), -(_1427286 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1427288), _1427286)))], (26525 ^ _776545) ^ [_1255291, _1255293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255291)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255291), _1255293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1255291)), hAPP(c_Int_Onat, _1255293)))], (14787 ^ _776545) ^ [_1043134, _1043136] : [14788 ^ _776545 : [(14789 ^ _776545) ^ [_1043184] : [_1043136 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043134), _1043184)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043134), _1043136)))], (2004 ^ _776545) ^ [_805370, _805372, _805374, _805376, _805378, _805380, _805382, _805384] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_805384, _805380, _805376, _805372) = c_SetInterval_Oord_OgreaterThanLessThan(_805382, _805378, _805374, _805370)), _805384 = _805382, _805380 = _805378, _805376 = _805374, _805372 = _805370], (44731 ^ _776545) ^ [_1670817, _1670819, _1670821, _1670823, _1670825] : [-(hAPP(hAPP(c_List_Odrop(_1670817), _1670819), hAPP(hAPP(c_List_Omap(_1670821, _1670817), _1670823), _1670825)) = hAPP(hAPP(c_List_Omap(_1670821, _1670817), _1670823), hAPP(hAPP(c_List_Odrop(_1670821), _1670819), _1670825)))], (29627 ^ _776545) ^ [_1307554] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1307554, 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, _1307554, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (480 ^ _776545) ^ [_783757, _783759] : [-(c_Nat__Transfer_Onat__set(_783757)), _783759 = _783757, c_Nat__Transfer_Onat__set(_783759)], (52537 ^ _776545) ^ [_1831991, _1831993] : [hBOOL(hAPP(hAPP(c_fdisj, _1831991), _1831993)), -(hBOOL(_1831991)), -(hBOOL(_1831993))], (9074 ^ _776545) ^ [_933401, _933403, _933405, _933407] : [class_Orderings_Opreorder(_933401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933401), _933403), _933405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933401), _933405), _933407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933401), _933403), _933407)))], (39713 ^ _776545) ^ [_1547669, _1547671, _1547673] : [39715 ^ _776545 : [(39718 ^ _776545) ^ [] : [hBOOL(hAPP(_1547671, 39714 ^ [_1547669, _1547671, _1547673]))], (39716 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547669), 39714 ^ [_1547669, _1547671, _1547673]), _1547673)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1547669, _1547671), _1547673)))], (6384 ^ _776545) ^ [_879568, _879570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879568, tc_HOL_Obool)), _879570), c_Orderings_Otop__class_Otop(tc_fun(_879568, tc_HOL_Obool)))))], (44228 ^ _776545) ^ [_1660942, _1660944] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660942)), hAPP(c_List_Otl(_1660942), _1660944)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660942)), _1660944)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (39097 ^ _776545) ^ [_1529841, _1529843, _1529845] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1529841, _1529843), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529841, _1529843), c_Orderings_Otop__class_Otop(tc_fun(_1529841, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1529843, tc_HOL_Obool), _1529841), _1529845))) = hAPP(hAPP(c_Product__Type_OSigma(_1529841, _1529843), c_Orderings_Otop__class_Otop(tc_fun(_1529841, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1529843, tc_HOL_Obool), _1529841), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529843, tc_HOL_Obool)), _1529845))))], (6128 ^ _776545) ^ [_874791, _874793, _874795] : [6136 ^ _776545 : [(6139 ^ _776545) ^ [] : [-(hBOOL(hAPP(_874795, 6135 ^ [_874791, _874793, _874795])))], (6137 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874791), 6135 ^ [_874791, _874793, _874795]), _874793)))]], 6129 ^ _776545 : [(6130 ^ _776545) ^ [_874866] : [hBOOL(hAPP(hAPP(c_member(_874791), _874866), _874793)), hBOOL(hAPP(_874795, _874866))]]], (51991 ^ _776545) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (16060 ^ _776545) ^ [_1066940, _1066942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066940)), _1066942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066940), _1066942)))], (28505 ^ _776545) ^ [_1288096] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1288096)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1288096), c_Int_OMin)))], (48742 ^ _776545) ^ [_1758926, _1758928, _1758930] : [-(_1758926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1758928), c_List_Oreplicate(_1758928, _1758926, _1758930)) = hAPP(hAPP(c_Set_Oinsert(_1758928), _1758930), c_Orderings_Obot__class_Obot(tc_fun(_1758928, tc_HOL_Obool))))], (30378 ^ _776545) ^ [_1321538, _1321540, _1321542, _1321544] : [class_Orderings_Olinorder(_1321538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321538), _1321540)), hBOOL(hAPP(hAPP(c_member(_1321538), _1321542), _1321540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321538), hAPP(hAPP(c_Finite__Set_Ofold(_1321538, _1321538, c_Orderings_Oord__class_Omin(_1321538)), _1321544), _1321540)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321538), _1321542), _1321544))))], (15416 ^ _776545) ^ [_1055061, _1055063, _1055065] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055061), _1055063)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055061), _1055065)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055061), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055061, tc_HOL_Obool)), _1055063), _1055065))), hAPP(c_Finite__Set_Ocard(_1055061), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055061, tc_HOL_Obool)), _1055063), _1055065))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055061), _1055063)), hAPP(c_Finite__Set_Ocard(_1055061), _1055065)))], (46081 ^ _776545) ^ [_1702101, _1702103, _1702105, _1702107, _1702109, _1702111] : [class_Orderings_Olinorder(_1702101), -(hBOOL(hAPP(_1702103, _1702105))), -(hAPP(c_List_Ofilter(_1702107, _1702103), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702107, _1702101, _1702109), _1702105), _1702111)) = hAPP(c_List_Ofilter(_1702107, _1702103), _1702111))], (9194 ^ _776545) ^ [_935282, _935284, _935286] : [class_Orderings_Opreorder(_935282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935282), _935284), _935286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935282), _935286), _935284))], (29277 ^ _776545) ^ [_1301211, _1301213] : [class_Groups_Omonoid__mult(_1301211), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301211), _1301213), 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(_1301211), _1301213), _1301213))], (32516 ^ _776545) ^ [_1363956, _1363958, _1363960, _1363962, _1363964, _1363966, _1363968] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363956, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363958, tc_fun(_1363956, tc_HOL_Obool)), _1363960), _1363962)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363964, tc_fun(_1363956, tc_HOL_Obool)), _1363966), _1363968)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363958, tc_fun(_1363956, tc_HOL_Obool)), _1363960), hAPP(hAPP(c_COMBB(tc_fun(_1363964, tc_fun(_1363956, tc_HOL_Obool)), tc_fun(_1363956, tc_HOL_Obool), _1363958), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363964, tc_fun(_1363956, tc_HOL_Obool)), _1363966)), hAPP(hAPP(c_COMBC(_1363958, tc_fun(_1363964, tc_fun(_1363956, tc_HOL_Obool)), tc_fun(_1363964, tc_fun(_1363956, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1363956, tc_HOL_Obool), tc_fun(_1363956, tc_HOL_Obool)), tc_fun(tc_fun(_1363964, tc_fun(_1363956, tc_HOL_Obool)), tc_fun(_1363964, tc_fun(_1363956, tc_HOL_Obool))), _1363958), c_COMBB(tc_fun(_1363956, tc_HOL_Obool), tc_fun(_1363956, tc_HOL_Obool), _1363964)), hAPP(hAPP(c_COMBB(tc_fun(_1363956, tc_HOL_Obool), tc_fun(tc_fun(_1363956, tc_HOL_Obool), tc_fun(_1363956, tc_HOL_Obool)), _1363958), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363956, tc_HOL_Obool))), _1363962))), _1363968))))], (19607 ^ _776545) ^ [_1130775, _1130777, _1130779] : [class_Rings_Olinordered__idom(_1130775), -(c_Groups_Osgn__class_Osgn(_1130775, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130775), _1130777), _1130779)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130775), c_Groups_Osgn__class_Osgn(_1130775, _1130777)), c_Groups_Osgn__class_Osgn(_1130775, _1130779)))], (6893 ^ _776545) ^ [_888406, _888408, _888410] : [class_Orderings_Oorder(_888406), 6896 ^ _776545 : [(6903 ^ 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_1338232, _1338234, _1338236] : [class_Orderings_Olinorder(_1338230), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338230), _1338232), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338230), _1338234), _1338236)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338230), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338230), _1338232), _1338234)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338230), _1338232), _1338236)))], (30968 ^ _776545) ^ [_1332079, _1332081, _1332083] : [class_Orderings_Olinorder(_1332079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332079), _1332081)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332079), _1332083)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332079, tc_HOL_Obool)), _1332081), _1332083) = c_Orderings_Obot__class_Obot(tc_fun(_1332079, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1332079), c_Big__Operators_Olinorder__class_OMin(_1332079, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332079, tc_HOL_Obool)), _1332081), _1332083))), 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[hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024309), _1024311), _1024313)), _1024315) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024309), _1024317), _1024313)), _1024319), -(_1024315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024309), _1024317), _1024311)), _1024313)), _1024319))]]], (52447 ^ _776545) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (25445 ^ _776545) ^ [_1236850, _1236852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236850), _1236852)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236850, _1236852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236850), _1236852))], (39461 ^ _776545) ^ [_1541274, _1541276, _1541278] : [-(hAPP(c_Product__Type_Omap__pair(_1541274, _1541274, _1541276, _1541276, c_COMBI(_1541274), c_COMBI(_1541276)), _1541278) = _1541278)], (1948 ^ _776545) ^ [_803777, _803779, _803781, _803783] : [-(v_P_H(_803781, _803777)), v_P_H(_803783, _803779), _803783 = _803781, _803779 = _803777], (8024 ^ _776545) ^ [_912682, _912684, _912686, _912688] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912682, tc_HOL_Obool)), _912684), hAPP(hAPP(c_Set_Oinsert(_912682), _912686), _912688)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912682, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912682, tc_HOL_Obool)), _912684), _912688)), hAPP(hAPP(c_Set_Oinsert(_912682), _912686), c_Orderings_Obot__class_Obot(tc_fun(_912682, tc_HOL_Obool)))))], (31192 ^ _776545) ^ [_1336266, _1336268, _1336270] : [class_Orderings_Olinorder(_1336266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336266, tc_HOL_Obool)), _1336268), _1336270)), -(_1336268 = c_Orderings_Obot__class_Obot(tc_fun(_1336266, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336266), _1336270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336266), c_Big__Operators_Olinorder__class_OMax(_1336266, _1336268)), c_Big__Operators_Olinorder__class_OMax(_1336266, _1336270))))], (51199 ^ _776545) ^ [_1813330, _1813332, _1813334] : [class_Divides_Osemiring__div(_1813330), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813330), _1813332), _1813334)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813330), _1813332), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813330), _1813334), _1813332)) = _1813334)], (30076 ^ _776545) ^ [_1316032, _1316034, _1316036, _1316038] : [class_Orderings_Olinorder(_1316032), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316032), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316032), _1316034), _1316036)), _1316038) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316032), _1316034), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316032), _1316036), _1316038)))], (4916 ^ _776545) ^ [_851456, _851458, _851460, _851462] : [-(c_Relation_Oinv__image(_851462, _851458) = c_Relation_Oinv__image(_851460, _851456)), _851462 = _851460, _851458 = _851456], (35487 ^ _776545) ^ [_1438635, _1438637, _1438639, _1438641, _1438643, _1438645] : [hAPP(_1438641, hAPP(c_Product__Type_Osnd(_1438639, _1438635), _1438643)) = hAPP(_1438645, hAPP(c_Product__Type_Osnd(_1438639, _1438635), _1438643)), -(hAPP(c_Product__Type_Oapsnd(_1438635, _1438637, _1438639, _1438641), _1438643) = hAPP(c_Product__Type_Oapsnd(_1438635, _1438637, _1438639, _1438645), _1438643))], (7136 ^ _776545) ^ [_892781, _892783, _892785] : [-(hAPP(hAPP(c_Set_Oinsert(_892781), _892783), hAPP(hAPP(c_Set_Oinsert(_892781), _892783), _892785)) = hAPP(hAPP(c_Set_Oinsert(_892781), _892783), _892785))], (35414 ^ _776545) ^ [_1436920, _1436922, _1436924, _1436926] : [_1436920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1436922), _1436924)), _1436926), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436920, _1436922), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436924), _1436926)))), 35421 ^ _776545 : [(35424 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436926), _1436922))], (35422 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436922)))]], 35429 ^ _776545 : [(35432 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436922), _1436926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436926), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35430 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436922))]]], (38235 ^ _776545) ^ [_1508731] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1508731)))], (42001 ^ _776545) ^ [_1607285, _1607287] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607285), tc_List_Olist(_1607285)), tc_HOL_Obool)), c_List_Olistrel(_1607285, _1607287)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607285), c_List_Olistrel1(_1607285, _1607287)))))], (30872 ^ _776545) ^ [_1330285, _1330287, _1330289] : [class_Orderings_Olinorder(_1330285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330285), _1330287)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330285), _1330289)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330285, tc_HOL_Obool)), _1330287), _1330289) = c_Orderings_Obot__class_Obot(tc_fun(_1330285, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330285), 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[_882889, _882891, _882893]))], (6582 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_882889, tc_HOL_Obool)), 6580 ^ [_882889, _882891, _882893]), _882891)))]], -(hBOOL(hAPP(hAPP(c_member(_882889), _882893), c_Complete__Lattice_OInf__class_OInf(tc_fun(_882889, tc_HOL_Obool), _882891))))], (51957 ^ _776545) ^ [_1825936, _1825938] : [-(class_HOL_Oequal(tc_fun(_1825936, _1825938))), class_Enum_Oenum(_1825936), class_HOL_Oequal(_1825938)], (43428 ^ _776545) ^ [_1642426, _1642428, _1642430, _1642432, _1642434] : [hAPP(hAPP(c_List_Oappend(_1642426), _1642428), hAPP(hAPP(c_List_Olist_OCons(_1642426), _1642430), c_List_Olist_ONil(_1642426))) = hAPP(hAPP(c_List_Oappend(_1642426), _1642432), hAPP(hAPP(c_List_Olist_OCons(_1642426), _1642434), c_List_Olist_ONil(_1642426))), 43431 ^ _776545 : [(43434 ^ _776545) ^ [] : [-(_1642430 = _1642434)], (43432 ^ _776545) ^ [] : [-(_1642428 = _1642432)]]], (5817 ^ _776545) ^ [_868668, _868670, _868672, _868674, _868676, _868678] : [c_Typedef_Otype__definition(_868668, _868670, _868672, _868674, _868676), -(hBOOL(hAPP(hAPP(c_member(_868670), hAPP(_868672, _868678)), _868676)))], (10917 ^ _776545) ^ [_965022, _965024, _965026, _965028] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_965022, _965024, hAPP(hAPP(c_Set_Oinsert(_965022), _965026), c_Orderings_Obot__class_Obot(tc_fun(_965022, tc_HOL_Obool)))), _965028)), -(_965026 = _965028)], (45936 ^ _776545) ^ [_1697996, _1697998] : [45938 ^ _776545 : [(45941 ^ _776545) ^ [] : [45937 ^ [_1697996, _1697998] = c_List_Olist_ONil(_1697996)], (45939 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697996)), 45937 ^ [_1697996, _1697998]), hAPP(c_List_Oset(tc_List_Olist(_1697996)), _1697998))))]], -(c_List_Olist_ONil(_1697996) = c_List_Oconcat(_1697996, _1697998))], (8741 ^ _776545) ^ [_926751, _926753, _926755] : [class_Lattices_Osemilattice__inf(_926751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926751), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926751), _926753), _926755)), _926753)))], (48237 ^ _776545) ^ [_1748128, _1748130, _1748132] : [c_List_Olist__all(_1748128, _1748130, _1748132), 48240 ^ _776545 : [(48241 ^ _776545) ^ [_1748209] : [hBOOL(hAPP(hAPP(c_member(_1748128), _1748209), hAPP(c_List_Oset(_1748128), _1748132))), -(hBOOL(hAPP(_1748130, _1748209)))]]], (2972 ^ _776545) ^ [_820654, _820656, _820658, _820660] : [-(c_Nitpick_OAbs__Frac(_820660, _820656) = c_Nitpick_OAbs__Frac(_820658, _820654)), _820660 = _820658, _820656 = _820654], (24972 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20551 ^ _776545) ^ [_1147467, _1147469, _1147471, _1147473] : [class_Fields_Olinordered__field(_1147467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147467), _1147469), c_Groups_Ozero__class_Ozero(_1147467))), 20558 ^ _776545 : [(20565 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147467), _1147473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147467), _1147471), _1147469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147467), _1147471), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147467), _1147473), _1147469))))], (20559 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147467), _1147471), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147467), _1147473), _1147469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147467), _1147473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147467), _1147471), _1147469))))]]], (43486 ^ _776545) ^ [_1643757, _1643759, _1643761, _1643763] : [hAPP(hAPP(c_List_Oappend(_1643757), _1643759), _1643761) = hAPP(hAPP(c_List_Oappend(_1643757), _1643763), _1643761), -(_1643759 = _1643763)], (13300 ^ _776545) ^ [_1012288, _1012290, _1012292, _1012294, _1012296] : [class_Groups_Oab__group__add(_1012288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012290), _1012292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012290, tc_HOL_Obool)), _1012294), _1012292)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012290, _1012288), _1012296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012290, tc_HOL_Obool)), _1012292), _1012294)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1012288), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012290, _1012288), _1012296), _1012292)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012290, _1012288), _1012296), _1012294)))], (3514 ^ _776545) ^ [_829075, _829077, _829079, _829081, _829083, _829085] : [-(c_List_Osublist(_829085, _829081, _829077) = c_List_Osublist(_829083, _829079, _829075)), _829085 = _829083, _829081 = _829079, _829077 = _829075], (33180 ^ _776545) ^ [_1384368, _1384370, _1384372] : [hBOOL(hAPP(_1384372, _1384370)), -(hBOOL(hAPP(hAPP(c_member(_1384368), _1384370), hAPP(c_Set_OCollect(_1384368), _1384372))))], (34678 ^ _776545) ^ [_1422582, _1422584, _1422586, _1422588, _1422590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1422582, _1422584)), hAPP(hAPP(c_Product__Type_OPair(_1422582, _1422584), _1422588), _1422590)), _1422586)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1422582, _1422584, _1422586), _1422588), _1422590)))], (25097 ^ _776545) ^ [_1230886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230886)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1230886) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230886), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24002 ^ _776545) ^ [_1211158, _1211160] : [class_Divides_Osemiring__div(_1211158), -(_1211160 = c_Groups_Ozero__class_Ozero(_1211158)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1211158), _1211160), _1211160) = c_Groups_Oone__class_Oone(_1211158))], (41688 ^ _776545) ^ [_1597444, _1597446, _1597448] : [c_Nitpick_Oless__frac(_1597444, _1597446, _1597448), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597444), c_Nitpick_Oplus__frac(_1597444, _1597446, c_Nitpick_Ouminus__frac(_1597444, _1597448)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41811 ^ _776545) ^ [_1601557, _1601559, _1601561, _1601563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1601557), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601559), _1601561))), -(hAPP(c_Random_Opick(_1601559, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601559)), _1601561), _1601563)), _1601557) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1601559), _1601561))], (28401 ^ _776545) ^ [_1286384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1286384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1286384)))], (40935 ^ _776545) ^ [_1578316] : [-(hAPP(c_Relation_ODomain(_1578316, _1578316), c_Relation_OId(_1578316)) = c_Orderings_Otop__class_Otop(tc_fun(_1578316, tc_HOL_Obool)))], (44050 ^ _776545) ^ [_1657354, _1657356, _1657358, _1657360] : [-(hAPP(c_List_Orotate1(_1657354), c_List_Olist_ONil(_1657354)) = c_List_Olist_ONil(_1657354))], (6208 ^ _776545) ^ [_876300, _876302] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_876300, tc_HOL_Obool)), _876302)))], (14819 ^ _776545) ^ [_1043771, _1043773] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043771), _1043773)), _1043771) = _1043773)], (25822 ^ _776545) ^ [_1243769, _1243771] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243769))), -(c_SMT_Oz3mod(_1243771, _1243769) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243771, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243769)))], (49712 ^ _776545) ^ [_1781339, _1781341] : [c_Relation_Osym(_1781339, _1781341), -(c_Relation_Osym(tc_List_Olist(_1781339), c_List_Olistrel(_1781339, _1781341)))], (13790 ^ _776545) ^ [_1022284, _1022286, _1022288, _1022290, _1022292] : [class_Rings_Osemiring(_1022284), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022284), _1022286), _1022288)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022284), _1022290), _1022288)), _1022292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022284), _1022286), _1022290)), _1022288)), _1022292))], (6316 ^ _776545) ^ [_878259, _878261, _878263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878259, tc_HOL_Obool), tc_HOL_Obool)), _878261), _878263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878259, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_878259, tc_HOL_Obool), _878263)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_878259, tc_HOL_Obool), _878261))))], (46646 ^ _776545) ^ [_1713984, _1713986, _1713988, _1713990] : [class_Orderings_Olinorder(_1713984), -(c_List_Olinorder__class_Osorted(_1713984, hAPP(hAPP(c_List_Omap(_1713986, _1713984), _1713988), c_List_Olinorder__class_Osort__key(_1713986, _1713984, _1713988, _1713990))))], (21243 ^ _776545) ^ [_1160732, _1160734, _1160736] : [class_Int_Onumber__ring(_1160732), -(hAPP(c_Int_Onumber__class_Onumber__of(_1160732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160734), _1160736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160732), hAPP(c_Int_Onumber__class_Onumber__of(_1160732), _1160734)), hAPP(c_Int_Onumber__class_Onumber__of(_1160732), _1160736)))], (41700 ^ _776545) ^ [_1597690, _1597692, _1597694] : [c_Nitpick_Oless__eq__frac(_1597690, _1597692, _1597694), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1597690), c_Nitpick_Oplus__frac(_1597690, _1597692, c_Nitpick_Ouminus__frac(_1597690, _1597694)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45072 ^ _776545) ^ [_1679078, _1679080, _1679082, _1679084] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679078)), _1679080) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679082)), _1679084), -(hAPP(hAPP(c_List_Omap(tc_prod(_1679078, _1679082), _1679078), c_Product__Type_Ofst(_1679078, _1679082)), hAPP(hAPP(c_List_Ozip(_1679078, _1679082), _1679080), _1679084)) = _1679080)], (39525 ^ _776545) ^ [_1542993, _1542995, _1542997] : [-(c_Relation_Orefl__on(_1542993, _1542995, _1542997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542993, _1542993), tc_HOL_Obool)), _1542997), hAPP(hAPP(c_Product__Type_OSigma(_1542993, _1542993), _1542995), hAPP(c_COMBK(tc_fun(_1542993, tc_HOL_Obool), _1542993), _1542995)))), 39531 ^ _776545 : [(39534 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542993, _1542993)), hAPP(hAPP(c_Product__Type_OPair(_1542993, _1542993), 39530 ^ [_1542993, _1542995, _1542997]), 39530 ^ [_1542993, _1542995, _1542997])), _1542997))], (39532 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542993), 39530 ^ [_1542993, _1542995, _1542997]), _1542995)))]]], (15698 ^ _776545) ^ [_1061233] : [hAPP(c_Nat_OSuc, _1061233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12407 ^ _776545) ^ [_994511, _994513, _994515] : [class_Lattices_Olattice(_994511), hBOOL(hAPP(c_Finite__Set_Ofinite(_994511), _994513)), -(_994513 = c_Orderings_Obot__class_Obot(tc_fun(_994511, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_994511), _994515)), -(_994515 = c_Orderings_Obot__class_Obot(tc_fun(_994511, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994511, tc_HOL_Obool)), _994513), _994515) = c_Orderings_Obot__class_Obot(tc_fun(_994511, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_994511, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_994511, tc_HOL_Obool)), _994513), _994515)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994511), c_Big__Operators_Olattice__class_OInf__fin(_994511, _994513)), c_Big__Operators_Olattice__class_OInf__fin(_994511, _994515)))], (7090 ^ _776545) ^ [_892016, _892018] : [hBOOL(hAPP(hAPP(c_member(_892016), 7091 ^ [_892016, _892018]), _892018)), -(c_Orderings_Otop__class_Otop(tc_fun(_892016, tc_HOL_Obool)) = _892018)], (7354 ^ _776545) ^ [_897003, _897005] : [-(c_Set_Othe__elem(_897003, hAPP(hAPP(c_Set_Oinsert(_897003), _897005), c_Orderings_Obot__class_Obot(tc_fun(_897003, tc_HOL_Obool)))) = _897005)], (43126 ^ _776545) ^ [_1635771, _1635773] : [hAPP(c_List_Oset(_1635771), _1635773) = c_Orderings_Obot__class_Obot(tc_fun(_1635771, tc_HOL_Obool)), -(_1635773 = c_List_Olist_ONil(_1635771))], (12179 ^ _776545) ^ [_990335, _990337, _990339] : [class_Lattices_Olattice(_990335), hBOOL(hAPP(c_Finite__Set_Ofinite(_990335), _990337)), -(_990339 = c_Orderings_Obot__class_Obot(tc_fun(_990335, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990335, tc_HOL_Obool)), _990339), _990337)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_990335), c_Big__Operators_Olattice__class_OInf__fin(_990335, _990339)), c_Big__Operators_Olattice__class_OInf__fin(_990335, _990337)) = c_Big__Operators_Olattice__class_OInf__fin(_990335, _990337))], (45410 ^ _776545) ^ [_1686631, _1686633, _1686635] : [hBOOL(hAPP(c_List_Olistsp(_1686631, hAPP(hAPP(c_COMBC(_1686631, tc_fun(_1686631, tc_HOL_Obool), tc_HOL_Obool), c_member(_1686631)), _1686633)), _1686635)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1686631)), _1686635), c_List_Olists(_1686631, _1686633))))], (43627 ^ _776545) ^ [_1646737, _1646739, _1646741] : [hAPP(hAPP(c_List_Oappend(_1646737), _1646739), _1646741) = _1646739, -(_1646741 = c_List_Olist_ONil(_1646737))], (5769 ^ _776545) ^ [_867815, _867817, _867819, _867821] : [_867815 = _867817, 5774 ^ _776545 : [(5777 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_867819), _867821), _867817)))], (5775 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_867819), _867821), _867815)))]], 5778 ^ _776545 : [(5781 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_867819), _867821), _867817))], (5779 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_867819), _867821), _867815))]]], (20955 ^ _776545) ^ [_1154952, _1154954, _1154956, _1154958] : [class_Fields_Olinordered__field(_1154952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154952), c_Groups_Ozero__class_Ozero(_1154952)), _1154954)), 20962 ^ _776545 : [(20969 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154952), _1154956), _1154954)), _1154958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154952), _1154956), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154952), _1154958), _1154954))))], (20963 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154952), _1154956), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154952), _1154958), _1154954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154952), _1154956), _1154954)), _1154958)))]]], (16200 ^ _776545) ^ [_1069291, _1069293] : [class_Rings_Ocomm__semiring__1(_1069291), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069291), c_Groups_Ozero__class_Ozero(_1069291)), _1069293) = _1069293)], (33579 ^ _776545) ^ [_1394664, _1394666, _1394668] : [class_Groups_Ocomm__monoid__mult(_1394664), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394666, _1394664), hAPP(c_COMBK(_1394664, _1394666), c_Groups_Oone__class_Oone(_1394664))), _1394668) = c_Groups_Oone__class_Oone(_1394664))], (7816 ^ _776545) ^ [_908003, _908005, _908007, _908009] : [hBOOL(hAPP(hAPP(c_member(_908003), _908005), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_908003, tc_HOL_Obool)), _908007), _908009))), -(hBOOL(hAPP(hAPP(c_member(_908003), _908005), _908009)))], (26637 ^ _776545) ^ [_1257339, _1257341] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257339)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257341)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257339)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257341))))], (8191 ^ _776545) ^ [_916428, _916430, _916432, _916434] : [class_Lattices_Olattice(_916428), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_916428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916428), _916430), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916428), _916432), _916434))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916428), _916430), _916432)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_916428), _916430), _916434)))))], (18488 ^ _776545) ^ [_1109254, _1109256, _1109258] : [class_Rings_Olinordered__idom(_1109254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109254), c_Groups_Ozero__class_Ozero(_1109254)), _1109256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109254), c_Groups_Ozero__class_Ozero(_1109254)), _1109258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109254), _1109258), c_Groups_Oone__class_Oone(_1109254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109254), _1109258), _1109256)), _1109256)))], (42311 ^ _776545) ^ [_1616160, _1616162, _1616164, _1616166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1616160), _1616162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616164, tc_HOL_Obool)), hAPP(c_List_Oset(_1616164), hAPP(hAPP(c_List_Otake(_1616164), _1616160), _1616166))), hAPP(c_List_Oset(_1616164), hAPP(hAPP(c_List_Otake(_1616164), _1616162), _1616166)))))], (44212 ^ _776545) ^ [_1660581, _1660583, _1660585] : [-(hAPP(c_List_Orotate(_1660581, hAPP(c_Nat_OSuc, _1660583)), _1660585) = hAPP(c_List_Orotate1(_1660581), hAPP(c_List_Orotate(_1660581, _1660583), _1660585)))], (33623 ^ _776545) ^ [_1396886, _1396888, _1396890, _1396892, _1396894, _1396896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1396888, _1396890)), hAPP(hAPP(c_Product__Type_OPair(_1396888, _1396890), _1396894), _1396896)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396886, tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1396886, tc_HOL_Obool))), _1396892))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396886, tc_fun(_1396888, tc_fun(_1396890, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1396886, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_fun(_1396888, tc_fun(_1396890, tc_HOL_Obool)), _1396886), hAPP(c_COMBC(_1396888, tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_fun(_1396890, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396890, tc_fun(tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_fun(_1396890, tc_HOL_Obool)), _1396888), c_COMBC(_1396890, tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396890, tc_prod(_1396888, _1396890)), tc_fun(_1396890, tc_fun(tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_HOL_Obool)), _1396888), hAPP(c_COMBB(tc_prod(_1396888, _1396890), tc_fun(tc_fun(tc_prod(_1396888, _1396890), tc_HOL_Obool), tc_HOL_Obool), _1396890), c_member(tc_prod(_1396888, _1396890)))), c_Product__Type_OPair(_1396888, _1396890))))), _1396892)), _1396894), _1396896)))], (28803 ^ _776545) ^ [_1292980] : [c_Int_OPls = c_Int_OBit0(_1292980), -(c_Int_OPls = _1292980)], (15696 ^ _776545) ^ [_1061198] : [hAPP(c_Nat_OSuc, _1061198) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (39141 ^ _776545) ^ [_1531407, _1531409, _1531411, _1531413, _1531415] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531407, _1531409), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531407, tc_HOL_Obool)), _1531411), _1531413)), hAPP(c_COMBK(tc_fun(_1531409, tc_HOL_Obool), _1531407), _1531415)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531407, _1531409), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531407, _1531409), _1531411), hAPP(c_COMBK(tc_fun(_1531409, tc_HOL_Obool), _1531407), _1531415))), hAPP(hAPP(c_Product__Type_OSigma(_1531407, _1531409), _1531413), hAPP(c_COMBK(tc_fun(_1531409, tc_HOL_Obool), _1531407), _1531415))))], (30014 ^ _776545) ^ [_1314828] : [class_Orderings_Olinorder(_1314828), -(c_Finite__Set_Ofun__left__comm__idem(_1314828, _1314828, c_Orderings_Oord__class_Omin(_1314828)))], (3282 ^ _776545) ^ [_825525, _825527, _825529, _825531, _825533, _825535] : [-(c_List_Olist_Olist__size(_825535, _825531, _825527) = c_List_Olist_Olist__size(_825533, _825529, _825525)), _825535 = _825533, _825531 = _825529, _825527 = _825525], (52045 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (6264 ^ _776545) ^ [_877242, _877244, _877246] : [class_Complete__Lattice_Ocomplete__lattice(_877242), 6267 ^ _776545 : [(6268 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877242), _877244), c_Complete__Lattice_OInf__class_OInf(_877242, _877246))), 6271 ^ _776545 : [(6272 ^ _776545) ^ [_877400] : [hBOOL(hAPP(hAPP(c_member(_877242), _877400), _877246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877242), _877244), _877400)))]]], (6278 ^ _776545) ^ [] : [6280 ^ _776545 : [(6283 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877242), _877244), 6279 ^ [_877242, _877244, _877246]))], (6281 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877242), 6279 ^ [_877242, _877244, _877246]), _877246)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877242), _877244), c_Complete__Lattice_OInf__class_OInf(_877242, _877246))))]]], (10086 ^ _776545) ^ [_949127, _949129, _949131] : [class_Orderings_Oorder(_949127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949127, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_949127), _949129)), c_SetInterval_Oord__class_OatLeastAtMost(_949127, _949129, _949131)) = c_Orderings_Obot__class_Obot(tc_fun(_949127, tc_HOL_Obool)))], (44184 ^ _776545) ^ [_1660074, _1660076, _1660078] : [hAPP(c_List_Orotate(_1660074, _1660076), _1660078) = c_List_Olist_ONil(_1660074), -(_1660078 = c_List_Olist_ONil(_1660074))], (12133 ^ _776545) ^ [_989605, _989607, _989609] : [class_Lattices_Olattice(_989605), hBOOL(hAPP(c_Finite__Set_Ofinite(_989605), _989607)), -(_989607 = c_Orderings_Obot__class_Obot(tc_fun(_989605, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_989605, hAPP(hAPP(c_Set_Oinsert(_989605), _989609), _989607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_989605), _989609), c_Big__Operators_Olattice__class_OSup__fin(_989605, _989607)))], (28797 ^ _776545) ^ [_1292887] : [_1292887 = c_Int_OPls, -(c_Int_OBit0(_1292887) = c_Int_OPls)], (40582 ^ _776545) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (52397 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (34773 ^ _776545) ^ [_1425236, _1425238, _1425240, _1425242, _1425244] : [hBOOL(hAPP(hAPP(_1425236, _1425238), _1425240)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425242, _1425244, tc_HOL_Obool), _1425236), hAPP(hAPP(c_Product__Type_OPair(_1425242, _1425244), _1425238), _1425240))))], (5150 ^ _776545) ^ [_855129, _855131] : [_855131 = _855129, -(c_Finite__Set_Ocard(_855131) = c_Finite__Set_Ocard(_855129))], (18178 ^ _776545) ^ [_1103324, _1103326] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1103324)), _1103326) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1103324, _1103326))], (26194 ^ _776545) ^ [_1249776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249776))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1249776)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22537 ^ _776545) ^ [_1185000, _1185002, _1185004, _1185006] : [class_Rings_Olinordered__semidom(_1185000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185000), _1185002), _1185004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185000), c_Groups_Ozero__class_Ozero(_1185000)), _1185002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185000), hAPP(hAPP(c_Power_Opower__class_Opower(_1185000), _1185002), _1185006)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185000), _1185004), _1185006))))], (190 ^ _776545) ^ [_779692, _779694] : [-(class_Rings_Odivision__ring__inverse__zero(_779692)), _779694 = _779692, class_Rings_Odivision__ring__inverse__zero(_779694)], (33068 ^ _776545) ^ [_1380771, _1380773, _1380775] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380771, tc_Nat_Onat), _1380773), _1380775)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380771, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1380771), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1380773)), _1380775))], (50271 ^ _776545) ^ [_1792749, _1792751, _1792753, _1792755, _1792757] : [hBOOL(hAPP(_1792749, hAPP(hAPP(c_Product__Type_OPair(_1792751, _1792753), _1792755), _1792757))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1792751, _1792753, tc_HOL_Obool, _1792749), _1792755), _1792757)))], (45301 ^ _776545) ^ [_1683830, _1683832, _1683834, _1683836] : [-(c_List_Opartition(_1683830, _1683832, hAPP(hAPP(c_List_Olist_OCons(_1683830), _1683834), _1683836)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1683830), tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1683830), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683830), tc_fun(tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), tc_fun(tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), tc_List_Olist(_1683830)), c_COMBS(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_fun(tc_List_Olist(_1683830), tc_fun(tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), tc_List_Olist(_1683830)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_fun(tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_List_Olist(_1683830)), hAPP(c_If(tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), hAPP(_1683832, _1683834)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1683830), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_List_Olist(_1683830)), c_Product__Type_OPair(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), hAPP(c_List_Olist_OCons(_1683830), _1683834))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1683830), tc_fun(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830))), tc_fun(tc_fun(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_fun(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), tc_List_Olist(_1683830)), c_COMBB(tc_List_Olist(_1683830), tc_prod(tc_List_Olist(_1683830), tc_List_Olist(_1683830)), tc_List_Olist(_1683830))), c_Product__Type_OPair(tc_List_Olist(_1683830), tc_List_Olist(_1683830)))), hAPP(c_List_Olist_OCons(_1683830), _1683834)))), c_List_Opartition(_1683830, _1683832, _1683836)))], (13114 ^ _776545) ^ [_1008240, _1008242, _1008244, _1008246, _1008248, _1008250] : [c_Finite__Set_Ofun__left__comm__idem(_1008240, _1008242, _1008244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008240), _1008246)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1008240, _1008242, _1008244), _1008248), hAPP(hAPP(c_Set_Oinsert(_1008240), _1008250), _1008246)) = hAPP(hAPP(_1008244, _1008250), hAPP(hAPP(c_Finite__Set_Ofold(_1008240, _1008242, _1008244), _1008248), _1008246)))], (26515 ^ _776545) ^ [_1255126, _1255128] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255126) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255128)), _1255126 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1255128)), 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), _1255128)))], (39109 ^ _776545) ^ [_1530371, _1530373, _1530375, _1530377, _1530379] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530371, _1530373), _1530375), hAPP(hAPP(c_COMBS(_1530371, tc_fun(_1530373, tc_HOL_Obool), tc_fun(_1530373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530373, tc_HOL_Obool), tc_fun(tc_fun(_1530373, tc_HOL_Obool), tc_fun(_1530373, tc_HOL_Obool)), _1530371), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530373, tc_HOL_Obool))), _1530377)), _1530379)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530371, _1530373), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530371, _1530373), _1530375), _1530377)), hAPP(hAPP(c_Product__Type_OSigma(_1530371, _1530373), _1530375), _1530379)))], (13413 ^ _776545) ^ [_1014845, _1014847, _1014849, _1014851] : [class_Lattices_Osemilattice__inf(_1014845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014845), _1014847)), 13423 ^ _776545 : [(13426 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014845), _1014849), 13422 ^ [_1014845, _1014847, _1014849, _1014851]))], (13424 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014845), 13422 ^ [_1014845, _1014847, _1014849, _1014851]), _1014847)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1014845), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014845), _1014849), _1014851)), hAPP(hAPP(c_Finite__Set_Ofold(_1014845, _1014845, c_Lattices_Osemilattice__inf__class_Oinf(_1014845)), _1014851), _1014847))))], (29095 ^ _776545) ^ [_1298063] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1298063)))], (11290 ^ _776545) ^ [_972750, _972752] : [class_Groups_Oordered__ab__group__add(_972750), -(hAPP(c_Set_Oimage(_972750, _972750, c_Groups_Ouminus__class_Ouminus(_972750)), hAPP(c_SetInterval_Oord__class_OatLeast(_972750), _972752)) = hAPP(c_SetInterval_Oord__class_OatMost(_972750), hAPP(c_Groups_Ouminus__class_Ouminus(_972750), _972752)))], (29021 ^ _776545) ^ [_1296812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1296812)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296812), c_Int_OMin)))], (46652 ^ _776545) ^ [_1714091, _1714093, _1714095, _1714097, _1714099] : [class_Orderings_Olinorder(_1714091), c_List_Olinorder__class_Osorted(_1714091, hAPP(hAPP(c_List_Omap(_1714093, _1714091), _1714095), _1714097)), -(c_List_Olinorder__class_Osorted(_1714091, hAPP(hAPP(c_List_Omap(_1714093, _1714091), _1714095), c_List_Olinorder__class_Oinsort__insert__key(_1714093, _1714091, _1714095, _1714099, _1714097))))], (3418 ^ _776545) ^ [_827579, _827581, _827583, _827585, _827587, _827589] : [-(c_Finite__Set_Ofold(_827589, _827585, _827581) = c_Finite__Set_Ofold(_827587, _827583, _827579)), _827589 = _827587, _827585 = _827583, _827581 = _827579], (24974 ^ _776545) ^ [_1228813, _1228815, _1228817] : [class_Divides_Osemiring__div(_1228813), -(c_Divides_Odiv__class_Omod(_1228813, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228813), _1228815), _1228817), _1228815) = c_Groups_Ozero__class_Ozero(_1228813))], (16510 ^ _776545) ^ [_1073800, _1073802] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073800), _1073802) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073802), _1073800) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1073800 = _1073802)], (26148 ^ _776545) ^ [_1249033, _1249035] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1249033)), hAPP(c_Int_Onat, _1249035)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249033), _1249035))], (28493 ^ _776545) ^ [_1287912] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287912))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1287912)))], (34455 ^ _776545) ^ [_1417717, _1417719, _1417721, _1417723, _1417725, _1417727] : [34456 ^ _776545 : [(34459 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1417723, _1417719), _1417721))], (34457 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1417717, _1417719), _1417721))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417725, tc_fun(_1417727, tc_HOL_Obool))), _1417723), _1417717), _1417719), _1417721)))], (38328 ^ _776545) ^ [_1510833, _1510835] : [-(c_FunDef_Oreduction__pair(_1510833, _1510835)), c_Wellfounded_Owf(_1510833, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool), tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool)), _1510835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510833, _1510833, _1510833), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool), tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool)), _1510835)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool), tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool)), _1510835))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool), tc_fun(tc_prod(_1510833, _1510833), tc_HOL_Obool)), _1510835)))], (49762 ^ _776545) ^ [_1782111, _1782113] : [-(c_Relation_Osym(_1782111, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1782111, _1782111), tc_HOL_Obool)), _1782113), hAPP(c_Relation_Oconverse(_1782111, _1782111), _1782113))))], (36380 ^ _776545) ^ [_1463803] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463803)), -(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))), _1463803)), c_FunDef_Omax__weak)))], (45283 ^ _776545) ^ [_1683400, _1683402, _1683404, _1683406, _1683408] : [c_List_Opartition(_1683400, _1683402, _1683404) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683400), tc_List_Olist(_1683400)), _1683406), _1683408), 45286 ^ _776545 : [(45293 ^ _776545) ^ [_1683662] : [hBOOL(hAPP(hAPP(c_member(_1683400), _1683662), hAPP(c_List_Oset(_1683400), _1683408))), hBOOL(hAPP(_1683402, _1683662))], (45287 ^ _776545) ^ [_1683553] : [hBOOL(hAPP(hAPP(c_member(_1683400), _1683553), hAPP(c_List_Oset(_1683400), _1683406))), -(hBOOL(hAPP(_1683402, _1683553)))]]], (42319 ^ _776545) ^ [_1616378, _1616380, _1616382] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1616378, tc_HOL_Obool)), hAPP(c_List_Oset(_1616378), c_List_Osublist(_1616378, _1616380, _1616382))), hAPP(c_List_Oset(_1616378), _1616380))))], (34996 ^ _776545) ^ [_1429497] : [-(c_Int_Oint__ge__less__than(_1429497) = 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), _1429497)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (45024 ^ _776545) ^ [_1678338, _1678340] : [hAPP(c_Code__Numeral_Oof__nat, _1678338) = hAPP(c_Code__Numeral_Oof__nat, _1678340), -(_1678338 = _1678340)], (16160 ^ _776545) ^ [_1068670, _1068672] : [class_Groups_Omonoid__add(_1068670), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068670), c_Groups_Ozero__class_Ozero(_1068670)), _1068672) = _1068672)], (49107 ^ _776545) ^ [_1766982, _1766984, _1766986, _1766988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1766982), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1766984, _1766986, _1766982, _1766988) = 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(_1766984)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1766984)))], (36612 ^ _776545) ^ [_1470355, _1470357, _1470359] : [-(hAPP(c_Relation_OField(_1470355), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1470355, _1470355), tc_HOL_Obool)), _1470357), _1470359)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470355, tc_HOL_Obool)), hAPP(c_Relation_OField(_1470355), _1470357)), hAPP(c_Relation_OField(_1470355), _1470359)))], (11252 ^ _776545) ^ [_971946, _971948, _971950] : [class_Groups_Oordered__ab__group__add(_971946), -(hAPP(c_Set_Oimage(_971946, _971946, c_Groups_Ouminus__class_Ouminus(_971946)), c_SetInterval_Oord__class_OgreaterThanLessThan(_971946, _971948, _971950)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_971946, hAPP(c_Groups_Ouminus__class_Ouminus(_971946), _971950), hAPP(c_Groups_Ouminus__class_Ouminus(_971946), _971948)))], (24946 ^ _776545) ^ [_1228277, _1228279] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228277)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228279)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228277), _1228279)))], (19855 ^ _776545) ^ [_1134847, _1134849] : [class_Groups_Osgn__if(_1134847), 19858 ^ _776545 : [(19865 ^ _776545) ^ [] : [-(_1134849 = c_Groups_Ozero__class_Ozero(_1134847)), 19868 ^ _776545 : [(19875 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134847), c_Groups_Ozero__class_Ozero(_1134847)), _1134849))), -(c_Groups_Osgn__class_Osgn(_1134847, _1134849) = hAPP(c_Groups_Ouminus__class_Ouminus(_1134847), c_Groups_Oone__class_Oone(_1134847)))], (19869 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134847), c_Groups_Ozero__class_Ozero(_1134847)), _1134849)), -(c_Groups_Osgn__class_Osgn(_1134847, _1134849) = c_Groups_Oone__class_Oone(_1134847))]]], (19859 ^ _776545) ^ [] : [_1134849 = c_Groups_Ozero__class_Ozero(_1134847), -(c_Groups_Osgn__class_Osgn(_1134847, _1134849) = c_Groups_Ozero__class_Ozero(_1134847))]]], (41156 ^ _776545) ^ [_1583534, _1583536, _1583538] : [-(hAPP(c_Relation_ORange(_1583534, _1583536), hAPP(c_Relation_Oconverse(_1583536, _1583534), _1583538)) = hAPP(c_Relation_ODomain(_1583536, _1583534), _1583538))], (39820 ^ _776545) ^ [_1551221, _1551223, _1551225, _1551227, _1551229, _1551231, _1551233, _1551235, _1551237, _1551239] : [-(c_Product__Type_Omap__pair(_1551221, _1551223, _1551225, _1551227, hAPP(c_Fun_Ocomp(_1551229, _1551223, _1551221, _1551231), _1551233), hAPP(c_Fun_Ocomp(_1551235, _1551227, _1551225, _1551237), _1551239)) = hAPP(c_Fun_Ocomp(tc_prod(_1551229, _1551235), tc_prod(_1551223, _1551227), tc_prod(_1551221, _1551225), c_Product__Type_Omap__pair(_1551229, _1551223, _1551235, _1551227, _1551231, _1551237)), c_Product__Type_Omap__pair(_1551221, _1551229, _1551225, _1551235, _1551233, _1551239)))], (33599 ^ _776545) ^ [_1395152, _1395154, _1395156, _1395158] : [hBOOL(hAPP(hAPP(c_member(_1395154), _1395158), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395152, tc_fun(_1395154, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395152, tc_HOL_Obool))), _1395156))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395152, tc_fun(_1395154, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395152, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1395154, tc_HOL_Obool), tc_fun(_1395154, tc_HOL_Obool), _1395152), hAPP(c_COMBC(_1395154, tc_fun(_1395154, tc_HOL_Obool), tc_HOL_Obool), c_member(_1395154))), _1395156)), _1395158)))], (52463 ^ _776545) ^ [_1830922] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1830922)))], (45102 ^ _776545) ^ [_1679753, _1679755] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1679753)), hAPP(c_Code__Numeral_Oof__nat, _1679755)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1679753), _1679755)))], (51189 ^ _776545) ^ [_1813117, _1813119, _1813121, _1813123] : [class_Divides_Osemiring__div(_1813117), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813117), _1813119), _1813121)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813117), _1813123), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813117), _1813121), _1813119)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813117), _1813123), _1813121)), _1813119))], (9116 ^ _776545) ^ [_934072, _934074, _934076, _934078] : [class_Orderings_Oorder(_934072), _934074 = _934076, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934072), _934078), _934076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934072), _934078), _934074)))], (8905 ^ _776545) ^ [_929941, _929943, _929945, _929947] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929941, tc_HOL_Obool)), _929943), hAPP(hAPP(c_Set_Oinsert(_929941), _929945), _929947)))), 8908 ^ _776545 : [(8911 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929941, tc_HOL_Obool)), _929943), _929947))], (8909 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929941), _929945), _929947)))]], 8912 ^ _776545 : [(8915 ^ _776545) ^ [] : [8916 ^ _776545 : [(8919 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929941, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929941, tc_HOL_Obool)), _929943), hAPP(hAPP(c_Set_Oinsert(_929941), _929945), c_Orderings_Obot__class_Obot(tc_fun(_929941, tc_HOL_Obool))))), _929947))], (8917 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929941), _929945), _929943)))]], 8920 ^ _776545 : [(8923 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929941, tc_HOL_Obool)), _929943), _929947))], (8921 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929941), _929945), _929943))]]], (8913 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929941), _929945), _929947))]]], (44972 ^ _776545) ^ [_1677091, _1677093, _1677095, _1677097] : [class_Groups_Ocomm__monoid__add(_1677091), hBOOL(hAPP(c_List_Odistinct(_1677093), _1677095)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677091), hAPP(hAPP(c_List_Omap(_1677093, _1677091), _1677097), _1677095)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1677093, _1677091), _1677097), hAPP(c_List_Oset(_1677093), _1677095)))], (40542 ^ _776545) ^ [_1567911, _1567913] : [c_Wellfounded_Owf(_1567911, _1567913), 40545 ^ _776545 : [(40546 ^ _776545) ^ [_1568043] : [40547 ^ _776545 : [(40548 ^ _776545) ^ [_1568148] : [hBOOL(hAPP(hAPP(c_member(_1567911), _1568148), _1568043))]], 40550 ^ _776545 : [(40553 ^ _776545) ^ [_1568270] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567911, _1567911)), hAPP(hAPP(c_Product__Type_OPair(_1567911, _1567911), _1568270), 40549 ^ [_1567911, _1567913, _1568043])), _1567913)), hBOOL(hAPP(hAPP(c_member(_1567911), _1568270), _1568043))], (40551 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567911), 40549 ^ [_1567911, _1567913, _1568043]), _1568043)))]]]]], (39946 ^ _776545) ^ [_1554173, _1554175, _1554177, _1554179, _1554181, _1554183] : [class_Groups_Ocomm__monoid__add(_1554173), c_Fun_Oinj__on(_1554175, _1554177, _1554179, _1554181), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554177, _1554173), _1554183), hAPP(c_Set_Oimage(_1554175, _1554177, _1554179), _1554181)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554175, _1554173), hAPP(c_Fun_Ocomp(_1554177, _1554173, _1554175, _1554183), _1554179)), _1554181))], (3614 ^ _776545) ^ [_830683, _830685, _830687, _830689] : [-(c_List_Olinorder__class_Osorted__list__of__set(_830689, _830685) = c_List_Olinorder__class_Osorted__list__of__set(_830687, _830683)), _830689 = _830687, _830685 = _830683], (22705 ^ _776545) ^ [_1187924, _1187926] : [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), _1187924), _1187926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1187924))), -(_1187926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8753 ^ _776545) ^ [_926965, _926967, _926969] : [class_Lattices_Obounded__lattice__bot(_926965), 8756 ^ _776545 : [(8765 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926965), _926967), _926969) = c_Orderings_Obot__class_Obot(_926965)), _926967 = c_Orderings_Obot__class_Obot(_926965), _926969 = c_Orderings_Obot__class_Obot(_926965)], (8757 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926965), _926967), _926969) = c_Orderings_Obot__class_Obot(_926965), 8760 ^ _776545 : [(8763 ^ _776545) ^ [] : [-(_926969 = c_Orderings_Obot__class_Obot(_926965))], (8761 ^ _776545) ^ [] : [-(_926967 = c_Orderings_Obot__class_Obot(_926965))]]]]], (2348 ^ _776545) ^ [_810808, _810810, _810812, _810814] : [-(c_Divides_Opdivmod(_810814, _810810) = c_Divides_Opdivmod(_810812, _810808)), _810814 = _810812, _810810 = _810808], (11194 ^ _776545) ^ [_970580, _970582, _970584, _970586, _970588] : [-(hAPP(c_Set_Oimage(_970580, _970582, _970584), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970580, tc_HOL_Obool)), _970586), _970588)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970582, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970580, _970582, _970584), _970586)), hAPP(c_Set_Oimage(_970580, _970582, _970584), _970588)))], (28275 ^ _776545) ^ [_1284190, _1284192] : [class_Int_Onumber__ring(_1284190), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1284190), hAPP(c_Int_Onumber__class_Onumber__of(_1284190), _1284192)), c_Groups_Oone__class_Oone(_1284190)) = hAPP(c_Int_Onumber__class_Onumber__of(_1284190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1284192), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (39513 ^ _776545) ^ [_1542676, _1542678, _1542680] : [c_Relation_Orefl__on(_1542676, _1542678, _1542680), 39516 ^ _776545 : [(39519 ^ _776545) ^ [_1542858] : [hBOOL(hAPP(hAPP(c_member(_1542676), _1542858), _1542678)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542676, _1542676)), hAPP(hAPP(c_Product__Type_OPair(_1542676, _1542676), _1542858), _1542858)), _1542680)))], (39517 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542676, _1542676), tc_HOL_Obool)), _1542680), hAPP(hAPP(c_Product__Type_OSigma(_1542676, _1542676), _1542678), hAPP(c_COMBK(tc_fun(_1542676, tc_HOL_Obool), _1542676), _1542678)))))]]], (22769 ^ _776545) ^ [_1189044, _1189046, _1189048] : [class_Rings_Olinordered__semidom(_1189044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189044), c_Groups_Oone__class_Oone(_1189044)), _1189046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189044), hAPP(hAPP(c_Power_Opower__class_Opower(_1189044), _1189046), _1189048)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189044), _1189046), hAPP(hAPP(c_Power_Opower__class_Opower(_1189044), _1189046), _1189048)))))], (34013 ^ _776545) ^ [_1407928] : [-(c_Finite__Set_Ofun__left__comm__idem(_1407928, tc_fun(_1407928, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1407928, tc_HOL_Obool), tc_fun(tc_fun(_1407928, tc_HOL_Obool), tc_fun(_1407928, tc_HOL_Obool)), _1407928), hAPP(c_COMBC(tc_fun(_1407928, tc_HOL_Obool), tc_fun(_1407928, tc_HOL_Obool), tc_fun(_1407928, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1407928, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1407928, tc_fun(_1407928, tc_HOL_Obool), tc_fun(_1407928, tc_HOL_Obool)), c_Set_Oinsert(_1407928)), c_Orderings_Obot__class_Obot(tc_fun(_1407928, tc_HOL_Obool))))))], (42632 ^ _776545) ^ [_1625328] : [c_List_Onat__list(_1625328), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1625328)))], (25321 ^ _776545) ^ [_1234797, _1234799] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234797), _1234799) = c_Groups_Oone__class_Oone(tc_Int_Oint), 25326 ^ _776545 : [(25329 ^ _776545) ^ [] : [-(_1234799 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25327 ^ _776545) ^ [] : [-(_1234797 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 25330 ^ _776545 : [(25333 ^ _776545) ^ [] : [-(_1234799 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25331 ^ _776545) ^ [] : [-(_1234797 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (34522 ^ _776545) ^ [_1419236, _1419238, _1419240, _1419242, _1419244, _1419246, _1419248] : [34524 ^ _776545 : [(34527 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1419244, 34523 ^ [_1419236, _1419238, _1419240, _1419242, _1419244, _1419246, _1419248]), _1419246), _1419248))], (34525 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419236), 34523 ^ [_1419236, _1419238, _1419240, _1419242, _1419244, _1419246, _1419248]), _1419242)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419236, tc_fun(_1419238, tc_fun(_1419240, tc_HOL_Obool))), _1419242), _1419244), _1419246), _1419248)))], (28593 ^ _776545) ^ [_1289514, _1289516] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289514), _1289516), hAPP(c_Int_Onumber__class_Onumber__of(_1289514), c_Int_OBit1(c_Int_OPls))) = _1289516), class_Fields_Ofield(_1289514), class_Int_Onumber__ring(_1289514)], (17825 ^ _776545) ^ [_1097329, _1097331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097329), _1097331)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097329), hAPP(c_Nat_OSuc, _1097331)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1097331), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097329), _1097331)))], (21309 ^ _776545) ^ [_1162247, _1162249] : [class_Rings_Ocomm__semiring__1(_1162247), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1162247), _1162249), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1162249)], (48808 ^ _776545) ^ [_1760351, _1760353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1760351), _1760353)), -(c_Lazy__Sequence_Osmall__lazy_H(_1760351, _1760353) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (44160 ^ _776545) ^ [_1659583, _1659585, _1659587] : [hBOOL(hAPP(c_List_Odistinct(_1659583), hAPP(c_List_Orotate(_1659583, _1659585), _1659587))), -(hBOOL(hAPP(c_List_Odistinct(_1659583), _1659587)))], (38911 ^ _776545) ^ [_1525280, _1525282, _1525284, _1525286] : [38912 ^ _776545 : [(38913 ^ _776545) ^ [_1525355] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525280, _1525284)), hAPP(hAPP(c_Product__Type_OPair(_1525280, _1525284), _1525282), _1525355)), _1525286))]], -(hBOOL(hAPP(hAPP(c_member(_1525280), _1525282), hAPP(c_Relation_ODomain(_1525280, _1525284), _1525286))))], (24882 ^ _776545) ^ [_1226963, _1226965, _1226967, _1226969, _1226971, _1226973] : [class_Divides_Oring__div(_1226963), c_Divides_Odiv__class_Omod(_1226963, _1226965, _1226967) = c_Divides_Odiv__class_Omod(_1226963, _1226969, _1226967), c_Divides_Odiv__class_Omod(_1226963, _1226971, _1226967) = c_Divides_Odiv__class_Omod(_1226963, _1226973, _1226967), -(c_Divides_Odiv__class_Omod(_1226963, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1226963), _1226965), _1226971), _1226967) = c_Divides_Odiv__class_Omod(_1226963, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1226963), _1226969), _1226973), _1226967))], (27553 ^ _776545) ^ [_1272200, _1272202, _1272204] : [class_Fields_Olinordered__field(_1272200), -(_1272202 = c_Groups_Ozero__class_Ozero(_1272200)), -(hAPP(c_Groups_Oabs__class_Oabs(_1272200), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272200), _1272204), _1272202)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272200), hAPP(c_Groups_Oabs__class_Oabs(_1272200), _1272204)), hAPP(c_Groups_Oabs__class_Oabs(_1272200), _1272202)))], (37919 ^ _776545) ^ [_1499628, _1499630, _1499632] : [hBOOL(hAPP(hAPP(c_member(_1499628), _1499632), c_Wellfounded_Oacc(_1499628, _1499630))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1499628, hAPP(hAPP(c_COMBC(_1499628, tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_fun(_1499628, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499628, tc_fun(tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_fun(_1499628, tc_HOL_Obool)), _1499628), c_COMBC(_1499628, tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499628, tc_prod(_1499628, _1499628)), tc_fun(_1499628, tc_fun(tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_HOL_Obool)), _1499628), hAPP(c_COMBB(tc_prod(_1499628, _1499628), tc_fun(tc_fun(tc_prod(_1499628, _1499628), tc_HOL_Obool), tc_HOL_Obool), _1499628), c_member(tc_prod(_1499628, _1499628)))), c_Product__Type_OPair(_1499628, _1499628)))), _1499630)), _1499632)))], (49385 ^ _776545) ^ [_1774385, _1774387, _1774389, _1774391] : [class_Complete__Lattice_Ocomplete__lattice(_1774385), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1774387, _1774385), _1774389), _1774391) = c_Complete__Lattice_OInf__class_OInf(_1774385, hAPP(c_Set_OCollect(_1774385), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool), tc_HOL_Obool, _1774385), c_HOL_OEx(tc_fun(_1774387, _1774385))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool), tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool), _1774385), hAPP(c_COMBS(tc_fun(_1774387, _1774385), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774387, _1774385)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774387, _1774385), tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774387, _1774385))), _1774389)))), hAPP(hAPP(c_COMBC(_1774385, tc_fun(tc_fun(_1774387, _1774385), _1774385), tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774385, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774387, _1774385), _1774385), tc_fun(tc_fun(_1774387, _1774385), tc_HOL_Obool)), _1774385), c_COMBB(_1774385, tc_HOL_Obool, tc_fun(_1774387, _1774385))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774387, _1774385), _1774387, _1774385), c_COMBI(tc_fun(_1774387, _1774385))), _1774391)))))))], (24018 ^ _776545) ^ [_1211359, _1211361] : [class_Rings_Oring__1(_1211359), -(hBOOL(hAPP(hAPP(c_member(_1211359), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211359), _1211361)), c_Int_Oring__1__class_OInts(_1211359))))], (17209 ^ _776545) ^ [_1086345, _1086347] : [class_Rings_Olinordered__ring(_1086345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086345), c_Groups_Ozero__class_Ozero(_1086345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086345), _1086347), _1086347))))], (43202 ^ _776545) ^ [_1637096, _1637098, _1637100] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637096), tc_List_Olist(_1637096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637096), tc_List_Olist(_1637096)), _1637098), c_List_Olist_ONil(_1637096))), c_List_Olistrel1(_1637096, _1637100)))], (23683 ^ _776545) ^ [_1205675, _1205677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205675), 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)), _1205677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205675), _1205677)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43803 ^ _776545) ^ [_1651071, _1651073, _1651075, _1651077, _1651079, _1651081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651071), tc_List_Olist(_1651071))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651071), tc_List_Olist(_1651071)), hAPP(hAPP(c_List_Oappend(_1651071), _1651073), hAPP(hAPP(c_List_Olist_OCons(_1651071), _1651075), c_List_Olist_ONil(_1651071)))), hAPP(hAPP(c_List_Oappend(_1651071), _1651077), hAPP(hAPP(c_List_Olist_OCons(_1651071), _1651079), c_List_Olist_ONil(_1651071))))), c_List_Olistrel1(_1651071, _1651081))), 43808 ^ _776545 : [(43811 ^ _776545) ^ [] : [-(_1651075 = _1651079)], (43809 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651071), tc_List_Olist(_1651071))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651071), tc_List_Olist(_1651071)), _1651073), _1651077)), c_List_Olistrel1(_1651071, _1651081))))]], 43812 ^ _776545 : [(43815 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651071, _1651071)), hAPP(hAPP(c_Product__Type_OPair(_1651071, _1651071), _1651075), _1651079)), _1651081)))], (43813 ^ _776545) ^ [] : [-(_1651073 = _1651077)]]], (44344 ^ _776545) ^ [_1663432, _1663434, _1663436, _1663438] : [class_Orderings_Olinorder(_1663432), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663434, _1663432, _1663436), _1663438), c_List_Olist_ONil(_1663434)) = hAPP(hAPP(c_List_Olist_OCons(_1663434), _1663438), c_List_Olist_ONil(_1663434)))], (37358 ^ _776545) ^ [_1487569, _1487571, _1487573, _1487575] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1487569), hAPP(c_Set_Oimage(_1487571, _1487569, _1487573), _1487575))), c_Fun_Oinj__on(_1487571, _1487569, _1487573, _1487575), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1487571), _1487575)))], (17141 ^ _776545) ^ [_1085165, _1085167, _1085169] : [class_Rings_Olinordered__ring__strict(_1085165), 17144 ^ _776545 : [(17159 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085165), _1085167), _1085169)), c_Groups_Ozero__class_Ozero(_1085165)))), 17160 ^ _776545 : [(17167 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), _1085167), c_Groups_Ozero__class_Ozero(_1085165))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), c_Groups_Ozero__class_Ozero(_1085165)), _1085169))], (17161 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), c_Groups_Ozero__class_Ozero(_1085165)), _1085167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), _1085169), c_Groups_Ozero__class_Ozero(_1085165)))]]], (17145 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085165), _1085167), _1085169)), c_Groups_Ozero__class_Ozero(_1085165))), 17150 ^ _776545 : [(17153 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), _1085169), c_Groups_Ozero__class_Ozero(_1085165))))], (17151 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), c_Groups_Ozero__class_Ozero(_1085165)), _1085167)))]], 17154 ^ _776545 : [(17157 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), c_Groups_Ozero__class_Ozero(_1085165)), _1085169)))], (17155 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085165), _1085167), c_Groups_Ozero__class_Ozero(_1085165))))]]]]], (2678 ^ _776545) ^ [_816111, _816113, _816115, _816117] : [-(c_Divides_Odivmod__nat(_816117, _816113) = c_Divides_Odivmod__nat(_816115, _816111)), _816117 = _816115, _816113 = _816111], (44751 ^ _776545) ^ [_1671293, _1671295, _1671297, _1671299, _1671301] : [c_Fun_Oinj__on(_1671293, _1671295, _1671297, c_Orderings_Otop__class_Otop(tc_fun(_1671293, tc_HOL_Obool))), 44754 ^ _776545 : [(44761 ^ _776545) ^ [] : [_1671299 = _1671301, -(hAPP(hAPP(c_List_Omap(_1671293, _1671295), _1671297), _1671299) = hAPP(hAPP(c_List_Omap(_1671293, _1671295), _1671297), _1671301))], (44755 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Omap(_1671293, _1671295), _1671297), _1671299) = hAPP(hAPP(c_List_Omap(_1671293, _1671295), _1671297), _1671301), -(_1671299 = _1671301)]]], (52531 ^ _776545) ^ [_1831904, _1831906] : [hBOOL(_1831904), -(hBOOL(hAPP(hAPP(c_fdisj, _1831906), _1831904)))], (21379 ^ _776545) ^ [_1163713, _1163715, _1163717, _1163719] : [class_Int_Onumber__ring(_1163713), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163713), hAPP(c_Int_Onumber__class_Onumber__of(_1163713), _1163715)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163713), _1163717), hAPP(c_Int_Onumber__class_Onumber__of(_1163713), _1163719))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163713), hAPP(c_Int_Onumber__class_Onumber__of(_1163713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163715), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163719)))), _1163717))], (35880 ^ _776545) ^ [_1447870, _1447872, _1447874] : [class_Orderings_Olinorder(_1447870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1447870), _1447872)), -(_1447872 = c_Orderings_Obot__class_Obot(tc_fun(_1447870, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1447870), _1447874), c_Big__Operators_Olattice_OInf__fin(_1447870, c_Orderings_Oord__class_Omin(_1447870), _1447872)) = c_Big__Operators_Olattice_OInf__fin(_1447870, c_Orderings_Oord__class_Omin(_1447870), hAPP(c_Set_OCollect(_1447870), hAPP(hAPP(c_COMBB(tc_fun(_1447870, tc_HOL_Obool), tc_HOL_Obool, _1447870), c_HOL_OEx(_1447870)), hAPP(hAPP(c_COMBC(_1447870, tc_fun(_1447870, tc_HOL_Obool), tc_fun(_1447870, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447870, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1447870, tc_HOL_Obool), tc_fun(_1447870, tc_HOL_Obool)), _1447870), c_COMBS(_1447870, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447870, tc_HOL_Obool), tc_fun(_1447870, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1447870), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1447870), c_fconj)), hAPP(hAPP(c_COMBC(_1447870, tc_fun(_1447870, _1447870), tc_fun(_1447870, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447870, tc_HOL_Obool), tc_fun(tc_fun(_1447870, _1447870), tc_fun(_1447870, tc_HOL_Obool)), _1447870), c_COMBB(_1447870, tc_HOL_Obool, _1447870)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1447870), _1447874))))), hAPP(hAPP(c_COMBC(_1447870, tc_fun(_1447870, tc_HOL_Obool), tc_HOL_Obool), c_member(_1447870)), _1447872))))))], (17463 ^ _776545) ^ [_1091039, _1091041, _1091043] : [class_Rings_Olinordered__semiring__strict(_1091039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091039), c_Groups_Ozero__class_Ozero(_1091039)), _1091041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091039), c_Groups_Ozero__class_Ozero(_1091039)), _1091043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091039), c_Groups_Ozero__class_Ozero(_1091039)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091039), _1091041), _1091043))))], (36446 ^ _776545) ^ [_1465473, _1465475] : [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)), _1465473), _1465475)), 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)), _1465473), 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)), _1465475), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (50247 ^ _776545) ^ [_1792295, _1792297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1792295), _1792297)), -(c_Quickcheck_Obeyond(_1792295, _1792297) = _1792297)], (51395 ^ _776545) ^ [_1816837, _1816839, _1816841, _1816843] : [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), _1816837, _1816839)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816841, _1816843))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816837), _1816839)), 51402 ^ _776545 : [(51405 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816839), _1816843)))], (51403 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816841), _1816837)))]]], (47259 ^ _776545) ^ [_1726729, _1726731, _1726733, _1726735, _1726737] : [-(c_List_OtakeWhile(_1726729, _1726731, hAPP(hAPP(c_List_Omap(_1726733, _1726729), _1726735), _1726737)) = hAPP(hAPP(c_List_Omap(_1726733, _1726729), _1726735), c_List_OtakeWhile(_1726733, hAPP(c_Fun_Ocomp(_1726729, tc_HOL_Obool, _1726733, _1726731), _1726735), _1726737)))], (1244 ^ _776545) ^ [_794959, _794961] : [-(class_Divides_Oring__div(_794959)), _794961 = _794959, class_Divides_Oring__div(_794961)], (34582 ^ _776545) ^ [_1420633, _1420635, _1420637, _1420639, _1420641, _1420643] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420633, tc_fun(_1420635, tc_HOL_Obool))), _1420637), _1420639), _1420641), _1420643)), -(hBOOL(hAPP(hAPP(_1420639, _1420641), _1420643)))], (31341 ^ _776545) ^ [_1339137, _1339139] : [class_Orderings_Olinorder(_1339137), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339137), _1339139), _1339139) = _1339139)], (33407 ^ _776545) ^ [_1390045, _1390047, _1390049, _1390051, _1390053] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390045, tc_fun(_1390047, tc_HOL_Obool)), _1390049), _1390051), _1390053))), 33408 ^ _776545 : [(33409 ^ _776545) ^ [_1390117] : [hBOOL(hAPP(hAPP(c_member(_1390045), _1390117), _1390049)), hBOOL(hAPP(hAPP(_1390051, _1390117), _1390053))]]], (52255 ^ _776545) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (5310 ^ _776545) ^ [_857599, _857601, _857603, _857605, _857607, _857609] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_857609, _857605, _857601) = c_Lazy__Sequence_Olazy__sequence_OInsert(_857607, _857603, _857599)), _857609 = _857607, _857605 = _857603, _857601 = _857599], (9922 ^ _776545) ^ [_946503, _946505, _946507] : [class_Orderings_Oorder(_946503), 9925 ^ _776545 : [(9932 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946503), _946505), _946507))), -(c_Orderings_Obot__class_Obot(tc_fun(_946503, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946503, _946505, _946507))], (9926 ^ _776545) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_946503, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946503, _946505, _946507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946503), _946505), _946507))]]], (48678 ^ _776545) ^ [_1757803, _1757805, _1757807, _1757809] : [hBOOL(hAPP(_1757803, _1757805)), -(hAPP(c_List_Ofilter(_1757807, _1757803), c_List_Oreplicate(_1757807, _1757809, _1757805)) = c_List_Oreplicate(_1757807, _1757809, _1757805))], (24164 ^ _776545) ^ [_1213686, _1213688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213686), _1213688)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1213686), _1213688) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (47116 ^ _776545) ^ [_1723609, _1723611] : [-(_1723609 = c_List_Olist_ONil(_1723611)), -(hAPP(c_List_Ohd(_1723611), hAPP(c_List_Orev(_1723611), _1723609)) = c_List_Olast(_1723611, _1723609))], (50534 ^ _776545) ^ [_1797977, _1797979, _1797981, _1797983] : [c_Fun_Obij__betw(_1797977, _1797979, _1797981, _1797983, c_Orderings_Obot__class_Obot(tc_fun(_1797979, tc_HOL_Obool))), -(_1797983 = c_Orderings_Obot__class_Obot(tc_fun(_1797977, tc_HOL_Obool)))], (46852 ^ _776545) ^ [_1717883, _1717885] : [class_Orderings_Olinorder(_1717883), 46855 ^ _776545 : [(46856 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1717883, _1717885), 46859 ^ _776545 : [(46860 ^ _776545) ^ [_1718054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718054), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717883)), _1717885))), 46863 ^ _776545 : [(46864 ^ _776545) ^ [_1718171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718171), _1718054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717883), hAPP(hAPP(c_List_Onth(_1717883), _1717885), _1718171)), hAPP(hAPP(c_List_Onth(_1717883), _1717885), _1718054))))]]]]], (46870 ^ _776545) ^ [] : [46872 ^ _776545 : [(46878 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717883), hAPP(hAPP(c_List_Onth(_1717883), _1717885), 46874 ^ [_1717883, _1717885])), hAPP(hAPP(c_List_Onth(_1717883), _1717885), 46871 ^ [_1717883, _1717885])))], (46876 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46874 ^ [_1717883, _1717885]), 46871 ^ [_1717883, _1717885])))], (46873 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46871 ^ [_1717883, _1717885]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717883)), _1717885))))]], -(c_List_Olinorder__class_Osorted(_1717883, _1717885))]]], (36657 ^ _776545) ^ [_1471551, _1471553] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471551), c_Orderings_Obot__class_Obot(tc_fun(_1471551, tc_HOL_Obool))), _1471553) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471551, tc_HOL_Obool), tc_HOL_Obool)))], (1374 ^ _776545) ^ [_796584, _796586] : [-(class_Lattices_Obounded__lattice__bot(_796584)), _796586 = _796584, class_Lattices_Obounded__lattice__bot(_796586)], (10477 ^ _776545) ^ [_956526, _956528, _956530] : [class_Groups_Oordered__ab__group__add(_956526), 10480 ^ _776545 : [(10487 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), _956530), hAPP(c_Groups_Ouminus__class_Ouminus(_956526), _956528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), _956528), hAPP(c_Groups_Ouminus__class_Ouminus(_956526), _956530))))], (10481 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), _956528), hAPP(c_Groups_Ouminus__class_Ouminus(_956526), _956530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956526), _956530), hAPP(c_Groups_Ouminus__class_Ouminus(_956526), _956528))))]]], (27399 ^ _776545) ^ [_1269347, _1269349] : [class_Groups_Oordered__ab__group__add__abs(_1269347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269347), c_Groups_Ozero__class_Ozero(_1269347)), _1269349)), -(hAPP(c_Groups_Oabs__class_Oabs(_1269347), _1269349) = _1269349)], (7530 ^ _776545) ^ [_900703, _900705, _900707, _900709] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900703, tc_HOL_Obool)), _900705), _900707), _900709)), -(hBOOL(hAPP(_900707, _900709)))], (46506 ^ _776545) ^ [_1711852, _1711854, _1711856] : [class_Orderings_Olinorder(_1711852), c_List_Olinorder__class_Osorted(_1711852, _1711854), -(c_List_Olinorder__class_Osorted(_1711852, c_List_Oremove1(_1711852, _1711856, _1711854)))], (25030 ^ _776545) ^ [_1229786, _1229788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229788)), -(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, _1229786, _1229788))))], (46219 ^ _776545) ^ [_1705858] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1705858)), c_List_Otranspose__rel(_1705858)), c_List_Olist_ONil(tc_List_Olist(_1705858)))), -(c_List_Otranspose(_1705858, c_List_Olist_ONil(tc_List_Olist(_1705858))) = c_List_Olist_ONil(tc_List_Olist(_1705858)))], (48862 ^ _776545) ^ [_1761529, _1761531, _1761533, _1761535, _1761537] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1761529, _1761531, _1761533, _1761535, _1761537) = c_Option_Ooption_Ooption__case(_1761529, tc_prod(_1761531, tc_Lazy__Sequence_Olazy__sequence(_1761531)), _1761533, hAPP(c_Product__Type_Oprod_Oprod__case(_1761531, tc_Lazy__Sequence_Olazy__sequence(_1761531), _1761529), _1761535), hAPP(c_Lazy__Sequence_Oyield(_1761531), _1761537)))], (8076 ^ _776545) ^ [_913817, _913819, _913821] : [class_Complete__Lattice_Ocomplete__lattice(_913817), -(c_Complete__Lattice_OSup__class_OSup(_913817, hAPP(hAPP(c_Set_Oinsert(_913817), _913819), _913821)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913817), _913819), c_Complete__Lattice_OSup__class_OSup(_913817, _913821)))], (23809 ^ _776545) ^ [_1207795, _1207797] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207795)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207797)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207795), _1207797)))], (35450 ^ _776545) ^ [_1437604, _1437606] : [-(c_Divides_Odivmod__int__rel(_1437604, _1437606) = 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, _1437604))), 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), _1437606)))))), 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)), _1437606))), 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)), _1437606))))), 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)), _1437606)))), 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), _1437606))), 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))))))))], (52237 ^ _776545) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (51473 ^ _776545) ^ [_1818260, _1818262] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818260), 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)))), _1818262)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818262), _1818260)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818260), _1818262)))], (39193 ^ _776545) ^ [_1533010, _1533012, _1533014, _1533016] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1533010, _1533012)), hAPP(hAPP(c_Product__Type_OSigma(_1533010, _1533012), hAPP(hAPP(c_Set_Oinsert(_1533010), _1533014), c_Orderings_Obot__class_Obot(tc_fun(_1533010, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1533012, tc_HOL_Obool), _1533010), _1533016))) = hAPP(c_Finite__Set_Ocard(_1533012), _1533016))], (28349 ^ _776545) ^ [_1285442, _1285444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285442)), c_Int_OBit1(_1285444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285442), _1285444)))], (12648 ^ _776545) ^ [_999467, _999469, _999471] : [class_Lattices_Oab__semigroup__idem__mult(_999467), hBOOL(hAPP(c_Finite__Set_Ofinite(_999467), _999469)), -(hAPP(c_Finite__Set_Ofold1(_999467, c_Groups_Otimes__class_Otimes(_999467)), hAPP(hAPP(c_Set_Oinsert(_999467), _999471), _999469)) = hAPP(hAPP(c_Finite__Set_Ofold(_999467, _999467, c_Groups_Otimes__class_Otimes(_999467)), _999471), _999469))], (1894 ^ _776545) ^ [_803084, _803086] : [-(class_Rings_Odvd(_803084)), _803086 = _803084, class_Rings_Odvd(_803086)], (41619 ^ _776545) ^ [_1595748, _1595750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595748, _1595748)), _1595750), c_Relation_OId(_1595748))), -(_1595750 = hAPP(hAPP(c_Product__Type_OPair(_1595748, _1595748), 41622 ^ [_1595748, _1595750]), 41622 ^ [_1595748, _1595750]))], (15634 ^ _776545) ^ [_1060155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060155), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26703 ^ _776545) ^ [_1258391, _1258393] : [c_Nat__Transfer_Onat__set(_1258391), c_Nat__Transfer_Onat__set(_1258393), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1258391), _1258393) = 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), _1258391)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1258393))))], (47076 ^ _776545) ^ [_1722779, _1722781, _1722783] : [_1722781 = hAPP(c_List_Orev(_1722779), _1722783), -(hAPP(c_List_Orev(_1722779), _1722781) = _1722783)], (15594 ^ _776545) ^ [_1059192, _1059194, _1059196, _1059198, _1059200] : [class_Groups_Ocomm__monoid__mult(_1059192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059194), _1059196)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059194), _1059198)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059192), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059192, _1059194, c_Groups_Otimes__class_Otimes(_1059192)), _1059200), c_Groups_Oone__class_Oone(_1059192)), _1059196)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059192, _1059194, c_Groups_Otimes__class_Otimes(_1059192)), _1059200), c_Groups_Oone__class_Oone(_1059192)), _1059198)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059192), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059192, _1059194, c_Groups_Otimes__class_Otimes(_1059192)), _1059200), c_Groups_Oone__class_Oone(_1059192)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1059194, tc_HOL_Obool)), _1059196), _1059198))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1059192, _1059194, c_Groups_Otimes__class_Otimes(_1059192)), _1059200), c_Groups_Oone__class_Oone(_1059192)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1059194, tc_HOL_Obool)), _1059196), _1059198))))], (52003 ^ _776545) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (24788 ^ _776545) ^ [_1224880, _1224882, _1224884, _1224886] : [class_Divides_Osemiring__div(_1224880), -(c_Divides_Odiv__class_Omod(_1224880, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224880), _1224882), _1224884), _1224886) = c_Divides_Odiv__class_Omod(_1224880, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224880), _1224882), c_Divides_Odiv__class_Omod(_1224880, _1224884, _1224886)), _1224886))], (51675 ^ _776545) ^ [_1821713, _1821715, _1821717, _1821719] : [class_Rings_Ocomm__semiring__1(_1821713), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821713), _1821715), _1821717)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821713), hAPP(hAPP(c_Power_Opower__class_Opower(_1821713), _1821715), _1821719)), hAPP(hAPP(c_Power_Opower__class_Opower(_1821713), _1821717), _1821719))))], (47652 ^ _776545) ^ [_1735132, _1735134] : [-(c_Wellfounded_Owf(_1735132, c_List_Omeasures(_1735132, _1735134)))], (39630 ^ _776545) ^ [_1545271, _1545273, _1545275, _1545277] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1545271), _1545273))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545275), hAPP(c_Set_Oimage(_1545271, _1545275, _1545277), _1545273))), 39638 ^ _776545 : [(39641 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545271), hAPP(c_Set_OCollect(_1545271), hAPP(hAPP(c_COMBS(_1545271, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545271), c_fconj), hAPP(hAPP(c_COMBC(_1545271, tc_fun(_1545271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545271)), _1545273))), hAPP(hAPP(c_COMBC(_1545271, _1545275, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1545275, tc_fun(_1545275, tc_HOL_Obool), _1545271), c_fequal), _1545277)), hAPP(_1545277, 39637 ^ [_1545271, _1545273, _1545275, _1545277]))))))], (39639 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545271), 39637 ^ [_1545271, _1545273, _1545275, _1545277]), _1545273)))]]], (43022 ^ _776545) ^ [_1634032, _1634034, _1634036] : [_1634032 = c_List_Olist_ONil(_1634034), -(c_List_Obutlast(_1634034, hAPP(hAPP(c_List_Olist_OCons(_1634034), _1634036), _1634032)) = c_List_Olist_ONil(_1634034))], (51519 ^ _776545) ^ [_1819058, _1819060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1819058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1819058), _1819060)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819060), _1819058))], (31269 ^ _776545) ^ [_1337664, _1337666, _1337668] : [class_Orderings_Olinorder(_1337664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337664), _1337666)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337664), _1337668)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337664, tc_HOL_Obool)), _1337666), _1337668) = c_Orderings_Obot__class_Obot(tc_fun(_1337664, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337664), c_Big__Operators_Olinorder__class_OMax(_1337664, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337664, tc_HOL_Obool)), _1337666), _1337668))), c_Big__Operators_Olinorder__class_OMax(_1337664, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337664, tc_HOL_Obool)), _1337666), _1337668))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1337664), c_Big__Operators_Olinorder__class_OMax(_1337664, _1337666)), c_Big__Operators_Olinorder__class_OMax(_1337664, _1337668)))], (26497 ^ _776545) ^ [_1254799, _1254801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254801)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1254799)), hAPP(c_Int_Onat, _1254801)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254799), _1254801)))], (7466 ^ _776545) ^ [_899472, _899474, _899476, _899478] : [hBOOL(hAPP(_899472, _899474)), hBOOL(hAPP(_899476, _899474)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899478, tc_HOL_Obool)), _899472), _899476), _899474)))], (52239 ^ _776545) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (26184 ^ _776545) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33815 ^ _776545) ^ [_1402850, _1402852, _1402854, _1402856, _1402858] : [-(_1402850 = c_Orderings_Obot__class_Obot(tc_fun(_1402852, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402852, tc_fun(_1402854, tc_HOL_Obool)), _1402850), hAPP(hAPP(c_COMBB(tc_fun(_1402854, tc_HOL_Obool), tc_fun(_1402854, tc_HOL_Obool), _1402852), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402854, tc_HOL_Obool)), _1402856)), _1402858)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402854, tc_HOL_Obool)), _1402856), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402852, tc_fun(_1402854, tc_HOL_Obool)), _1402850), _1402858)))], (29645 ^ _776545) ^ [_1307961, _1307963, _1307965] : [class_Rings_Olinordered__idom(_1307961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307961), c_Groups_Ozero__class_Ozero(_1307961)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307961), _1307963), 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)))), _1307965))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307961), c_Groups_Ozero__class_Ozero(_1307961)), _1307963)))], (48506 ^ _776545) ^ [_1753963, _1753965, _1753967, _1753969, _1753971] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753963, _1753965, _1753967), _1753969), _1753971)), -(hBOOL(hAPP(hAPP(_1753967, _1753971), _1753969)))], (31999 ^ _776545) ^ [_1351541, _1351543] : [class_Orderings_Olinorder(_1351541), -(c_Big__Operators_Olattice_OSup__fin(_1351541, c_Orderings_Oord__class_Omax(_1351541), hAPP(hAPP(c_Set_Oinsert(_1351541), _1351543), c_Orderings_Obot__class_Obot(tc_fun(_1351541, tc_HOL_Obool)))) = _1351543)], (43276 ^ _776545) ^ [_1638757, _1638759, _1638761] : [-(hBOOL(hAPP(hAPP(c_member(_1638757), _1638759), hAPP(c_List_Oset(_1638757), _1638761)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638757)), c_List_Oremove1(_1638757, _1638759, _1638761)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638757)), _1638761))], (41895 ^ _776545) ^ [_1603940, _1603942] : [-(c_List_Olistrel1(_1603940, hAPP(c_Relation_Oconverse(_1603940, _1603940), _1603942)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1603940), tc_List_Olist(_1603940)), c_List_Olistrel1(_1603940, _1603942)))], (302 ^ _776545) ^ [_781146, _781148, _781150, _781152] : [-(c_Nitpick_Owf_H(_781150, _781146)), c_Nitpick_Owf_H(_781152, _781148), _781152 = _781150, _781148 = _781146], (788 ^ _776545) ^ [_788391, _788393, _788395, _788397] : [-(c_Relation_Otrans(_788395, _788391)), c_Relation_Otrans(_788397, _788393), _788397 = _788395, _788393 = _788391], (39281 ^ _776545) ^ [_1535220, _1535222, _1535224, _1535226, _1535228, _1535230, _1535232, _1535234] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1535220, _1535222), tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535220, _1535222), _1535228), hAPP(c_COMBK(tc_fun(_1535222, tc_HOL_Obool), _1535220), _1535230))), hAPP(c_Product__Type_Oprod_Oprod__case(_1535220, _1535222, tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1535220, tc_fun(_1535222, tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool))), tc_fun(_1535222, tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool)), tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool)), tc_fun(tc_fun(_1535222, tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool))), tc_fun(_1535222, tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool))), _1535220), c_COMBB(tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool)), tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool), _1535222)), hAPP(hAPP(c_COMBB(tc_fun(_1535224, tc_HOL_Obool), tc_fun(tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool)), tc_fun(tc_prod(_1535224, _1535226), tc_HOL_Obool)), _1535220), c_Product__Type_OSigma(_1535224, _1535226)), _1535232))), hAPP(hAPP(c_COMBB(tc_fun(_1535226, tc_HOL_Obool), tc_fun(_1535224, tc_fun(_1535226, tc_HOL_Obool)), _1535222), c_COMBK(tc_fun(_1535226, tc_HOL_Obool), _1535224)), _1535234)))) = hAPP(hAPP(c_Product__Type_OSigma(_1535224, _1535226), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535220, tc_fun(_1535224, tc_HOL_Obool)), _1535228), _1535232)), hAPP(c_COMBK(tc_fun(_1535226, tc_HOL_Obool), _1535224), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535222, tc_fun(_1535226, tc_HOL_Obool)), _1535230), _1535234))))], (13748 ^ _776545) ^ [_1021475, _1021477, _1021479, _1021481] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021475), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021475), _1021477), _1021479)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021475), _1021477), _1021481)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021475), _1021479), _1021481))))], (52317 ^ _776545) ^ [_1829431] : [-(class_Nat_Osize(tc_Option_Ooption(_1829431)))], (17373 ^ _776545) ^ [_1089383, _1089385, _1089387] : [class_Rings_Olinordered__semiring__strict(_1089383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089383), _1089385), c_Groups_Ozero__class_Ozero(_1089383))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089383), c_Groups_Ozero__class_Ozero(_1089383)), _1089387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089383), _1089385), _1089387)), c_Groups_Ozero__class_Ozero(_1089383))))], (7956 ^ _776545) ^ [_911070, _911072] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911070, tc_HOL_Obool)), _911072), c_Orderings_Otop__class_Otop(tc_fun(_911070, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_911070, tc_HOL_Obool)))], (34095 ^ _776545) ^ [_1409632, _1409634, _1409636, _1409638, _1409640, _1409642] : [class_Groups_Ocomm__monoid__add(_1409632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409634), _1409636)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409634, _1409632), hAPP(hAPP(c_COMBS(_1409634, _1409632, _1409632), hAPP(hAPP(c_COMBS(_1409634, _1409632, tc_fun(_1409632, _1409632)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409632, tc_fun(_1409632, _1409632)), _1409634), c_If(_1409632)), _1409638)), _1409640)), _1409642)), _1409636) = 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hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1424069))))]]], (34739 ^ _776545) ^ [] : [_1424069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1424067), _1424069) = c_Groups_Ozero__class_Ozero(_1424067))]]], (48126 ^ _776545) ^ [_1745805, _1745807, _1745809, _1745811] : [c_List_Olist__ex(_1745805, _1745807, hAPP(hAPP(c_List_Olist_OCons(_1745805), _1745809), _1745811)), -(hBOOL(hAPP(_1745807, _1745809))), -(c_List_Olist__ex(_1745805, _1745807, _1745811))], (31451 ^ _776545) ^ [_1341299, _1341301, _1341303, _1341305] : [class_Orderings_Olinorder(_1341299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341299), _1341301), _1341303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341299), _1341305), _1341303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341299), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341299), _1341301), _1341305)), _1341303)))], (4616 ^ _776545) ^ [_846694, _846696] : [_846696 = _846694, -(c_Code__Numeral_OSuc__code__numeral(_846696) = c_Code__Numeral_OSuc__code__numeral(_846694))], (444 ^ _776545) ^ [_783219, _783221, _783223, _783225, _783227, _783229] : [-(c_Nitpick_Oless__frac(_783227, _783223, _783219)), c_Nitpick_Oless__frac(_783229, _783225, _783221), _783229 = _783227, _783225 = _783223, _783221 = _783219], (11220 ^ _776545) ^ [_971344, _971346, _971348] : [class_Groups_Oordered__ab__group__add(_971344), -(hAPP(c_Set_Oimage(_971344, _971344, c_Groups_Ouminus__class_Ouminus(_971344)), c_SetInterval_Oord__class_OatLeastAtMost(_971344, _971346, _971348)) = c_SetInterval_Oord__class_OatLeastAtMost(_971344, hAPP(c_Groups_Ouminus__class_Ouminus(_971344), _971348), hAPP(c_Groups_Ouminus__class_Ouminus(_971344), _971346)))], (35989 ^ _776545) ^ [_1452214, _1452216, _1452218] : [class_Lattices_Odistrib__lattice(_1452214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452214), _1452216)), -(_1452216 = c_Orderings_Obot__class_Obot(tc_fun(_1452214, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452214), _1452218), c_Big__Operators_Olattice__class_OSup__fin(_1452214, _1452216)) = c_Big__Operators_Olattice__class_OSup__fin(_1452214, hAPP(c_Set_OCollect(_1452214), hAPP(hAPP(c_COMBB(tc_fun(_1452214, tc_HOL_Obool), tc_HOL_Obool, _1452214), c_HOL_OEx(_1452214)), hAPP(hAPP(c_COMBC(_1452214, tc_fun(_1452214, tc_HOL_Obool), tc_fun(_1452214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452214, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1452214, tc_HOL_Obool), tc_fun(_1452214, tc_HOL_Obool)), _1452214), c_COMBS(_1452214, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452214, tc_HOL_Obool), tc_fun(_1452214, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1452214), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452214), c_fconj)), hAPP(hAPP(c_COMBC(_1452214, tc_fun(_1452214, _1452214), tc_fun(_1452214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452214, tc_HOL_Obool), tc_fun(tc_fun(_1452214, _1452214), tc_fun(_1452214, tc_HOL_Obool)), _1452214), c_COMBB(_1452214, tc_HOL_Obool, _1452214)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452214), _1452218))))), hAPP(hAPP(c_COMBC(_1452214, tc_fun(_1452214, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452214)), _1452216))))))], (27365 ^ _776545) ^ [_1268852] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1268852) = c_Int_OPls)], (44214 ^ _776545) ^ [_1660628, _1660630, _1660632] : [-(hAPP(c_List_Otl(_1660628), hAPP(hAPP(c_List_Oappend(_1660628), _1660630), _1660632)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1660628), _1660628, hAPP(c_List_Otl(_1660628), _1660632), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1660628), tc_List_Olist(_1660628)), _1660628), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660628), tc_List_Olist(_1660628), tc_List_Olist(_1660628)), c_List_Oappend(_1660628)), _1660632))), _1660630))], (43038 ^ _776545) ^ [_1634318, _1634320, _1634322, _1634324] : [_1634318 = _1634320, -(c_List_Oremove1(_1634322, _1634318, hAPP(hAPP(c_List_Olist_OCons(_1634322), _1634320), _1634324)) = _1634324)], (3194 ^ _776545) ^ [_824095, _824097, _824099, _824101] : [-(c_Big__Operators_Olinorder__class_OMin(_824101, _824097) = c_Big__Operators_Olinorder__class_OMin(_824099, _824095)), _824101 = _824099, _824097 = _824095], (4386 ^ _776545) ^ [_843045, _843047, _843049, _843051, _843053, _843055, _843057, _843059, _843061, _843063, _843065, _843067] : [-(c_New__Random__Sequence_Opos__union(_843067, _843063, _843059, _843055, _843051, _843047) = c_New__Random__Sequence_Opos__union(_843065, _843061, _843057, _843053, _843049, _843045)), _843067 = _843065, _843063 = _843061, _843059 = _843057, _843055 = _843053, _843051 = _843049, _843047 = _843045], (40584 ^ _776545) ^ [_1569022, _1569024] : [c_Wellfounded_Oacyclic(_1569022, _1569024), 40587 ^ _776545 : [(40588 ^ _776545) ^ [_1569107] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569022, _1569022)), hAPP(hAPP(c_Product__Type_OPair(_1569022, _1569022), _1569107), _1569107)), c_Transitive__Closure_Otrancl(_1569022, _1569024)))]]], (11161 ^ _776545) ^ [_969775, _969777, _969779, _969781] : [_969781 = c_Orderings_Obot__class_Obot(tc_fun(_969777, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_969775, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_969777, _969775, _969779), _969781))], (9322 ^ _776545) ^ [_936908, _936910, _936912] : [class_Orderings_Oorder(_936908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936908), _936910), _936912)), -(c_SetInterval_Oord__class_OatLeastAtMost(_936908, _936912, _936910) = c_Orderings_Obot__class_Obot(tc_fun(_936908, tc_HOL_Obool)))], (39467 ^ _776545) ^ [_1541399, _1541401, _1541403, _1541405] : [-(c_Product__Type_Oapsnd(_1541399, _1541401, _1541403, _1541405) = c_Product__Type_Omap__pair(_1541403, _1541403, _1541399, _1541401, c_Fun_Oid(_1541403), _1541405))], (44112 ^ _776545) ^ [_1658912, _1658914, _1658916] : [_1658912 = c_List_Olist_ONil(_1658914), -(hAPP(c_List_Ohd(_1658914), hAPP(hAPP(c_List_Oappend(_1658914), _1658912), _1658916)) = hAPP(c_List_Ohd(_1658914), _1658916))], (8937 ^ _776545) ^ [_930675, _930677, _930679, _930681, _930683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930675, tc_HOL_Obool)), _930677), _930679)), 8943 ^ _776545 : [(8948 ^ _776545) ^ [] : [hBOOL(hAPP(_930683, 8942 ^ [_930675, _930677, _930679, _930681, _930683]))], (8946 ^ _776545) ^ [] : [-(hBOOL(hAPP(_930681, 8942 ^ [_930675, _930677, _930679, _930681, _930683])))], (8944 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930675), 8942 ^ [_930675, _930677, _930679, _930681, _930683]), _930677)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930675, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930675, tc_HOL_Obool)), _930677), hAPP(c_Set_OCollect(_930675), _930681))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930675, tc_HOL_Obool)), _930679), hAPP(c_Set_OCollect(_930675), _930683)))))], (45964 ^ _776545) ^ [_1698599, _1698601, _1698603, _1698605] : [-(hAPP(hAPP(c_List_Omap(_1698599, _1698601), _1698603), c_List_Oconcat(_1698599, _1698605)) = c_List_Oconcat(_1698601, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698599), tc_List_Olist(_1698601)), hAPP(c_List_Omap(_1698599, _1698601), _1698603)), _1698605)))], (30006 ^ _776545) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (42693 ^ _776545) ^ [_1626551, _1626553, _1626555, _1626557, _1626559, _1626561, _1626563] : [-(hAPP(hAPP(c_List_Ozip(_1626551, _1626553), hAPP(hAPP(c_List_Olist__update(_1626551, _1626555), _1626557), _1626559)), hAPP(hAPP(c_List_Olist__update(_1626553, _1626561), _1626557), _1626563)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1626551, _1626553), hAPP(hAPP(c_List_Ozip(_1626551, _1626553), _1626555), _1626561)), _1626557), hAPP(hAPP(c_Product__Type_OPair(_1626551, _1626553), _1626559), _1626563)))], (200 ^ _776545) ^ [_779817, _779819] : [-(class_Rings_Odivision__ring(_779817)), _779819 = _779817, class_Rings_Odivision__ring(_779819)], (38022 ^ _776545) ^ [_1503360, _1503362, _1503364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1503360, _1503360), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1503360, _1503360, _1503360), _1503362), _1503364)), _1503362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1503360, _1503362)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1503360, _1503364)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1503360, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1503360, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1503360, tc_HOL_Obool), tc_fun(_1503360, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1503360, _1503362))))], (29329 ^ _776545) ^ [_1302103] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1302103)), 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, _1302103, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (32830 ^ _776545) ^ [_1373387, _1373389, _1373391, _1373393, _1373395] : [32832 ^ _776545 : [(32835 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373387, tc_HOL_Obool)), _1373389), hAPP(_1373395, 32831 ^ [_1373387, _1373389, _1373391, _1373393, _1373395])))], (32833 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373391), 32831 ^ [_1373387, _1373389, _1373391, _1373393, _1373395]), _1373393)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373387, tc_HOL_Obool)), _1373389), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1373391, tc_fun(_1373387, tc_HOL_Obool)), _1373393), _1373395))))], (24571 ^ _776545) ^ [_1221017, _1221019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221017)), -(c_SMT_Oz3div(_1221019, _1221017) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221019), _1221017))], (29779 ^ _776545) ^ [_1310597, _1310599] : [_1310597 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1310597, _1310599) = _1310599)], (18762 ^ _776545) ^ [_1114430, _1114432, _1114434, _1114436] : [class_Groups_Ocomm__monoid__add(_1114430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114432), _1114434)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114430), _1114436), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1114432), _1114434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114430), hAPP(_1114436, _1114432)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114430), _1114436), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1114432)), _1114434))))], (11580 ^ _776545) ^ [_979048, _979050] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979048), c_Complete__Lattice_OSup__class_OSup(tc_fun(_979048, tc_HOL_Obool), _979050))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979048, tc_HOL_Obool)), _979050)))], (12363 ^ _776545) ^ [_993686, _993688, _993690] : [class_Lattices_Olattice(_993686), hBOOL(hAPP(c_Finite__Set_Ofinite(_993686), _993688)), -(_993688 = c_Orderings_Obot__class_Obot(tc_fun(_993686, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_993686), _993690)), -(_993690 = c_Orderings_Obot__class_Obot(tc_fun(_993686, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993686, tc_HOL_Obool)), _993688), _993690) = c_Orderings_Obot__class_Obot(tc_fun(_993686, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_993686, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993686, tc_HOL_Obool)), _993688), _993690)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_993686), c_Big__Operators_Olattice__class_OSup__fin(_993686, _993688)), c_Big__Operators_Olattice__class_OSup__fin(_993686, _993690)))], (49798 ^ _776545) ^ [_1782631, _1782633, _1782635] : [-(c_Equiv__Relations_Oequiv(_1782631, _1782633, _1782635)), c_Relation_Orefl__on(_1782631, _1782633, _1782635), c_Relation_Osym(_1782631, _1782635), c_Relation_Otrans(_1782631, _1782635)], (6528 ^ _776545) ^ [_881950, _881952] : [-(hBOOL(hAPP(hAPP(c_member(_881950), _881952), c_Orderings_Otop__class_Otop(tc_fun(_881950, tc_HOL_Obool)))))], (39179 ^ _776545) ^ [_1532644, _1532646, _1532648, _1532650, _1532652, _1532654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532644, _1532646)), hAPP(hAPP(c_Product__Type_OPair(_1532644, _1532646), _1532648), _1532650)), hAPP(hAPP(c_Product__Type_OSigma(_1532644, _1532646), _1532652), _1532654))), -(hBOOL(hAPP(hAPP(c_member(_1532646), _1532650), hAPP(_1532654, _1532648))))], (45052 ^ _776545) ^ [_1678781, _1678783] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678781), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1678783), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45059 ^ _776545 : [(45066 ^ _776545) ^ [] : [_1678781 = _1678783, -(hAPP(c_Code__Numeral_Oof__nat, _1678781) = hAPP(c_Code__Numeral_Oof__nat, _1678783))], (45060 ^ _776545) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1678781) = hAPP(c_Code__Numeral_Oof__nat, _1678783), -(_1678781 = _1678783)]]], (16102 ^ _776545) ^ [_1067614, _1067616] : [16103 ^ _776545 : [(16106 ^ _776545) ^ [] : [_1067614 = hAPP(c_Nat_OSuc, _1067616)], (16104 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067614), _1067616))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067614), hAPP(c_Nat_OSuc, _1067616))))], (3264 ^ _776545) ^ [_825224, _825226, _825228, _825230, _825232, _825234, _825236, _825238] : [-(c_Nitpick_Osetsum_H(_825238, _825234, _825230, _825226) = c_Nitpick_Osetsum_H(_825236, _825232, _825228, _825224)), _825238 = _825236, _825234 = _825232, _825230 = _825228, _825226 = _825224], (31353 ^ _776545) ^ [_1339337, _1339339, _1339341] : [class_Orderings_Olinorder(_1339337), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339337), _1339339), _1339341) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339337), _1339341), _1339339))], (41383 ^ _776545) ^ [_1589100, _1589102, _1589104, _1589106, _1589108] : [c_Relation_Osingle__valued(_1589100, _1589102, hAPP(c_Relation_Oconverse(_1589102, _1589100), _1589104)), -(hAPP(c_Relation_OImage(_1589102, _1589100, _1589104), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589102, tc_HOL_Obool)), _1589106), _1589108)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589100, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1589102, _1589100, _1589104), _1589106)), hAPP(c_Relation_OImage(_1589102, _1589100, _1589104), _1589108)))], (26821 ^ _776545) ^ [_1260045, _1260047] : [c_Nat__Transfer_Ois__nat(_1260045), c_Nat__Transfer_Ois__nat(_1260047), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1260045, _1260047)))], (32622 ^ _776545) ^ [_1368111, _1368113, _1368115] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368111, tc_HOL_Obool)), _1368113), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1368111, tc_HOL_Obool), _1368115)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1368111, tc_HOL_Obool), tc_fun(_1368111, tc_HOL_Obool)), _1368115), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368111, tc_HOL_Obool)), _1368113)))], (16128 ^ _776545) ^ [_1068097, _1068099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068097), hAPP(c_Nat_OSuc, _1068099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068097), _1068099))), -(_1068097 = hAPP(c_Nat_OSuc, _1068099))], (28939 ^ _776545) ^ [_1295326, _1295328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295326)), c_Int_OBit1(_1295328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295326), _1295328)))], (31287 ^ _776545) ^ [_1338012, _1338014, _1338016] : [class_Orderings_Olinorder(_1338012), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338012), _1338014), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338012), _1338014), _1338016)) = _1338014)], (8333 ^ _776545) ^ [_919351, _919353, _919355] : [class_Lattices_Olattice(_919351), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919351), _919353), _919355) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919351), _919355), _919353))], (47128 ^ _776545) ^ [_1723827, _1723829, _1723831] : [-(hAPP(c_List_Orev(_1723827), hAPP(hAPP(c_List_Odrop(_1723827), _1723829), _1723831)) = hAPP(hAPP(c_List_Otake(_1723827), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723827)), _1723831)), _1723829)), hAPP(c_List_Orev(_1723827), _1723831)))], (51507 ^ _776545) ^ [_1818890] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818890), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1818890 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41395 ^ _776545) ^ [_1589490, _1589492] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589490, _1589490)), hAPP(hAPP(c_Product__Type_OPair(_1589490, _1589490), 41396 ^ [_1589490, _1589492]), 41396 ^ [_1589490, _1589492])), c_Transitive__Closure_Otrancl(_1589490, _1589492)))), -(c_Wellfounded_Oacyclic(_1589490, _1589492))], (48784 ^ _776545) ^ [_1759871, _1759873, _1759875, _1759877] : [-(c_Lazy__Sequence_Oappend(_1759871, c_Lazy__Sequence_Olazy__sequence_OInsert(_1759871, _1759873, _1759875), _1759877) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1759871, _1759873, c_Lazy__Sequence_Oappend(_1759871, _1759875, _1759877)))], (28897 ^ _776545) ^ [_1294604, _1294606] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1294604), _1294606)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1294604)), c_Int_OBit0(_1294606))))], (52197 ^ _776545) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (40739 ^ _776545) ^ [_1573505, _1573507] : [-(c_Transitive__Closure_Ortrancl(_1573505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1573505, _1573505), tc_HOL_Obool)), _1573507), c_Relation_OId(_1573505))) = c_Transitive__Closure_Ortrancl(_1573505, _1573507))], (36202 ^ _776545) ^ [_1459264, _1459266, _1459268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1459264, 36203 ^ [_1459264, _1459266, _1459268])), hAPP(_1459266, 36203 ^ [_1459264, _1459266, _1459268]))), -(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), _1459266), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459268))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1459264), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459268))) = 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)), _1459266)), _1459264)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459268)))], (36496 ^ _776545) ^ [_1467173, _1467175, _1467177, _1467179, _1467181, _1467183] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467179, _1467179)), hAPP(hAPP(c_Product__Type_OPair(_1467179, _1467179), hAPP(_1467183, _1467175)), hAPP(_1467183, _1467177))), _1467181)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1467173, _1467173)), hAPP(hAPP(c_Product__Type_OPair(_1467173, _1467173), _1467175), _1467177)), hAPP(hAPP(c_Relation_Oinv__image(_1467179, _1467173), _1467181), _1467183))))], (33109 ^ _776545) ^ [_1381850, _1381852, _1381854, _1381856, _1381858] : [-(hBOOL(hAPP(hAPP(c_member(_1381850), _1381852), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381854, tc_fun(_1381850, tc_HOL_Obool)), _1381856), _1381858)))), 33110 ^ _776545 : [(33111 ^ _776545) ^ [_1381932] : [hBOOL(hAPP(hAPP(c_member(_1381854), _1381932), _1381856)), hBOOL(hAPP(hAPP(c_member(_1381850), _1381852), hAPP(_1381858, _1381932)))]]], (43573 ^ _776545) ^ [_1645783, _1645785, _1645787] : [-(c_List_Olist_ONil(_1645783) = hAPP(hAPP(c_List_Oappend(_1645783), _1645785), _1645787)), _1645785 = c_List_Olist_ONil(_1645783), _1645787 = c_List_Olist_ONil(_1645783)], (32990 ^ _776545) ^ [_1378770, _1378772, _1378774] : [hBOOL(hAPP(_1378770, _1378772)), -(hAPP(c_Set_OCollect(_1378774), hAPP(hAPP(c_COMBS(_1378774, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378774), c_fconj), hAPP(hAPP(c_COMBC(_1378774, _1378774, tc_HOL_Obool), c_fequal), _1378772))), _1378770)) = hAPP(hAPP(c_Set_Oinsert(_1378774), _1378772), c_Orderings_Obot__class_Obot(tc_fun(_1378774, tc_HOL_Obool))))], (42161 ^ _776545) ^ [_1612025, _1612027, _1612029] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612025)), _1612027), c_List_Olists(_1612025, c_Wellfounded_Oacc(_1612025, _1612029)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612025)), _1612027), c_Wellfounded_Oacc(tc_List_Olist(_1612025), c_List_Olistrel1(_1612025, _1612029)))))], (45467 ^ _776545) ^ [_1688224, _1688226, _1688228, _1688230, _1688232, _1688234, _1688236] : [c_List_Olist__all2(_1688224, _1688232, hAPP(hAPP(c_COMBC(_1688224, tc_fun(_1688232, _1688226), tc_fun(_1688232, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688226, tc_HOL_Obool), tc_fun(tc_fun(_1688232, _1688226), tc_fun(_1688232, tc_HOL_Obool)), _1688224), c_COMBB(_1688226, tc_HOL_Obool, _1688232)), _1688228)), _1688234), _1688230, _1688236), -(c_List_Olist__all2(_1688224, _1688226, _1688228, _1688230, hAPP(hAPP(c_List_Omap(_1688232, _1688226), _1688234), _1688236)))], (1454 ^ _776545) ^ [_797584, _797586] : [-(class_Groups_Ouminus(_797584)), _797586 = _797584, class_Groups_Ouminus(_797586)], (2614 ^ _776545) ^ [_815105, _815107] : [_815107 = _815105, -(c_Nitpick_Ozero__frac(_815107) = c_Nitpick_Ozero__frac(_815105))], (49121 ^ _776545) ^ [_1767524, _1767526, _1767528] : [-(c_Random__Sequence_Oempty(_1767524, _1767526, _1767528) = 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(_1767524)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1767524)))], (38544 ^ _776545) ^ [_1515721, _1515723, _1515725, _1515727] : [38545 ^ _776545 : [(38546 ^ _776545) ^ [_1515796] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515725, _1515721)), hAPP(hAPP(c_Product__Type_OPair(_1515725, _1515721), _1515796), _1515723)), _1515727))]], -(hBOOL(hAPP(hAPP(c_member(_1515721), _1515723), hAPP(c_Relation_ORange(_1515725, _1515721), _1515727))))], (24032 ^ _776545) ^ [_1211630, _1211632] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211630)), _1211632) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211630), _1211632)))], (33963 ^ _776545) ^ [_1406556, _1406558, _1406560, _1406562, _1406564, _1406566] : [class_Groups_Ocomm__monoid__add(_1406556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406558), _1406560)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406558, _1406556), _1406562), _1406560) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406564, _1406556), hAPP(hAPP(c_COMBB(tc_fun(_1406558, tc_HOL_Obool), _1406556, _1406564), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406558, _1406556), _1406562)), hAPP(hAPP(c_COMBB(tc_fun(_1406558, tc_HOL_Obool), tc_fun(_1406558, tc_HOL_Obool), _1406564), c_Set_OCollect(_1406558)), hAPP(hAPP(c_COMBB(tc_fun(_1406558, tc_HOL_Obool), tc_fun(_1406558, tc_HOL_Obool), _1406564), hAPP(c_COMBS(_1406558, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1406558), c_fconj), hAPP(hAPP(c_COMBC(_1406558, tc_fun(_1406558, tc_HOL_Obool), tc_HOL_Obool), c_member(_1406558)), _1406560)))), hAPP(c_COMBC(_1406558, _1406564, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1406564, tc_fun(_1406564, tc_HOL_Obool), _1406558), c_fequal), _1406566)))))), hAPP(c_Set_Oimage(_1406558, _1406564, _1406566), _1406560)))], (39643 ^ _776545) ^ [_1545736, _1545738, _1545740] : [c_Predicate_Oreflp(_1545736, _1545738), -(hBOOL(hAPP(hAPP(_1545738, _1545740), _1545740)))], (8859 ^ _776545) ^ [_928989, _928991, _928993] : [class_Orderings_Olinorder(_928989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928989), _928991), _928993)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928989, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_928989, _928991, _928993)), hAPP(hAPP(c_Set_Oinsert(_928989), _928993), c_Orderings_Obot__class_Obot(tc_fun(_928989, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_928989, _928991, _928993))], (33036 ^ _776545) ^ [_1379784, _1379786, _1379788, _1379790] : [class_Fields_Olinordered__field(_1379784), -(hAPP(c_Groups_Oabs__class_Oabs(_1379784), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379786, _1379784), _1379788), _1379790)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379786, _1379784), hAPP(hAPP(c_COMBB(_1379784, _1379784, _1379786), c_Groups_Oabs__class_Oabs(_1379784)), _1379788)), _1379790))], (25040 ^ _776545) ^ [_1229935, _1229937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1229935, _1229937)), _1229935)))], (40122 ^ _776545) ^ [_1558191, _1558193, _1558195, _1558197, _1558199, _1558201, _1558203, _1558205] : [c_Finite__Set_Ofolding(_1558191, _1558193, _1558195, _1558197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558191), _1558199)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558191), _1558201)), -(hAPP(c_Fun_Ocomp(_1558193, _1558193, _1558203, hAPP(_1558197, _1558201)), hAPP(c_Fun_Ocomp(_1558193, _1558193, _1558203, hAPP(_1558197, _1558199)), _1558205)) = hAPP(c_Fun_Ocomp(_1558193, _1558193, _1558203, hAPP(_1558197, _1558199)), hAPP(c_Fun_Ocomp(_1558193, _1558193, _1558203, hAPP(_1558197, _1558201)), _1558205)))], (12269 ^ _776545) ^ [_991924, _991926, _991928] : [class_Lattices_Olattice(_991924), hBOOL(hAPP(c_Finite__Set_Ofinite(_991924), _991926)), -(hBOOL(hAPP(hAPP(c_member(_991924), _991928), _991926))), -(_991926 = c_Orderings_Obot__class_Obot(tc_fun(_991924, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_991924, hAPP(hAPP(c_Set_Oinsert(_991924), _991928), _991926)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_991924), _991928), c_Big__Operators_Olattice__class_OSup__fin(_991924, _991926)))], (34379 ^ _776545) ^ [_1416523, _1416525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416523), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416525)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416523)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416525))], (29503 ^ _776545) ^ [_1305007, _1305009, _1305011] : [class_Rings_Oring__1(_1305007), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305007), hAPP(c_Groups_Ouminus__class_Ouminus(_1305007), _1305009)), 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)))), _1305011)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1305007), _1305009), 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)))), _1305011)))], (32402 ^ _776545) ^ [_1359562] : [-(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)), _1359562)))))], (5066 ^ _776545) ^ [_853779, _853781, _853783, _853785, _853787, _853789, _853791, _853793] : [-(c_Product__Type_Ocurry(_853793, _853789, _853785, _853781) = c_Product__Type_Ocurry(_853791, _853787, _853783, _853779)), _853793 = _853791, _853789 = _853787, _853785 = _853783, _853781 = _853779], (50261 ^ _776545) ^ [_1792454, _1792456, _1792458, _1792460, _1792462, _1792464] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792454, _1792456, _1792458, _1792460, c_Lazy__Sequence_Olazy__sequence_OInsert(_1792456, _1792462, _1792464)) = hAPP(hAPP(hAPP(_1792460, _1792462), _1792464), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792454, _1792456, _1792458, _1792460, _1792464)))], (43200 ^ _776545) ^ [_1637028, _1637030, _1637032] : [-(hAPP(hAPP(c_List_Otake(_1637028), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1637028), _1637030), _1637032)) = hAPP(hAPP(c_List_Olist_OCons(_1637028), _1637030), c_List_Olist_ONil(_1637028)))], (28529 ^ _776545) ^ [_1288450, _1288452] : [class_Int_Onumber__ring(_1288450), -(hAPP(c_Int_Onumber__class_Onumber__of(_1288450), c_Int_OBit1(_1288452)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288450), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288450), c_Groups_Oone__class_Oone(_1288450)), hAPP(c_Int_Onumber__class_Onumber__of(_1288450), _1288452))), hAPP(c_Int_Onumber__class_Onumber__of(_1288450), _1288452)))], (29785 ^ _776545) ^ [_1310674, _1310676] : [-(_1310674 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1310674, _1310676) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1310674), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1310676)))], (13447 ^ _776545) ^ [_1015573, _1015575, _1015577, _1015579, _1015581, _1015583, _1015585, _1015587] : [class_Groups_Ocomm__monoid__add(_1015573), class_Orderings_Oord(_1015575), _1015577 = _1015579, _1015581 = _1015583, 13465 ^ _776545 : [(13470 ^ _776545) ^ [] : [hAPP(_1015585, 13464 ^ [_1015573, _1015575, _1015577, _1015579, _1015581, _1015583, _1015585, _1015587]) = hAPP(_1015587, 13464 ^ [_1015573, _1015575, _1015577, _1015579, _1015581, _1015583, _1015585, _1015587])], (13468 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015575), 13464 ^ [_1015573, _1015575, _1015577, _1015579, _1015581, _1015583, _1015585, _1015587]), _1015583)))], (13466 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015575), _1015579), 13464 ^ [_1015573, _1015575, _1015577, _1015579, _1015581, _1015583, _1015585, _1015587])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1015575, _1015573), _1015585), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1015575, _1015577), _1015581)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1015575, _1015573), _1015587), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1015575, _1015579), _1015583)))], (41911 ^ _776545) ^ [_1604533, _1604535, _1604537, _1604539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604533), tc_List_Olist(_1604533))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604533), tc_List_Olist(_1604533)), _1604535), _1604537)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1604533), c_List_Olistrel1(_1604533, _1604539)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604533)), _1604535) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604533)), _1604537))], (45900 ^ _776545) ^ [_1697319, _1697321, _1697323, _1697325] : [class_Orderings_Olinorder(_1697319), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697321)), c_List_Olinorder__class_Osort__key(_1697321, _1697319, _1697323, _1697325)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697321)), _1697325))], (24776 ^ _776545) ^ [_1224662, _1224664, _1224666] : [class_Divides_Osemiring__div(_1224662), -(c_Divides_Odiv__class_Omod(_1224662, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224662), _1224664), _1224666), _1224666) = c_Divides_Odiv__class_Omod(_1224662, _1224664, _1224666))], (9750 ^ _776545) ^ [_943489, _943491, _943493, _943495] : [class_Lattices_Osemilattice__inf(_943489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943489), _943491), _943493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943489), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_943489), _943495), _943491)), _943493)))], (29671 ^ _776545) ^ [_1308482, _1308484] : [class_Int_Onumber__ring(_1308482), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1308482), hAPP(c_Int_Onumber__class_Onumber__of(_1308482), 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)))), _1308484)) = c_Groups_Oone__class_Oone(_1308482))], (27665 ^ _776545) ^ [_1274060, _1274062, _1274064] : [class_Groups_Oordered__ab__group__add__abs(_1274060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274060), hAPP(c_Groups_Oabs__class_Oabs(_1274060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1274060), _1274062), _1274064))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1274060), hAPP(c_Groups_Oabs__class_Oabs(_1274060), _1274062)), hAPP(c_Groups_Oabs__class_Oabs(_1274060), _1274064)))))], (4002 ^ _776545) ^ [_836987, _836989, _836991, _836993, _836995, _836997, _836999, _837001] : [-(c_Lazy__Sequence_Ohb__bind(_837001, _836997, _836993, _836989) = c_Lazy__Sequence_Ohb__bind(_836999, _836995, _836991, _836987)), _837001 = _836999, _836997 = _836995, _836993 = _836991, _836989 = _836987], (38967 ^ _776545) ^ [_1526967, _1526969] : [c_Nitpick_Owf_H(_1526967, _1526969), 38970 ^ _776545 : [(38973 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1526967, _1526967)), _1526969))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (38971 ^ _776545) ^ [] : [-(c_Wellfounded_Oacyclic(_1526967, _1526969))]]], (27871 ^ _776545) ^ [_1277651, _1277653] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1277651), hAPP(hAPP(c_Power_Opower__class_Opower(_1277651), hAPP(c_Int_Onumber__class_Onumber__of(_1277651), c_Int_OMin)), _1277653)) = c_Groups_Oone__class_Oone(_1277651)), class_Int_Onumber__ring(_1277651), class_Rings_Olinordered__idom(_1277651)], (1104 ^ _776545) ^ [_793209, _793211] : [-(class_Groups_Oordered__ab__group__add__abs(_793209)), _793211 = _793209, class_Groups_Oordered__ab__group__add__abs(_793211)], (36577 ^ _776545) ^ [_1469557, _1469559, _1469561, _1469563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469557), _1469563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469561), _1469559))), -(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), _1469557), _1469559)), 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), _1469561), _1469563)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (25135 ^ _776545) ^ [_1231500, _1231502, _1231504, _1231506] : [class_Divides_Osemiring__div(_1231500), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231500), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231500), _1231502), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231500), _1231504), _1231502))), c_Divides_Odiv__class_Omod(_1231500, _1231504, _1231502))), _1231506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231500), _1231504), _1231506))], (41949 ^ _776545) ^ [_1605763, _1605765, _1605767, _1605769, _1605771, _1605773] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605763), tc_List_Olist(_1605763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605763), tc_List_Olist(_1605763)), hAPP(hAPP(c_List_Olist_OCons(_1605763), _1605765), _1605767)), hAPP(hAPP(c_List_Olist_OCons(_1605763), _1605769), _1605771))), c_List_Olistrel1(_1605763, _1605773)))), 41950 ^ _776545 : [(41957 ^ _776545) ^ [] : [_1605765 = _1605769, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605763), tc_List_Olist(_1605763))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605763), tc_List_Olist(_1605763)), _1605767), _1605771)), c_List_Olistrel1(_1605763, _1605773)))], (41951 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605763, _1605763)), hAPP(hAPP(c_Product__Type_OPair(_1605763, _1605763), _1605765), _1605769)), _1605773)), _1605767 = _1605771]]], (31333 ^ _776545) ^ [_1339000, _1339002] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1339000)), hAPP(c_Nat_OSuc, _1339002)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1339000), _1339002)))], (52039 ^ _776545) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (16793 ^ _776545) ^ [_1078757, _1078759, _1078761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078759), _1078761)), -(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, _1078757)), _1078759)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078757)), _1078761))))], (36614 ^ _776545) ^ [_1470422, _1470424] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1470422, _1470422)), _1470424)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1470422), hAPP(c_Relation_OField(_1470422), _1470424))))], (33054 ^ _776545) ^ [_1380281, _1380283, _1380285, _1380287, _1380289, _1380291] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380281, tc_fun(_1380283, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380285, _1380281, _1380287), _1380289)), _1380291) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380285, tc_fun(_1380283, tc_HOL_Obool)), _1380289), hAPP(hAPP(c_COMBB(_1380281, tc_fun(_1380283, tc_HOL_Obool), _1380285), _1380291), _1380287)))], (47283 ^ _776545) ^ [_1727141, _1727143, _1727145] : [hBOOL(hAPP(c_List_Odistinct(_1727141), _1727143)), -(hBOOL(hAPP(c_List_Odistinct(_1727141), c_List_OtakeWhile(_1727141, _1727145, _1727143))))], (32876 ^ _776545) ^ [_1375589, _1375591, _1375593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375589, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1375589, tc_fun(_1375589, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375589)), _1375591)), hAPP(hAPP(c_COMBC(_1375589, tc_fun(_1375589, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375589)), _1375593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375589, tc_HOL_Obool)), _1375591), _1375593)))], (50977 ^ _776545) ^ [_1808901] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1808901)))], (5204 ^ _776545) ^ [_855962, _855964, _855966, _855968] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_855968, _855964) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_855966, _855962)), _855968 = _855966, _855964 = _855962], (33639 ^ _776545) ^ [_1397653, _1397655, _1397657, _1397659] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397653, tc_fun(_1397655, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397653, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1397655, tc_HOL_Obool), tc_fun(_1397655, tc_HOL_Obool), _1397653), hAPP(c_COMBC(_1397655, tc_fun(_1397655, tc_HOL_Obool), tc_HOL_Obool), c_member(_1397655))), _1397657)), _1397659)), -(hBOOL(hAPP(hAPP(c_member(_1397655), _1397659), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397653, tc_fun(_1397655, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1397653, tc_HOL_Obool))), _1397657))))], (28611 ^ _776545) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (43543 ^ _776545) ^ [_1645030, _1645032, _1645034] : [class_Groups_Omonoid__add(_1645030), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645030), hAPP(hAPP(c_List_Oappend(_1645030), _1645032), _1645034)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645030), hAPP(c_List_Omonoid__add__class_Olistsum(_1645030), _1645032)), hAPP(c_List_Omonoid__add__class_Olistsum(_1645030), _1645034)))], (27036 ^ _776545) ^ [_1263478] : [class_Int_Onumber__ring(_1263478), -(hAPP(c_Int_Oring__1__class_Oof__int(_1263478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1263478), c_Int_OMin))], (26795 ^ _776545) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (1304 ^ _776545) ^ [_795709, _795711] : [-(class_Rings_Oring__1(_795709)), _795711 = _795709, class_Rings_Oring__1(_795711)], (42537 ^ _776545) ^ [_1623065, _1623067, _1623069, _1623071, _1623073, _1623075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623065, _1623067)), hAPP(hAPP(c_Product__Type_OPair(_1623065, _1623067), _1623069), _1623071)), hAPP(c_List_Oset(tc_prod(_1623065, _1623067)), hAPP(hAPP(c_List_Ozip(_1623065, _1623067), _1623073), _1623075)))), 42540 ^ _776545 : [(42543 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623067), _1623071), hAPP(c_List_Oset(_1623067), _1623075))))], (42541 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623065), _1623069), hAPP(c_List_Oset(_1623065), _1623073))))]]], (26324 ^ _776545) ^ [_1251866, _1251868] : [hAPP(c_Int_Onat, _1251866) = _1251868, 26327 ^ _776545 : [(26334 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251866))), -(_1251868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26328 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251866)), -(_1251866 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251868))]]], (32412 ^ _776545) ^ [_1359787, _1359789, _1359791, _1359793] : [class_Groups_Oordered__ab__group__add__abs(_1359787), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359787), c_Groups_Ozero__class_Ozero(_1359787)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359789, _1359787), hAPP(hAPP(c_COMBB(_1359787, _1359787, _1359789), c_Groups_Oabs__class_Oabs(_1359787)), _1359791)), _1359793))))], (41214 ^ _776545) ^ [_1585147, _1585149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1585147, _1585147)), _1585149)), c_Wellfounded_Oacyclic(_1585147, _1585149), -(c_Wellfounded_Owf(_1585147, hAPP(c_Relation_Oconverse(_1585147, _1585147), _1585149)))], (21367 ^ _776545) ^ [_1163413, _1163415, _1163417] : [class_Rings_Ocomm__semiring__1(_1163413), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163413), hAPP(hAPP(c_Power_Opower__class_Opower(_1163413), _1163415), _1163417)), _1163415) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163413), _1163415), hAPP(c_Nat_OSuc, _1163417)))], (39295 ^ _776545) ^ [_1536007, _1536009, _1536011, _1536013, _1536015, _1536017, _1536019] : [class_Rings_Osemiring__0(_1536007), c_Fun_Oinj__on(tc_prod(_1536009, _1536011), _1536007, hAPP(c_Product__Type_Oprod_Oprod__case(_1536009, _1536011, _1536007), hAPP(hAPP(c_COMBC(_1536009, tc_fun(_1536011, _1536007), tc_fun(_1536011, _1536007)), hAPP(hAPP(c_COMBB(tc_fun(_1536007, _1536007), tc_fun(tc_fun(_1536011, _1536007), tc_fun(_1536011, _1536007)), _1536009), c_COMBB(_1536007, _1536007, _1536011)), hAPP(hAPP(c_COMBB(_1536007, tc_fun(_1536007, _1536007), _1536009), c_Groups_Otimes__class_Otimes(_1536007)), _1536013))), _1536015)), hAPP(hAPP(c_Product__Type_OSigma(_1536009, _1536011), _1536017), hAPP(c_COMBK(tc_fun(_1536011, tc_HOL_Obool), _1536009), _1536019))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1536007), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536009, _1536007), _1536013), _1536017)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536011, _1536007), _1536015), _1536019)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536007, _1536007), c_Fun_Oid(_1536007)), hAPP(c_Set_OCollect(_1536007), hAPP(hAPP(c_COMBB(tc_fun(_1536009, tc_HOL_Obool), tc_HOL_Obool, _1536007), c_HOL_OEx(_1536009)), hAPP(hAPP(c_COMBB(tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool)), tc_fun(_1536009, tc_HOL_Obool), _1536007), hAPP(c_COMBB(tc_fun(_1536011, tc_HOL_Obool), tc_HOL_Obool, _1536009), c_HOL_OEx(_1536011))), hAPP(hAPP(c_COMBC(_1536007, tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool)), tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536009, tc_fun(tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool))), tc_fun(tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool)), tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool))), _1536007), c_COMBS(_1536009, tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536009, tc_fun(_1536011, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1536009, tc_fun(tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool))), _1536007), hAPP(c_COMBB(tc_fun(_1536011, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool)), _1536009), c_COMBS(_1536011, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool)), tc_fun(_1536009, tc_fun(_1536011, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1536007), hAPP(c_COMBB(tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536009), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536011), c_fconj))), hAPP(hAPP(c_COMBC(_1536007, tc_fun(_1536009, tc_fun(_1536011, _1536007)), tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536011, _1536007), tc_fun(_1536011, tc_HOL_Obool)), tc_fun(tc_fun(_1536009, tc_fun(_1536011, _1536007)), tc_fun(_1536009, tc_fun(_1536011, tc_HOL_Obool))), _1536007), c_COMBB(tc_fun(_1536011, _1536007), tc_fun(_1536011, tc_HOL_Obool), _1536009)), hAPP(hAPP(c_COMBB(tc_fun(_1536007, tc_HOL_Obool), tc_fun(tc_fun(_1536011, _1536007), tc_fun(_1536011, tc_HOL_Obool)), _1536007), c_COMBB(_1536007, tc_HOL_Obool, _1536011)), c_fequal))), hAPP(hAPP(c_COMBC(_1536009, tc_fun(_1536011, _1536007), tc_fun(_1536011, _1536007)), hAPP(hAPP(c_COMBB(tc_fun(_1536007, _1536007), tc_fun(tc_fun(_1536011, _1536007), tc_fun(_1536011, _1536007)), _1536009), c_COMBB(_1536007, _1536007, _1536011)), hAPP(hAPP(c_COMBB(_1536007, tc_fun(_1536007, _1536007), _1536009), c_Groups_Otimes__class_Otimes(_1536007)), _1536013))), _1536015)))))), hAPP(hAPP(c_COMBC(_1536009, tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536011, tc_HOL_Obool), tc_fun(_1536011, tc_HOL_Obool)), _1536009), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536011)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536009), c_fconj), hAPP(hAPP(c_COMBC(_1536009, tc_fun(_1536009, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536009)), _1536017)))), hAPP(hAPP(c_COMBC(_1536011, tc_fun(_1536011, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536011)), _1536019))))))))], (36541 ^ _776545) ^ [] : [-(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))))))], (2444 ^ _776545) ^ [_812422, _812424] : [_812424 = _812422, -(c_Int_OBit0(_812424) = c_Int_OBit0(_812422))], (10249 ^ _776545) ^ [_952709, _952711, _952713] : [class_Lattices_Oboolean__algebra(_952709), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952709), _952711), _952713) = c_Orderings_Obot__class_Obot(_952709), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952709), _952711), _952713) = c_Orderings_Otop__class_Otop(_952709), -(hAPP(c_Groups_Ouminus__class_Ouminus(_952709), _952711) = _952713)], (44370 ^ _776545) ^ [_1663941, _1663943] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663941), _1663943) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1663941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44376 ^ _776545 : [(44379 ^ _776545) ^ [] : [44375 ^ [_1663941, _1663943] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44377 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44375 ^ [_1663941, _1663943]), hAPP(c_List_Oset(tc_Nat_Onat), _1663943))))]]], (25816 ^ _776545) ^ [_1243680, _1243682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243680)), -(c_SMT_Oz3mod(_1243682, _1243680) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243682, _1243680))], (27719 ^ _776545) ^ [_1275117, _1275119, _1275121] : [class_Rings_Olinordered__idom(_1275117), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275117), c_Groups_Ozero__class_Ozero(_1275117)), hAPP(hAPP(c_Power_Opower__class_Opower(_1275117), hAPP(c_Groups_Oabs__class_Oabs(_1275117), _1275119)), _1275121))))], (42751 ^ _776545) ^ [_1627954, _1627956, _1627958, _1627960, _1627962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627954), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627956)), _1627958))), 42754 ^ _776545 : [(42761 ^ _776545) ^ [] : [-(_1627954 = _1627960), -(hAPP(hAPP(c_List_Onth(_1627956), hAPP(hAPP(c_List_Olist__update(_1627956, _1627958), _1627954), _1627962)), _1627960) = hAPP(hAPP(c_List_Onth(_1627956), _1627958), _1627960))], (42755 ^ _776545) ^ [] : [_1627954 = _1627960, -(hAPP(hAPP(c_List_Onth(_1627956), hAPP(hAPP(c_List_Olist__update(_1627956, _1627958), _1627954), _1627962)), _1627960) = _1627962)]]], (14899 ^ _776545) ^ [_1045263] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045263), _1045263)))))], (27339 ^ _776545) ^ [_1268368] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1268368)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1268368))], (51759 ^ _776545) ^ [_1823122, _1823124] : [51766 ^ _776545 : [(51769 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823124), _1823122))], (51767 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823122), _1823124)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823122), _1823124)), -(_1823122 = _1823124)], (17645 ^ _776545) ^ [_1094283] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1094283)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1094283)], (5046 ^ _776545) ^ [_853473, _853475] : [_853475 = _853473, -(c_Lattices_Osemilattice__sup__class_Osup(_853475) = c_Lattices_Osemilattice__sup__class_Osup(_853473))], (5995 ^ _776545) ^ [_872112, _872114, _872116, _872118] : [hBOOL(hAPP(hAPP(c_member(_872112), _872114), c_SetInterval_Oord_OatMost(_872112, _872116, _872118))), -(hBOOL(hAPP(hAPP(_872116, _872114), _872118)))], (35440 ^ _776545) ^ [_1437382, _1437384, _1437386, _1437388, _1437390] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1437382, _1437384), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1437386), _1437388))), -(_1437384 = 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), _1437390), _1437382), _1437384), 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), _1437390), _1437386)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1437390), _1437388)), _1437384))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1437390), _1437388), _1437384)))))], (48794 ^ _776545) ^ [_1760061, _1760063, _1760065, _1760067, _1760069] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1760061, _1760063, _1760065) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760061, _1760067, _1760069)), _1760063 = _1760067, _1760065 = _1760069], (43150 ^ _776545) ^ [_1636206, _1636208, _1636210, _1636212] : [_1636208 = c_List_Olist_ONil(_1636206), -(hAPP(hAPP(c_List_Olist__update(_1636206, _1636208), _1636210), _1636212) = c_List_Olist_ONil(_1636206))], (14404 ^ _776545) ^ [_1036570, _1036572, _1036574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036574), _1036572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036570), _1036572)), _1036574)))], (35368 ^ _776545) ^ [_1436018, _1436020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436018), 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)), _1436020)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436018, _1436020), c_Divides_OnegDivAlg(_1436018, _1436020))))], (46407 ^ _776545) ^ [_1709778, _1709780] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1709778, _1709780) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1709778), hAPP(c_Nat_OSuc, _1709780))))], (42821 ^ _776545) ^ [_1629685, _1629687, _1629689] : [hBOOL(hAPP(c_List_Odistinct(_1629685), _1629687)), -(hBOOL(hAPP(c_List_Odistinct(_1629685), hAPP(hAPP(c_List_Otake(_1629685), _1629689), _1629687))))], (9312 ^ _776545) ^ [_936711, _936713, _936715, _936717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936711, tc_HOL_Obool)), _936713), _936715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936711, tc_HOL_Obool)), _936715), _936717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936711, tc_HOL_Obool)), _936713), _936717)))], (10589 ^ _776545) ^ [_958631, _958633, _958635, _958637, _958639] : [class_Orderings_Olinorder(_958631), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958631, _958633), _958635) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_958631, _958637), _958639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958631), _958633), _958635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958631), _958637), _958639)), -(_958635 = _958639)], (28313 ^ _776545) ^ [_1284813, _1284815] : [c_Int_OBit1(_1284813) = c_Int_OBit1(_1284815), -(_1284813 = _1284815)], (52007 ^ _776545) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (32328 ^ _776545) ^ [_1357941, _1357943, _1357945, _1357947, _1357949, _1357951] : [hBOOL(hAPP(hAPP(c_member(_1357941), _1357943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357945, tc_fun(_1357941, tc_HOL_Obool)), _1357947), _1357949))), hBOOL(hAPP(hAPP(c_member(_1357945), _1357951), _1357947)), -(hBOOL(hAPP(hAPP(c_member(_1357941), _1357943), hAPP(_1357949, _1357951))))], (41402 ^ _776545) ^ [_1589562, _1589564, _1589566] : [c_Relation_Osingle__valued(_1589562, _1589562, _1589564), -(c_Relation_Osingle__valued(_1589562, _1589562, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589562, _1589562), tc_HOL_Obool), _1589566), _1589564)))], (11386 ^ _776545) ^ [_975180, _975182, _975184, _975186, _975188, _975190, _975192] : [c_Finite__Set_Ofun__left__comm(_975180, _975182, _975184), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975180, _975182, _975184, _975186, hAPP(hAPP(c_Set_Oinsert(_975180), _975188), _975190)), _975192)), -(hBOOL(hAPP(hAPP(c_member(_975180), _975188), _975190))), 11398 ^ _776545 : [(11401 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975180, _975182, _975184, _975186, _975190), 11397 ^ [_975180, _975182, _975184, _975186, _975188, _975190, _975192])))], (11399 ^ _776545) ^ [] : [-(_975192 = hAPP(hAPP(_975184, _975188), 11397 ^ [_975180, _975182, _975184, _975186, _975188, _975190, _975192]))]]], (14694 ^ _776545) ^ [_1041408, _1041410] : [14695 ^ _776545 : [(14698 ^ _776545) ^ [] : [_1041408 = _1041410], (14696 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041408), _1041410))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041408), _1041410)))], (18868 ^ _776545) ^ [_1116501, _1116503] : [-(_1116501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116501), _1116503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116501), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1116503)))], (14066 ^ _776545) ^ [_1028734, _1028736, _1028738, _1028740, _1028742] : [class_Groups_Ocomm__monoid__add(_1028734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028736), _1028738)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028736), _1028740)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1028736, tc_HOL_Obool)), _1028738), _1028740) = c_Orderings_Obot__class_Obot(tc_fun(_1028736, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028736, _1028734), _1028742), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1028736, tc_HOL_Obool)), _1028738), _1028740)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028734), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028736, _1028734), _1028742), _1028738)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028736, _1028734), _1028742), _1028740)))], (18426 ^ _776545) ^ [_1108069, _1108071, _1108073, _1108075, _1108077] : [class_Rings_Olinordered__semiring__strict(_1108069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108069), _1108071), _1108073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108069), _1108075), _1108077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108069), c_Groups_Ozero__class_Ozero(_1108069)), _1108073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108069), c_Groups_Ozero__class_Ozero(_1108069)), _1108075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108069), _1108071), _1108075)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108069), _1108073), _1108077))))], (34473 ^ _776545) ^ [_1418058, _1418060, _1418062, _1418064, _1418066, _1418068] : [hBOOL(hAPP(hAPP(_1418058, _1418060), _1418062)), hBOOL(hAPP(hAPP(_1418064, _1418060), _1418062)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418066, tc_fun(_1418068, tc_HOL_Obool))), _1418058), _1418064), _1418060), _1418062)))], (11916 ^ _776545) ^ [_985829, _985831, _985833, _985835] : [-(c_Fun_Ofun__upd(_985829, _985831, _985833, _985835, hAPP(_985833, _985835)) = _985833)], (36699 ^ _776545) ^ [_1472523, _1472525, _1472527] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1472523), hAPP(hAPP(c_Set_Oinsert(_1472523), _1472525), c_Orderings_Obot__class_Obot(tc_fun(_1472523, tc_HOL_Obool)))), _1472527) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1472523, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472523, _1472523, _1472527), hAPP(hAPP(c_Set_Oinsert(_1472523), _1472525), c_Orderings_Obot__class_Obot(tc_fun(_1472523, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1472523, tc_HOL_Obool), tc_HOL_Obool))))], (6516 ^ _776545) ^ [_881756, _881758, _881760] : [class_Orderings_Otop(_881756), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_881758, _881756)), _881760) = c_Orderings_Otop__class_Otop(_881756))], (52291 ^ _776545) ^ [_1829101, _1829103] : [-(class_Enum_Oenum(tc_sum(_1829101, _1829103))), class_Enum_Oenum(_1829101), class_Enum_Oenum(_1829103)], (17449 ^ _776545) ^ [_1090784, _1090786, _1090788] : [class_Rings_Olinordered__semiring__strict(_1090784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090784), c_Groups_Ozero__class_Ozero(_1090784)), _1090786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090784), _1090788), c_Groups_Ozero__class_Ozero(_1090784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090784), _1090786), _1090788)), c_Groups_Ozero__class_Ozero(_1090784))))], (42219 ^ _776545) ^ [_1613708, _1613710, _1613712] : [-(_1613708 = _1613710), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613712)), _1613708) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613712)), _1613710), 42225 ^ _776545 : [(42228 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Onth(_1613712), _1613708), 42224 ^ [_1613708, _1613710, _1613712]) = hAPP(hAPP(c_List_Onth(_1613712), _1613710), 42224 ^ [_1613708, _1613710, _1613712])], (42226 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42224 ^ [_1613708, _1613710, _1613712]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613712)), _1613708))))]]], (36663 ^ _776545) ^ [_1471730, _1471732, _1471734] : [-(hAPP(c_Relation_OImage(_1471730, _1471730, c_Relation_OId__on(_1471730, _1471732)), _1471734) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471730, tc_HOL_Obool)), _1471732), _1471734))], (40485 ^ _776545) ^ [_1566567, _1566569, _1566571, _1566573, _1566575] : [_1566567 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1566569, _1566571, _1566567, _1566573), _1566575) = hAPP(c_Product__Type_OPair(_1566569, _1566571), _1566575))], (2590 ^ _776545) ^ [_814719, _814721] : [_814721 = _814719, -(c_Int_Oint__ge__less__than2(_814721) = c_Int_Oint__ge__less__than2(_814719))], (3954 ^ _776545) ^ [_836097, _836099, _836101, _836103, _836105, _836107, _836109, _836111, _836113, _836115, _836117, _836119, _836121, _836123] : [-(c_New__Random__Sequence_Opos__decr__bind(_836123, _836119, _836115, _836111, _836107, _836103, _836099) = c_New__Random__Sequence_Opos__decr__bind(_836121, _836117, _836113, _836109, _836105, _836101, _836097)), _836123 = _836121, _836119 = _836117, _836115 = _836113, _836111 = _836109, _836107 = _836105, _836103 = _836101, _836099 = _836097], (2108 ^ _776545) ^ [_807120, _807122, _807124, _807126] : [-(c_SMT_Oz3mod(_807126, _807122) = c_SMT_Oz3mod(_807124, _807120)), _807126 = _807124, _807122 = _807120], (16831 ^ _776545) ^ [_1079460, _1079462, _1079464] : [class_Groups_Oordered__comm__monoid__add(_1079460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079460), c_Groups_Ozero__class_Ozero(_1079460)), _1079462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079460), c_Groups_Ozero__class_Ozero(_1079460)), _1079464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079460), c_Groups_Ozero__class_Ozero(_1079460)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079460), _1079462), _1079464))))], (43651 ^ _776545) ^ [_1647147, _1647149, _1647151] : [_1647147 = _1647149, -(_1647147 = hAPP(hAPP(c_List_Oappend(_1647151), c_List_Olist_ONil(_1647151)), _1647149))], (7654 ^ _776545) ^ [_903775, _903777, _903779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903775, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903775, tc_HOL_Obool)), _903777), _903779)), _903779) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903775, tc_HOL_Obool)), _903777), _903779))], (16610 ^ _776545) ^ [_1075287, _1075289, _1075291, _1075293] : [class_Groups_Ocomm__monoid__add(_1075287), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075289), _1075291)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1075289, _1075287), _1075293), _1075291) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075287, _1075289, c_Groups_Oplus__class_Oplus(_1075287)), _1075293), c_Groups_Ozero__class_Ozero(_1075287)), _1075291))], (24998 ^ _776545) ^ [_1229277, _1229279] : [class_Divides_Osemiring__div(_1229277), -(c_Divides_Odiv__class_Omod(_1229277, _1229279, c_Groups_Oone__class_Oone(_1229277)) = c_Groups_Ozero__class_Ozero(_1229277))], (35652 ^ _776545) ^ [_1442088, _1442090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442090)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442088), _1442090) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1442088, _1442090)))], (9876 ^ _776545) ^ [_945751, _945753, _945755] : [class_Orderings_Oord(_945751), 9879 ^ _776545 : [(9886 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945751), _945753), _945755)), -(hBOOL(hAPP(hAPP(c_member(_945751), _945753), hAPP(c_SetInterval_Oord__class_OlessThan(_945751), _945755))))], (9880 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945751), _945753), hAPP(c_SetInterval_Oord__class_OlessThan(_945751), _945755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945751), _945753), _945755)))]]], (41558 ^ _776545) ^ [_1593737, _1593739, _1593741, _1593743, _1593745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593737, _1593737)), hAPP(hAPP(c_Product__Type_OPair(_1593737, _1593737), _1593739), _1593741)), c_Transitive__Closure_Ortrancl(_1593737, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593737, _1593737), tc_HOL_Obool)), _1593743), _1593745)))), 41564 ^ _776545 : [(41570 ^ _776545) ^ [] : [41566 ^ [_1593737, _1593739, _1593741, _1593743, _1593745] = 41563 ^ [_1593737, _1593739, _1593741, _1593743, _1593745]], (41568 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593737, _1593737)), hAPP(hAPP(c_Product__Type_OPair(_1593737, _1593737), 41566 ^ [_1593737, _1593739, _1593741, _1593743, _1593745]), 41563 ^ [_1593737, _1593739, _1593741, _1593743, _1593745])), _1593745)))], (41565 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593737, _1593737)), hAPP(hAPP(c_Product__Type_OPair(_1593737, _1593737), 41563 ^ [_1593737, _1593739, _1593741, _1593743, _1593745]), _1593741)), c_Transitive__Closure_Ortrancl(_1593737, _1593743))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593737, _1593737)), hAPP(hAPP(c_Product__Type_OPair(_1593737, _1593737), _1593739), _1593741)), c_Transitive__Closure_Ortrancl(_1593737, _1593743))))], (37763 ^ _776545) ^ [_1495947, _1495949, _1495951, _1495953] : [c_Fun_Oinj__on(_1495947, tc_fun(tc_fun(_1495947, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1495947, tc_fun(tc_prod(_1495947, _1495947), tc_HOL_Obool), tc_fun(tc_fun(_1495947, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495947, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1495947, _1495947), tc_HOL_Obool), tc_fun(tc_fun(_1495947, tc_HOL_Obool), tc_HOL_Obool)), _1495947), c_Equiv__Relations_Oquotient(_1495947)), hAPP(hAPP(c_COMBC(_1495947, tc_fun(_1495947, tc_HOL_Obool), tc_fun(_1495947, tc_HOL_Obool)), c_Set_Oinsert(_1495947)), c_Orderings_Obot__class_Obot(tc_fun(_1495947, tc_HOL_Obool))))), _1495949), _1495951), hBOOL(hAPP(hAPP(c_member(_1495947), _1495953), _1495951)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495947), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495947, tc_HOL_Obool)), _1495951), hAPP(hAPP(c_Set_Oinsert(_1495947), _1495953), c_Orderings_Obot__class_Obot(tc_fun(_1495947, tc_HOL_Obool))))), _1495949) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1495947, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495947), _1495951), _1495949)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495947), hAPP(hAPP(c_Set_Oinsert(_1495947), _1495953), c_Orderings_Obot__class_Obot(tc_fun(_1495947, tc_HOL_Obool)))), _1495949)))], (30392 ^ _776545) ^ [_1321805, _1321807, _1321809] : [class_Orderings_Olinorder(_1321805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321805), _1321807)), hBOOL(hAPP(hAPP(c_member(_1321805), _1321809), _1321807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321805), hAPP(c_Finite__Set_Ofold1(_1321805, c_Orderings_Oord__class_Omin(_1321805)), _1321807)), _1321809)))], (38427 ^ _776545) ^ [_1513189, _1513191, _1513193, _1513195] : [-(_1513189 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1513191, tc_HOL_Obool), tc_HOL_Obool))), 38433 ^ _776545 : [(38436 ^ _776545) ^ [] : [c_Fun_Oinj__on(_1513191, _1513193, _1513195, 38432 ^ [_1513189, _1513191, _1513193, _1513195])], (38434 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1513191, tc_HOL_Obool)), 38432 ^ [_1513189, _1513191, _1513193, _1513195]), _1513189)))]], -(c_Fun_Oinj__on(_1513191, _1513193, _1513195, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1513191, tc_HOL_Obool), _1513189)))], (14728 ^ _776545) ^ [_1041992, _1041994, _1041996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041992), _1041994)), _1041996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041992), _1041996)))], (47416 ^ _776545) ^ [_1729904, _1729906, _1729908] : [hBOOL(hAPP(c_List_Odistinct(_1729904), _1729906)), -(hBOOL(hAPP(c_List_Odistinct(_1729904), c_List_OdropWhile(_1729904, _1729908, _1729906))))], (41274 ^ _776545) ^ [_1586388, _1586390, _1586392] : [c_Relation_Ototal__on(_1586388, _1586390, hAPP(c_Relation_Oconverse(_1586388, _1586388), _1586392)), -(c_Relation_Ototal__on(_1586388, _1586390, _1586392))], (25720 ^ _776545) ^ [_1241975, _1241977, _1241979, _1241981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241977), _1241979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241979), 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), _1241977), _1241975)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241977), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241981, _1241975))), _1241979))))], (36812 ^ _776545) ^ [_1475049, _1475051, _1475053, _1475055, _1475057, _1475059, _1475061] : [c_Equiv__Relations_Oequiv(_1475049, _1475051, _1475053), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475049, tc_HOL_Obool)), _1475055), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475049), _1475051), _1475053))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1475049, tc_HOL_Obool)), _1475057), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1475049), _1475051), _1475053))), hBOOL(hAPP(hAPP(c_member(_1475049), _1475059), _1475055)), hBOOL(hAPP(hAPP(c_member(_1475049), _1475061), _1475057)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475049, _1475049)), hAPP(hAPP(c_Product__Type_OPair(_1475049, _1475049), _1475059), _1475061)), _1475053)), -(_1475055 = _1475057)], (45776 ^ _776545) ^ [_1695004, _1695006] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695004)), c_List_Oremdups(_1695004, _1695006)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695004)), _1695006), -(c_List_Oremdups(_1695004, _1695006) = _1695006)], (17781 ^ _776545) ^ [_1096588, _1096590, _1096592] : [class_Groups_Ogroup__add(_1096588), 17784 ^ _776545 : [(17791 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096588), _1096590), _1096592) = c_Groups_Ozero__class_Ozero(_1096588), -(_1096590 = hAPP(c_Groups_Ouminus__class_Ouminus(_1096588), _1096592))], (17785 ^ _776545) ^ [] : [_1096590 = hAPP(c_Groups_Ouminus__class_Ouminus(_1096588), _1096592), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096588), _1096590), _1096592) = c_Groups_Ozero__class_Ozero(_1096588))]]], (14272 ^ _776545) ^ [_1033495, _1033497, _1033499, _1033501] : [class_Rings_Ocomm__semiring__1(_1033495), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033495), _1033497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033495), _1033499), _1033501)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033495), _1033499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033495), _1033497), _1033501)))], (24682 ^ _776545) ^ [_1223170, _1223172] : [class_Int_Onumber__ring(_1223170), 24685 ^ _776545 : [(24692 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223172)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223172)) = hAPP(c_Int_Onumber__class_Onumber__of(_1223170), _1223172))], (24686 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223172))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1223172)) = c_Groups_Ozero__class_Ozero(_1223170))]]], (10092 ^ _776545) ^ [_949254, _949256, _949258, _949260] : [class_Orderings_Oorder(_949254), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949254, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949254, _949256, _949258)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949254, _949258, _949260)) = c_Orderings_Obot__class_Obot(tc_fun(_949254, tc_HOL_Obool)))], (48586 ^ _776545) ^ [_1756103, _1756105, _1756107] : [-(_1756103 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1756105, c_List_Oreplicate(_1756105, _1756103, _1756107)) = _1756107)], (6019 ^ _776545) ^ [_872602, _872604, _872606, _872608] : [hBOOL(hAPP(hAPP(c_member(_872602), _872604), c_SetInterval_Oord_OlessThan(_872602, _872606, _872608))), -(hBOOL(hAPP(hAPP(_872606, _872604), _872608)))], (24856 ^ _776545) ^ [_1226402, _1226404, _1226406, _1226408] : [class_Divides_Osemiring__div(_1226402), -(c_Divides_Odiv__class_Omod(_1226402, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226402), _1226404), _1226406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226402), _1226408), _1226406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226402), c_Divides_Odiv__class_Omod(_1226402, _1226404, _1226408)), _1226406))], (22425 ^ _776545) ^ [_1183058, _1183060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183058), _1183060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183060), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (17803 ^ _776545) ^ [_1096949, _1096951] : [class_Groups_Oab__group__add(_1096949), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096949), hAPP(c_Groups_Ouminus__class_Ouminus(_1096949), _1096951)), _1096951) = c_Groups_Ozero__class_Ozero(_1096949))], (28757 ^ _776545) ^ [_1292059, _1292061] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1292059)))), _1292061) = 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)))), _1292059)), _1292061))], (44966 ^ _776545) ^ [_1676958, _1676960, _1676962] : [c_Fun_Oinj__on(_1676958, _1676960, _1676962, c_Orderings_Otop__class_Otop(tc_fun(_1676958, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1676958), tc_List_Olist(_1676960), hAPP(c_List_Omap(_1676958, _1676960), _1676962), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676958), tc_HOL_Obool))))], (31317 ^ _776545) ^ [_1338707, _1338709, _1338711, _1338713] : [class_Orderings_Olinorder(_1338707), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338707), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338707), _1338709), _1338711)), _1338713) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338707), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338707), _1338709), _1338713)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338707), _1338711), _1338713)))], (8339 ^ _776545) ^ [_919460, _919462, _919464] : [class_Lattices_Osemilattice__sup(_919460), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919460), _919462), _919464) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919460), _919464), _919462))], (11155 ^ _776545) ^ [_969664, _969666, _969668, _969670] : [c_Orderings_Obot__class_Obot(tc_fun(_969664, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_969666, _969664, _969668), _969670), -(_969670 = c_Orderings_Obot__class_Obot(tc_fun(_969666, tc_HOL_Obool)))], (6238 ^ _776545) ^ [_876795] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_876795, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_876795, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_876795, tc_HOL_Obool)))], (28993 ^ _776545) ^ [_1296265, _1296267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296265), _1296267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296265)), c_Int_OBit0(_1296267))))], (5528 ^ _776545) ^ [_861000, _861002] : [_861002 = _861000, -(c_Power_Opower__class_Opower(_861002) = c_Power_Opower__class_Opower(_861000))], (41286 ^ _776545) ^ [_1586576, _1586578, _1586580, _1586582, _1586584, _1586586] : [c_Relation_Osingle__valued(_1586576, _1586578, _1586580), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586576, _1586578)), hAPP(hAPP(c_Product__Type_OPair(_1586576, _1586578), _1586582), _1586584)), _1586580)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586576, _1586578)), hAPP(hAPP(c_Product__Type_OPair(_1586576, _1586578), _1586582), _1586586)), _1586580)), -(_1586584 = _1586586)], (32514 ^ _776545) ^ [_1363847, _1363849, _1363851, _1363853, _1363855] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363847, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363849, tc_fun(_1363847, tc_HOL_Obool)), _1363851), _1363853)), _1363855) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363849, tc_fun(_1363847, tc_HOL_Obool)), _1363851), hAPP(hAPP(c_COMBC(_1363849, tc_fun(_1363847, tc_HOL_Obool), tc_fun(_1363847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1363847, tc_HOL_Obool), tc_fun(tc_fun(_1363847, tc_HOL_Obool), tc_fun(_1363847, tc_HOL_Obool)), _1363849), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363847, tc_HOL_Obool))), _1363853)), _1363855)))], (45134 ^ _776545) ^ [_1680500] : [-(_1680500 = 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)), _1680500)))], (434 ^ _776545) ^ [_783094, _783096] : [-(class_Rings_Oinverse(_783094)), _783096 = _783094, class_Rings_Oinverse(_783096)], (48860 ^ _776545) ^ [_1761336, _1761338, _1761340] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1761336, _1761338), _1761340) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1761336, tc_Lazy__Sequence_Olazy__sequence(_1761336)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1761336, tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1761336, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat)), _1761336), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1761336), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1761336)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1761336, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761336), tc_Nat_Onat)), _1761336), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1761336))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1761336), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1761338))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1761336, _1761338))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1761336), _1761340)))], (48418 ^ _776545) ^ [_1751721, _1751723, _1751725, _1751727, _1751729] : [-(_1751721 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1751723, _1751725, _1751727, _1751729), _1751721) = c_Lazy__Sequence_Ohb__bind(_1751723, _1751725, hAPP(_1751727, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1751721), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1751723, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1751725))), _1751729), _1751721)))], (23615 ^ _776545) ^ [_1204513] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1204513) = 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)), _1204513)))], (37927 ^ _776545) ^ [_1500423, _1500425, _1500427, _1500429, _1500431, _1500433, _1500435, _1500437] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500423, _1500425)), hAPP(hAPP(c_Product__Type_OPair(_1500423, _1500425), _1500427), _1500429)), _1500431)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500425, _1500433)), hAPP(hAPP(c_Product__Type_OPair(_1500425, _1500433), _1500429), _1500435)), _1500437)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500423, _1500433)), hAPP(hAPP(c_Product__Type_OPair(_1500423, _1500433), _1500427), _1500435)), hAPP(hAPP(c_Relation_Orel__comp(_1500423, _1500425, _1500433), _1500431), _1500437))))], (46077 ^ _776545) ^ [_1701985, _1701987, _1701989, _1701991] : [-(hAPP(c_List_Ofilter(_1701985, _1701987), c_List_Oremove1(_1701985, _1701989, _1701991)) = c_List_Oremove1(_1701985, _1701989, hAPP(c_List_Ofilter(_1701985, _1701987), _1701991)))], (36600 ^ _776545) ^ [_1470015, _1470017, _1470019, _1470021] : [-(hAPP(c_Relation_OField(_1470015), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1470015, _1470015)), hAPP(hAPP(c_Product__Type_OPair(_1470015, _1470015), _1470017), _1470019)), _1470021)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470015, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1470015), _1470017), hAPP(hAPP(c_Set_Oinsert(_1470015), _1470019), c_Orderings_Obot__class_Obot(tc_fun(_1470015, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1470015), _1470021)))], (14416 ^ _776545) ^ [_1036818, _1036820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036818), _1036820)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036820), _1036818)) = _1036820)], (28491 ^ _776545) ^ [_1287865] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1287865)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1287865))))], (490 ^ _776545) ^ [_783882, _783884, _783886, _783888, _783890, _783892, _783894, _783896] : [-(c_List_Olistrelp(_783894, _783890, _783886, _783882)), c_List_Olistrelp(_783896, _783892, _783888, _783884), _783896 = _783894, _783892 = _783890, _783888 = _783886, _783884 = _783882], (6977 ^ _776545) ^ [_889864, _889866, _889868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889864, tc_HOL_Obool)), _889866), _889868)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_889864, tc_HOL_Obool)), _889866), hAPP(c_Set_OPow(_889864), _889868))))], (40793 ^ _776545) ^ [_1574845, _1574847, _1574849, _1574851] : [40794 ^ _776545 : [(40797 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574845, _1574845)), _1574847), c_Transitive__Closure_Ortrancl(_1574845, _1574851)))], (40795 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574845, _1574845)), _1574847), c_Transitive__Closure_Ortrancl(_1574845, _1574849)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574845, _1574845)), _1574847), c_Transitive__Closure_Ortrancl(_1574845, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574845, _1574845), tc_HOL_Obool)), _1574849), _1574851)))))], (39439 ^ _776545) ^ [_1540579, _1540581, _1540583, _1540585, _1540587, _1540589] : [hAPP(c_Set_Oimage(_1540579, _1540581, _1540583), c_Orderings_Otop__class_Otop(tc_fun(_1540579, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540581, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1540585, _1540587, _1540589), c_Orderings_Otop__class_Otop(tc_fun(_1540585, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540587, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1540579, _1540585), tc_prod(_1540581, _1540587), c_Product__Type_Omap__pair(_1540579, _1540581, _1540585, _1540587, _1540583, _1540589)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540579, _1540585), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540581, _1540587), tc_HOL_Obool)))], (48488 ^ _776545) ^ [_1753564, _1753566, _1753568, _1753570] : [-(c_Predicate_Oconversep(_1753564, _1753566, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1753564, tc_fun(_1753566, tc_HOL_Obool))), _1753568), _1753570)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1753566, tc_fun(_1753564, tc_HOL_Obool))), c_Predicate_Oconversep(_1753564, _1753566, _1753568)), c_Predicate_Oconversep(_1753564, _1753566, _1753570)))], (23779 ^ _776545) ^ [_1207222, _1207224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207222), _1207224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207222)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207224))))], (52201 ^ _776545) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (6256 ^ _776545) ^ [_877107] : [class_Complete__Lattice_Ocomplete__lattice(_877107), -(c_Complete__Lattice_OSup__class_OSup(_877107, c_Orderings_Otop__class_Otop(tc_fun(_877107, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_877107))], (7848 ^ _776545) ^ [_908661, _908663] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908661, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_908661, tc_HOL_Obool))), _908663) = _908663)], (4606 ^ _776545) ^ [_846545, _846547, _846549, _846551] : [-(c_List_Oupto(_846551, _846547) = c_List_Oupto(_846549, _846545)), _846551 = _846549, _846547 = _846545], (26020 ^ _776545) ^ [_1246926, _1246928] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246926), _1246928))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1246926, _1246928) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246926), _1246928), _1246928))], (8273 ^ _776545) ^ [_918009, _918011, _918013, _918015] : [class_Lattices_Osemilattice__sup(_918009), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918009), _918011), _918013)), _918015) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918009), _918011), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918009), _918013), _918015)))], (31985 ^ _776545) ^ [_1351294, _1351296, _1351298] : [class_Orderings_Olinorder(_1351294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351294), _1351296)), hBOOL(hAPP(hAPP(c_member(_1351294), _1351298), _1351296)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351294), _1351298), c_Big__Operators_Olattice_OSup__fin(_1351294, c_Orderings_Oord__class_Omax(_1351294), _1351296)) = c_Big__Operators_Olattice_OSup__fin(_1351294, c_Orderings_Oord__class_Omax(_1351294), _1351296))], (41224 ^ _776545) ^ [_1585302, _1585304, _1585306] : [-(hAPP(c_Relation_Oconverse(_1585302, _1585304), _1585306) = hAPP(c_Set_OCollect(tc_prod(_1585304, _1585302)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585304, _1585302, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585304, tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_fun(_1585302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585302, tc_fun(tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_fun(_1585302, tc_HOL_Obool)), _1585304), c_COMBC(_1585302, tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585302, tc_prod(_1585302, _1585304)), tc_fun(_1585302, tc_fun(tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_HOL_Obool)), _1585304), hAPP(c_COMBB(tc_prod(_1585302, _1585304), tc_fun(tc_fun(tc_prod(_1585302, _1585304), tc_HOL_Obool), tc_HOL_Obool), _1585302), c_member(tc_prod(_1585302, _1585304)))), hAPP(c_COMBC(_1585302, _1585304, tc_prod(_1585302, _1585304)), c_Product__Type_OPair(_1585302, _1585304))))), _1585306))))], (2178 ^ _776545) ^ [_808141, _808143, _808145, _808147, _808149, _808151, _808153, _808155] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808155, _808151, _808147, _808143) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808153, _808149, _808145, _808141)), _808155 = _808153, _808151 = _808149, _808147 = _808145, _808143 = _808141], (28189 ^ _776545) ^ [_1282692] : [class_Rings_Osemiring__1(_1282692), -(hBOOL(hAPP(hAPP(c_member(_1282692), c_Groups_Oone__class_Oone(_1282692)), c_Nat_Osemiring__1__class_ONats(_1282692))))], (7684 ^ _776545) ^ [_904751, _904753, _904755] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904751, tc_HOL_Obool)), _904753), _904755) = c_Orderings_Obot__class_Obot(tc_fun(_904751, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904751, tc_HOL_Obool)), _904753), _904755) = _904753)], (9426 ^ _776545) ^ [_938604, _938606, _938608] : [class_Orderings_Olinorder(_938604), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938604), _938606), _938608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938604), _938608), _938606)))], (49956 ^ _776545) ^ [_1785355, _1785357] : [c_Equiv__Relations_Opart__equivp(_1785355, _1785357), 49960 ^ _776545 : [(49965 ^ _776545) ^ [] : [-(c_Predicate_Otransp(_1785355, _1785357))], (49963 ^ _776545) ^ [] : [-(c_Predicate_Osymp(_1785355, _1785357))], (49961 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1785357, 49959 ^ [_1785355, _1785357]), 49959 ^ [_1785355, _1785357])))]]], (8535 ^ _776545) ^ [_923165, _923167, _923169, _923171] : [class_Lattices_Osemilattice__sup(_923165), 8538 ^ _776545 : [(8547 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923165), _923167), _923169)), _923171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), _923167), _923171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), _923169), _923171))], (8539 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923165), _923167), _923169)), _923171)), 8542 ^ _776545 : [(8545 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), _923169), _923171)))], (8543 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923165), _923167), _923171)))]]]]], (24992 ^ _776545) ^ [_1229150, _1229152, _1229154, _1229156] : [class_Divides_Osemiring__div(_1229150), -(c_Divides_Odiv__class_Omod(_1229150, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229150), _1229152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229150), _1229154), _1229156)), _1229156) = c_Divides_Odiv__class_Omod(_1229150, _1229152, _1229156))], (40915 ^ _776545) ^ [_1577770, _1577772, _1577774, _1577776, _1577778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577770, _1577770)), hAPP(hAPP(c_Product__Type_OPair(_1577770, _1577770), _1577772), _1577774)), c_Transitive__Closure_Otrancl(_1577770, _1577776))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577770, _1577770)), hAPP(hAPP(c_Product__Type_OPair(_1577770, _1577770), _1577774), _1577778)), c_Transitive__Closure_Ortrancl(_1577770, _1577776))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577770, _1577770)), hAPP(hAPP(c_Product__Type_OPair(_1577770, _1577770), _1577772), _1577778)), c_Transitive__Closure_Otrancl(_1577770, _1577776))))], (7954 ^ _776545) ^ [_911022, _911024, _911026] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911022, tc_HOL_Obool)), _911024), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911022, tc_HOL_Obool)), _911024), _911026))))], (41431 ^ _776545) ^ [_1590241, _1590243, _1590245] : [41432 ^ _776545 : [(41433 ^ _776545) ^ [_1590317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590241, _1590241)), _1590243), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590241, _1590241), tc_HOL_Obool), _1590317), _1590245)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590241, _1590241)), _1590243), c_Transitive__Closure_Ortrancl(_1590241, _1590245))))], (7698 ^ _776545) ^ [_905102, _905104, _905106, _905108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905102, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905102, tc_HOL_Obool)), _905104), _905106)), _905108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905102, tc_HOL_Obool)), _905104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905102, tc_HOL_Obool)), _905106), _905108))))], (10511 ^ _776545) ^ [_957193, _957195, _957197] : [-(hBOOL(hAPP(hAPP(c_member(_957193), _957195), _957197))), -(hBOOL(hAPP(hAPP(c_member(_957193), _957195), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957193, tc_HOL_Obool)), _957197))))], (22395 ^ _776545) ^ [_1182558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182558), 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)), _1182558)), _1182558)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39884 ^ _776545) ^ [_1552636, _1552638, _1552640, _1552642, _1552644, _1552646] : [-(hAPP(c_Set_Ovimage(_1552636, _1552638, hAPP(c_Fun_Ocomp(_1552640, _1552638, _1552636, _1552642), _1552644)), _1552646) = hAPP(c_Set_Ovimage(_1552636, _1552640, _1552644), hAPP(c_Set_Ovimage(_1552640, _1552638, _1552642), _1552646)))], (7098 ^ _776545) ^ [_892148] : [-(hBOOL(hAPP(hAPP(c_member(_892148), 7096 ^ [_892148]), c_Orderings_Otop__class_Otop(tc_fun(_892148, tc_HOL_Obool)))))], (29509 ^ _776545) ^ [_1305138, _1305140, _1305142] : [class_Rings_Olinordered__semidom(_1305138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305138), hAPP(hAPP(c_Power_Opower__class_Opower(_1305138), _1305140), 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(_1305138), _1305142), 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(_1305138), c_Groups_Ozero__class_Ozero(_1305138)), _1305142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305138), _1305140), _1305142)))], (38491 ^ _776545) ^ [_1514465, _1514467] : [-(c_HOL_OThe(_1514465, hAPP(c_fequal, _1514467)) = _1514467)], (42345 ^ _776545) ^ [_1616927, _1616929, _1616931, _1616933] : [hBOOL(hAPP(hAPP(c_member(_1616927), _1616929), hAPP(c_List_Oset(_1616927), hAPP(hAPP(c_List_Otake(_1616927), _1616931), _1616933)))), -(hBOOL(hAPP(hAPP(c_member(_1616927), _1616929), hAPP(c_List_Oset(_1616927), _1616933))))], (8381 ^ _776545) ^ [_920323, _920325, _920327, _920329] : [class_Lattices_Olattice(_920323), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920323), _920325), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920323), _920327), _920329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920323), _920327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920323), _920325), _920329)))], (14644 ^ _776545) ^ [_1040651, _1040653, _1040655, _1040657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040651), _1040653)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040655), _1040653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040651), _1040657), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040655), _1040657)))], (52015 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (27231 ^ _776545) ^ [_1266585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266585), 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), _1266585)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51967 ^ _776545) ^ [_1826065, _1826067] : [-(class_Enum_Oenum(tc_fun(_1826065, _1826067))), class_Enum_Oenum(_1826065), class_Enum_Oenum(_1826067)], (16302 ^ _776545) ^ [_1070808, _1070810, _1070812] : [class_Groups_Ogroup__add(_1070808), 16305 ^ _776545 : [(16312 ^ _776545) ^ [] : [_1070810 = _1070812, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070808), _1070810), _1070812) = c_Groups_Ozero__class_Ozero(_1070808))], (16306 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070808), _1070810), _1070812) = c_Groups_Ozero__class_Ozero(_1070808), -(_1070810 = _1070812)]]], (2636 ^ _776545) ^ [_815424, _815426, _815428, _815430] : [-(c_Nitpick_Onorm__frac(_815430, _815426) = c_Nitpick_Onorm__frac(_815428, _815424)), _815430 = _815428, _815426 = _815424], (5598 ^ _776545) ^ [_862021, _862023] : [_862023 = _862021, -(tc_Lazy__Sequence_Olazy__sequence(_862023) = tc_Lazy__Sequence_Olazy__sequence(_862021))], (39697 ^ _776545) ^ [_1547361, _1547363, _1547365] : [hBOOL(hAPP(hAPP(c_member(_1547363), _1547361), c_Orderings_Obot__class_Obot(tc_fun(_1547363, tc_HOL_Obool)))), -(hBOOL(hAPP(_1547365, _1547361)))], (41424 ^ _776545) ^ [_1590082, _1590084, _1590086] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590082, _1590082)), _1590084), c_Transitive__Closure_Ortrancl(_1590082, _1590086))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590082, _1590082)), _1590084), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590082, _1590082), tc_HOL_Obool), 41427 ^ [_1590082, _1590084, _1590086]), _1590086))))], (11586 ^ _776545) ^ [_979174, _979176] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979174, tc_HOL_Obool)), hAPP(c_Set_OPow(_979174), _979176))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979174), _979176)))], (20975 ^ _776545) ^ [_1155333, _1155335, _1155337, _1155339] : [class_Fields_Olinordered__field(_1155333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155333), c_Groups_Ozero__class_Ozero(_1155333)), _1155335)), 20982 ^ _776545 : [(20989 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155333), _1155337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155333), _1155339), _1155335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155333), _1155337), _1155335)), _1155339)))], (20983 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155333), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155333), _1155337), _1155335)), _1155339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155333), _1155337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155333), _1155339), _1155335))))]]], (50301 ^ 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108873), _1108875), _1108877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108873), _1108875), _1108879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108873), _1108877), _1108879)))]]], (16530 ^ _776545) ^ [_1074083, _1074085, _1074087] : [16531 ^ _776545 : [(16534 ^ _776545) ^ [] : [_1074085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16532 ^ _776545) ^ [] : [_1074083 = _1074087]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074083), _1074085) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074087), _1074085))], (5848 ^ _776545) ^ [_869425, _869427] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869425, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869425)), tc_HOL_Obool)), _869427), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869425, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869425)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869425)))), -(_869427 = hAPP(c_Hoare__Mirabelle_ORep__triple(_869425), 5851 ^ [_869425, _869427]))], (13774 ^ _776545) ^ [_1021977, _1021979, _1021981, _1021983] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1021977), 13777 ^ _776545 : [(13784 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021977), _1021979), _1021983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021977), _1021979), _1021981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021977), _1021983), _1021981))))], (13778 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021977), _1021979), _1021981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021977), _1021983), _1021981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021977), _1021979), _1021983)))]]], (1414 ^ _776545) ^ [_797084, _797086] : [-(class_Lattices_Oboolean__algebra(_797084)), _797086 = _797084, class_Lattices_Oboolean__algebra(_797086)], (38634 ^ _776545) ^ [_1518755, _1518757, _1518759] : [-(hAPP(c_Set_Ovimage(_1518755, _1518757, _1518759), c_Orderings_Otop__class_Otop(tc_fun(_1518757, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1518755, tc_HOL_Obool)))], (41492 ^ _776545) ^ [_1591945, _1591947, _1591949] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591945, _1591945)), _1591947), c_Transitive__Closure_Otrancl(_1591945, _1591949)))), 41493 ^ _776545 : [(41494 ^ _776545) ^ [_1592024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1592024)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591945, _1591945)), _1591947), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591945, _1591945), tc_HOL_Obool), _1592024), _1591949)))]]], (33995 ^ _776545) ^ [_1407612, _1407614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1407612), _1407614)), -(hAPP(c_Finite__Set_Ocard(_1407612), _1407614) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1407612, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1407612), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407614))], (13202 ^ _776545) ^ [_1010250] : [-(c_Finite__Set_Ofun__left__comm__idem(_1010250, tc_fun(_1010250, tc_HOL_Obool), c_Set_Oinsert(_1010250)))], (41248 ^ _776545) ^ [_1585950] : [-(c_Relation_Osingle__valued(_1585950, _1585950, c_Relation_OId(_1585950)))], (7126 ^ _776545) ^ [_892641, _892643, _892645, _892647] : [hBOOL(hAPP(hAPP(c_member(_892641), _892643), hAPP(hAPP(c_Set_Oinsert(_892641), _892645), _892647))), -(_892643 = _892645), -(hBOOL(hAPP(hAPP(c_member(_892641), _892643), _892647)))], (19304 ^ _776545) ^ [_1125064, _1125066] : [class_Rings_Olinordered__idom(_1125064), hBOOL(hAPP(hAPP(c_member(_1125064), _1125066), c_Int_Oring__1__class_OInts(_1125064))), 19311 ^ _776545 : [(19318 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125064), _1125066), c_Groups_Ozero__class_Ozero(_1125064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125064), c_Groups_Oone__class_Oone(_1125064)), _1125066)), _1125066)), c_Groups_Ozero__class_Ozero(_1125064))))], (19312 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125064), c_Groups_Oone__class_Oone(_1125064)), _1125066)), _1125066)), c_Groups_Ozero__class_Ozero(_1125064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125064), _1125066), c_Groups_Ozero__class_Ozero(_1125064))))]]], (43689 ^ _776545) ^ [_1648051, _1648053, _1648055, _1648057] : [-(hBOOL(hAPP(hAPP(c_member(_1648051), _1648053), hAPP(c_List_Oset(_1648051), _1648055)))), -(c_List_Oremove1(_1648051, _1648053, hAPP(hAPP(c_List_Oappend(_1648051), _1648055), _1648057)) = hAPP(hAPP(c_List_Oappend(_1648051), _1648055), c_List_Oremove1(_1648051, _1648053, _1648057)))], (48114 ^ _776545) ^ [_1745600, _1745602, _1745604] : [c_List_Olist__ex(_1745600, _1745602, hAPP(c_List_Orev(_1745600), _1745604)), -(c_List_Olist__ex(_1745600, _1745602, _1745604))], (27891 ^ _776545) ^ [_1277980, _1277982] : [27892 ^ _776545 : [(27895 ^ _776545) ^ [] : [_1277982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27893 ^ _776545) ^ [] : [-(_1277980 = 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), _1277980)), _1277982))))], (38949 ^ _776545) ^ [_1526039, _1526041] : [-(hAPP(c_Relation_OField(_1526039), _1526041) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526039, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1526039, _1526039), _1526041)), hAPP(c_Relation_ORange(_1526039, _1526039), _1526041)))], (39770 ^ _776545) ^ [_1549675, _1549677] : [39772 ^ _776545 : [(39775 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1549677), 39771 ^ [_1549675, _1549677]))], (39773 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39771 ^ [_1549675, _1549677]), _1549675)))]], -(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)), _1549677), _1549675))], (7186 ^ _776545) ^ [_893647, _893649, _893651, _893653] : [-(hBOOL(hAPP(hAPP(c_member(_893647), _893649), _893651))), -(hBOOL(hAPP(hAPP(c_member(_893647), _893649), _893653))), 7193 ^ _776545 : [(7200 ^ _776545) ^ [] : [_893651 = _893653, -(hAPP(hAPP(c_Set_Oinsert(_893647), _893649), _893651) = hAPP(hAPP(c_Set_Oinsert(_893647), _893649), _893653))], (7194 ^ _776545) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_893647), _893649), _893651) = hAPP(hAPP(c_Set_Oinsert(_893647), _893649), _893653), -(_893651 = _893653)]]], (49267 ^ _776545) ^ [_1771407, _1771409] : [c_Relation_Otrans(_1771407, _1771409), -(c_Relation_Otrans(_1771407, hAPP(c_Relation_Oconverse(_1771407, _1771407), _1771409)))], (14248 ^ _776545) ^ [_1032923, _1032925, _1032927, _1032929] : [class_Rings_Ocomm__semiring__1(_1032923), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032923), _1032925), _1032927)), _1032929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032923), _1032925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032923), _1032927), _1032929)))], (52367 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (26042 ^ _776545) ^ [_1247246, _1247248, _1247250] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247246), _1247248)), _1247250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247246), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247248), _1247250))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247246), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247248, _1247250))), _1247250)))], (49628 ^ _776545) ^ [_1779502, _1779504] : [c_Relation_Oantisym(_1779502, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1779502, _1779502), tc_HOL_Obool)), _1779504), c_Relation_OId(_1779502))), -(c_Relation_Oantisym(_1779502, _1779504))], (14586 ^ _776545) ^ [_1039544, _1039546] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039544), _1039546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039546), _1039544)))], (28489 ^ _776545) ^ [_1287835] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1287835)), c_Int_OPls))], (27373 ^ _776545) ^ [] : [c_Int_OMin = c_Int_OPls], (2876 ^ _776545) ^ [_819204, _819206, _819208, _819210] : [-(c_Relation_ODomain(_819210, _819206) = c_Relation_ODomain(_819208, _819204)), _819210 = _819208, _819206 = _819204], (1614 ^ _776545) ^ [_799584, _799586] : [-(class_Rings_Olinordered__semidom(_799584)), _799586 = _799584, class_Rings_Olinordered__semidom(_799586)], (48544 ^ _776545) ^ [_1754712, _1754714, _1754716, _1754718, _1754720] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754712, _1754714, hAPP(hAPP(c_COMBC(_1754712, tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_fun(_1754714, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754714, tc_fun(tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_fun(_1754714, tc_HOL_Obool)), _1754712), c_COMBC(_1754714, tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754714, tc_prod(_1754712, _1754714)), tc_fun(_1754714, tc_fun(tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_HOL_Obool)), _1754712), hAPP(c_COMBB(tc_prod(_1754712, _1754714), tc_fun(tc_fun(tc_prod(_1754712, _1754714), tc_HOL_Obool), tc_HOL_Obool), _1754714), c_member(tc_prod(_1754712, _1754714)))), c_Product__Type_OPair(_1754712, _1754714)))), _1754716)), _1754718), _1754720)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1754714, _1754712)), hAPP(hAPP(c_Product__Type_OPair(_1754714, _1754712), _1754718), _1754720)), hAPP(c_Relation_Oconverse(_1754712, _1754714), _1754716))))], (44655 ^ _776545) ^ [_1669381, _1669383] : [-(_1669381 = c_List_Olist_ONil(_1669383)), -(hAPP(hAPP(c_List_Oappend(_1669383), c_List_Obutlast(_1669383, _1669381)), hAPP(hAPP(c_List_Olist_OCons(_1669383), c_List_Olast(_1669383, _1669381)), c_List_Olist_ONil(_1669383))) = _1669381)], (47424 ^ _776545) ^ [_1730072, _1730074, _1730076, _1730078, _1730080] : [hBOOL(hAPP(hAPP(c_member(_1730072), _1730074), hAPP(c_List_Oset(_1730072), _1730076))), -(hBOOL(hAPP(_1730078, _1730074))), -(c_List_OdropWhile(_1730072, _1730078, hAPP(hAPP(c_List_Oappend(_1730072), _1730076), _1730080)) = hAPP(hAPP(c_List_Oappend(_1730072), c_List_OdropWhile(_1730072, _1730078, _1730076)), _1730080))], (7664 ^ _776545) ^ [_904171, _904173, _904175, _904177] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904171, tc_HOL_Obool)), _904173), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904171, tc_HOL_Obool)), _904175), _904177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904171, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904171, tc_HOL_Obool)), _904173), _904175)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904171, tc_HOL_Obool)), _904173), _904177)))], (47654 ^ _776545) ^ [_1735175, _1735177, _1735179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1735175, _1735175)), hAPP(hAPP(c_Product__Type_OPair(_1735175, _1735175), _1735177), _1735179)), c_List_Omeasures(_1735175, c_List_Olist_ONil(tc_fun(_1735175, tc_Nat_Onat)))))], (40711 ^ _776545) ^ [_1572872, _1572874, _1572876] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572872, _1572872)), _1572874), _1572876)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572872, _1572872)), _1572874), c_Transitive__Closure_Ortrancl(_1572872, _1572876))))], (35228 ^ _776545) ^ [_1433920, _1433922, _1433924] : [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), _1433920), _1433922))), -(hBOOL(hAPP(hAPP(_1433924, _1433920), _1433922))), 35235 ^ _776545 : [(35238 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1433924, 35233 ^ [_1433920, _1433922, _1433924]), 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)))), 35234 ^ [_1433920, _1433922, _1433924])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 35233 ^ [_1433920, _1433922, _1433924]), 35234 ^ [_1433920, _1433922, _1433924]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35234 ^ [_1433920, _1433922, _1433924]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35248 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1433924, 35233 ^ [_1433920, _1433922, _1433924]), 35234 ^ [_1433920, _1433922, _1433924]))], (35236 ^ _776545) ^ [] : [-(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), 35233 ^ [_1433920, _1433922, _1433924]), 35234 ^ [_1433920, _1433922, _1433924]))))]]], (50259 ^ _776545) ^ [_1792428] : [-(c_Quickcheck_Obeyond(_1792428, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (26719 ^ _776545) ^ [_1258639, _1258641, _1258643] : [class_Int_Oring__char__0(_1258639), 26722 ^ _776545 : [(26729 ^ _776545) ^ [] : [_1258641 = _1258643, -(hAPP(c_Int_Oring__1__class_Oof__int(_1258639), _1258641) = hAPP(c_Int_Oring__1__class_Oof__int(_1258639), _1258643))], (26723 ^ _776545) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1258639), _1258641) = hAPP(c_Int_Oring__1__class_Oof__int(_1258639), _1258643), -(_1258641 = _1258643)]]], (18033 ^ _776545) ^ [_1100822, _1100824, _1100826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100822), _1100824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100826), _1100824))), 18036 ^ _776545 : [(18039 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100822), _1100826)))], (18037 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100824)))]]], (51155 ^ _776545) ^ [_1812406, _1812408, _1812410, _1812412, _1812414] : [class_Divides_Osemiring__div(_1812406), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812406), _1812408), _1812410)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812406), _1812412), _1812414)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812406), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812406), _1812410), _1812408)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812406), _1812414), _1812412)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812406), _1812410), _1812414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1812406), _1812408), _1812412)))], (25305 ^ _776545) ^ [_1234485, _1234487, _1234489] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234485), _1234487)), _1234489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234485), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234487), _1234489))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234485), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234487, _1234489))), _1234489)))], (13586 ^ _776545) ^ [_1018352, _1018354, _1018356, _1018358] : [class_Groups_Ocancel__ab__semigroup__add(_1018352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018352), _1018354), _1018356) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018352), _1018354), _1018358), -(_1018356 = _1018358)], (52319 ^ _776545) ^ [_1829455, _1829457] : [-(class_HOL_Oequal(tc_Nitpick_Opair__box(_1829455, _1829457)))], (4966 ^ _776545) ^ [_852209, _852211, _852213, _852215] : [-(c_Quickcheck_Obeyond(_852215, _852211) = c_Quickcheck_Obeyond(_852213, _852209)), _852215 = _852213, _852211 = _852209], (38106 ^ _776545) ^ [_1506405] : [-(c_Wellfounded_Owf(_1506405, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1506405, _1506405), tc_HOL_Obool))))], (37562 ^ _776545) ^ [_1491480, _1491482, _1491484, _1491486, _1491488, _1491490] : [c_Fun_Oinj__on(_1491480, _1491482, _1491484, _1491486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491480, tc_HOL_Obool)), _1491488), _1491486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491480, tc_HOL_Obool)), _1491490), _1491486)), -(hAPP(c_Set_Oimage(_1491480, _1491482, _1491484), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491480, tc_HOL_Obool)), _1491488), _1491490)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491482, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1491480, _1491482, _1491484), _1491488)), hAPP(c_Set_Oimage(_1491480, _1491482, _1491484), _1491490)))], (42027 ^ _776545) ^ [_1608092, _1608094, _1608096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1608092, _1608092), tc_HOL_Obool)), _1608094), _1608096)), c_Relation_Orefl__on(_1608092, c_Orderings_Otop__class_Otop(tc_fun(_1608092, tc_HOL_Obool)), _1608096), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1608092), tc_List_Olist(_1608092)), tc_HOL_Obool)), c_List_Olistrel1(_1608092, _1608094)), c_List_Olistrel(_1608092, _1608096))))], (44725 ^ _776545) ^ [_1670676, _1670678, _1670680, _1670682, _1670684] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1670676), tc_List_Olist(_1670678), tc_List_Olist(_1670680), hAPP(c_List_Omap(_1670676, _1670678), _1670682)), hAPP(c_List_Omap(_1670680, _1670676), _1670684)) = hAPP(c_List_Omap(_1670680, _1670678), hAPP(c_Fun_Ocomp(_1670676, _1670678, _1670680, _1670682), _1670684)))], (4682 ^ _776545) ^ [_847767, _847769, _847771, _847773, _847775, _847777] : [-(c_Random__Sequence_Oempty(_847777, _847773, _847769) = c_Random__Sequence_Oempty(_847775, _847771, _847767)), _847777 = _847775, _847773 = _847771, _847769 = _847767], (23133 ^ _776545) ^ [_1195717, _1195719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195717), _1195719)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1195719, _1195717) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (46040 ^ _776545) ^ [_1701233, _1701235, _1701237] : [hBOOL(hAPP(c_List_Odistinct(_1701233), _1701235)), -(hBOOL(hAPP(c_List_Odistinct(_1701233), hAPP(c_List_Ofilter(_1701233, _1701237), _1701235))))], (27479 ^ _776545) ^ [_1270909, _1270911, _1270913] : [class_Groups_Oordered__ab__group__add__abs(_1270909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270909), hAPP(c_Groups_Oabs__class_Oabs(_1270909), _1270911)), _1270913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270909), hAPP(c_Groups_Ouminus__class_Ouminus(_1270909), _1270911)), _1270913)))], (34785 ^ _776545) ^ [_1425536, _1425538, _1425540, _1425542, _1425544] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425536, _1425538, tc_HOL_Obool), _1425540), hAPP(hAPP(c_Product__Type_OPair(_1425536, _1425538), _1425542), _1425544))), -(hBOOL(hAPP(hAPP(_1425540, _1425542), _1425544)))], (48164 ^ _776545) ^ [_1746638, _1746640, _1746642] : [hBOOL(hAPP(hAPP(c_member(_1746638), _1746640), hAPP(c_List_Oset(_1746638), _1746642))), 48169 ^ _776545 : [(48172 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1746638), _1746640), hAPP(c_List_Oset(_1746638), 48168 ^ [_1746638, _1746640, _1746642])))], (48170 ^ _776545) ^ [] : [-(_1746642 = hAPP(hAPP(c_List_Oappend(_1746638), 48167 ^ [_1746638, _1746640, _1746642]), hAPP(hAPP(c_List_Olist_OCons(_1746638), _1746640), 48168 ^ [_1746638, _1746640, _1746642])))]]], (6212 ^ _776545) ^ [_876372, _876374, _876376, _876378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876372, tc_HOL_Obool)), _876374), _876376)), hBOOL(hAPP(_876374, _876378)), -(hBOOL(hAPP(_876376, _876378)))], (29453 ^ _776545) ^ [_1304250, _1304252] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1304250), hAPP(c_Int_Onumber__class_Onumber__of(_1304250), _1304252)), 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(_1304250), hAPP(c_Int_Onumber__class_Onumber__of(_1304250), _1304252)), hAPP(c_Int_Onumber__class_Onumber__of(_1304250), _1304252))), class_Groups_Omonoid__mult(_1304250), class_Int_Onumber(_1304250)], (36101 ^ _776545) ^ [_1456498, _1456500, _1456502, _1456504, _1456506, _1456508] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1456498), _1456500)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456502), _1456504)), 36111 ^ _776545 : [(36114 ^ _776545) ^ [] : [hAPP(c_Finite__Set_Ocard(_1456498), hAPP(c_Set_OCollect(_1456498), hAPP(hAPP(c_COMBS(_1456498, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1456498), c_fconj), hAPP(hAPP(c_COMBC(_1456498, tc_fun(_1456498, tc_HOL_Obool), tc_HOL_Obool), c_member(_1456498)), _1456500))), hAPP(hAPP(c_COMBC(_1456498, _1456502, tc_HOL_Obool), _1456506), 36110 ^ [_1456498, _1456500, _1456502, _1456504, _1456506, _1456508])))) = hAPP(_1456508, 36110 ^ [_1456498, _1456500, _1456502, _1456504, _1456506, _1456508])], (36112 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456502), 36110 ^ [_1456498, _1456500, _1456502, _1456504, _1456506, _1456508]), _1456504)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456498, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1456502, tc_HOL_Obool), tc_Nat_Onat, _1456498), c_Finite__Set_Ocard(_1456502)), hAPP(hAPP(c_COMBB(tc_fun(_1456502, tc_HOL_Obool), tc_fun(_1456502, tc_HOL_Obool), _1456498), c_Set_OCollect(_1456502)), hAPP(hAPP(c_COMBB(tc_fun(_1456502, tc_HOL_Obool), tc_fun(_1456502, tc_HOL_Obool), _1456498), hAPP(c_COMBS(_1456502, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1456502), c_fconj), hAPP(hAPP(c_COMBC(_1456502, tc_fun(_1456502, tc_HOL_Obool), tc_HOL_Obool), c_member(_1456502)), _1456504)))), _1456506)))), _1456500) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456502, tc_Nat_Onat), _1456508), _1456504))], (27801 ^ _776545) ^ [_1276454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276454), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276454))], (35586 ^ _776545) ^ [_1440698, _1440700, _1440702, _1440704] : [_1440698 = _1440700, 35589 ^ _776545 : [(35592 ^ _776545) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1440702, _1440704), _1440698) = hAPP(c_Product__Type_Osnd(_1440702, _1440704), _1440700))], (35590 ^ _776545) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1440702, _1440704), _1440698) = hAPP(c_Product__Type_Ofst(_1440702, _1440704), _1440700))]]], (48578 ^ _776545) ^ [_1756009, _1756011, _1756013] : [-(_1756009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1756011), c_List_Oreplicate(_1756011, _1756009, _1756013)) = _1756013)], (52429 ^ _776545) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (38028 ^ _776545) ^ [_1503761, _1503763, _1503765, _1503767, _1503769, _1503771, _1503773] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1503761, _1503763, _1503765, hAPP(hAPP(c_COMBC(_1503761, tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_fun(_1503763, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503763, tc_fun(tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_fun(_1503763, tc_HOL_Obool)), _1503761), c_COMBC(_1503763, tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503763, tc_prod(_1503761, _1503763)), tc_fun(_1503763, tc_fun(tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_HOL_Obool)), _1503761), hAPP(c_COMBB(tc_prod(_1503761, _1503763), tc_fun(tc_fun(tc_prod(_1503761, _1503763), tc_HOL_Obool), tc_HOL_Obool), _1503763), c_member(tc_prod(_1503761, _1503763)))), c_Product__Type_OPair(_1503761, _1503763)))), _1503767), hAPP(hAPP(c_COMBC(_1503763, tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_fun(_1503765, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503765, tc_fun(tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_fun(_1503765, tc_HOL_Obool)), _1503763), c_COMBC(_1503765, tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503765, tc_prod(_1503763, _1503765)), tc_fun(_1503765, tc_fun(tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_HOL_Obool)), _1503763), hAPP(c_COMBB(tc_prod(_1503763, _1503765), tc_fun(tc_fun(tc_prod(_1503763, _1503765), tc_HOL_Obool), tc_HOL_Obool), _1503765), c_member(tc_prod(_1503763, _1503765)))), c_Product__Type_OPair(_1503763, _1503765)))), _1503769)), _1503771), _1503773)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1503761, _1503765)), hAPP(hAPP(c_Product__Type_OPair(_1503761, _1503765), _1503771), _1503773)), hAPP(hAPP(c_Relation_Orel__comp(_1503761, _1503763, _1503765), _1503767), _1503769))))], (46415 ^ _776545) ^ [_1709941, _1709943, _1709945, _1709947] : [class_Groups_Ocomm__monoid__add(_1709941), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1709941), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1709941), _1709943), c_List_Oupt(_1709945, _1709947))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1709941), _1709943), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1709945, _1709947))))], (7424 ^ _776545) ^ [_898720, _898722, _898724] : [class_Orderings_Oorder(_898720), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_898720, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_898720, _898722, _898724)), hAPP(c_SetInterval_Oord__class_OatLeast(_898720), _898724)) = c_Orderings_Obot__class_Obot(tc_fun(_898720, tc_HOL_Obool)))], (38791 ^ _776545) ^ [_1522470, _1522472, _1522474, _1522476, _1522478, _1522480] : [hBOOL(hAPP(hAPP(c_member(_1522470), _1522472), _1522474)), 38794 ^ _776545 : [(38801 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522470), _1522476), _1522474))), -(hAPP(c_Set_Ovimage(_1522478, _1522470, hAPP(hAPP(c_COMBC(_1522478, _1522470, _1522470), hAPP(hAPP(c_COMBC(_1522478, _1522470, tc_fun(_1522470, _1522470)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1522470, tc_fun(_1522470, _1522470)), _1522478), c_If(_1522470)), hAPP(hAPP(c_COMBC(_1522478, tc_fun(_1522478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522478)), _1522480))), _1522472)), _1522476)), _1522474) = _1522480)], (38795 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1522470), _1522476), _1522474)), -(hAPP(c_Set_Ovimage(_1522478, _1522470, hAPP(hAPP(c_COMBC(_1522478, _1522470, _1522470), hAPP(hAPP(c_COMBC(_1522478, _1522470, tc_fun(_1522470, _1522470)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1522470, tc_fun(_1522470, _1522470)), _1522478), c_If(_1522470)), hAPP(hAPP(c_COMBC(_1522478, tc_fun(_1522478, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522478)), _1522480))), _1522472)), _1522476)), _1522474) = c_Orderings_Otop__class_Otop(tc_fun(_1522478, tc_HOL_Obool)))]]], (51285 ^ _776545) ^ [_1814873, _1814875, _1814877, _1814879] : [class_Rings_Oidom(_1814873), 51288 ^ _776545 : [(51289 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814873), _1814875), _1814877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814873), _1814875), _1814879))), -(_1814875 = c_Groups_Ozero__class_Ozero(_1814873)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814873), _1814877), _1814879)))], (51299 ^ _776545) ^ [] : [51300 ^ _776545 : [(51303 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814873), _1814877), _1814879))], (51301 ^ _776545) ^ [] : [_1814875 = c_Groups_Ozero__class_Ozero(_1814873)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814873), _1814875), _1814877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814873), _1814875), _1814879))))]]], (25263 ^ _776545) ^ [_1233858] : [class_Int_Onumber__ring(_1233858), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1233858), c_Groups_Oone__class_Oone(_1233858)) = hAPP(c_Int_Onumber__class_Onumber__of(_1233858), c_Int_OMin))], (52141 ^ _776545) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (48458 ^ _776545) ^ [_1752803, _1752805, _1752807, _1752809] : [-(c_New__Random__Sequence_Opos__map(_1752803, _1752805, _1752807, _1752809) = c_New__Random__Sequence_Opos__bind(_1752803, _1752805, _1752809, hAPP(c_Fun_Ocomp(_1752805, 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(_1752805))))), _1752803, c_New__Random__Sequence_Opos__single(_1752805)), _1752807)))], (45237 ^ _776545) ^ [_1682553, _1682555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1682553), _1682555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682553)), hAPP(c_Code__Numeral_Onat__of, _1682555))))], (1982 ^ _776545) ^ [_805051, _805053, _805055, _805057] : [-(tc_Datatype_Onode(_805057, _805053) = tc_Datatype_Onode(_805055, _805051)), _805057 = _805055, _805053 = _805051], (22675 ^ _776545) ^ [_1187460] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1187460) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52377 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (42845 ^ _776545) ^ [_1630159, _1630161, _1630163] : [hBOOL(hAPP(c_List_Odistinct(_1630159), hAPP(hAPP(c_List_Olist_OCons(_1630159), _1630161), _1630163))), 42848 ^ _776545 : [(42851 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1630159), _1630163)))], (42849 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630159), _1630161), hAPP(c_List_Oset(_1630159), _1630163)))]]], (34570 ^ _776545) ^ [_1420379, _1420381, _1420383] : [_1420379 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1420381, _1420381), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1420381, _1420381), tc_HOL_Obool)), _1420379), _1420383)))], (25355 ^ _776545) ^ [_1235301] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235301), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235301))], (31729 ^ _776545) ^ [_1346520, _1346522, _1346524, _1346526, _1346528] : [class_Orderings_Olinorder(_1346520), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346520, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1346520, _1346522, _1346524)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1346520, _1346526, _1346528)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1346520, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346520), _1346522), _1346526), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1346520), _1346524), _1346528)))], (33240 ^ _776545) ^ [_1385737, _1385739, _1385741, _1385743] : [33242 ^ _776545 : [(33245 ^ _776545) ^ [] : [hAPP(_1385743, 33241 ^ [_1385737, _1385739, _1385741, _1385743]) = c_Orderings_Obot__class_Obot(tc_fun(_1385737, tc_HOL_Obool))], (33243 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1385739), 33241 ^ [_1385737, _1385739, _1385741, _1385743]), _1385741)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1385737, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385739, tc_fun(_1385737, tc_HOL_Obool)), _1385741), _1385743))], (20571 ^ _776545) ^ [_1147848, _1147850, _1147852, _1147854] : [class_Fields_Olinordered__field(_1147848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147848), c_Groups_Ozero__class_Ozero(_1147848)), _1147850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147848), _1147852), _1147850)), _1147854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147848), _1147852), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147848), _1147854), _1147850))))], (12091 ^ _776545) ^ [_989014, _989016] : [class_Complete__Lattice_Ocomplete__lattice(_989014), hBOOL(hAPP(c_Finite__Set_Ofinite(_989014), _989016)), -(_989016 = c_Orderings_Obot__class_Obot(tc_fun(_989014, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_989014, _989016) = c_Complete__Lattice_OSup__class_OSup(_989014, _989016))], (22527 ^ _776545) ^ [_1184817, _1184819, _1184821] : [class_Rings_Olinordered__semidom(_1184817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184817), c_Groups_Ozero__class_Ozero(_1184817)), _1184819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184817), c_Groups_Ozero__class_Ozero(_1184817)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184817), _1184819), _1184821))))], (40941 ^ _776545) ^ [] : [-(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))))], (45235 ^ _776545) ^ [] : [-(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))], (2098 ^ _776545) ^ [_806971, _806973, _806975, _806977] : [-(c_SMT_Oz3div(_806977, _806973) = c_SMT_Oz3div(_806975, _806971)), _806977 = _806975, _806973 = _806971], (47070 ^ _776545) ^ [_1722684, _1722686, _1722688] : [hAPP(c_List_Orev(_1722684), _1722686) = _1722688, -(_1722686 = hAPP(c_List_Orev(_1722684), _1722688))], (45968 ^ _776545) ^ [_1698715, _1698717] : [-(hAPP(c_List_Oset(_1698715), c_List_Oconcat(_1698715, _1698717)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1698715), tc_fun(_1698715, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1698715)), _1698717)), c_List_Oset(_1698715)))], (34791 ^ _776545) ^ [_1425665, _1425667, _1425669, _1425671, _1425673, _1425675, _1425677] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425665, _1425667, tc_fun(_1425669, tc_HOL_Obool)), _1425671), hAPP(hAPP(c_Product__Type_OPair(_1425665, _1425667), _1425673), _1425675)), _1425677)), -(hBOOL(hAPP(hAPP(hAPP(_1425671, _1425673), _1425675), _1425677)))], (41053 ^ _776545) ^ [_1580966, _1580968, _1580970, _1580972, _1580974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580966, _1580966)), hAPP(hAPP(c_Product__Type_OPair(_1580966, _1580966), hAPP(_1580968, hAPP(c_Nat_OSuc, 41054 ^ [_1580966, _1580968, _1580970, _1580972, _1580974]))), hAPP(_1580968, 41054 ^ [_1580966, _1580968, _1580970, _1580972, _1580974]))), c_Transitive__Closure_Ortrancl(_1580966, _1580970))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580966, _1580966)), hAPP(hAPP(c_Product__Type_OPair(_1580966, _1580966), hAPP(_1580968, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1580972), _1580974))), hAPP(_1580968, _1580972))), c_Transitive__Closure_Ortrancl(_1580966, _1580970))))], (26274 ^ _776545) ^ [_1251046, _1251048] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1251046), _1251048)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1251048), _1251046)))], (2560 ^ _776545) ^ [_814264, _814266, _814268, _814270] : [-(c_Wellfounded_Omin__ext(_814270, _814266) = c_Wellfounded_Omin__ext(_814268, _814264)), _814270 = _814268, _814266 = _814264], (50285 ^ _776545) ^ [_1793055, _1793057, _1793059] : [c_Fun_Obij__betw(_1793055, _1793057, _1793059, c_Orderings_Otop__class_Otop(tc_fun(_1793055, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793057, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1793057, _1793055, c_Orderings_Otop__class_Otop(tc_fun(_1793057, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1793055, _1793057, c_Orderings_Otop__class_Otop(tc_fun(_1793055, tc_HOL_Obool)), _1793059)) = _1793059)], (22159 ^ _776545) ^ [_1178399, _1178401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178399), _1178401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178399)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178401))))], (41965 ^ _776545) ^ [_1606191, _1606193, _1606195, _1606197, _1606199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606191, _1606191)), hAPP(hAPP(c_Product__Type_OPair(_1606191, _1606191), _1606193), _1606195)), _1606197)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606191), tc_List_Olist(_1606191))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606191), tc_List_Olist(_1606191)), hAPP(hAPP(c_List_Olist_OCons(_1606191), _1606193), _1606199)), hAPP(hAPP(c_List_Olist_OCons(_1606191), _1606195), _1606199))), c_List_Olistrel1(_1606191, _1606197))))], (31437 ^ _776545) ^ [_1341050, _1341052, _1341054, _1341056] : [class_Orderings_Olinorder(_1341050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341050), _1341052), _1341054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341050), _1341056), _1341054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341050), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341050), _1341052), _1341056)), _1341054)))], (2066 ^ _776545) ^ [_806449, _806451, _806453, _806455, _806457, _806459, _806461, _806463] : [-(c_Sum__Type_OPlus(_806463, _806459, _806455, _806451) = c_Sum__Type_OPlus(_806461, _806457, _806453, _806449)), _806463 = _806461, _806459 = _806457, _806455 = _806453, _806451 = _806449], (21477 ^ _776545) ^ [_1165665, _1165667, _1165669, _1165671] : [class_Fields_Ofield__inverse__zero(_1165665), class_Int_Onumber(_1165665), 21484 ^ _776545 : [(21485 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165665), _1165669), _1165671), 21488 ^ _776545 : [(21495 ^ _776545) ^ [] : [_1165671 = c_Groups_Ozero__class_Ozero(_1165665), -(hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667) = c_Groups_Ozero__class_Ozero(_1165665))], (21489 ^ _776545) ^ [] : [-(_1165671 = c_Groups_Ozero__class_Ozero(_1165665)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165665), hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667)), _1165671) = _1165669)]]], (21501 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165665), _1165669), _1165671)), 21504 ^ _776545 : [(21507 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165665), hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667)), _1165671) = _1165669], (21505 ^ _776545) ^ [] : [_1165671 = c_Groups_Ozero__class_Ozero(_1165665)]], 21508 ^ _776545 : [(21511 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165665), _1165667) = c_Groups_Ozero__class_Ozero(_1165665)], (21509 ^ _776545) ^ [] : [-(_1165671 = c_Groups_Ozero__class_Ozero(_1165665))]]]]], (22197 ^ _776545) ^ [_1179118, _1179120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179118), _1179120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179118), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179120), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (16903 ^ _776545) ^ [_1080692, _1080694, _1080696] : [class_Groups_Oordered__comm__monoid__add(_1080692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080692), _1080694), c_Groups_Ozero__class_Ozero(_1080692))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080692), _1080696), c_Groups_Ozero__class_Ozero(_1080692))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080692), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080692), _1080694), _1080696)), c_Groups_Ozero__class_Ozero(_1080692))))], (34307 ^ _776545) ^ [_1415072, _1415074] : [34308 ^ _776545 : [(34311 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1415074), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34309 ^ _776545) ^ [] : [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), _1415072), _1415074)))]], -(c_Divides_OnegDivAlg(_1415072, _1415074) = 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), _1415072), _1415074)))], (19537 ^ _776545) ^ [_1129486, _1129488] : [class_Rings_Olinordered__idom(_1129486), -(c_Groups_Osgn__class_Osgn(_1129486, c_Groups_Osgn__class_Osgn(_1129486, _1129488)) = c_Groups_Osgn__class_Osgn(_1129486, _1129488))], (30052 ^ _776545) ^ [_1315478, _1315480, _1315482] : [class_Orderings_Olinorder(_1315478), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315478), _1315480), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315478), _1315480), _1315482)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315478), _1315480), _1315482))], (35135 ^ _776545) ^ [_1432287, _1432289, _1432291] : [35137 ^ _776545 : [(35140 ^ _776545) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1432287, _1432289), 35136 ^ [_1432287, _1432289, _1432291]))], (35138 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1432289, 35136 ^ [_1432287, _1432289, _1432291]), _1432291)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1432287, _1432289), _1432291)))], (37316 ^ _776545) ^ [_1486855, _1486857, _1486859, _1486861, _1486863, _1486865] : [c_Fun_Oinj__on(_1486855, _1486857, _1486859, _1486861), hBOOL(hAPP(hAPP(c_member(_1486855), _1486863), _1486861)), hBOOL(hAPP(hAPP(c_member(_1486855), _1486865), _1486861)), 37327 ^ _776545 : [(37334 ^ _776545) ^ [] : [_1486863 = _1486865, -(hAPP(_1486859, _1486863) = hAPP(_1486859, _1486865))], (37328 ^ _776545) ^ [] : [hAPP(_1486859, _1486863) = hAPP(_1486859, _1486865), -(_1486863 = _1486865)]]], (4080 ^ _776545) ^ [_838276, _838278, _838280, _838282, _838284, _838286, _838288, _838290] : [-(c_New__Random__Sequence_Oneg__bind(_838290, _838286, _838282, _838278) = c_New__Random__Sequence_Oneg__bind(_838288, _838284, _838280, _838276)), _838290 = _838288, _838286 = _838284, _838282 = _838280, _838278 = _838276], (49428 ^ _776545) ^ [_1775900, _1775902] : [c_Relation_Otrans(_1775900, hAPP(c_Set_OCollect(tc_prod(_1775900, _1775900)), hAPP(c_Product__Type_Oprod_Oprod__case(_1775900, _1775900, tc_HOL_Obool), _1775902))), -(c_Predicate_Otransp(_1775900, _1775902))], (46688 ^ _776545) ^ [_1714768, _1714770, _1714772, _1714774, _1714776] : [class_Orderings_Olinorder(_1714768), -(c_List_Olinorder__class_Osorted(_1714768, hAPP(hAPP(c_List_Omap(_1714770, _1714768), _1714772), hAPP(c_List_Ofilter(_1714770, hAPP(hAPP(c_COMBC(_1714770, _1714768, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1714768, tc_fun(_1714768, tc_HOL_Obool), _1714770), c_fequal), _1714772)), hAPP(_1714774, _1714776))), _1714776))))], (32572 ^ _776545) ^ [_1365772, _1365774, _1365776, _1365778] : [hBOOL(hAPP(hAPP(c_member(_1365772), _1365778), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365772, tc_HOL_Obool)), _1365774), _1365776))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365772, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1365772, tc_fun(_1365772, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365772)), _1365774)), hAPP(hAPP(c_COMBC(_1365772, tc_fun(_1365772, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365772)), _1365776)), _1365778)))], (47958 ^ _776545) ^ [_1742606, _1742608] : [class_Enum_Oenum(_1742606), 47961 ^ _776545 : [(47968 ^ _776545) ^ [] : [hBOOL(hAPP(_1742608, 47969 ^ [_1742606, _1742608])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742606), _1742608)))], (47962 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742606), _1742608)), 47965 ^ _776545 : [(47966 ^ _776545) ^ [_1742732] : [-(hBOOL(hAPP(_1742608, _1742732)))]]]]], (42827 ^ _776545) ^ [_1629796, _1629798, _1629800] : [hBOOL(hAPP(c_List_Odistinct(_1629796), _1629798)), -(hBOOL(hAPP(c_List_Odistinct(_1629796), c_List_Osublist(_1629796, _1629798, _1629800))))], (11072 ^ _776545) ^ [_968023, _968025, _968027] : [class_Rings_Oring(_968023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968023), hAPP(c_Groups_Ouminus__class_Ouminus(_968023), _968025)), _968027) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968023), _968025), hAPP(c_Groups_Ouminus__class_Ouminus(_968023), _968027)))], (1294 ^ _776545) ^ [_795584, _795586] : [-(class_Groups_Oabs__if(_795584)), _795586 = _795584, class_Groups_Oabs__if(_795586)], (164 ^ _776545) ^ [_779247, _779249, _779251, _779253, _779255, _779257, _779259, _779261, _779263, _779265] : [-(c_Big__Operators_Ocomm__monoid__big(_779263, _779259, _779255, _779251, _779247)), c_Big__Operators_Ocomm__monoid__big(_779265, _779261, _779257, _779253, _779249), _779265 = _779263, _779261 = _779259, _779257 = _779255, _779253 = _779251, _779249 = _779247], (4240 ^ _776545) ^ [_840794, _840796] : [_840796 = _840794, -(c_List_Ohd(_840796) = c_List_Ohd(_840794))], (14158 ^ _776545) ^ [_1030953, _1030955, _1030957, _1030959, _1030961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030953), _1030955)), 14161 ^ _776545 : [(14168 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030959), 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), _1030955), _1030953)), _1030957)), _1030961))), -(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), _1030953), _1030957)), _1030959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030955), _1030957)), _1030961))))], (14162 ^ _776545) ^ [] : [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), _1030953), _1030957)), _1030959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030955), _1030957)), _1030961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030959), 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), _1030955), _1030953)), _1030957)), _1030961))))]]], (39401 ^ _776545) ^ [_1539653, _1539655, _1539657, _1539659] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539653), _1539655)), 39407 ^ _776545 : [(39410 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539657), hAPP(_1539659, 39406 ^ [_1539653, _1539655, _1539657, _1539659])))], (39408 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539653), 39406 ^ [_1539653, _1539655, _1539657, _1539659]), _1539655)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1539653, _1539657)), hAPP(hAPP(c_Product__Type_OSigma(_1539653, _1539657), _1539655), _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)), _1539659)), _1539655))], (51273 ^ _776545) ^ [_1814659, _1814661, _1814663] : [class_Rings_Ocomm__semiring__1(_1814659), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814659), _1814661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814659), _1814663), _1814661))))], (32978 ^ _776545) ^ [_1378284, _1378286, _1378288, _1378290, _1378292] : [class_Groups_Oab__group__add(_1378284), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378286, _1378284), hAPP(hAPP(c_COMBS(_1378286, _1378284, _1378284), hAPP(hAPP(c_COMBB(_1378284, tc_fun(_1378284, _1378284), _1378286), c_Groups_Ominus__class_Ominus(_1378284)), _1378288)), _1378290)), _1378292) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1378284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378286, _1378284), _1378288), _1378292)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1378286, _1378284), _1378290), _1378292)))], (6563 ^ _776545) ^ [_882611, _882613, _882615, _882617, _882619] : [class_Orderings_Oord(_882611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882613, _882611)), _882615), _882617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882611), hAPP(_882615, _882619)), hAPP(_882617, _882619))))], (36083 ^ _776545) ^ [_1455948, _1455950, _1455952, _1455954] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455948, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36084 ^ [_1455948, _1455950, _1455952, _1455954])), _1455950) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455948, 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), 36084 ^ [_1455948, _1455950, _1455952, _1455954]), _1455952))), _1455954), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455948, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455950) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455948, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455954))], (23313 ^ _776545) ^ [_1199002, _1199004, _1199006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199002)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1199004), _1199006)), 23320 ^ _776545 : [(23321 ^ _776545) ^ [_1199192] : [23323 ^ _776545 : [(23329 ^ _776545) ^ [] : [-(_1199192 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23325 ^ [_1199002, _1199004, _1199006, _1199192]), 23322 ^ [_1199002, _1199004, _1199006, _1199192]))], (23327 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23325 ^ [_1199002, _1199004, _1199006, _1199192]), _1199006)))], (23324 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23322 ^ [_1199002, _1199004, _1199006, _1199192]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1199002))))]], -(_1199192 = _1199004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199192), _1199002) = _1199004]]], (19358 ^ _776545) ^ [_1126052, _1126054, _1126056] : [class_Rings_Oring__1(_1126052), hBOOL(hAPP(hAPP(c_member(_1126052), _1126054), c_Int_Oring__1__class_OInts(_1126052))), hBOOL(hAPP(hAPP(c_member(_1126052), _1126056), c_Int_Oring__1__class_OInts(_1126052))), -(hBOOL(hAPP(hAPP(c_member(_1126052), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126052), _1126054), _1126056)), c_Int_Oring__1__class_OInts(_1126052))))], (14668 ^ _776545) ^ [_1041078, _1041080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041078), _1041080)), -(_1041078 = _1041080), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041078), _1041080)))], (52323 ^ _776545) ^ [_1829509, _1829511] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1829509, _1829511))), class_Lazy__Sequence_Osmall__lazy(_1829509), class_Lazy__Sequence_Osmall__lazy(_1829511)], (27617 ^ _776545) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (11147 ^ _776545) ^ [_969482, _969484, _969486, _969488] : [_969488 = c_Orderings_Obot__class_Obot(tc_fun(_969482, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_969482, _969484, _969486), _969488) = c_Orderings_Obot__class_Obot(tc_fun(_969484, tc_HOL_Obool)))], (10803 ^ _776545) ^ [_962659, _962661, _962663, _962665, _962667, _962669, _962671] : [-(hBOOL(hAPP(hAPP(c_member(_962659), _962661), _962663))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962659, _962665, _962667, _962669, _962663), _962671)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962659, _962665, _962667, _962669, hAPP(hAPP(c_Set_Oinsert(_962659), _962661), _962663)), hAPP(hAPP(_962667, _962661), _962671))))], (28609 ^ _776545) ^ [_1289719] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289719)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1289719)))], (19573 ^ _776545) ^ [_1130238, _1130240] : [class_Rings_Odivision__ring(_1130238), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130238), _1130240), c_Groups_Oone__class_Oone(_1130238)) = _1130240)], (50934 ^ _776545) ^ [_1808015, _1808017, _1808019, _1808021] : [-(hAPP(c_Lazy__Sequence_Obind(_1808015, _1808017, _1808019), _1808021) = c_Lazy__Sequence_Oflat(_1808017, c_Lazy__Sequence_Omap(_1808015, tc_Lazy__Sequence_Olazy__sequence(_1808017), _1808021, _1808019)))], (43898 ^ _776545) ^ [_1653620, _1653622, _1653624] : [-(hAPP(hAPP(c_List_Odrop(_1653620), _1653622), c_List_Obutlast(_1653620, _1653624)) = c_List_Obutlast(_1653620, hAPP(hAPP(c_List_Odrop(_1653620), _1653622), _1653624)))], (10685 ^ _776545) ^ [_960430] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960430, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_960430, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_960430, tc_HOL_Obool)))], (29305 ^ _776545) ^ [_1301684, _1301686, _1301688] : [class_Groups_Omonoid__mult(_1301684), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301684), _1301686), 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)))), _1301688)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301684), hAPP(hAPP(c_Power_Opower__class_Opower(_1301684), _1301686), _1301688)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44250 ^ _776545) ^ [_1661363, _1661365, _1661367] : [class_Orderings_Olinorder(_1661363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1661363), _1661365)), -(c_List_Olinorder__class_Osorted__list__of__set(_1661363, hAPP(hAPP(c_Set_Oinsert(_1661363), _1661367), _1661365)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661363, _1661363, c_COMBI(_1661363)), _1661367), c_List_Olinorder__class_Osorted__list__of__set(_1661363, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1661363, tc_HOL_Obool)), _1661365), hAPP(hAPP(c_Set_Oinsert(_1661363), _1661367), c_Orderings_Obot__class_Obot(tc_fun(_1661363, tc_HOL_Obool)))))))], (28631 ^ _776545) ^ [] : [-(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))))))], (7206 ^ _776545) ^ [_894013, _894015, _894017, _894019] : [hBOOL(hAPP(hAPP(c_member(_894013), _894015), hAPP(hAPP(c_Set_Oinsert(_894013), _894017), _894019))), -(_894015 = _894017), -(hBOOL(hAPP(hAPP(c_member(_894013), _894015), _894019)))], (12558 ^ _776545) ^ [_997487, _997489, _997491, _997493] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997487), _997489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997487, tc_HOL_Obool)), _997489), _997491)), hBOOL(hAPP(_997493, c_Orderings_Obot__class_Obot(tc_fun(_997487, tc_HOL_Obool)))), 12573 ^ _776545 : [(12574 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_997487), 12572 ^ [_997487, _997489, _997491, _997493])))], (12578 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_997487), 12571 ^ [_997487, _997489, _997491, _997493]), 12572 ^ [_997487, _997489, _997491, _997493]))], (12582 ^ _776545) ^ [] : [hBOOL(hAPP(_997493, hAPP(hAPP(c_Set_Oinsert(_997487), 12571 ^ [_997487, _997489, _997491, _997493]), 12572 ^ [_997487, _997489, _997491, _997493])))], (12580 ^ _776545) ^ [] : [-(hBOOL(hAPP(_997493, 12572 ^ [_997487, _997489, _997491, _997493])))], (12576 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997487), 12571 ^ [_997487, _997489, _997491, _997493]), _997491)))]], -(hBOOL(hAPP(_997493, _997489)))], (44326 ^ _776545) ^ [_1662987, _1662989, _1662991, _1662993, _1662995, _1662997] : [-(hAPP(c_List_Ofoldl(_1662987, _1662989, _1662991, _1662993), hAPP(hAPP(c_List_Olist_OCons(_1662989), _1662995), _1662997)) = hAPP(c_List_Ofoldl(_1662987, _1662989, _1662991, hAPP(hAPP(_1662991, _1662993), _1662995)), _1662997))], (18668 ^ _776545) ^ [_1112615, _1112617, _1112619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112615), _1112617)), 18671 ^ _776545 : [(18691 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112615, tc_Nat_Onat), _1112619), _1112617) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 18692 ^ _776545 : [(18693 ^ _776545) ^ [_1113096] : [hBOOL(hAPP(hAPP(c_member(_1112615), _1113096), _1112617)), hAPP(_1112619, _1113096) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 18701 ^ _776545 : [(18706 ^ _776545) ^ [] : [hAPP(_1112619, 18700 ^ [_1112615, _1112617, _1112619, _1113096]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18704 ^ _776545) ^ [] : [_1113096 = 18700 ^ [_1112615, _1112617, _1112619, _1113096]], (18702 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112615), 18700 ^ [_1112615, _1112617, _1112619, _1113096]), _1112617)))]]]]], (18672 ^ _776545) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1112615, tc_Nat_Onat), _1112619), _1112617) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 18676 ^ _776545 : [(18681 ^ _776545) ^ [_1112935] : [hBOOL(hAPP(hAPP(c_member(_1112615), _1112935), _1112617)), -(18675 ^ [_1112615, _1112617, _1112619] = _1112935), -(hAPP(_1112619, _1112935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18679 ^ _776545) ^ [] : [-(hAPP(_1112619, 18675 ^ [_1112615, _1112617, _1112619]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18677 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1112615), 18675 ^ [_1112615, _1112617, _1112619]), _1112617)))]]]]], (31234 ^ _776545) ^ [_1337078, _1337080, _1337082] : [class_Orderings_Olinorder(_1337078), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337078), _1337080)), 31244 ^ _776545 : [(31247 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337078), 31243 ^ [_1337078, _1337080, _1337082]), _1337082))], (31245 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337078), 31243 ^ [_1337078, _1337080, _1337082]), _1337080)))]], hBOOL(hAPP(hAPP(c_member(_1337078), _1337082), _1337080)), -(c_Big__Operators_Olinorder__class_OMax(_1337078, _1337080) = _1337082)], (17967 ^ _776545) ^ [_1099709] : [-(hAPP(c_Finite__Set_Ocard(_1099709), c_Orderings_Obot__class_Obot(tc_fun(_1099709, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38442 ^ _776545) ^ [_1513478, _1513480] : [-(c_Nitpick_Onumber__of__frac(_1513478, _1513480) = c_Nitpick_OAbs__Frac(_1513478, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1513480), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (6087 ^ _776545) ^ [_873971, _873973, _873975, _873977, _873979, _873981] : [-(hBOOL(hAPP(hAPP(c_member(_873971), _873973), c_SetInterval_Oord_OgreaterThanAtMost(_873971, _873975, _873977, _873979, _873981)))), hBOOL(hAPP(hAPP(_873977, _873979), _873973)), hBOOL(hAPP(hAPP(_873975, _873973), _873981))], (35116 ^ _776545) ^ [_1431897, _1431899, _1431901] : [35118 ^ _776545 : [(35121 ^ _776545) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431897, _1431899), 35117 ^ [_1431897, _1431899, _1431901]))], (35119 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1431899, 35117 ^ [_1431897, _1431899, _1431901]), _1431901)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431897, _1431899), _1431901)))], (14825 ^ _776545) ^ [_1043902, _1043904, _1043906] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043904), _1043906)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043902), _1043904)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1043902), _1043906)))], (44106 ^ _776545) ^ [_1658842, _1658844, _1658846] : [-(_1658842 = c_List_Olist_ONil(_1658844)), -(hAPP(c_List_Ohd(_1658844), hAPP(hAPP(c_List_Oappend(_1658844), _1658842), _1658846)) = hAPP(c_List_Ohd(_1658844), _1658842))], (14444 ^ _776545) ^ [_1037355, _1037357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037355), _1037357)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037357), _1037355)), _1037355) = _1037357)], (51829 ^ _776545) ^ [_1824219, _1824221, _1824223] : [_1824219 = _1824221, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824221), _1824223)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824219), _1824223)))], (40729 ^ _776545) ^ [_1573295, _1573297] : [-(c_Transitive__Closure_Otrancl(_1573295, c_Transitive__Closure_Ortrancl(_1573295, _1573297)) = c_Transitive__Closure_Ortrancl(_1573295, _1573297))], (33805 ^ _776545) ^ [_1402425, _1402427, _1402429, _1402431] : [-(hAPP(c_Set_Oimage(_1402425, _1402427, _1402429), _1402431) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402425, tc_fun(_1402427, tc_HOL_Obool)), _1402431), hAPP(hAPP(c_COMBC(_1402425, tc_fun(_1402427, tc_HOL_Obool), tc_fun(_1402427, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1402427, tc_fun(tc_fun(_1402427, tc_HOL_Obool), tc_fun(_1402427, tc_HOL_Obool)), _1402425), c_Set_Oinsert(_1402427)), _1402429)), c_Orderings_Obot__class_Obot(tc_fun(_1402427, tc_HOL_Obool)))))], (43769 ^ _776545) ^ [_1650041, _1650043, _1650045, _1650047, _1650049] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1650041), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650043)), _1650045)))), -(hAPP(hAPP(c_List_Olist__update(_1650043, hAPP(hAPP(c_List_Oappend(_1650043), _1650045), _1650047)), _1650041), _1650049) = hAPP(hAPP(c_List_Oappend(_1650043), _1650045), hAPP(hAPP(c_List_Olist__update(_1650043, _1650047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650041), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650043)), _1650045))), _1650049)))], (50566 ^ _776545) ^ [_1798603, _1798605, _1798607, _1798609, _1798611, _1798613, _1798615] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798603, tc_HOL_Obool)), _1798605), _1798607) = c_Orderings_Obot__class_Obot(tc_fun(_1798603, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1798609, tc_HOL_Obool)), _1798611), _1798613) = c_Orderings_Obot__class_Obot(tc_fun(_1798609, tc_HOL_Obool)), c_Fun_Obij__betw(_1798603, _1798609, _1798615, _1798605, _1798611), c_Fun_Obij__betw(_1798603, _1798609, _1798615, _1798607, _1798613), -(c_Fun_Obij__betw(_1798603, _1798609, _1798615, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798603, tc_HOL_Obool)), _1798605), _1798607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1798609, tc_HOL_Obool)), _1798611), _1798613)))], (7061 ^ _776545) ^ [_891492, _891494, _891496] : [class_Orderings_Oorder(_891492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891492), _891494), _891496)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_891492, _891496, _891494) = c_Orderings_Obot__class_Obot(tc_fun(_891492, tc_HOL_Obool)))], (33334 ^ _776545) ^ [_1388228, _1388230, _1388232, _1388234, _1388236, _1388238] : [class_Complete__Lattice_Ocomplete__lattice(_1388228), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388230, tc_fun(_1388232, _1388228)), _1388234), _1388236), _1388238) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388230, _1388228), _1388234), hAPP(hAPP(c_COMBC(_1388230, _1388232, _1388228), _1388236), _1388238)))], (4228 ^ _776545) ^ [_840624, _840626] : [_840626 = _840624, -(c_List_Orev(_840626) = c_List_Orev(_840624))], (47605 ^ _776545) ^ [_1733860, _1733862, _1733864] : [-(hAPP(c_List_Oset(_1733860), c_List_Oinsert(_1733860, _1733862, _1733864)) = hAPP(hAPP(c_Set_Oinsert(_1733860), _1733862), hAPP(c_List_Oset(_1733860), _1733864)))], (41408 ^ _776545) ^ [_1589669, _1589671, _1589673, _1589675] : [-(hAPP(_1589669, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589671, _1589671), _1589673), _1589669), _1589675)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589671, _1589671), _1589673), _1589669), hAPP(_1589669, _1589675)))], (39259 ^ _776545) ^ [_1534682, _1534684, _1534686, _1534688] : [-(_1534682 = c_Orderings_Obot__class_Obot(tc_fun(_1534684, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1534684, _1534686), _1534686, c_Product__Type_Osnd(_1534684, _1534686)), hAPP(hAPP(c_Product__Type_OSigma(_1534684, _1534686), _1534682), hAPP(c_COMBK(tc_fun(_1534686, tc_HOL_Obool), _1534684), _1534688))) = _1534688)], (52105 ^ _776545) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (15690 ^ _776545) ^ [_1061093] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061093)], (22881 ^ _776545) ^ [_1191087, _1191089, _1191091] : [class_Rings_Oring__1(_1191087), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191087), hAPP(c_Groups_Ouminus__class_Ouminus(_1191087), _1191089)), _1191091) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191087), hAPP(hAPP(c_Power_Opower__class_Opower(_1191087), hAPP(c_Groups_Ouminus__class_Ouminus(_1191087), c_Groups_Oone__class_Oone(_1191087))), _1191091)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191087), _1191089), _1191091)))], (19199 ^ _776545) ^ [_1122672, _1122674, _1122676, _1122678, _1122680] : [class_Groups_Ocomm__monoid__add(_1122672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122674), _1122676)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122674), _1122678)), 19213 ^ _776545 : [(19216 ^ _776545) ^ [] : [hAPP(_1122680, 19212 ^ [_1122672, _1122674, _1122676, _1122678, _1122680]) = c_Groups_Ozero__class_Ozero(_1122672)], (19214 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122674), 19212 ^ [_1122672, _1122674, _1122676, _1122678, _1122680]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122674, tc_HOL_Obool)), _1122676), _1122678))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122674, _1122672), _1122680), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122674, tc_HOL_Obool)), _1122676), _1122678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122672), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122674, _1122672), _1122680), _1122676)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1122674, _1122672), _1122680), _1122678)))], (41455 ^ _776545) ^ [_1590883, _1590885, _1590887] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590883, _1590883)), hAPP(hAPP(c_Product__Type_OPair(_1590883, _1590883), _1590885), _1590885)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590883, _1590883), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590887))))], (10202 ^ _776545) ^ [_951692, _951694, _951696] : [class_Orderings_Olinorder(_951692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951692), _951694), _951696)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951692, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951692, _951694), _951696)), hAPP(hAPP(c_Set_Oinsert(_951692), _951696), c_Orderings_Obot__class_Obot(tc_fun(_951692, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_951692, _951694, _951696))], (15011 ^ _776545) ^ [_1047435, _1047437, _1047439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047435), _1047437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047435), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047437), _1047439))))], (8927 ^ _776545) ^ [_930480, _930482, _930484] : [class_Orderings_Olinorder(_930480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930480), _930482), _930484)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_930480, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_930480), _930482)), c_SetInterval_Oord__class_OatLeastAtMost(_930480, _930482, _930484)) = hAPP(c_SetInterval_Oord__class_OatMost(_930480), _930484))], (36553 ^ _776545) ^ [_1468739, _1468741, _1468743, _1468745] : [-(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), _1468739), _1468741)), 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), _1468743), _1468745)), 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), _1468739), _1468743)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468741), _1468745))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45970 ^ _776545) ^ [_1698771, _1698773, _1698775, _1698777, _1698779] : [class_Orderings_Olinorder(_1698771), -(c_List_Olinorder__class_Osort__key(_1698773, _1698771, _1698775, hAPP(hAPP(c_List_Olist_OCons(_1698773), _1698777), _1698779)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1698773, _1698771, _1698775), _1698777), c_List_Olinorder__class_Osort__key(_1698773, _1698771, _1698775, _1698779)))], (48518 ^ _776545) ^ [_1754183, _1754185, _1754187, _1754189, _1754191] : [hBOOL(hAPP(hAPP(_1754183, _1754185), _1754187)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754189, _1754191, _1754183), _1754187), _1754185)))], (26054 ^ _776545) ^ [_1247498, _1247500] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247498), _1247500)), _1247500) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247498), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247498, _1247500)))], (14999 ^ _776545) ^ [_1047227, _1047229, _1047231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047227), _1047229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047229), _1047231))))], (41727 ^ _776545) ^ [_1598184, _1598186] : [-(c_List_Olenlex(_1598184, _1598186) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1598184)), tc_List_Olist(_1598184)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1598184), c_Wellfounded_Oless__than, c_List_Olex(_1598184, _1598186))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1598184), tc_List_Olist(_1598184), tc_prod(tc_Nat_Onat, tc_List_Olist(_1598184))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1598184), tc_prod(tc_Nat_Onat, tc_List_Olist(_1598184))), tc_List_Olist(_1598184)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1598184))), c_Nat_Osize__class_Osize(tc_List_Olist(_1598184)))), c_COMBI(tc_List_Olist(_1598184)))))], (7650 ^ _776545) ^ [_903642, _903644, _903646, _903648] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903642, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903642, tc_HOL_Obool)), _903644), _903646)), _903648) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903642, tc_HOL_Obool)), _903644), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903642, tc_HOL_Obool)), _903646), _903648)))], (11528 ^ _776545) ^ [_978062, _978064] : [class_Finite__Set_Ofinite(_978062), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978062), _978064)))], (34715 ^ _776545) ^ [_1423527, _1423529, _1423531, _1423533] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423527, _1423529, _1423531), hAPP(c_Nat_OSuc, _1423533)) = hAPP(hAPP(_1423531, _1423533), hAPP(c_Nat_Onat_Onat__rec(_1423527, _1423529, _1423531), _1423533)))], (42125 ^ _776545) ^ [_1611273, _1611275, _1611277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611273, tc_HOL_Obool)), _1611275), _1611277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1611273), tc_HOL_Obool)), c_List_Olists(_1611273, _1611275)), c_List_Olists(_1611273, _1611277))))], (40416 ^ _776545) ^ [_1564723, _1564725, _1564727] : [-(hBOOL(hAPP(hAPP(c_member(_1564723), _1564725), c_Wellfounded_Oacc(_1564723, _1564727)))), 40420 ^ _776545 : [(40423 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564723), 40419 ^ [_1564723, _1564725, _1564727]), c_Wellfounded_Oacc(_1564723, _1564727)))], (40421 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564723, _1564723)), hAPP(hAPP(c_Product__Type_OPair(_1564723, _1564723), 40419 ^ [_1564723, _1564725, _1564727]), _1564725)), _1564727)))]]], (5954 ^ _776545) ^ [_871297, _871299, _871301, _871303, _871305, _871307, _871309] : [c_Typedef_Otype__definition(_871297, _871299, _871301, _871303, _871305), 5960 ^ _776545 : [(5963 ^ _776545) ^ [] : [hBOOL(hAPP(_871307, hAPP(_871303, 5959 ^ [_871297, _871299, _871301, _871303, _871305, _871307, _871309])))], (5961 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_871299), 5959 ^ [_871297, _871299, _871301, _871303, _871305, _871307, _871309]), _871305)))]], -(hBOOL(hAPP(_871307, _871309)))], (40286 ^ _776545) ^ [_1561863, _1561865, _1561867, _1561869, _1561871, _1561873, _1561875] : [c_Finite__Set_Ofolding__idem(_1561863, _1561865, _1561867, _1561869), -(hAPP(c_Fun_Ocomp(_1561865, _1561865, _1561871, hAPP(_1561867, _1561873)), hAPP(c_Fun_Ocomp(_1561865, _1561865, _1561871, hAPP(_1561867, _1561873)), _1561875)) = hAPP(c_Fun_Ocomp(_1561865, _1561865, _1561871, hAPP(_1561867, _1561873)), _1561875))], (22515 ^ _776545) ^ [_1184567, _1184569, _1184571, _1184573] : [class_Fields_Ofield__inverse__zero(_1184567), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184567), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184567), _1184569), _1184571)), _1184573) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184567), hAPP(hAPP(c_Power_Opower__class_Opower(_1184567), _1184569), _1184573)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184567), _1184571), _1184573)))], (17029 ^ _776545) ^ [_1083083, _1083085, _1083087, _1083089] : [class_Rings_Oordered__comm__semiring(_1083083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083083), _1083085), _1083087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083083), c_Groups_Ozero__class_Ozero(_1083083)), _1083089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083083), _1083089), _1083085)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083083), _1083089), _1083087))))], (27034 ^ _776545) ^ [_1263453] : [-(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)), _1263453)))], (24986 ^ _776545) ^ [_1229023, _1229025, _1229027, _1229029] : [class_Divides_Osemiring__div(_1229023), -(c_Divides_Odiv__class_Omod(_1229023, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229023), _1229025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229023), _1229027), _1229029)), _1229027) = c_Divides_Odiv__class_Omod(_1229023, _1229025, _1229027))], (12505 ^ _776545) ^ [_996422, _996424] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_996422, tc_HOL_Obool)), _996424)), 12511 ^ _776545 : [(12514 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996422), 12510 ^ [_996422, _996424]))], (12512 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_996422, tc_HOL_Obool)), 12510 ^ [_996422, _996424]), _996424)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_996422), c_Complete__Lattice_OSup__class_OSup(tc_fun(_996422, tc_HOL_Obool), _996424))))], (41349 ^ _776545) ^ [_1588128, _1588130, _1588132] : [41351 ^ _776545 : [(41352 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588128), 41350 ^ [_1588128, _1588130, _1588132]), _1588130)))], (41357 ^ _776545) ^ [] : [41350 ^ [_1588128, _1588130, _1588132] = 41353 ^ [_1588128, _1588130, _1588132]], (41361 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588128, _1588128)), hAPP(hAPP(c_Product__Type_OPair(_1588128, _1588128), 41353 ^ [_1588128, _1588130, _1588132]), 41350 ^ [_1588128, _1588130, _1588132])), _1588132))], (41359 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588128, _1588128)), hAPP(hAPP(c_Product__Type_OPair(_1588128, _1588128), 41350 ^ [_1588128, _1588130, _1588132]), 41353 ^ [_1588128, _1588130, _1588132])), _1588132))], (41355 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588128), 41353 ^ [_1588128, _1588130, _1588132]), _1588130)))]], -(c_Relation_Ototal__on(_1588128, _1588130, _1588132))], (14528 ^ _776545) ^ [_1038538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038538), _1038538))], (2842 ^ _776545) ^ [_818669, _818671, _818673, _818675, _818677, _818679, _818681, _818683] : [-(c_Random_Oiterate(_818683, _818679, _818675, _818671) = c_Random_Oiterate(_818681, _818677, _818673, _818669)), _818683 = _818681, _818679 = _818677, _818675 = _818673, _818671 = _818669], (36079 ^ _776545) ^ [_1455856] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1455856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1455856)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51495 ^ _776545) ^ [_1818670, _1818672] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818670), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818672))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818670), _1818672)))], (38618 ^ _776545) ^ [_1518378, _1518380, _1518382, _1518384, _1518386, _1518388] : [hAPP(_1518378, _1518380) = _1518382, hBOOL(hAPP(hAPP(c_member(_1518384), _1518382), _1518386)), -(hBOOL(hAPP(hAPP(c_member(_1518388), _1518380), hAPP(c_Set_Ovimage(_1518388, _1518384, _1518378), _1518386))))], (42465 ^ _776545) ^ [_1619746, _1619748] : [-(hAPP(c_List_Oset(_1619746), _1619748) = hAPP(c_Set_OCollect(_1619746), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1619746), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1619746, 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)), _1619746), 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)), _1619746), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1619746, tc_fun(tc_Nat_Onat, _1619746), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619746, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1619746), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1619746), c_COMBB(_1619746, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1619746), _1619748))))), 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(_1619746)), _1619748))))))], (34197 ^ _776545) ^ [_1412260, _1412262] : [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(_1412260))), 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)), _1412262)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412260)), hAPP(c_Nat_OSuc, _1412262))))], (22187 ^ _776545) ^ [_1178943] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1178943) = _1178943)], (52253 ^ _776545) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (8345 ^ _776545) ^ [_919569, _919571] : [class_Lattices_Osemilattice__sup(_919569), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919569), _919571), _919571) = _919571)], (29089 ^ _776545) ^ [_1297963, _1297965] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297963)), c_Int_OBit1(_1297965)))], (12287 ^ _776545) ^ [_992161, _992163, _992165] : [class_Lattices_Olattice(_992161), hBOOL(hAPP(c_Finite__Set_Ofinite(_992161), _992163)), -(hBOOL(hAPP(hAPP(c_member(_992161), _992165), _992163))), -(_992163 = c_Orderings_Obot__class_Obot(tc_fun(_992161, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_992161, hAPP(hAPP(c_Set_Oinsert(_992161), _992165), _992163)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_992161), _992165), c_Big__Operators_Olattice__class_OInf__fin(_992161, _992163)))], (9348 ^ _776545) ^ [_937363, _937365, _937367, _937369, _937371] : [class_Groups_Oordered__ab__group__add(_937363), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937363), _937365), _937367) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_937363), _937369), _937371), 9355 ^ _776545 : [(9362 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937363), _937369), _937371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937363), _937365), _937367)))], (9356 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937363), _937365), _937367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937363), _937369), _937371)))]]], (26106 ^ _776545) ^ [_1248341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248341), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1248341) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16600 ^ _776545) ^ [_1075149] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075149), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (18601 ^ _776545) ^ [_1111325, _1111327, _1111329] : [-(hBOOL(hAPP(_1111325, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1111327), _1111329)))), 18604 ^ _776545 : [(18607 ^ _776545) ^ [] : [hBOOL(hAPP(_1111325, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18605 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111327), _1111329)))]], 18609 ^ _776545 : [(18612 ^ _776545) ^ [] : [hBOOL(hAPP(_1111325, 18608 ^ [_1111325, _1111327, _1111329]))], (18610 ^ _776545) ^ [] : [-(_1111327 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111329), 18608 ^ [_1111325, _1111327, _1111329]))]]], (46526 ^ _776545) ^ [_1712138, _1712140] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1712138, _1712140)))], (50479 ^ _776545) ^ [_1797085, _1797087, _1797089] : [c_Fun_Obij__betw(_1797085, _1797085, c_Fun_Oid(_1797085), _1797087, _1797089), -(_1797087 = _1797089)], (49058 ^ _776545) ^ [_1766125, _1766127, _1766129] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766125) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1766125, _1766127, _1766129)], (41971 ^ _776545) ^ [_1606404, _1606406, _1606408, _1606410] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1606404), tc_List_Olist(_1606404), c_List_Olistrel(_1606404, _1606406)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1606404)), hAPP(hAPP(c_List_Olist_OCons(_1606404), _1606408), _1606410)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1606404), tc_HOL_Obool)))) = c_List_Oset__Cons(_1606404, hAPP(c_Relation_OImage(_1606404, _1606404, _1606406), hAPP(hAPP(c_Set_Oinsert(_1606404), _1606408), c_Orderings_Obot__class_Obot(tc_fun(_1606404, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1606404), tc_List_Olist(_1606404), c_List_Olistrel(_1606404, _1606406)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1606404)), _1606410), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1606404), tc_HOL_Obool))))))], (28289 ^ _776545) ^ [_1284474] : [c_Int_OMin = c_Int_OBit1(_1284474), -(c_Int_OMin = _1284474)], (52127 ^ _776545) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (7306 ^ _776545) ^ [_896099, _896101, _896103, _896105] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896099, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_896099), _896101), _896103)), _896105))), hBOOL(hAPP(hAPP(c_member(_896099), _896101), _896105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896099, tc_HOL_Obool)), _896103), _896105))], (10665 ^ _776545) ^ [_960025, _960027] : [class_Lattices_Oboolean__algebra(_960025), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_960025), _960027), hAPP(c_Groups_Ouminus__class_Ouminus(_960025), _960027)) = c_Orderings_Otop__class_Otop(_960025))], (39934 ^ _776545) ^ [_1553891, _1553893, _1553895, _1553897, _1553899, _1553901, _1553903] : [-(hAPP(c_Product__Type_Oapfst(_1553891, _1553893, _1553895, _1553897), hAPP(c_Product__Type_Oapfst(_1553899, _1553891, _1553895, _1553901), _1553903)) = hAPP(c_Product__Type_Oapfst(_1553899, _1553893, _1553895, hAPP(c_Fun_Ocomp(_1553891, _1553893, _1553899, _1553897), _1553901)), _1553903))], (43639 ^ _776545) ^ [_1646951, _1646953, _1646955] : [hAPP(hAPP(c_List_Oappend(_1646951), _1646953), _1646955) = _1646955, -(_1646953 = c_List_Olist_ONil(_1646951))], (27467 ^ _776545) ^ [_1270603, _1270605, _1270607] : [class_Groups_Oordered__ab__group__add__abs(_1270603), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270603), hAPP(c_Groups_Oabs__class_Oabs(_1270603), _1270605)), hAPP(c_Groups_Oabs__class_Oabs(_1270603), _1270607))), hAPP(c_Groups_Oabs__class_Oabs(_1270603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270603), _1270605), _1270607)))))], (41747 ^ _776545) ^ [_1599208, _1599210, _1599212] : [-(hAPP(c_List_Olexn(_1599208, _1599210), hAPP(c_Nat_OSuc, _1599212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1599208), tc_List_Olist(_1599208)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1599208, tc_List_Olist(_1599208)), tc_prod(_1599208, tc_List_Olist(_1599208))), tc_prod(tc_List_Olist(_1599208), tc_List_Olist(_1599208)), c_Product__Type_Omap__pair(tc_prod(_1599208, tc_List_Olist(_1599208)), tc_List_Olist(_1599208), tc_prod(_1599208, tc_List_Olist(_1599208)), tc_List_Olist(_1599208), hAPP(c_Product__Type_Oprod_Oprod__case(_1599208, tc_List_Olist(_1599208), tc_List_Olist(_1599208)), c_List_Olist_OCons(_1599208)), hAPP(c_Product__Type_Oprod_Oprod__case(_1599208, tc_List_Olist(_1599208), tc_List_Olist(_1599208)), c_List_Olist_OCons(_1599208)))), c_Wellfounded_Olex__prod(_1599208, tc_List_Olist(_1599208), _1599210, hAPP(c_List_Olexn(_1599208, _1599210), _1599212)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1599208), tc_List_Olist(_1599208))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1599208), tc_List_Olist(_1599208), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1599208), tc_fun(tc_List_Olist(_1599208), tc_HOL_Obool), tc_fun(tc_List_Olist(_1599208), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1599208), tc_HOL_Obool), tc_fun(tc_List_Olist(_1599208), tc_HOL_Obool)), tc_List_Olist(_1599208)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1599208))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1599208)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1599208), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1599208)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1599208)))), hAPP(c_Nat_OSuc, _1599212))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1599208), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1599208)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1599208)))), hAPP(c_Nat_OSuc, _1599212)))))))], (38511 ^ _776545) ^ [_1514896, _1514898, _1514900] : [hAPP(c_Relation_ORange(_1514896, _1514898), _1514900) = c_Orderings_Obot__class_Obot(tc_fun(_1514898, tc_HOL_Obool)), -(_1514900 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514896, _1514898), tc_HOL_Obool)))], (45742 ^ _776545) ^ [_1694338, _1694340, _1694342, _1694344, _1694346] : [c_Fun_Oinj__on(_1694338, _1694340, _1694342, hAPP(hAPP(c_Set_Oinsert(_1694338), _1694344), hAPP(c_List_Oset(_1694338), _1694346))), -(hAPP(hAPP(c_List_Omap(_1694338, _1694340), _1694342), hAPP(c_List_OremoveAll(_1694338, _1694344), _1694346)) = hAPP(c_List_OremoveAll(_1694340, hAPP(_1694342, _1694344)), hAPP(hAPP(c_List_Omap(_1694338, _1694340), _1694342), _1694346)))], (46315 ^ _776545) ^ [_1708085, _1708087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708085), _1708087)), -(c_List_Oupt(_1708085, hAPP(c_Nat_OSuc, _1708087)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1708085, _1708087)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1708087), c_List_Olist_ONil(tc_Nat_Onat))))], (19701 ^ _776545) ^ [_1132320, _1132322] : [class_Rings_Odivision__ring(_1132320), -(_1132322 = c_Groups_Ozero__class_Ozero(_1132320)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132320), _1132322), _1132322) = c_Groups_Oone__class_Oone(_1132320))], (27013 ^ _776545) ^ [_1263141] : [27015 ^ _776545 : [(27018 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27014 ^ [_1263141]))], (27016 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27014 ^ [_1263141]), _1263141)))]], -(c_Nat__Transfer_Onat__set(_1263141))], (15638 ^ _776545) ^ [_1060208] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1060208))))], (27022 ^ _776545) ^ [_1263301] : [c_Nat__Transfer_Ois__nat(_1263301), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263301)))], (16937 ^ _776545) ^ [_1081323, _1081325, _1081327] : [class_Rings_Oordered__ring(_1081323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081323), c_Groups_Ozero__class_Ozero(_1081323)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081323), _1081325), _1081327)))), 16942 ^ _776545 : [(16949 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081323), _1081325), c_Groups_Ozero__class_Ozero(_1081323))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081323), _1081327), c_Groups_Ozero__class_Ozero(_1081323)))], (16943 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081323), c_Groups_Ozero__class_Ozero(_1081323)), _1081325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081323), c_Groups_Ozero__class_Ozero(_1081323)), _1081327))]]], (40526 ^ _776545) ^ [_1567530, _1567532, _1567534, _1567536, _1567538, _1567540, _1567542] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567530, _1567532, _1567534, _1567536), _1567538), _1567540), _1567542) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1567532, _1567534, _1567536), _1567540), hAPP(_1567538, _1567542)))], (43504 ^ _776545) ^ [_1644111, _1644113, _1644115, _1644117] : [_1644115 = _1644117, -(hAPP(hAPP(c_List_Oappend(_1644111), _1644113), _1644115) = hAPP(hAPP(c_List_Oappend(_1644111), _1644113), _1644117))], (46170 ^ _776545) ^ [_1704003, _1704005, _1704007] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1704003, tc_HOL_Obool)), hAPP(c_List_Oset(_1704003), _1704005)), hAPP(hAPP(c_Set_Oinsert(_1704003), _1704007), c_Orderings_Obot__class_Obot(tc_fun(_1704003, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1704003), hAPP(c_List_Ofilter(_1704003, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1704003), c_fNot), hAPP(hAPP(c_COMBC(_1704003, _1704003, tc_HOL_Obool), c_fequal), _1704007))), _1704005)))], (28407 ^ _776545) ^ [_1286467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1286467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1286467))))], (4346 ^ _776545) ^ [_842355, _842357, _842359, _842361, _842363, _842365, _842367, _842369, _842371, _842373] : [-(c_Predicate_Opred__comp(_842373, _842369, _842365, _842361, _842357) = c_Predicate_Opred__comp(_842371, _842367, _842363, _842359, _842355)), _842373 = _842371, _842369 = _842367, _842365 = _842363, _842361 = _842359, _842357 = _842355], (41668 ^ _776545) ^ [_1596973, _1596975, _1596977] : [-(c_Product__Type_Ointernal__split(_1596973, _1596975, _1596977) = c_Product__Type_Oprod_Oprod__case(_1596973, _1596975, _1596977))], (8185 ^ _776545) ^ [_916301, _916303, _916305, _916307] : [class_Orderings_Oorder(_916301), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916301, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_916301, _916303, _916305)), c_SetInterval_Oord__class_OgreaterThanLessThan(_916301, _916305, _916307)) = c_Orderings_Obot__class_Obot(tc_fun(_916301, tc_HOL_Obool)))], (11970 ^ _776545) ^ [_986696, _986698, _986700, _986702, _986704] : [11972 ^ _776545 : [(11975 ^ _776545) ^ [] : [hBOOL(hAPP(_986704, 11971 ^ [_986696, _986698, _986700, _986702, _986704]))], (11973 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986696), 11971 ^ [_986696, _986698, _986700, _986702, _986704]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986698, tc_fun(_986696, tc_HOL_Obool)), _986700), _986702))))]], 11976 ^ _776545 : [(11977 ^ _776545) ^ [_986918] : [hBOOL(hAPP(hAPP(c_member(_986698), _986918), _986700)), 11980 ^ _776545 : [(11981 ^ _776545) ^ [_987015] : [hBOOL(hAPP(hAPP(c_member(_986696), _987015), hAPP(_986702, _986918))), -(hBOOL(hAPP(_986704, _987015)))]]]]], (32512 ^ _776545) ^ [_1363757, _1363759, _1363761, _1363763, _1363765] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363757, tc_HOL_Obool)), _1363759), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363761, tc_fun(_1363757, tc_HOL_Obool)), _1363763), _1363765)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363761, tc_fun(_1363757, tc_HOL_Obool)), _1363763), hAPP(hAPP(c_COMBB(tc_fun(_1363757, tc_HOL_Obool), tc_fun(_1363757, tc_HOL_Obool), _1363761), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363757, tc_HOL_Obool)), _1363759)), _1363765)))], (648 ^ _776545) ^ [_786299, _786301, _786303, _786305, _786307, _786309, _786311, _786313] : [-(c_Nat__Transfer_Otransfer__morphism(_786311, _786307, _786303, _786299)), c_Nat__Transfer_Otransfer__morphism(_786313, _786309, _786305, _786301), _786313 = _786311, _786309 = _786307, _786305 = _786303, _786301 = _786299], (18111 ^ _776545) ^ [_1102203, _1102205] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102203), _1102205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102203), _1102205)))], (11403 ^ _776545) ^ [_975506, _975508, _975510, _975512, _975514] : [c_Finite__Set_Ofolding__one(_975506, _975508, _975510), hBOOL(hAPP(c_Finite__Set_Ofinite(_975506), _975512)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975506), _975514)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975506, tc_HOL_Obool)), 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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)))), _1409335)), _1409337))))], (18942 ^ _776545) ^ [_1117726, _1117728, _1117730] : [class_Rings_Olinordered__ring(_1117726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117726), c_Groups_Ozero__class_Ozero(_1117726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117726), _1117728), _1117728)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117726), _1117730), _1117730)))))], (24551 ^ _776545) ^ [_1220628, _1220630, _1220632] : [-(hBOOL(hAPP(_1220628, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220630), _1220632))))), 24554 ^ _776545 : [(24557 ^ _776545) ^ [] : [hBOOL(hAPP(_1220628, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220630)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220632))))], (24555 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220632), _1220630)))]], 24558 ^ _776545 : [(24561 ^ _776545) ^ [] : [hBOOL(hAPP(_1220628, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24559 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220630), _1220632)))]]], (20151 ^ _776545) ^ [_1140373, _1140375, _1140377] : [class_Fields_Olinordered__field(_1140373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140373), _1140375), c_Groups_Ozero__class_Ozero(_1140373))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140373), c_Groups_Ozero__class_Ozero(_1140373)), _1140377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140373), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140373), _1140375), _1140377)), c_Groups_Ozero__class_Ozero(_1140373))))], (7440 ^ _776545) ^ [_899042, _899044, _899046, _899048] : [7441 ^ _776545 : [(7444 ^ _776545) ^ [] : [hBOOL(hAPP(_899046, _899044))], (7442 ^ _776545) ^ [] : [hBOOL(hAPP(_899042, _899044))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899048, tc_HOL_Obool)), _899046), _899042), _899044)))], (16636 ^ _776545) ^ [_1075754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1075754)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1075754), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1075754)], (4744 ^ _776545) ^ [_848760, _848762] : [_848762 = _848760, -(c_Random__Sequence_Osingle(_848762) = c_Random__Sequence_Osingle(_848760))], (37384 ^ _776545) ^ [_1487997, _1487999, _1488001, _1488003, _1488005] : [c_Fun_Oinj__on(_1487997, _1487999, _1488001, c_Orderings_Otop__class_Otop(tc_fun(_1487997, tc_HOL_Obool))), hAPP(_1488001, _1488003) = hAPP(_1488001, _1488005), -(_1488003 = _1488005)], (4568 ^ _776545) ^ [_845922, _845924] : [_845924 = _845922, 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564333, _1564339), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1564333, _1564339), _1564335), _1564341)), hAPP(hAPP(c_Product__Type_OSigma(_1564333, _1564339), _1564337), _1564343))))], (42321 ^ _776545) ^ [_1616429, _1616431, _1616433, _1616435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1616429), _1616431)), -(hAPP(hAPP(c_List_Onth(_1616433), hAPP(hAPP(c_List_Otake(_1616433), _1616431), _1616435)), _1616429) = hAPP(hAPP(c_List_Onth(_1616433), _1616435), _1616429))], (41889 ^ _776545) ^ [_1603789, _1603791, _1603793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1603789, _1603789), tc_HOL_Obool)), _1603791), _1603793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1603789), tc_List_Olist(_1603789)), tc_HOL_Obool)), c_List_Olistrel1(_1603789, _1603791)), c_List_Olistrel1(_1603789, _1603793))))], (52173 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (28607 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29033 ^ _776545) ^ [_1297020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1297020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1297020)))], (12776 ^ _776545) ^ [_1001953, _1001955] : [class_Lattices_Olattice(_1001953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001953), _1001955)), -(c_Big__Operators_Olattice__class_OSup__fin(_1001953, _1001955) = hAPP(c_Finite__Set_Ofold1(_1001953, c_Lattices_Osemilattice__sup__class_Osup(_1001953)), _1001955))], (44262 ^ _776545) ^ [_1661641, _1661643, _1661645, _1661647, _1661649] : [class_Orderings_Olinorder(_1661641), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661643, _1661641, _1661645), _1661647), _1661649) = c_List_Olist_ONil(_1661643)], (28025 ^ _776545) ^ [_1280154, 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(24944 ^ _776545) ^ [_1228231, _1228233] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228231), _1228233)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228231)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228233)))], (25834 ^ _776545) ^ [_1243939, _1243941] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243939)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243939)), _1243941)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1243939))), _1243941))], (7494 ^ _776545) ^ [_899988, _899990, _899992, _899994] : [hBOOL(hAPP(hAPP(c_member(_899988), _899990), _899992)), hBOOL(hAPP(hAPP(c_member(_899988), _899990), _899994)), -(hBOOL(hAPP(hAPP(c_member(_899988), _899990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899988, tc_HOL_Obool)), _899992), _899994))))], (42131 ^ _776545) ^ [_1611408, _1611410, _1611412] : [c_Equiv__Relations_Oequiv(_1611408, _1611410, _1611412), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1611408), c_List_Olists(_1611408, _1611410), c_List_Olistrel(_1611408, _1611412)))], (50540 ^ _776545) ^ [_1798084, _1798086, _1798088, _1798090, _1798092] : [c_Fun_Obij__betw(_1798084, _1798086, _1798088, _1798090, _1798092), -(hAPP(c_Finite__Set_Ocard(_1798084), _1798090) = hAPP(c_Finite__Set_Ocard(_1798086), _1798092))], (33088 ^ _776545) ^ [_1381390, _1381392] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381390, tc_HOL_Obool)), _1381392)), -(hBOOL(hAPP(hAPP(c_member(_1381390), _1381392), c_Orderings_Obot__class_Obot(tc_fun(_1381390, tc_HOL_Obool)))))], (16556 ^ _776545) ^ [_1074514, _1074516] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074514), _1074516) = 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_918158)))], (26619 ^ _776545) ^ [_1256965, _1256967] : [class_Int_Onumber__ring(_1256965), -(hAPP(c_Int_Onumber__class_Onumber__of(_1256965), c_Int_Osucc(_1256967)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256965), c_Groups_Oone__class_Oone(_1256965)), hAPP(c_Int_Onumber__class_Onumber__of(_1256965), _1256967)))], (24274 ^ _776545) ^ [_1215551, _1215553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215551), _1215553)), -(_1215553 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215551), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 24277 ^ [_1215551, _1215553]))))], (34067 ^ _776545) ^ [_1409016, _1409018, _1409020] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1409016, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1409018)), _1409020) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409016, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1409016, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1409018)), _1409020)), hAPP(_1409020, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35850 ^ _776545) ^ [_1446442, _1446444, _1446446, _1446448, _1446450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1446442, _1446444)), hAPP(_1446442, _1446446))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446448, _1446448)), hAPP(hAPP(c_Product__Type_OPair(_1446448, _1446448), _1446444), _1446446)), c_Wellfounded_Omlex__prod(_1446448, _1446442, _1446450))))], (50409 ^ _776545) ^ [_1795698, _1795700, _1795702, _1795704] : [c_Fun_Obij__betw(_1795698, _1795700, _1795702, c_Orderings_Otop__class_Otop(tc_fun(_1795698, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795700, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1795698, _1795700, _1795702), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1795698, tc_HOL_Obool)), _1795704)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1795700, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795698, _1795700, _1795702), _1795704)))], (44936 ^ _776545) ^ [_1676227, _1676229] : [class_Groups_Oordered__ab__group__add__abs(_1676227), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676227), hAPP(c_Groups_Oabs__class_Oabs(_1676227), hAPP(c_List_Omonoid__add__class_Olistsum(_1676227), _1676229))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676227), hAPP(hAPP(c_List_Omap(_1676227, _1676227), c_Groups_Oabs__class_Oabs(_1676227)), _1676229)))))], (1834 ^ _776545) ^ [_802334, _802336] : [-(class_Orderings_Oord(_802334)), _802336 = _802334, class_Orderings_Oord(_802336)], (16566 ^ _776545) ^ [_1074612, _1074614] : [16567 ^ _776545 : [(16570 ^ _776545) ^ [] : [_1074614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16568 ^ _776545) ^ [] : [_1074612 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074612), _1074614) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37951 ^ _776545) ^ [_1501313, _1501315, _1501317, _1501319, _1501321, _1501323, _1501325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501313, _1501315), tc_HOL_Obool)), _1501317), _1501319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501315, _1501321), tc_HOL_Obool)), _1501323), _1501325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501313, _1501321), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501313, _1501315, _1501321), _1501317), _1501323)), hAPP(hAPP(c_Relation_Orel__comp(_1501313, _1501315, _1501321), _1501319), _1501325))))], (47434 ^ _776545) ^ [_1730270, _1730272, _1730274, _1730276, _1730278] : [c_List_OdropWhile(_1730270, _1730272, _1730274) = hAPP(hAPP(c_List_Olist_OCons(_1730270), _1730276), _1730278), 47437 ^ _776545 : [(47440 ^ _776545) ^ [] : [hBOOL(hAPP(_1730272, _1730276))], (47438 ^ _776545) ^ [] : [-(_1730274 = hAPP(hAPP(c_List_Oappend(_1730270), c_List_OtakeWhile(_1730270, _1730272, _1730274)), hAPP(hAPP(c_List_Olist_OCons(_1730270), _1730276), _1730278)))]]], (28565 ^ _776545) ^ [_1289078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1289078), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1289078)), c_Int_OPls)))], (27687 ^ _776545) ^ [_1274599, _1274601] : [class_Groups_Oordered__ab__group__add__abs(_1274599), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274599), hAPP(c_Groups_Ouminus__class_Ouminus(_1274599), hAPP(c_Groups_Oabs__class_Oabs(_1274599), _1274601))), c_Groups_Ozero__class_Ozero(_1274599))))], (32288 ^ _776545) ^ [_1357093, _1357095, _1357097, _1357099, _1357101, _1357103, _1357105, _1357107] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357093, tc_fun(_1357095, tc_fun(_1357097, tc_HOL_Obool))), _1357099), _1357101), _1357103), _1357105)), -(hBOOL(hAPP(hAPP(hAPP(_1357101, _1357107), _1357103), _1357105))), hBOOL(hAPP(hAPP(c_member(_1357093), _1357107), _1357099))], (42665 ^ _776545) ^ [_1626044, _1626046, _1626048, _1626050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626044)), _1626046)), _1626048)), -(hAPP(hAPP(c_List_Olist__update(_1626044, _1626046), _1626048), _1626050) = _1626046)], (23401 ^ _776545) ^ [_1200602, _1200604, _1200606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200602)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1200604), _1200606)), 23408 ^ _776545 : [(23409 ^ _776545) ^ [_1200798] : [23411 ^ _776545 : [(23417 ^ _776545) ^ [] : [-(_1200798 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23413 ^ [_1200602, _1200604, _1200606, _1200798]), 23410 ^ [_1200602, _1200604, _1200606, _1200798]))], (23415 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23413 ^ [_1200602, _1200604, _1200606, _1200798]), _1200606)))], (23412 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23410 ^ [_1200602, _1200604, _1200606, _1200798]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1200602))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200604), _1200798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1200798), _1200602))))]]], (49422 ^ _776545) ^ [_1775797, _1775799] : [c_Predicate_Otransp(_1775797, _1775799), -(c_Relation_Otrans(_1775797, hAPP(c_Set_OCollect(tc_prod(_1775797, _1775797)), hAPP(c_Product__Type_Oprod_Oprod__case(_1775797, _1775797, tc_HOL_Obool), _1775799))))], (11950 ^ _776545) ^ [_986302, _986304, _986306, _986308, _986310, _986312] : [-(c_Fun_Ofun__upd(_986302, _986304, c_Fun_Ofun__upd(_986302, _986304, _986306, _986308, _986310), _986308, _986312) = c_Fun_Ofun__upd(_986302, _986304, _986306, _986308, _986312))], (35070 ^ _776545) ^ [_1431079, _1431081, _1431083, _1431085, _1431087, _1431089] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1431079, _1431081, _1431083, _1431085, c_Nitpick_Opair__box_OPairBox(_1431079, _1431081, _1431087, _1431089)) = hAPP(hAPP(_1431085, _1431087), _1431089))], (14933 ^ _776545) ^ [_1045921, _1045923, _1045925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045923), _1045925))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045921), _1045925)), _1045923)))], (52391 ^ _776545) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (8074 ^ _776545) ^ [_913771, _913773] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913771, tc_HOL_Obool)), _913773), c_Orderings_Otop__class_Otop(tc_fun(_913771, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_913771, tc_HOL_Obool)))], (19141 ^ _776545) ^ [_1121402, _1121404] : [class_Groups_Olinordered__ab__group__add(_1121402), 19144 ^ _776545 : [(19151 ^ _776545) ^ [] : [_1121404 = c_Groups_Ozero__class_Ozero(_1121402), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121402), _1121404), _1121404) = c_Groups_Ozero__class_Ozero(_1121402))], (19145 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121402), _1121404), _1121404) = c_Groups_Ozero__class_Ozero(_1121402), -(_1121404 = c_Groups_Ozero__class_Ozero(_1121402))]]], (37298 ^ _776545) ^ [_1486546, _1486548, _1486550, _1486552, _1486554, _1486556] : [c_Fun_Oinj__on(_1486546, _1486548, _1486550, _1486552), hAPP(_1486550, _1486554) = hAPP(_1486550, _1486556), hBOOL(hAPP(hAPP(c_member(_1486546), _1486554), _1486552)), hBOOL(hAPP(hAPP(c_member(_1486546), _1486556), _1486552)), -(_1486554 = _1486556)], (3648 ^ _776545) ^ [_831202, _831204, _831206, _831208] : [-(c_List_Olist__update(_831208, _831204) = c_List_Olist__update(_831206, _831202)), _831208 = _831206, _831204 = _831202], (26188 ^ _776545) ^ [_1249691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249691)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1249691)) = _1249691)], (39241 ^ _776545) ^ [_1534275, _1534277, _1534279, _1534281] : [_1534275 = c_Orderings_Obot__class_Obot(tc_fun(_1534277, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1534279, _1534277), _1534279, c_Product__Type_Ofst(_1534279, _1534277)), hAPP(hAPP(c_Product__Type_OSigma(_1534279, _1534277), _1534281), hAPP(c_COMBK(tc_fun(_1534277, tc_HOL_Obool), _1534279), _1534275))) = c_Orderings_Obot__class_Obot(tc_fun(_1534279, tc_HOL_Obool)))], (38896 ^ _776545) ^ [_1524943, _1524945, _1524947] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524943, _1524945)), _1524947)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524943), hAPP(c_Relation_ODomain(_1524943, _1524945), _1524947))))], (49096 ^ _776545) ^ [_1766744, _1766746, _1766748] : [49098 ^ _776545 : [(49101 ^ _776545) ^ [] : [hBOOL(hAPP(_1766744, 49097 ^ [_1766744, _1766746, _1766748]))], (49099 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49097 ^ [_1766744, _1766746, _1766748]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1766746, _1766748))))]], -(c_List_Oall__interval__int(_1766744, _1766746, _1766748))], (52193 ^ _776545) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (18276 ^ _776545) ^ [_1105186, _1105188, _1105190, _1105192] : [class_Rings_Olinordered__semiring__strict(_1105186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105186), _1105188), _1105190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105186), _1105188), _1105192))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105186), c_Groups_Ozero__class_Ozero(_1105186)), _1105188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105186), _1105190), _1105192)))], (41917 ^ _776545) ^ [_1604712, _1604714, _1604716, _1604718] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604712), tc_List_Olist(_1604712))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604712), tc_List_Olist(_1604712)), _1604714), _1604716)), c_List_Olistrel1(_1604712, _1604718))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604712)), _1604714) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604712)), _1604716))], (14466 ^ _776545) ^ [_1037725, _1037727, _1037729] : [14467 ^ _776545 : [(14470 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1037729, _1037727), _1037725))], (14468 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037725), _1037727)))]], 14473 ^ _776545 : [(14476 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1037729, _1037727), _1037725))], (14474 ^ _776545) ^ [] : [-(_1037725 = _1037727)]], 14479 ^ _776545 : [(14482 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1037729, _1037727), _1037725))], (14480 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037727), _1037725)))]], -(hBOOL(hAPP(hAPP(_1037729, _1037727), _1037725)))], (15047 ^ _776545) ^ [_1048245, _1048247, _1048249, _1048251, _1048253] : [class_Groups_Ocomm__monoid__add(_1048245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048249), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048245), _1048251), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1048247, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048249), _1048253))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048245), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048245), _1048251), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1048247, _1048249))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1048245), _1048251), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048249), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1048249), _1048253)))))], (45860 ^ _776545) ^ [_1696493, _1696495, _1696497] : [-(hBOOL(hAPP(hAPP(c_member(_1696493), _1696495), hAPP(c_List_Oset(_1696493), _1696497)))), -(c_List_Oremdups(_1696493, hAPP(hAPP(c_List_Olist_OCons(_1696493), _1696495), _1696497)) = hAPP(hAPP(c_List_Olist_OCons(_1696493), _1696495), c_List_Oremdups(_1696493, _1696497)))], (14684 ^ _776545) ^ [_1041302, _1041304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041302), _1041304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041302), _1041304))), -(_1041302 = _1041304)], (33196 ^ _776545) ^ [_1384735, _1384737, _1384739] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1384735), hAPP(c_Set_OCollect(_1384735), hAPP(hAPP(c_COMBS(_1384735, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1384735), c_fdisj), _1384737)), _1384739))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384735), hAPP(c_Set_OCollect(_1384735), _1384737))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384735), hAPP(c_Set_OCollect(_1384735), _1384739)))], (33058 ^ _776545) ^ [_1380442, _1380444, _1380446, _1380448, _1380450, _1380452] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380442, tc_fun(_1380444, tc_HOL_Obool)), _1380446), hAPP(hAPP(c_COMBB(_1380448, tc_fun(_1380444, tc_HOL_Obool), _1380442), _1380450), _1380452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1380448, tc_fun(_1380444, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380442, _1380448, _1380452), _1380446)), _1380450))], (42510 ^ _776545) ^ [_1622335, _1622337, _1622339, _1622341, _1622343, _1622345] : [-(hAPP(hAPP(c_List_Ozip(_1622335, _1622337), hAPP(hAPP(c_List_Olist_OCons(_1622335), _1622339), _1622341)), hAPP(hAPP(c_List_Olist_OCons(_1622337), _1622343), _1622345)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1622335, _1622337)), hAPP(hAPP(c_Product__Type_OPair(_1622335, _1622337), _1622339), _1622343)), hAPP(hAPP(c_List_Ozip(_1622335, _1622337), _1622341), _1622345)))], (28583 ^ _776545) ^ [_1289363, _1289365] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289363), _1289365), hAPP(c_Int_Onumber__class_Onumber__of(_1289363), c_Int_OBit1(c_Int_OPls))) = _1289365), class_Fields_Ofield(_1289363), class_Int_Onumber__ring(_1289363)], (25401 ^ _776545) ^ [_1235991, _1235993, _1235995] : [hBOOL(hAPP(_1235991, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235993), _1235995))), 25404 ^ _776545 : [(25411 ^ _776545) ^ [] : [-(_1235995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25414 ^ _776545 : [(25415 ^ _776545) ^ [_1236243, _1236245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236243), _1235995)), _1235993 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235995), _1236245)), _1236243), -(hBOOL(hAPP(_1235991, _1236245)))]]], (25405 ^ _776545) ^ [] : [_1235995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1235991, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (35072 ^ _776545) ^ [_1431129, _1431131, _1431133, _1431135, _1431137, _1431139] : [-(c_Nitpick_Opair__box_Opair__box__case(_1431129, _1431131, _1431133, _1431135, c_Nitpick_Opair__box_OPairBox(_1431129, _1431131, _1431137, _1431139)) = hAPP(hAPP(_1431135, _1431137), _1431139))], (41481 ^ _776545) ^ [_1591693, _1591695] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591693, _1591693), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591695) = c_Fun_Oid(_1591693))], (49261 ^ _776545) ^ [_1771322, _1771324] : [c_Relation_Otrans(_1771322, hAPP(c_Relation_Oconverse(_1771322, _1771322), _1771324)), -(c_Relation_Otrans(_1771322, _1771324))], (32668 ^ _776545) ^ [_1369767, _1369769, _1369771, _1369773, _1369775] : [class_Groups_Ocomm__monoid__add(_1369767), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369767), _1369769), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369771), _1369773)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369775), _1369773))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1369767), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369767, tc_Nat_Onat), _1369769), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1369773))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1369771), _1369775)))], (540 ^ _776545) ^ [_784629, _784631, _784633, _784635, _784637, _784639, _784641, _784643, _784645, _784647] : [-(c_Typedef_Otype__definition(_784645, _784641, _784637, _784633, _784629)), c_Typedef_Otype__definition(_784647, _784643, _784639, _784635, _784631), _784647 = _784645, _784643 = _784641, _784639 = _784637, _784635 = _784633, _784631 = _784629], (28749 ^ _776545) ^ [_1291863, _1291865] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291863))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1291865)) = 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)))), _1291863), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1291865)))], (33465 ^ _776545) ^ [_1391962, _1391964, _1391966, _1391968] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1391962), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391964, tc_Int_Oint), _1391966), _1391968)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391964, _1391962), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1391962, _1391964), c_Int_Oring__1__class_Oof__int(_1391962)), _1391966)), _1391968)), class_Groups_Ocomm__monoid__mult(_1391962), class_Rings_Oring__1(_1391962)], (5737 ^ _776545) ^ [_866979, _866981] : [-(hAPP(c_Hoare__Mirabelle_OAbs__triple(_866979), hAPP(c_Hoare__Mirabelle_ORep__triple(_866979), _866981)) = _866981)], (45682 ^ _776545) ^ [_1693040, _1693042, _1693044] : [hBOOL(hAPP(c_List_Odistinct(_1693040), _1693042)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1693040)), c_Enum_On__lists(_1693040, _1693044, _1693042))))], (23868 ^ _776545) ^ [_1208883, _1208885] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208883)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208885)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208883), _1208885)))], (23719 ^ _776545) ^ [_1206152] : [-(hBOOL(hAPP(_1206152, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23726 ^ [_1206152])))), 23720 ^ _776545 : [(23721 ^ _776545) ^ [_1206204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206204)), hBOOL(hAPP(_1206152, _1206204))]]], (50085 ^ _776545) ^ [_1788365, _1788367, _1788369, _1788371, _1788373] : [c_Fun_Oinj__on(_1788365, _1788367, _1788369, c_Orderings_Otop__class_Otop(tc_fun(_1788365, tc_HOL_Obool))), hAPP(_1788369, _1788371) = _1788373, -(hAPP(c_Hilbert__Choice_Oinv__into(_1788365, _1788367, c_Orderings_Otop__class_Otop(tc_fun(_1788365, tc_HOL_Obool)), _1788369), _1788373) = _1788371)], (10345 ^ _776545) ^ [_954229, _954231, _954233] : [class_Lattices_Oboolean__algebra(_954229), 10348 ^ _776545 : [(10355 ^ _776545) ^ [] : [_954231 = _954233, -(hAPP(c_Groups_Ouminus__class_Ouminus(_954229), _954231) = hAPP(c_Groups_Ouminus__class_Ouminus(_954229), _954233))], (10349 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_954229), _954231) = hAPP(c_Groups_Ouminus__class_Ouminus(_954229), _954233), -(_954231 = _954233)]]], (24970 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (3786 ^ _776545) ^ [_833347, _833349, _833351, _833353, _833355, _833357, _833359, _833361] : [-(c_List_Ofoldl(_833361, _833357, _833353, _833349) = c_List_Ofoldl(_833359, _833355, _833351, _833347)), _833361 = _833359, _833357 = _833355, _833353 = _833351, _833349 = _833347], (23595 ^ _776545) ^ [_1204177, _1204179] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204177), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204179)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204177)), _1204179))], (13596 ^ _776545) ^ [_1018519, _1018521, _1018523, _1018525] : [class_Groups_Ocancel__semigroup__add(_1018519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018519), _1018521), _1018523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018519), _1018525), _1018523), -(_1018521 = _1018525)], (33875 ^ _776545) ^ [_1404221, _1404223, _1404225, _1404227, _1404229] : [class_Complete__Lattice_Ocomplete__lattice(_1404221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404223), _1404225)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1404221), _1404227), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404223, _1404221), _1404225), _1404229)) = hAPP(hAPP(c_Finite__Set_Ofold(_1404223, _1404221, hAPP(hAPP(c_COMBB(_1404221, tc_fun(_1404221, _1404221), _1404223), c_Lattices_Osemilattice__inf__class_Oinf(_1404221)), _1404229)), _1404227), _1404225))], (26236 ^ _776545) ^ [_1250419, _1250421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250421)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1250419)), hAPP(c_Int_Onat, _1250421)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250419), _1250421)))], (48207 ^ _776545) ^ [_1747672, _1747674, _1747676, _1747678] : [c_List_Olist__all(_1747672, _1747674, hAPP(hAPP(c_List_Oappend(_1747672), _1747676), _1747678)), 48210 ^ _776545 : [(48213 ^ _776545) ^ [] : [-(c_List_Olist__all(_1747672, _1747674, _1747678))], (48211 ^ _776545) ^ [] : [-(c_List_Olist__all(_1747672, _1747674, _1747676))]]], (11481 ^ _776545) ^ [_977099, _977101, _977103] : [11482 ^ _776545 : [(11485 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977099), _977103))], (11483 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_977099), _977101))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_977099), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977099, tc_HOL_Obool)), _977101), _977103))))], (39757 ^ _776545) ^ [_1549388, _1549390, _1549392, _1549394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549388), _1549390)), 39763 ^ _776545 : [(39766 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549392), hAPP(_1549394, 39762 ^ [_1549388, _1549390, _1549392, _1549394])))], (39764 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549388), 39762 ^ [_1549388, _1549390, _1549392, _1549394]), _1549390)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1549392), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549388, tc_fun(_1549392, tc_HOL_Obool)), _1549390), _1549394))))], (14780 ^ _776545) ^ [_1043027, _1043029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043027), _1043029)), -(_1043029 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043027), 14783 ^ [_1043027, _1043029]))], (39918 ^ _776545) ^ [_1553474, _1553476, _1553478, _1553480, _1553482, _1553484, _1553486] : [hAPP(c_Fun_Ocomp(_1553474, _1553476, _1553478, _1553480), _1553482) = _1553484, -(hAPP(_1553480, hAPP(_1553482, _1553486)) = hAPP(_1553484, _1553486))], (48075 ^ _776545) ^ [_1744910, _1744912] : [c_List_Olist__ex(_1744910, _1744912, c_List_Olist_ONil(_1744910))], (8591 ^ _776545) ^ [_924122, _924124, _924126] : [class_Lattices_Olattice(_924122), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924122), _924124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924122), _924124), _924126))))], (25353 ^ _776545) ^ [_1235254, _1235256] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235254, _1235256) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235254), _1235256)), _1235256)))], (36890 ^ _776545) ^ [_1476734, _1476736, _1476738, _1476740, _1476742] : [hAPP(c_Relation_OImage(_1476734, _1476734, _1476736), hAPP(hAPP(c_Set_Oinsert(_1476734), _1476738), c_Orderings_Obot__class_Obot(tc_fun(_1476734, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1476734, _1476734, _1476736), hAPP(hAPP(c_Set_Oinsert(_1476734), _1476740), c_Orderings_Obot__class_Obot(tc_fun(_1476734, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1476734, _1476742, _1476736), hBOOL(hAPP(hAPP(c_member(_1476734), _1476740), _1476742)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476734, _1476734)), hAPP(hAPP(c_Product__Type_OPair(_1476734, _1476734), _1476738), _1476740)), _1476736)))], (39427 ^ _776545) ^ [_1540277, _1540279, _1540281, _1540283, _1540285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540277, _1540279)), _1540281), hAPP(hAPP(c_Product__Type_OSigma(_1540277, _1540279), _1540283), _1540285))), 39431 ^ _776545 : [(39437 ^ _776545) ^ [] : [-(_1540281 = hAPP(hAPP(c_Product__Type_OPair(_1540277, _1540279), 39430 ^ [_1540277, _1540279, _1540281, _1540283, _1540285]), 39433 ^ [_1540277, _1540279, _1540281, _1540283, _1540285]))], (39435 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540279), 39433 ^ [_1540277, _1540279, _1540281, _1540283, _1540285]), hAPP(_1540285, 39430 ^ [_1540277, _1540279, _1540281, _1540283, _1540285]))))], (39432 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540277), 39430 ^ [_1540277, _1540279, _1540281, _1540283, _1540285]), _1540283)))]]], (10 ^ _776545) ^ [_776668, _776670, _776672] : [-(_776672 = _776668), _776672 = _776670, _776670 = _776668], (38628 ^ _776545) ^ [_1518571, _1518573, _1518575] : [-(hAPP(c_Set_Ovimage(_1518571, _1518573, _1518575), c_Orderings_Obot__class_Obot(tc_fun(_1518573, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1518571, tc_HOL_Obool)))], (37250 ^ _776545) ^ [_1485460, _1485462, _1485464, _1485466, _1485468] : [c_Fun_Oinj__on(_1485460, _1485462, _1485464, _1485466), c_Fun_Oinj__on(_1485460, _1485462, _1485464, _1485468), -(c_Fun_Oinj__on(_1485460, _1485462, _1485464, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485460, tc_HOL_Obool)), _1485466), _1485468)))], (22497 ^ _776545) ^ [_1184188, _1184190, _1184192] : [class_Groups_Omonoid__mult(_1184188), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184188), hAPP(hAPP(c_Power_Opower__class_Opower(_1184188), _1184190), _1184192)), _1184190) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184188), _1184190), hAPP(hAPP(c_Power_Opower__class_Opower(_1184188), _1184190), _1184192)))], (32286 ^ _776545) ^ [_1357057] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1357057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1357057)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29053 ^ _776545) ^ [_1297352] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297352))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297352)))))], (25093 ^ _776545) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32674 ^ _776545) ^ [_1369958, _1369960] : [-(hAPP(c_Finite__Set_Ocard(_1369958), _1369960) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369958, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1369958), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1369960))], (43585 ^ _776545) ^ [_1645999, _1646001, _1646003] : [_1645999 = hAPP(hAPP(c_List_Oappend(_1646001), _1645999), _1646003), -(_1646003 = c_List_Olist_ONil(_1646001))], (51219 ^ _776545) ^ [_1813686, _1813688, _1813690, _1813692] : [class_Rings_Ocomm__semiring__1(_1813686), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813686), _1813688), _1813690)), _1813692)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813686), _1813688), _1813692)))], (8327 ^ _776545) ^ [_919242, _919244, _919246] : [class_Lattices_Osemilattice__sup(_919242), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919242), _919244), _919246) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919242), _919246), _919244))], (1084 ^ _776545) ^ [_792959, _792961] : [-(class_Lattices_Obounded__lattice(_792959)), _792961 = _792959, class_Lattices_Obounded__lattice(_792961)], (23575 ^ _776545) ^ [_1203867, _1203869, _1203871] : [class_Nat_Osemiring__char__0(_1203867), 23578 ^ _776545 : [(23585 ^ _776545) ^ [] : [_1203869 = _1203871, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203867), _1203869) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203867), _1203871))], (23579 ^ _776545) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203867), _1203869) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1203867), _1203871), -(_1203869 = _1203871)]]], (43364 ^ _776545) ^ [_1640987, _1640989, _1640991, _1640993] : [-(c_List_Osublist(_1640987, hAPP(hAPP(c_List_Olist_OCons(_1640987), _1640989), _1640991), _1640993) = hAPP(hAPP(c_List_Oappend(_1640987), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1640987)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1640993)), hAPP(hAPP(c_List_Olist_OCons(_1640987), _1640989), c_List_Olist_ONil(_1640987))), c_List_Olist_ONil(_1640987))), c_List_Osublist(_1640987, _1640991, 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)), _1640993)))))], (12824 ^ _776545) ^ [_1002801, _1002803] : [class_Complete__Lattice_Ocomplete__lattice(_1002801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002801), _1002803)), -(c_Complete__Lattice_OSup__class_OSup(_1002801, _1002803) = hAPP(hAPP(c_Finite__Set_Ofold(_1002801, _1002801, c_Lattices_Osemilattice__sup__class_Osup(_1002801)), c_Orderings_Obot__class_Obot(_1002801)), _1002803))], (47579 ^ _776545) ^ [_1733483, _1733485, _1733487] : [-(hBOOL(hAPP(hAPP(c_member(_1733483), _1733485), hAPP(c_List_Oset(_1733483), _1733487)))), -(c_List_Oinsert(_1733483, _1733485, _1733487) = hAPP(hAPP(c_List_Olist_OCons(_1733483), _1733485), _1733487))], (44960 ^ _776545) ^ [_1676831, _1676833, _1676835] : [c_Fun_Oinj__on(tc_List_Olist(_1676831), tc_List_Olist(_1676833), hAPP(c_List_Omap(_1676831, _1676833), _1676835), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1676831), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1676831, _1676833, _1676835, c_Orderings_Otop__class_Otop(tc_fun(_1676831, tc_HOL_Obool))))], (7656 ^ _776545) ^ [_903835, _903837, _903839, _903841] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903835, tc_HOL_Obool)), _903837), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903835, tc_HOL_Obool)), _903839), _903841)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903835, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903835, tc_HOL_Obool)), _903837), _903839)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903835, tc_HOL_Obool)), _903837), _903841)))], (34717 ^ _776545) ^ [_1423579] : [-(c_Divides_Odivmod__nat(_1423579, 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)), _1423579))], (52455 ^ _776545) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (2620 ^ _776545) ^ [_815190, _815192] : [_815192 = _815190, -(c_Nitpick_Oone__frac(_815192) = c_Nitpick_Oone__frac(_815190))], (35541 ^ _776545) ^ [_1439654, _1439656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439654), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439656), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439654, _1439656) = 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), _1439654), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1439656)))))], (43397 ^ _776545) ^ [_1641762, _1641764, _1641766, _1641768, _1641770] : [hAPP(hAPP(c_List_Olist_OCons(_1641762), _1641764), _1641766) = hAPP(hAPP(c_List_Oappend(_1641762), _1641768), _1641770), 43402 ^ _776545 : [(43405 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641762), _1641764), _1641766) = _1641770)], (43403 ^ _776545) ^ [] : [-(_1641768 = c_List_Olist_ONil(_1641762))]], 43407 ^ _776545 : [(43410 ^ _776545) ^ [] : [-(_1641766 = hAPP(hAPP(c_List_Oappend(_1641762), 43406 ^ [_1641762, _1641764, _1641766, _1641768, _1641770]), _1641770))], (43408 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641762), _1641764), 43406 ^ [_1641762, _1641764, _1641766, _1641768, _1641770]) = _1641768)]]], (38955 ^ _776545) ^ [_1526244, _1526246, _1526248, _1526250] : [hBOOL(hAPP(c_Predicate_ODomainP(_1526244, _1526246, hAPP(hAPP(c_COMBC(_1526244, tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_fun(_1526246, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526246, tc_fun(tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_fun(_1526246, tc_HOL_Obool)), _1526244), c_COMBC(_1526246, tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526246, tc_prod(_1526244, _1526246)), tc_fun(_1526246, tc_fun(tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_HOL_Obool)), _1526244), hAPP(c_COMBB(tc_prod(_1526244, _1526246), tc_fun(tc_fun(tc_prod(_1526244, _1526246), tc_HOL_Obool), tc_HOL_Obool), _1526246), c_member(tc_prod(_1526244, _1526246)))), c_Product__Type_OPair(_1526244, _1526246)))), _1526248)), _1526250)), -(hBOOL(hAPP(hAPP(c_member(_1526244), _1526250), hAPP(c_Relation_ODomain(_1526244, _1526246), _1526248))))], (34970 ^ _776545) ^ [_1428933, _1428935] : [_1428933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428933, _1428935) = 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)))], (52249 ^ _776545) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (42095 ^ _776545) ^ [_1610404, _1610406, _1610408, _1610410, _1610412, _1610414] : [-(c_List_Olistrelp(_1610404, _1610406, hAPP(hAPP(c_List_Olist_OCons(_1610404), _1610408), _1610410), hAPP(hAPP(c_List_Olist_OCons(_1610404), _1610412), _1610414))), hBOOL(hAPP(hAPP(_1610406, _1610408), _1610412)), c_List_Olistrelp(_1610404, _1610406, _1610410, _1610414)], (8423 ^ _776545) ^ [_921202, _921204, _921206] : [class_Lattices_Osemilattice__inf(_921202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921202), _921204), _921206) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921202), _921206), _921204))], (14254 ^ _776545) ^ [_1033066, _1033068, _1033070, _1033072] : [class_Rings_Ocomm__semiring__1(_1033066), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033066), _1033068), _1033070)), _1033072) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033066), _1033068), _1033072)), _1033070))], (40366 ^ _776545) ^ [_1563596, _1563598] : [-(c_Hilbert__Choice_OEps(_1563596, hAPP(c_fequal, _1563598)) = _1563598)], (34884 ^ _776545) ^ [] : [-(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)))))], (46590 ^ _776545) ^ [_1713199] : [class_Orderings_Olinorder(_1713199), -(c_List_Olinorder__class_Osorted(_1713199, c_List_Olist_ONil(_1713199)))], (52301 ^ _776545) ^ [_1829230, _1829232] : [-(class_Nat_Osize(tc_sum(_1829230, _1829232)))], (4726 ^ _776545) ^ [_848459, _848461, _848463, _848465, _848467, _848469, _848471, _848473] : [-(c_Random__Sequence_Obind(_848473, _848469, _848465, _848461) = c_Random__Sequence_Obind(_848471, _848467, _848463, _848459)), _848473 = _848471, _848469 = _848467, _848465 = _848463, _848461 = _848459], (23083 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (27042 ^ _776545) ^ [_1263571, _1263573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263571)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1263571, _1263573)))], (35479 ^ _776545) ^ [_1438405, _1438407, _1438409, _1438411, _1438413] : [-(hAPP(c_Product__Type_Osnd(_1438405, _1438407), hAPP(c_Product__Type_Oapsnd(_1438409, _1438407, _1438405, _1438411), _1438413)) = hAPP(_1438411, hAPP(c_Product__Type_Osnd(_1438405, _1438409), _1438413)))], (6013 ^ _776545) ^ [_872466, _872468, _872470, _872472] : [hBOOL(hAPP(hAPP(_872470, _872472), _872468)), -(hBOOL(hAPP(hAPP(c_member(_872466), _872468), c_SetInterval_Oord_OatLeast(_872466, _872470, _872472))))], (29321 ^ _776545) ^ [_1301968, _1301970] : [class_Rings_Olinordered__idom(_1301968), -(hAPP(c_Groups_Oabs__class_Oabs(_1301968), hAPP(hAPP(c_Power_Opower__class_Opower(_1301968), _1301970), 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(_1301968), _1301970), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (28875 ^ _776545) ^ [_1294216, _1294218] : [_1294216 = _1294218, -(c_Int_OBit0(_1294216) = c_Int_OBit0(_1294218))], (13964 ^ _776545) ^ [_1026380, _1026382, _1026384, _1026386, _1026388, _1026390] : [class_Rings_Oordered__ring(_1026380), 13967 ^ _776545 : [(13974 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026380), _1026386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026380), _1026388), _1026382)), _1026384)), _1026390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), _1026382), _1026384)), _1026386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), _1026388), _1026384)), _1026390))))], (13968 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), _1026382), _1026384)), _1026386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), _1026388), _1026384)), _1026390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1026380), _1026386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1026380), _1026388), _1026382)), _1026384)), _1026390))))]]], (40528 ^ _776545) ^ [_1567592, _1567594, _1567596, _1567598, _1567600, _1567602, _1567604] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567592, _1567594, _1567596, _1567598), _1567600), _1567602), _1567604) = hAPP(hAPP(_1567602, hAPP(c_Product__Type_Ofst(_1567594, _1567596), hAPP(_1567600, _1567604))), hAPP(c_Product__Type_Osnd(_1567594, _1567596), hAPP(_1567600, _1567604))))], (16074 ^ _776545) ^ [_1067195, _1067197] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067195)), _1067197) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067195), _1067197)))], (15390 ^ _776545) ^ [_1054480, _1054482, _1054484, _1054486] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054480), _1054482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054484), hAPP(c_Set_Oimage(_1054480, _1054484, _1054486), _1054482))), hAPP(c_Finite__Set_Ocard(_1054480), _1054482))))], (32392 ^ _776545) ^ [_1359365, _1359367, _1359369, _1359371, _1359373, _1359375] : [hBOOL(hAPP(hAPP(c_member(_1359365), _1359367), _1359369)), hBOOL(hAPP(hAPP(_1359371, _1359367), _1359373)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359365, tc_fun(_1359375, tc_HOL_Obool)), _1359369), _1359371), _1359373)))], (11606 ^ _776545) ^ [_979547, _979549, _979551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979547), _979551)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979547), hAPP(hAPP(c_Set_Oinsert(_979547), _979549), _979551))))], (20261 ^ _776545) ^ [_1142318, _1142320, _1142322, _1142324] : [class_Fields_Ofield__inverse__zero(_1142318), 20264 ^ _776545 : [(20265 ^ _776545) ^ [] : [_1142320 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142318), _1142322), _1142324), 20268 ^ _776545 : [(20275 ^ _776545) ^ [] : [_1142324 = c_Groups_Ozero__class_Ozero(_1142318), -(_1142320 = c_Groups_Ozero__class_Ozero(_1142318))], (20269 ^ _776545) ^ [] : [-(_1142324 = c_Groups_Ozero__class_Ozero(_1142318)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142318), _1142320), _1142324) = _1142322)]]], (20281 ^ _776545) ^ [] : [-(_1142320 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142318), _1142322), _1142324)), 20284 ^ _776545 : [(20287 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142318), _1142320), _1142324) = _1142322], (20285 ^ _776545) ^ [] : [_1142324 = c_Groups_Ozero__class_Ozero(_1142318)]], 20288 ^ _776545 : [(20291 ^ _776545) ^ [] : [_1142320 = c_Groups_Ozero__class_Ozero(_1142318)], (20289 ^ _776545) ^ [] : [-(_1142324 = c_Groups_Ozero__class_Ozero(_1142318))]]]]], (34157 ^ _776545) ^ [_1411168, _1411170] : [class_Rings_Ocomm__semiring__1(_1411168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411168), c_Groups_Oone__class_Oone(_1411168)), c_Groups_Oone__class_Oone(_1411168))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1411168), c_Nat_Osemiring__1__class_Oof__nat(_1411168)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1411170))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411168), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1411168), _1411170)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411168), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1411168), _1411170)), c_Groups_Oone__class_Oone(_1411168))))], (8032 ^ _776545) ^ [_912936, _912938, _912940, _912942] : [hBOOL(hAPP(hAPP(c_member(_912936), _912938), _912940)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912936, tc_HOL_Obool)), _912940), hAPP(hAPP(c_Set_Oinsert(_912936), _912938), _912942)) = hAPP(hAPP(c_Set_Oinsert(_912936), _912938), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912936, tc_HOL_Obool)), _912940), _912942)))], (23183 ^ _776545) ^ [_1196446, _1196448, _1196450, _1196452, _1196454] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1196446, _1196448, _1196450), _1196452), hAPP(c_Nat_OSuc, _1196454)) = hAPP(hAPP(_1196450, _1196452), hAPP(hAPP(c_Power_Opower_Opower(_1196446, _1196448, _1196450), _1196452), _1196454)))], (9248 ^ _776545) ^ [_935982, _935984, _935986] : [class_Orderings_Olinorder(_935982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935982), _935984), _935986))), -(_935984 = _935986), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935982), _935986), _935984)))], (22509 ^ _776545) ^ [_1184428, _1184430, _1184432, _1184434] : [class_Groups_Omonoid__mult(_1184428), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184428), _1184430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184432), _1184434)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1184428), hAPP(hAPP(c_Power_Opower__class_Opower(_1184428), _1184430), _1184432)), _1184434))], (52437 ^ _776545) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (51407 ^ _776545) ^ [_1817058, _1817060, _1817062, _1817064] : [-(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), _1817058, _1817060)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817062, _1817064)))), 51408 ^ _776545 : [(51411 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817062), _1817058)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817060), _1817064))], (51409 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817058), _1817060)))]]], (9796 ^ _776545) ^ [_944327, _944329, _944331] : [9797 ^ _776545 : [(9800 ^ _776545) ^ [] : [_944329 = _944331], (9798 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944327, tc_HOL_Obool)), _944329), _944331))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944327, tc_HOL_Obool)), _944329), _944331)))], (33100 ^ _776545) ^ [_1381642, _1381644, _1381646, _1381648, _1381650] : [hBOOL(hAPP(hAPP(c_member(_1381642), _1381644), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1381646, tc_fun(_1381642, tc_HOL_Obool)), _1381648), _1381650))), 33104 ^ _776545 : [(33107 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381642), _1381644), hAPP(_1381650, 33103 ^ [_1381642, _1381644, _1381646, _1381648, _1381650]))))], (33105 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381646), 33103 ^ [_1381642, _1381644, _1381646, _1381648, _1381650]), _1381648)))]]], (21273 ^ _776545) ^ [_1161441, _1161443, _1161445, _1161447] : [class_Int_Onumber__ring(_1161441), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161441), hAPP(c_Int_Onumber__class_Onumber__of(_1161441), _1161443)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161441), hAPP(c_Int_Onumber__class_Onumber__of(_1161441), _1161445)), _1161447)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161441), hAPP(c_Int_Onumber__class_Onumber__of(_1161441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161443), _1161445))), _1161447))], (6186 ^ _776545) ^ [_875905, _875907] : [-(hBOOL(hAPP(hAPP(c_member(_875905), _875907), c_Orderings_Otop__class_Otop(tc_fun(_875905, tc_HOL_Obool)))))], (37622 ^ _776545) ^ [_1492800, _1492802, _1492804, _1492806, _1492808] : [c_Fun_Oinj__on(_1492800, _1492802, _1492804, c_Orderings_Otop__class_Otop(tc_fun(_1492800, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1492800, _1492802, _1492804), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492800, tc_HOL_Obool)), _1492806), _1492808)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492802, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1492800, _1492802, _1492804), _1492806)), hAPP(c_Set_Oimage(_1492800, _1492802, _1492804), _1492808)))], (15968 ^ _776545) ^ [_1065560, _1065562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065560), hAPP(c_Nat_OSuc, _1065562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065560), _1065562))), -(_1065560 = _1065562)], (27703 ^ _776545) ^ [_1274877, _1274879] : [class_Groups_Oabs__if(_1274877), 27706 ^ _776545 : [(27713 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274877), _1274879), c_Groups_Ozero__class_Ozero(_1274877)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274877), _1274879) = _1274879)], (27707 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274877), _1274879), c_Groups_Ozero__class_Ozero(_1274877))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274877), _1274879) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274877), _1274879))]]], (16787 ^ _776545) ^ [_1078626, _1078628, _1078630] : [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, _1078626)), _1078628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078626)), _1078630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078628), _1078630)))], (26567 ^ _776545) ^ [_1256089, _1256091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256089)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1256089), _1256091)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1256089)), _1256091))], (44447 ^ _776545) ^ [_1665460, _1665462, _1665464] : [class_Orderings_Olinorder(_1665460), -(c_Big__Operators_Olattice_OInf__fin(_1665460, c_Orderings_Oord__class_Omin(_1665460), hAPP(c_List_Oset(_1665460), hAPP(hAPP(c_List_Olist_OCons(_1665460), _1665462), _1665464))) = hAPP(c_List_Ofoldl(_1665460, _1665460, c_Orderings_Oord__class_Omin(_1665460), _1665462), _1665464))], (45231 ^ _776545) ^ [_1682457] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682457)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (24832 ^ _776545) ^ [_1225846, _1225848, _1225850, _1225852] : [class_Divides_Osemiring__div(_1225846), -(c_Divides_Odiv__class_Omod(_1225846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225846), _1225848), _1225850), _1225852) = c_Divides_Odiv__class_Omod(_1225846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225846), _1225848), c_Divides_Odiv__class_Omod(_1225846, _1225850, _1225852)), _1225852))], (14296 ^ _776545) ^ [_1034067, _1034069, _1034071, _1034073, _1034075] : [class_Rings_Ocomm__semiring__1(_1034067), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), _1034069), _1034071)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), _1034073), _1034075)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), _1034069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), _1034071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034067), _1034073), _1034075))))], (46160 ^ _776545) ^ [_1703829, _1703831, _1703833, _1703835] : [hBOOL(hAPP(hAPP(c_member(_1703829), _1703831), hAPP(c_List_Oset(_1703829), _1703833))), -(hBOOL(hAPP(_1703835, _1703831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703829)), hAPP(c_List_Ofilter(_1703829, _1703835), _1703833))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703829)), _1703833))))], (27751 ^ _776545) ^ [_1275683] : [_1275683 = 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), _1275683)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40979 ^ _776545) ^ [_1579195, _1579197, _1579199, _1579201] : [c_Wellfounded_Owf(_1579195, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579195, _1579195)), hAPP(hAPP(c_Product__Type_OPair(_1579195, _1579195), _1579197), _1579199)), _1579201)), 40982 ^ _776545 : [(40985 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579195, _1579195)), hAPP(hAPP(c_Product__Type_OPair(_1579195, _1579195), _1579199), _1579197)), c_Transitive__Closure_Ortrancl(_1579195, _1579201)))], (40983 ^ _776545) ^ [] : [-(c_Wellfounded_Owf(_1579195, _1579201))]]], (25351 ^ _776545) ^ [_1235207, _1235209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235207), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235209), _1235207)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1235209), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235209, _1235207)))], (38412 ^ _776545) ^ [_1512916, _1512918] : [-(hAPP(c_List_Olexn(_1512916, _1512918), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1512916), tc_List_Olist(_1512916)), tc_HOL_Obool)))], (43900 ^ _776545) ^ [_1653669, _1653671, _1653673, _1653675] : [-(hAPP(hAPP(c_List_Odrop(_1653669), _1653671), hAPP(hAPP(c_List_Otake(_1653669), _1653673), _1653675)) = hAPP(hAPP(c_List_Otake(_1653669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653673), _1653671)), hAPP(hAPP(c_List_Odrop(_1653669), _1653671), _1653675)))], (45303 ^ _776545) ^ [_1684249, _1684251, _1684253] : [-(c_List_Olistsp(_1684249, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684249, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1684249, tc_fun(_1684249, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684249)), _1684251)), hAPP(hAPP(c_COMBC(_1684249, tc_fun(_1684249, tc_HOL_Obool), tc_HOL_Obool), c_member(_1684249)), _1684253))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1684249), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684249), tc_fun(tc_List_Olist(_1684249), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1684249))), c_List_Olists(_1684249, _1684251))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684249), tc_fun(tc_List_Olist(_1684249), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1684249))), c_List_Olists(_1684249, _1684253))))], (34588 ^ _776545) ^ [_1420766, _1420768, _1420770, _1420772, _1420774, _1420776] : [hBOOL(hAPP(hAPP(_1420766, _1420768), _1420770)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420772, tc_fun(_1420774, tc_HOL_Obool))), _1420776), _1420766), _1420768), _1420770)))], (2916 ^ _776545) ^ [_819808, _819810, _819812, _819814, _819816, _819818] : [-(c_Nitpick_Otimes__frac(_819818, _819814, _819810) = c_Nitpick_Otimes__frac(_819816, _819812, _819808)), _819818 = _819816, _819814 = _819812, _819810 = _819808], (43260 ^ _776545) ^ [_1638390, _1638392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638390)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638392)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638390), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1638392)) = c_List_Olist_ONil(tc_Int_Oint))], (8203 ^ _776545) ^ [_916774, _916776, _916778, _916780, _916782] : [class_Groups_Ominus(_916774), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916776, _916774)), _916778), _916780), _916782) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_916774), hAPP(_916778, _916782)), hAPP(_916780, _916782)))], (26631 ^ _776545) ^ [_1257234, _1257236] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257234))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257234)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257236)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7280 ^ _776545) ^ [_895550, _895552, _895554] : [hBOOL(hAPP(hAPP(c_member(_895550), _895552), hAPP(hAPP(c_Set_Oinsert(_895550), _895554), c_Orderings_Obot__class_Obot(tc_fun(_895550, tc_HOL_Obool))))), -(_895552 = _895554)], (3810 ^ _776545) ^ [_833733, _833735, _833737, _833739, _833741, _833743, _833745, _833747] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_833747, _833743, _833739, _833735) = c_New__Random__Sequence_Opos__not__random__dseq(_833745, _833741, _833737, _833733)), _833747 = _833745, _833743 = _833741, _833739 = _833737, _833735 = _833733], (42457 ^ _776545) ^ [_1619525, _1619527, _1619529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619527)), _1619529))), -(hBOOL(hAPP(hAPP(c_member(_1619527), hAPP(hAPP(c_List_Onth(_1619527), _1619529), _1619525)), hAPP(c_List_Oset(_1619527), _1619529))))], (50016 ^ _776545) ^ [_1786862, _1786864, _1786866] : [hAPP(_1786866, hAPP(c_Hilbert__Choice_Oinv__into(_1786862, _1786864, c_Orderings_Otop__class_Otop(tc_fun(_1786862, tc_HOL_Obool)), _1786866), 50017 ^ [_1786862, _1786864, _1786866])) = 50017 ^ [_1786862, _1786864, _1786866], -(hAPP(c_Set_Oimage(_1786862, _1786864, _1786866), c_Orderings_Otop__class_Otop(tc_fun(_1786862, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1786864, tc_HOL_Obool)))], (42244 ^ _776545) ^ [_1614299, _1614301, _1614303, _1614305] : [-(_1614299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1614301), hAPP(hAPP(c_List_Olist_OCons(_1614301), _1614303), _1614305)), _1614299) = hAPP(hAPP(c_List_Onth(_1614301), _1614305), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1614299), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (22307 ^ _776545) ^ [_1180952, _1180954, _1180956] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180952), _1180954)), _1180956) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180954), _1180956)))], (38947 ^ _776545) ^ [_1525957, _1525959, _1525961, _1525963] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525957, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1525957, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525957, _1525959), _1525961)), hAPP(c_Relation_ODomain(_1525957, _1525959), _1525963))), hAPP(c_Relation_ODomain(_1525957, _1525959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1525957, _1525959), tc_HOL_Obool)), _1525961), _1525963)))))], (2712 ^ _776545) ^ [_816630, _816632, _816634, _816636, _816638, _816640] : [-(c_FunDef_Oin__rel(_816640, _816636, _816632) = c_FunDef_Oin__rel(_816638, _816634, _816630)), _816640 = _816638, _816636 = _816634, _816632 = _816630], (8285 ^ _776545) ^ [_918295, _918297, _918299, _918301] : [class_Lattices_Osemilattice__sup(_918295), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918295), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918295), _918297), _918299)), _918301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918295), _918297), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918295), _918299), _918301)))], (25905 ^ _776545) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29047 ^ _776545) ^ [_1297257] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1297257)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1297257))))], (1344 ^ _776545) ^ [_796209, _796211] : [-(class_Orderings_Owellorder(_796209)), _796211 = _796209, class_Orderings_Owellorder(_796211)], (36651 ^ _776545) ^ [_1471428, _1471430, _1471432] : [_1471430 = c_Orderings_Obot__class_Obot(tc_fun(_1471428, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471428, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471428), _1471430), _1471432))], (48558 ^ _776545) ^ [_1755601, _1755603, _1755605] : [-(_1755601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1755603), c_List_Oreplicate(_1755603, _1755601, _1755605)) = c_List_Oreplicate(_1755603, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1755601), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1755605))], (50245 ^ _776545) ^ [_1792249, _1792251, _1792253, _1792255] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1792249, _1792251, _1792253, _1792255, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1792251)) = _1792253)], (24766 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (7732 ^ _776545) ^ [_906215, _906217, _906219, _906221] : [hBOOL(hAPP(hAPP(c_member(_906215), _906217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906215, tc_HOL_Obool)), _906219), _906221))), 7735 ^ _776545 : [(7738 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_906215), _906217), _906221))], (7736 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906215), _906217), _906219)))]]], (28829 ^ _776545) ^ [_1293392, _1293394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1293392)), c_Int_OBit0(_1293394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1293392), _1293394)))], (52245 ^ _776545) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (34503 ^ _776545) ^ [_1418736, _1418738, _1418740, _1418742, _1418744] : [34505 ^ _776545 : [(34508 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1418742, 34504 ^ [_1418736, _1418738, _1418740, _1418742, _1418744]), _1418744))], (34506 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418736), 34504 ^ [_1418736, _1418738, _1418740, _1418742, _1418744]), _1418740)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418736, tc_fun(_1418738, tc_HOL_Obool)), _1418740), _1418742), _1418744)))], (33509 ^ _776545) ^ [_1393035, _1393037] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393035, tc_fun(_1393035, tc_HOL_Obool)), _1393037), hAPP(hAPP(c_COMBC(_1393035, tc_fun(_1393035, tc_HOL_Obool), tc_fun(_1393035, tc_HOL_Obool)), c_Set_Oinsert(_1393035)), c_Orderings_Obot__class_Obot(tc_fun(_1393035, tc_HOL_Obool)))) = _1393037)], (41410 ^ _776545) ^ [_1589728, _1589730, _1589732, _1589734] : [-(hAPP(hAPP(c_Nat_Ocompow(_1589728, _1589728), _1589730), hAPP(hAPP(c_Nat_Ocompow(_1589728, _1589728), _1589732), _1589734)) = hAPP(hAPP(c_Nat_Ocompow(_1589728, _1589728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1589732), _1589730)), _1589734))], (44054 ^ _776545) ^ [_1657466, _1657468, _1657470, _1657472] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657466) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1657468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657466)), hAPP(hAPP(c_List_Olist_OCons(_1657468), _1657470), _1657472)) = hAPP(hAPP(c_List_Olist_OCons(_1657468), _1657470), _1657472))], (42305 ^ _776545) ^ [_1616041, _1616043, _1616045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616041)), _1616043)), _1616045)), -(hAPP(hAPP(c_List_Otake(_1616041), _1616045), _1616043) = _1616043)], (50029 ^ _776545) ^ [_1787209, _1787211, _1787213, _1787215] : [hAPP(c_Set_Oimage(_1787209, _1787211, _1787213), c_Orderings_Otop__class_Otop(tc_fun(_1787209, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1787211, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1787209, _1787211, _1787213), hAPP(c_Set_Oimage(_1787211, _1787209, c_Hilbert__Choice_Oinv__into(_1787209, _1787211, c_Orderings_Otop__class_Otop(tc_fun(_1787209, tc_HOL_Obool)), _1787213)), _1787215)) = _1787215)], (26058 ^ _776545) ^ [_1247592, _1247594] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247592, _1247594) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247592), _1247594)), _1247594)))], (41420 ^ _776545) ^ [_1589956, _1589958] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589956, _1589956), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1589958) = _1589958)], (2752 ^ _776545) ^ [_817242, _817244, _817246, _817248] : [-(c_Predicate_OPowp(_817248, _817244) = c_Predicate_OPowp(_817246, _817242)), _817248 = _817246, _817244 = _817242], (32904 ^ _776545) ^ [_1376359, _1376361, _1376363, _1376365, _1376367] : [class_Complete__Lattice_Ocomplete__lattice(_1376359), hBOOL(hAPP(hAPP(c_member(_1376361), _1376363), _1376365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376359), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376361, _1376359), _1376365), _1376367)), hAPP(_1376367, _1376363))))], (25947 ^ _776545) ^ [_1245728] : [25948 ^ _776545 : [(25949 ^ _776545) ^ [_1245785] : [hBOOL(hAPP(_1245728, _1245785))]], 25951 ^ _776545 : [(25954 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1245728, hAPP(c_Int_Onat, 25950 ^ [_1245728]))))], (25952 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25950 ^ [_1245728])))]]], (28623 ^ _776545) ^ [] : [-(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)))))], (43896 ^ _776545) ^ [_1653571, _1653573, _1653575] : [-(c_List_Obutlast(_1653571, hAPP(hAPP(c_List_Odrop(_1653571), _1653573), _1653575)) = hAPP(hAPP(c_List_Odrop(_1653571), _1653573), c_List_Obutlast(_1653571, _1653575)))], (6222 ^ _776545) ^ [_876537, _876539, _876541, _876543] : [hBOOL(hAPP(_876537, _876539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876541, tc_HOL_Obool)), _876537), _876543)), -(hBOOL(hAPP(_876543, _876539)))], (52441 ^ _776545) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (41080 ^ _776545) ^ [_1581883, _1581885, _1581887, _1581889, _1581891] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581883, _1581885)), hAPP(hAPP(c_Product__Type_OPair(_1581883, _1581885), _1581887), _1581889)), _1581891)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581885, _1581883)), hAPP(hAPP(c_Product__Type_OPair(_1581885, _1581883), _1581889), _1581887)), hAPP(c_Relation_Oconverse(_1581883, _1581885), _1581891))))], (2996 ^ _776545) ^ [_821024, _821026, _821028, _821030] : [-(c_Nitpick_Ouminus__frac(_821030, _821026) = c_Nitpick_Ouminus__frac(_821028, _821024)), _821030 = _821028, _821026 = _821024], (46976 ^ _776545) ^ [_1720720, _1720722, _1720724] : [_1720722 = hAPP(hAPP(c_List_Olist_OCons(_1720720), _1720724), c_List_Olist_ONil(_1720720)), -(hAPP(c_List_Orev(_1720720), _1720722) = hAPP(hAPP(c_List_Olist_OCons(_1720720), _1720724), c_List_Olist_ONil(_1720720)))], (1354 ^ _776545) ^ [_796334, _796336] : [-(class_Complete__Lattice_Ocomplete__lattice(_796334)), _796336 = _796334, class_Complete__Lattice_Ocomplete__lattice(_796336)], (30948 ^ _776545) ^ [_1331609, _1331611, _1331613] : [class_Orderings_Olinorder(_1331609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331609), _1331611)), 30955 ^ _776545 : [(30962 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331609, tc_HOL_Obool)), _1331611), hAPP(hAPP(c_Set_Oinsert(_1331609), _1331613), c_Orderings_Obot__class_Obot(tc_fun(_1331609, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331609, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1331609, hAPP(hAPP(c_Set_Oinsert(_1331609), _1331613), _1331611)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331609), _1331613), c_Big__Operators_Olinorder__class_OMin(_1331609, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331609, tc_HOL_Obool)), _1331611), hAPP(hAPP(c_Set_Oinsert(_1331609), _1331613), c_Orderings_Obot__class_Obot(tc_fun(_1331609, tc_HOL_Obool)))))))], (30956 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331609, tc_HOL_Obool)), _1331611), hAPP(hAPP(c_Set_Oinsert(_1331609), _1331613), c_Orderings_Obot__class_Obot(tc_fun(_1331609, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331609, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1331609, hAPP(hAPP(c_Set_Oinsert(_1331609), _1331613), _1331611)) = _1331613)]]], (10883 ^ _776545) ^ [_964386, _964388, _964390, _964392, _964394] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964386, _964386, _964388, _964390, _964392), _964394)), -(hBOOL(hAPP(hAPP(c_member(_964386), _964390), _964392))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_964386, _964388, hAPP(hAPP(c_Set_Oinsert(_964386), _964390), _964392)), _964394)))], (8849 ^ _776545) ^ [_928780, _928782, _928784] : [class_Orderings_Olinorder(_928780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928780), _928782), _928784)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928780, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_928780), _928782), c_Orderings_Obot__class_Obot(tc_fun(_928780, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_928780, _928782, _928784)) = c_SetInterval_Oord__class_OatLeastAtMost(_928780, _928782, _928784))], (5592 ^ _776545) ^ [_861936, _861938] : [_861938 = _861936, -(tc_Hoare__Mirabelle_Otriple(_861938) = tc_Hoare__Mirabelle_Otriple(_861936))], (29271 ^ _776545) ^ [_1301104, _1301106] : [class_Rings_Ocomm__semiring__1(_1301104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301104), _1301106), _1301106) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301104), _1301106), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35531 ^ _776545) ^ [_1439473, _1439475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439475), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439473, _1439475) = 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), _1439473), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1439475)))))], (5156 ^ _776545) ^ [_855214, _855216, _855218, _855220] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855220, _855216) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855218, _855214)), _855220 = _855218, _855216 = _855214], (26687 ^ _776545) ^ [_1258129, _1258131] : [class_Rings_Oring__1(_1258129), 26690 ^ _776545 : [(26697 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258131), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258129), _1258131) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258129), hAPP(c_Int_Onat, _1258131)))], (26691 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258131), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1258129), _1258131) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258129), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1258129), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1258131)))))]]], (37773 ^ _776545) ^ [] : [-(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))], (19819 ^ _776545) ^ [_1134234, _1134236] : [class_Rings_Olinordered__idom(_1134234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134234), c_Groups_Ozero__class_Ozero(_1134234)), _1134236)), -(c_Groups_Osgn__class_Osgn(_1134234, _1134236) = c_Groups_Oone__class_Oone(_1134234))], (45255 ^ _776545) ^ [_1682869, _1682871] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1682869), _1682871) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682869)), hAPP(c_Code__Numeral_Onat__of, _1682871))))], (42198 ^ _776545) ^ [_1613183, _1613185, _1613187] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613183, _1613183)), hAPP(hAPP(c_Product__Type_OPair(_1613183, _1613183), 42199 ^ [_1613183, _1613185, _1613187]), 42199 ^ [_1613183, _1613185, _1613187])), _1613185))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613183), tc_List_Olist(_1613183))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613183), tc_List_Olist(_1613183)), _1613187), _1613187)), c_List_Olexord(_1613183, _1613185)))], (938 ^ _776545) ^ [_790616, _790618, _790620, _790622] : [-(c_Wellfounded_Owf(_790620, _790616)), c_Wellfounded_Owf(_790622, _790618), _790622 = _790620, _790618 = _790616], (17679 ^ _776545) ^ [_1094857, _1094859] : [class_Groups_Oordered__ab__group__add(_1094857), 17682 ^ _776545 : [(17689 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094857), c_Groups_Ozero__class_Ozero(_1094857)), _1094859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094857), hAPP(c_Groups_Ouminus__class_Ouminus(_1094857), _1094859)), c_Groups_Ozero__class_Ozero(_1094857))))], (17683 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094857), hAPP(c_Groups_Ouminus__class_Ouminus(_1094857), _1094859)), c_Groups_Ozero__class_Ozero(_1094857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094857), c_Groups_Ozero__class_Ozero(_1094857)), _1094859)))]]], (27725 ^ _776545) ^ [_1275238, _1275240, _1275242] : [class_Fields_Olinordered__field__inverse__zero(_1275238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275238), c_Groups_Ozero__class_Ozero(_1275238)), _1275240)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275238), hAPP(c_Groups_Oabs__class_Oabs(_1275238), _1275242)), _1275240) = hAPP(c_Groups_Oabs__class_Oabs(_1275238), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275238), _1275242), _1275240)))], (1384 ^ _776545) ^ [_796709, _796711] : [-(class_Lattices_Osemilattice__sup(_796709)), _796711 = _796709, class_Lattices_Osemilattice__sup(_796711)], (830 ^ _776545) ^ [_788970, _788972, _788974, _788976] : [-(c_Predicate_Otransp(_788974, _788970)), c_Predicate_Otransp(_788976, _788972), _788976 = _788974, _788972 = _788970], (45690 ^ _776545) ^ [_1693201, _1693203] : [_1693201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1693203, _1693201, c_List_Olist_ONil(_1693203)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1693203)), c_List_Olist_ONil(_1693203)), c_List_Olist_ONil(tc_List_Olist(_1693203))))], (38594 ^ _776545) ^ [_1517804, _1517806, _1517808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517804, tc_HOL_Obool)), _1517806), hAPP(hAPP(c_Set_Oinsert(_1517804), _1517808), c_Orderings_Obot__class_Obot(tc_fun(_1517804, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1517804, _1517808, _1517806) = _1517808)], (46375 ^ _776545) ^ [_1709185, _1709187, _1709189, _1709191] : [-(c_List_Oupt(_1709185, _1709187) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1709189), _1709191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1709185), _1709187)), _1709185 = _1709189, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1709185), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1709187) = _1709191], (33669 ^ _776545) ^ [_1398464, _1398466, _1398468, _1398470] : [class_Groups_Ocomm__monoid__add(_1398464), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1398464), _1398466), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398468)), hAPP(c_Nat_OSuc, _1398470))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1398464), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1398464, tc_Nat_Onat), _1398466), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1398468), _1398470)))], (33855 ^ _776545) ^ [_1403791, _1403793, _1403795, _1403797] : [class_Groups_Ocomm__monoid__mult(_1403791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403793), _1403795)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1403793, _1403791), hAPP(c_COMBK(_1403791, _1403793), _1403797)), _1403795) = hAPP(hAPP(c_Power_Opower__class_Opower(_1403791), _1403797), hAPP(c_Finite__Set_Ocard(_1403793), _1403795)))], (43214 ^ _776545) ^ [_1637510, _1637512, _1637514, _1637516] : [-(hAPP(hAPP(c_List_Otake(_1637510), _1637512), hAPP(hAPP(c_List_Olist_OCons(_1637510), _1637514), _1637516)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1637510), c_List_Olist_ONil(_1637510), hAPP(hAPP(c_COMBB(tc_List_Olist(_1637510), tc_List_Olist(_1637510), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1637510), _1637514)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1637510), tc_List_Olist(_1637510)), c_List_Otake(_1637510)), _1637516)), _1637512))], (27593 ^ _776545) ^ [_1272873, _1272875] : [class_Int_Onumber__ring(_1272873), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272873), _1272875), hAPP(c_Int_Onumber__class_Onumber__of(_1272873), c_Int_OPls)) = _1272875)], (14877 ^ _776545) ^ [_1044836, _1044838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044836), _1044838)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044838), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044838), _1044836)) = _1044836)], (3040 ^ _776545) ^ [_821662, _821664, _821666, _821668, _821670, _821672, _821674, _821676, _821678, _821680, _821682, _821684] : [-(c_Product__Type_Omap__pair(_821684, _821680, _821676, _821672, _821668, _821664) = c_Product__Type_Omap__pair(_821682, _821678, _821674, _821670, _821666, _821662)), _821684 = _821682, _821680 = _821678, _821676 = _821674, _821672 = _821670, _821668 = _821666, _821664 = _821662], (12766 ^ _776545) ^ [_1001760, _1001762, _1001764, _1001766, _1001768] : [c_Finite__Set_Ofolding__one__idem(_1001760, _1001762, _1001764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001760), _1001766)), -(hAPP(_1001764, hAPP(hAPP(c_Set_Oinsert(_1001760), _1001768), _1001766)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001760, _1001760, _1001762), _1001768), _1001766))], (21759 ^ _776545) ^ [_1170717, _1170719, _1170721, _1170723] : [class_Fields_Olinordered__field__inverse__zero(_1170717), class_Int_Onumber(_1170717), 21766 ^ _776545 : [(21767 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170717), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))), _1170723)), 21770 ^ _776545 : [(21777 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)))), 21780 ^ _776545 : [(21787 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)), c_Groups_Ozero__class_Ozero(_1170717)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), _1170723)))], (21781 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)), c_Groups_Ozero__class_Ozero(_1170717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170717), _1170723), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))), _1170719)))]]], (21771 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), _1170719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170717), _1170723), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)))))]]], (21793 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1170717), _1170719), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))), _1170723))), 21796 ^ _776545 : [(21799 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), _1170719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170717), _1170723), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))))], (21797 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))))]], 21800 ^ _776545 : [(21803 ^ _776545) ^ [] : [21804 ^ _776545 : [(21807 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170717), _1170723), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721))), _1170719))], (21805 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)), c_Groups_Ozero__class_Ozero(_1170717))))]], 21808 ^ _776545 : [(21811 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), _1170723))], (21809 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)), c_Groups_Ozero__class_Ozero(_1170717)))]]], (21801 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170717), c_Groups_Ozero__class_Ozero(_1170717)), hAPP(c_Int_Onumber__class_Onumber__of(_1170717), _1170721)))]]]]], (340 ^ _776545) ^ [_781657, _781659, _781661, _781663, _781665, _781667, _781669, _781671] : [-(c_Finite__Set_Ofolding(_781669, _781665, _781661, _781657)), c_Finite__Set_Ofolding(_781671, _781667, _781663, _781659), _781671 = _781669, _781667 = _781665, _781663 = _781661, _781659 = _781657], (34540 ^ _776545) ^ [_1419744, _1419746, _1419748, _1419750, _1419752, _1419754, _1419756] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419744, tc_fun(_1419746, tc_fun(_1419748, tc_HOL_Obool))), _1419750), _1419752), _1419754), _1419756))), 34541 ^ _776545 : [(34542 ^ _776545) ^ [_1419829] : [hBOOL(hAPP(hAPP(c_member(_1419744), _1419829), _1419750)), hBOOL(hAPP(hAPP(hAPP(_1419752, _1419829), _1419754), _1419756))]]], (42630 ^ _776545) ^ [_1625275, _1625277] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1625275, _1625277) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1625275), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1625277)))], (15876 ^ _776545) ^ [_1063946, _1063948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1063948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063946), _1063948))))], (49646 ^ _776545) ^ [_1779801, _1779803, _1779805, _1779807, _1779809, _1779811] : [-(c_Partial__Function_Ofun__lub(_1779801, _1779803, _1779805, _1779807, _1779809, _1779811) = hAPP(_1779807, hAPP(c_Set_OCollect(_1779801), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool), tc_HOL_Obool, _1779801), c_HOL_OEx(tc_fun(_1779805, _1779801))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool), tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool), _1779801), hAPP(c_COMBS(tc_fun(_1779805, _1779801), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779805, _1779801)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779805, _1779801), tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779805, _1779801))), _1779809)))), hAPP(hAPP(c_COMBC(_1779801, tc_fun(tc_fun(_1779805, _1779801), _1779801), tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779801, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779805, _1779801), _1779801), tc_fun(tc_fun(_1779805, _1779801), tc_HOL_Obool)), _1779801), c_COMBB(_1779801, tc_HOL_Obool, tc_fun(_1779805, _1779801))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779805, _1779801), _1779805, _1779801), c_COMBI(tc_fun(_1779805, _1779801))), _1779811)))))))], (28445 ^ _776545) ^ [_1287089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1287089), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1287089)), c_Int_OMin)))], (47975 ^ _776545) ^ [_1742859, _1742861] : [class_Enum_Oenum(_1742859), 47978 ^ _776545 : [(47986 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742859), _1742861)), 47989 ^ _776545 : [(47990 ^ _776545) ^ [_1743077] : [-(hBOOL(hAPP(_1742861, _1743077)))]]], (47979 ^ _776545) ^ [] : [hBOOL(hAPP(_1742861, 47980 ^ [_1742859, _1742861])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1742859), _1742861)))]]], (29797 ^ _776545) ^ [_1310795] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1310795)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1310795)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44569 ^ _776545) ^ [_1668041, _1668043, _1668045] : [_1668041 = c_List_Olist_ONil(_1668043), -(c_List_Olast(_1668043, hAPP(hAPP(c_List_Olist_OCons(_1668043), _1668045), _1668041)) = _1668045)], (26304 ^ _776545) ^ [_1251536, _1251538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251538)), 26311 ^ _776545 : [(26318 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251536), _1251538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251536)), hAPP(c_Int_Onat, _1251538))))], (26312 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251536)), hAPP(c_Int_Onat, _1251538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251536), _1251538)))]]], (27783 ^ _776545) ^ [_1276175] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276175) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276175), c_Int_OPls)))], (18506 ^ _776545) ^ [_1109577, _1109579, _1109581] : [class_Rings_Olinordered__idom(_1109577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109577), c_Groups_Ozero__class_Ozero(_1109577)), _1109579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109577), c_Groups_Ozero__class_Ozero(_1109577)), _1109581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109577), _1109581), c_Groups_Oone__class_Oone(_1109577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109577), _1109579), _1109581)), _1109579)))], (50129 ^ _776545) ^ [_1789427, _1789429, _1789431, _1789433, _1789435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789427, tc_HOL_Obool)), _1789429), hAPP(c_Set_Oimage(_1789431, _1789427, _1789433), _1789435))), -(c_Fun_Oinj__on(_1789427, _1789431, c_Hilbert__Choice_Oinv__into(_1789431, _1789427, _1789435, _1789433), _1789429))], (48460 ^ _776545) ^ [_1752866, _1752868, _1752870, _1752872, _1752874] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1752866), _1752868), _1752870), _1752872), _1752874) = c_New__DSequence_Opos__single(_1752866, _1752868))], (33531 ^ _776545) ^ [_1393548, _1393550, _1393552, _1393554] : [-(_1393548 = c_Orderings_Obot__class_Obot(tc_fun(_1393550, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393550, tc_fun(_1393552, tc_HOL_Obool)), _1393548), hAPP(c_COMBK(tc_fun(_1393552, tc_HOL_Obool), _1393550), _1393554)) = _1393554)], (45666 ^ _776545) ^ [_1692502, _1692504] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1692502))), c_Enum_Osublists(_1692502, _1692504)) = 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(_1692502)), _1692504)))], (28457 ^ _776545) ^ [_1287297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1287297), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1287297)), c_Int_OMin)))], (32426 ^ _776545) ^ [_1360162, _1360164, _1360166, _1360168, _1360170] : [_1360162 = c_Orderings_Obot__class_Obot(tc_fun(_1360164, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360166, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360164, tc_fun(_1360166, tc_HOL_Obool)), _1360162), _1360168)), _1360170) = _1360170)], (52185 ^ _776545) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (27623 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (45393 ^ _776545) ^ [_1686256, _1686258, _1686260] : [45395 ^ _776545 : [(45398 ^ _776545) ^ [] : [hBOOL(hAPP(_1686258, 45394 ^ [_1686256, _1686258, _1686260]))], (45396 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686256), 45394 ^ [_1686256, _1686258, _1686260]), hAPP(c_List_Oset(_1686256), _1686260))))]], -(hBOOL(hAPP(c_List_Olistsp(_1686256, _1686258), _1686260)))], (234 ^ _776545) ^ [_780260, _780262] : [-(class_Fields_Olinordered__field(_780260)), _780262 = _780260, class_Fields_Olinordered__field(_780262)], (47022 ^ _776545) ^ [_1721621, _1721623, _1721625, _1721627] : [-(hAPP(c_List_Orev(_1721621), hAPP(hAPP(c_List_Omap(_1721623, _1721621), _1721625), _1721627)) = hAPP(hAPP(c_List_Omap(_1721623, _1721621), _1721625), hAPP(c_List_Orev(_1721623), _1721627)))], (10687 ^ _776545) ^ [_960471, _960473] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960471, tc_HOL_Obool)), _960473), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960471, tc_HOL_Obool)), _960473)) = c_Orderings_Obot__class_Obot(tc_fun(_960471, tc_HOL_Obool)))], (45317 ^ _776545) ^ [_1684711, _1684713, _1684715, _1684717] : [hBOOL(hAPP(c_List_Olistsp(_1684711, _1684713), hAPP(hAPP(c_List_Oappend(_1684711), _1684715), _1684717))), 45320 ^ _776545 : [(45323 ^ _776545) ^ [] : 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023912), _1023914), _1023916)), _1023918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023912), _1023920), _1023916)), _1023922), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023912), _1023914), _1023920)), _1023916)), _1023918) = _1023922)]]], (38270 ^ _776545) ^ [_1509460, _1509462, _1509464] : [c_Wellfounded_Owf(_1509460, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509460, _1509460), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509460, _1509460), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509460, _1509460, _1509460), _1509462), _1509462)), hAPP(hAPP(c_Relation_Orel__comp(_1509460, _1509460, _1509460), _1509464), _1509462))), _1509464)), -(c_Wellfounded_Owf(_1509460, 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c_Groups_Oone__class_Oone(_1290739)), hAPP(c_Int_Onumber__class_Onumber__of(_1290739), _1290741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1290741)))]]], (28969 ^ _776545) ^ [_1295864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295864), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1295864)), c_Int_OPls)))], (10653 ^ _776545) ^ [_959781, _959783, _959785] : [class_Lattices_Oboolean__algebra(_959781), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959781), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959781), _959783), _959785)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959781), hAPP(c_Groups_Ouminus__class_Ouminus(_959781), _959783)), hAPP(c_Groups_Ouminus__class_Ouminus(_959781), _959785)))], (2320 ^ _776545) ^ [_810358, _810360, _810362, _810364, _810366, _810368, _810370, _810372] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810372, _810368, _810364, _810360) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810370, _810366, _810362, _810358)), _810372 = _810370, _810368 = _810366, _810364 = _810362, _810360 = _810358], (37000 ^ _776545) ^ [_1479678, _1479680, _1479682, _1479684] : [c_Equiv__Relations_Oequivp(_1479678, _1479680), hBOOL(hAPP(hAPP(_1479680, _1479682), _1479684)), -(hBOOL(hAPP(hAPP(_1479680, _1479684), _1479682)))], (38440 ^ _776545) ^ [_1513450] : [-(c_Nitpick_Oone__frac(_1513450) = c_Nitpick_OAbs__Frac(_1513450, 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))))], (36366 ^ _776545) ^ [_1463522, _1463524, _1463526, _1463528] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463522), _1463524)), 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)), _1463522), _1463526)), 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)), _1463524), _1463528)), 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)), _1463524), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1463526), _1463528))), c_FunDef_Omin__strict)))], (15322 ^ _776545) ^ [_1053045, _1053047] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1053045, _1053047)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053047), _1053045))], (3534 ^ _776545) ^ [_829381, _829383] : [_829383 = _829381, -(c_SetInterval_Oord__class_OlessThan(_829383) = c_SetInterval_Oord__class_OlessThan(_829381))], (41777 ^ _776545) ^ [_1600071, _1600073, _1600075] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600071)), hAPP(hAPP(c_List_Olist_OCons(_1600071), _1600073), _1600075)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600071)), _1600075)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4802 ^ _776545) ^ [_849665, _849667, _849669, _849671] : [-(c_List_Olexord(_849671, _849667) = c_List_Olexord(_849669, _849665)), _849671 = _849669, _849667 = _849665], (34964 ^ _776545) ^ [_1428874, _1428876] : [-(_1428874 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1428876, _1428874) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428876), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428874)))], (51993 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (45926 ^ _776545) ^ [_1697790, _1697792] : [c_List_Olist_ONil(_1697790) = c_List_Oconcat(_1697790, _1697792), 45929 ^ _776545 : [(45930 ^ _776545) ^ [_1697881] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697790)), _1697881), hAPP(c_List_Oset(tc_List_Olist(_1697790)), _1697792))), -(_1697881 = c_List_Olist_ONil(_1697790))]]], (50369 ^ _776545) ^ [_1794915, _1794917, _1794919, _1794921, _1794923, _1794925, _1794927, _1794929] : [c_Fun_Obij__betw(_1794915, _1794917, _1794919, _1794921, _1794923), c_Fun_Obij__betw(_1794917, _1794925, _1794927, _1794923, _1794929), -(c_Fun_Obij__betw(_1794915, _1794925, hAPP(c_Fun_Ocomp(_1794917, _1794925, _1794915, _1794927), _1794919), _1794921, _1794929))], (46824 ^ _776545) ^ [_1717421, _1717423] : [class_Orderings_Olinorder(_1717421), hBOOL(hAPP(c_Finite__Set_Ofinite(_1717421), _1717423)), 46831 ^ _776545 : [(46836 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1717421), c_List_Olinorder__class_Osorted__list__of__set(_1717421, _1717423))))], (46834 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1717421, c_List_Olinorder__class_Osorted__list__of__set(_1717421, _1717423)))], (46832 ^ _776545) ^ [] : [-(hAPP(c_List_Oset(_1717421), c_List_Olinorder__class_Osorted__list__of__set(_1717421, _1717423)) = _1717423)]]], (27447 ^ _776545) ^ [_1270129, _1270131, _1270133, _1270135, _1270137] : [class_Rings_Olinordered__idom(_1270129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270129), hAPP(c_Groups_Oabs__class_Oabs(_1270129), _1270131)), _1270133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270129), hAPP(c_Groups_Oabs__class_Oabs(_1270129), _1270135)), _1270137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270129), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270129), hAPP(c_Groups_Oabs__class_Oabs(_1270129), _1270131)), hAPP(c_Groups_Oabs__class_Oabs(_1270129), _1270135))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270129), _1270133), _1270137))))], (39069 ^ _776545) ^ [_1529070, _1529072, _1529074, _1529076, _1529078, _1529080] : [class_Groups_Ocomm__monoid__add(_1529070), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529072, _1529070), hAPP(hAPP(c_COMBC(_1529072, tc_fun(_1529074, tc_HOL_Obool), _1529070), hAPP(hAPP(c_COMBB(tc_fun(_1529074, _1529070), tc_fun(tc_fun(_1529074, tc_HOL_Obool), _1529070), _1529072), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529074, _1529070)), _1529076)), _1529078)), _1529080) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1529072, _1529074), _1529070), hAPP(c_Product__Type_Oprod_Oprod__case(_1529072, _1529074, _1529070), _1529076)), hAPP(hAPP(c_Product__Type_OSigma(_1529072, _1529074), _1529080), hAPP(c_COMBK(tc_fun(_1529074, tc_HOL_Obool), _1529072), _1529078))))], (46335 ^ _776545) ^ [_1708431, _1708433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708431), _1708433)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1708431, _1708433)) = _1708431)], (43412 ^ _776545) ^ [_1642055, _1642057, _1642059, _1642061, _1642063] : [-(hAPP(hAPP(c_List_Olist_OCons(_1642055), _1642057), _1642059) = hAPP(hAPP(c_List_Oappend(_1642055), _1642061), _1642063)), 43413 ^ _776545 : [(43420 ^ _776545) ^ [_1642238] : [hAPP(hAPP(c_List_Olist_OCons(_1642055), _1642057), _1642238) = _1642061, _1642059 = hAPP(hAPP(c_List_Oappend(_1642055), _1642238), _1642063)], (43414 ^ _776545) ^ [] : [_1642061 = c_List_Olist_ONil(_1642055), hAPP(hAPP(c_List_Olist_OCons(_1642055), _1642057), _1642059) = _1642063]]], (16256 ^ _776545) ^ [_1070114, _1070116, _1070118] : [class_Rings_Oring__no__zero__divisors(_1070114), 16259 ^ _776545 : [(16260 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070114), _1070116), _1070118) = c_Groups_Ozero__class_Ozero(_1070114), -(_1070116 = c_Groups_Ozero__class_Ozero(_1070114)), -(_1070118 = c_Groups_Ozero__class_Ozero(_1070114))], (16270 ^ _776545) ^ [] : [16271 ^ _776545 : [(16274 ^ _776545) ^ [] : [_1070118 = c_Groups_Ozero__class_Ozero(_1070114)], (16272 ^ _776545) ^ [] : [_1070116 = c_Groups_Ozero__class_Ozero(_1070114)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070114), _1070116), _1070118) = c_Groups_Ozero__class_Ozero(_1070114))]]], (42021 ^ _776545) ^ [_1607885, _1607887, _1607889, _1607891] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607885), tc_List_Olist(_1607885))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607885), tc_List_Olist(_1607885)), _1607887), _1607889)), c_List_Olistrel1(_1607885, _1607891))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607885), tc_List_Olist(_1607885))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607885), tc_List_Olist(_1607885)), _1607887), _1607889)), c_List_Olistrel(_1607885, c_Transitive__Closure_Ortrancl(_1607885, _1607891)))))], (28881 ^ _776545) ^ [_1294312] : [c_Int_OBit0(_1294312) = c_Int_OMin], (42587 ^ _776545) ^ [_1624443, _1624445] : [class_Groups_Ocomm__monoid__add(_1624443), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1624443), _1624445) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1624443), hAPP(c_List_Onth(_1624443), _1624445)), 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(_1624443)), _1624445))))], (13124 ^ _776545) ^ [_1008463, _1008465, _1008467, _1008469, _1008471, _1008473] : [c_Finite__Set_Ofun__left__comm__idem(_1008463, _1008465, _1008467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008463), _1008469)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1008463, _1008465, _1008467), _1008471), hAPP(hAPP(c_Set_Oinsert(_1008463), _1008473), _1008469)) = hAPP(hAPP(c_Finite__Set_Ofold(_1008463, _1008465, _1008467), hAPP(hAPP(_1008467, _1008473), _1008471)), _1008469))], (37260 ^ _776545) ^ [_1485635, _1485637, _1485639, _1485641, _1485643] : [c_Fun_Oinj__on(_1485635, _1485637, _1485639, _1485641), -(c_Fun_Oinj__on(_1485635, _1485637, _1485639, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485635, tc_HOL_Obool)), _1485641), _1485643)))], (31703 ^ _776545) ^ [_1345955, _1345957, _1345959] : [class_Orderings_Olinorder(_1345955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345955), _1345957)), hBOOL(hAPP(hAPP(c_member(_1345955), _1345959), _1345957)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345955), _1345959), c_Big__Operators_Olinorder__class_OMax(_1345955, _1345957)) = c_Big__Operators_Olinorder__class_OMax(_1345955, _1345957))], (39585 ^ _776545) ^ [_1544288, _1544290, _1544292, _1544294, _1544296] : [c_Relation_Orefl__on(_1544288, _1544290, _1544292), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544288, _1544288)), hAPP(hAPP(c_Product__Type_OPair(_1544288, _1544288), _1544294), _1544296)), _1544292)), -(hBOOL(hAPP(hAPP(c_member(_1544288), _1544294), _1544290)))], (52469 ^ _776545) ^ [_1831014, _1831016, _1831018, _1831020, _1831022, _1831024] : [-(hAPP(hAPP(hAPP(c_COMBB(_1831014, _1831016, _1831018), _1831020), _1831022), _1831024) = hAPP(_1831020, hAPP(_1831022, _1831024)))], (24024 ^ _776545) ^ [_1211462, _1211464, _1211466] : [class_Rings_Osemiring__1(_1211462), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211462), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211464), _1211466)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1211462), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211462), _1211464)), _1211466))], (14242 ^ _776545) ^ [_1032780, _1032782, _1032784, _1032786] : [class_Rings_Ocomm__semiring__1(_1032780), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032780), _1032782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032780), _1032784), _1032786)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032780), _1032782), _1032784)), _1032786))], (29295 ^ _776545) ^ [_1301500, _1301502] : [class_Rings_Oring__1(_1301500), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301500), hAPP(c_Groups_Ouminus__class_Ouminus(_1301500), _1301502)), 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(_1301500), _1301502), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44880 ^ _776545) ^ [_1675081, _1675083, _1675085, _1675087, _1675089] : [c_Fun_Oinj__on(_1675081, _1675083, _1675085, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1675081, tc_HOL_Obool)), hAPP(c_List_Oset(_1675081), _1675087)), hAPP(c_List_Oset(_1675081), _1675089))), 44883 ^ _776545 : [(44890 ^ _776545) ^ [] : [_1675087 = _1675089, -(hAPP(hAPP(c_List_Omap(_1675081, _1675083), _1675085), _1675087) = hAPP(hAPP(c_List_Omap(_1675081, _1675083), _1675085), _1675089))], (44884 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Omap(_1675081, _1675083), _1675085), _1675087) = hAPP(hAPP(c_List_Omap(_1675081, _1675083), _1675085), _1675089), -(_1675087 = _1675089)]]], (858 ^ _776545) ^ [_789356, _789358, _789360, _789362, _789364, _789366, _789368, _789370] : [-(c_Fun_Oinj__on(_789368, _789364, _789360, _789356)), c_Fun_Oinj__on(_789370, _789366, _789362, _789358), _789370 = _789368, _789366 = _789364, _789362 = _789360, _789358 = _789356], (12746 ^ _776545) ^ [_1001388, _1001390, _1001392] : [class_Complete__Lattice_Ocomplete__lattice(_1001388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001388), _1001390)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1001388), _1001392), c_Complete__Lattice_OInf__class_OInf(_1001388, _1001390)) = hAPP(hAPP(c_Finite__Set_Ofold(_1001388, _1001388, c_Lattices_Osemilattice__inf__class_Oinf(_1001388)), _1001392), _1001390))], (45758 ^ _776545) ^ [_1694698, _1694700] : [hBOOL(hAPP(c_List_Odistinct(_1694698), _1694700)), -(c_List_Oremdups(_1694698, _1694700) = _1694700)], (584 ^ _776545) ^ [_785343, _785345] : [-(c_List_Onat__list(_785343)), _785345 = _785343, c_List_Onat__list(_785345)], (18786 ^ _776545) ^ [_1114941, _1114943, _1114945, _1114947] : [class_Groups_Ocomm__monoid__add(_1114941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114943), _1114945)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114941), _1114947), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1114943, _1114945)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114941), hAPP(_1114947, _1114943)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1114941), _1114947), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1114943), _1114945))))], (28867 ^ _776545) ^ [_1294089] : [-(c_Int_OBit0(_1294089) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1294089), _1294089))], (19845 ^ _776545) ^ [_1134636, _1134638, _1134640, _1134642] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1134636), _1134638)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134640), _1134642)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1134636, _1134640)), c_Sum__Type_OPlus(_1134636, _1134640, _1134638, _1134642)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1134636), _1134638)), hAPP(c_Finite__Set_Ocard(_1134640), _1134642)))], (6340 ^ _776545) ^ [_878754, _878756, _878758] : [_878754 = _878756, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878758, tc_HOL_Obool)), _878756), _878754)))], (19082 ^ _776545) ^ [_1120379, _1120381] : [class_Rings_Olinordered__idom(_1120379), 19085 ^ _776545 : [(19092 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120379), _1120381), c_Groups_Ozero__class_Ozero(_1120379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120379), _1120381), _1120381)), c_Groups_Ozero__class_Ozero(_1120379))))], (19086 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120379), _1120381), _1120381)), c_Groups_Ozero__class_Ozero(_1120379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120379), _1120381), c_Groups_Ozero__class_Ozero(_1120379))))]]], (23569 ^ _776545) ^ [_1203743, _1203745] : [-(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), _1203743))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203745))))], (45748 ^ _776545) ^ [_1694517, _1694519] : [-(hBOOL(hAPP(c_List_Odistinct(_1694517), c_List_Oremdups(_1694517, _1694519))))], (7692 ^ _776545) ^ [_904938, _904940, _904942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904938, tc_HOL_Obool)), _904940), _904942)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904938, tc_HOL_Obool)), _904940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904938, tc_HOL_Obool)), _904942), _904940)) = _904942)], (48868 ^ _776545) ^ [_1761673, _1761675, _1761677, _1761679, _1761681] : [48870 ^ _776545 : [(48873 ^ _776545) ^ [] : [c_Relation_Orefl__on(_1761677, hAPP(_1761679, 48869 ^ [_1761673, _1761675, _1761677, _1761679, _1761681]), hAPP(_1761681, 48869 ^ [_1761673, _1761675, _1761677, _1761679, _1761681]))], (48871 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1761673), 48869 ^ [_1761673, _1761675, _1761677, _1761679, _1761681]), _1761675)))]], -(c_Relation_Orefl__on(_1761677, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1761673, tc_fun(_1761677, tc_HOL_Obool)), _1761675), _1761679), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1761673, tc_fun(tc_prod(_1761677, _1761677), tc_HOL_Obool)), _1761675), _1761681)))], (2306 ^ _776545) ^ [_810137, _810139, _810141, _810143, _810145, _810147] : [-(c_Nat_Onat_Onat__rec(_810147, _810143, _810139) = c_Nat_Onat_Onat__rec(_810145, _810141, _810137)), _810147 = _810145, _810143 = _810141, _810139 = _810137], (29409 ^ _776545) ^ [_1303541, _1303543] : [class_Rings_Olinordered__idom(_1303541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303541), hAPP(hAPP(c_Power_Opower__class_Opower(_1303541), _1303543), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1303541)))], (43194 ^ _776545) ^ [_1636979, _1636981] : [-(_1636981 = c_List_Olist_ONil(_1636979)), -(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(_1636979)), _1636981))))], (4198 ^ _776545) ^ [_840169, _840171, _840173, _840175] : [-(c_New__DSequence_Opos__single(_840175, _840171) = c_New__DSequence_Opos__single(_840173, _840169)), _840175 = _840173, _840171 = _840169], (42173 ^ _776545) ^ [_1612332, _1612334, _1612336, _1612338] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612332), tc_List_Olist(_1612332))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612332), tc_List_Olist(_1612332)), _1612334), _1612336)), c_List_Olistrel(_1612332, _1612338))), 42176 ^ _776545 : [(42179 ^ _776545) ^ [_1612561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612561), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612332)), _1612334))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612332, _1612332)), hAPP(hAPP(c_Product__Type_OPair(_1612332, _1612332), hAPP(hAPP(c_List_Onth(_1612332), _1612334), _1612561)), hAPP(hAPP(c_List_Onth(_1612332), _1612336), _1612561))), _1612338)))], (42177 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612332)), _1612334) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612332)), _1612336))]]], (26915 ^ _776545) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (23532 ^ _776545) ^ [_1203091, _1203093, _1203095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203091)), 23538 ^ _776545 : [(23541 ^ _776545) ^ [] : [hBOOL(hAPP(_1203093, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23537 ^ [_1203091, _1203093, _1203095]), _1203091)))], (23539 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1203093, 23537 ^ [_1203091, _1203093, _1203095])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203095)), 23546 ^ _776545 : [(23547 ^ _776545) ^ [_1203380] : [hBOOL(hAPP(_1203093, _1203380)), -(hBOOL(hAPP(_1203093, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1203380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203095), _1203091)))))]]], (49706 ^ _776545) ^ [_1781248, _1781250] : [hAPP(c_Relation_Oconverse(_1781248, _1781248), _1781250) = _1781250, -(c_Relation_Osym(_1781248, _1781250))], (43282 ^ _776545) ^ [_1638827, _1638829] : [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), _1638827), _1638829))), 43285 ^ _776545 : [(43292 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638827), _1638829))), -(c_List_Oupto(_1638827, _1638829) = c_List_Olist_ONil(tc_Int_Oint))], (43286 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638827), _1638829)), -(c_List_Oupto(_1638827, _1638829) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1638827), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1638827), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1638829)))]]], (264 ^ _776545) ^ [_780635, _780637, _780639, _780641] : [-(c_Nitpick_Orefl_H(_780639, _780635)), c_Nitpick_Orefl_H(_780641, _780637), _780641 = _780639, _780637 = _780635], (38781 ^ _776545) ^ [_1522226, _1522228, _1522230, _1522232, _1522234] : [c_Fun_Oinj__on(_1522226, _1522228, _1522230, c_Orderings_Otop__class_Otop(tc_fun(_1522226, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522228, tc_HOL_Obool)), _1522232), hAPP(c_Set_Oimage(_1522226, _1522228, _1522230), _1522234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522226, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522226, _1522228, _1522230), _1522232)), _1522234)))], (17759 ^ _776545) ^ [_1096215, _1096217] : [class_Rings_Olinordered__idom(_1096215), 17762 ^ _776545 : [(17769 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096215), _1096217), c_Groups_Ozero__class_Ozero(_1096215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096215), _1096217), hAPP(c_Groups_Ouminus__class_Ouminus(_1096215), _1096217))))], (17763 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096215), _1096217), hAPP(c_Groups_Ouminus__class_Ouminus(_1096215), _1096217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096215), _1096217), c_Groups_Ozero__class_Ozero(_1096215))))]]], (15956 ^ _776545) ^ [_1065394, _1065396] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065394), _1065396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065396), hAPP(c_Nat_OSuc, _1065394))))], (15640 ^ _776545) ^ [_1060236, _1060238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060236), _1060238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060236)), hAPP(c_Nat_OSuc, _1060238))))], (41074 ^ _776545) ^ [_1581710, _1581712, _1581714, _1581716, _1581718] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581712, _1581710)), hAPP(hAPP(c_Product__Type_OPair(_1581712, _1581710), _1581716), _1581714)), _1581718)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581710, _1581712)), hAPP(hAPP(c_Product__Type_OPair(_1581710, _1581712), _1581714), _1581716)), hAPP(c_Relation_Oconverse(_1581712, _1581710), _1581718))))], (25233 ^ _776545) ^ [_1233380, _1233382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233380), _1233382)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233380, _1233382) = _1233380)], (43120 ^ _776545) ^ [_1635653, _1635655] : [_1635655 = c_List_Olist_ONil(_1635653), -(c_Orderings_Obot__class_Obot(tc_fun(_1635653, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635653), _1635655))], (15406 ^ _776545) ^ [_1054804, _1054806, _1054808] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054804), _1054806)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054804), _1054808)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054804), _1054806)), hAPP(c_Finite__Set_Ocard(_1054804), _1054808)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054804, tc_HOL_Obool)), _1054806), _1054808))), hAPP(c_Finite__Set_Ocard(_1054804), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054804, tc_HOL_Obool)), _1054806), _1054808))))], (16290 ^ _776545) ^ [_1070610, _1070612] : [class_Rings_Ocomm__semiring__1(_1070610), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070610), c_Groups_Ozero__class_Ozero(_1070610)), _1070612) = c_Groups_Ozero__class_Ozero(_1070610))], (31555 ^ _776545) ^ [_1343078, _1343080, _1343082, _1343084] : [class_Orderings_Olinorder(_1343078), 31558 ^ _776545 : [(31559 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343078), _1343082), _1343084))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), _1343082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), _1343084)))], (31569 ^ _776545) ^ [] : [31570 ^ _776545 : [(31573 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), _1343084))], (31571 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), _1343082))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343078), _1343080), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343078), _1343082), _1343084))))]]], (16212 ^ _776545) ^ [_1069481, _1069483, _1069485] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1069481), 16215 ^ _776545 : [(16222 ^ _776545) ^ [] : [_1069485 = c_Groups_Ozero__class_Ozero(_1069481), -(_1069483 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069481), _1069483), _1069485))], (16216 ^ _776545) ^ [] : [_1069483 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069481), _1069483), _1069485), -(_1069485 = c_Groups_Ozero__class_Ozero(_1069481))]]], (1854 ^ _776545) ^ [_802584, _802586] : [-(class_Power_Opower(_802584)), _802586 = _802584, class_Power_Opower(_802586)], (39914 ^ _776545) ^ [_1553357, _1553359, _1553361, _1553363, _1553365, _1553367] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553357, _1553359, _1553361, _1553363), _1553365), _1553367) = hAPP(_1553363, hAPP(_1553365, _1553367)))], (7522 ^ _776545) ^ [_900524, _900526, _900528, _900530] : [hBOOL(hAPP(hAPP(c_member(_900524), _900526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900524, tc_HOL_Obool)), _900528), _900530))), 7525 ^ _776545 : [(7528 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900524), _900526), _900530))], (7526 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900524), _900526), _900528)))]]], (8671 ^ _776545) ^ [_925543, _925545, _925547, _925549] : [class_Lattices_Osemilattice__inf(_925543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925543), _925545), _925547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925543), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925543), _925549), _925545)), _925547)))], (3706 ^ _776545) ^ [_832123, _832125] : [_832125 = _832123, -(c_List_Oreturn__list(_832125) = c_List_Oreturn__list(_832123))], (6503 ^ _776545) ^ [_881610, _881612] : [-(hBOOL(hAPP(_881612, 6504 ^ [_881610, _881612]))), -(hAPP(c_Set_OCollect(_881610), _881612) = c_Orderings_Obot__class_Obot(tc_fun(_881610, tc_HOL_Obool)))], (45277 ^ _776545) ^ [_1683231, _1683233, _1683235, _1683237, _1683239] : [c_List_Opartition(_1683231, _1683233, _1683235) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683231), tc_List_Olist(_1683231)), _1683237), _1683239), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1683231, tc_HOL_Obool)), hAPP(c_List_Oset(_1683231), _1683237)), hAPP(c_List_Oset(_1683231), _1683239)) = hAPP(c_List_Oset(_1683231), _1683235))], (2206 ^ _776545) ^ [_808591, _808593, _808595, _808597, _808599, _808601] : [-(c_Random_Ominus__shift(_808601, _808597, _808593) = c_Random_Ominus__shift(_808599, _808595, _808591)), _808601 = _808599, _808597 = _808595, _808593 = _808591], (41479 ^ _776545) ^ [_1591623, _1591625, _1591627, _1591629] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591623, _1591623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1591625), _1591627)), _1591629) = hAPP(c_Fun_Ocomp(_1591623, _1591623, _1591623, hAPP(hAPP(c_Nat_Ocompow(_1591623, _1591623), _1591625), _1591629)), hAPP(hAPP(c_Nat_Ocompow(_1591623, _1591623), _1591627), _1591629)))], (52071 ^ _776545) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52497 ^ _776545) ^ [_1831469] : [-(hBOOL(_1831469)), -(hBOOL(hAPP(c_fNot, _1831469)))], (37646 ^ _776545) ^ [_1493317] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1493317)), c_Int_OInteg)))], (462 ^ _776545) ^ [_783488, _783490, _783492, _783494, _783496, _783498] : [-(c_Nitpick_Oless__eq__frac(_783496, _783492, _783488)), c_Nitpick_Oless__eq__frac(_783498, _783494, _783490), _783498 = _783496, _783494 = _783492, _783490 = _783488], (10689 ^ _776545) ^ [_960520, _960522] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960520, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960520, tc_HOL_Obool)), _960522)), _960522) = c_Orderings_Obot__class_Obot(tc_fun(_960520, tc_HOL_Obool)))], (39743 ^ _776545) ^ [_1548755, _1548757, _1548759, _1548761] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548755, tc_fun(_1548757, tc_HOL_Obool)), _1548759), _1548761) = hAPP(c_Set_OCollect(_1548757), hAPP(hAPP(c_COMBB(tc_fun(_1548755, tc_HOL_Obool), tc_HOL_Obool, _1548757), c_HOL_OAll(_1548755)), hAPP(hAPP(c_COMBB(tc_fun(_1548755, tc_HOL_Obool), tc_fun(_1548755, tc_HOL_Obool), _1548757), hAPP(c_COMBS(_1548755, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548755), c_fimplies), hAPP(hAPP(c_COMBC(_1548755, tc_fun(_1548755, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548755)), _1548759)))), hAPP(hAPP(c_COMBC(_1548757, tc_fun(_1548755, tc_fun(_1548757, tc_HOL_Obool)), tc_fun(_1548755, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1548757, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1548755, tc_fun(_1548757, tc_HOL_Obool)), tc_fun(_1548755, tc_HOL_Obool)), _1548757), c_COMBB(tc_fun(_1548757, tc_HOL_Obool), tc_HOL_Obool, _1548755)), c_member(_1548757))), _1548761)))))], (7224 ^ _776545) ^ [_894312, _894314, _894316] : [-(hBOOL(hAPP(hAPP(c_member(_894312), _894314), hAPP(hAPP(c_Set_Oinsert(_894312), _894314), _894316))))], (44104 ^ _776545) ^ [_1658806, _1658808, _1658810] : [-(hAPP(c_List_Ohd(_1658806), hAPP(hAPP(c_List_Olist_OCons(_1658806), _1658808), _1658810)) = _1658808)], (20783 ^ _776545) ^ [_1151766, _1151768, _1151770, _1151772, _1151774] : [class_Fields_Ofield(_1151766), -(_1151768 = c_Groups_Ozero__class_Ozero(_1151766)), -(_1151770 = c_Groups_Ozero__class_Ozero(_1151766)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151766), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151766), _1151772), _1151768)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151766), _1151774), _1151770)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151766), _1151772), _1151770)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151766), _1151774), _1151768))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151766), _1151768), _1151770)))], (44411 ^ _776545) ^ [_1664714, _1664716] : [class_Complete__Lattice_Ocomplete__lattice(_1664714), -(c_Complete__Lattice_OSup__class_OSup(_1664714, hAPP(c_List_Oset(_1664714), _1664716)) = hAPP(c_List_Ofoldl(_1664714, _1664714, c_Lattices_Osemilattice__sup__class_Osup(_1664714), c_Orderings_Obot__class_Obot(_1664714)), _1664716))], (29683 ^ _776545) ^ [_1308716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1308716)), -(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), _1308716), 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)))))))], (37088 ^ _776545) ^ [_1481376, _1481378, _1481380, _1481382, _1481384, _1481386, _1481388, _1481390, _1481392] : [c_Equiv__Relations_Oequiv(_1481376, _1481378, _1481380), c_Equiv__Relations_Oequiv(_1481382, _1481384, _1481386), c_Equiv__Relations_Ocongruent2(_1481376, _1481382, tc_fun(_1481388, tc_HOL_Obool), _1481380, _1481386, _1481390), hBOOL(hAPP(hAPP(c_member(_1481382), _1481392), _1481384)), -(c_Equiv__Relations_Ocongruent(_1481376, tc_fun(_1481388, tc_HOL_Obool), _1481380, hAPP(hAPP(c_COMBB(tc_fun(_1481382, tc_fun(_1481388, tc_HOL_Obool)), tc_fun(_1481388, tc_HOL_Obool), _1481376), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481382, tc_fun(_1481388, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1481382, _1481382, _1481386), hAPP(hAPP(c_Set_Oinsert(_1481382), _1481392), c_Orderings_Obot__class_Obot(tc_fun(_1481382, tc_HOL_Obool)))))), _1481390)))], (14136 ^ _776545) ^ [_1030391, _1030393, _1030395, _1030397, _1030399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030391), _1030393)), 14139 ^ _776545 : [(14146 ^ _776545) ^ [] : [_1030397 = 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), _1030393), _1030391)), _1030395)), _1030399), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030391), _1030395)), _1030397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030393), _1030395)), _1030399))], (14140 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030391), _1030395)), _1030397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030393), _1030395)), _1030399), -(_1030397 = 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), _1030393), _1030391)), _1030395)), _1030399))]]], (27899 ^ _776545) ^ [_1278116, _1278118] : [class_Int_Onumber__ring(_1278116), class_Rings_Olinordered__idom(_1278116), 27906 ^ _776545 : [(27913 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1278118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278116), c_Groups_Ozero__class_Ozero(_1278116)), hAPP(c_Int_Onumber__class_Onumber__of(_1278116), _1278118))))], (27907 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278116), c_Groups_Ozero__class_Ozero(_1278116)), hAPP(c_Int_Onumber__class_Onumber__of(_1278116), _1278118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1278118)))]]], (42839 ^ _776545) ^ [_1630020, _1630022, _1630024, _1630026] : [hBOOL(hAPP(c_List_Odistinct(_1630020), _1630022)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1630024, _1630020)), hAPP(hAPP(c_List_Ozip(_1630024, _1630020), _1630026), _1630022))))], (33685 ^ _776545) ^ [_1398995, _1398997, _1398999, _1399001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1398995, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398997, tc_fun(tc_fun(_1398995, tc_HOL_Obool), tc_HOL_Obool)), _1398999), hAPP(hAPP(c_COMBB(tc_fun(_1398995, tc_HOL_Obool), tc_fun(tc_fun(_1398995, tc_HOL_Obool), tc_HOL_Obool), _1398997), c_Set_OPow(_1398995)), _1399001))), hAPP(c_Set_OPow(_1398995), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398997, tc_fun(_1398995, tc_HOL_Obool)), _1398999), _1399001)))))], (8123 ^ _776545) ^ [_914932, _914934, _914936, _914938] : [class_Orderings_Oorder(_914932), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914932, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914932, _914934, _914936)), c_SetInterval_Oord__class_OgreaterThanAtMost(_914932, _914936, _914938)) = c_Orderings_Obot__class_Obot(tc_fun(_914932, tc_HOL_Obool)))], (43028 ^ _776545) ^ [_1634135, _1634137, _1634139] : [-(_1634135 = c_List_Olist_ONil(_1634137)), -(c_List_Obutlast(_1634137, hAPP(hAPP(c_List_Olist_OCons(_1634137), _1634139), _1634135)) = hAPP(hAPP(c_List_Olist_OCons(_1634137), _1634139), c_List_Obutlast(_1634137, _1634135)))], (43304 ^ _776545) ^ [_1639141] : [-(c_List_Olistset(_1639141, c_List_Olist_ONil(tc_fun(_1639141, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639141)), c_List_Olist_ONil(_1639141)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639141), tc_HOL_Obool))))], (32093 ^ _776545) ^ [_1353162, _1353164, _1353166] : [class_Orderings_Olinorder(_1353162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353162), _1353164)), -(hBOOL(hAPP(hAPP(c_member(_1353162), _1353166), _1353164))), -(_1353164 = c_Orderings_Obot__class_Obot(tc_fun(_1353162, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1353162, c_Orderings_Oord__class_Omax(_1353162), hAPP(hAPP(c_Set_Oinsert(_1353162), _1353166), _1353164)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353162), _1353166), c_Big__Operators_Olattice_OSup__fin(_1353162, c_Orderings_Oord__class_Omax(_1353162), _1353164)))], (48370 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44471 ^ _776545) ^ [_1666072, _1666074] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1666072), hAPP(c_List_Oset(tc_Nat_Onat), _1666074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1666072), 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)), _1666074))))], (45299 ^ _776545) ^ [_1683782, _1683784] : [-(c_List_Opartition(_1683782, _1683784, c_List_Olist_ONil(_1683782)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683782), tc_List_Olist(_1683782)), c_List_Olist_ONil(_1683782)), c_List_Olist_ONil(_1683782)))], (43034 ^ _776545) ^ [_1634214, _1634216, _1634218] : [c_List_Olist_ONil(_1634214) = hAPP(hAPP(c_List_Olist_OCons(_1634214), _1634216), _1634218)], (51713 ^ _776545) ^ [_1822364, _1822366] : [-(_1822364 = _1822366), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822364), _1822366)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822366), _1822364))], (15202 ^ _776545) ^ [_1050837, _1050839, _1050841] : [class_Rings_Olinordered__semidom(_1050837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050837), c_Groups_Oone__class_Oone(_1050837)), _1050839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050837), c_Groups_Oone__class_Oone(_1050837)), _1050841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050837), c_Groups_Oone__class_Oone(_1050837)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050837), _1050839), _1050841))))], (42545 ^ _776545) ^ [_1623300, _1623302, _1623304, _1623306, _1623308, _1623310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623300, _1623302)), hAPP(hAPP(c_Product__Type_OPair(_1623300, _1623302), _1623304), _1623306)), hAPP(c_List_Oset(tc_prod(_1623300, _1623302)), hAPP(hAPP(c_List_Ozip(_1623300, _1623302), _1623308), _1623310)))), -(hBOOL(hAPP(hAPP(c_member(_1623302), _1623306), hAPP(c_List_Oset(_1623302), _1623310))))], (48490 ^ _776545) ^ [_1753633] : [-(c_Predicate_Oconversep(_1753633, _1753633, c_fequal) = c_fequal)], (22303 ^ _776545) ^ [_1180872, _1180874] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1180872)), _1180874) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180872), _1180874)))], (48877 ^ _776545) ^ [_1761959, _1761961, _1761963] : [hBOOL(hAPP(hAPP(c_List_Omember(_1761959), _1761961), _1761963)), -(hBOOL(hAPP(hAPP(c_member(_1761959), _1761963), hAPP(c_List_Oset(_1761959), _1761961))))], (33675 ^ _776545) ^ [_1398635, _1398637, _1398639, _1398641] : [class_Rings_Osemiring__1(_1398635), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1398635), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398637, tc_Nat_Onat), _1398639), _1398641)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398637, _1398635), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1398635, _1398637), c_Nat_Osemiring__1__class_Oof__nat(_1398635)), _1398639)), _1398641))], (9436 ^ _776545) ^ [_938722, _938724, _938726] : [class_Orderings_Oorder(_938722), 9439 ^ _776545 : [(9448 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938722), _938724), _938726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938722), _938724), _938726)), -(_938724 = _938726)], (9440 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938722), _938724), _938726)), 9443 ^ _776545 : [(9446 ^ _776545) ^ [] : [_938724 = _938726], (9444 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938722), _938724), _938726)))]]]]], (11175 ^ _776545) ^ [_970131, _970133, _970135, _970137, _970139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970131, tc_HOL_Obool)), _970133), hAPP(c_Set_Oimage(_970135, _970131, _970137), _970139))), 11179 ^ _776545 : [(11182 ^ _776545) ^ [] : [-(_970133 = hAPP(c_Set_Oimage(_970135, _970131, _970137), 11178 ^ [_970131, _970133, _970135, _970137, _970139]))], (11180 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970135, tc_HOL_Obool)), 11178 ^ [_970131, _970133, _970135, _970137, _970139]), _970139)))]]], (35467 ^ _776545) ^ [_1438105, _1438107, _1438109, _1438111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1438105, _1438105)), hAPP(hAPP(c_Product__Type_OPair(_1438105, _1438105), _1438107), _1438109)), hAPP(c_Wellfounded_Omeasure(_1438105), _1438111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1438111, _1438107)), hAPP(_1438111, _1438109))))], (42775 ^ _776545) ^ [_1628439, _1628441, _1628443, _1628445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628439), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628441)), _1628443))), -(hBOOL(hAPP(hAPP(c_member(_1628441), _1628445), hAPP(c_List_Oset(_1628441), hAPP(hAPP(c_List_Olist__update(_1628441, _1628443), _1628439), _1628445)))))], (49942 ^ _776545) ^ [_1785126, _1785128, _1785130, _1785132, _1785134] : [c_Equiv__Relations_Opart__equivp(_1785126, _1785128), hBOOL(hAPP(hAPP(_1785128, _1785130), _1785132)), hBOOL(hAPP(hAPP(_1785128, _1785132), _1785134)), -(hBOOL(hAPP(hAPP(_1785128, _1785130), _1785134)))], (35817 ^ _776545) ^ [_1445398, _1445400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1445398)), -(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(_1445398), _1445400))), _1445398)))], (39335 ^ _776545) ^ [_1538116, _1538118] : [-(hAPP(c_Fun_Oid(_1538116), _1538118) = _1538118)], (1174 ^ _776545) ^ [_794084, _794086] : [-(class_Rings_Oordered__ring__abs(_794084)), _794086 = _794084, class_Rings_Oordered__ring__abs(_794086)], (42143 ^ _776545) ^ [_1611627, _1611629, _1611631, _1611633] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611627)), hAPP(hAPP(c_List_Olist_OCons(_1611627), _1611629), _1611631)), c_List_Olists(_1611627, _1611633))), 42146 ^ _776545 : [(42149 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611627)), _1611631), c_List_Olists(_1611627, _1611633))))], (42147 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611627), _1611629), _1611633)))]]], (28791 ^ _776545) ^ [_1292812] : [c_Int_OBit0(_1292812) = c_Int_OPls, -(_1292812 = c_Int_OPls)], (29431 ^ _776545) ^ [_1303875, _1303877, _1303879] : [class_Rings_Olinordered__idom(_1303875), 29434 ^ _776545 : [(29443 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303875), hAPP(hAPP(c_Power_Opower__class_Opower(_1303875), _1303877), 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(_1303875), _1303879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1303875)), _1303877 = c_Groups_Ozero__class_Ozero(_1303875), _1303879 = c_Groups_Ozero__class_Ozero(_1303875)], (29435 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303875), hAPP(hAPP(c_Power_Opower__class_Opower(_1303875), _1303877), 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(_1303875), _1303879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1303875), 29438 ^ _776545 : [(29441 ^ _776545) ^ [] : [-(_1303879 = c_Groups_Ozero__class_Ozero(_1303875))], (29439 ^ _776545) ^ [] : [-(_1303877 = c_Groups_Ozero__class_Ozero(_1303875))]]]]], (33212 ^ _776545) ^ [_1385217, _1385219, _1385221] : [class_Orderings_Obot(_1385217), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1385219, _1385217)), _1385221) = c_Orderings_Obot__class_Obot(_1385217))], (49736 ^ _776545) ^ [_1781698] : [-(c_Relation_Osym(_1781698, c_Relation_OId(_1781698)))], (50616 ^ _776545) ^ [_1799693, _1799695, _1799697, _1799699, _1799701] : [c_Fun_Obij__betw(_1799693, _1799695, _1799697, c_Orderings_Otop__class_Otop(tc_fun(_1799693, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799695, tc_HOL_Obool))), 50619 ^ _776545 : [(50626 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799695, tc_HOL_Obool)), _1799699), hAPP(c_Set_Oimage(_1799693, _1799695, _1799697), _1799701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799693, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1799693, _1799695, _1799697), _1799699)), _1799701)))], (50620 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799693, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1799693, _1799695, _1799697), _1799699)), _1799701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799695, tc_HOL_Obool)), _1799699), hAPP(c_Set_Oimage(_1799693, _1799695, _1799697), _1799701))))]]], (42711 ^ _776545) ^ [_1627089, _1627091, _1627093] : [hBOOL(hAPP(hAPP(c_member(_1627089), _1627091), hAPP(c_List_Oset(_1627089), c_List_Obutlast(_1627089, _1627093)))), -(hBOOL(hAPP(hAPP(c_member(_1627089), _1627091), hAPP(c_List_Oset(_1627089), _1627093))))], (26056 ^ _776545) ^ [_1247545, _1247547] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247545), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247547), _1247545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247547), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247547, _1247545)))], (26164 ^ _776545) ^ [_1249299, _1249301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249301)), 26171 ^ _776545 : [(26178 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249299), _1249301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1249299)), hAPP(c_Int_Onat, _1249301))))], (26172 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1249299)), hAPP(c_Int_Onat, _1249301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249299), _1249301)))]]], (12810 ^ _776545) ^ [_1002534, _1002536, _1002538, _1002540] : [class_Lattices_Osemilattice__inf(_1002534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002534), _1002536)), hBOOL(hAPP(hAPP(c_member(_1002534), _1002538), _1002536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002534), hAPP(hAPP(c_Finite__Set_Ofold(_1002534, _1002534, c_Lattices_Osemilattice__inf__class_Oinf(_1002534)), _1002540), _1002536)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1002534), _1002538), _1002540))))], (45842 ^ _776545) ^ [_1696193, _1696195, _1696197] : [-(hBOOL(hAPP(hAPP(c_member(_1696193), _1696195), hAPP(c_List_Oset(_1696193), _1696197)))), -(hAPP(c_List_OremoveAll(_1696193, _1696195), _1696197) = _1696197)], (41877 ^ _776545) ^ [_1603488, _1603490, _1603492, _1603494] : [-(c_List_Olist_Olist__size(_1603488, _1603490, hAPP(hAPP(c_List_Olist_OCons(_1603488), _1603492), _1603494)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1603490, _1603492)), c_List_Olist_Olist__size(_1603488, _1603490, _1603494))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52431 ^ _776545) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (29133 ^ _776545) ^ [_1298704, _1298706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298704), _1298706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298704)), c_Int_OBit1(_1298706))))], (23872 ^ _776545) ^ [_1208975] : [class_Rings_Osemiring__1(_1208975), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208975), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1208975))], (36320 ^ _776545) ^ [_1462695] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462695)), -(_1462695 = 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))), _1462695)), c_FunDef_Omax__strict)))], (47688 ^ _776545) ^ [_1736123, _1736125, _1736127, _1736129, _1736131, _1736133, _1736135, _1736137] : [47690 ^ _776545 : [(47693 ^ _776545) ^ [] : [hAPP(c_Fun_Ocomp(_1736127, _1736127, _1736129, hAPP(_1736131, 47689 ^ [_1736123, _1736125, _1736127, _1736129, _1736131, _1736133, _1736135, _1736137])), _1736133) = hAPP(c_Fun_Ocomp(_1736129, _1736127, _1736129, _1736133), hAPP(_1736135, 47689 ^ [_1736123, _1736125, _1736127, _1736129, _1736131, _1736133, _1736135, _1736137]))], (47691 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736123), 47689 ^ [_1736123, _1736125, _1736127, _1736129, _1736131, _1736133, _1736135, _1736137]), hAPP(c_List_Oset(_1736123), _1736125))))]], -(hAPP(c_List_Ofoldl(_1736127, _1736123, hAPP(c_COMBC(_1736123, _1736127, _1736127), _1736131), hAPP(_1736133, _1736137)), _1736125) = hAPP(_1736133, hAPP(c_List_Ofoldl(_1736129, _1736123, hAPP(c_COMBC(_1736123, _1736129, _1736129), _1736135), _1736137), _1736125)))], (36306 ^ _776545) ^ [_1462414, _1462416, _1462418, _1462420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462414), _1462416)), 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)), _1462418), _1462414)), 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)), _1462420), _1462416)), 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)), _1462418), _1462420)), _1462416)), c_FunDef_Omax__strict)))], (11302 ^ _776545) ^ [_972996, _972998, _973000, _973002, _973004] : [class_Groups_Oab__semigroup__mult(_972996), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972996, _972996, c_Groups_Otimes__class_Otimes(_972996), _972998, _973000), _973002)), -(hBOOL(hAPP(hAPP(c_member(_972996), _972998), _973000))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972996, _972996, c_Groups_Otimes__class_Otimes(_972996), _973004, hAPP(hAPP(c_Set_Oinsert(_972996), _972998), _973000)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972996), _973004), _973002))))], (48368 ^ _776545) ^ [_1750662, _1750664] : [c_List_Olist__ex1(_1750662, _1750664, c_List_Olist_ONil(_1750662))], (14923 ^ _776545) ^ [_1045740, _1045742, _1045744] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045742), _1045744)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045740), _1045742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045740), _1045744)))], (35939 ^ _776545) ^ [_1450143, _1450145, _1450147] : [class_Groups_Olinordered__ab__semigroup__add(_1450143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450143), _1450145)), -(_1450145 = c_Orderings_Obot__class_Obot(tc_fun(_1450143, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450143), _1450147), c_Big__Operators_Olinorder__class_OMin(_1450143, _1450145)) = c_Big__Operators_Olinorder__class_OMin(_1450143, hAPP(c_Set_OCollect(_1450143), hAPP(hAPP(c_COMBB(tc_fun(_1450143, tc_HOL_Obool), tc_HOL_Obool, _1450143), c_HOL_OEx(_1450143)), hAPP(hAPP(c_COMBC(_1450143, tc_fun(_1450143, tc_HOL_Obool), tc_fun(_1450143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1450143, tc_HOL_Obool), tc_fun(_1450143, tc_HOL_Obool)), _1450143), c_COMBS(_1450143, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450143, tc_HOL_Obool), tc_fun(_1450143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1450143), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1450143), c_fconj)), hAPP(hAPP(c_COMBC(_1450143, tc_fun(_1450143, _1450143), tc_fun(_1450143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450143, tc_HOL_Obool), tc_fun(tc_fun(_1450143, _1450143), tc_fun(_1450143, tc_HOL_Obool)), _1450143), c_COMBB(_1450143, tc_HOL_Obool, _1450143)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1450143), _1450147))))), hAPP(hAPP(c_COMBC(_1450143, tc_fun(_1450143, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450143)), _1450145))))))], (5258 ^ _776545) ^ [_856779, _856781, _856783, _856785] : [-(c_List_Oupt(_856785, _856781) = c_List_Oupt(_856783, _856779)), _856785 = _856783, _856781 = _856779], (27851 ^ _776545) ^ [_1277299, _1277301] : [class_Int_Onumber__ring(_1277299), class_Rings_Olinordered__idom(_1277299), 27858 ^ _776545 : [(27865 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277299), hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301)), c_Groups_Ozero__class_Ozero(_1277299)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1277299), hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301)) = hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301))], (27859 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277299), hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301)), c_Groups_Ozero__class_Ozero(_1277299))), -(hAPP(c_Groups_Oabs__class_Oabs(_1277299), hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1277299), hAPP(c_Int_Onumber__class_Onumber__of(_1277299), _1277301)))]]], (28751 ^ _776545) ^ [_1291914, _1291916] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291914))), _1291916) = 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)))), _1291914), _1291916))], (44190 ^ _776545) ^ [_1660169, _1660171, _1660173] : [_1660173 = c_List_Olist_ONil(_1660169), -(hAPP(c_List_Orotate(_1660169, _1660171), _1660173) = c_List_Olist_ONil(_1660169))], (21355 ^ _776545) ^ [_1163151, _1163153, _1163155] : [class_Rings_Ocomm__semiring__1(_1163151), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1163151), _1163153), hAPP(c_Nat_OSuc, _1163155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163151), _1163153), hAPP(hAPP(c_Power_Opower__class_Opower(_1163151), _1163153), _1163155)))], (33917 ^ _776545) ^ [_1405267, _1405269, _1405271] : [class_Groups_Ocomm__monoid__add(_1405267), class_Groups_Ocomm__monoid__mult(_1405267), c_Nat__Transfer_Onat__set(_1405269), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1405267), _1405271), _1405269) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1405267), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1405267, tc_Nat_Onat), _1405271), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1405269)))], (42551 ^ _776545) ^ [_1623481, _1623483, _1623485, _1623487, _1623489, _1623491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623481, _1623483)), hAPP(hAPP(c_Product__Type_OPair(_1623481, _1623483), _1623485), _1623487)), hAPP(c_List_Oset(tc_prod(_1623481, _1623483)), hAPP(hAPP(c_List_Ozip(_1623481, _1623483), _1623489), _1623491)))), -(hBOOL(hAPP(hAPP(c_member(_1623481), _1623485), hAPP(c_List_Oset(_1623481), _1623489))))], (36551 ^ _776545) ^ [_1468695] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1468695) = 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), _1468695), 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))))))], (38961 ^ _776545) ^ [_1526595, _1526597, _1526599, _1526601] : [hBOOL(hAPP(hAPP(c_member(_1526595), _1526601), hAPP(c_Relation_ODomain(_1526595, _1526597), _1526599))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526595, _1526597, hAPP(hAPP(c_COMBC(_1526595, tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_fun(_1526597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526597, tc_fun(tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_fun(_1526597, tc_HOL_Obool)), _1526595), c_COMBC(_1526597, tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526597, tc_prod(_1526595, _1526597)), tc_fun(_1526597, tc_fun(tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_HOL_Obool)), _1526595), hAPP(c_COMBB(tc_prod(_1526595, _1526597), tc_fun(tc_fun(tc_prod(_1526595, _1526597), tc_HOL_Obool), tc_HOL_Obool), _1526597), c_member(tc_prod(_1526595, _1526597)))), c_Product__Type_OPair(_1526595, _1526597)))), _1526599)), _1526601)))], (38209 ^ _776545) ^ [_1508185, _1508187, _1508189, _1508191] : [c_Wellfounded_Owf(_1508185, _1508187), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508185, _1508185)), hAPP(hAPP(c_Product__Type_OPair(_1508185, _1508185), _1508189), _1508191)), _1508187)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508185, _1508185)), hAPP(hAPP(c_Product__Type_OPair(_1508185, _1508185), _1508191), _1508189)), _1508187))], (46277 ^ _776545) ^ [_1707424, _1707426] : [46278 ^ _776545 : [(46281 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707426), _1707424))], (46279 ^ _776545) ^ [] : [_1707426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1707424, _1707426) = c_List_Olist_ONil(tc_Nat_Onat))], (26949 ^ _776545) ^ [_1261939, _1261941, _1261943] : [class_Rings_Oring__1(_1261939), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261941), _1261943)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1261939), hAPP(c_Int_Oring__1__class_Oof__int(_1261939), _1261941)), hAPP(c_Int_Oring__1__class_Oof__int(_1261939), _1261943)))], (8691 ^ _776545) ^ [_925901, _925903, _925905, _925907] : [class_Lattices_Osemilattice__inf(_925901), 8694 ^ _776545 : [(8703 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925901), _925905), _925907)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), _925905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), _925907))], (8695 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925901), _925905), _925907))), 8698 ^ _776545 : [(8701 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), _925907)))], (8699 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925901), _925903), _925905)))]]]]], (10703 ^ _776545) ^ [_960927, _960929, _960931] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960927, tc_HOL_Obool)), _960929), _960931) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960927, tc_HOL_Obool)), _960929), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960927, tc_HOL_Obool)), _960931)))], (2438 ^ _776545) ^ [_812337, _812339] : [_812339 = _812337, -(c_Divides_Oadjust(_812339) = c_Divides_Oadjust(_812337))], (7216 ^ _776545) ^ [_894147, _894149, _894151, _894153] : [7217 ^ _776545 : [(7220 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894147), _894149), _894153))], (7218 ^ _776545) ^ [] : [_894149 = _894151]], -(hBOOL(hAPP(hAPP(c_member(_894147), _894149), hAPP(hAPP(c_Set_Oinsert(_894147), _894151), _894153))))], (45782 ^ _776545) ^ [_1695117, _1695119] : [c_List_Oremdups(_1695117, _1695119) = _1695119, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695117)), c_List_Oremdups(_1695117, _1695119)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695117)), _1695119))], (39551 ^ _776545) ^ [_1543633, _1543635] : [-(c_Relation_Orefl__on(_1543633, _1543635, c_Relation_OId__on(_1543633, _1543635)))], (29303 ^ _776545) ^ [_1301652] : [-(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)))), _1301652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301652), _1301652))], (39724 ^ _776545) ^ [_1548004, _1548006, _1548008, _1548010] : [c_Equiv__Relations_Ocongruent(_1548004, _1548006, _1548008, _1548010), 39727 ^ _776545 : [(39728 ^ _776545) ^ [_1548149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548004, _1548004)), _1548149), _1548008)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548004, _1548004, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548004, tc_fun(_1548004, _1548006), tc_fun(_1548004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548006, tc_HOL_Obool), tc_fun(tc_fun(_1548004, _1548006), tc_fun(_1548004, tc_HOL_Obool)), _1548004), c_COMBB(_1548006, tc_HOL_Obool, _1548004)), hAPP(hAPP(c_COMBB(_1548006, tc_fun(_1548006, tc_HOL_Obool), _1548004), c_fequal), _1548010))), _1548010)), _1548149)))]]], (46099 ^ _776545) ^ [_1702482, _1702484, _1702486, _1702488] : [-(hAPP(c_List_Ofilter(_1702482, _1702484), hAPP(hAPP(c_List_Oappend(_1702482), _1702486), _1702488)) = hAPP(hAPP(c_List_Oappend(_1702482), hAPP(c_List_Ofilter(_1702482, _1702484), _1702486)), hAPP(c_List_Ofilter(_1702482, _1702484), _1702488)))], (39471 ^ _776545) ^ [_1541483, _1541485, _1541487, _1541489, _1541491, _1541493] : [-(c_Product__Type_Omap__pair(_1541483, _1541485, _1541487, _1541489, _1541491, _1541493) = hAPP(c_Product__Type_Oprod_Oprod__case(_1541483, _1541487, tc_prod(_1541485, _1541489)), hAPP(hAPP(c_COMBC(_1541483, tc_fun(_1541487, _1541489), tc_fun(_1541487, tc_prod(_1541485, _1541489))), hAPP(hAPP(c_COMBB(tc_fun(_1541489, tc_prod(_1541485, _1541489)), tc_fun(tc_fun(_1541487, _1541489), tc_fun(_1541487, tc_prod(_1541485, _1541489))), _1541483), c_COMBB(_1541489, tc_prod(_1541485, _1541489), _1541487)), hAPP(hAPP(c_COMBB(_1541485, tc_fun(_1541489, tc_prod(_1541485, _1541489)), _1541483), c_Product__Type_OPair(_1541485, _1541489)), _1541491))), _1541493)))], (27489 ^ _776545) ^ [_1271088, _1271090, _1271092] : [class_Groups_Oordered__ab__group__add__abs(_1271088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271088), _1271090), _1271092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271088), hAPP(c_Groups_Ouminus__class_Ouminus(_1271088), _1271090)), _1271092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271088), hAPP(c_Groups_Oabs__class_Oabs(_1271088), _1271090)), _1271092)))], (16040 ^ _776545) ^ [_1066653, _1066655, _1066657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066653), _1066655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066655), _1066657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1066653)), _1066657)))], (46235 ^ _776545) ^ [_1706406, _1706408, _1706410] : [class_Groups_Oab__semigroup__add(_1706406), -(c_List_Ofoldr(_1706406, _1706406, c_Groups_Oplus__class_Oplus(_1706406), _1706408, _1706410) = hAPP(c_List_Ofoldl(_1706406, _1706406, c_Groups_Oplus__class_Oplus(_1706406), _1706410), _1706408))], (50049 ^ _776545) ^ [_1787665, _1787667, _1787669, _1787671, _1787673] : [hBOOL(hAPP(hAPP(c_member(_1787665), _1787667), hAPP(c_Set_Oimage(_1787669, _1787665, _1787671), _1787673))), -(hBOOL(hAPP(hAPP(c_member(_1787669), hAPP(c_Hilbert__Choice_Oinv__into(_1787669, _1787665, _1787673, _1787671), _1787667)), _1787673)))], (46093 ^ _776545) ^ [_1702294, _1702296, _1702298] : [-(c_List_Opartition(_1702294, _1702296, _1702298) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702294), tc_List_Olist(_1702294)), hAPP(c_List_Ofilter(_1702294, _1702296), _1702298)), hAPP(c_List_Ofilter(_1702294, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1702294, c_fNot), _1702296)), _1702298)))], (38576 ^ _776545) ^ [_1516748, _1516750] : [c_Wellfounded_Owf(_1516748, _1516750), -(c_Wellfounded_OwfP(_1516748, hAPP(hAPP(c_COMBC(_1516748, tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_fun(_1516748, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516748, tc_fun(tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_fun(_1516748, tc_HOL_Obool)), _1516748), c_COMBC(_1516748, tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516748, tc_prod(_1516748, _1516748)), tc_fun(_1516748, tc_fun(tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_HOL_Obool)), _1516748), hAPP(c_COMBB(tc_prod(_1516748, _1516748), tc_fun(tc_fun(tc_prod(_1516748, _1516748), tc_HOL_Obool), tc_HOL_Obool), _1516748), c_member(tc_prod(_1516748, _1516748)))), c_Product__Type_OPair(_1516748, _1516748)))), _1516750)))], (10613 ^ _776545) ^ [_959047, _959049, _959051, _959053] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_959047, _959049, _959051, _959053, c_Orderings_Obot__class_Obot(tc_fun(_959047, tc_HOL_Obool))), _959053)))], (38229 ^ _776545) ^ [_1508613, _1508615, _1508617] : [c_Wellfounded_Owf(_1508613, _1508615), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508613, _1508613)), hAPP(hAPP(c_Product__Type_OPair(_1508613, _1508613), _1508617), _1508617)), _1508615))], (21132 ^ _776545) ^ [_1158728, _1158730, _1158732, _1158734, _1158736, _1158738] : [class_Groups_Oab__semigroup__mult(_1158728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158730), _1158732)), 21142 ^ _776545 : [(21145 ^ _776545) ^ [] : [hAPP(_1158734, 21141 ^ [_1158728, _1158730, _1158732, _1158734, _1158736, _1158738]) = hAPP(_1158736, 21141 ^ [_1158728, _1158730, _1158732, _1158734, _1158736, _1158738])], (21143 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158730), 21141 ^ [_1158728, _1158730, _1158732, _1158734, _1158736, _1158738]), _1158732)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158728, _1158730, c_Groups_Otimes__class_Otimes(_1158728)), _1158734), _1158738), _1158732) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1158728, _1158730, c_Groups_Otimes__class_Otimes(_1158728)), _1158736), _1158738), _1158732))], (51455 ^ _776545) ^ [_1817928, _1817930] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1817928), 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)))), _1817930)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817928), _1817930)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817930), _1817928)))], (40697 ^ _776545) ^ [_1571756, _1571758, _1571760, _1571762] : [-(c_Transitive__Closure_Otrancl(_1571756, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1571756, _1571756)), hAPP(hAPP(c_Product__Type_OPair(_1571756, _1571756), _1571758), _1571760)), _1571762)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571756, _1571756), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571756, _1571762)), hAPP(c_Set_OCollect(tc_prod(_1571756, _1571756)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571756, _1571756, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571756, tc_fun(_1571756, tc_HOL_Obool), tc_fun(_1571756, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571756, tc_HOL_Obool), tc_fun(_1571756, tc_HOL_Obool)), _1571756), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571756)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571756), c_fconj), hAPP(hAPP(c_COMBC(_1571756, tc_fun(tc_prod(_1571756, _1571756), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571756, _1571756), tc_fun(tc_fun(tc_prod(_1571756, _1571756), tc_HOL_Obool), tc_HOL_Obool), _1571756), c_member(tc_prod(_1571756, _1571756))), hAPP(hAPP(c_COMBC(_1571756, _1571756, tc_prod(_1571756, _1571756)), c_Product__Type_OPair(_1571756, _1571756)), _1571758))), c_Transitive__Closure_Ortrancl(_1571756, _1571762))))), hAPP(hAPP(c_COMBC(_1571756, tc_fun(tc_prod(_1571756, _1571756), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571756, _1571756), tc_fun(tc_fun(tc_prod(_1571756, _1571756), tc_HOL_Obool), tc_HOL_Obool), _1571756), c_member(tc_prod(_1571756, _1571756))), hAPP(c_Product__Type_OPair(_1571756, _1571756), _1571760))), c_Transitive__Closure_Ortrancl(_1571756, _1571762)))))))], (8557 ^ _776545) ^ [_923545, _923547, _923549] : [class_Lattices_Osemilattice__sup(_923545), 8560 ^ _776545 : [(8567 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923545), _923547), _923549) = _923549, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923545), _923547), _923549)))], (8561 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923545), _923547), _923549)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923545), _923547), _923549) = _923549)]]], (11421 ^ _776545) ^ [_975862, _975864, _975866, _975868, _975870] : [c_Finite__Set_Ofolding__one(_975862, _975864, _975866), hBOOL(hAPP(c_Finite__Set_Ofinite(_975862), _975868)), -(_975868 = c_Orderings_Obot__class_Obot(tc_fun(_975862, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_975862), _975870)), -(_975870 = c_Orderings_Obot__class_Obot(tc_fun(_975862, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975862, tc_HOL_Obool)), _975868), _975870) = c_Orderings_Obot__class_Obot(tc_fun(_975862, tc_HOL_Obool)), -(hAPP(_975866, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975862, tc_HOL_Obool)), _975868), _975870)) = hAPP(hAPP(_975864, hAPP(_975866, _975868)), hAPP(_975866, _975870)))], (34229 ^ _776545) ^ [_1413045, _1413047] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413045)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413047)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413047))), 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, _1413045))), 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), _1413045)), c_Int_Onat)))))], (52227 ^ _776545) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (8008 ^ _776545) ^ [_912296, _912298, _912300, _912302] : [hBOOL(hAPP(hAPP(c_member(_912296), _912298), _912300)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912296, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912296), _912298), _912302)), _912300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912296, tc_HOL_Obool)), _912302), _912300))], (34419 ^ _776545) ^ [_1417120, _1417122, _1417124, _1417126, _1417128] : [-(c_Nat_Onat_Onat__case(_1417120, _1417122, _1417124, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417126)), _1417128)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417126))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417120, _1417120), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417120, tc_fun(_1417120, _1417120)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417120, tc_fun(_1417120, _1417120)), tc_Int_Oint), c_If(_1417120)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1417120, _1417122, _1417124, _1417128))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417120, tc_Int_Oint), _1417124), 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)), _1417128)))))], (5703 ^ _776545) ^ [_866504] : [class_HOL_Oequal(_866504), -(c_HOL_Oequal__class_Oequal(_866504) = c_fequal)], (15692 ^ _776545) ^ [_1061128] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061128)], (15268 ^ _776545) ^ [_1052082, _1052084] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1052082), _1052084)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052084), _1052082))], (34779 ^ _776545) ^ [_1425365, _1425367, _1425369, _1425371, _1425373, _1425375, _1425377] : [hBOOL(hAPP(hAPP(c_member(_1425365), _1425367), hAPP(hAPP(_1425369, _1425371), _1425373))), -(hBOOL(hAPP(hAPP(c_member(_1425365), _1425367), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425375, _1425377, tc_fun(_1425365, tc_HOL_Obool)), _1425369), hAPP(hAPP(c_Product__Type_OPair(_1425375, _1425377), _1425371), _1425373)))))], (35690 ^ _776545) ^ [_1442807, _1442809, _1442811, _1442813, _1442815] : [hBOOL(hAPP(hAPP(_1442807, _1442809), _1442811)), -(hBOOL(hAPP(hAPP(_1442807, hAPP(c_Product__Type_Osnd(_1442813, _1442815), hAPP(hAPP(c_Product__Type_OPair(_1442813, _1442815), _1442811), _1442809))), hAPP(c_Product__Type_Ofst(_1442813, _1442815), hAPP(hAPP(c_Product__Type_OPair(_1442813, _1442815), _1442811), _1442809)))))], (27677 ^ _776545) ^ [_1274434, _1274436] : [class_Groups_Oordered__ab__group__add__abs(_1274434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274434), _1274436), c_Groups_Ozero__class_Ozero(_1274434))), -(hAPP(c_Groups_Oabs__class_Oabs(_1274434), _1274436) = hAPP(c_Groups_Ouminus__class_Ouminus(_1274434), _1274436))], (48684 ^ _776545) ^ [_1757910, _1757912, _1757914, _1757916] : [-(hBOOL(hAPP(_1757910, _1757912))), -(hAPP(c_List_Ofilter(_1757914, _1757910), c_List_Oreplicate(_1757914, _1757916, _1757912)) = c_List_Olist_ONil(_1757914))], (27299 ^ _776545) ^ [_1267744] : [class_Rings_Olinordered__idom(_1267744), -(hAPP(c_Groups_Oabs__class_Oabs(_1267744), c_Groups_Oone__class_Oone(_1267744)) = c_Groups_Oone__class_Oone(_1267744))], (52149 ^ _776545) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (43056 ^ _776545) ^ [_1634576, _1634578] : [-(hAPP(hAPP(c_List_Otake(_1634576), _1634578), c_List_Olist_ONil(_1634576)) = c_List_Olist_ONil(_1634576))], (41066 ^ _776545) ^ [_1581427, _1581429, _1581431, _1581433, _1581435] : [-(hAPP(c_Relation_Oconverse(_1581427, _1581429), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581431, tc_fun(tc_prod(_1581427, _1581429), tc_HOL_Obool)), _1581433), _1581435)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581431, tc_fun(tc_prod(_1581429, _1581427), tc_HOL_Obool)), _1581433), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581427, _1581429), tc_HOL_Obool), tc_fun(tc_prod(_1581429, _1581427), tc_HOL_Obool), _1581431), c_Relation_Oconverse(_1581427, _1581429)), _1581435)))], (7826 ^ _776545) ^ [_908216, _908218] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908216, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_908216, tc_HOL_Obool))), _908218) = c_Orderings_Obot__class_Obot(tc_fun(_908216, tc_HOL_Obool)))], (34049 ^ _776545) ^ [_1408626, _1408628] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408626))), -(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)), _1408626))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1408628)))) = 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)), _1408626))), 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, _1408628))))))], (29061 ^ _776545) ^ [_1297484] : [-(c_Int_Opred(c_Int_OBit1(_1297484)) = c_Int_OBit0(_1297484))], (40737 ^ _776545) ^ [_1573464, _1573466] : [-(c_Transitive__Closure_Otrancl(_1573464, _1573466) = hAPP(hAPP(c_Relation_Orel__comp(_1573464, _1573464, _1573464), _1573466), c_Transitive__Closure_Ortrancl(_1573464, _1573466)))], (38703 ^ _776545) ^ [_1520393, _1520395, _1520397, _1520399] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520393, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1520395, _1520393, _1520397), hAPP(c_Set_Ovimage(_1520395, _1520393, _1520397), _1520399))), _1520399)))], (39341 ^ _776545) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (52025 ^ _776545) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (2746 ^ _776545) ^ [_817157, _817159] : [_817159 = _817157, -(c_Set_OBall(_817159) = c_Set_OBall(_817157))], (4426 ^ _776545) ^ [_843751, _843753] : [_843753 = _843751, -(c_Lazy__Sequence_Oempty(_843753) = c_Lazy__Sequence_Oempty(_843751))], (13216 ^ _776545) ^ [_1010437] : [class_Lattices_Osemilattice__inf(_1010437), -(c_Finite__Set_Ofun__left__comm__idem(_1010437, _1010437, c_Lattices_Osemilattice__inf__class_Oinf(_1010437)))], (30356 ^ _776545) ^ [_1321029, _1321031, _1321033, _1321035] : [class_Orderings_Olinorder(_1321029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321029), _1321031)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1321029, _1321029, c_Orderings_Oord__class_Omin(_1321029)), _1321033), hAPP(hAPP(c_Set_Oinsert(_1321029), _1321035), _1321031)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321029), _1321035), hAPP(hAPP(c_Finite__Set_Ofold(_1321029, _1321029, c_Orderings_Oord__class_Omin(_1321029)), _1321033), _1321031)))], (3624 ^ _776545) ^ [_830832, _830834, _830836, _830838, _830840, _830842] : [-(c_List_Oremove1(_830842, _830838, _830834) = c_List_Oremove1(_830840, _830836, _830832)), _830842 = _830840, _830838 = _830836, _830834 = _830832], (32348 ^ _776545) ^ [_1358379, _1358381, _1358383, _1358385, _1358387, _1358389, _1358391, _1358393] : [hBOOL(hAPP(hAPP(c_member(_1358379), _1358381), _1358383)), hBOOL(hAPP(hAPP(hAPP(_1358385, _1358381), _1358387), _1358389)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1358379, tc_fun(_1358391, tc_fun(_1358393, tc_HOL_Obool))), _1358383), _1358385), _1358387), _1358389)))], (42729 ^ _776545) ^ [_1627521, _1627523, _1627525, _1627527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627523)), _1627525))), -(hAPP(hAPP(c_List_Onth(_1627523), hAPP(hAPP(c_List_Olist__update(_1627523, _1627525), _1627521), _1627527)), _1627521) = _1627527)], (36398 ^ _776545) ^ [] : [-(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)))], (9694 ^ _776545) ^ [_942482, _942484, _942486, _942488] : [class_Orderings_Oorder(_942482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942482), _942484), _942486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942482), _942488), _942484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942482), _942488), _942486)))], (45800 ^ _776545) ^ [_1695501, _1695503, _1695505, _1695507] : [-(_1695501 = _1695503), -(hAPP(c_List_OremoveAll(_1695505, _1695501), hAPP(hAPP(c_List_Olist_OCons(_1695505), _1695503), _1695507)) = hAPP(hAPP(c_List_Olist_OCons(_1695505), _1695503), hAPP(c_List_OremoveAll(_1695505, _1695501), _1695507)))], (44733 ^ _776545) ^ [_1670878, _1670880, _1670882, _1670884] : [-(_1670878 = c_List_Olist_ONil(_1670880)), -(hAPP(c_List_Ohd(_1670882), hAPP(hAPP(c_List_Omap(_1670880, _1670882), _1670884), _1670878)) = hAPP(_1670884, hAPP(c_List_Ohd(_1670880), _1670878)))], (512 ^ _776545) ^ [_784235, _784237] : [-(class_Lattices_Oab__semigroup__idem__mult(_784235)), _784237 = _784235, class_Lattices_Oab__semigroup__idem__mult(_784237)], (28621 ^ _776545) ^ [] : [-(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)))], (22389 ^ _776545) ^ [_1182449] : [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)), _1182449)), _1182449)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182449), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (45854 ^ _776545) ^ [_1696368, _1696370, _1696372] : [hBOOL(hAPP(hAPP(c_member(_1696368), _1696370), hAPP(c_List_Oset(_1696368), _1696372))), -(c_List_Oremdups(_1696368, hAPP(hAPP(c_List_Olist_OCons(_1696368), _1696370), _1696372)) = c_List_Oremdups(_1696368, _1696372))], (8000 ^ _776545) ^ [_912046, _912048, _912050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_912046, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_912046, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_912046), _912048)), hAPP(c_Set_OPow(_912046), _912050))), hAPP(c_Set_OPow(_912046), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912046, tc_HOL_Obool)), _912048), _912050)))))], (33887 ^ _776545) ^ [_1404493] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1404493) = 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), _1404493), c_Int_Onat)))))], (10371 ^ _776545) ^ [_954649, _954651, _954653] : [class_Lattices_Oboolean__algebra(_954649), 10374 ^ _776545 : [(10381 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954649), _954653), _954651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954649), hAPP(c_Groups_Ouminus__class_Ouminus(_954649), _954651)), hAPP(c_Groups_Ouminus__class_Ouminus(_954649), _954653))))], (10375 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954649), hAPP(c_Groups_Ouminus__class_Ouminus(_954649), _954651)), hAPP(c_Groups_Ouminus__class_Ouminus(_954649), _954653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954649), _954653), _954651)))]]], (10615 ^ _776545) ^ [_959089, _959091, _959093, _959095] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_959089, _959091, _959093, _959095, c_Orderings_Obot__class_Obot(tc_fun(_959089, tc_HOL_Obool))), _959095)))], (33697 ^ _776545) ^ [_1399293, _1399295, _1399297] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399293, tc_Nat_Onat), _1399295), _1399297) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399293, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1399293), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1399295)), _1399297)))], (15292 ^ _776545) ^ [_1052464, _1052466, _1052468, _1052470] : [class_Groups_Ocomm__monoid__mult(_1052464), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052466), _1052468))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052466, _1052464), _1052470), _1052468) = c_Groups_Oone__class_Oone(_1052464))], (50711 ^ _776545) ^ [_1801611, _1801613, _1801615] : [hBOOL(hAPP(c_Quotient_ORespects(_1801611, _1801613), _1801615)), -(hBOOL(hAPP(hAPP(_1801613, _1801615), _1801615)))], (17991 ^ _776545) ^ [_1100056, _1100058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100058), _1100056)), -(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), _1100056), _1100058))))], (18248 ^ _776545) ^ [_1104676, _1104678, _1104680] : [class_Groups_Oordered__comm__monoid__add(_1104676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104676), c_Groups_Ozero__class_Ozero(_1104676)), _1104678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104676), c_Groups_Ozero__class_Ozero(_1104676)), _1104680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104676), c_Groups_Ozero__class_Ozero(_1104676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104676), _1104678), _1104680))))], (49998 ^ _776545) ^ [_1786440] : [-(c_Hilbert__Choice_Oinv__into(_1786440, _1786440, c_Orderings_Otop__class_Otop(tc_fun(_1786440, tc_HOL_Obool)), c_Fun_Oid(_1786440)) = c_Fun_Oid(_1786440))], (15716 ^ _776545) ^ [_1061529] : [hAPP(c_Nat_OSuc, _1061529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22183 ^ _776545) ^ [_1178863, _1178865] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178863), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1178865) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1178863, _1178865))], (8014 ^ _776545) ^ [_912445, _912447, _912449, _912451] : [-(hBOOL(hAPP(hAPP(c_member(_912445), _912447), _912449))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912445, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912445), _912447), _912451)), _912449) = hAPP(hAPP(c_Set_Oinsert(_912445), _912447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912445, tc_HOL_Obool)), _912451), _912449)))], (6457 ^ _776545) ^ [_880857, _880859] : [_880859 = c_Orderings_Obot__class_Obot(tc_fun(_880857, tc_HOL_Obool)), 6460 ^ _776545 : [(6461 ^ _776545) ^ [_880937] : [hBOOL(hAPP(hAPP(c_member(_880857), _880937), _880859))]]], (43964 ^ _776545) ^ [_1655201, _1655203, _1655205, _1655207] : [hAPP(hAPP(c_List_Oappend(_1655201), _1655203), _1655205) = _1655207, 43967 ^ _776545 : [(43970 ^ _776545) ^ [] : [-(_1655205 = hAPP(hAPP(c_List_Odrop(_1655201), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655201)), _1655203)), _1655207))], (43968 ^ _776545) ^ [] : [-(_1655203 = hAPP(hAPP(c_List_Otake(_1655201), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655201)), _1655203)), _1655207))]]], (48442 ^ _776545) ^ [_1752285, _1752287] : [-(hAPP(c_New__DSequence_Opos__empty(_1752285), _1752287) = c_Lazy__Sequence_Oempty(_1752285))], (7448 ^ _776545) ^ [_899197, _899199, _899201, _899203] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899197, tc_HOL_Obool)), _899199), _899201), _899203)), -(hBOOL(hAPP(_899199, _899203))), -(hBOOL(hAPP(_899201, _899203)))], (46243 ^ _776545) ^ [_1706586, _1706588, _1706590] : [class_Groups_Omonoid__add(_1706586), -(hAPP(c_List_Ofoldl(_1706586, _1706586, c_Groups_Oplus__class_Oplus(_1706586), _1706588), _1706590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1706586), _1706588), c_List_Ofoldr(_1706586, _1706586, c_Groups_Oplus__class_Oplus(_1706586), _1706590, c_Groups_Ozero__class_Ozero(_1706586))))], (11196 ^ _776545) ^ [_970654, _970656, _970658, _970660, _970662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970654, tc_HOL_Obool)), hAPP(c_Set_Oimage(_970656, _970654, _970658), _970660)), _970662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_970654, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_970656, tc_HOL_Obool), tc_fun(_970654, tc_HOL_Obool), c_Set_Oimage(_970656, _970654, _970658)), hAPP(c_Set_OPow(_970656), _970660))), hAPP(c_Set_OPow(_970654), _970662))))], (6818 ^ _776545) ^ [_886936, _886938, _886940] : [class_Complete__Lattice_Ocomplete__lattice(_886936), 6824 ^ _776545 : [(6827 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886936), _886940), 6823 ^ [_886936, _886938, _886940]))], (6825 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886936), 6823 ^ [_886936, _886938, _886940]), _886938)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886936), _886940), c_Complete__Lattice_OInf__class_OInf(_886936, _886938))))], (41583 ^ _776545) ^ [_1594604, _1594606, _1594608, _1594610, _1594612] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594604, _1594604)), hAPP(hAPP(c_Product__Type_OPair(_1594604, _1594604), _1594606), _1594608)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594604, _1594604), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594610)), _1594612))), 41587 ^ _776545 : [(41590 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594604, _1594604)), hAPP(hAPP(c_Product__Type_OPair(_1594604, _1594604), 41586 ^ [_1594604, _1594606, _1594608, _1594610, _1594612]), _1594608)), _1594612)))], (41588 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594604, _1594604)), hAPP(hAPP(c_Product__Type_OPair(_1594604, _1594604), _1594606), 41586 ^ [_1594604, _1594606, _1594608, _1594610, _1594612])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594604, _1594604), tc_HOL_Obool), _1594610), _1594612))))]]], (47208 ^ _776545) ^ [_1725612, _1725614] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725612), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1725612))), _1725614))), -(c_List_Otranspose(_1725612, c_List_Otranspose(_1725612, _1725614)) = c_List_OtakeWhile(tc_List_Olist(_1725612), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1725612)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1725612), tc_List_Olist(_1725612), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1725612))), _1725614))], (19460 ^ _776545) ^ [_1127932, _1127934] : [-(hBOOL(hAPP(_1127932, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1127932, _1127934)), 19468 ^ _776545 : [(19471 ^ _776545) ^ [_1128170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128170), 19467 ^ [_1127932, _1127934])), hBOOL(hAPP(_1127932, _1128170))], (19477 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1127932, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19467 ^ [_1127932, _1127934]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (19469 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19467 ^ [_1127932, _1127934]), _1127934)))]]], (3936 ^ _776545) ^ [_835796, _835798, _835800, _835802, _835804, _835806, _835808, _835810] : [-(c_New__DSequence_Oneg__decr__bind(_835810, _835806, _835802, _835798) = c_New__DSequence_Oneg__decr__bind(_835808, _835804, _835800, _835796)), _835810 = _835808, _835806 = _835804, _835802 = _835800, _835798 = _835796], (4528 ^ _776545) ^ [_845318, _845320] : [_845320 = _845318, -(c_List_Omember(_845320) = c_List_Omember(_845318))], (49756 ^ _776545) ^ [_1782012, _1782014, _1782016, _1782018] : [c_Relation_Osym(_1782012, _1782014), -(c_Relation_Osym(_1782016, hAPP(hAPP(c_Relation_Oinv__image(_1782012, _1782016), _1782014), _1782018)))], (16464 ^ _776545) ^ [_1073118, _1073120] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073118), _1073120) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 16467 ^ _776545 : [(16470 ^ _776545) ^ [] : [-(_1073120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16468 ^ _776545) ^ [] : [-(_1073118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (12710 ^ _776545) ^ [_1000618, _1000620, _1000622] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000618), _1000620)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000618, tc_HOL_Obool)), _1000620), _1000622) = hAPP(hAPP(c_Finite__Set_Ofold(_1000618, tc_fun(_1000618, tc_HOL_Obool), c_Set_Oinsert(_1000618)), _1000622), _1000620))], (6352 ^ _776545) ^ [_878970, _878972, _878974] : [_878970 = _878972, 6355 ^ _776545 : [(6358 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878974, tc_HOL_Obool)), _878972), _878970)))], (6356 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878974, tc_HOL_Obool)), _878970), _878972)))]]], (27257 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (2886 ^ _776545) ^ [_819353, _819355] : [_819355 = _819353, -(c_Nat_Ofunpow(_819355) = c_Nat_Ofunpow(_819353))], (47796 ^ _776545) ^ [_1738612, _1738614, _1738616, _1738618, _1738620] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738612)), _1738614) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738616)), _1738618), 47802 ^ _776545 : [(47805 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1738620, hAPP(hAPP(c_List_Onth(_1738612), _1738614), 47801 ^ [_1738612, _1738614, _1738616, _1738618, _1738620])), hAPP(hAPP(c_List_Onth(_1738616), _1738618), 47801 ^ [_1738612, _1738614, _1738616, _1738618, _1738620])))], (47803 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47801 ^ [_1738612, _1738614, _1738616, _1738618, _1738620]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738612)), _1738614))))]], -(c_List_Olist__all2(_1738612, _1738616, _1738620, _1738614, _1738618))], (28719 ^ _776545) ^ [_1291358, _1291360] : [class_Int_Onumber__ring(_1291358), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291358), hAPP(c_Int_Onumber__class_Onumber__of(_1291358), _1291360)), c_Groups_Oone__class_Oone(_1291358)) = hAPP(c_Int_Onumber__class_Onumber__of(_1291358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1291360), c_Int_OBit1(c_Int_OPls))))], (43996 ^ _776545) ^ [_1655881, _1655883, _1655885, _1655887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655881), _1655883)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655885)), _1655887))), -(hAPP(hAPP(c_List_Onth(_1655885), hAPP(hAPP(c_List_Odrop(_1655885), _1655881), _1655887)), _1655883) = hAPP(hAPP(c_List_Onth(_1655885), _1655887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655881), _1655883)))], (16138 ^ _776545) ^ [_1068221, _1068223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068221)), _1068223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068221), _1068223)))], (39649 ^ _776545) ^ [_1545843, _1545845, _1545847] : [c_Relation_Orefl__on(_1545843, _1545845, _1545847), 39652 ^ _776545 : [(39659 ^ _776545) ^ [_1546327] : [hBOOL(hAPP(hAPP(c_member(_1545843), _1546327), _1545845)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545843, _1545843)), hAPP(hAPP(c_Product__Type_OPair(_1545843, _1545843), _1546327), _1546327)), _1545847)))], (39653 ^ _776545) ^ [_1546054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545843, _1545843)), _1546054), _1545847)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545843, _1545843, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1545843, tc_fun(_1545843, tc_HOL_Obool), tc_fun(_1545843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545843, tc_HOL_Obool), tc_fun(_1545843, tc_HOL_Obool)), _1545843), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545843)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545843), c_fconj), hAPP(hAPP(c_COMBC(_1545843, tc_fun(_1545843, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545843)), _1545845)))), hAPP(hAPP(c_COMBC(_1545843, tc_fun(_1545843, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545843)), _1545845))), _1546054)))]]], (14392 ^ _776545) ^ [_1036296, _1036298, _1036300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036296), _1036298)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036298), _1036296)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036300), _1036296)), _1036298))], (37925 ^ _776545) ^ [_1499975, _1499977, _1499979, _1499981, _1499983] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1499975, _1499977, _1499979), _1499981), _1499983) = hAPP(c_Set_OCollect(tc_prod(_1499975, _1499979)), hAPP(c_Product__Type_Oprod_Oprod__case(_1499975, _1499979, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1499979, tc_fun(_1499977, tc_HOL_Obool)), tc_fun(_1499979, tc_HOL_Obool), _1499975), hAPP(c_COMBB(tc_fun(_1499977, tc_HOL_Obool), tc_HOL_Obool, _1499979), c_HOL_OEx(_1499977))), hAPP(hAPP(c_COMBC(_1499975, tc_fun(_1499979, tc_fun(_1499977, tc_HOL_Obool)), tc_fun(_1499979, tc_fun(_1499977, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1499977, tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), tc_fun(tc_fun(_1499979, tc_fun(_1499977, tc_HOL_Obool)), tc_fun(_1499979, tc_fun(_1499977, tc_HOL_Obool))), _1499975), c_COMBB(tc_fun(_1499977, tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool), _1499979)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1499977, tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), _1499975), c_COMBS(_1499977, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_HOL_Obool), tc_fun(_1499977, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1499975), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499977), c_fconj)), hAPP(hAPP(c_COMBC(_1499975, tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_fun(tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), _1499975), c_COMBC(_1499977, tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_prod(_1499975, _1499977)), tc_fun(_1499977, tc_fun(tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_HOL_Obool)), _1499975), hAPP(c_COMBB(tc_prod(_1499975, _1499977), tc_fun(tc_fun(tc_prod(_1499975, _1499977), tc_HOL_Obool), tc_HOL_Obool), _1499977), c_member(tc_prod(_1499975, _1499977)))), c_Product__Type_OPair(_1499975, _1499977)))), _1499981))))), hAPP(hAPP(c_COMBC(_1499979, tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_fun(tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_fun(_1499977, tc_HOL_Obool)), _1499979), c_COMBC(_1499977, tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499977, tc_prod(_1499977, _1499979)), tc_fun(_1499977, tc_fun(tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_HOL_Obool)), _1499979), hAPP(c_COMBB(tc_prod(_1499977, _1499979), tc_fun(tc_fun(tc_prod(_1499977, _1499979), tc_HOL_Obool), tc_HOL_Obool), _1499977), c_member(tc_prod(_1499977, _1499979)))), hAPP(c_COMBC(_1499977, _1499979, tc_prod(_1499977, _1499979)), c_Product__Type_OPair(_1499977, _1499979))))), _1499983))))))], (26961 ^ _776545) ^ [_1262175, _1262177, _1262179] : [class_Rings_Oring__1(_1262175), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1262177), _1262179)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262175), hAPP(c_Int_Oring__1__class_Oof__int(_1262175), _1262177)), hAPP(c_Int_Oring__1__class_Oof__int(_1262175), _1262179)))], (37140 ^ _776545) ^ [_1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789, _1482791, _1482793] : [c_Equiv__Relations_Oequiv(_1482773, _1482775, _1482777), c_Equiv__Relations_Oequiv(_1482779, _1482781, _1482783), c_Equiv__Relations_Ocongruent2(_1482773, _1482779, tc_fun(_1482785, tc_HOL_Obool), _1482777, _1482783, _1482787), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482773, tc_HOL_Obool)), _1482789), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482773), _1482775), _1482777))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1482779, tc_HOL_Obool)), _1482791), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1482779), _1482781), _1482783))), 37162 ^ _776545 : [(37168 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1482785, tc_HOL_Obool)), hAPP(hAPP(_1482787, 37161 ^ [_1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789, _1482791, _1482793]), 37164 ^ [_1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789, _1482791, _1482793])), _1482793))], (37166 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482779), 37164 ^ [_1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789, _1482791, _1482793]), _1482781)))], (37163 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482773), 37161 ^ [_1482773, _1482775, _1482777, _1482779, _1482781, _1482783, _1482785, _1482787, _1482789, _1482791, _1482793]), _1482775)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1482785, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482773, tc_fun(_1482785, tc_HOL_Obool)), _1482789), hAPP(hAPP(c_COMBB(tc_fun(_1482779, tc_fun(_1482785, tc_HOL_Obool)), tc_fun(_1482785, tc_HOL_Obool), _1482773), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482779, tc_fun(_1482785, tc_HOL_Obool)), _1482791)), _1482787))), _1482793)))], (5522 ^ _776545) ^ [_860915, _860917] : [_860917 = _860915, -(c_Groups_Oone__class_Oone(_860917) = c_Groups_Oone__class_Oone(_860915))], (52133 ^ _776545) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (10929 ^ _776545) ^ [_965272, _965274] : [-(_965272 = c_Orderings_Obot__class_Obot(tc_fun(_965274, tc_HOL_Obool))), 10934 ^ _776545 : [(10937 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_965274), 10932 ^ [_965272, _965274]), 10933 ^ [_965272, _965274]))], (10935 ^ _776545) ^ [] : [-(_965272 = hAPP(hAPP(c_Set_Oinsert(_965274), 10932 ^ [_965272, _965274]), 10933 ^ [_965272, _965274]))]]], (38856 ^ _776545) ^ [_1524156, _1524158] : [-(hAPP(c_Relation_ODomain(_1524156, _1524156), c_Relation_OId__on(_1524156, _1524158)) = _1524158)], (44286 ^ _776545) ^ [_1662108, _1662110, _1662112, _1662114, _1662116, _1662118] : [class_Orderings_Olinorder(_1662108), -(hAPP(_1662110, _1662112) = hAPP(_1662110, _1662114)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662116, _1662108, _1662110), _1662114), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662116, _1662108, _1662110), _1662112), _1662118)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662116, _1662108, _1662110), _1662112), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1662116, _1662108, _1662110), _1662114), _1662118)))], (41716 ^ _776545) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42565 ^ _776545) ^ [_1623882, _1623884, _1623886, _1623888] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623882, _1623882)), hAPP(hAPP(c_Product__Type_OPair(_1623882, _1623882), _1623884), _1623886)), hAPP(c_List_Oset(tc_prod(_1623882, _1623882)), hAPP(hAPP(c_List_Ozip(_1623882, _1623882), _1623888), _1623888))))), hBOOL(hAPP(hAPP(c_member(_1623882), _1623884), hAPP(c_List_Oset(_1623882), _1623888))), _1623884 = _1623886], (50445 ^ _776545) ^ [_1796397, _1796399, _1796401, _1796403] : [c_Fun_Oinj__on(_1796397, _1796399, _1796401, _1796403), -(c_Fun_Obij__betw(_1796397, _1796399, _1796401, _1796403, hAPP(c_Set_Oimage(_1796397, _1796399, _1796401), _1796403)))], (38991 ^ _776545) ^ [_1527264, _1527266, _1527268, _1527270] : [hBOOL(hAPP(hAPP(c_member(_1527264), _1527266), hAPP(c_Relation_ODomain(_1527264, _1527268), _1527270))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527264, _1527268)), hAPP(hAPP(c_Product__Type_OPair(_1527264, _1527268), _1527266), 38994 ^ [_1527264, _1527266, _1527268, _1527270])), _1527270)))], (9214 ^ _776545) ^ [_935588, _935590, _935592] : [class_Orderings_Olinorder(_935588), -(_935590 = _935592), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935588), _935590), _935592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935588), _935592), _935590)))], (22385 ^ _776545) ^ [_1182364] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182364)), _1182364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44124 ^ _776545) ^ [_1659081, _1659083] : [-(_1659081 = c_List_Olist_ONil(_1659083)), -(hBOOL(hAPP(hAPP(c_member(_1659083), hAPP(c_List_Ohd(_1659083), _1659081)), hAPP(c_List_Oset(_1659083), _1659081))))], (15700 ^ _776545) ^ [_1061268] : [hAPP(c_Nat_OSuc, _1061268) = _1061268], (13808 ^ _776545) ^ [_1022745, _1022747, _1022749] : [class_Groups_Ogroup__add(_1022745), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022745), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1022745), _1022747), _1022749)), _1022749) = _1022747)], (27809 ^ _776545) ^ [_1276580, _1276582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276580)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276582))), 27812 ^ _776545 : [(27813 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276580), _1276582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1276582)))], (27819 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276580), _1276582)))]]], (32418 ^ _776545) ^ [_1359926, _1359928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359926), _1359928)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1359926, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1359926, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1359926, tc_HOL_Obool), tc_fun(_1359926, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1359926, tc_HOL_Obool))), _1359928)))))], (7051 ^ _776545) ^ [_891283, _891285, _891287, _891289, _891291] : [class_Complete__Lattice_Ocomplete__lattice(_891283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891285, tc_HOL_Obool)), _891287), _891289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891283), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891285, _891283), _891287), _891291)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891285, _891283), _891289), _891291))))], (42773 ^ _776545) ^ [_1628391, _1628393] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628391)), c_List_Obutlast(_1628391, _1628393)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628391)), _1628393)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4658 ^ _776545) ^ [_847381, _847383] : [_847383 = _847381, -(c_DSequence_Ounion(_847383) = c_DSequence_Ounion(_847381))], (14548 ^ _776545) ^ [_1038945, _1038947, _1038949] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038945), _1038947) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038949), _1038947), -(_1038945 = _1038949)], (24908 ^ _776545) ^ [_1227524, _1227526, _1227528, _1227530] : [class_Divides_Oring__div(_1227524), -(c_Divides_Odiv__class_Omod(_1227524, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227524), _1227526), _1227528), _1227530) = c_Divides_Odiv__class_Omod(_1227524, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1227524), _1227526), c_Divides_Odiv__class_Omod(_1227524, _1227528, _1227530)), _1227530))], (3130 ^ _776545) ^ [_823113, _823115, _823117, _823119, _823121, _823123, _823125, _823127] : [-(c_Nat_Onat_Onat__case(_823127, _823123, _823119, _823115) = c_Nat_Onat_Onat__case(_823125, _823121, _823117, _823113)), _823127 = _823125, _823123 = _823121, _823119 = _823117, _823115 = _823113], (25375 ^ _776545) ^ [_1235571, _1235573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235573), _1235571))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235573), _1235571) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235573), _1235571)), _1235571)))], (44529 ^ _776545) ^ [_1667211, _1667213, _1667215] : [class_Orderings_Olinorder(_1667211), -(hBOOL(hAPP(hAPP(c_member(_1667211), _1667213), hAPP(c_List_Oset(_1667211), _1667215)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1667211, _1667211, c_COMBI(_1667211), _1667213, _1667215) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1667211, _1667211, c_COMBI(_1667211)), _1667213), _1667215))], (27441 ^ _776545) ^ [_1269976, _1269978, _1269980] : [class_Groups_Oordered__ab__group__add__abs(_1269976), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269976), hAPP(c_Groups_Oabs__class_Oabs(_1269976), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269976), _1269978), _1269980))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269976), hAPP(c_Groups_Oabs__class_Oabs(_1269976), _1269978)), hAPP(c_Groups_Oabs__class_Oabs(_1269976), _1269980)))))], (48194 ^ _776545) ^ [_1747397, _1747399, _1747401] : [48196 ^ _776545 : [(48199 ^ _776545) ^ [] : [hBOOL(hAPP(_1747399, hAPP(hAPP(c_List_Onth(_1747397), _1747401), 48195 ^ [_1747397, _1747399, _1747401])))], (48197 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48195 ^ [_1747397, _1747399, _1747401]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747397)), _1747401))))]], -(c_List_Olist__all(_1747397, _1747399, _1747401))], (15608 ^ _776545) ^ [_1059617, _1059619, _1059621, _1059623, _1059625, _1059627] : [class_Rings_Olinordered__semiring__1__strict(_1059617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059617), _1059619), _1059621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059617), _1059623), _1059621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059617), c_Groups_Ozero__class_Ozero(_1059617)), _1059625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059617), c_Groups_Ozero__class_Ozero(_1059617)), _1059627)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059617), _1059625), _1059627) = c_Groups_Oone__class_Oone(_1059617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059617), _1059625), _1059619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059617), _1059627), _1059623))), _1059621)))], (44198 ^ _776545) ^ [_1660319, _1660321] : [-(c_List_Orotate(_1660319, _1660321) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1660319), tc_List_Olist(_1660319)), _1660321), c_List_Orotate1(_1660319)))], (7268 ^ _776545) ^ [_895242, _895244, _895246, _895248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895242, tc_HOL_Obool)), _895244), _895246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895242, tc_HOL_Obool)), _895244), hAPP(hAPP(c_Set_Oinsert(_895242), _895248), _895246))))], (5324 ^ _776545) ^ [_857820, _857822] : [_857822 = _857820, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_857822) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_857820))], (3748 ^ _776545) ^ [_832748, _832750, _832752, _832754, _832756, _832758, _832760, _832762] : [-(c_List_Omaps(_832762, _832758, _832754, _832750) = c_List_Omaps(_832760, _832756, _832752, _832748)), _832762 = _832760, _832758 = _832756, _832754 = _832752, _832750 = _832748], (19909 ^ _776545) ^ [_1135768, _1135770, _1135772, _1135774] : [class_Fields_Olinordered__field(_1135768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135768), _1135770), _1135772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135768), c_Groups_Ozero__class_Ozero(_1135768)), _1135774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135768), c_Groups_Ozero__class_Ozero(_1135768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135768), _1135772), _1135770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135768), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135768), _1135774), _1135772)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135768), _1135774), _1135770))))], (38564 ^ _776545) ^ [_1516339, _1516341] : [c_Wellfounded_Owf(_1516339, _1516341), -(c_Wellfounded_OwfP(_1516339, c_FunDef_Oin__rel(_1516339, _1516339, _1516341)))], (39998 ^ _776545) ^ [_1555223, _1555225, _1555227, _1555229, _1555231] : [class_Groups_Ocomm__monoid__mult(_1555223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555225), _1555227)), c_Fun_Oinj__on(_1555225, _1555225, _1555229, _1555227), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555225, _1555223), _1555231), hAPP(c_Set_Oimage(_1555225, _1555225, _1555229), _1555227)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555225, _1555223), hAPP(c_Fun_Ocomp(_1555225, _1555223, _1555225, _1555231), _1555229)), _1555227))], (14634 ^ _776545) ^ [_1040460, _1040462, _1040464, _1040466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040460), _1040462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040464), _1040466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040460), _1040464)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040462), _1040466))))], (134 ^ _776545) ^ [_778702, _778704, _778706, _778708, _778710, _778712, _778714, _778716, _778718, _778720, _778722, _778724] : [-(c_Finite__Set_Ofolding__image__simple(_778722, _778718, _778714, _778710, _778706, _778702)), c_Finite__Set_Ofolding__image__simple(_778724, _778720, _778716, _778712, _778708, _778704), _778724 = _778722, _778720 = _778718, _778716 = _778714, _778712 = _778710, _778708 = _778706, _778704 = _778702], (1714 ^ _776545) ^ [_800834, _800836] : [-(class_Rings_Ocomm__semiring(_800834)), _800836 = _800834, class_Rings_Ocomm__semiring(_800836)], (32536 ^ _776545) ^ [_1364702, _1364704, _1364706, _1364708, _1364710] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364702, tc_fun(_1364704, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364702, tc_HOL_Obool)), _1364706), _1364708)), _1364710) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364704, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364702, tc_fun(_1364704, tc_HOL_Obool)), _1364706), _1364710)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364702, tc_fun(_1364704, tc_HOL_Obool)), _1364708), _1364710)))], (32888 ^ _776545) ^ [_1375945, _1375947, _1375949, _1375951, _1375953] : [hBOOL(hAPP(hAPP(c_member(_1375945), _1375947), _1375949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1375951, tc_HOL_Obool)), hAPP(_1375953, _1375947)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1375945, tc_fun(_1375951, tc_HOL_Obool)), _1375949), _1375953))))], (3110 ^ _776545) ^ [_822815, _822817, _822819, _822821] : [-(c_List_Olistset(_822821, _822817) = c_List_Olistset(_822819, _822815)), _822821 = _822819, _822817 = _822815], (5300 ^ _776545) ^ [_857450, _857452, _857454, _857456] : [-(c_Lazy__Sequence_Oflat(_857456, _857452) = c_Lazy__Sequence_Oflat(_857454, _857450)), _857456 = _857454, _857452 = _857450], (26811 ^ _776545) ^ [_1259910, _1259912] : [c_Nat__Transfer_Ois__nat(_1259910), c_Nat__Transfer_Ois__nat(_1259912), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1259910), _1259912)))], (34882 ^ _776545) ^ [_1427419, _1427421, _1427423, _1427425, _1427427, _1427429, _1427431, _1427433] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427419, _1427421, _1427423), _1427425), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427427, _1427429, tc_prod(_1427419, _1427421)), _1427431), _1427433)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427427, _1427429, _1427423), hAPP(hAPP(c_COMBB(tc_fun(_1427429, tc_prod(_1427419, _1427421)), tc_fun(_1427429, _1427423), _1427427), hAPP(c_COMBB(tc_prod(_1427419, _1427421), _1427423, _1427429), hAPP(c_Product__Type_Oprod_Oprod__case(_1427419, _1427421, _1427423), _1427425))), _1427431)), _1427433))], (52195 ^ _776545) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52107 ^ _776545) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (29717 ^ _776545) ^ [_1309374] : [-(_1309374 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 29720 ^ _776545 : [(29727 ^ _776545) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1309374, 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, _1309374) = 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), _1309374), 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)))], (29721 ^ _776545) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1309374, 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, _1309374) = 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), _1309374), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (9184 ^ _776545) ^ [_935122, _935124, _935126] : [class_Orderings_Opreorder(_935122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935122), _935124), _935126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935122), _935126), _935124))], (22551 ^ _776545) ^ [_1185269, _1185271, _1185273] : [class_Rings_Olinordered__semidom(_1185269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185269), c_Groups_Ozero__class_Ozero(_1185269)), _1185271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185269), c_Groups_Ozero__class_Ozero(_1185269)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185269), _1185271), _1185273))))], (33129 ^ _776545) ^ [_1382366, _1382368, _1382370, _1382372, _1382374] : [33131 ^ _776545 : [(33134 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1382366), _1382368), hAPP(_1382374, 33130 ^ [_1382366, _1382368, _1382370, _1382372, _1382374])))], (33132 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382370), 33130 ^ [_1382366, _1382368, _1382370, _1382372, _1382374]), _1382372)))]], -(hBOOL(hAPP(hAPP(c_member(_1382366), _1382368), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1382370, tc_fun(_1382366, tc_HOL_Obool)), _1382372), _1382374))))], (38371 ^ _776545) ^ [_1512035, _1512037, _1512039, _1512041] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512035), _1512037)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512035), _1512039)), -(_1512039 = c_Orderings_Obot__class_Obot(tc_fun(_1512035, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1512035, tc_HOL_Obool), tc_fun(_1512035, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1512035, tc_HOL_Obool), tc_fun(_1512035, tc_HOL_Obool)), _1512037), _1512039)), c_Wellfounded_Omax__ext(_1512035, _1512041)))), 38385 ^ _776545 : [(38388 ^ _776545) ^ [_1512440] : [hBOOL(hAPP(hAPP(c_member(_1512035), _1512440), _1512039)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512035, _1512035)), hAPP(hAPP(c_Product__Type_OPair(_1512035, _1512035), 38384 ^ [_1512035, _1512037, _1512039, _1512041]), _1512440)), _1512041))], (38386 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512035), 38384 ^ [_1512035, _1512037, _1512039, _1512041]), _1512037)))]]], (52063 ^ _776545) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (8387 ^ _776545) ^ [_920466, _920468, _920470, _920472] : [class_Lattices_Osemilattice__inf(_920466), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920466), _920468), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920466), _920470), _920472)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920466), _920470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920466), _920468), _920472)))], (13314 ^ _776545) ^ [_1012605, _1012607, _1012609, _1012611, _1012613] : [class_Groups_Ocomm__monoid__mult(_1012605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012607), _1012609)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012607, _1012605), _1012611), hAPP(hAPP(c_Set_Oinsert(_1012607), _1012613), _1012609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012605), hAPP(_1012611, _1012613)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1012607, _1012605), _1012611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012607, tc_HOL_Obool)), _1012609), hAPP(hAPP(c_Set_Oinsert(_1012607), _1012613), c_Orderings_Obot__class_Obot(tc_fun(_1012607, tc_HOL_Obool)))))))], (10729 ^ _776545) ^ [_961430, _961432, _961434] : [class_Orderings_Oorder(_961430), 10732 ^ _776545 : [(10739 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961430), _961432), _961434))), -(c_Orderings_Obot__class_Obot(tc_fun(_961430, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961430, _961432), _961434))], (10733 ^ _776545) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_961430, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961430, _961432), _961434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961430), _961432), _961434))]]], (47475 ^ _776545) ^ [_1731293, _1731295] : [class_Orderings_Olinorder(_1731293), 47482 ^ _776545 : [(47487 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731293), hAPP(hAPP(c_List_Onth(_1731293), _1731295), 47480 ^ [_1731293, _1731295])), hAPP(hAPP(c_List_Onth(_1731293), _1731295), 47481 ^ [_1731293, _1731295])))], (47485 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47481 ^ [_1731293, _1731295]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731293)), _1731295))))], (47483 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47480 ^ [_1731293, _1731295]), 47481 ^ [_1731293, _1731295])))]], -(c_List_Olinorder__class_Osorted(_1731293, _1731295))], (8100 ^ _776545) ^ [_914404, _914406, _914408] : [8102 ^ _776545 : [(8105 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914404, tc_HOL_Obool)), 8101 ^ [_914404, _914406, _914408]), _914408) = c_Orderings_Obot__class_Obot(tc_fun(_914404, tc_HOL_Obool))], (8103 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_914404, tc_HOL_Obool)), 8101 ^ [_914404, _914406, _914408]), _914406)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914404, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_914404, tc_HOL_Obool), _914406)), _914408) = c_Orderings_Obot__class_Obot(tc_fun(_914404, tc_HOL_Obool)))], (50491 ^ _776545) ^ [_1797261, _1797263, _1797265, _1797267, _1797269] : [c_Fun_Obij__betw(_1797261, _1797263, _1797265, _1797267, _1797269), 50494 ^ _776545 : [(50501 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797263), _1797269)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1797261), _1797267)))], (50495 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797261), _1797267)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1797263), _1797269)))]]], (39227 ^ _776545) ^ [_1533850, _1533852, _1533854, _1533856] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1533850, _1533852)), hAPP(hAPP(c_Product__Type_OSigma(_1533850, _1533852), _1533854), hAPP(c_COMBK(tc_fun(_1533852, tc_HOL_Obool), _1533850), _1533856)))), -(_1533854 = c_Orderings_Obot__class_Obot(tc_fun(_1533850, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533852), _1533856)))], (40108 ^ _776545) ^ [_1557782, _1557784, _1557786, _1557788, _1557790, _1557792] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1557782, _1557784), _1557784, tc_prod(_1557786, _1557788), c_Product__Type_Osnd(_1557782, _1557784)), c_Product__Type_Omap__pair(_1557786, _1557782, _1557788, _1557784, _1557790, _1557792)) = hAPP(c_Fun_Ocomp(_1557788, _1557784, tc_prod(_1557786, _1557788), _1557792), c_Product__Type_Osnd(_1557786, _1557788)))], (42996 ^ _776545) ^ [_1633561, _1633563, _1633565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633561), tc_List_Olist(_1633561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633561), tc_List_Olist(_1633561)), c_List_Olist_ONil(_1633561)), _1633563)), c_List_Olistrel(_1633561, _1633565))), -(_1633563 = c_List_Olist_ONil(_1633561))], (10974 ^ _776545) ^ [_966252, _966254] : [class_Lattices_Olattice(_966252), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966252), _966254), _966254) = _966254)], (18634 ^ _776545) ^ [_1111993, _1111995, _1111997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111993), _1111995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111997), _1111995))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111993), _1111997)))], (16606 ^ _776545) ^ [] : [-(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)))], (37648 ^ _776545) ^ [_1493348, _1493350, _1493352, _1493354, _1493356, _1493358] : [c_Fun_Oinj__on(_1493348, _1493350, _1493352, _1493354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493350, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493348, _1493350, _1493352), _1493354)), _1493356)), c_Fun_Oinj__on(_1493350, _1493348, _1493358, _1493356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493348, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493350, _1493348, _1493358), _1493356)), _1493354)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493348), _1493354)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493350), _1493356)), -(hAPP(c_Finite__Set_Ocard(_1493348), _1493354) = hAPP(c_Finite__Set_Ocard(_1493350), _1493356))], (23061 ^ _776545) ^ [_1194385, _1194387] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1194385, _1194387))))], (7458 ^ _776545) ^ [_899327, _899329, _899331, _899333] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_899327, tc_HOL_Obool)), _899329), _899331), _899333)), 7461 ^ _776545 : [(7464 ^ _776545) ^ [] : [-(hBOOL(hAPP(_899331, _899333)))], (7462 ^ _776545) ^ [] : [-(hBOOL(hAPP(_899329, _899333)))]]], (11360 ^ _776545) ^ [_974428, _974430, _974432, _974434, _974436] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974428, _974430, hAPP(hAPP(c_Set_Oinsert(_974428), _974432), _974434)), _974436)), 11365 ^ _776545 : [(11370 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974428), 11363 ^ [_974428, _974430, _974432, _974434, _974436]), 11364 ^ [_974428, _974430, _974432, _974434, _974436]))], (11368 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974428, _974428, _974430, 11363 ^ [_974428, _974430, _974432, _974434, _974436], 11364 ^ [_974428, _974430, _974432, _974434, _974436]), _974436)))], (11366 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_974428), _974432), _974434) = hAPP(hAPP(c_Set_Oinsert(_974428), 11363 ^ [_974428, _974430, _974432, _974434, _974436]), 11364 ^ [_974428, _974430, _974432, _974434, _974436]))]]], (48450 ^ _776545) ^ [_1752537, _1752539, _1752541, _1752543] : [-(c_New__Random__Sequence_Oneg__map(_1752537, _1752539, _1752541, _1752543) = c_New__Random__Sequence_Oneg__bind(_1752537, _1752539, _1752543, hAPP(c_Fun_Ocomp(_1752539, 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(_1752539)))))), _1752537, c_New__Random__Sequence_Oneg__single(_1752539)), _1752541)))], (22479 ^ _776545) ^ [_1183819, _1183821, _1183823] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183819), _1183821)), _1183823) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1183819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183821), _1183823)))], (26112 ^ _776545) ^ [_1248444] : [hAPP(c_Int_Onat, _1248444) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248444), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14492 ^ _776545) ^ [_1038159, _1038161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038159), _1038161)), _1038161 = _1038159], (16588 ^ _776545) ^ [_1074926, _1074928, _1074930] : [16589 ^ _776545 : [(16592 ^ _776545) ^ [] : [_1074928 = _1074930], (16590 ^ _776545) ^ [] : [_1074926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074926), _1074928) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074926), _1074930))], (43204 ^ _776545) ^ [_1637170, _1637172, _1637174] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637170), tc_List_Olist(_1637170))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637170), tc_List_Olist(_1637170)), c_List_Olist_ONil(_1637170)), _1637172)), c_List_Olistrel1(_1637170, _1637174)))], (51639 ^ _776545) ^ [_1821086, _1821088, _1821090, _1821092] : [class_Divides_Osemiring__div(_1821086), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), _1821088), _1821090)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), _1821088), _1821092)), 51650 ^ _776545 : [(51657 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), _1821090), _1821092)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1821086), _1821090), _1821088)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1821086), _1821092), _1821088))))], (51651 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1821086), _1821090), _1821088)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1821086), _1821092), _1821088))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821086), _1821090), _1821092)))]]], (43763 ^ _776545) ^ [_1649872, _1649874, _1649876, _1649878, _1649880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649872), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649874)), _1649876))), -(hAPP(hAPP(c_List_Olist__update(_1649874, hAPP(hAPP(c_List_Oappend(_1649874), _1649876), _1649878)), _1649872), _1649880) = hAPP(hAPP(c_List_Oappend(_1649874), hAPP(hAPP(c_List_Olist__update(_1649874, _1649876), _1649872), _1649880)), _1649878))], (27605 ^ _776545) ^ [_1273081, _1273083] : [class_Rings_Olinordered__idom(_1273081), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273081), c_Groups_Osgn__class_Osgn(_1273081, _1273083)), hAPP(c_Groups_Oabs__class_Oabs(_1273081), _1273083)) = _1273083)], (46970 ^ _776545) ^ [_1720595, _1720597, _1720599] : [hAPP(c_List_Orev(_1720595), _1720597) = hAPP(hAPP(c_List_Olist_OCons(_1720595), _1720599), c_List_Olist_ONil(_1720595)), -(_1720597 = hAPP(hAPP(c_List_Olist_OCons(_1720595), _1720599), c_List_Olist_ONil(_1720595)))], (26082 ^ _776545) ^ [_1247948, _1247950] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247948))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247948), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247950)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26967 ^ _776545) ^ [_1262310] : [class_Rings_Oring__1(_1262310), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262310), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1262310))], (46148 ^ _776545) ^ [_1703387, _1703389] : [-(c_List_Otranspose(_1703387, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1703387)), c_List_Olist_ONil(_1703387)), _1703389)) = c_List_Otranspose(_1703387, _1703389))], (14596 ^ _776545) ^ [_1039669, _1039671] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039669), _1039671) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039671), _1039669))], (50135 ^ _776545) ^ [_1789558, _1789560, _1789562, _1789564, _1789566] : [c_Fun_Oinj__on(_1789558, _1789560, _1789562, _1789564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789558, tc_HOL_Obool)), _1789566), _1789564)), -(hAPP(c_Set_Oimage(_1789560, _1789558, c_Hilbert__Choice_Oinv__into(_1789558, _1789560, _1789564, _1789562)), hAPP(c_Set_Oimage(_1789558, _1789560, _1789562), _1789566)) = _1789566)], (4574 ^ _776545) ^ [_846007, _846009, _846011, _846013] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846013, _846009) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_846011, _846007)), _846013 = _846011, _846009 = _846007], (33931 ^ _776545) ^ [_1405530, _1405532, _1405534] : [hBOOL(hAPP(c_Predicate_OPowp(_1405530, hAPP(hAPP(c_COMBC(_1405530, tc_fun(_1405530, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405530)), _1405532)), _1405534)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1405530, tc_HOL_Obool)), _1405534), hAPP(c_Set_OPow(_1405530), _1405532))))], (31625 ^ _776545) ^ [_1344324, _1344326, _1344328, _1344330] : [class_Orderings_Olinorder(_1344324), 31628 ^ _776545 : [(31629 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344324), _1344328), _1344330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), _1344328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), _1344330)))], (31639 ^ _776545) ^ [] : [31640 ^ _776545 : [(31643 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), _1344330))], (31641 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), _1344328))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344324), _1344326), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344324), _1344328), _1344330))))]]], (20851 ^ _776545) ^ [_1153046, _1153048, _1153050, _1153052] : [class_Fields_Olinordered__field__inverse__zero(_1153046), 20854 ^ _776545 : [(20855 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153048), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153046), _1153050), _1153052))), 20858 ^ _776545 : [(20865 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), c_Groups_Ozero__class_Ozero(_1153046)), _1153052))), 20868 ^ _776545 : [(20875 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), _1153052), c_Groups_Ozero__class_Ozero(_1153046)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153048), c_Groups_Ozero__class_Ozero(_1153046))))], (20869 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), _1153052), c_Groups_Ozero__class_Ozero(_1153046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153046), _1153048), _1153052))))]]], (20859 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), c_Groups_Ozero__class_Ozero(_1153046)), _1153052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153046), _1153048), _1153052)), _1153050)))]]], (20881 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153048), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153046), _1153050), _1153052)))), 20884 ^ _776545 : [(20887 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153046), _1153048), _1153052)), _1153050))], (20885 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), c_Groups_Ozero__class_Ozero(_1153046)), _1153052)))]], 20888 ^ _776545 : [(20891 ^ _776545) ^ [] : [20892 ^ _776545 : [(20895 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153046), _1153048), _1153052)))], (20893 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), _1153052), c_Groups_Ozero__class_Ozero(_1153046))))]], 20896 ^ _776545 : [(20899 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153046), _1153048), c_Groups_Ozero__class_Ozero(_1153046)))], (20897 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), _1153052), c_Groups_Ozero__class_Ozero(_1153046)))]]], (20889 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153046), c_Groups_Ozero__class_Ozero(_1153046)), _1153052))]]]]], (39004 ^ _776545) ^ [_1527555, _1527557, _1527559, _1527561] : [hBOOL(hAPP(c_Predicate_ODomainP(_1527555, _1527557, _1527559), _1527561)), -(hBOOL(hAPP(hAPP(_1527559, _1527561), 39007 ^ [_1527555, _1527557, _1527559, _1527561])))], (38711 ^ _776545) ^ [_1520589, _1520591, _1520593, _1520595] : [-(hAPP(c_Set_Ovimage(_1520589, _1520591, _1520593), _1520595) = hAPP(c_Set_OCollect(_1520589), hAPP(hAPP(c_COMBC(_1520589, tc_fun(_1520591, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1520591, tc_fun(tc_fun(_1520591, tc_HOL_Obool), tc_HOL_Obool), _1520589), c_member(_1520591)), _1520593)), _1520595)))], (2796 ^ _776545) ^ [_817918, _817920, _817922, _817924, _817926, _817928, _817930, _817932] : [-(c_Product__Type_Oapsnd(_817932, _817928, _817924, _817920) = c_Product__Type_Oapsnd(_817930, _817926, _817922, _817918)), _817932 = _817930, _817928 = _817926, _817924 = _817922, _817920 = _817918], (7704 ^ _776545) ^ [_905263, _905265, _905267, _905269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905263, tc_HOL_Obool)), _905265), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905263, tc_HOL_Obool)), _905267), _905269))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905263, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905263, tc_HOL_Obool)), _905265), _905267)), _905269)))], (30094 ^ _776545) ^ [_1316361, _1316363, _1316365, _1316367] : [class_Groups_Oordered__ab__group__add(_1316361), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316361), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316361), _1316363), _1316365)), _1316367) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316361), _1316363), _1316367)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1316361), _1316365), _1316367)))], (50612 ^ _776545) ^ [_1799611, _1799613, _1799615, _1799617] : [-(c_Product__Type_Ocurry(_1799611, _1799613, _1799615, hAPP(c_Product__Type_Oprod_Oprod__case(_1799611, _1799613, _1799615), _1799617)) = _1799617)], (50353 ^ _776545) ^ [_1794624, _1794626, _1794628, _1794630, _1794632, _1794634, _1794636, _1794638] : [c_Fun_Obij__betw(_1794624, _1794626, _1794628, _1794630, _1794632), 50356 ^ _776545 : [(50363 ^ _776545) ^ [] : [c_Fun_Obij__betw(_1794624, _1794634, hAPP(c_Fun_Ocomp(_1794626, _1794634, _1794624, _1794636), _1794628), _1794630, _1794638), -(c_Fun_Obij__betw(_1794626, _1794634, _1794636, _1794632, _1794638))], (50357 ^ _776545) ^ [] : [c_Fun_Obij__betw(_1794626, _1794634, _1794636, _1794632, _1794638), -(c_Fun_Obij__betw(_1794624, _1794634, hAPP(c_Fun_Ocomp(_1794626, _1794634, _1794624, _1794636), _1794628), _1794630, _1794638))]]], (46554 ^ _776545) ^ [_1712560, _1712562, _1712564, _1712566] : [class_Orderings_Olinorder(_1712560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712560), _1712562), _1712564)), c_List_Olinorder__class_Osorted(_1712560, hAPP(hAPP(c_List_Olist_OCons(_1712560), _1712564), _1712566)), -(c_List_Olinorder__class_Osorted(_1712560, hAPP(hAPP(c_List_Olist_OCons(_1712560), _1712562), hAPP(hAPP(c_List_Olist_OCons(_1712560), _1712564), _1712566))))], (47371 ^ _776545) ^ [_1729082, _1729084, _1729086] : [class_Orderings_Olinorder(_1729082), c_List_Olinorder__class_Osorted(_1729082, _1729084), -(c_List_Olinorder__class_Osorted(_1729082, c_List_OdropWhile(_1729082, _1729086, _1729084)))], (44150 ^ _776545) ^ [_1659369, _1659371, _1659373] : [-(hAPP(c_List_Otl(_1659369), hAPP(hAPP(c_List_Odrop(_1659369), _1659371), _1659373)) = hAPP(hAPP(c_List_Odrop(_1659369), _1659371), hAPP(c_List_Otl(_1659369), _1659373)))], (52073 ^ _776545) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (29415 ^ _776545) ^ [_1303651, _1303653] : [class_Rings_Olinordered__idom(_1303651), 29418 ^ _776545 : [(29425 ^ _776545) ^ [] : [-(_1303653 = c_Groups_Ozero__class_Ozero(_1303651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303651), c_Groups_Ozero__class_Ozero(_1303651)), hAPP(hAPP(c_Power_Opower__class_Opower(_1303651), _1303653), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29419 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303651), c_Groups_Ozero__class_Ozero(_1303651)), hAPP(hAPP(c_Power_Opower__class_Opower(_1303651), _1303653), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1303653 = c_Groups_Ozero__class_Ozero(_1303651)]]], (45191 ^ _776545) ^ [_1681797] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1681797)) = _1681797)], (32656 ^ _776545) ^ [_1369471, _1369473, _1369475, _1369477] : [-(hBOOL(hAPP(hAPP(c_member(_1369471), _1369473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369471, tc_HOL_Obool)), _1369475), hAPP(c_Set_OCollect(_1369471), _1369477))))), hBOOL(hAPP(hAPP(c_member(_1369471), _1369473), _1369475)), hBOOL(hAPP(_1369477, _1369473))], (49340 ^ _776545) ^ [_1772567, _1772569, _1772571] : [-(c_List_Olist__ex(_1772567, _1772569, _1772571)), 49341 ^ _776545 : [(49342 ^ _776545) ^ [_1772624] : [hBOOL(hAPP(hAPP(c_member(_1772567), _1772624), hAPP(c_List_Oset(_1772567), _1772571))), hBOOL(hAPP(_1772569, _1772624))]]], (13738 ^ _776545) ^ [_1021280, _1021282, _1021284, _1021286] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021280), _1021282), _1021284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021280), _1021286), _1021282)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021280), _1021286), _1021284))))], (1514 ^ _776545) ^ [_798334, _798336] : [-(class_Rings_Olinordered__comm__semiring__strict(_798334)), _798336 = _798334, class_Rings_Olinordered__comm__semiring__strict(_798336)], (22231 ^ _776545) ^ [_1179702, _1179704] : [22232 ^ _776545 : [(22235 ^ _776545) ^ [] : [_1179702 = _1179704], (22233 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179702), _1179704))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179704), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14308 ^ _776545) ^ [_1034421, _1034423, _1034425, _1034427, _1034429] : [class_Rings_Ocomm__semiring__1(_1034421), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), _1034423), _1034425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), _1034427), _1034429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), _1034423), _1034427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034421), _1034425), _1034429)))], (21064 ^ _776545) ^ [_1157223, _1157225, _1157227, _1157229] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1157223, tc_Nat_Onat), _1157225), _1157227) = hAPP(c_Nat_OSuc, _1157229), 21068 ^ _776545 : [(21071 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1157225, 21067 ^ [_1157223, _1157225, _1157227, _1157229]))))], (21069 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1157223), 21067 ^ [_1157223, _1157225, _1157227, _1157229]), _1157227)))]]], (44617 ^ _776545) ^ [_1668693, _1668695] : [-(_1668693 = c_List_Olist_ONil(_1668695)), -(hBOOL(hAPP(hAPP(c_member(_1668695), c_List_Olast(_1668695, _1668693)), hAPP(c_List_Oset(_1668695), _1668693))))], (21297 ^ _776545) ^ [_1161997, _1161999] : [class_Int_Onumber__ring(_1161997), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1161997), hAPP(c_Int_Onumber__class_Onumber__of(_1161997), _1161999)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161997), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161999)))], (26064 ^ _776545) ^ [_1247699, _1247701] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247699), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247701)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247699, _1247701)))], (24331 ^ _776545) ^ [_1216615, _1216617, _1216619, _1216621] : [class_Divides_Osemiring__div(_1216615), -(_1216617 = c_Groups_Ozero__class_Ozero(_1216615)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216615), _1216619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216615), _1216617), _1216621))), _1216617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216615), _1216621), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216615), _1216619), _1216617)))], (24489 ^ _776545) ^ [_1219460, _1219462, _1219464] : [-(hBOOL(hAPP(_1219460, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1219462), _1219464)))), 24492 ^ _776545 : [(24495 ^ _776545) ^ [] : [hBOOL(hAPP(_1219460, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24493 ^ _776545) ^ [] : [-(_1219464 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24498 ^ _776545 : [(24499 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219464)))], (24505 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24501 ^ [_1219460, _1219462, _1219464]), _1219464)))], (24509 ^ _776545) ^ [] : [hBOOL(hAPP(_1219460, 24500 ^ [_1219460, _1219462, _1219464]))], (24507 ^ _776545) ^ [] : [-(_1219462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219464), 24500 ^ [_1219460, _1219462, _1219464])), 24501 ^ [_1219460, _1219462, _1219464]))], (24503 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24501 ^ [_1219460, _1219462, _1219464])))]], 24510 ^ _776545 : [(24511 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219464), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24517 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24513 ^ [_1219460, _1219462, _1219464]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24521 ^ _776545) ^ [] : [hBOOL(hAPP(_1219460, 24512 ^ [_1219460, _1219462, _1219464]))], (24519 ^ _776545) ^ [] : [-(_1219462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219464), 24512 ^ [_1219460, _1219462, _1219464])), 24513 ^ [_1219460, _1219462, _1219464]))], (24515 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219464), 24513 ^ [_1219460, _1219462, _1219464])))]]], (23773 ^ _776545) ^ [_1207117, _1207119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207117)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207117), _1207119)))], (15646 ^ _776545) ^ [_1060345] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1060345), hAPP(c_Nat_OSuc, _1060345))))], (51945 ^ _776545) ^ [_1825778, _1825780] : [class_Groups_Ouminus(_1825778), -(class_Groups_Ouminus(tc_fun(_1825780, _1825778)))], (39503 ^ _776545) ^ [_1542325, _1542327, _1542329, _1542331, _1542333, _1542335, _1542337, _1542339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542325, _1542327)), _1542329), hAPP(c_Set_Oimage(tc_prod(_1542331, _1542333), tc_prod(_1542325, _1542327), c_Product__Type_Omap__pair(_1542331, _1542325, _1542333, _1542327, _1542335, _1542337)), _1542339))), 39508 ^ _776545 : [(39511 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542331, _1542333)), hAPP(hAPP(c_Product__Type_OPair(_1542331, _1542333), 39506 ^ [_1542325, _1542327, _1542329, _1542331, _1542333, _1542335, _1542337, _1542339]), 39507 ^ [_1542325, _1542327, _1542329, _1542331, _1542333, _1542335, _1542337, _1542339])), _1542339)))], (39509 ^ _776545) ^ [] : [-(_1542329 = hAPP(hAPP(c_Product__Type_OPair(_1542325, _1542327), hAPP(_1542335, 39506 ^ [_1542325, _1542327, _1542329, _1542331, _1542333, _1542335, _1542337, _1542339])), hAPP(_1542337, 39507 ^ [_1542325, _1542327, _1542329, _1542331, _1542333, _1542335, _1542337, _1542339])))]]], (39247 ^ _776545) ^ [_1534432, _1534434, _1534436, _1534438] : [-(_1534432 = c_Orderings_Obot__class_Obot(tc_fun(_1534434, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1534436, _1534434), _1534436, c_Product__Type_Ofst(_1534436, _1534434)), hAPP(hAPP(c_Product__Type_OSigma(_1534436, _1534434), _1534438), hAPP(c_COMBK(tc_fun(_1534434, tc_HOL_Obool), _1534436), _1534432))) = _1534438)], (24361 ^ _776545) ^ [_1217135, _1217137, _1217139] : [class_Divides_Osemiring__div(_1217135), -(_1217137 = c_Groups_Ozero__class_Ozero(_1217135)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217135), _1217139), _1217137)), _1217137) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217135), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1217135), _1217139), _1217137)), c_Groups_Oone__class_Oone(_1217135)))], (16765 ^ _776545) ^ [_1078125, _1078127, _1078129] : [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, _1078125)), _1078127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078125)), _1078129))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078127), _1078129)))], (51279 ^ _776545) ^ [_1814766, _1814768, _1814770] : [class_Rings_Ocomm__semiring__1(_1814766), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814766), _1814768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814766), _1814768), _1814770))))], (49754 ^ _776545) ^ [_1781967, _1781969] : [-(c_Relation_Osym(_1781967, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1781967, _1781967), tc_HOL_Obool)), _1781969), hAPP(c_Relation_Oconverse(_1781967, _1781967), _1781969))))], (31873 ^ _776545) ^ [_1349076, _1349078, _1349080] : [class_Orderings_Olinorder(_1349076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349076), _1349078)), 31880 ^ _776545 : [(31887 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349076, tc_HOL_Obool)), _1349078), hAPP(hAPP(c_Set_Oinsert(_1349076), _1349080), c_Orderings_Obot__class_Obot(tc_fun(_1349076, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349076, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1349076, hAPP(hAPP(c_Set_Oinsert(_1349076), _1349080), _1349078)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349076), _1349080), c_Big__Operators_Olinorder__class_OMax(_1349076, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349076, tc_HOL_Obool)), _1349078), hAPP(hAPP(c_Set_Oinsert(_1349076), _1349080), c_Orderings_Obot__class_Obot(tc_fun(_1349076, tc_HOL_Obool)))))))], (31881 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349076, tc_HOL_Obool)), _1349078), hAPP(hAPP(c_Set_Oinsert(_1349076), _1349080), c_Orderings_Obot__class_Obot(tc_fun(_1349076, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349076, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1349076, hAPP(hAPP(c_Set_Oinsert(_1349076), _1349080), _1349078)) = _1349080)]]], (17289 ^ _776545) ^ [_1087783, _1087785, _1087787, _1087789] : [class_Rings_Olinordered__ring__strict(_1087783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087783), _1087785), _1087787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087783), _1087789), c_Groups_Ozero__class_Ozero(_1087783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087783), _1087789), _1087787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087783), _1087789), _1087785))))], (42438 ^ _776545) ^ [_1619101, _1619103, _1619105] : [hBOOL(hAPP(hAPP(c_member(_1619101), _1619103), hAPP(c_List_Oset(_1619101), _1619105))), 42442 ^ _776545 : [(42445 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1619101), _1619105), 42441 ^ [_1619101, _1619103, _1619105]) = _1619103)], (42443 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42441 ^ [_1619101, _1619103, _1619105]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619101)), _1619105))))]]], (36338 ^ _776545) ^ [_1462960, _1462962, _1462964, _1462966] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462960), _1462962)), 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)), _1462960), _1462964)), 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)), _1462962), _1462966)), 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)), _1462962), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462964), _1462966))), c_FunDef_Omin__weak)))], (24740 ^ _776545) ^ [_1224123, _1224125] : [_1224123 = _1224125, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224123) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224125))], (30314 ^ _776545) ^ [_1320257, _1320259, _1320261, _1320263] : [class_Orderings_Olinorder(_1320257), 30317 ^ _776545 : [(30326 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320257), _1320261), _1320263)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), _1320261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), _1320263))], (30318 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320257), _1320261), _1320263))), 30321 ^ _776545 : [(30324 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), _1320263)))], (30322 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320257), _1320259), _1320261)))]]]]], (44948 ^ _776545) ^ [_1676533, _1676535, _1676537, _1676539] : [c_Fun_Oinj__on(_1676533, _1676535, _1676537, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1676533, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1676533), tc_fun(_1676533, tc_HOL_Obool), c_List_Oset(_1676533)), _1676539))), -(c_Fun_Oinj__on(tc_List_Olist(_1676533), tc_List_Olist(_1676535), hAPP(c_List_Omap(_1676533, _1676535), _1676537), _1676539))], (29573 ^ _776545) ^ [_1306315, _1306317, _1306319] : [class_Rings_Olinordered__idom(_1306315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306315), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306315), hAPP(hAPP(c_Power_Opower__class_Opower(_1306315), _1306317), 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(_1306315), _1306319), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1306315)))], (24413 ^ _776545) ^ [_1218013, _1218015, _1218017, _1218019] : [_1218013 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218015), _1218017)), _1218019), -(_1218015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1218013), _1218015) = _1218017), 24420 ^ _776545 : [(24423 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218019), _1218015))], (24421 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218015)))]], 24428 ^ _776545 : [(24431 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218015), _1218019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1218019), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24429 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218015))]]], (34001 ^ _776545) ^ [_1407754, _1407756] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1407754), _1407756)), -(hAPP(c_Finite__Set_Ocard(_1407754), _1407756) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1407754, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1407754), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407756))], (37864 ^ _776545) ^ [_1498255, _1498257, _1498259, _1498261] : [c_Fun_Oinj__on(_1498255, _1498257, _1498259, _1498261), -(hAPP(c_Set_Oimage(_1498257, _1498255, c_Fun_Othe__inv__into(_1498255, _1498257, _1498261, _1498259)), hAPP(c_Set_Oimage(_1498255, _1498257, _1498259), _1498261)) = _1498261)], (45020 ^ _776545) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (28903 ^ _776545) ^ [_1294723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1294723)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294723), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9822 ^ _776545) ^ [_944831, _944833, _944835] : [class_Complete__Lattice_Ocomplete__lattice(_944831), class_Orderings_Olinorder(_944831), 9829 ^ _776545 : [(9839 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944831), _944833), c_Complete__Lattice_OSup__class_OSup(_944831, _944835)))), 9840 ^ _776545 : [(9841 ^ _776545) ^ [_945137] : [hBOOL(hAPP(hAPP(c_member(_944831), _945137), _944835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944831), _944833), _945137))]]], (9830 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944831), _944833), c_Complete__Lattice_OSup__class_OSup(_944831, _944835))), 9834 ^ _776545 : [(9837 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944831), _944833), 9833 ^ [_944831, _944833, _944835])))], (9835 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944831), 9833 ^ [_944831, _944833, _944835]), _944835)))]]]]], (34295 ^ _776545) ^ [_1414686, _1414688] : [-(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), _1414686)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414688), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414686))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (52183 ^ _776545) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (25153 ^ _776545) ^ [_1231933, _1231935, _1231937] : [class_Divides_Osemiring__div(_1231933), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1231933), c_Divides_Odiv__class_Omod(_1231933, _1231935, _1231937)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231933), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231933), _1231935), _1231937)), _1231937)) = _1231935)], (12161 ^ _776545) ^ [_990021, _990023, _990025] : [class_Lattices_Olattice(_990021), hBOOL(hAPP(c_Finite__Set_Ofinite(_990021), _990023)), -(_990025 = c_Orderings_Obot__class_Obot(tc_fun(_990021, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990021, tc_HOL_Obool)), _990025), _990023)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_990021), c_Big__Operators_Olattice__class_OSup__fin(_990021, _990025)), c_Big__Operators_Olattice__class_OSup__fin(_990021, _990023)) = c_Big__Operators_Olattice__class_OSup__fin(_990021, _990023))], (42043 ^ _776545) ^ [_1608520, _1608522, _1608524, _1608526, _1608528, _1608530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608520, _1608520)), hAPP(hAPP(c_Product__Type_OPair(_1608520, _1608520), _1608522), _1608524)), _1608526)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608520), tc_List_Olist(_1608520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608520), tc_List_Olist(_1608520)), _1608528), _1608530)), c_List_Olistrel(_1608520, _1608526))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608520), tc_List_Olist(_1608520))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608520), tc_List_Olist(_1608520)), hAPP(hAPP(c_List_Olist_OCons(_1608520), _1608522), _1608528)), hAPP(hAPP(c_List_Olist_OCons(_1608520), _1608524), _1608530))), c_List_Olistrel(_1608520, _1608526))))], (14314 ^ _776545) ^ [_1034598, _1034600, _1034602, _1034604, _1034606] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1034598), 14317 ^ _776545 : [(14318 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034600), _1034602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034604), _1034606)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034600), _1034606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034604), _1034602)), -(_1034600 = _1034604), -(_1034602 = _1034606)], (14328 ^ _776545) ^ [] : [14329 ^ _776545 : [(14332 ^ _776545) ^ [] : [_1034602 = _1034606], (14330 ^ _776545) ^ [] : [_1034600 = _1034604]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034600), _1034602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034604), _1034606)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034600), _1034606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034598), _1034604), _1034602)))]]], (16110 ^ _776545) ^ [_1067778, _1067780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067778)), hAPP(c_Nat_OSuc, _1067780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067778), _1067780)))], (10893 ^ _776545) ^ [_964542, _964544, _964546, _964548, _964550] : [class_Groups_Oab__semigroup__mult(_964542), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964542, _964542, c_Groups_Otimes__class_Otimes(_964542), _964544, _964546), _964548)), hBOOL(hAPP(hAPP(c_member(_964542), _964550), _964546)), -(hBOOL(hAPP(hAPP(c_member(_964542), _964544), _964546))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_964542, _964542, c_Groups_Otimes__class_Otimes(_964542), _964550, hAPP(hAPP(c_Set_Oinsert(_964542), _964544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964542, tc_HOL_Obool)), _964546), hAPP(hAPP(c_Set_Oinsert(_964542), _964550), c_Orderings_Obot__class_Obot(tc_fun(_964542, tc_HOL_Obool)))))), _964548)))], (44611 ^ _776545) ^ [_1668641, _1668643, _1668645] : [-(_1668641 = c_List_Olist_ONil(_1668643)), -(c_List_Olast(_1668643, hAPP(hAPP(c_List_Oappend(_1668643), _1668645), _1668641)) = c_List_Olast(_1668643, _1668641))], (4708 ^ _776545) ^ [_848158, _848160, _848162, _848164, _848166, _848168, _848170, _848172] : [-(c_Random__Sequence_Omap(_848172, _848168, _848164, _848160) = c_Random__Sequence_Omap(_848170, _848166, _848162, _848158)), _848172 = _848170, _848168 = _848166, _848164 = _848162, _848160 = _848158], (42705 ^ _776545) ^ [_1626870, _1626872, _1626874, _1626876, _1626878] : [-(hAPP(hAPP(c_List_Olist__update(_1626870, hAPP(hAPP(c_List_Olist_OCons(_1626870), _1626872), _1626874)), _1626876), _1626878) = c_Nat_Onat_Onat__case(tc_List_Olist(_1626870), hAPP(hAPP(c_List_Olist_OCons(_1626870), _1626878), _1626874), hAPP(hAPP(c_COMBB(tc_List_Olist(_1626870), tc_List_Olist(_1626870), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1626870), _1626872)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1626870, tc_List_Olist(_1626870)), c_List_Olist__update(_1626870, _1626874)), _1626878)), _1626876))], (25291 ^ _776545) ^ [_1234286, _1234288] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234286, _1234288) = 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), _1234286), _1234288) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10835 ^ _776545) ^ [_963376, _963378, _963380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963376, tc_HOL_Obool)), _963378), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_963376, tc_HOL_Obool)), _963380))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963376, tc_HOL_Obool)), _963378), _963380) = c_Orderings_Obot__class_Obot(tc_fun(_963376, tc_HOL_Obool)))], (48480 ^ _776545) ^ [_1753348, _1753350] : [c_Wellfounded_Oacyclic(_1753348, hAPP(c_Set_OCollect(tc_prod(_1753348, _1753348)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753348, _1753348, tc_HOL_Obool), _1753350))), -(c_Wellfounded_Oacyclic(_1753348, hAPP(c_Set_OCollect(tc_prod(_1753348, _1753348)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753348, _1753348, tc_HOL_Obool), c_Predicate_Oconversep(_1753348, _1753348, _1753350)))))], (40761 ^ _776545) ^ [_1574103, _1574105, _1574107] : [-(c_Transitive__Closure_Ortrancl(_1574103, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574103, _1574103), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574103, _1574105)), c_Transitive__Closure_Ortrancl(_1574103, _1574107))) = c_Transitive__Closure_Ortrancl(_1574103, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574103, _1574103), tc_HOL_Obool)), _1574105), _1574107)))], (32131 ^ _776545) ^ [_1353899, _1353901, _1353903] : [class_Orderings_Olinorder(_1353899), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353899), _1353901)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353899), _1353903)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353899, tc_HOL_Obool)), _1353901), _1353903) = c_Orderings_Obot__class_Obot(tc_fun(_1353899, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353899), c_Big__Operators_Olattice_OSup__fin(_1353899, c_Orderings_Oord__class_Omax(_1353899), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353899, tc_HOL_Obool)), _1353901), _1353903))), c_Big__Operators_Olattice_OSup__fin(_1353899, c_Orderings_Oord__class_Omax(_1353899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353899, tc_HOL_Obool)), _1353901), _1353903))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353899), c_Big__Operators_Olattice_OSup__fin(_1353899, c_Orderings_Oord__class_Omax(_1353899), _1353901)), c_Big__Operators_Olattice_OSup__fin(_1353899, c_Orderings_Oord__class_Omax(_1353899), _1353903)))], (37216 ^ _776545) ^ [_1484886, _1484888] : [class_Groups_Oordered__ab__group__add(_1484886), -(c_Fun_Oinj__on(_1484886, _1484886, c_Groups_Ouminus__class_Ouminus(_1484886), _1484888))], (24266 ^ _776545) ^ [_1215425] : [_1215425 = 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), _1215425)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8573 ^ _776545) ^ [_923801, _923803, _923805] : [class_Lattices_Osemilattice__sup(_923801), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923801), _923803), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923801), _923805), _923803))))], (5176 ^ _776545) ^ [_855512, _855514, _855516, _855518, _855520, _855522, _855524, _855526] : [-(c_Quotient_OBabs(_855526, _855522, _855518, _855514) = c_Quotient_OBabs(_855524, _855520, _855516, _855512)), _855526 = _855524, _855522 = _855520, _855518 = _855516, _855514 = _855512], (26625 ^ _776545) ^ [_1257084, _1257086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257084), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257084), _1257086)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1257084))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1257086))))], (4310 ^ _776545) ^ [_841815, _841817, _841819, _841821] : [-(c_List_Omap(_841821, _841817) = c_List_Omap(_841819, _841815)), _841821 = _841819, _841817 = _841815], (20811 ^ _776545) ^ [_1152260, _1152262, _1152264, _1152266] : [class_Fields_Ofield(_1152260), -(_1152262 = c_Groups_Ozero__class_Ozero(_1152260)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152260), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152260), _1152264), _1152262)), _1152266) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1152260), _1152264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152260), _1152262), _1152266))), _1152262))], (43858 ^ _776545) ^ [_1652673, _1652675] : [-(hAPP(c_List_Orotate1(_1652673), _1652675) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1652673), _1652673, c_List_Olist_ONil(_1652673), hAPP(hAPP(c_COMBB(tc_List_Olist(_1652673), tc_fun(tc_List_Olist(_1652673), tc_List_Olist(_1652673)), _1652673), hAPP(c_COMBC(tc_List_Olist(_1652673), tc_List_Olist(_1652673), tc_List_Olist(_1652673)), c_List_Oappend(_1652673))), hAPP(hAPP(c_COMBC(_1652673, tc_List_Olist(_1652673), tc_List_Olist(_1652673)), c_List_Olist_OCons(_1652673)), c_List_Olist_ONil(_1652673)))), _1652675))], (24932 ^ _776545) ^ [_1228003, _1228005, _1228007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228003), _1228005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228003), _1228007)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228005), _1228007))))], (29333 ^ _776545) ^ [_1302184, _1302186] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1302184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1302186))) = 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), _1302184), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1302186))))], (41064 ^ _776545) ^ [_1581335, _1581337, _1581339, _1581341, _1581343] : [-(hAPP(c_Relation_Oconverse(_1581335, _1581337), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581339, tc_fun(tc_prod(_1581335, _1581337), tc_HOL_Obool)), _1581341), _1581343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581339, tc_fun(tc_prod(_1581337, _1581335), tc_HOL_Obool)), _1581341), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581335, _1581337), tc_HOL_Obool), tc_fun(tc_prod(_1581337, _1581335), tc_HOL_Obool), _1581339), c_Relation_Oconverse(_1581335, _1581337)), _1581343)))], (43984 ^ _776545) ^ [_1655686, _1655688, _1655690, _1655692] : [_1655686 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1655688), _1655686), hAPP(hAPP(c_List_Olist_OCons(_1655688), _1655690), _1655692)) = hAPP(hAPP(c_List_Olist_OCons(_1655688), _1655690), _1655692))], (44328 ^ _776545) ^ [_1663050, _1663052, _1663054, _1663056, _1663058, _1663060] : [class_Orderings_Olinorder(_1663050), 44331 ^ _776545 : [(44338 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1663050), hAPP(_1663052, _1663054)), hAPP(_1663052, _1663056)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663058, _1663050, _1663052), _1663054), hAPP(hAPP(c_List_Olist_OCons(_1663058), _1663056), _1663060)) = hAPP(hAPP(c_List_Olist_OCons(_1663058), _1663056), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663058, _1663050, _1663052), _1663054), _1663060)))], (44332 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1663050), hAPP(_1663052, _1663054)), hAPP(_1663052, _1663056))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663058, _1663050, _1663052), _1663054), hAPP(hAPP(c_List_Olist_OCons(_1663058), _1663056), _1663060)) = hAPP(hAPP(c_List_Olist_OCons(_1663058), _1663054), hAPP(hAPP(c_List_Olist_OCons(_1663058), _1663056), _1663060)))]]], (50922 ^ _776545) ^ [_1807877, _1807879, _1807881] : [c_List_Olist__ex(tc_Nat_Onat, _1807877, c_List_Oupt(_1807879, _1807881)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1807877), _1807879, _1807881)], (1864 ^ _776545) ^ [_802709, _802711] : [-(class_Groups_Ozero(_802709)), _802711 = _802709, class_Groups_Ozero(_802711)], (43366 ^ _776545) ^ [_1641098, _1641100, _1641102, _1641104, _1641106] : [hAPP(hAPP(c_List_Oappend(_1641098), _1641100), _1641102) = hAPP(hAPP(c_List_Olist_OCons(_1641098), _1641104), _1641106), 43371 ^ _776545 : [(43374 ^ _776545) ^ [] : [-(_1641102 = hAPP(hAPP(c_List_Olist_OCons(_1641098), _1641104), _1641106))], (43372 ^ _776545) ^ [] : [-(_1641100 = c_List_Olist_ONil(_1641098))]], 43376 ^ _776545 : [(43379 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1641098), 43375 ^ [_1641098, _1641100, _1641102, _1641104, _1641106]), _1641102) = _1641106)], (43377 ^ _776545) ^ [] : [-(_1641100 = hAPP(hAPP(c_List_Olist_OCons(_1641098), _1641104), 43375 ^ [_1641098, _1641100, _1641102, _1641104, _1641106]))]]], (11618 ^ _776545) ^ [_979785, _979787, _979789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979785, tc_HOL_Obool)), _979787), _979789)), hBOOL(hAPP(c_Finite__Set_Ofinite(_979785), _979789)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979785), _979787)))], (26647 ^ _776545) ^ [_1257494, _1257496] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1257494, _1257496)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1257494), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (11688 ^ _776545) ^ [_981017, _981019, _981021, _981023, _981025, _981027] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_981017, _981019, _981021, _981023, _981025), _981027)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981017), _981025)))], (45132 ^ _776545) ^ [_1680438, _1680440, _1680442] : [-(c_List_Olist_Olist__size(_1680438, _1680440, _1680442) = 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(_1680438, tc_Nat_Onat), _1680440), _1680442))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680438)), _1680442)))], (47517 ^ _776545) ^ [_1732189, _1732191, _1732193, _1732195] : [47519 ^ _776545 : [(47522 ^ _776545) ^ [] : [hBOOL(hAPP(_1732191, hAPP(hAPP(c_List_Onth(_1732193), _1732195), 47518 ^ [_1732189, _1732191, _1732193, _1732195])))], (47520 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47518 ^ [_1732189, _1732191, _1732193, _1732195]), _1732189)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732189), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732193)), _1732195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1732189), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732193)), c_List_OtakeWhile(_1732193, _1732191, _1732195)))))], (26661 ^ _776545) ^ [_1257746, _1257748] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257746))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257746)), _1257748) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257748))], (7772 ^ _776545) ^ [_907034, _907036, _907038, _907040] : [7773 ^ _776545 : [(7776 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907034), _907036), _907040))], (7774 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907034), _907036), _907038))]], -(hBOOL(hAPP(hAPP(c_member(_907034), _907036), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907034, tc_HOL_Obool)), _907038), _907040))))], (14827 ^ _776545) ^ [_1043959, _1043961, _1043963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043959), _1043961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043959), _1043963)), 14834 ^ _776545 : [(14841 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043961), _1043963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043961), _1043959)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043963), _1043959))))], (14835 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043961), _1043959)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043963), _1043959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043961), _1043963)))]]], (33249 ^ _776545) ^ [_1385967, _1385969, _1385971] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385967, tc_fun(_1385969, tc_HOL_Obool)), _1385971), hAPP(c_COMBK(tc_fun(_1385969, tc_HOL_Obool), _1385967), c_Orderings_Obot__class_Obot(tc_fun(_1385969, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1385969, tc_HOL_Obool)))], (38300 ^ _776545) ^ [_1510161, _1510163, _1510165] : [c_Wellfounded_Owf(_1510161, _1510163), c_Wellfounded_Owf(_1510161, _1510165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510161, _1510161), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510161, _1510161, _1510161), _1510163), _1510165)), _1510163)), -(c_Wellfounded_Owf(_1510161, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510161, _1510161), tc_HOL_Obool)), _1510163), _1510165)))], (4020 ^ _776545) ^ [_837288, _837290, _837292, _837294, _837296, _837298, _837300, _837302] : [-(c_New__Random__Sequence_Opos__empty(_837302, _837298, _837294, _837290) = c_New__Random__Sequence_Opos__empty(_837300, _837296, _837292, _837288)), _837302 = _837300, _837298 = _837296, _837294 = _837292, _837290 = _837288], (9720 ^ _776545) ^ [_942952, _942954, _942956, _942958] : [class_Lattices_Osemilattice__sup(_942952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942952), _942954), _942956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942952), _942954), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942952), _942956), _942958))))], (29217 ^ _776545) ^ [_1300232] : [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), _1300232))), 29220 ^ _776545 : [(29223 ^ _776545) ^ [] : [-(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(_1300232)))))], (29221 ^ _776545) ^ [] : [-(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(_1300232)))))]]], (36243 ^ _776545) ^ [_1460421, _1460423, _1460425, _1460427, _1460429, _1460431] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool)), _1460423), _1460425)), c_Wellfounded_Omax__ext(_1460421, _1460427))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool)), _1460429), _1460431)), c_Wellfounded_Omax__ext(_1460421, _1460427))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1460421, tc_HOL_Obool), tc_fun(_1460421, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460421, tc_HOL_Obool)), _1460423), _1460429)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460421, tc_HOL_Obool)), _1460425), _1460431))), c_Wellfounded_Omax__ext(_1460421, _1460427))))], (32432 ^ _776545) ^ [_1360295, _1360297, _1360299, _1360301, _1360303] : [-(_1360295 = c_Orderings_Obot__class_Obot(tc_fun(_1360297, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360299, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360297, tc_fun(_1360299, tc_HOL_Obool)), _1360295), _1360301)), _1360303) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360297, tc_fun(_1360299, tc_HOL_Obool)), _1360295), hAPP(hAPP(c_COMBC(_1360297, tc_fun(_1360299, tc_HOL_Obool), tc_fun(_1360299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360299, tc_HOL_Obool), tc_fun(tc_fun(_1360299, tc_HOL_Obool), tc_fun(_1360299, tc_HOL_Obool)), _1360297), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360299, tc_HOL_Obool))), _1360301)), _1360303)))], (42982 ^ _776545) ^ [_1633286, _1633288, _1633290, _1633292] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633286) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1633288), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633286)), hAPP(hAPP(c_List_Olist_OCons(_1633288), _1633290), _1633292)) = hAPP(hAPP(c_List_Olist_OCons(_1633288), _1633290), hAPP(hAPP(c_List_Otake(_1633288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633286)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1633292)))], (16296 ^ _776545) ^ [_1070709, _1070711] : [class_Rings_Ocomm__semiring__1(_1070709), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070709), _1070711), c_Groups_Ozero__class_Ozero(_1070709)) = c_Groups_Ozero__class_Ozero(_1070709))], (31673 ^ _776545) ^ [_1345238, _1345240, _1345242, _1345244] : [class_Orderings_Olinorder(_1345238), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345238), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345238), _1345240), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345238), _1345242), _1345244))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1345238), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345238), _1345240), _1345242)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345238), _1345240), _1345244)))))], (12965 ^ _776545) ^ [_1005320, _1005322, _1005324] : [class_Lattices_Oab__semigroup__idem__mult(_1005320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005320), _1005322)), -(_1005322 = c_Orderings_Obot__class_Obot(tc_fun(_1005320, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005320), _1005324)), -(_1005324 = c_Orderings_Obot__class_Obot(tc_fun(_1005320, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1005320, c_Groups_Otimes__class_Otimes(_1005320)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1005320, tc_HOL_Obool)), _1005322), _1005324)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005320), hAPP(c_Finite__Set_Ofold1(_1005320, c_Groups_Otimes__class_Otimes(_1005320)), _1005322)), hAPP(c_Finite__Set_Ofold1(_1005320, c_Groups_Otimes__class_Otimes(_1005320)), _1005324)))], (23067 ^ _776545) ^ [_1194480, _1194482] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1194480, _1194482))))], (10677 ^ _776545) ^ [_960264, _960266] : [_960266 = c_Orderings_Obot__class_Obot(tc_fun(_960264, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960264, tc_HOL_Obool)), _960266), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960264, tc_HOL_Obool)), _960266))))], (43098 ^ _776545) ^ [_1635286, _1635288] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635286)), _1635288) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1635288 = c_List_Olist_ONil(_1635286))], (1764 ^ _776545) ^ [_801459, _801461] : [-(class_Groups_Omonoid__mult(_801459)), _801461 = _801459, class_Groups_Omonoid__mult(_801461)], (43270 ^ _776545) ^ [_1638612, _1638614, _1638616] : [hBOOL(hAPP(hAPP(c_member(_1638612), _1638614), hAPP(c_List_Oset(_1638612), _1638616))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638612)), c_List_Oremove1(_1638612, _1638614, _1638616)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638612)), _1638616)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9154 ^ _776545) ^ [_934670, _934672, _934674] : [class_Orderings_Opreorder(_934670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934670), _934672), _934674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934670), _934674), _934672))], (40605 ^ _776545) ^ [_1569456, _1569458, _1569460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569456, _1569456)), _1569458), _1569460)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569456, _1569456)), _1569458), c_Transitive__Closure_Otrancl(_1569456, _1569460))))], (7828 ^ _776545) ^ [_908280, _908282, _908284] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908280, tc_HOL_Obool)), _908282), _908284) = c_Orderings_Obot__class_Obot(tc_fun(_908280, tc_HOL_Obool)), 7831 ^ _776545 : [(7834 ^ _776545) ^ [] : [-(_908284 = c_Orderings_Obot__class_Obot(tc_fun(_908280, tc_HOL_Obool)))], (7832 ^ _776545) ^ [] : [-(_908282 = c_Orderings_Obot__class_Obot(tc_fun(_908280, tc_HOL_Obool)))]]], (46229 ^ _776545) ^ [_1706251, _1706253, _1706255, _1706257, _1706259, _1706261] : [-(c_List_Ofoldr(_1706251, _1706253, _1706255, hAPP(hAPP(c_List_Oappend(_1706251), _1706257), _1706259), _1706261) = c_List_Ofoldr(_1706251, _1706253, _1706255, _1706257, c_List_Ofoldr(_1706251, _1706253, _1706255, _1706259, _1706261)))], (52235 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (21373 ^ _776545) ^ [_1163544, _1163546, _1163548, _1163550] : [class_Int_Onumber__ring(_1163544), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163546)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), _1163548)), _1163550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163544), hAPP(c_Int_Onumber__class_Onumber__of(_1163544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1163546), _1163548))), _1163550))], (40170 ^ _776545) ^ [_1559263, _1559265, _1559267, _1559269] : [c_Finite__Set_Ofolding(_1559263, _1559265, _1559267, _1559269), -(hAPP(_1559269, c_Orderings_Obot__class_Obot(tc_fun(_1559263, tc_HOL_Obool))) = c_Fun_Oid(_1559265))], (25734 ^ _776545) ^ [_1242246, _1242248, _1242250, _1242252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242248), _1242250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242250), 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), _1242248), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242252, _1242246))), _1242250)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40497 ^ _776545) ^ [_1566752, _1566754, _1566756, _1566758, _1566760, _1566762, _1566764, _1566766] : [class_Groups_Ocomm__monoid__add(_1566752), c_Fun_Oinj__on(_1566754, _1566756, _1566758, _1566760), _1566762 = hAPP(c_Set_Oimage(_1566754, _1566756, _1566758), _1566760), 40511 ^ _776545 : [(40514 ^ _776545) ^ [] : [hAPP(_1566764, 40510 ^ [_1566752, _1566754, _1566756, _1566758, _1566760, _1566762, _1566764, _1566766]) = hAPP(_1566766, hAPP(_1566758, 40510 ^ [_1566752, _1566754, _1566756, _1566758, _1566760, _1566762, _1566764, _1566766]))], (40512 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566754), 40510 ^ [_1566752, _1566754, _1566756, _1566758, _1566760, _1566762, _1566764, _1566766]), _1566760)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566756, _1566752), _1566766), _1566762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566754, _1566752), _1566764), _1566760))], (1874 ^ _776545) ^ [_802834, _802836] : [-(class_Int_Onumber(_802834)), _802836 = _802834, class_Int_Onumber(_802836)], (10397 ^ _776545) ^ [_955111, _955113, _955115] : [class_Groups_Oordered__ab__group__add(_955111), 10400 ^ _776545 : [(10407 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955111), _955115), _955113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955111), hAPP(c_Groups_Ouminus__class_Ouminus(_955111), _955113)), hAPP(c_Groups_Ouminus__class_Ouminus(_955111), _955115))))], (10401 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955111), hAPP(c_Groups_Ouminus__class_Ouminus(_955111), _955113)), hAPP(c_Groups_Ouminus__class_Ouminus(_955111), _955115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955111), _955115), _955113)))]]], (26270 ^ _776545) ^ [_1250983] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1250983), c_Int_OMin) = c_Int_Osucc(_1250983))], (12433 ^ _776545) ^ [_994988, _994990, _994992, _994994, _994996] : [c_Finite__Set_Ofolding__one__idem(_994988, _994990, _994992), hBOOL(hAPP(c_Finite__Set_Ofinite(_994988), _994994)), -(_994994 = c_Orderings_Obot__class_Obot(tc_fun(_994988, tc_HOL_Obool))), -(hAPP(_994992, hAPP(hAPP(c_Set_Oinsert(_994988), _994996), _994994)) = hAPP(hAPP(_994990, _994996), hAPP(_994992, _994994)))], (46516 ^ _776545) ^ [_1711991, _1711993, _1711995] : [class_Orderings_Olinorder(_1711991), c_List_Olinorder__class_Osorted(_1711991, _1711993), -(c_List_Olinorder__class_Osorted(_1711991, hAPP(hAPP(c_List_Otake(_1711991), _1711995), _1711993)))], (45422 ^ _776545) ^ [_1686915, _1686917, _1686919, _1686921, _1686923] : [-(c_Enum_Oproduct(_1686915, _1686917, hAPP(hAPP(c_List_Olist_OCons(_1686915), _1686919), _1686921), _1686923) = hAPP(hAPP(c_List_Oappend(tc_prod(_1686915, _1686917)), hAPP(hAPP(c_List_Omap(_1686917, tc_prod(_1686915, _1686917)), hAPP(c_Product__Type_OPair(_1686915, _1686917), _1686919)), _1686923)), c_Enum_Oproduct(_1686915, _1686917, _1686921, _1686923)))], (8133 ^ _776545) ^ [_915177, _915179, _915181] : [-(hBOOL(hAPP(hAPP(c_member(_915177), _915179), _915181))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915177, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915177), _915179), _915181)), hAPP(hAPP(c_Set_Oinsert(_915177), _915179), c_Orderings_Obot__class_Obot(tc_fun(_915177, tc_HOL_Obool)))) = _915181)], (28963 ^ _776545) ^ [_1295769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1295769)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295769), c_Int_OPls)))], (48883 ^ _776545) ^ [_1762072, _1762074, _1762076] : [hBOOL(hAPP(hAPP(c_member(_1762072), _1762076), hAPP(c_List_Oset(_1762072), _1762074))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762072), _1762074), _1762076)))], (15992 ^ _776545) ^ [_1065935, _1065937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065935), _1065937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065935)), hAPP(c_Nat_OSuc, _1065937))))], (31763 ^ _776545) ^ [_1347281, _1347283, _1347285, _1347287] : [class_Orderings_Olinorder(_1347281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347281), _1347283)), hBOOL(hAPP(hAPP(c_member(_1347281), _1347285), _1347283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347281), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347281), _1347285), _1347287)), hAPP(hAPP(c_Finite__Set_Ofold(_1347281, _1347281, c_Orderings_Oord__class_Omax(_1347281)), _1347287), _1347283))))], (38444 ^ _776545) ^ [_1513515, _1513517, _1513519] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1513515), _1513517), _1513519) = c_Nitpick_OAbs__Frac(_1513515, c_Nitpick_Onorm__frac(_1513517, _1513519)))], (12700 ^ _776545) ^ [_1000453, _1000455, _1000457, _1000459] : [c_Finite__Set_Ofolding__one(_1000453, _1000455, _1000457), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000453), _1000459)), -(hAPP(_1000457, _1000459) = hAPP(c_Finite__Set_Ofold1(_1000453, _1000455), _1000459))], (25800 ^ _776545) ^ [_1243397, _1243399] : [-(_1243397 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25803 ^ _776545 : [(25810 ^ _776545) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243399, _1243397) = 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), _1243399)), _1243397) = 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), _1243399), _1243397))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25804 ^ _776545) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243399, _1243397) = 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), _1243399)), _1243397) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243399), _1243397)))]]], (36474 ^ _776545) ^ [_1466475, _1466477, _1466479, _1466481, _1466483, _1466485] : [-(hAPP(c_Relation_OImage(_1466475, _1466477, _1466479), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1466481, tc_fun(_1466475, tc_HOL_Obool)), _1466483), _1466485)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1466481, tc_fun(_1466477, tc_HOL_Obool)), _1466483), hAPP(hAPP(c_COMBB(tc_fun(_1466475, tc_HOL_Obool), tc_fun(_1466477, tc_HOL_Obool), _1466481), c_Relation_OImage(_1466475, _1466477, _1466479)), _1466485)))], (9892 ^ _776545) ^ [_946019, _946021, _946023, _946025] : [class_Orderings_Olinorder(_946019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946019), _946021), _946023)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946019), _946023), _946025)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946019, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_946019, _946021, _946023)), c_SetInterval_Oord__class_OatLeastAtMost(_946019, _946023, _946025)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_946019, _946021, _946025))], (43938 ^ _776545) ^ [_1654550, _1654552, _1654554, _1654556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1654550), _1654552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654554, tc_HOL_Obool)), hAPP(c_List_Oset(_1654554), hAPP(hAPP(c_List_Odrop(_1654554), _1654552), _1654556))), hAPP(c_List_Oset(_1654554), hAPP(hAPP(c_List_Odrop(_1654554), _1654550), _1654556)))))], (18974 ^ _776545) ^ [_1118291] : [-(hAPP(c_Nat_OSuc, _1118291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1118291), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16642 ^ _776545) ^ [] : [-(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))))], (47094 ^ _776545) ^ [_1723121, _1723123, _1723125, _1723127, _1723129] : [-(hAPP(c_List_Ofoldl(_1723121, _1723123, _1723125, _1723127), _1723129) = c_List_Ofoldr(_1723123, _1723121, hAPP(c_COMBC(_1723121, _1723123, _1723121), _1723125), hAPP(c_List_Orev(_1723123), _1723129), _1723127))], (16432 ^ _776545) ^ [_1072743] : [-(_1072743 = 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)), _1072743)))], (43860 ^ _776545) ^ [_1652767, _1652769, _1652771, _1652773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652767), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652769)), _1652771))), -(hAPP(hAPP(c_List_Olist__update(_1652769, _1652771), _1652767), _1652773) = hAPP(hAPP(c_List_Oappend(_1652769), hAPP(hAPP(c_List_Otake(_1652769), _1652767), _1652771)), hAPP(hAPP(c_List_Olist_OCons(_1652769), _1652773), hAPP(hAPP(c_List_Odrop(_1652769), hAPP(c_Nat_OSuc, _1652767)), _1652771))))], (36620 ^ _776545) ^ [_1470531, _1470533] : [-(c_Relation_OId__on(_1470531, _1470533) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470531, tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool)), _1470533), hAPP(hAPP(c_COMBC(_1470531, tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool), tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1470531, _1470531), tc_fun(tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool), tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool)), _1470531), c_Set_Oinsert(tc_prod(_1470531, _1470531))), hAPP(hAPP(c_COMBS(_1470531, _1470531, tc_prod(_1470531, _1470531)), c_Product__Type_OPair(_1470531, _1470531)), c_COMBI(_1470531)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1470531, _1470531), tc_HOL_Obool)))))], (22943 ^ _776545) ^ [_1192268, _1192270, _1192272, _1192274] : [class_Rings_Olinordered__semidom(_1192268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192270), _1192272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192268), c_Groups_Ozero__class_Ozero(_1192268)), _1192274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192268), _1192274), c_Groups_Oone__class_Oone(_1192268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192268), hAPP(hAPP(c_Power_Opower__class_Opower(_1192268), _1192274), _1192272)), hAPP(hAPP(c_Power_Opower__class_Opower(_1192268), _1192274), _1192270))))], (10761 ^ _776545) ^ [_961880, _961882] : [class_Orderings_Olinorder(_961880), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961880, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_961880), _961882)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_961880), _961882))], (30010 ^ _776545) ^ [_1314773] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1314773), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9050 ^ _776545) ^ [_933008, _933010, _933012] : [class_Orderings_Opreorder(_933008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933008), _933010), _933012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933008), _933012), _933010))], (51447 ^ _776545) ^ [_1817783, _1817785] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1817783), 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)))), _1817785))), 51450 ^ _776545 : [(51453 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817785), _1817783))], (51451 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817783), _1817785)))]]], (28287 ^ _776545) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (50111 ^ _776545) ^ [_1788994, _1788996, _1788998, _1789000] : [c_Fun_Oinj__on(_1788994, _1788996, _1788998, c_Orderings_Otop__class_Otop(tc_fun(_1788994, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1788996, _1788994, c_Hilbert__Choice_Oinv__into(_1788994, _1788996, c_Orderings_Otop__class_Otop(tc_fun(_1788994, tc_HOL_Obool)), _1788998)), hAPP(c_Set_Oimage(_1788994, _1788996, _1788998), _1789000)) = _1789000)], (40883 ^ _776545) ^ [_1576974, _1576976, _1576978, _1576980, _1576982] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576974, _1576974)), hAPP(hAPP(c_Product__Type_OPair(_1576974, _1576974), _1576976), _1576978)), _1576980)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576974, _1576974)), hAPP(hAPP(c_Product__Type_OPair(_1576974, _1576974), _1576978), _1576982)), c_Transitive__Closure_Ortrancl(_1576974, _1576980))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576974, _1576974)), hAPP(hAPP(c_Product__Type_OPair(_1576974, _1576974), _1576976), _1576982)), c_Transitive__Closure_Otrancl(_1576974, _1576980))))], (34604 ^ _776545) ^ [_1421104] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1421104) = 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)))], (49039 ^ _776545) ^ [_1765726, _1765728] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1765726)), _1765728)), 49043 ^ _776545 : [(49044 ^ _776545) ^ [_1765827] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765726)), _1765827), _1765728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765726)), _1765827)), 49042 ^ [_1765726, _1765728])))]]], (15524 ^ _776545) ^ [_1057618, _1057620, _1057622, _1057624, _1057626] : [class_Groups_Ocomm__monoid__mult(_1057618), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057620), _1057622)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057620), _1057624)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057620, tc_HOL_Obool)), _1057622), _1057624) = c_Orderings_Obot__class_Obot(tc_fun(_1057620, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057618, _1057620, c_Groups_Otimes__class_Otimes(_1057618)), _1057626), c_Groups_Oone__class_Oone(_1057618)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057620, tc_HOL_Obool)), _1057622), _1057624)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057618), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057618, _1057620, c_Groups_Otimes__class_Otimes(_1057618)), _1057626), c_Groups_Oone__class_Oone(_1057618)), _1057622)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1057618, _1057620, c_Groups_Otimes__class_Otimes(_1057618)), _1057626), c_Groups_Oone__class_Oone(_1057618)), _1057624)))], (15682 ^ _776545) ^ [_1060923, _1060925] : [hAPP(_1060923, 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), _1060923), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060925)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1060923), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1060925)))], (43669 ^ _776545) ^ [_1647427, _1647429, _1647431, _1647433] : [-(hAPP(hAPP(c_List_Onth(_1647427), hAPP(hAPP(c_List_Oappend(_1647427), _1647429), hAPP(hAPP(c_List_Olist_OCons(_1647427), _1647431), _1647433))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647427)), _1647429)) = _1647431)], (1962 ^ _776545) ^ [_803966, _803968, _803970, _803972] : [-(v_Q(_803970, _803966)), v_Q(_803972, _803968), _803972 = _803970, _803968 = _803966], (35515 ^ _776545) ^ [_1439199, _1439201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439201)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439199, _1439201) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1439199, _1439201)))], (49688 ^ _776545) ^ [_1780972, _1780974] : [c_Relation_Osym(_1780972, hAPP(c_Relation_Oconverse(_1780972, _1780972), _1780974)), -(c_Relation_Osym(_1780972, _1780974))], (17603 ^ _776545) ^ [_1093563, _1093565, _1093567, _1093569, _1093571, _1093573] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1093563), -(_1093565 = c_Groups_Ozero__class_Ozero(_1093563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093563), _1093567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093563), _1093565), _1093571)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093563), _1093569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093563), _1093565), _1093573)), _1093567 = _1093569, -(_1093571 = _1093573)], (44825 ^ _776545) ^ [_1673221, _1673223, _1673225, _1673227, _1673229] : [44827 ^ _776545 : [(44830 ^ _776545) ^ [] : [hAPP(_1673225, 44826 ^ [_1673221, _1673223, _1673225, _1673227, _1673229]) = hAPP(_1673229, 44826 ^ [_1673221, _1673223, _1673225, _1673227, _1673229])], (44828 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673221), 44826 ^ [_1673221, _1673223, _1673225, _1673227, _1673229]), hAPP(c_List_Oset(_1673221), _1673227))))]], -(hAPP(hAPP(c_List_Omap(_1673221, _1673223), _1673225), _1673227) = hAPP(hAPP(c_List_Omap(_1673221, _1673223), _1673229), _1673227))], (15676 ^ _776545) ^ [_1060800] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060800)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1060800))], (38016 ^ _776545) ^ [_1502989, _1502991, _1502993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502989, _1502989), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1502989, _1502989, _1502989), _1502991), _1502993)), _1502991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502989, _1502991)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502989, _1502993)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1502989, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1502989, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1502989, tc_HOL_Obool), tc_fun(_1502989, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1502989, _1502991))))], (24535 ^ _776545) ^ [_1220339, _1220341, _1220343] : [hBOOL(hAPP(_1220339, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220341), _1220343)))), 24538 ^ _776545 : [(24545 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220341), _1220343)), -(hBOOL(hAPP(_1220339, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24539 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220343), _1220341)), -(hBOOL(hAPP(_1220339, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220341)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220343)))))]]], (32926 ^ _776545) ^ [_1376769, _1376771] : [-(hAPP(c_Set_OPow(_1376769), _1376771) = hAPP(c_Set_OCollect(tc_fun(_1376769, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1376769, tc_HOL_Obool), tc_fun(_1376769, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1376769, tc_HOL_Obool))), _1376771)))], (1644 ^ _776545) ^ [_799959, _799961] : [-(class_Groups_Oab__semigroup__add(_799959)), _799961 = _799959, class_Groups_Oab__semigroup__add(_799961)], (34727 ^ _776545) ^ [_1423751, _1423753, _1423755, _1423757] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423751, _1423753, _1423755), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423757)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1423751), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423757))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423751, _1423751), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1423751, tc_fun(_1423751, _1423751)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1423751, tc_fun(_1423751, _1423751)), tc_Int_Oint), c_If(_1423751)), c_Nat__Numeral_Oneg)), _1423753)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423751, _1423751), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1423751, _1423751), tc_Int_Oint), _1423755), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423751, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1423751, _1423753, _1423755)), c_Int_Onat)))))], (44060 ^ _776545) ^ [_1657601, _1657603, _1657605, _1657607] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1657603), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657601)), hAPP(hAPP(c_List_Olist_OCons(_1657603), _1657605), _1657607)) = hAPP(hAPP(c_List_Odrop(_1657603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1657601)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1657607))], (16228 ^ _776545) ^ [_1069722, _1069724, _1069726] : [class_Rings_Ono__zero__divisors(_1069722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069722), _1069724), _1069726) = c_Groups_Ozero__class_Ozero(_1069722), -(_1069724 = c_Groups_Ozero__class_Ozero(_1069722)), -(_1069726 = c_Groups_Ozero__class_Ozero(_1069722))], (52097 ^ _776545) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (22419 ^ _776545) ^ [_1182953, _1182955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182955), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182953), _1182955)))], (50415 ^ _776545) ^ [_1795865, _1795867, _1795869] : [c_Fun_Obij__betw(_1795865, _1795867, _1795869, c_Orderings_Otop__class_Otop(tc_fun(_1795865, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795867, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1795865, _1795867, _1795869, c_Orderings_Otop__class_Otop(tc_fun(_1795865, tc_HOL_Obool))))], (1914 ^ _776545) ^ [_803334, _803336] : [-(class_Nat_Osize(_803334)), _803336 = _803334, class_Nat_Osize(_803336)], (17949 ^ _776545) ^ [_1099458, _1099460] : [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), _1099458), _1099460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099460)))], (19220 ^ _776545) ^ [_1123167, _1123169, _1123171, _1123173, _1123175] : [class_Groups_Ocomm__monoid__add(_1123167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123169), _1123171)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123169), _1123173)), 19234 ^ _776545 : [(19237 ^ _776545) ^ [] : [hAPP(_1123175, 19233 ^ [_1123167, _1123169, _1123171, _1123173, _1123175]) = c_Groups_Ozero__class_Ozero(_1123167)], (19235 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1123169), 19233 ^ [_1123167, _1123169, _1123171, _1123173, _1123175]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1123169, tc_HOL_Obool)), _1123171), _1123173))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123169, _1123167), _1123175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123169, tc_HOL_Obool)), _1123171), _1123173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123167), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123169, _1123167), _1123175), _1123171)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1123169, _1123167), _1123175), _1123173)))], (46486 ^ _776545) ^ [_1711568, _1711570, _1711572] : [class_Orderings_Olinorder(_1711568), c_List_Olinorder__class_Osorted(_1711568, _1711570), -(c_List_Olinorder__class_Osorted(_1711568, c_List_Olinorder__class_Oinsort__insert__key(_1711568, _1711568, c_COMBI(_1711568), _1711572, _1711570)))], (49273 ^ _776545) ^ [_1771498, _1771500, _1771502] : [hBOOL(hAPP(hAPP(c_member(_1771500), _1771498), c_Orderings_Obot__class_Obot(tc_fun(_1771500, tc_HOL_Obool)))), hBOOL(hAPP(_1771502, _1771498))], (42679 ^ _776545) ^ [_1626289, _1626291, _1626293, _1626295] : [_1626289 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626291)), _1626293)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1626291, hAPP(hAPP(c_List_Olist__update(_1626291, _1626293), _1626289), _1626295)) = c_List_Obutlast(_1626291, _1626293))], (48225 ^ _776545) ^ [_1747958] : [class_Nat_Osize(_1747958), -(c_FunDef_Ois__measure(_1747958, c_Nat_Osize__class_Osize(_1747958)))], (21197 ^ _776545) ^ [_1159911, _1159913, _1159915] : [class_Int_Onumber__ring(_1159911), class_Rings_Olinordered__idom(_1159911), 21204 ^ _776545 : [(21211 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159913), _1159915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159911), hAPP(c_Int_Onumber__class_Onumber__of(_1159911), _1159913)), hAPP(c_Int_Onumber__class_Onumber__of(_1159911), _1159915))))], (21205 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159911), hAPP(c_Int_Onumber__class_Onumber__of(_1159911), _1159913)), hAPP(c_Int_Onumber__class_Onumber__of(_1159911), _1159915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159913), _1159915)))]]], (25503 ^ _776545) ^ [_1237878, _1237880, _1237882] : [hBOOL(hAPP(_1237878, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237880), _1237882))), 25508 ^ _776545 : [(25511 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1237878, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25509 ^ _776545) ^ [] : [-(_1237882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25513 ^ _776545 : [(25518 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1237878, 25512 ^ [_1237878, _1237880, _1237882])))], (25516 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237882), hAPP(c_Nat_OSuc, 25512 ^ [_1237878, _1237880, _1237882])))))], (25514 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237882), 25512 ^ [_1237878, _1237880, _1237882])), _1237880)))]]], (6989 ^ _776545) ^ [_890140, _890142, _890144] : [class_Orderings_Oord(_890140), 6992 ^ _776545 : [(6999 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890140), _890142), _890144)), -(hBOOL(hAPP(hAPP(c_member(_890140), _890142), hAPP(c_SetInterval_Oord__class_OatMost(_890140), _890144))))], (6993 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890140), _890142), hAPP(c_SetInterval_Oord__class_OatMost(_890140), _890144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890140), _890142), _890144)))]]], (43448 ^ _776545) ^ [_1642879, _1642881, _1642883, _1642885, _1642887, _1642889] : [hAPP(hAPP(c_List_Olist_OCons(_1642879), _1642881), _1642883) = _1642885, _1642887 = hAPP(hAPP(c_List_Oappend(_1642879), _1642883), _1642889), -(hAPP(hAPP(c_List_Olist_OCons(_1642879), _1642881), _1642887) = hAPP(hAPP(c_List_Oappend(_1642879), _1642885), _1642889))], (2790 ^ _776545) ^ [_817833, _817835] : [_817835 = _817833, -(c_HOL_OAll(_817835) = c_HOL_OAll(_817833))], (25058 ^ _776545) ^ [_1230253, _1230255] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230253, _1230255) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1230253 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230255), 25061 ^ [_1230253, _1230255]))], (45449 ^ _776545) ^ [_1687713, _1687715, _1687717, _1687719, _1687721, _1687723, _1687725] : [c_List_Olist__all2(_1687713, _1687715, _1687717, hAPP(hAPP(c_List_Omap(_1687719, _1687713), _1687721), _1687723), _1687725), -(c_List_Olist__all2(_1687719, _1687715, hAPP(hAPP(c_COMBB(_1687713, tc_fun(_1687715, tc_HOL_Obool), _1687719), _1687717), _1687721), _1687723, _1687725))], (25481 ^ _776545) ^ [_1237476, _1237478, _1237480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237476)), 25484 ^ _776545 : [(25485 ^ _776545) ^ [] : [-(_1237478 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237480), _1237476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237476), _1237478)), _1237480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237476), hAPP(c_Nat_OSuc, _1237478))))], (25495 ^ _776545) ^ [] : [_1237478 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237480), _1237476), 25498 ^ _776545 : [(25501 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237476), hAPP(c_Nat_OSuc, _1237478)))))], (25499 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237476), _1237478)), _1237480)))]]]]], (46395 ^ _776545) ^ [_1709537, _1709539] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1709537, _1709539)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1709537), hAPP(c_Nat_OSuc, _1709539)))], (49113 ^ _776545) ^ [_1767113, _1767115, _1767117, _1767119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1767113), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1767115, _1767117, _1767113, _1767119) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1767115, 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(_1767115)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1767117, _1767119)), 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(_1767115)))), 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(_1767115)))), 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(_1767115)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1767115, 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(_1767115)))), 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(_1767115)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1767115, _1767117, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1767113), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1767119))), 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(_1767115)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115)))), 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(_1767115)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1767115, 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(_1767115)))), 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(_1767115)))), 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(_1767115))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115)))), 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(_1767115)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115))))), tc_prod(_1767115, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1767115)), hAPP(hAPP(c_COMBB(_1767115, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1767115)))), tc_prod(_1767115, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1767115)), c_Product__Type_Ofst(_1767115, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (1976 ^ _776545) ^ [_804966, _804968] : [_804968 = _804966, -(c_Hoare__Mirabelle_OAbs__triple(_804968) = c_Hoare__Mirabelle_OAbs__triple(_804966))], (12920 ^ _776545) ^ [_1004472, _1004474, _1004476] : [class_Lattices_Osemilattice__inf(_1004472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004472), _1004474)), -(_1004474 = c_Orderings_Obot__class_Obot(tc_fun(_1004472, tc_HOL_Obool))), 12931 ^ _776545 : [(12932 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), _1004476), hAPP(c_Finite__Set_Ofold1(_1004472, c_Lattices_Osemilattice__inf__class_Oinf(_1004472)), _1004474))), 12935 ^ _776545 : [(12936 ^ _776545) ^ [_1004765] : [hBOOL(hAPP(hAPP(c_member(_1004472), _1004765), _1004474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), _1004476), _1004765)))]]], (12942 ^ _776545) ^ [] : [12944 ^ _776545 : [(12947 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), _1004476), 12943 ^ [_1004472, _1004474, _1004476]))], (12945 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004472), 12943 ^ [_1004472, _1004474, _1004476]), _1004474)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004472), _1004476), hAPP(c_Finite__Set_Ofold1(_1004472, c_Lattices_Osemilattice__inf__class_Oinf(_1004472)), _1004474))))]]], (50755 ^ _776545) ^ [_1802413, _1802415, _1802417, _1802419] : [c_Equiv__Relations_Oequivp(_1802413, _1802415), -(c_Quotient_OBabs(_1802413, _1802417, c_Quotient_ORespects(_1802413, _1802415), _1802419) = _1802419)], (44230 ^ _776545) ^ [_1660992, _1660994, _1660996] : [-(hAPP(c_List_Otl(_1660992), hAPP(hAPP(c_List_Otake(_1660992), _1660994), _1660996)) = hAPP(hAPP(c_List_Otake(_1660992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1660994), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1660992), _1660996)))], (40831 ^ _776545) ^ [_1575877, _1575879] : [-(c_Transitive__Closure_Ortrancl(_1575877, c_Transitive__Closure_Ortrancl(_1575877, _1575879)) = c_Transitive__Closure_Ortrancl(_1575877, _1575879))], (26613 ^ _776545) ^ [_1256862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256862)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1256862)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1256862)))], (7021 ^ _776545) ^ [_890676, _890678] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_890676, tc_HOL_Obool), tc_HOL_Obool)), _890678), hAPP(c_Set_OPow(_890676), c_Complete__Lattice_OSup__class_OSup(tc_fun(_890676, tc_HOL_Obool), _890678)))))], (8787 ^ _776545) ^ [_927482, _927484] : [class_Lattices_Obounded__lattice__bot(_927482), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927482), _927484), c_Orderings_Obot__class_Obot(_927482)) = c_Orderings_Obot__class_Obot(_927482))], (17113 ^ _776545) ^ [_1084655, _1084657, _1084659] : [class_Rings_Oordered__cancel__semiring(_1084655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084655), c_Groups_Ozero__class_Ozero(_1084655)), _1084657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084655), _1084659), c_Groups_Ozero__class_Ozero(_1084655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084655), _1084657), _1084659)), c_Groups_Ozero__class_Ozero(_1084655))))], (18404 ^ _776545) ^ [_1107646, _1107648, _1107650, _1107652, _1107654] : [class_Rings_Olinordered__semiring__strict(_1107646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107646), _1107648), _1107650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107646), _1107652), _1107654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107646), c_Groups_Ozero__class_Ozero(_1107646)), _1107648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107646), c_Groups_Ozero__class_Ozero(_1107646)), _1107652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107646), _1107648), _1107652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107646), _1107650), _1107654))))], (2656 ^ _776545) ^ [_815722, _815724, _815726, _815728, _815730, _815732, _815734, _815736, _815738, _815740] : [-(c_Finite__Set_Ofold__graph(_815740, _815736, _815732, _815728, _815724) = c_Finite__Set_Ofold__graph(_815738, _815734, _815730, _815726, _815722)), _815740 = _815738, _815736 = _815734, _815732 = _815730, _815728 = _815726, _815724 = _815722], (9480 ^ _776545) ^ [_939415, _939417, _939419] : [class_Orderings_Oorder(_939415), 9483 ^ _776545 : [(9484 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939415), _939417), _939419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939415), _939417), _939419))), -(_939417 = _939419)], (9494 ^ _776545) ^ [] : [9495 ^ _776545 : [(9498 ^ _776545) ^ [] : [_939417 = _939419], (9496 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939415), _939417), _939419))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939415), _939417), _939419)))]]], (40997 ^ _776545) ^ [_1579637, _1579639, _1579641, _1579643] : [c_Wellfounded_Oacyclic(_1579637, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579637, _1579637)), hAPP(hAPP(c_Product__Type_OPair(_1579637, _1579637), _1579639), _1579641)), _1579643)), 41000 ^ _776545 : [(41003 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579637, _1579637)), hAPP(hAPP(c_Product__Type_OPair(_1579637, _1579637), _1579641), _1579639)), c_Transitive__Closure_Ortrancl(_1579637, _1579643)))], (41001 ^ _776545) ^ [] : [-(c_Wellfounded_Oacyclic(_1579637, _1579643))]]], (24254 ^ _776545) ^ [_1215195, _1215197, _1215199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215195)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1215199), _1215195)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215197), _1215199)), _1215195))], (36555 ^ _776545) ^ [_1468840, _1468842] : [-(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), _1468840), _1468842)), 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), _1468840), _1468842))], (39310 ^ _776545) ^ [_1537422, _1537424, _1537426, _1537428, _1537430, _1537432] : [class_Groups_Ocomm__monoid__mult(_1537422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537424), _1537426)), 39320 ^ _776545 : [(39323 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537428), hAPP(_1537430, 39319 ^ [_1537422, _1537424, _1537426, _1537428, _1537430, _1537432])))], (39321 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537424), 39319 ^ [_1537422, _1537424, _1537426, _1537428, _1537430, _1537432]), _1537426)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1537422, _1537424, c_Groups_Otimes__class_Otimes(_1537422)), hAPP(hAPP(c_COMBS(_1537424, tc_fun(_1537428, tc_HOL_Obool), _1537422), hAPP(hAPP(c_COMBC(_1537424, _1537422, tc_fun(tc_fun(_1537428, tc_HOL_Obool), _1537422)), hAPP(hAPP(c_COMBB(tc_fun(_1537428, _1537422), tc_fun(_1537422, tc_fun(tc_fun(_1537428, tc_HOL_Obool), _1537422)), _1537424), c_Finite__Set_Ofold__image(_1537422, _1537428, c_Groups_Otimes__class_Otimes(_1537422))), _1537432)), c_Groups_Oone__class_Oone(_1537422))), _1537430)), c_Groups_Oone__class_Oone(_1537422)), _1537426) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1537422, tc_prod(_1537424, _1537428), c_Groups_Otimes__class_Otimes(_1537422)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537424, _1537428, _1537422), _1537432)), c_Groups_Oone__class_Oone(_1537422)), hAPP(hAPP(c_Product__Type_OSigma(_1537424, _1537428), _1537426), _1537430)))], (8145 ^ _776545) ^ [_915411, _915413, _915415] : [class_Complete__Lattice_Ocomplete__lattice(_915411), -(c_Complete__Lattice_OSup__class_OSup(_915411, hAPP(hAPP(c_Set_Oinsert(_915411), _915413), hAPP(hAPP(c_Set_Oinsert(_915411), _915415), c_Orderings_Obot__class_Obot(tc_fun(_915411, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915411), _915413), _915415))], (7244 ^ _776545) ^ [_894750, _894752, _894754, _894756, _894758] : [-(hAPP(hAPP(c_Set_Oinsert(_894750), _894752), hAPP(hAPP(c_Set_Oinsert(_894750), _894754), c_Orderings_Obot__class_Obot(tc_fun(_894750, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_894750), _894756), hAPP(hAPP(c_Set_Oinsert(_894750), _894758), c_Orderings_Obot__class_Obot(tc_fun(_894750, tc_HOL_Obool))))), 7245 ^ _776545 : [(7252 ^ _776545) ^ [] : [_894752 = _894758, _894754 = _894756], (7246 ^ _776545) ^ [] : [_894752 = _894756, _894754 = _894758]]], (5679 ^ _776545) ^ [_866098, _866100, _866102] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(_866098)), _866100), _866102)), -(_866100 = _866102)], (36231 ^ _776545) ^ [_1460151, _1460153, _1460155, _1460157, _1460159, _1460161, _1460163] : [-(hAPP(c_Product__Type_Oapsnd(_1460151, _1460153, _1460155, _1460157), hAPP(c_Product__Type_Oapfst(_1460159, _1460155, _1460151, _1460161), _1460163)) = hAPP(c_Product__Type_Oapfst(_1460159, _1460155, _1460153, _1460161), hAPP(c_Product__Type_Oapsnd(_1460151, _1460153, _1460159, _1460157), _1460163)))], (28637 ^ _776545) ^ [] : [-(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)))))], (7368 ^ _776545) ^ [_897330, _897332] : [class_Orderings_Olinorder(_897330), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897330, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_897330), _897332)), hAPP(hAPP(c_Set_Oinsert(_897330), _897332), c_Orderings_Obot__class_Obot(tc_fun(_897330, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_897330), _897332))], (24698 ^ _776545) ^ [_1223425, _1223427] : [_1223425 = _1223427, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223425) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223427))], (1114 ^ _776545) ^ [_793334, _793336] : [-(class_Groups_Olinordered__ab__group__add(_793334)), _793336 = _793334, class_Groups_Olinordered__ab__group__add(_793336)], (48572 ^ _776545) ^ [_1755876, _1755878, _1755880] : [-(c_List_Oreplicate(_1755876, hAPP(c_Nat_OSuc, _1755878), _1755880) = hAPP(hAPP(c_List_Olist_OCons(_1755876), _1755880), c_List_Oreplicate(_1755876, _1755878, _1755880)))], (13043 ^ _776545) ^ [_1006697, _1006699, _1006701, _1006703] : [c_Big__Operators_Osemilattice__big(_1006697, _1006699, _1006701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006697), _1006703)), -(hAPP(_1006701, _1006703) = hAPP(c_Finite__Set_Ofold1(_1006697, _1006699), _1006703))], (51585 ^ _776545) ^ [_1820189, _1820191, _1820193, _1820195] : [class_Divides_Osemiring__div(_1820189), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820189), _1820191), _1820193)), -(c_Divides_Odiv__class_Omod(_1820189, c_Divides_Odiv__class_Omod(_1820189, _1820195, _1820193), _1820191) = c_Divides_Odiv__class_Omod(_1820189, _1820195, _1820191))], (44553 ^ _776545) ^ [_1667751, _1667753, _1667755, _1667757] : [-(_1667751 = c_List_Olist_ONil(_1667753)), 44556 ^ _776545 : [(44563 ^ _776545) ^ [] : [-(_1667755 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667753)), _1667751)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1667753, hAPP(hAPP(c_List_Olist__update(_1667753, _1667751), _1667755), _1667757)) = c_List_Olast(_1667753, _1667751))], (44557 ^ _776545) ^ [] : [_1667755 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667753)), _1667751)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1667753, hAPP(hAPP(c_List_Olist__update(_1667753, _1667751), _1667755), _1667757)) = _1667757)]]], (41755 ^ _776545) ^ [_1599650, _1599652, _1599654] : [_1599650 = hAPP(hAPP(c_List_Olist_OCons(_1599652), _1599654), _1599650)], (35384 ^ _776545) ^ [_1436230, _1436232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436232)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436230, _1436232), c_Divides_OposDivAlg(_1436230, _1436232))))], (43326 ^ _776545) ^ [_1639968, _1639970, _1639972] : [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), _1639968), _1639970))), -(hBOOL(hAPP(hAPP(_1639972, _1639968), _1639970))), 43333 ^ _776545 : [(43336 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43331 ^ [_1639968, _1639970, _1639972]), 43332 ^ [_1639968, _1639970, _1639972])), -(hBOOL(hAPP(hAPP(_1639972, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43331 ^ [_1639968, _1639970, _1639972]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43332 ^ [_1639968, _1639970, _1639972])))], (43342 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1639972, 43331 ^ [_1639968, _1639970, _1639972]), 43332 ^ [_1639968, _1639970, _1639972]))], (43334 ^ _776545) ^ [] : [-(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), 43331 ^ [_1639968, _1639970, _1639972]), 43332 ^ [_1639968, _1639970, _1639972]))))]]], (7150 ^ _776545) ^ [_893028, _893030, _893032, _893034] : [7151 ^ _776545 : [(7154 ^ _776545) ^ [] : [hBOOL(hAPP(_893032, _893034))], (7152 ^ _776545) ^ [] : [_893030 = _893034]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_893028), _893030), _893032), _893034)))], (50477 ^ _776545) ^ [_1797029] : [-(c_Fun_Obij__betw(_1797029, _1797029, c_Fun_Oid(_1797029), c_Orderings_Otop__class_Otop(tc_fun(_1797029, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797029, tc_HOL_Obool))))], (48858 ^ _776545) ^ [_1761240, _1761242] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1761240)), _1761242) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1761240, tc_Lazy__Sequence_Olazy__sequence(_1761240)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1761240, tc_Lazy__Sequence_Olazy__sequence(_1761240), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1761240), tc_Nat_Onat), _1761240), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1761240), 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(_1761240)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1761240)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1761240), _1761242)))], (39155 ^ _776545) ^ [_1532055, _1532057, _1532059, _1532061, _1532063, _1532065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532055, _1532057)), hAPP(hAPP(c_Product__Type_OPair(_1532055, _1532057), _1532059), _1532061)), hAPP(hAPP(c_Product__Type_OSigma(_1532055, _1532057), _1532063), _1532065))), 39158 ^ _776545 : [(39161 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532057), _1532061), hAPP(_1532065, _1532059))))], (39159 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532055), _1532059), _1532063)))]]], (23591 ^ _776545) ^ [_1204108] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204108) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30584 ^ _776545) ^ [_1325415, _1325417, _1325419] : [class_Orderings_Olinorder(_1325415), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325415), _1325417)), -(hBOOL(hAPP(hAPP(c_member(_1325415), _1325419), _1325417))), -(c_Big__Operators_Olinorder__class_OMin(_1325415, hAPP(hAPP(c_Set_Oinsert(_1325415), _1325419), _1325417)) = hAPP(hAPP(c_Finite__Set_Ofold(_1325415, _1325415, c_Orderings_Oord__class_Omin(_1325415)), _1325419), _1325417))], (37394 ^ _776545) ^ [_1488164, _1488166, _1488168, _1488170] : [c_Fun_Oinj__on(_1488164, _1488166, _1488168, c_Orderings_Otop__class_Otop(tc_fun(_1488164, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1488164, tc_fun(_1488170, _1488166), hAPP(hAPP(c_COMBB(_1488166, tc_fun(_1488170, _1488166), _1488164), c_COMBK(_1488166, _1488170)), _1488168), c_Orderings_Otop__class_Otop(tc_fun(_1488164, tc_HOL_Obool))))], (24838 ^ _776545) ^ [_1225981, _1225983, _1225985, _1225987] : [class_Divides_Osemiring__div(_1225981), -(c_Divides_Odiv__class_Omod(_1225981, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225981), _1225983), _1225985), _1225987) = c_Divides_Odiv__class_Omod(_1225981, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225981), c_Divides_Odiv__class_Omod(_1225981, _1225983, _1225987)), _1225985), _1225987))], (1534 ^ _776545) ^ [_798584, _798586] : [-(class_Rings_Olinordered__semiring__strict(_798584)), _798586 = _798584, class_Rings_Olinordered__semiring__strict(_798586)], (10052 ^ _776545) ^ [_948549, _948551, _948553, _948555, _948557] : [class_Groups_Oab__group__add(_948549), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948549), _948551), _948553) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948549), _948555), _948557), 10059 ^ _776545 : [(10066 ^ _776545) ^ [] : [_948555 = _948557, -(_948551 = _948553)], (10060 ^ _776545) ^ [] : [_948551 = _948553, -(_948555 = _948557)]]], (7158 ^ _776545) ^ [_893173, _893175, _893177] : [class_Orderings_Olinorder(_893173), 7161 ^ _776545 : [(7168 ^ _776545) ^ [] : [_893175 = _893177, -(hAPP(c_SetInterval_Oord__class_OlessThan(_893173), _893175) = hAPP(c_SetInterval_Oord__class_OlessThan(_893173), _893177))], (7162 ^ _776545) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_893173), _893175) = hAPP(c_SetInterval_Oord__class_OlessThan(_893173), _893177), -(_893175 = _893177)]]], (41905 ^ _776545) ^ [_1604298, _1604300, _1604302, _1604304, _1604306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604298), tc_List_Olist(_1604298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604298), tc_List_Olist(_1604298)), _1604300), _1604302)), c_List_Olistrel1(_1604298, _1604304))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604298), tc_List_Olist(_1604298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604298), tc_List_Olist(_1604298)), hAPP(hAPP(c_List_Olist_OCons(_1604298), _1604306), _1604300)), hAPP(hAPP(c_List_Olist_OCons(_1604298), _1604306), _1604302))), c_List_Olistrel1(_1604298, _1604304))))], (49582 ^ _776545) ^ [_1778466, _1778468] : [c_Relation_Oantisym(_1778466, _1778468), -(c_Relation_Oantisym(_1778466, hAPP(c_Relation_Oconverse(_1778466, _1778466), _1778468)))], (52231 ^ _776545) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (12035 ^ _776545) ^ [_988086, _988088, _988090] : [class_Lattices_Olattice(_988086), hBOOL(hAPP(c_Finite__Set_Ofinite(_988086), _988088)), hBOOL(hAPP(hAPP(c_member(_988086), _988090), _988088)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_988086), _988090), c_Big__Operators_Olattice__class_OSup__fin(_988086, _988088)) = c_Big__Operators_Olattice__class_OSup__fin(_988086, _988088))], (44465 ^ _776545) ^ [_1665901, _1665903, _1665905, _1665907] : [class_Complete__Lattice_Ocomplete__lattice(_1665901), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665903, _1665901), hAPP(c_List_Oset(_1665903), _1665905)), _1665907) = hAPP(c_List_Ofoldl(_1665901, _1665903, hAPP(c_COMBC(_1665903, _1665901, _1665901), hAPP(hAPP(c_COMBB(_1665901, tc_fun(_1665901, _1665901), _1665903), c_Lattices_Osemilattice__inf__class_Oinf(_1665901)), _1665907)), c_Orderings_Otop__class_Otop(_1665901)), _1665905))], (23377 ^ _776545) ^ [_1200130, _1200132, _1200134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200130)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1200132), _1200134)), 23384 ^ _776545 : [(23385 ^ _776545) ^ [_1200326] : [23387 ^ _776545 : [(23393 ^ _776545) ^ [] : [-(_1200326 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23389 ^ [_1200130, _1200132, _1200134, _1200326]), 23386 ^ [_1200130, _1200132, _1200134, _1200326]))], (23391 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23389 ^ [_1200130, _1200132, _1200134, _1200326]), _1200134)))], (23388 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23386 ^ [_1200130, _1200132, _1200134, _1200326]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1200130))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200326), _1200132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200326), _1200130)), _1200132)))]]], (10110 ^ _776545) ^ [_949635, _949637, _949639] : [class_Orderings_Oorder(_949635), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949635, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949635, _949637, _949639)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949635), _949639)) = c_Orderings_Obot__class_Obot(tc_fun(_949635, tc_HOL_Obool)))], (4850 ^ _776545) ^ [_850367, _850369, _850371, _850373, _850375, _850377, _850379, _850381, _850383, _850385, _850387, _850389] : [-(c_Partial__Function_Ofun__lub(_850389, _850385, _850381, _850377, _850373, _850369) = c_Partial__Function_Ofun__lub(_850387, _850383, _850379, _850375, _850371, _850367)), _850389 = _850387, _850385 = _850383, _850381 = _850379, _850377 = _850375, _850373 = _850371, _850369 = _850367], (18023 ^ _776545) ^ [_1100621, _1100623, _1100625] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100621), _1100623)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100621), _1100625)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100623), _1100625))], (15744 ^ _776545) ^ [_1061946, _1061948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1061946), hAPP(c_Nat_OSuc, _1061948))), -(_1061946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15752 ^ _776545 : [(15755 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15751 ^ [_1061946, _1061948]), _1061948)))], (15753 ^ _776545) ^ [] : [-(_1061946 = hAPP(c_Nat_OSuc, 15751 ^ [_1061946, _1061948]))]]], (24924 ^ _776545) ^ [_1227846, _1227848, _1227850] : [class_Divides_Oring__div(_1227846), -(c_Divides_Odiv__class_Omod(_1227846, hAPP(c_Groups_Ouminus__class_Ouminus(_1227846), _1227848), _1227850) = c_Divides_Odiv__class_Omod(_1227846, hAPP(c_Groups_Ouminus__class_Ouminus(_1227846), c_Divides_Odiv__class_Omod(_1227846, _1227848, _1227850)), _1227850))], (2450 ^ _776545) ^ [_812507, _812509, _812511, _812513] : [-(c_Nitpick_Onat__gcd(_812513, _812509) = c_Nitpick_Onat__gcd(_812511, _812507)), _812513 = _812511, _812509 = _812507], (23255 ^ _776545) ^ [_1197900, _1197902, _1197904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197900)), 23258 ^ _776545 : [(23259 ^ _776545) ^ [_1198034] : [23261 ^ _776545 : [(23267 ^ _776545) ^ [] : [-(_1198034 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23263 ^ [_1197900, _1197902, _1197904, _1198034]), 23260 ^ [_1197900, _1197902, _1197904, _1198034]))], (23265 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23263 ^ [_1197900, _1197902, _1197904, _1198034]), _1197902)))], (23262 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23260 ^ [_1197900, _1197902, _1197904, _1198034]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1197900))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197904), _1198034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198034), _1197900))))]]], (8068 ^ _776545) ^ [_913692, _913694, _913696, _913698] : [-(hBOOL(hAPP(hAPP(c_member(_913692), _913694), _913696))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913692, tc_HOL_Obool)), _913696), hAPP(hAPP(c_Set_Oinsert(_913692), _913694), _913698)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913692, tc_HOL_Obool)), _913696), _913698))], (44836 ^ _776545) ^ [_1673571, _1673573, _1673575, _1673577] : [c_List_Olist_ONil(_1673571) = hAPP(hAPP(c_List_Omap(_1673573, _1673571), _1673575), _1673577), -(_1673577 = c_List_Olist_ONil(_1673573))], (42735 ^ _776545) ^ [_1627660, _1627662, _1627664, _1627666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627660), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627662)), _1627664))), 42738 ^ _776545 : [(42745 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Onth(_1627662), _1627664), _1627660) = _1627666, -(hAPP(hAPP(c_List_Olist__update(_1627662, _1627664), _1627660), _1627666) = _1627664)], (42739 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1627662, _1627664), _1627660), _1627666) = _1627664, -(hAPP(hAPP(c_List_Onth(_1627662), _1627664), _1627660) = _1627666)]]], (47092 ^ _776545) ^ [_1723064, _1723066, _1723068, _1723070, _1723072] : [-(c_List_Ofoldr(_1723064, _1723066, _1723068, _1723070, _1723072) = hAPP(c_List_Ofoldl(_1723066, _1723064, hAPP(c_COMBC(_1723064, _1723066, _1723066), _1723068), _1723072), hAPP(c_List_Orev(_1723064), _1723070)))], (5855 ^ _776545) ^ [_869616, _869618, _869620, _869622, _869624, _869626, _869628] : [c_Typedef_Otype__definition(_869616, _869618, _869620, _869622, _869624), 5858 ^ _776545 : [(5865 ^ _776545) ^ [] : [_869626 = _869628, -(hAPP(_869620, _869626) = hAPP(_869620, _869628))], (5859 ^ _776545) ^ [] : [hAPP(_869620, _869626) = hAPP(_869620, _869628), -(_869626 = _869628)]]], (27599 ^ _776545) ^ [_1272974, _1272976] : [class_Rings_Olinordered__idom(_1272974), -(hAPP(c_Groups_Oabs__class_Oabs(_1272974), _1272976) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272974), _1272976), c_Groups_Osgn__class_Osgn(_1272974, _1272976)))], (39145 ^ _776545) ^ [_1531600, _1531602] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531600, _1531600), tc_HOL_Obool)), c_Relation_OId__on(_1531600, _1531602)), hAPP(hAPP(c_Product__Type_OSigma(_1531600, _1531600), _1531602), hAPP(c_COMBK(tc_fun(_1531600, tc_HOL_Obool), _1531600), _1531602)))))], (21827 ^ _776545) ^ [_1171985, _1171987, _1171989, _1171991] : [class_Fields_Olinordered__field__inverse__zero(_1171985), class_Int_Onumber(_1171985), 21834 ^ _776545 : [(21835 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171985), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))), _1171991)), 21838 ^ _776545 : [(21845 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)))), 21848 ^ _776545 : [(21855 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)), c_Groups_Ozero__class_Ozero(_1171985)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), _1171991)))], (21849 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)), c_Groups_Ozero__class_Ozero(_1171985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171985), _1171991), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))), _1171987)))]]], (21839 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), _1171987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171985), _1171991), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)))))]]], (21861 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1171985), _1171987), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))), _1171991))), 21864 ^ _776545 : [(21867 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), _1171987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171985), _1171991), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))))], (21865 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))))]], 21868 ^ _776545 : [(21871 ^ _776545) ^ [] : [21872 ^ _776545 : [(21875 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171985), _1171991), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989))), _1171987))], (21873 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)), c_Groups_Ozero__class_Ozero(_1171985))))]], 21876 ^ _776545 : [(21879 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), _1171991))], (21877 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)), c_Groups_Ozero__class_Ozero(_1171985)))]]], (21869 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171985), c_Groups_Ozero__class_Ozero(_1171985)), hAPP(c_Int_Onumber__class_Onumber__of(_1171985), _1171989)))]]]]], (45874 ^ _776545) ^ [_1696775, _1696777, _1696779] : [-(hAPP(c_List_Oset(_1696775), hAPP(c_List_OremoveAll(_1696775, _1696777), _1696779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1696775, tc_HOL_Obool)), hAPP(c_List_Oset(_1696775), _1696779)), hAPP(hAPP(c_Set_Oinsert(_1696775), _1696777), c_Orderings_Obot__class_Obot(tc_fun(_1696775, tc_HOL_Obool)))))], (44136 ^ _776545) ^ [_1659179, _1659181] : [-(_1659179 = c_List_Olist_ONil(_1659181)), -(hAPP(c_List_Orotate1(_1659181), _1659179) = hAPP(hAPP(c_List_Oappend(_1659181), hAPP(c_List_Otl(_1659181), _1659179)), hAPP(hAPP(c_List_Olist_OCons(_1659181), hAPP(c_List_Ohd(_1659181), _1659179)), c_List_Olist_ONil(_1659181))))], (45479 ^ _776545) ^ [_1688539, _1688541, _1688543, _1688545] : [_1688545 = c_List_Olist_ONil(_1688539), -(c_List_Olist__all2(_1688539, _1688541, _1688543, _1688545, c_List_Olist_ONil(_1688541)))], (5572 ^ _776545) ^ [_861638, _861640, _861642, _861644] : [-(tc_Nitpick_Opair__box(_861644, _861640) = tc_Nitpick_Opair__box(_861642, _861638)), _861644 = _861642, _861640 = _861638], (44206 ^ _776545) ^ [_1660424, _1660426, _1660428] : [-(hAPP(hAPP(c_List_Otake(_1660424), _1660426), hAPP(c_List_Otl(_1660424), _1660428)) = hAPP(c_List_Otl(_1660424), hAPP(hAPP(c_List_Otake(_1660424), hAPP(c_Nat_OSuc, _1660426)), _1660428)))], (2832 ^ _776545) ^ [_818520, _818522, _818524, _818526] : [-(c_Wellfounded_Omax__ext(_818526, _818522) = c_Wellfounded_Omax__ext(_818524, _818520)), _818526 = _818524, _818522 = _818520], (42783 ^ _776545) ^ [_1628656, _1628658, _1628660, _1628662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628656), tc_List_Olist(_1628656))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628656), tc_List_Olist(_1628656)), _1628658), _1628660)), c_List_Olistrel1(_1628656, _1628662))), 42788 ^ _776545 : [(42793 ^ _776545) ^ [] : [-(_1628660 = hAPP(hAPP(c_List_Olist__update(_1628656, _1628658), 42787 ^ [_1628656, _1628658, _1628660, _1628662]), 42786 ^ [_1628656, _1628658, _1628660, _1628662]))], (42791 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42787 ^ [_1628656, _1628658, _1628660, _1628662]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628656)), _1628658))))], (42789 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628656, _1628656)), hAPP(hAPP(c_Product__Type_OPair(_1628656, _1628656), hAPP(hAPP(c_List_Onth(_1628656), _1628658), 42787 ^ [_1628656, _1628658, _1628660, _1628662])), 42786 ^ [_1628656, _1628658, _1628660, _1628662])), _1628662)))]]], (26979 ^ _776545) ^ [_1262532, _1262534] : [class_Rings_Oring__1(_1262532), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262532), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1262534)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1262532), _1262534))], (4320 ^ _776545) ^ [_841964, _841966, _841968, _841970, _841972, _841974] : [-(c_List_Oreplicate(_841974, _841970, _841966) = c_List_Oreplicate(_841972, _841968, _841964)), _841974 = _841972, _841970 = _841968, _841966 = _841964], (2150 ^ _776545) ^ [_807737, _807739, _807741, _807743] : [-(c_Nitpick_Onat__lcm(_807743, _807739) = c_Nitpick_Onat__lcm(_807741, _807737)), _807743 = _807741, _807739 = _807737], (45402 ^ _776545) ^ [_1686446, _1686448] : [-(hBOOL(hAPP(c_List_Olistsp(_1686446, _1686448), c_List_Olist_ONil(_1686446))))], (3214 ^ _776545) ^ [_824393, _824395, _824397, _824399, _824401, _824403] : [-(c_Big__Operators_Olattice_OInf__fin(_824403, _824399, _824395) = c_Big__Operators_Olattice_OInf__fin(_824401, _824397, _824393)), _824403 = _824401, _824399 = _824397, _824395 = _824393], (15962 ^ _776545) ^ [_1065439, _1065441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065441), hAPP(c_Nat_OSuc, _1065439))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065439), _1065441))], (19418 ^ _776545) ^ [_1127087, _1127089, _1127091, _1127093] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1127087, _1127091)), c_Sum__Type_OPlus(_1127087, _1127091, _1127089, _1127093)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127087), _1127089)), hAPP(c_Finite__Set_Ocard(_1127091), _1127093))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127087), _1127089)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127091), _1127093))], (50825 ^ _776545) ^ [_1804742, _1804744, _1804746, _1804748, _1804750, _1804752, _1804754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744)), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804746), _1804748)), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804750), _1804752))), c_Transitive__Closure_Ortrancl(tc_prod(_1804742, _1804744), _1804754))), -(hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804746), _1804748) = hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804750), _1804752)), 50834 ^ _776545 : [(50837 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744)), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), 50832 ^ [_1804742, _1804744, _1804746, _1804748, _1804750, _1804752, _1804754]), 50833 ^ [_1804742, _1804744, _1804746, _1804748, _1804750, _1804752, _1804754])), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804750), _1804752))), c_Transitive__Closure_Ortrancl(tc_prod(_1804742, _1804744), _1804754))))], (50835 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1804742, _1804744), tc_prod(_1804742, _1804744)), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), _1804746), _1804748)), hAPP(hAPP(c_Product__Type_OPair(_1804742, _1804744), 50832 ^ [_1804742, _1804744, _1804746, _1804748, _1804750, _1804752, _1804754]), 50833 ^ [_1804742, _1804744, _1804746, _1804748, _1804750, _1804752, _1804754]))), _1804754)))]]], (44661 ^ _776545) ^ [_1669439, _1669441] : [-(_1669439 = c_List_Olist_ONil(_1669441)), -(c_List_Olast(_1669441, _1669439) = hAPP(hAPP(c_List_Onth(_1669441), _1669439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669441)), _1669439)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (7081 ^ _776545) ^ [_891818, _891820, _891822] : [7083 ^ _776545 : [(7086 ^ _776545) ^ [] : [hBOOL(hAPP(_891820, 7082 ^ [_891818, _891820, _891822]))], (7084 ^ _776545) ^ [] : [-(hBOOL(hAPP(_891818, 7082 ^ [_891818, _891820, _891822])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891822, tc_HOL_Obool)), hAPP(c_Set_OCollect(_891822), _891818)), hAPP(c_Set_OCollect(_891822), _891820))))], (1444 ^ _776545) ^ [_797459, _797461] : [-(class_Orderings_Obot(_797459)), _797461 = _797459, class_Orderings_Obot(_797461)], (33785 ^ _776545) ^ [_1401887, _1401889, _1401891, _1401893, _1401895] : [class_Groups_Ocomm__monoid__mult(_1401887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401889), _1401891)), 33792 ^ _776545 : [(33799 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401889), _1401893), _1401891))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401889, _1401887), hAPP(hAPP(c_COMBC(_1401889, _1401887, _1401887), hAPP(hAPP(c_COMBS(_1401889, _1401887, tc_fun(_1401887, _1401887)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401887, tc_fun(_1401887, _1401887)), _1401889), c_If(_1401887)), hAPP(hAPP(c_COMBC(_1401889, _1401889, tc_HOL_Obool), c_fequal), _1401893))), _1401895)), c_Groups_Oone__class_Oone(_1401887))), _1401891) = c_Groups_Oone__class_Oone(_1401887))], (33793 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1401889), _1401893), _1401891)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401889, _1401887), hAPP(hAPP(c_COMBC(_1401889, _1401887, _1401887), hAPP(hAPP(c_COMBS(_1401889, _1401887, tc_fun(_1401887, _1401887)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1401887, tc_fun(_1401887, _1401887)), _1401889), c_If(_1401887)), hAPP(hAPP(c_COMBC(_1401889, _1401889, tc_HOL_Obool), c_fequal), _1401893))), _1401895)), c_Groups_Oone__class_Oone(_1401887))), _1401891) = hAPP(_1401895, _1401893))]]], (52041 ^ _776545) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52439 ^ _776545) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (2892 ^ _776545) ^ [_819438, _819440, _819442, _819444] : [-(c_Nitpick_Oint__lcm(_819444, _819440) = c_Nitpick_Oint__lcm(_819442, _819438)), _819444 = _819442, _819440 = _819438], (19521 ^ _776545) ^ [_1129224, _1129226] : [class_Rings_Olinordered__idom(_1129224), 19524 ^ _776545 : [(19531 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129224), _1129226), c_Groups_Ozero__class_Ozero(_1129224))), -(c_Groups_Osgn__class_Osgn(_1129224, _1129226) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129224), c_Groups_Oone__class_Oone(_1129224)))], (19525 ^ _776545) ^ [] : [c_Groups_Osgn__class_Osgn(_1129224, _1129226) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129224), c_Groups_Oone__class_Oone(_1129224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129224), _1129226), c_Groups_Ozero__class_Ozero(_1129224))))]]], (39185 ^ _776545) ^ [_1532805, _1532807, _1532809, _1532811, _1532813, _1532815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532805, _1532807)), hAPP(hAPP(c_Product__Type_OPair(_1532805, _1532807), _1532809), _1532811)), hAPP(hAPP(c_Product__Type_OSigma(_1532805, _1532807), _1532813), _1532815))), 39188 ^ _776545 : [(39191 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532807), _1532811), hAPP(_1532815, _1532809))))], (39189 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1532805), _1532809), _1532813)))]]], (8453 ^ _776545) ^ [_921716, _921718, _921720, _921722, _921724] : [class_Lattices_Osemilattice__sup(_921716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921716), _921718), _921720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921716), _921722), _921724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921716), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921716), _921718), _921722)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_921716), _921720), _921724))))], (16492 ^ _776545) ^ [_1073548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073548), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1073548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16242 ^ _776545) ^ [_1069894, _1069896, _1069898] : [class_Rings_Ono__zero__divisors(_1069894), -(_1069896 = c_Groups_Ozero__class_Ozero(_1069894)), -(_1069898 = c_Groups_Ozero__class_Ozero(_1069894)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069894), _1069896), _1069898) = c_Groups_Ozero__class_Ozero(_1069894)], (37010 ^ _776545) ^ [_1479835, _1479837, _1479839] : [c_Equiv__Relations_Oequivp(_1479835, _1479837), -(hBOOL(hAPP(hAPP(_1479837, _1479839), _1479839)))], (21315 ^ _776545) ^ [_1162338, _1162340, _1162342] : [class_Int_Onumber(_1162338), class_Orderings_Olinorder(_1162338), 21322 ^ _776545 : [(21329 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162338), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162342)), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162340)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162338), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162340)), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162342))))], (21323 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162338), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162340)), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162342))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162338), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162342)), hAPP(c_Int_Onumber__class_Onumber__of(_1162338), _1162340)))]]], (37582 ^ _776545) ^ [_1491998, _1492000, _1492002, _1492004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491998), _1492000)), 37585 ^ _776545 : [(37592 ^ _776545) ^ [] : [hAPP(c_Finite__Set_Ocard(_1492002), hAPP(c_Set_Oimage(_1491998, _1492002, _1492004), _1492000)) = hAPP(c_Finite__Set_Ocard(_1491998), _1492000), -(c_Fun_Oinj__on(_1491998, _1492002, _1492004, _1492000))], (37586 ^ _776545) ^ [] : [c_Fun_Oinj__on(_1491998, _1492002, _1492004, _1492000), -(hAPP(c_Finite__Set_Ocard(_1492002), hAPP(c_Set_Oimage(_1491998, _1492002, _1492004), _1492000)) = hAPP(c_Finite__Set_Ocard(_1491998), _1492000))]]], (44487 ^ _776545) ^ [_1666353, _1666355, _1666357, _1666359] : [44488 ^ _776545 : [(44489 ^ _776545) ^ [_1666450, _1666452] : [_1666353 = hAPP(hAPP(c_List_Olist_OCons(_1666355), _1666452), _1666450)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666355), tc_List_Olist(_1666355))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666355), tc_List_Olist(_1666355)), _1666357), hAPP(hAPP(c_List_Oappend(_1666355), _1666357), _1666353))), c_List_Olexord(_1666355, _1666359))))], (50241 ^ _776545) ^ [_1792186] : [-(_1792186 = hAPP(c_Code__Numeral_Oof__nat, 50239 ^ [_1792186]))], (11012 ^ _776545) ^ [_966837, _966839, _966841] : [_966839 = _966841, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966837, tc_HOL_Obool)), _966839) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966837, tc_HOL_Obool)), _966841))], (40659 ^ _776545) ^ [_1570733, _1570735, _1570737, _1570739, _1570741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570733, _1570733)), hAPP(hAPP(c_Product__Type_OPair(_1570733, _1570733), _1570735), _1570737)), c_Transitive__Closure_Otrancl(_1570733, _1570739))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570733, _1570733)), hAPP(hAPP(c_Product__Type_OPair(_1570733, _1570733), _1570737), _1570741)), c_Transitive__Closure_Otrancl(_1570733, _1570739))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570733, _1570733)), hAPP(hAPP(c_Product__Type_OPair(_1570733, _1570733), _1570735), _1570741)), c_Transitive__Closure_Otrancl(_1570733, _1570739))))], (47002 ^ _776545) ^ [_1721263, _1721265] : [_1721265 = c_List_Olist_ONil(_1721263), -(c_List_Olist_ONil(_1721263) = hAPP(c_List_Orev(_1721263), _1721265))], (21119 ^ _776545) ^ [_1158528, _1158530] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1158528), _1158530)), 21125 ^ _776545 : [(21128 ^ _776545) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21126 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158528), 21124 ^ [_1158528, _1158530]), _1158530)))]], -(hAPP(c_Finite__Set_Ocard(_1158528), _1158530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21883 ^ _776545) ^ [_1173099, _1173101, _1173103, _1173105] : [class_Fields_Olinordered__field__inverse__zero(_1173099), class_Int_Onumber(_1173099), 21890 ^ _776545 : [(21891 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173099), _1173101), _1173103)), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105))), 21894 ^ _776545 : [(21901 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), _1173103))), 21904 ^ _776545 : [(21911 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), _1173103), c_Groups_Ozero__class_Ozero(_1173099)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105))))], (21905 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), _1173103), c_Groups_Ozero__class_Ozero(_1173099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173099), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)), _1173103)), _1173101)))]]], (21895 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), _1173103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), _1173101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173099), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)), _1173103))))]]], (21917 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173099), _1173101), _1173103)), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)))), 21920 ^ _776545 : [(21923 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), _1173101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173099), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)), _1173103)))], (21921 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), _1173103)))]], 21924 ^ _776545 : [(21927 ^ _776545) ^ [] : [21928 ^ _776545 : [(21931 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173099), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)), _1173103)), _1173101))], (21929 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), _1173103), c_Groups_Ozero__class_Ozero(_1173099))))]], 21932 ^ _776545 : [(21935 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), hAPP(c_Int_Onumber__class_Onumber__of(_1173099), _1173105)))], (21933 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), _1173103), c_Groups_Ozero__class_Ozero(_1173099)))]]], (21925 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173099), c_Groups_Ozero__class_Ozero(_1173099)), _1173103))]]]]], (14907 ^ _776545) ^ [_1045426, _1045428, _1045430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045426), _1045428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045430), _1045426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045430), _1045428))))], (14200 ^ _776545) ^ [_1031965, _1031967] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1031965, _1031967))))], (22989 ^ _776545) ^ [_1193065, _1193067, _1193069] : [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), _1193065), _1193067)), _1193069))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193069), _1193065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193067)))], (8661 ^ _776545) ^ [_925382, _925384, _925386] : [class_Lattices_Osemilattice__inf(_925382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925382), _925384), _925386)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925382), _925384), _925386) = _925384)], (36904 ^ _776545) ^ [_1477067, _1477069, _1477071, _1477073, _1477075] : [c_Equiv__Relations_Oequiv(_1477067, _1477069, _1477071), hBOOL(hAPP(hAPP(c_member(tc_prod(_1477067, _1477067)), hAPP(hAPP(c_Product__Type_OPair(_1477067, _1477067), _1477073), _1477075)), _1477071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477067, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477067, _1477067, _1477071), hAPP(hAPP(c_Set_Oinsert(_1477067), _1477073), c_Orderings_Obot__class_Obot(tc_fun(_1477067, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1477067, _1477067, _1477071), hAPP(hAPP(c_Set_Oinsert(_1477067), _1477075), c_Orderings_Obot__class_Obot(tc_fun(_1477067, tc_HOL_Obool)))))))], (22305 ^ _776545) ^ [_1180915, _1180917] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180915), _1180917) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180917), _1180915))], (50729 ^ _776545) ^ [_1801930, _1801932, _1801934] : [hBOOL(hAPP(hAPP(_1801934, _1801932), _1801932)), -(hBOOL(hAPP(hAPP(c_member(_1801930), _1801932), c_Quotient_ORespects(_1801930, _1801934))))], (47138 ^ _776545) ^ [_1724143, _1724145, _1724147, _1724149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724143), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724145)), _1724147))), -(hAPP(c_List_Orev(_1724145), hAPP(hAPP(c_List_Olist__update(_1724145, _1724147), _1724143), _1724149)) = hAPP(hAPP(c_List_Olist__update(_1724145, hAPP(c_List_Orev(_1724145), _1724147)), 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(_1724145)), _1724147)), _1724143)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1724149))], (39465 ^ _776545) ^ [_1541356, _1541358, _1541360, _1541362] : [-(c_Product__Type_Oapfst(_1541356, _1541358, _1541360, _1541362) = c_Product__Type_Omap__pair(_1541356, _1541358, _1541360, _1541360, _1541362, c_Fun_Oid(_1541360)))], (13502 ^ _776545) ^ [_1016778, _1016780] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1016778), _1016780))))], (11184 ^ _776545) ^ [_970335, _970337, _970339, _970341, _970343] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970335, tc_HOL_Obool)), _970337), hAPP(c_Set_Oimage(_970339, _970335, _970341), _970343)))), 11185 ^ _776545 : [(11186 ^ _776545) ^ [_970415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970339, tc_HOL_Obool)), _970415), _970343)), _970337 = hAPP(c_Set_Oimage(_970339, _970335, _970341), _970415)]]], (13898 ^ _776545) ^ [_1024706, _1024708, _1024710] : [class_Groups_Ogroup__add(_1024706), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024706), _1024708), _1024710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024706), _1024708), hAPP(c_Groups_Ouminus__class_Ouminus(_1024706), _1024710)))], (27281 ^ _776545) ^ [_1267349, _1267351] : [class_Rings_Olinordered__idom(_1267349), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267349), hAPP(c_Groups_Oabs__class_Oabs(_1267349), _1267351)), hAPP(c_Groups_Oabs__class_Oabs(_1267349), _1267351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267349), _1267351), _1267351))], (1214 ^ _776545) ^ [_794584, _794586] : [-(class_Rings_Oordered__ring(_794584)), _794586 = _794584, class_Rings_Oordered__ring(_794586)], (39265 ^ _776545) ^ [_1534760, _1534762, _1534764, _1534766, _1534768, _1534770] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534760, _1534762), hAPP(hAPP(c_Set_Oinsert(_1534760), _1534764), _1534766)), hAPP(c_COMBK(tc_fun(_1534762, tc_HOL_Obool), _1534760), hAPP(hAPP(c_Set_Oinsert(_1534762), _1534768), _1534770))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1534760, _1534762)), hAPP(hAPP(c_Product__Type_OPair(_1534760, _1534762), _1534764), _1534768)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1534760, _1534762), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534760, _1534762), _1534766), hAPP(c_COMBK(tc_fun(_1534762, tc_HOL_Obool), _1534760), hAPP(hAPP(c_Set_Oinsert(_1534762), _1534768), _1534770)))), hAPP(hAPP(c_Product__Type_OSigma(_1534760, _1534762), hAPP(hAPP(c_Set_Oinsert(_1534760), _1534764), _1534766)), hAPP(c_COMBK(tc_fun(_1534762, tc_HOL_Obool), _1534760), _1534770)))))], (49086 ^ _776545) ^ [_1766563, _1766565, _1766567] : [c_List_Oall__interval__int(_1766563, _1766565, _1766567), 49089 ^ _776545 : [(49090 ^ _776545) ^ [_1766641] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1766641), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1766565, _1766567))), -(hBOOL(hAPP(_1766563, _1766641)))]]], (41745 ^ _776545) ^ [_1599142, _1599144, _1599146] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599142)), c_List_Osublist(_1599142, _1599144, _1599146)) = 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(_1599142)), _1599144)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1599146)))))], (14202 ^ _776545) ^ [_1031996] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1031996))))], (47098 ^ _776545) ^ [_1723262, _1723264, _1723266, _1723268] : [hAPP(c_List_Orev(_1723262), _1723264) = hAPP(hAPP(c_List_Olist_OCons(_1723262), _1723266), _1723268), -(_1723264 = hAPP(hAPP(c_List_Oappend(_1723262), hAPP(c_List_Orev(_1723262), _1723268)), hAPP(hAPP(c_List_Olist_OCons(_1723262), _1723266), c_List_Olist_ONil(_1723262))))], (1424 ^ _776545) ^ [_797209, _797211] : [-(class_Lattices_Olattice(_797209)), _797211 = _797209, class_Lattices_Olattice(_797211)], (384 ^ _776545) ^ [_782363, _782365, _782367, _782369] : [-(c_Relation_Oirrefl(_782367, _782363)), c_Relation_Oirrefl(_782369, _782365), _782369 = _782367, _782365 = _782363], (2258 ^ _776545) ^ [_809435, _809437] : [_809437 = _809435, -(c_SetInterval_Oord__class_OatLeast(_809437) = c_SetInterval_Oord__class_OatLeast(_809435))], (47615 ^ _776545) ^ [_1734082, _1734084, _1734086, _1734088, _1734090] : [-(c_List_Omaps(_1734082, _1734084, _1734086, hAPP(hAPP(c_List_Olist_OCons(_1734082), _1734088), _1734090)) = hAPP(hAPP(c_List_Oappend(_1734084), hAPP(_1734086, _1734088)), c_List_Omaps(_1734082, _1734084, _1734086, _1734090)))], (26140 ^ _776545) ^ [_1248898, _1248900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1248898)), hAPP(c_Int_Onat, _1248900))), 26143 ^ _776545 : [(26146 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248898), _1248900)))], (26144 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248900)))]]], (6478 ^ _776545) ^ [_881203, _881205, _881207] : [_881203 = c_Orderings_Obot__class_Obot(tc_fun(_881205, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_881205), _881207), _881203))], (31293 ^ _776545) ^ [_1338121, _1338123, _1338125] : [class_Orderings_Olinorder(_1338121), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338121), _1338123), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338121), _1338123), _1338125)) = _1338123)], (36752 ^ _776545) ^ [_1473826, _1473828, _1473830, _1473832, _1473834] : [c_Equiv__Relations_Oequiv(_1473826, _1473828, _1473830), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473826, tc_HOL_Obool)), _1473832), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473826), _1473828), _1473830))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1473826, tc_HOL_Obool)), _1473834), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473826), _1473828), _1473830))), -(_1473832 = _1473834), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473826, tc_HOL_Obool)), _1473832), _1473834) = c_Orderings_Obot__class_Obot(tc_fun(_1473826, tc_HOL_Obool)))], (39384 ^ _776545) ^ [_1539176, _1539178, _1539180, _1539182, _1539184, _1539186] : [class_Groups_Ocomm__monoid__add(_1539176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539178), _1539180)), 39394 ^ _776545 : [(39397 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539182), hAPP(_1539184, 39393 ^ [_1539176, _1539178, _1539180, _1539182, _1539184, _1539186])))], (39395 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539178), 39393 ^ [_1539176, _1539178, _1539180, _1539182, _1539184, _1539186]), _1539180)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539178, _1539176), hAPP(hAPP(c_COMBS(_1539178, tc_fun(_1539182, tc_HOL_Obool), _1539176), hAPP(hAPP(c_COMBB(tc_fun(_1539182, _1539176), tc_fun(tc_fun(_1539182, tc_HOL_Obool), _1539176), _1539178), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539182, _1539176)), _1539186)), _1539184)), _1539180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1539178, _1539182), _1539176), hAPP(c_Product__Type_Oprod_Oprod__case(_1539178, _1539182, _1539176), _1539186)), hAPP(hAPP(c_Product__Type_OSigma(_1539178, _1539182), _1539180), _1539184)))], (278 ^ _776545) ^ [_780828, _780830] : [-(c_Nat__Transfer_Ois__nat(_780828)), _780830 = _780828, c_Nat__Transfer_Ois__nat(_780830)], (11214 ^ _776545) ^ [_971125, _971127, _971129, _971131] : [-(hBOOL(hAPP(hAPP(c_member(_971125), hAPP(_971127, _971129)), hAPP(c_Set_Oimage(_971131, _971125, _971127), c_Orderings_Otop__class_Otop(tc_fun(_971131, tc_HOL_Obool))))))], (18318 ^ _776545) ^ [_1105993, _1105995, _1105997, _1105999] : [class_Rings_Olinordered__semiring(_1105993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105993), _1105995), _1105997)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105993), _1105995), _1105999))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105993), c_Groups_Ozero__class_Ozero(_1105993)), _1105995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105993), _1105997), _1105999)))], (22975 ^ _776545) ^ [_1192836, _1192838, _1192840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192836)), _1192836 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192836), _1192840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192840), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (4262 ^ _776545) ^ [_841113, _841115, _841117, _841119] : [-(c_List_Ozip(_841119, _841115) = c_List_Ozip(_841117, _841113)), _841119 = _841117, _841115 = _841113], (7292 ^ _776545) ^ [_895786, _895788, _895790] : [hBOOL(hAPP(hAPP(c_member(_895786), _895788), hAPP(hAPP(c_Set_Oinsert(_895786), _895790), c_Orderings_Obot__class_Obot(tc_fun(_895786, tc_HOL_Obool))))), -(_895788 = _895790)], (52207 ^ _776545) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (9708 ^ _776545) ^ [_942715, _942717, _942719, _942721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942715, tc_HOL_Obool)), _942717), _942719)), hBOOL(hAPP(hAPP(c_member(_942715), _942721), _942717)), -(hBOOL(hAPP(hAPP(c_member(_942715), _942721), _942719)))], (41897 ^ _776545) ^ [_1603987, _1603989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1603987), tc_List_Olist(_1603987)), tc_HOL_Obool)), c_List_Olistrel1(_1603987, c_Transitive__Closure_Ortrancl(_1603987, _1603989))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603987), c_List_Olistrel1(_1603987, _1603989)))))], (52209 ^ _776545) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (6463 ^ _776545) ^ [_880988, _880990] : [6464 ^ _776545 : [(6465 ^ _776545) ^ [_881041] : [hBOOL(hAPP(hAPP(c_member(_880988), _881041), _880990))]], _880990 = c_Orderings_Obot__class_Obot(tc_fun(_880988, tc_HOL_Obool))], (25828 ^ _776545) ^ [_1243828, _1243830] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1243828))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1243828)), _1243830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1243830))], (9580 ^ _776545) ^ [_940848, _940850, _940852] : [class_Orderings_Opreorder(_940848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940848), _940850), _940852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_940848), _940850), _940852)))], (19408 ^ _776545) ^ [_1126886, _1126888] : [class_Int_Oring__char__0(_1126886), hBOOL(hAPP(hAPP(c_member(_1126886), _1126888), c_Int_Oring__1__class_OInts(_1126886))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126886), c_Groups_Oone__class_Oone(_1126886)), _1126888)), _1126888) = c_Groups_Ozero__class_Ozero(_1126886)], (34994 ^ _776545) ^ [_1429451] : [-(c_Int_Oint__ge__less__than2(_1429451) = 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), _1429451)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (42695 ^ _776545) ^ [_1626643, _1626645, _1626647, _1626649, _1626651, _1626653] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1626643, _1626645), hAPP(hAPP(c_List_Ozip(_1626643, _1626645), _1626647), _1626649)), _1626651), _1626653) = hAPP(hAPP(c_List_Ozip(_1626643, _1626645), hAPP(hAPP(c_List_Olist__update(_1626643, _1626647), _1626651), hAPP(c_Product__Type_Ofst(_1626643, _1626645), _1626653))), hAPP(hAPP(c_List_Olist__update(_1626645, _1626649), _1626651), hAPP(c_Product__Type_Osnd(_1626643, _1626645), _1626653))))], (49397 ^ _776545) ^ [_1775271, _1775273, _1775275, _1775277] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775271), _1775273)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1775271), _1775275)), -(_1775275 = c_Orderings_Obot__class_Obot(tc_fun(_1775271, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1775271, _1775277, _1775273, _1775275)), 49411 ^ _776545 : [(49414 ^ _776545) ^ [_1775616] : [hBOOL(hAPP(hAPP(c_member(_1775271), _1775616), _1775275)), hBOOL(hAPP(hAPP(_1775277, 49410 ^ [_1775271, _1775273, _1775275, _1775277]), _1775616))], (49412 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775271), 49410 ^ [_1775271, _1775273, _1775275, _1775277]), _1775273)))]]], (45670 ^ _776545) ^ [_1692593, _1692595, _1692597] : [-(c_Enum_Osublists(_1692593, hAPP(hAPP(c_List_Olist_OCons(_1692593), _1692595), _1692597)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1692593)), tc_List_Olist(tc_List_Olist(_1692593))), c_Enum_Osublists(_1692593, _1692597)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1692593)), tc_List_Olist(tc_List_Olist(_1692593)), tc_List_Olist(tc_List_Olist(_1692593))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1692593)), tc_fun(tc_List_Olist(tc_List_Olist(_1692593)), tc_List_Olist(tc_List_Olist(_1692593))), tc_List_Olist(tc_List_Olist(_1692593))), c_List_Oappend(tc_List_Olist(_1692593))), hAPP(c_List_Omap(tc_List_Olist(_1692593), tc_List_Olist(_1692593)), hAPP(c_List_Olist_OCons(_1692593), _1692595)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1692593))))))], (49285 ^ _776545) ^ [_1771691, _1771693] : [c_Relation_Otrans(_1771691, _1771693), -(c_Relation_Otrans(tc_List_Olist(_1771691), c_List_Olexord(_1771691, _1771693)))], (13188 ^ _776545) ^ [_1009927, _1009929, _1009931, _1009933, _1009935] : [class_Groups_Oab__group__add(_1009927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1009929), _1009931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1009931), _1009933)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009927), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009927), _1009935), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009929), _1009933))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009927), _1009935), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009929), _1009931))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1009927), _1009935), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1009931), _1009933)))], (33558 ^ _776545) ^ [_1394166, _1394168, _1394170, _1394172] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394166, tc_fun(_1394168, tc_HOL_Obool)), _1394170), _1394172) = c_Orderings_Otop__class_Otop(tc_fun(_1394168, tc_HOL_Obool)), 33561 ^ _776545 : [(33562 ^ _776545) ^ [_1394282] : [hBOOL(hAPP(hAPP(c_member(_1394166), _1394282), _1394170)), -(hAPP(_1394172, _1394282) = c_Orderings_Otop__class_Otop(tc_fun(_1394168, tc_HOL_Obool)))]]], (33206 ^ _776545) ^ [_1384964, _1384966, _1384968, _1384970, _1384972] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384964, tc_fun(_1384966, tc_HOL_Obool)), _1384968), hAPP(hAPP(c_COMBB(tc_fun(_1384966, tc_HOL_Obool), tc_fun(_1384966, tc_HOL_Obool), _1384964), hAPP(c_Set_Oinsert(_1384966), _1384970)), _1384972)) = hAPP(hAPP(c_Set_Oinsert(_1384966), _1384970), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1384964, tc_fun(_1384966, tc_HOL_Obool)), _1384968), _1384972)))], (39605 ^ _776545) ^ [_1544689, _1544691] : [c_Predicate_Oreflp(_1544689, _1544691), -(c_Relation_Orefl__on(_1544689, c_Orderings_Otop__class_Otop(tc_fun(_1544689, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544689, _1544689)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544689, _1544689, tc_HOL_Obool), _1544691))))], (41104 ^ _776545) ^ [_1582601, _1582603, _1582605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582601, _1582603)), hAPP(c_Relation_Oconverse(_1582603, _1582601), _1582605))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582603, _1582601)), _1582605)))], (43268 ^ _776545) ^ [_1638525, _1638527] : [-(c_List_Oset__Cons(_1638525, _1638527, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1638525)), c_List_Olist_ONil(_1638525)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1638525), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1638525, tc_List_Olist(_1638525), hAPP(hAPP(c_COMBC(_1638525, tc_List_Olist(_1638525), tc_List_Olist(_1638525)), c_List_Olist_OCons(_1638525)), c_List_Olist_ONil(_1638525))), _1638527))], (13134 ^ _776545) ^ [_1008686, _1008688, _1008690, _1008692, _1008694] : [class_Rings_Oring(_1008686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1008688), _1008690)), hBOOL(hAPP(hAPP(c_member(_1008688), _1008692), _1008690)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008688, _1008686), _1008694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008688, tc_HOL_Obool)), _1008690), hAPP(hAPP(c_Set_Oinsert(_1008688), _1008692), c_Orderings_Obot__class_Obot(tc_fun(_1008688, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1008686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008688, _1008686), _1008694), _1008690)), hAPP(_1008694, _1008692)))], (11258 ^ _776545) ^ [_972092, _972094, _972096] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_972092, _972094, c_Orderings_Obot__class_Obot(tc_fun(_972092, tc_HOL_Obool))), _972096))], (52115 ^ _776545) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (35338 ^ _776545) ^ [_1435646, _1435648, _1435650] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435646, _1435646), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435648), _1435650))), -(_1435646 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1435648 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (43358 ^ _776545) ^ [_1640693, _1640695, _1640697, _1640699, _1640701] : [-(_1640693 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1640695, _1640697, _1640699), _1640693), _1640701) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1640697), _1640695), tc_prod(_1640697, _1640695), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640697), _1640695), c_List_Olist_ONil(_1640697)), _1640701), hAPP(c_Product__Type_Oprod_Oprod__case(_1640697, _1640695, tc_prod(tc_List_Olist(_1640697), _1640695)), hAPP(hAPP(c_COMBC(_1640697, tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695)), tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1640697), _1640695), tc_prod(tc_List_Olist(_1640697), _1640695)), tc_fun(tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695)), tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695))), _1640697), c_COMBB(tc_prod(tc_List_Olist(_1640697), _1640695), tc_prod(tc_List_Olist(_1640697), _1640695), _1640695)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640697), tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695))), tc_fun(tc_prod(tc_List_Olist(_1640697), _1640695), tc_prod(tc_List_Olist(_1640697), _1640695)), _1640697), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1640697), _1640695, tc_prod(tc_List_Olist(_1640697), _1640695))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1640697), tc_List_Olist(_1640697)), tc_fun(tc_List_Olist(_1640697), tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695))), _1640697), hAPP(c_COMBB(tc_List_Olist(_1640697), tc_fun(_1640695, tc_prod(tc_List_Olist(_1640697), _1640695)), tc_List_Olist(_1640697)), c_Product__Type_OPair(tc_List_Olist(_1640697), _1640695))), c_List_Olist_OCons(_1640697))))), hAPP(c_Lazy__Sequence_Oanamorph(_1640695, _1640697, _1640699), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1640693), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1640699, _1640701)))], (41180 ^ _776545) ^ [_1584224, _1584226, _1584228, _1584230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584224, _1584224)), hAPP(hAPP(c_Product__Type_OPair(_1584224, _1584224), _1584226), _1584228)), hAPP(c_Relation_Oconverse(_1584224, _1584224), c_Transitive__Closure_Otrancl(_1584224, _1584230)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584224, _1584224)), hAPP(hAPP(c_Product__Type_OPair(_1584224, _1584224), _1584226), _1584228)), c_Transitive__Closure_Otrancl(_1584224, hAPP(c_Relation_Oconverse(_1584224, _1584224), _1584230)))))], (35840 ^ _776545) ^ [_1446195, _1446197, _1446199, _1446201, _1446203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1446195, _1446197)), hAPP(_1446195, _1446199))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1446201, _1446201)), hAPP(hAPP(c_Product__Type_OPair(_1446201, _1446201), _1446197), _1446199)), _1446203)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446201, _1446201)), hAPP(hAPP(c_Product__Type_OPair(_1446201, _1446201), _1446197), _1446199)), c_Wellfounded_Omlex__prod(_1446201, _1446195, _1446203))))], (31577 ^ _776545) ^ [_1343427, _1343429, _1343431, _1343433] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1343427), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343427), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343427), _1343429), _1343431)), _1343433) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343427), _1343429), _1343433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343427), _1343431), _1343433)))], (47024 ^ _776545) ^ [_1721678, _1721680, _1721682] : [-(hAPP(c_List_Orev(_1721678), hAPP(c_List_Ofilter(_1721678, _1721680), _1721682)) = hAPP(c_List_Ofilter(_1721678, _1721680), hAPP(c_List_Orev(_1721678), _1721682)))], (51057 ^ _776545) ^ [_1810489, _1810491, _1810493, _1810495] : [class_Rings_Ocomm__ring(_1810489), class_Rings_Odvd(_1810489), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810489), _1810491), _1810493)), 51068 ^ _776545 : [(51075 ^ _776545) ^ [_1810915, _1810917] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810489), _1810491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810489), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1810489), _1810917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1810489), _1810915), _1810493))), _1810495))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810489), _1810491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810489), _1810917), _1810495))))], (51069 ^ _776545) ^ [_1810742, _1810744] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810489), _1810491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810489), _1810744), _1810495))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1810489), _1810491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1810489), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1810489), _1810744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1810489), _1810742), _1810493))), _1810495))))]]], (38398 ^ _776545) ^ [_1512684, _1512686] : [c_Wellfounded_Owf(_1512684, _1512686), -(c_Wellfounded_Owf(tc_List_Olist(_1512684), c_List_Olex(_1512684, _1512686)))], (7005 ^ _776545) ^ [_890408, _890410, _890412] : [class_Orderings_Oord(_890408), 7008 ^ _776545 : [(7015 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890408), _890412), _890410)), -(hBOOL(hAPP(hAPP(c_member(_890408), _890410), hAPP(c_SetInterval_Oord__class_OatLeast(_890408), _890412))))], (7009 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890408), _890410), hAPP(c_SetInterval_Oord__class_OatLeast(_890408), _890412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_890408), _890412), _890410)))]]], (30598 ^ _776545) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (37172 ^ _776545) ^ [_1483775, _1483777, _1483779, _1483781, _1483783, _1483785, _1483787] : [c_Equiv__Relations_Oequiv(_1483775, _1483777, _1483779), c_Equiv__Relations_Ocongruent(_1483775, tc_fun(_1483781, tc_HOL_Obool), _1483779, _1483783), hBOOL(hAPP(hAPP(c_member(tc_fun(_1483775, tc_HOL_Obool)), _1483785), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483775), _1483777), _1483779))), 37186 ^ _776545 : [(37189 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1483781, tc_HOL_Obool)), hAPP(_1483783, 37185 ^ [_1483775, _1483777, _1483779, _1483781, _1483783, _1483785, _1483787])), _1483787))], (37187 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483775), 37185 ^ [_1483775, _1483777, _1483779, _1483781, _1483783, _1483785, _1483787]), _1483777)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1483781, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483775, tc_fun(_1483781, tc_HOL_Obool)), _1483785), _1483783)), _1483787)))], (42491 ^ _776545) ^ [_1621228, _1621230, _1621232, _1621234] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621228), tc_List_Olist(_1621228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621228), tc_List_Olist(_1621228)), _1621230), _1621232)), c_List_Olistrel(_1621228, _1621234)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621228)), _1621230) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621228)), _1621232), 42497 ^ _776545 : [(42500 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1621228, _1621228, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1621228, tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_fun(_1621228, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1621228, tc_fun(tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_fun(_1621228, tc_HOL_Obool)), _1621228), c_COMBC(_1621228, tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1621228, tc_prod(_1621228, _1621228)), tc_fun(_1621228, tc_fun(tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_HOL_Obool)), _1621228), hAPP(c_COMBB(tc_prod(_1621228, _1621228), tc_fun(tc_fun(tc_prod(_1621228, _1621228), tc_HOL_Obool), tc_HOL_Obool), _1621228), c_member(tc_prod(_1621228, _1621228)))), c_Product__Type_OPair(_1621228, _1621228)))), _1621234)), 42496 ^ [_1621228, _1621230, _1621232, _1621234]))], (42498 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621228, _1621228)), 42496 ^ [_1621228, _1621230, _1621232, _1621234]), hAPP(c_List_Oset(tc_prod(_1621228, _1621228)), hAPP(hAPP(c_List_Ozip(_1621228, _1621228), _1621230), _1621232)))))]]], (22335 ^ _776545) ^ [_1181428, _1181430] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181428), _1181430)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181428)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181430)))], (40613 ^ _776545) ^ [_1569623, _1569625] : [-(hAPP(c_Relation_ODomain(_1569623, _1569623), c_Transitive__Closure_Otrancl(_1569623, _1569625)) = hAPP(c_Relation_ODomain(_1569623, _1569623), _1569625))], (5672 ^ _776545) ^ [_865954, _865956] : [hAPP(_865954, 5673 ^ [_865954, _865956]) = hAPP(_865956, 5673 ^ [_865954, _865956]), -(_865954 = _865956)], (29689 ^ _776545) ^ [_1308823, _1308825] : [class_Rings_Osemiring__1(_1308823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308825)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308823), 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)))), _1308825))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1308823), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308823), hAPP(c_Int_Onat, _1308825))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1308823), hAPP(c_Int_Onat, _1308825))))], (40839 ^ _776545) ^ [_1576025, _1576027] : [-(c_Relation_Orefl__on(_1576025, c_Orderings_Otop__class_Otop(tc_fun(_1576025, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1576025, _1576027)))], (52087 ^ _776545) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (244 ^ _776545) ^ [_780385, _780387] : [-(class_Fields_Ofield__inverse__zero(_780385)), _780387 = _780385, class_Fields_Ofield__inverse__zero(_780387)], (37628 ^ _776545) ^ [_1492983, _1492985, _1492987, _1492989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1492983), hAPP(c_Set_Oimage(_1492985, _1492983, _1492987), _1492989))), hAPP(c_Finite__Set_Ocard(_1492985), _1492989))), c_Fun_Oinj__on(_1492985, _1492983, _1492987, _1492989)], (29523 ^ _776545) ^ [_1305401, _1305403, _1305405] : [class_Rings_Olinordered__idom(_1305401), 29526 ^ _776545 : [(29535 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305401), hAPP(hAPP(c_Power_Opower__class_Opower(_1305401), _1305403), 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(_1305401), _1305405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1305401)))), _1305403 = c_Groups_Ozero__class_Ozero(_1305401), _1305405 = c_Groups_Ozero__class_Ozero(_1305401)], (29527 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305401), hAPP(hAPP(c_Power_Opower__class_Opower(_1305401), _1305403), 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(_1305401), _1305405), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1305401))), 29530 ^ _776545 : [(29533 ^ _776545) ^ [] : [-(_1305405 = c_Groups_Ozero__class_Ozero(_1305401))], (29531 ^ _776545) ^ [] : [-(_1305403 = c_Groups_Ozero__class_Ozero(_1305401))]]]]], (15718 ^ _776545) ^ [_1061555, _1061557] : [hAPP(c_Nat_OSuc, _1061555) = hAPP(c_Nat_OSuc, _1061557), -(_1061555 = _1061557)], (48550 ^ _776545) ^ [_1755095, _1755097, _1755099, _1755101, _1755103] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755097, _1755095)), hAPP(hAPP(c_Product__Type_OPair(_1755097, _1755095), _1755101), _1755103)), hAPP(c_Relation_Oconverse(_1755095, _1755097), _1755099))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1755095, _1755097, hAPP(hAPP(c_COMBC(_1755095, tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_fun(_1755097, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755097, tc_fun(tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_fun(_1755097, tc_HOL_Obool)), _1755095), c_COMBC(_1755097, tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755097, tc_prod(_1755095, _1755097)), tc_fun(_1755097, tc_fun(tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_HOL_Obool)), _1755095), hAPP(c_COMBB(tc_prod(_1755095, _1755097), tc_fun(tc_fun(tc_prod(_1755095, _1755097), tc_HOL_Obool), tc_HOL_Obool), _1755097), c_member(tc_prod(_1755095, _1755097)))), c_Product__Type_OPair(_1755095, _1755097)))), _1755099)), _1755101), _1755103)))], (40383 ^ _776545) ^ [_1563885, _1563887] : [40384 ^ _776545 : [(40385 ^ _776545) ^ [_1563931] : [hBOOL(hAPP(_1563885, _1563931))]], -(hBOOL(hAPP(_1563885, c_Hilbert__Choice_OEps(_1563887, _1563885))))], (24287 ^ _776545) ^ [_1215811, _1215813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215811)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1215813)))), 24290 ^ _776545 : [(24293 ^ _776545) ^ [] : [-(_1215813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24291 ^ _776545) ^ [] : [-(_1215811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34624 ^ _776545) ^ [_1421498, _1421500] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1421498), hAPP(c_Nat_OSuc, _1421500)) = 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)), _1421500)), _1421498))], (1664 ^ _776545) ^ [_800209, _800211] : [-(class_Rings_Ono__zero__divisors(_800209)), _800211 = _800209, class_Rings_Ono__zero__divisors(_800211)], (45325 ^ _776545) ^ [_1684860, _1684862, _1684864, _1684866] : [-(hBOOL(hAPP(c_List_Olistsp(_1684860, _1684862), hAPP(hAPP(c_List_Oappend(_1684860), _1684864), _1684866)))), hBOOL(hAPP(c_List_Olistsp(_1684860, _1684862), _1684864)), hBOOL(hAPP(c_List_Olistsp(_1684860, _1684862), _1684866))], (45473 ^ _776545) ^ [_1688448, _1688450, _1688452, _1688454] : [c_List_Olist__all2(_1688448, _1688450, _1688452, _1688454, c_List_Olist_ONil(_1688450)), -(_1688454 = c_List_Olist_ONil(_1688448))], (42709 ^ _776545) ^ [_1627035, _1627037, _1627039, _1627041] : [-(hAPP(hAPP(c_List_Olist__update(_1627035, hAPP(hAPP(c_List_Olist_OCons(_1627035), _1627037), _1627039)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1627041) = hAPP(hAPP(c_List_Olist_OCons(_1627035), _1627041), _1627039))], (1704 ^ _776545) ^ [_800709, _800711] : [-(class_Divides_Osemiring__div(_800709)), _800711 = _800709, class_Divides_Osemiring__div(_800711)], (9370 ^ _776545) ^ [_937756, _937758, _937760, _937762] : [-(c_Nitpick_Ofold__graph_H(_937756, _937758, _937760, _937762, c_Orderings_Obot__class_Obot(tc_fun(_937756, tc_HOL_Obool)), _937762))], (17477 ^ _776545) ^ [_1091294, _1091296, _1091298, _1091300] : [class_Rings_Olinordered__ring__strict(_1091294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091294), c_Groups_Ozero__class_Ozero(_1091294)), _1091296)), 17484 ^ _776545 : [(17491 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091294), _1091298), _1091300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091294), _1091296), _1091298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091294), _1091296), _1091300))))], (17485 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091294), _1091296), _1091298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091294), _1091296), _1091300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091294), _1091298), _1091300)))]]], (31925 ^ _776545) ^ [_1350110, _1350112] : [class_Orderings_Olinorder(_1350110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350110), _1350112)), -(_1350112 = c_Orderings_Obot__class_Obot(tc_fun(_1350110, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1350110), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350110), 31938 ^ [_1350110, _1350112]), 31939 ^ [_1350110, _1350112])), hAPP(hAPP(c_Set_Oinsert(_1350110), 31938 ^ [_1350110, _1350112]), hAPP(hAPP(c_Set_Oinsert(_1350110), 31939 ^ [_1350110, _1350112]), c_Orderings_Obot__class_Obot(tc_fun(_1350110, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1350110), c_Big__Operators_Olinorder__class_OMax(_1350110, _1350112)), _1350112)))], (36701 ^ _776545) ^ [_1472610, _1472612, _1472614, _1472616, _1472618, _1472620] : [c_Equiv__Relations_Oequiv(_1472610, _1472612, _1472614), hBOOL(hAPP(hAPP(c_member(_1472610), _1472616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472610, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472610, _1472610, _1472614), hAPP(hAPP(c_Set_Oinsert(_1472610), _1472618), c_Orderings_Obot__class_Obot(tc_fun(_1472610, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472610, _1472610, _1472614), hAPP(hAPP(c_Set_Oinsert(_1472610), _1472620), c_Orderings_Obot__class_Obot(tc_fun(_1472610, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472610, _1472610)), hAPP(hAPP(c_Product__Type_OPair(_1472610, _1472610), _1472618), _1472620)), _1472614)))], (49373 ^ _776545) ^ [_1773499, _1773501, _1773503, _1773505] : [class_Complete__Lattice_Ocomplete__lattice(_1773499), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773501, _1773499), _1773503), _1773505) = c_Complete__Lattice_OSup__class_OSup(_1773499, hAPP(c_Set_OCollect(_1773499), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool), tc_HOL_Obool, _1773499), c_HOL_OEx(tc_fun(_1773501, _1773499))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool), tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool), _1773499), hAPP(c_COMBS(tc_fun(_1773501, _1773499), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1773501, _1773499)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1773501, _1773499), tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1773501, _1773499))), _1773503)))), hAPP(hAPP(c_COMBC(_1773499, tc_fun(tc_fun(_1773501, _1773499), _1773499), tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773499, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1773501, _1773499), _1773499), tc_fun(tc_fun(_1773501, _1773499), tc_HOL_Obool)), _1773499), c_COMBB(_1773499, tc_HOL_Obool, tc_fun(_1773501, _1773499))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1773501, _1773499), _1773501, _1773499), c_COMBI(tc_fun(_1773501, _1773499))), _1773505)))))))], (32628 ^ _776545) ^ [_1368351, _1368353, _1368355, _1368357, _1368359] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368351, tc_fun(_1368353, tc_HOL_Obool)), _1368355), hAPP(hAPP(c_COMBC(_1368351, tc_fun(_1368353, tc_HOL_Obool), tc_fun(_1368353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368353, tc_HOL_Obool), tc_fun(tc_fun(_1368353, tc_HOL_Obool), tc_fun(_1368353, tc_HOL_Obool)), _1368351), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368353, tc_HOL_Obool))), _1368357)), _1368359)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1368353, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1368351, tc_fun(_1368353, tc_HOL_Obool)), _1368355), _1368357)), _1368359))], (34037 ^ _776545) ^ [_1408414, _1408416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408414), 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)), _1408416)), -(c_Divides_OnegDivAlg(_1408414, _1408416) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1408414), _1408416)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1408414, _1408416)))], (16777 ^ _776545) ^ [_1078393, _1078395] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078393)), _1078395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1078395), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078393), _1078395)))], (37937 ^ _776545) ^ [_1500710, _1500712, _1500714, _1500716, _1500718, _1500720, _1500722] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500710, _1500712, _1500714), _1500716), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500718, tc_fun(tc_prod(_1500712, _1500714), tc_HOL_Obool)), _1500720), _1500722)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500718, tc_fun(tc_prod(_1500710, _1500714), tc_HOL_Obool)), _1500720), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500712, _1500714), tc_HOL_Obool), tc_fun(tc_prod(_1500710, _1500714), tc_HOL_Obool), _1500718), hAPP(c_Relation_Orel__comp(_1500710, _1500712, _1500714), _1500716)), _1500722)))], (32175 ^ _776545) ^ [_1354766, _1354768, _1354770] : [class_Orderings_Olinorder(_1354766), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354766), _1354768)), -(hBOOL(hAPP(hAPP(c_member(_1354766), _1354770), _1354768))), -(c_Big__Operators_Olattice_OSup__fin(_1354766, c_Orderings_Oord__class_Omax(_1354766), hAPP(hAPP(c_Set_Oinsert(_1354766), _1354770), _1354768)) = hAPP(hAPP(c_Finite__Set_Ofold(_1354766, _1354766, c_Orderings_Oord__class_Omax(_1354766)), _1354770), _1354768))], (28425 ^ _776545) ^ [_1286764] : [-(c_Int_OBit1(_1286764) = 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)), _1286764)), _1286764))], (14500 ^ _776545) ^ [_1038280, _1038282] : [-(_1038280 = _1038282), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038280), _1038282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038282), _1038280)))], (23767 ^ _776545) ^ [_1206991, _1206993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206991), _1206993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206991)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206993))))], (10629 ^ _776545) ^ [_959341, _959343, _959345] : [class_Lattices_Oboolean__algebra(_959341), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959341), _959343), _959345) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959341), _959343), hAPP(c_Groups_Ouminus__class_Ouminus(_959341), _959345)))], (29287 ^ _776545) ^ [_1301371] : [-(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)))), _1301371) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1301371)))], (17435 ^ _776545) ^ [_1090529, _1090531, _1090533] : [class_Rings_Olinordered__semiring__strict(_1090529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090529), c_Groups_Ozero__class_Ozero(_1090529)), _1090531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090529), _1090533), c_Groups_Ozero__class_Ozero(_1090529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090529), _1090533), _1090531)), c_Groups_Ozero__class_Ozero(_1090529))))], (47402 ^ _776545) ^ [_1729681, _1729683] : [-(c_List_OdropWhile(_1729681, _1729683, c_List_Olist_ONil(_1729681)) = c_List_Olist_ONil(_1729681))], (27369 ^ _776545) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (44142 ^ _776545) ^ [_1659246, _1659248, _1659250] : [-(_1659246 = c_List_Olist_ONil(_1659248)), -(hAPP(c_List_Ohd(_1659248), hAPP(c_List_Orotate(_1659248, _1659250), _1659246)) = hAPP(hAPP(c_List_Onth(_1659248), _1659246), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1659250, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659248)), _1659246))))], (48536 ^ _776545) ^ [_1754561, _1754563, _1754565] : [-(_1754563 = _1754565), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754561, _1754561, hAPP(hAPP(c_COMBB(tc_fun(_1754561, tc_HOL_Obool), tc_fun(_1754561, tc_HOL_Obool), _1754561), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754561), c_fNot)), c_fequal)), _1754563), _1754565)))], (49602 ^ _776545) ^ [_1778841, _1778843] : [c_Relation_Oantisym(_1778841, _1778843), 49605 ^ _776545 : [(49606 ^ _776545) ^ [_1778953, _1778955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778841, _1778841)), hAPP(hAPP(c_Product__Type_OPair(_1778841, _1778841), _1778955), _1778953)), _1778843)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778841, _1778841)), hAPP(hAPP(c_Product__Type_OPair(_1778841, _1778841), _1778953), _1778955)), _1778843)), -(_1778955 = _1778953)]]], (40733 ^ _776545) ^ [_1573376, _1573378] : [-(c_Transitive__Closure_Otrancl(_1573376, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573376, _1573376), tc_HOL_Obool)), _1573378), c_Relation_OId(_1573376))) = c_Transitive__Closure_Ortrancl(_1573376, _1573378))], (22481 ^ _776545) ^ [_1183870, _1183872, _1183874] : [class_Rings_Oring__1__no__zero__divisors(_1183870), -(_1183872 = c_Groups_Ozero__class_Ozero(_1183870)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183870), _1183872), _1183874) = c_Groups_Ozero__class_Ozero(_1183870)], (45868 ^ _776545) ^ [_1696612, _1696614, _1696616, _1696618, _1696620] : [c_Fun_Oinj__on(_1696612, _1696614, _1696616, c_Orderings_Otop__class_Otop(tc_fun(_1696612, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1696612, _1696614), _1696616), hAPP(c_List_OremoveAll(_1696612, _1696618), _1696620)) = hAPP(c_List_OremoveAll(_1696614, hAPP(_1696616, _1696618)), hAPP(hAPP(c_List_Omap(_1696612, _1696614), _1696616), _1696620)))], (52303 ^ _776545) ^ [_1829257] : [class_Finite__Set_Ofinite(_1829257), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1829257)))], (29205 ^ _776545) ^ [_1299970] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1299970)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1299970)))], (19030 ^ _776545) ^ [_1119394, _1119396] : [19038 ^ _776545 : [(19041 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1119396, 19037 ^ [_1119394, _1119396])))], (19039 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19037 ^ [_1119394, _1119396]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119394))))]], 19031 ^ _776545 : [(19032 ^ _776545) ^ [_1119462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119462), _1119394)), hBOOL(hAPP(_1119396, _1119462))]]], (25297 ^ _776545) ^ [_1234379, _1234381] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234379, _1234381) = 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), _1234379), _1234381) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1234381), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234379, _1234381)))], (19056 ^ _776545) ^ [_1119874, _1119876] : [19058 ^ _776545 : [(19061 ^ _776545) ^ [] : [hBOOL(hAPP(_1119876, 19057 ^ [_1119874, _1119876]))], (19059 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19057 ^ [_1119874, _1119876]), _1119874)))]], 19062 ^ _776545 : [(19063 ^ _776545) ^ [_1120024] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1120024), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119874))), -(hBOOL(hAPP(_1119876, _1120024)))]]], (44777 ^ _776545) ^ [_1671777, _1671779, _1671781, _1671783, _1671785] : [class_Groups_Oab__group__add(_1671777), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671777), hAPP(hAPP(c_List_Omap(_1671779, _1671777), hAPP(hAPP(c_COMBS(_1671779, _1671777, _1671777), hAPP(hAPP(c_COMBB(_1671777, tc_fun(_1671777, _1671777), _1671779), c_Groups_Ominus__class_Ominus(_1671777)), _1671781)), _1671783)), _1671785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1671777), hAPP(c_List_Omonoid__add__class_Olistsum(_1671777), hAPP(hAPP(c_List_Omap(_1671779, _1671777), _1671781), _1671785))), hAPP(c_List_Omonoid__add__class_Olistsum(_1671777), hAPP(hAPP(c_List_Omap(_1671779, _1671777), _1671783), _1671785))))], (49060 ^ _776545) ^ [_1766158, _1766160, _1766162, _1766164] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1766158, _1766160, _1766162, _1766164, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766160)) = _1766162)], (32476 ^ _776545) ^ [_1361405, _1361407, _1361409] : [-(hAPP(c_Set_OCollect(_1361405), hAPP(hAPP(c_COMBS(_1361405, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361405), c_fimplies), _1361407)), _1361409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361405, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1361405, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1361405), _1361407))), hAPP(c_Set_OCollect(_1361405), _1361409)))], (36583 ^ _776545) ^ [_1469771, _1469773] : [c_Relation_Oirrefl(_1469771, _1469773), 36586 ^ _776545 : [(36587 ^ _776545) ^ [_1469853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469771, _1469771)), hAPP(hAPP(c_Product__Type_OPair(_1469771, _1469771), _1469853), _1469853)), _1469773))]]], (9130 ^ _776545) ^ [_934291, _934293, _934295, _934297] : [class_Orderings_Oord(_934291), _934293 = _934295, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934295), _934297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934293), _934297)))], (38414 ^ _776545) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (10647 ^ _776545) ^ [_959642, _959644, _959646] : [class_Lattices_Oboolean__algebra(_959642), -(hAPP(c_Groups_Ouminus__class_Ouminus(_959642), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959642), _959644), _959646)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959642), hAPP(c_Groups_Ouminus__class_Ouminus(_959642), _959644)), hAPP(c_Groups_Ouminus__class_Ouminus(_959642), _959646)))], (8151 ^ _776545) ^ [_915552, _915554, _915556] : [class_Complete__Lattice_Ocomplete__lattice(_915552), -(c_Complete__Lattice_OInf__class_OInf(_915552, hAPP(hAPP(c_Set_Oinsert(_915552), _915554), hAPP(hAPP(c_Set_Oinsert(_915552), _915556), c_Orderings_Obot__class_Obot(tc_fun(_915552, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_915552), _915554), _915556))], (31305 ^ _776545) ^ [_1338389, _1338391, _1338393, _1338395] : [class_Orderings_Olinorder(_1338389), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338389), _1338391), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338389), _1338393), _1338395)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1338389), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338389), _1338391), _1338393)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338389), _1338391), _1338395)))], (52033 ^ _776545) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (34061 ^ _776545) ^ [_1408839, _1408841] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408839)), -(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)), _1408839))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1408841))))) = 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)), _1408839))), 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, _1408841))))))], (51015 ^ _776545) ^ [_1809543, _1809545, _1809547, _1809549, _1809551] : [class_Groups_Ocomm__monoid__mult(_1809543), class_Rings_Odvd(_1809543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1809545), _1809547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809545, tc_HOL_Obool)), _1809549), _1809547)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809543), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1809545, _1809543), _1809551), _1809549)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1809545, _1809543), _1809551), _1809547))))], (11232 ^ _776545) ^ [_971588, _971590, _971592, _971594, _971596] : [c_Typedef_Otype__definition(_971588, _971590, _971592, _971594, _971596), -(hAPP(c_Set_Oimage(_971588, _971590, _971592), c_Orderings_Otop__class_Otop(tc_fun(_971588, tc_HOL_Obool))) = _971596)], (26909 ^ _776545) ^ [_1261280] : [class_Rings_Oring__1(_1261280), -(hAPP(c_Int_Oring__1__class_Oof__int(_1261280), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1261280))], (49125 ^ _776545) ^ [_1767634, _1767636, _1767638, _1767640] : [-(c_Random__Sequence_Omap(_1767634, _1767636, _1767638, _1767640) = c_Random__Sequence_Obind(_1767634, _1767636, _1767640, hAPP(c_Fun_Ocomp(_1767636, 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(_1767636)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1767634, c_Random__Sequence_Osingle(_1767636)), _1767638)))], (40741 ^ _776545) ^ [_1573552, _1573554, _1573556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573552, _1573552), tc_HOL_Obool)), c_Relation_OId(_1573552)), _1573554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573552, _1573552), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1573552, _1573552, _1573552), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1573552, _1573552), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573552, _1573556)), _1573554)), _1573556)), _1573554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573552, _1573552), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573552, _1573556)), _1573554)))], (14901 ^ _776545) ^ [_1045303, _1045305, _1045307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045303), _1045305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045303), _1045307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045305), _1045307))))], (40669 ^ _776545) ^ [_1571006, _1571008, _1571010, _1571012] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571006, _1571006)), _1571008), c_Transitive__Closure_Otrancl(_1571006, _1571010))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571006, _1571006), tc_HOL_Obool)), _1571010), _1571012)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571006, _1571006)), _1571008), c_Transitive__Closure_Otrancl(_1571006, _1571012))))], (4622 ^ _776545) ^ [_846779, _846781, _846783, _846785, _846787, _846789, _846791, _846793] : [-(c_Product__Type_Oscomp(_846793, _846789, _846785, _846781) = c_Product__Type_Oscomp(_846791, _846787, _846783, _846779)), _846793 = _846791, _846789 = _846787, _846785 = _846783, _846781 = _846779], (9394 ^ _776545) ^ [_938186, _938188, _938190] : [class_Orderings_Olinorder(_938186), 9397 ^ _776545 : [(9404 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938186), _938190), _938188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938186), _938188), _938190))], (9398 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938186), _938188), _938190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938186), _938190), _938188)))]]], (43208 ^ _776545) ^ [_1637303, _1637305, _1637307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637303), tc_List_Olist(_1637303))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637303), tc_List_Olist(_1637303)), _1637305), c_List_Olist_ONil(_1637303))), c_List_Olexord(_1637303, _1637307)))], (39779 ^ _776545) ^ [_1549850, _1549852, _1549854] : [c_Wellfounded_OwfP(_1549850, hAPP(_1549852, 39780 ^ [_1549850, _1549852, _1549854])), 39787 ^ _776545 : [(39790 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549850, tc_HOL_Obool)), c_Predicate_ODomainP(_1549850, _1549850, hAPP(_1549852, 39785 ^ [_1549850, _1549852, _1549854]))), c_Predicate_ORangeP(_1549850, _1549850, hAPP(_1549852, 39786 ^ [_1549850, _1549852, _1549854]))) = c_Orderings_Obot__class_Obot(tc_fun(_1549850, tc_HOL_Obool))], (39788 ^ _776545) ^ [] : [hAPP(_1549852, 39785 ^ [_1549850, _1549852, _1549854]) = hAPP(_1549852, 39786 ^ [_1549850, _1549852, _1549854])]], -(c_Wellfounded_OwfP(_1549850, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549854, tc_fun(_1549850, tc_fun(_1549850, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1549854, tc_HOL_Obool))), _1549852)))], (4926 ^ _776545) ^ [_851605, _851607, _851609, _851611] : [-(c_Relation_Oconverse(_851611, _851607) = c_Relation_Oconverse(_851609, _851605)), _851611 = _851609, _851607 = _851605], (31423 ^ _776545) ^ [_1340779, _1340781, _1340783, _1340785, _1340787] : [class_Orderings_Olinorder(_1340779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340779), _1340781), _1340783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340779), _1340785), _1340787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340779), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340779), _1340781), _1340785)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340779), _1340783), _1340787))))], (8799 ^ _776545) ^ [_927680, _927682, _927684, _927686] : [class_Lattices_Odistrib__lattice(_927680), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927680), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927680), _927682), _927684)), _927686) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927680), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927680), _927682), _927686)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927680), _927684), _927686)))], (32702 ^ _776545) ^ [_1370654] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1370654) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370654)))], (27757 ^ _776545) ^ [_1275782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275782), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1275782) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1275782))], (43132 ^ _776545) ^ [_1635868, _1635870] : [_1635870 = c_List_Olist_ONil(_1635868), -(hAPP(c_List_Oset(_1635868), _1635870) = c_Orderings_Obot__class_Obot(tc_fun(_1635868, tc_HOL_Obool)))], (27435 ^ _776545) ^ [_1269872, _1269874] : [class_Groups_Oordered__ab__group__add__abs(_1269872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269872), hAPP(c_Groups_Oabs__class_Oabs(_1269872), _1269874)), c_Groups_Ozero__class_Ozero(_1269872)))], (25385 ^ _776545) ^ [_1235719, _1235721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235719)), 25388 ^ _776545 : [(25395 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235721), _1235719))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235721), _1235719) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235721), _1235719)), _1235719)))], (25389 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235721), _1235719)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235721), _1235719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36559 ^ _776545) ^ [_1468951, _1468953, _1468955, _1468957] : [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), _1468951), _1468953)), 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), _1468955), _1468957)), 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), _1468951), _1468957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468955), _1468953))))], (23972 ^ _776545) ^ [_1210706, _1210708, _1210710] : [class_Divides_Osemiring__div(_1210706), -(_1210708 = c_Groups_Ozero__class_Ozero(_1210706)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210706), _1210708), _1210710)), _1210708) = _1210710)], (1724 ^ _776545) ^ [_800959, _800961] : [-(class_Nat_Osemiring__char__0(_800959)), _800961 = _800959, class_Nat_Osemiring__char__0(_800961)], (40717 ^ _776545) ^ [_1572997, _1572999, _1573001] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572997, _1572997)), hAPP(hAPP(c_Product__Type_OPair(_1572997, _1572997), _1572999), _1572999)), c_Transitive__Closure_Ortrancl(_1572997, _1573001))))], (47020 ^ _776545) ^ [_1721563, _1721565] : [-(hAPP(c_List_Orev(_1721563), c_List_Oconcat(_1721563, _1721565)) = c_List_Oconcat(_1721563, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1721563), tc_List_Olist(_1721563)), c_List_Orev(_1721563)), hAPP(c_List_Orev(tc_List_Olist(_1721563)), _1721565))))], (35678 ^ _776545) ^ [_1442549, _1442551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1442549), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442551), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442549), _1442551) = 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), _1442549), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1442551)))))], (41158 ^ _776545) ^ [_1583579, _1583581, _1583583] : [-(hAPP(c_Relation_ODomain(_1583579, _1583581), hAPP(c_Relation_Oconverse(_1583581, _1583579), _1583583)) = hAPP(c_Relation_ORange(_1583581, _1583579), _1583583))], (52345 ^ _776545) ^ [_1829794, _1829796] : [-(class_Enum_Oenum(tc_prod(_1829794, _1829796))), class_Enum_Oenum(_1829794), class_Enum_Oenum(_1829796)], (9164 ^ _776545) ^ [_934830, _934832, _934834] : [class_Orderings_Oorder(_934830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934830), _934832), _934834)), _934834 = _934832], (42990 ^ _776545) ^ [_1633414, _1633416, _1633418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633414), tc_List_Olist(_1633414))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633414), tc_List_Olist(_1633414)), _1633416), c_List_Olist_ONil(_1633414))), c_List_Olistrel(_1633414, _1633418))), -(_1633416 = c_List_Olist_ONil(_1633414))], (1934 ^ _776545) ^ [_803584, _803586, _803588, _803590] : [-(v_P(_803588, _803584)), v_P(_803590, _803586), _803590 = _803588, _803586 = _803584], (29705 ^ _776545) ^ [_1309151, _1309153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309151), 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)))), _1309153))), 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)))), _1309151)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309153), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1309151))], (43721 ^ _776545) ^ [_1648850, _1648852, _1648854, _1648856, _1648858] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648850), tc_List_Olist(_1648850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648850), tc_List_Olist(_1648850)), _1648852), _1648854)), c_List_Olexord(_1648850, _1648856))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648850), tc_List_Olist(_1648850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648850), tc_List_Olist(_1648850)), hAPP(hAPP(c_List_Oappend(_1648850), _1648858), _1648852)), hAPP(hAPP(c_List_Oappend(_1648850), _1648858), _1648854))), c_List_Olexord(_1648850, _1648856))))], (32266 ^ _776545) ^ [_1356618, _1356620, _1356622, _1356624, _1356626, _1356628] : [-(c_Nitpick_Opair__box_Opair__box__size(_1356618, _1356620, _1356622, _1356624, c_Nitpick_Opair__box_OPairBox(_1356618, _1356620, _1356626, _1356628)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1356622, _1356626)), hAPP(_1356624, _1356628))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44906 ^ _776545) ^ [_1675629, _1675631, _1675633, _1675635, _1675637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675629), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675631)), _1675633))), -(hAPP(hAPP(c_List_Onth(_1675635), hAPP(hAPP(c_List_Omap(_1675631, _1675635), _1675637), _1675633)), _1675629) = hAPP(_1675637, hAPP(hAPP(c_List_Onth(_1675631), _1675633), _1675629)))], (35640 ^ _776545) ^ [_1441862, _1441864, _1441866, _1441868, _1441870] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1441862, _1441864, _1441866), _1441868), _1441870) = hAPP(hAPP(_1441868, hAPP(c_Product__Type_Ofst(_1441862, _1441864), _1441870)), hAPP(c_Product__Type_Osnd(_1441862, _1441864), _1441870)))], (33042 ^ _776545) ^ [_1379933, _1379935, _1379937, _1379939] : [class_Groups_Oordered__ab__group__add__abs(_1379933), -(hAPP(c_Groups_Oabs__class_Oabs(_1379933), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379935, _1379933), hAPP(hAPP(c_COMBB(_1379933, _1379933, _1379935), c_Groups_Oabs__class_Oabs(_1379933)), _1379937)), _1379939)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1379935, _1379933), hAPP(hAPP(c_COMBB(_1379933, _1379933, _1379935), c_Groups_Oabs__class_Oabs(_1379933)), _1379937)), _1379939))], (7986 ^ _776545) ^ [_911747, _911749, _911751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911747, tc_HOL_Obool)), _911749), _911751)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911747, tc_HOL_Obool)), _911749), _911751) = _911749)], (33891 ^ _776545) ^ [_1404585, _1404587, _1404589] : [class_Groups_Ocomm__monoid__add(_1404585), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404585), _1404587), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404589))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404585), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1404585), _1404587), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1404589))), hAPP(_1404587, _1404589)))], (40727 ^ _776545) ^ [_1573261, _1573263] : [-(c_Transitive__Closure_Ortrancl(_1573261, c_Transitive__Closure_Otrancl(_1573261, _1573263)) = c_Transitive__Closure_Ortrancl(_1573261, _1573263))], (39916 ^ _776545) ^ [_1553407, _1553409, _1553411, _1553413, _1553415, _1553417, _1553419] : [-(hAPP(c_Fun_Ocomp(_1553407, _1553409, _1553411, _1553413), hAPP(c_Fun_Ocomp(_1553415, _1553407, _1553411, _1553417), _1553419)) = hAPP(c_Fun_Ocomp(_1553415, _1553409, _1553411, hAPP(c_Fun_Ocomp(_1553407, _1553409, _1553415, _1553413), _1553417)), _1553419))], (43078 ^ _776545) ^ [_1634921, _1634923] : [-(c_List_Osublist(_1634921, c_List_Olist_ONil(_1634921), _1634923) = c_List_Olist_ONil(_1634921))], (2554 ^ _776545) ^ [_814179, _814181] : [_814181 = _814179, -(c_Wellfounded_Omeasure(_814181) = c_Wellfounded_Omeasure(_814179))], (51939 ^ _776545) ^ [_1825699, _1825701] : [class_Orderings_Obot(_1825699), -(class_Orderings_Obot(tc_fun(_1825701, _1825699)))], (48104 ^ _776545) ^ [_1745386, _1745388, _1745390] : [-(c_List_Olist__ex(_1745386, _1745388, _1745390)), 48105 ^ _776545 : [(48106 ^ _776545) ^ [_1745443] : [hBOOL(hAPP(hAPP(c_member(_1745386), _1745443), hAPP(c_List_Oset(_1745386), _1745390))), hBOOL(hAPP(_1745388, _1745443))]]], (48782 ^ _776545) ^ [_1759820, _1759822, _1759824] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1759820)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1759820, _1759822, _1759824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1759820)), _1759824)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (52145 ^ _776545) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (21181 ^ _776545) ^ [_1159670, _1159672, _1159674] : [class_Int_Onumber(_1159670), 21184 ^ _776545 : [(21191 ^ _776545) ^ [] : [_1159674 = hAPP(c_Int_Onumber__class_Onumber__of(_1159670), _1159672), -(hAPP(c_Int_Onumber__class_Onumber__of(_1159670), _1159672) = _1159674)], (21185 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1159670), _1159672) = _1159674, -(_1159674 = hAPP(c_Int_Onumber__class_Onumber__of(_1159670), _1159672))]]], (44152 ^ _776545) ^ [_1659422, _1659424, _1659426] : [-(hAPP(c_List_Otl(_1659422), hAPP(hAPP(c_List_Olist_OCons(_1659422), _1659424), _1659426)) = _1659426)], (42557 ^ _776545) ^ [_1623683, _1623685, _1623687, _1623689] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623683, _1623683)), hAPP(hAPP(c_Product__Type_OPair(_1623683, _1623683), _1623685), _1623687)), hAPP(c_List_Oset(tc_prod(_1623683, _1623683)), hAPP(hAPP(c_List_Ozip(_1623683, _1623683), _1623689), _1623689)))), 42560 ^ _776545 : [(42563 ^ _776545) ^ [] : [-(_1623685 = _1623687)], (42561 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1623683), _1623685), hAPP(c_List_Oset(_1623683), _1623689))))]]], (48274 ^ _776545) ^ [_1748841, _1748843, _1748845] : [c_List_Olist__all(_1748841, _1748843, _1748845), -(c_List_Olist__all(_1748841, _1748843, hAPP(c_List_Orev(_1748841), _1748845)))], (39153 ^ _776545) ^ [_1531967, _1531969] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531967, _1531969), c_Orderings_Otop__class_Otop(tc_fun(_1531967, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1531969, tc_HOL_Obool), _1531967), c_Orderings_Otop__class_Otop(tc_fun(_1531969, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1531967, _1531969), tc_HOL_Obool)))], (3724 ^ _776545) ^ [_832378, _832380, _832382, _832384] : [-(c_List_Oremdups(_832384, _832380) = c_List_Oremdups(_832382, _832378)), _832384 = _832382, _832380 = _832378], (14236 ^ _776545) ^ [_1032637, _1032639, _1032641, _1032643] : [class_Rings_Ocomm__semiring__1(_1032637), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032637), _1032639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032637), _1032641), _1032643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032637), _1032641), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1032637), _1032639), _1032643)))], (41973 ^ _776545) ^ [_1606527, _1606529, _1606531, _1606533] : [41976 ^ _776545 : [(41981 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606527, _1606527)), hAPP(hAPP(c_Product__Type_OPair(_1606527, _1606527), 41975 ^ [_1606527, _1606529, _1606531, _1606533]), 41974 ^ [_1606527, _1606529, _1606531, _1606533])), _1606529))], (41979 ^ _776545) ^ [] : [41974 ^ [_1606527, _1606529, _1606531, _1606533] = 41975 ^ [_1606527, _1606529, _1606531, _1606533]], (41977 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606527, _1606527)), hAPP(hAPP(c_Product__Type_OPair(_1606527, _1606527), 41974 ^ [_1606527, _1606529, _1606531, _1606533]), 41975 ^ [_1606527, _1606529, _1606531, _1606533])), _1606529))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606527), tc_List_Olist(_1606527))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606527), tc_List_Olist(_1606527)), _1606531), _1606533)), c_List_Olexord(_1606527, _1606529)))), -(_1606531 = _1606533), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606527), tc_List_Olist(_1606527))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606527), tc_List_Olist(_1606527)), _1606533), _1606531)), c_List_Olexord(_1606527, _1606529))))], (6869 ^ _776545) ^ [_887944] : [-(hAPP(c_Set_OPow(_887944), c_Orderings_Otop__class_Otop(tc_fun(_887944, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_887944, tc_HOL_Obool), tc_HOL_Obool)))], (33568 ^ _776545) ^ [_1394395, _1394397, _1394399, _1394401] : [33570 ^ _776545 : [(33573 ^ _776545) ^ [] : [hAPP(_1394401, 33569 ^ [_1394395, _1394397, _1394399, _1394401]) = c_Orderings_Otop__class_Otop(tc_fun(_1394397, tc_HOL_Obool))], (33571 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394395), 33569 ^ [_1394395, _1394397, _1394399, _1394401]), _1394399)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394395, tc_fun(_1394397, tc_HOL_Obool)), _1394399), _1394401) = c_Orderings_Otop__class_Otop(tc_fun(_1394397, tc_HOL_Obool)))], (27375 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (49119 ^ _776545) ^ [_1767492, _1767494, _1767496] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1767492, _1767494, _1767496, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1767494)], (41809 ^ _776545) ^ [_1601007, _1601009, _1601011] : [-(c_List_Oset__Cons(_1601007, _1601009, _1601011) = hAPP(c_Set_OCollect(tc_List_Olist(_1601007)), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1601007)), c_HOL_OEx(_1601007)), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_fun(_1601007, tc_HOL_Obool), tc_List_Olist(_1601007)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_HOL_Obool, _1601007), c_HOL_OEx(tc_List_Olist(_1601007)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601007), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_fun(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), tc_fun(tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), tc_List_Olist(_1601007)), c_COMBS(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1601007, tc_fun(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), tc_List_Olist(_1601007)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601007), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), _1601007), c_COMBS(tc_List_Olist(_1601007), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1601007)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1601007), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1601007)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601007), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_List_Olist(_1601007))), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1601007), tc_List_Olist(_1601007)), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_fun(tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_List_Olist(_1601007))), tc_fun(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool))), tc_List_Olist(_1601007)), c_COMBB(tc_fun(tc_List_Olist(_1601007), tc_List_Olist(_1601007)), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), _1601007)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1601007), tc_List_Olist(_1601007)), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), tc_List_Olist(_1601007)), c_COMBB(tc_List_Olist(_1601007), tc_HOL_Obool, tc_List_Olist(_1601007))), c_fequal))), c_List_Olist_OCons(_1601007)))))), hAPP(hAPP(c_COMBC(_1601007, tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool)), _1601007), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1601007))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1601007), c_fconj), hAPP(hAPP(c_COMBC(_1601007, tc_fun(_1601007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601007)), _1601009)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601007), tc_fun(tc_List_Olist(_1601007), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1601007))), _1601011)))))))], (52415 ^ _776545) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (47126 ^ _776545) ^ [_1723761, _1723763, _1723765] : [-(hAPP(c_List_Orev(_1723761), hAPP(hAPP(c_List_Otake(_1723761), _1723763), _1723765)) = hAPP(hAPP(c_List_Odrop(_1723761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723761)), _1723765)), _1723763)), hAPP(c_List_Orev(_1723761), _1723765)))], (34767 ^ _776545) ^ [_1425107, _1425109, _1425111, _1425113, _1425115] : [hBOOL(hAPP(hAPP(_1425107, _1425109), _1425111)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1425113, _1425115, tc_HOL_Obool), _1425107), hAPP(hAPP(c_Product__Type_OPair(_1425113, _1425115), _1425109), _1425111))))], (8315 ^ _776545) ^ [_918992, _918994, _918996] : [class_Lattices_Olattice(_918992), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918992), _918994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918992), _918994), _918996)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918992), _918994), _918996))], (28847 ^ _776545) ^ [_1293716, _1293718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293716), _1293718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293716)), c_Int_OBit0(_1293718))))], (16080 ^ _776545) ^ [_1067330, _1067332] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067330), _1067332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067332)), _1067330)))], (41653 ^ _776545) ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596464, _1596466)), _1596468), hAPP(hAPP(c_Relation_Orel__comp(_1596464, _1596470, _1596466), _1596472), _1596474))), 41659 ^ _776545 : [(41664 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596470, _1596466)), hAPP(hAPP(c_Product__Type_OPair(_1596470, _1596466), 41657 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474]), 41658 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474])), _1596474)))], (41662 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596464, _1596470)), hAPP(hAPP(c_Product__Type_OPair(_1596464, _1596470), 41656 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474]), 41657 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474])), _1596472)))], (41660 ^ _776545) ^ [] : [-(_1596468 = hAPP(hAPP(c_Product__Type_OPair(_1596464, _1596466), 41656 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474]), 41658 ^ [_1596464, _1596466, _1596468, _1596470, _1596472, _1596474]))]]], (13260 ^ _776545) ^ [_1011269, _1011271, _1011273, _1011275, _1011277] : [class_Groups_Ocomm__monoid__mult(_1011269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011271), _1011273)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011271), _1011275)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011269), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011271, _1011269), _1011277), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011271, tc_HOL_Obool)), _1011273), _1011275))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011271, _1011269), _1011277), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011271, tc_HOL_Obool)), _1011273), _1011275))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1011269), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011271, _1011269), _1011277), _1011273)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1011271, _1011269), _1011277), _1011275)))], (39555 ^ _776545) ^ [_1543699, _1543701, _1543703, _1543705, _1543707] : [c_Relation_Orefl__on(_1543699, _1543701, _1543703), c_Relation_Orefl__on(_1543699, _1543705, _1543707), -(c_Relation_Orefl__on(_1543699, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543699, tc_HOL_Obool)), _1543701), _1543705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543699, _1543699), tc_HOL_Obool)), _1543703), _1543707)))], (34628 ^ _776545) ^ [_1421588, _1421590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1421590)), -(c_Divides_OposDivAlg(_1421588, _1421590) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1421588), _1421590)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1421588, _1421590)))], (30600 ^ _776545) ^ [_1325647, _1325649] : [class_Orderings_Olinorder(_1325647), -(c_Big__Operators_Olinorder__class_OMin(_1325647, hAPP(hAPP(c_Set_Oinsert(_1325647), _1325649), c_Orderings_Obot__class_Obot(tc_fun(_1325647, tc_HOL_Obool)))) = _1325649)], (44210 ^ _776545) ^ [_1660530, _1660532, _1660534] : [-(hAPP(hAPP(c_List_Odrop(_1660530), hAPP(c_Nat_OSuc, _1660532)), _1660534) = hAPP(hAPP(c_List_Odrop(_1660530), _1660532), hAPP(c_List_Otl(_1660530), _1660534)))], (6490 ^ _776545) ^ [_881430, _881432] : [-(hBOOL(hAPP(_881432, 6491 ^ [_881430, _881432]))), -(c_Orderings_Obot__class_Obot(tc_fun(_881430, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_881430), _881432))], (5370 ^ _776545) ^ [_858595, _858597] : [_858597 = _858595, -(c_Finite__Set_Ofinite(_858597) = c_Finite__Set_Ofinite(_858595))], (45764 ^ _776545) ^ [_1694791, _1694793, _1694795] : [hBOOL(hAPP(c_List_Odistinct(_1694791), _1694793)), -(hBOOL(hAPP(c_List_Odistinct(_1694791), hAPP(c_List_OremoveAll(_1694791, _1694795), _1694793))))], (50463 ^ _776545) ^ [_1796772, _1796774, _1796776, _1796778, _1796780, _1796782, _1796784] : [c_Fun_Obij__betw(_1796772, _1796774, _1796776, _1796778, _1796780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1796772, tc_HOL_Obool)), _1796782), _1796778)), hAPP(c_Set_Oimage(_1796772, _1796774, _1796776), _1796782) = _1796784, -(c_Fun_Obij__betw(_1796772, _1796774, _1796776, _1796782, _1796784))], (26561 ^ _776545) ^ [_1255972, _1255974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255972)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1255972)), _1255974) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1255972), _1255974)))], (35525 ^ _776545) ^ [_1439356] : [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), _1439356))), -(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), _1439356)) = 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), _1439356))))], (3096 ^ _776545) ^ [_822594, _822596, _822598, _822600, _822602, _822604] : [-(c_List_Oset__Cons(_822604, _822600, _822596) = c_List_Oset__Cons(_822602, _822598, _822594)), _822604 = _822602, _822600 = _822598, _822596 = _822594], (33943 ^ _776545) ^ [_1405826, _1405828, _1405830, _1405832, _1405834] : [class_Groups_Ocomm__monoid__add(_1405826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405828), _1405830)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405828, _1405826), _1405832), hAPP(c_Set_OCollect(_1405828), hAPP(hAPP(c_COMBS(_1405828, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1405828), c_fconj), hAPP(hAPP(c_COMBC(_1405828, tc_fun(_1405828, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405828)), _1405830))), hAPP(hAPP(c_COMBC(_1405828, tc_fun(_1405828, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405828)), _1405834)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405828, _1405826), hAPP(hAPP(c_COMBC(_1405828, _1405826, _1405826), hAPP(hAPP(c_COMBS(_1405828, _1405826, tc_fun(_1405826, _1405826)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1405826, tc_fun(_1405826, _1405826)), _1405828), c_If(_1405826)), hAPP(hAPP(c_COMBC(_1405828, tc_fun(_1405828, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405828)), _1405834))), _1405832)), c_Groups_Ozero__class_Ozero(_1405826))), _1405830))], (45638 ^ _776545) ^ [_1691897, _1691899, _1691901, _1691903, _1691905, _1691907, _1691909, _1691911] : [c_List_Olist__all2(_1691897, _1691899, _1691901, _1691903, _1691905), hBOOL(hAPP(hAPP(_1691901, _1691907), _1691909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691911), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691899)), _1691905))), -(c_List_Olist__all2(_1691897, _1691899, _1691901, hAPP(hAPP(c_List_Olist__update(_1691897, _1691903), _1691911), _1691907), hAPP(hAPP(c_List_Olist__update(_1691899, _1691905), _1691911), _1691909)))], (36094 ^ _776545) ^ [_1456272, _1456274, _1456276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456272, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1456272, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36095 ^ [_1456272, _1456274, _1456276])), _1456274)), _1456276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1456272, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1456272, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1456274)), _1456276)))], (47090 ^ _776545) ^ [_1723020, _1723022] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723020)), hAPP(c_List_Orev(_1723020), _1723022)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723020)), _1723022))], (52153 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11272 ^ _776545) ^ [_972369, _972371, _972373] : [class_Groups_Oordered__ab__group__add(_972369), -(hAPP(c_Set_Oimage(_972369, _972369, c_Groups_Ouminus__class_Ouminus(_972369)), c_SetInterval_Oord__class_OgreaterThanAtMost(_972369, _972371, _972373)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_972369, hAPP(c_Groups_Ouminus__class_Ouminus(_972369), _972373)), hAPP(c_Groups_Ouminus__class_Ouminus(_972369), _972371)))], (51357 ^ _776545) ^ [_1816091, _1816093, _1816095, _1816097] : [class_Rings_Ocomm__semiring__1(_1816091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816093), _1816095)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816091), hAPP(hAPP(c_Power_Opower__class_Opower(_1816091), _1816097), _1816093)), hAPP(hAPP(c_Power_Opower__class_Opower(_1816091), _1816097), _1816095))))], (44842 ^ _776545) ^ [_1673674, _1673676, _1673678, _1673680] : [_1673680 = c_List_Olist_ONil(_1673676), -(c_List_Olist_ONil(_1673674) = hAPP(hAPP(c_List_Omap(_1673676, _1673674), _1673678), _1673680))], (1474 ^ _776545) ^ [_797834, _797836] : [-(class_Finite__Set_Ofinite(_797834)), _797836 = _797834, class_Finite__Set_Ofinite(_797836)], (25967 ^ _776545) ^ [_1246062] : [hBOOL(hAPP(_1246062, 25968 ^ [_1246062])), 25971 ^ _776545 : [(25972 ^ _776545) ^ [_1246156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246156)), -(hBOOL(hAPP(_1246062, hAPP(c_Int_Onat, _1246156))))]]], (48474 ^ _776545) ^ [_1753207, _1753209] : [c_Wellfounded_Oacyclic(_1753207, hAPP(c_Set_OCollect(tc_prod(_1753207, _1753207)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753207, _1753207, tc_HOL_Obool), c_Predicate_Oconversep(_1753207, _1753207, _1753209)))), -(c_Wellfounded_Oacyclic(_1753207, hAPP(c_Set_OCollect(tc_prod(_1753207, _1753207)), hAPP(c_Product__Type_Oprod_Oprod__case(_1753207, _1753207, tc_HOL_Obool), _1753209))))], (16148 ^ _776545) ^ [_1068442, _1068444, _1068446] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068442)), _1068444) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068442)), _1068446), -(_1068444 = _1068446)], (36734 ^ _776545) ^ [] : [-(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))], (2398 ^ _776545) ^ [_811647, _811649, _811651, _811653, _811655, _811657, _811659, _811661, _811663, _811665] : [-(c_Nitpick_Opair__box_Opair__box__case(_811665, _811661, _811657, _811653, _811649) = c_Nitpick_Opair__box_Opair__box__case(_811663, _811659, _811655, _811651, _811647)), _811665 = _811663, _811661 = _811659, _811657 = _811655, _811653 = _811651, _811649 = _811647], (23946 ^ _776545) ^ [_1210272, _1210274, _1210276, _1210278] : [class_Divides_Osemiring__div(_1210272), 23949 ^ _776545 : [(23956 ^ _776545) ^ [] : [-(_1210274 = c_Groups_Ozero__class_Ozero(_1210272)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210272), _1210274), _1210276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210272), _1210274), _1210278)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210272), _1210276), _1210278))], (23950 ^ _776545) ^ [] : [_1210274 = c_Groups_Ozero__class_Ozero(_1210272), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210272), _1210274), _1210276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210272), _1210274), _1210278)) = c_Groups_Ozero__class_Ozero(_1210272))]]], (7542 ^ _776545) ^ [_900925, _900927, _900929, _900931] : [hBOOL(hAPP(_900925, _900927)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900929, tc_HOL_Obool)), _900931), _900925), _900927)))], (8303 ^ _776545) ^ [_918724, _918726, _918728, _918730] : [class_Lattices_Osemilattice__sup(_918724), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918724), _918726), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918724), _918728), _918730)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918724), _918728), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918724), _918726), _918730)))], (40368 ^ _776545) ^ [_1563627, _1563629] : [-(c_Hilbert__Choice_OEps(_1563627, hAPP(hAPP(c_COMBC(_1563627, _1563627, tc_HOL_Obool), c_fequal), _1563629)) = _1563629)], (28699 ^ _776545) ^ [_1291044, _1291046] : [class_Int_Onumber__ring(_1291044), class_Rings_Olinordered__idom(_1291044), 28706 ^ _776545 : [(28713 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291046), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291044), hAPP(c_Int_Onumber__class_Onumber__of(_1291044), _1291046)), c_Groups_Oone__class_Oone(_1291044))))], (28707 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291044), hAPP(c_Int_Onumber__class_Onumber__of(_1291044), _1291046)), c_Groups_Oone__class_Oone(_1291044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291046), c_Int_OBit1(c_Int_OPls))))]]], (23822 ^ _776545) ^ [_1208075, _1208077] : [23823 ^ _776545 : [(23824 ^ _776545) ^ [_1208128] : [_1208077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1208075), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1208128))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1208075), _1208077)))], (24577 ^ _776545) ^ [_1221110, _1221112] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221110))), -(c_SMT_Oz3div(_1221112, _1221110) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221112), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1221110))))], (10285 ^ _776545) ^ [_953294, _953296, _953298] : [class_Groups_Ogroup__add(_953294), 10288 ^ _776545 : [(10295 ^ _776545) ^ [] : [_953298 = hAPP(c_Groups_Ouminus__class_Ouminus(_953294), _953296), -(_953296 = hAPP(c_Groups_Ouminus__class_Ouminus(_953294), _953298))], (10289 ^ _776545) ^ [] : [_953296 = hAPP(c_Groups_Ouminus__class_Ouminus(_953294), _953298), -(_953298 = hAPP(c_Groups_Ouminus__class_Ouminus(_953294), _953296))]]], (25778 ^ _776545) ^ [_1242970, _1242972, _1242974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242970)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242972, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242974), _1242970)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242974), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1242972), _1242974), _1242970))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242972, _1242974)))], (41793 ^ _776545) ^ [_1600551, _1600553, _1600555, _1600557, _1600559, _1600561] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600551), tc_List_Olist(_1600551))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600551), tc_List_Olist(_1600551)), hAPP(hAPP(c_List_Olist_OCons(_1600551), _1600553), _1600555)), hAPP(hAPP(c_List_Olist_OCons(_1600551), _1600557), _1600559))), c_List_Olex(_1600551, _1600561)))), 41794 ^ _776545 : [(41801 ^ _776545) ^ [] : [_1600553 = _1600557, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600551), tc_List_Olist(_1600551))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600551), tc_List_Olist(_1600551)), _1600555), _1600559)), c_List_Olex(_1600551, _1600561)))], (41795 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600551, _1600551)), hAPP(hAPP(c_Product__Type_OPair(_1600551, _1600551), _1600553), _1600557)), _1600561)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600551)), _1600555) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600551)), _1600559)]]], (6871 ^ _776545) ^ [_887985, _887987, _887989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887985, tc_HOL_Obool)), _887987), _887989)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_887985, tc_HOL_Obool)), _887987), hAPP(c_Set_OPow(_887985), _887989))))], (36092 ^ _776545) ^ [] : [-(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))], (31389 ^ _776545) ^ [_1340125, _1340127, _1340129, _1340131] : [class_Orderings_Olinorder(_1340125), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340125), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340125), _1340127), _1340129)), _1340131) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340125), _1340127), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340125), _1340129), _1340131)))], (21939 ^ _776545) ^ [_1174168, _1174170, _1174172, _1174174] : [class_Fields_Olinordered__field__inverse__zero(_1174168), class_Int_Onumber(_1174168), 21946 ^ _776545 : [(21947 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174168), _1174172), _1174174))), 21950 ^ _776545 : [(21957 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), c_Groups_Ozero__class_Ozero(_1174168)), _1174174))), 21960 ^ _776545 : [(21967 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), _1174174), c_Groups_Ozero__class_Ozero(_1174168)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), c_Groups_Ozero__class_Ozero(_1174168))))], (21961 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), _1174174), c_Groups_Ozero__class_Ozero(_1174168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), _1174172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), _1174174))))]]], (21951 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), c_Groups_Ozero__class_Ozero(_1174168)), _1174174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), _1174174)), _1174172)))]]], (21973 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174168), _1174172), _1174174)))), 21976 ^ _776545 : [(21979 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), _1174174)), _1174172))], (21977 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), c_Groups_Ozero__class_Ozero(_1174168)), _1174174)))]], 21980 ^ _776545 : [(21983 ^ _776545) ^ [] : [21984 ^ _776545 : [(21987 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), _1174172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), _1174174)))], (21985 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), _1174174), c_Groups_Ozero__class_Ozero(_1174168))))]], 21988 ^ _776545 : [(21991 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174168), hAPP(c_Int_Onumber__class_Onumber__of(_1174168), _1174170)), c_Groups_Ozero__class_Ozero(_1174168)))], (21989 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), _1174174), c_Groups_Ozero__class_Ozero(_1174168)))]]], (21981 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174168), c_Groups_Ozero__class_Ozero(_1174168)), _1174174))]]]]], (32444 ^ _776545) ^ [_1360573, _1360575, _1360577, _1360579, _1360581] : [-(_1360573 = c_Orderings_Obot__class_Obot(tc_fun(_1360575, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360577, tc_HOL_Obool)), _1360579), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360575, tc_fun(_1360577, tc_HOL_Obool)), _1360573), _1360581)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360575, tc_fun(_1360577, tc_HOL_Obool)), _1360573), hAPP(hAPP(c_COMBB(tc_fun(_1360577, tc_HOL_Obool), tc_fun(_1360577, tc_HOL_Obool), _1360575), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360577, tc_HOL_Obool)), _1360579)), _1360581)))], (33455 ^ _776545) ^ [_1391665, _1391667, _1391669, _1391671] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391665, tc_fun(_1391667, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1391665, tc_HOL_Obool), _1391669)), _1391671) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1391665, tc_HOL_Obool), tc_fun(_1391667, tc_HOL_Obool)), _1391669), hAPP(hAPP(c_COMBC(tc_fun(_1391665, tc_HOL_Obool), tc_fun(_1391665, tc_fun(_1391667, tc_HOL_Obool)), tc_fun(_1391667, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391665, tc_fun(_1391667, tc_HOL_Obool))), _1391671)))], (13342 ^ _776545) ^ [_1013269, _1013271, _1013273, _1013275, _1013277] : [class_Groups_Ocomm__monoid__mult(_1013269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013271), _1013273)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013271), _1013275)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013271, tc_HOL_Obool)), _1013273), _1013275) = c_Orderings_Obot__class_Obot(tc_fun(_1013271, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013271, _1013269), _1013277), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013271, tc_HOL_Obool)), _1013273), _1013275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013269), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013271, _1013269), _1013277), _1013273)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1013271, _1013269), _1013277), _1013275)))], (19567 ^ _776545) ^ [_1130079, _1130081, _1130083, _1130085] : [class_Rings_Odivision__ring(_1130079), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130079), _1130081), _1130083)), _1130085) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130079), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130079), _1130081), _1130085)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130079), _1130083), _1130085)))], (20227 ^ _776545) ^ [_1141728, _1141730, _1141732] : [class_Fields_Olinordered__field__inverse__zero(_1141728), 20230 ^ _776545 : [(20245 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141728), _1141730), _1141732)))), 20246 ^ _776545 : [(20253 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), _1141730), c_Groups_Ozero__class_Ozero(_1141728))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), _1141732), c_Groups_Ozero__class_Ozero(_1141728)))], (20247 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), _1141730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), _1141732))]]], (20231 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141728), _1141730), _1141732))), 20236 ^ _776545 : [(20239 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), _1141732)))], (20237 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), c_Groups_Ozero__class_Ozero(_1141728)), _1141730)))]], 20240 ^ _776545 : [(20243 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), _1141732), c_Groups_Ozero__class_Ozero(_1141728))))], (20241 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141728), _1141730), c_Groups_Ozero__class_Ozero(_1141728))))]]]]], (17565 ^ _776545) ^ [_1092887, _1092889] : [class_Rings_Olinordered__ring(_1092887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092887), _1092889), _1092889)), c_Groups_Ozero__class_Ozero(_1092887)))], (11598 ^ _776545) ^ [_979390] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_979390), c_Orderings_Obot__class_Obot(tc_fun(_979390, tc_HOL_Obool)))))], (22455 ^ _776545) ^ [_1183494] : [_1183494 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1183494) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11716 ^ _776545) ^ [_981650, _981652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), _981652)), 11719 ^ _776545 : [(11726 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), c_Orderings_Otop__class_Otop(tc_fun(_981650, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_981650, tc_HOL_Obool)), _981652))))], (11720 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_981650, tc_HOL_Obool)), _981652))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981650), c_Orderings_Otop__class_Otop(tc_fun(_981650, tc_HOL_Obool)))))]]], (23748 ^ _776545) ^ [_1206640] : [hBOOL(hAPP(_1206640, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23749 ^ [_1206640]))), 23752 ^ _776545 : [(23753 ^ _776545) ^ [_1206740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206740)), -(hBOOL(hAPP(_1206640, _1206740)))]]], (52061 ^ _776545) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (8735 ^ _776545) ^ [_926644, _926646, _926648] : [class_Lattices_Olattice(_926644), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926644), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926644), _926646), _926648)), _926648)))], (16154 ^ _776545) ^ [_1068553, _1068555, _1068557] : [_1068555 = _1068557, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068553)), _1068555) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068553)), _1068557))], (34606 ^ _776545) ^ [_1421130, _1421132] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421130)), _1421132) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1421130), 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), _1421130)), _1421132))], (32952 ^ _776545) ^ [_1377508, _1377510, _1377512, _1377514, _1377516] : [_1377508 = c_Orderings_Obot__class_Obot(tc_fun(_1377510, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377512, tc_HOL_Obool)), _1377514), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377510, tc_fun(_1377512, tc_HOL_Obool)), _1377508), _1377516)) = _1377514)], (16452 ^ _776545) ^ [_1072978] : [-(_1072978 = 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)), _1072978)))], (29091 ^ _776545) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (35481 ^ _776545) ^ [_1438486, _1438488, _1438490, _1438492, _1438494, _1438496] : [hAPP(c_Product__Type_Oapsnd(_1438486, _1438488, _1438490, _1438492), _1438494) = hAPP(c_Product__Type_Oapsnd(_1438486, _1438488, _1438490, _1438496), _1438494), -(hAPP(_1438492, hAPP(c_Product__Type_Osnd(_1438490, _1438486), _1438494)) = hAPP(_1438496, hAPP(c_Product__Type_Osnd(_1438490, _1438486), _1438494)))], (51419 ^ _776545) ^ [_1817290, _1817292, _1817294] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817292), _1817294))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817290), _1817292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1817294), _1817292)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817290), _1817294)))], (8157 ^ _776545) ^ [_915693, _915695] : [class_Orderings_Oorder(_915693), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915693, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915693), _915695), c_Orderings_Obot__class_Obot(tc_fun(_915693, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_915693), _915695)) = hAPP(hAPP(c_Set_Oinsert(_915693), _915695), c_Orderings_Obot__class_Obot(tc_fun(_915693, tc_HOL_Obool))))], (32542 ^ _776545) ^ [_1364923, _1364925, _1364927, _1364929, _1364931] : [_1364923 = c_Orderings_Obot__class_Obot(tc_fun(_1364925, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1364925, tc_fun(_1364927, tc_HOL_Obool)), _1364923), hAPP(hAPP(c_COMBC(_1364925, tc_fun(_1364927, tc_HOL_Obool), tc_fun(_1364927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1364927, tc_HOL_Obool), tc_fun(tc_fun(_1364927, tc_HOL_Obool), tc_fun(_1364927, tc_HOL_Obool)), _1364925), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364927, tc_HOL_Obool))), _1364929)), _1364931)) = c_Orderings_Otop__class_Otop(tc_fun(_1364927, tc_HOL_Obool)))], (52085 ^ _776545) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (38739 ^ _776545) ^ [_1521315, _1521317, _1521319, _1521321, _1521323] : [hAPP(c_Set_Oimage(_1521315, _1521317, _1521319), c_Orderings_Otop__class_Otop(tc_fun(_1521315, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1521317, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521315, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521315, _1521317, _1521319), _1521321)), _1521323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521317, tc_HOL_Obool)), _1521321), hAPP(c_Set_Oimage(_1521315, _1521317, _1521319), _1521323))))], (26044 ^ _776545) ^ [_1247319, _1247321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247319), _1247321)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247321, _1247319) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247321), _1247319), _1247319))], (5933 ^ _776545) ^ [_870925, _870927, _870929] : [hBOOL(hAPP(hAPP(c_member(_870925), _870927), hAPP(c_fequal, _870929))), -(_870927 = _870929)], (43908 ^ _776545) ^ [_1653895, _1653897, _1653899, _1653901, _1653903] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1653895, _1653897)), _1653899), hAPP(hAPP(c_List_Ozip(_1653895, _1653897), _1653901), _1653903)) = hAPP(hAPP(c_List_Ozip(_1653895, _1653897), hAPP(hAPP(c_List_Odrop(_1653895), _1653899), _1653901)), hAPP(hAPP(c_List_Odrop(_1653897), _1653899), _1653903)))], (33683 ^ _776545) ^ [_1398913, _1398915, _1398917, _1398919] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1398913, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1398915)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1398913, tc_HOL_Obool), tc_Nat_Onat), _1398917), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1398919))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1398913, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1398919, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398915), _1398919))), _1398917))], (42508 ^ _776545) ^ [_1622267, _1622269, _1622271, _1622273] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1622267, _1622269))), hAPP(hAPP(c_List_Ozip(_1622267, _1622269), _1622271), _1622273)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622267)), _1622271)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622269)), _1622273)))], (7740 ^ _776545) ^ [_906390, _906392, _906394, _906396] : [-(hBOOL(hAPP(hAPP(c_member(_906390), _906392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906390, tc_HOL_Obool)), _906394), _906396)))), hBOOL(hAPP(hAPP(c_member(_906390), _906392), _906394)), -(hBOOL(hAPP(hAPP(c_member(_906390), _906392), _906396)))], (362 ^ _776545) ^ [_782010, _782012, _782014, _782016, _782018, _782020, _782022, _782024] : [-(c_Finite__Set_Ofolding__idem(_782022, _782018, _782014, _782010)), c_Finite__Set_Ofolding__idem(_782024, _782020, _782016, _782012), _782024 = _782022, _782020 = _782018, _782016 = _782014, _782012 = _782010], (26104 ^ _776545) ^ [] : [-(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))))], (22333 ^ _776545) ^ [_1181371, _1181373, _1181375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181373), _1181375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181371), _1181373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181371), _1181375)))], (39077 ^ _776545) ^ [_1529394, _1529396, _1529398, _1529400] : [hAPP(hAPP(c_Product__Type_OSigma(_1529394, _1529396), _1529398), hAPP(c_COMBK(tc_fun(_1529396, tc_HOL_Obool), _1529394), _1529400)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529394, _1529396), tc_HOL_Obool)), -(_1529398 = c_Orderings_Obot__class_Obot(tc_fun(_1529394, tc_HOL_Obool))), -(_1529400 = c_Orderings_Obot__class_Obot(tc_fun(_1529396, tc_HOL_Obool)))], (29603 ^ _776545) ^ [_1307113, _1307115] : [class_Rings_Oring__1(_1307113), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307113), hAPP(c_Groups_Ouminus__class_Ouminus(_1307113), c_Groups_Oone__class_Oone(_1307113))), 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)))), _1307115)) = c_Groups_Oone__class_Oone(_1307113))], (34231 ^ _776545) ^ [_1413117, _1413119, _1413121] : [class_Int_Onumber__ring(_1413117), 34234 ^ _776545 : [(34241 ^ _776545) ^ [] : [-(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), _1413119)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413117), _1413121), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413119))) = c_Groups_Oone__class_Oone(_1413117))], (34235 ^ _776545) ^ [] : [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), _1413119))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413117), _1413121), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413119))) = hAPP(hAPP(c_HOL_OLet(_1413117, _1413117), hAPP(hAPP(c_Power_Opower__class_Opower(_1413117), _1413121), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413119))), hAPP(hAPP(c_COMBS(_1413117, _1413117, _1413117), hAPP(hAPP(c_COMBB(_1413117, tc_fun(_1413117, _1413117), _1413117), c_Groups_Otimes__class_Otimes(_1413117)), hAPP(c_Groups_Otimes__class_Otimes(_1413117), _1413121))), c_COMBI(_1413117))))]]], (47275 ^ _776545) ^ [_1727023, _1727025, _1727027, _1727029, _1727031] : [-(hBOOL(hAPP(_1727023, _1727025))), -(c_List_OtakeWhile(_1727027, _1727023, hAPP(hAPP(c_List_Oappend(_1727027), _1727029), hAPP(hAPP(c_List_Olist_OCons(_1727027), _1727025), _1727031))) = c_List_OtakeWhile(_1727027, _1727023, _1727029))], (12688 ^ _776545) ^ [_1000224, _1000226, _1000228] : [-(hAPP(c_Finite__Set_Ofold1(_1000224, _1000226), hAPP(hAPP(c_Set_Oinsert(_1000224), _1000228), c_Orderings_Obot__class_Obot(tc_fun(_1000224, tc_HOL_Obool)))) = _1000228)], (44743 ^ _776545) ^ [_1671084, _1671086, _1671088, _1671090] : [-(hAPP(c_List_Oset(_1671084), hAPP(hAPP(c_List_Omap(_1671086, _1671084), _1671088), _1671090)) = hAPP(c_Set_Oimage(_1671086, _1671084, _1671088), hAPP(c_List_Oset(_1671086), _1671090)))], (52203 ^ _776545) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (46263 ^ _776545) ^ [_1707244, _1707246] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1707244), _1707246) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1707244, _1707246)))], (28053 ^ _776545) ^ [_1280582, _1280584] : [class_Int_Onumber__ring(_1280582), 28056 ^ _776545 : [(28063 ^ _776545) ^ [] : [c_Int_Oiszero(_1280582, hAPP(c_Int_Onumber__class_Onumber__of(_1280582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1280584)))), -(c_Groups_Ozero__class_Ozero(_1280582) = hAPP(c_Int_Onumber__class_Onumber__of(_1280582), _1280584))], (28057 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1280582) = hAPP(c_Int_Onumber__class_Onumber__of(_1280582), _1280584), -(c_Int_Oiszero(_1280582, hAPP(c_Int_Onumber__class_Onumber__of(_1280582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1280584)))))]]], (27219 ^ _776545) ^ [_1266285, _1266287, _1266289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1266285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1266287), 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), _1266287), _1266289))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1266285))), _1266289)))], (26955 ^ _776545) ^ [_1262074, _1262076] : [class_Int_Onumber__ring(_1262074), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262074), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262076)) = hAPP(c_Int_Onumber__class_Onumber__of(_1262074), _1262076))], (7716 ^ _776545) ^ [_905636, _905638, _905640, _905642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905636, tc_HOL_Obool)), _905642), _905638)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905636, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905636, tc_HOL_Obool)), _905638), _905640)), _905642) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905636, tc_HOL_Obool)), _905638), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905636, tc_HOL_Obool)), _905640), _905642)))], (906 ^ _776545) ^ [_790154, _790156, _790158, _790160, _790162, _790164] : [-(c_Relation_Orefl__on(_790162, _790158, _790154)), c_Relation_Orefl__on(_790164, _790160, _790156), _790164 = _790162, _790160 = _790158, _790156 = _790154], (49360 ^ _776545) ^ [_1772971, _1772973, _1772975] : [c_List_Olist__ex(_1772971, _1772975, _1772973), 49364 ^ _776545 : [(49367 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1772975, 49363 ^ [_1772971, _1772973, _1772975])))], (49365 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772971), 49363 ^ [_1772971, _1772973, _1772975]), hAPP(c_List_Oset(_1772971), _1772973))))]]], (50391 ^ _776545) ^ [_1795352, _1795354, _1795356, _1795358, _1795360, _1795362] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1795352, _1795354, _1795356, _1795358), _1795360), _1795362) = hAPP(_1795358, hAPP(hAPP(c_Product__Type_OPair(_1795352, _1795354), _1795360), _1795362)))], (19829 ^ _776545) ^ [_1134389, _1134391] : [class_Rings_Olinordered__idom(_1134389), 19832 ^ _776545 : [(19839 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134389), c_Groups_Ozero__class_Ozero(_1134389)), _1134391)), -(c_Groups_Osgn__class_Osgn(_1134389, _1134391) = c_Groups_Oone__class_Oone(_1134389))], (19833 ^ _776545) ^ [] : [c_Groups_Osgn__class_Osgn(_1134389, _1134391) = c_Groups_Oone__class_Oone(_1134389), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134389), c_Groups_Ozero__class_Ozero(_1134389)), _1134391)))]]], (38701 ^ _776545) ^ [_1520319, _1520321, _1520323, _1520325, _1520327] : [-(hAPP(c_Set_Ovimage(_1520319, _1520321, _1520323), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520321, tc_HOL_Obool)), _1520325), _1520327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520319, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1520319, _1520321, _1520323), _1520325)), hAPP(c_Set_Ovimage(_1520319, _1520321, _1520323), _1520327)))], (41021 ^ _776545) ^ [_1580290, _1580292] : [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), _1580290), _1580292)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580290), _1580292)))], (35096 ^ _776545) ^ [_1431526, _1431528, _1431530, _1431532] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1431526, _1431528), _1431530)), hBOOL(hAPP(hAPP(_1431528, _1431532), _1431530)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1431526, _1431528), _1431532)))], (47787 ^ _776545) ^ [_1738394, _1738396, _1738398, _1738400] : [47789 ^ _776545 : [(47792 ^ _776545) ^ [] : [hBOOL(hAPP(_1738398, 47788 ^ [_1738394, _1738396, _1738398, _1738400]))], (47790 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738394), 47788 ^ [_1738394, _1738396, _1738398, _1738400]), hAPP(c_List_Oset(_1738394), _1738396))))]], -(c_List_OdropWhile(_1738394, _1738398, hAPP(hAPP(c_List_Oappend(_1738394), _1738396), _1738400)) = c_List_OdropWhile(_1738394, _1738398, _1738400))], (14056 ^ _776545) ^ [_1028465, _1028467, _1028469, _1028471, _1028473] : [class_Groups_Ocomm__monoid__add(_1028465), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028467), _1028469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028467, _1028465), _1028471), hAPP(hAPP(c_Set_Oinsert(_1028467), _1028473), _1028469)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1028465), hAPP(_1028471, _1028473)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028467, _1028465), _1028471), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028467, tc_HOL_Obool)), _1028469), hAPP(hAPP(c_Set_Oinsert(_1028467), _1028473), c_Orderings_Obot__class_Obot(tc_fun(_1028467, tc_HOL_Obool)))))))], (6971 ^ _776545) ^ [_889739, _889741, _889743] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_889739, tc_HOL_Obool)), _889741), hAPP(c_Set_OPow(_889739), _889743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889739, tc_HOL_Obool)), _889741), _889743)))], (29093 ^ _776545) ^ [_1298024] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1298024)), c_Int_OMin))], (33651 ^ _776545) ^ [_1398097, _1398099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398097), hAPP(c_Set_OCollect(_1398097), _1398099))), 33654 ^ _776545 : [(33661 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398097), c_Orderings_Otop__class_Otop(tc_fun(_1398097, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1398097), hAPP(c_Set_OCollect(_1398097), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1398097), c_fNot), _1398099)))))], (33655 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398097), hAPP(c_Set_OCollect(_1398097), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1398097), c_fNot), _1398099)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1398097), c_Orderings_Otop__class_Otop(tc_fun(_1398097, tc_HOL_Obool)))))]]], (21821 ^ _776545) ^ [_1171923, _1171925] : [-(_1171923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171925), _1171923) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1171925), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171925), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171923), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (40102 ^ _776545) ^ [_1557619, _1557621, _1557623, _1557625, _1557627, _1557629, _1557631, _1557633, _1557635, _1557637, _1557639] : [c_Finite__Set_Ofolding(_1557619, _1557621, _1557623, _1557625), -(hAPP(c_Fun_Ocomp(_1557627, _1557629, _1557631, _1557633), hAPP(c_Fun_Ocomp(_1557635, _1557627, _1557631, _1557637), _1557639)) = hAPP(c_Fun_Ocomp(_1557635, _1557629, _1557631, hAPP(c_Fun_Ocomp(_1557627, _1557629, _1557635, _1557633), _1557637)), _1557639))], (50638 ^ _776545) ^ [_1800201, _1800203] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800201), _1800203)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1800201, 50641 ^ [_1800201, _1800203], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1800201), _1800203)), _1800203))], (5889 ^ _776545) ^ [_870193, _870195, _870197] : [hBOOL(hAPP(hAPP(c_member(_870193), _870195), _870197)), -(hBOOL(hAPP(_870197, _870195)))], (27003 ^ _776545) ^ [_1262984] : [c_Nat__Transfer_Onat__set(_1262984), 27006 ^ _776545 : [(27007 ^ _776545) ^ [_1263050] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1263050), _1262984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263050)))]]], (12017 ^ _776545) ^ [_987763, _987765, _987767, _987769, _987771, _987773] : [c_Finite__Set_Ofolding__image__simple(_987763, _987765, _987767, _987769, _987771, _987773), -(hAPP(_987773, c_Orderings_Obot__class_Obot(tc_fun(_987765, tc_HOL_Obool))) = _987769)], (42232 ^ _776545) ^ [_1614023, _1614025, _1614027, _1614029] : [-(hAPP(hAPP(c_List_Onth(_1614023), hAPP(hAPP(c_List_Olist_OCons(_1614023), _1614025), _1614027)), hAPP(c_Nat_OSuc, _1614029)) = hAPP(hAPP(c_List_Onth(_1614023), _1614027), _1614029))], (26218 ^ _776545) ^ [_1250097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250097)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1250097)) = _1250097)], (9458 ^ _776545) ^ [_939058, _939060, _939062] : [class_Orderings_Opreorder(_939058), 9461 ^ _776545 : [(9470 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939058), _939060), _939062))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939058), _939060), _939062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939058), _939062), _939060)))], (9462 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939058), _939060), _939062)), 9465 ^ _776545 : [(9468 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939058), _939062), _939060))], (9466 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939058), _939060), _939062)))]]]]], (27621 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (25024 ^ _776545) ^ [_1229722, _1229724, _1229726] : [-(_1229722 = 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), _1229722), _1229724)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229722), _1229726)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229724), _1229726))], (51849 ^ _776545) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (29733 ^ _776545) ^ [] : [-(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)))], (9760 ^ _776545) ^ [_943668, _943670, _943672, _943674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943668, tc_HOL_Obool)), _943670), _943672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943668, tc_HOL_Obool)), _943672), _943674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943668, tc_HOL_Obool)), _943670), _943674)))], (33230 ^ _776545) ^ [_1385508, _1385510, _1385512, _1385514] : [c_Orderings_Obot__class_Obot(tc_fun(_1385508, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1385510, tc_fun(_1385508, tc_HOL_Obool)), _1385512), _1385514), 33233 ^ _776545 : [(33234 ^ _776545) ^ [_1385624] : [hBOOL(hAPP(hAPP(c_member(_1385510), _1385624), _1385512)), -(hAPP(_1385514, _1385624) = c_Orderings_Obot__class_Obot(tc_fun(_1385508, tc_HOL_Obool)))]]], (24728 ^ _776545) ^ [_1223912, _1223914] : [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)), _1223912)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1223912), _1223914)))], (40096 ^ _776545) ^ [_1557474, _1557476, _1557478, _1557480, _1557482, _1557484] : [c_Finite__Set_Ofolding(_1557474, _1557476, _1557478, _1557480), -(hAPP(c_Fun_Ocomp(_1557476, _1557476, _1557476, hAPP(_1557478, _1557482)), hAPP(_1557478, _1557484)) = hAPP(c_Fun_Ocomp(_1557476, _1557476, _1557476, hAPP(_1557478, _1557484)), hAPP(_1557478, _1557482)))], (5743 ^ _776545) ^ [_867157, _867159] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867157, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867157)), tc_HOL_Obool)), _867159), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867157, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867157)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867157)))), -(hAPP(c_Hoare__Mirabelle_ORep__triple(_867157), hAPP(c_Hoare__Mirabelle_OAbs__triple(_867157), _867159)) = _867159)], (39565 ^ _776545) ^ [_1543896, _1543898, _1543900, _1543902, _1543904] : [c_Relation_Orefl__on(_1543896, _1543898, _1543900), c_Relation_Orefl__on(_1543896, _1543902, _1543904), -(c_Relation_Orefl__on(_1543896, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543896, tc_HOL_Obool)), _1543898), _1543902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1543896, _1543896), tc_HOL_Obool)), _1543900), _1543904)))], (7226 ^ _776545) ^ [_894369, _894371, _894373] : [c_Orderings_Obot__class_Obot(tc_fun(_894369, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_894369), _894371), _894373)], (36604 ^ _776545) ^ [_1470169] : [-(hAPP(c_Relation_OField(_1470169), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1470169, _1470169), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1470169, tc_HOL_Obool)))], (38470 ^ _776545) ^ [_1514128, _1514130] : [c_Wellfounded_OwfP(_1514128, _1514130), 38473 ^ _776545 : [(38474 ^ _776545) ^ [_1514192] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1514128, _1514130), _1514192)))]]], (48235 ^ _776545) ^ [_1748085, _1748087] : [-(c_FunDef_Ois__measure(_1748085, _1748087))], (8375 ^ _776545) ^ [_920180, _920182, _920184, _920186] : [class_Lattices_Osemilattice__inf(_920180), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920180), _920182), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920180), _920184), _920186)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920180), _920184), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920180), _920182), _920186)))], (40272 ^ _776545) ^ [_1561592, _1561594, _1561596, _1561598, _1561600, _1561602] : [c_Finite__Set_Ofolding__idem(_1561592, _1561594, _1561596, _1561598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561592), _1561600)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1561592, tc_HOL_Obool)), _1561602), _1561600)), -(hAPP(c_Fun_Ocomp(_1561594, _1561594, _1561594, hAPP(_1561598, _1561600)), hAPP(_1561598, _1561602)) = hAPP(_1561598, _1561600))], (44260 ^ _776545) ^ [_1661602, _1661604, _1661606, _1661608] : [-(hAPP(c_List_Ofoldl(_1661602, _1661604, _1661606, _1661608), c_List_Olist_ONil(_1661604)) = _1661608)], (32368 ^ _776545) ^ [_1358830, _1358832, _1358834] : [hBOOL(hAPP(_1358830, _1358832)), -(hBOOL(hAPP(hAPP(c_member(_1358834), _1358832), hAPP(c_Set_OCollect(_1358834), _1358830))))], (32382 ^ _776545) ^ [_1359148, _1359150, _1359152, _1359154, _1359156, _1359158] : [hBOOL(hAPP(hAPP(c_member(_1359148), _1359150), _1359152)), hBOOL(hAPP(hAPP(c_member(_1359154), _1359156), hAPP(_1359158, _1359150))), -(hBOOL(hAPP(hAPP(c_member(_1359154), _1359156), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1359148, tc_fun(_1359154, tc_HOL_Obool)), _1359152), _1359158))))], (4824 ^ _776545) ^ [_849984, _849986] : [_849986 = _849984, -(c_List_Oset(_849986) = c_List_Oset(_849984))], (48889 ^ _776545) ^ [_1762203, _1762205] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762203), c_List_Olist_ONil(_1762203)), _1762205))], (40186 ^ _776545) ^ [_1559557, _1559559, _1559561, _1559563, _1559565, _1559567, _1559569] : [c_Finite__Set_Ofolding__image(_1559557, _1559559, _1559561, _1559563, _1559565), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559559), _1559567)), -(hAPP(hAPP(_1559565, _1559569), _1559567) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559557, _1559559, _1559561), _1559569), _1559563), _1559567))], (20401 ^ _776545) ^ [_1144589, _1144591, _1144593, _1144595, _1144597] : [class_Fields_Olinordered__field(_1144589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144589), c_Groups_Ozero__class_Ozero(_1144589)), _1144591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144589), _1144591), _1144593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144589), c_Groups_Ozero__class_Ozero(_1144589)), _1144595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144589), _1144595), _1144597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144589), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144589), _1144591), _1144597)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144589), _1144593), _1144595))))], (43906 ^ _776545) ^ [_1653862, _1653864] : [-(hAPP(hAPP(c_List_Odrop(_1653862), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1653864) = _1653864)], (9986 ^ _776545) ^ [_947428, _947430, _947432, _947434, _947436] : [class_Orderings_Oorder(_947428), 9989 ^ _776545 : [(10002 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947428, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_947428, _947430, _947432)), c_SetInterval_Oord__class_OatLeastAtMost(_947428, _947434, _947436)))), 10003 ^ _776545 : [(10006 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947434), _947430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947432), _947436))], (10004 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947430), _947432)))]]], (9990 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947428, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_947428, _947430, _947432)), c_SetInterval_Oord__class_OatLeastAtMost(_947428, _947434, _947436))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947430), _947432)), 9997 ^ _776545 : [(10000 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947432), _947436)))], (9998 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947428), _947434), _947430)))]]]]], (44130 ^ _776545) ^ [_1659132, _1659134] : [-(_1659132 = c_List_Olist_ONil(_1659134)), -(hAPP(c_List_Ohd(_1659134), _1659132) = hAPP(hAPP(c_List_Onth(_1659134), _1659132), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30064 ^ _776545) ^ [_1315746, _1315748, _1315750, _1315752] : [class_Orderings_Olinorder(_1315746), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315746), _1315748), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315746), _1315750), _1315752)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315746), _1315750), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315746), _1315748), _1315752)))], (26224 ^ _776545) ^ [_1250203, _1250205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250203), hAPP(c_Int_Onat, _1250205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250203)), _1250205)))], (51905 ^ _776545) ^ [_1825254, _1825256] : [-(class_Finite__Set_Ofinite(tc_fun(_1825254, _1825256))), class_Finite__Set_Ofinite(_1825254), class_Finite__Set_Ofinite(_1825256)], (29887 ^ _776545) ^ [_1312517, _1312519] : [-(c_Random_Olog(_1312517, _1312519) = 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(_1312517, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1312519), _1312517)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1312517), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1312519), _1312517)))], (33593 ^ _776545) ^ [_1394933, _1394935, _1394937, _1394939] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394933, tc_fun(_1394935, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1394933, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1394935, tc_HOL_Obool), tc_fun(_1394935, tc_HOL_Obool), _1394933), hAPP(c_COMBC(_1394935, tc_fun(_1394935, tc_HOL_Obool), tc_HOL_Obool), c_member(_1394935))), _1394937)), _1394939)), -(hBOOL(hAPP(hAPP(c_member(_1394935), _1394939), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1394933, tc_fun(_1394935, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1394933, tc_HOL_Obool))), _1394937))))], (41142 ^ _776545) ^ [_1583271, _1583273] : [-(c_Transitive__Closure_Otrancl(_1583271, hAPP(c_Relation_Oconverse(_1583271, _1583271), _1583273)) = hAPP(c_Relation_Oconverse(_1583271, _1583271), c_Transitive__Closure_Otrancl(_1583271, _1583273)))], (52371 ^ _776545) ^ [_1830076] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1830076)))], (49764 ^ _776545) ^ [_1782156, _1782158, _1782160] : [c_Equiv__Relations_Oequiv(_1782156, _1782158, _1782160), 49767 ^ _776545 : [(49772 ^ _776545) ^ [] : [-(c_Relation_Otrans(_1782156, _1782160))], (49770 ^ _776545) ^ [] : [-(c_Relation_Osym(_1782156, _1782160))], (49768 ^ _776545) ^ [] : [-(c_Relation_Orefl__on(_1782156, _1782158, _1782160))]]], (43775 ^ _776545) ^ [_1650144, _1650146, _1650148, _1650150] : [-(c_List_Osublist(_1650144, hAPP(hAPP(c_List_Oappend(_1650144), _1650146), _1650148), _1650150) = hAPP(hAPP(c_List_Oappend(_1650144), c_List_Osublist(_1650144, _1650146, _1650150)), c_List_Osublist(_1650144, _1650148, 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(_1650144)), _1650146)))), _1650150)))))], (17633 ^ _776545) ^ [_1094092] : [class_Rings_Olinordered__semidom(_1094092), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094092), c_Groups_Ozero__class_Ozero(_1094092)), c_Groups_Oone__class_Oone(_1094092))))], (23089 ^ _776545) ^ [_1194848, _1194850, _1194852, _1194854, _1194856, _1194858] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194848), _1194850)), _1194852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194854), _1194856)), _1194858), 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), _1194854), _1194856)), _1194858)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194852), _1194848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194854), _1194848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194856), _1194850)))], (33030 ^ _776545) ^ [_1379711, _1379713, _1379715, _1379717] : [-(_1379711 = c_Orderings_Obot__class_Obot(tc_fun(_1379713, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1379713, _1379715, hAPP(c_COMBK(_1379715, _1379713), _1379717)), _1379711) = hAPP(hAPP(c_Set_Oinsert(_1379715), _1379717), c_Orderings_Obot__class_Obot(tc_fun(_1379715, tc_HOL_Obool))))], (3066 ^ _776545) ^ [_822147, _822149, _822151, _822153] : [-(c_List_Olexn(_822153, _822149) = c_List_Olexn(_822151, _822147)), _822153 = _822151, _822149 = _822147], (31327 ^ _776545) ^ [_1338921] : [class_Orderings_Olinorder(_1338921), -(c_Finite__Set_Ofun__left__comm__idem(_1338921, _1338921, c_Orderings_Oord__class_Omax(_1338921)))], (1404 ^ _776545) ^ [_796959, _796961] : [-(class_Lattices_Odistrib__lattice(_796959)), _796961 = _796959, class_Lattices_Odistrib__lattice(_796961)], (32966 ^ _776545) ^ [_1377839, _1377841, _1377843, _1377845, _1377847] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377839, tc_fun(_1377841, tc_HOL_Obool)), _1377843), hAPP(hAPP(c_COMBC(_1377839, tc_fun(_1377841, tc_HOL_Obool), tc_fun(_1377841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377841, tc_HOL_Obool), tc_fun(tc_fun(_1377841, tc_HOL_Obool), tc_fun(_1377841, tc_HOL_Obool)), _1377839), c_Groups_Ominus__class_Ominus(tc_fun(_1377841, tc_HOL_Obool))), _1377845)), _1377847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377841, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377839, tc_fun(_1377841, tc_HOL_Obool)), _1377843), _1377845)), _1377847))], (30216 ^ _776545) ^ [_1318572, _1318574, _1318576] : [class_Orderings_Olinorder(_1318572), 30219 ^ _776545 : [(30226 ^ _776545) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318572), _1318574), _1318576) = _1318574, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318572), _1318574), _1318576)))], (30220 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318572), _1318574), _1318576)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318572), _1318574), _1318576) = _1318574)]]], (16490 ^ _776545) ^ [_1073511] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073511)))], (26418 ^ _776545) ^ [_1253292, _1253294] : [-(hBOOL(hAPP(_1253292, hAPP(c_Int_Onat, _1253294)))), 26422 ^ _776545 : [(26425 ^ _776545) ^ [] : [hBOOL(hAPP(_1253292, 26421 ^ [_1253292, _1253294]))], (26423 ^ _776545) ^ [] : [-(_1253294 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 26421 ^ [_1253292, _1253294]))]], 26426 ^ _776545 : [(26429 ^ _776545) ^ [] : [hBOOL(hAPP(_1253292, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26427 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (1154 ^ _776545) ^ [_793834, _793836] : [-(class_Rings_Olinordered__semiring__1(_793834)), _793836 = _793834, class_Rings_Olinordered__semiring__1(_793836)], (31791 ^ _776545) ^ [_1347756, _1347758, _1347760] : [class_Orderings_Olinorder(_1347756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347756), _1347758)), -(_1347760 = c_Orderings_Obot__class_Obot(tc_fun(_1347756, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1347756, tc_HOL_Obool)), _1347760), _1347758)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347756), c_Big__Operators_Olinorder__class_OMax(_1347756, _1347760)), c_Big__Operators_Olinorder__class_OMax(_1347756, _1347758)) = c_Big__Operators_Olinorder__class_OMax(_1347756, _1347758))], (30046 ^ _776545) ^ [_1315353, _1315355, _1315357] : [class_Orderings_Olinorder(_1315353), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315353), _1315355), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315353), _1315355), _1315357)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315353), _1315355), _1315357))], (11764 ^ _776545) ^ [_982498, _982500, _982502, _982504, _982506, _982508, _982510, _982512] : [c_Finite__Set_Ofolding__image__simple(_982498, _982500, _982502, _982504, _982506, _982508), hBOOL(hAPP(c_Finite__Set_Ofinite(_982500), _982510)), hBOOL(hAPP(c_Finite__Set_Ofinite(_982500), _982512)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982500, tc_HOL_Obool)), _982510), _982512) = c_Orderings_Obot__class_Obot(tc_fun(_982500, tc_HOL_Obool)), -(hAPP(_982508, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982500, tc_HOL_Obool)), _982510), _982512)) = hAPP(hAPP(_982502, hAPP(_982508, _982510)), hAPP(_982508, _982512)))], (23511 ^ _776545) ^ [_1202679, _1202681, _1202683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202679)), 23517 ^ _776545 : [(23520 ^ _776545) ^ [] : [hBOOL(hAPP(_1202681, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23516 ^ [_1202679, _1202681, _1202683]), _1202679)))], (23518 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1202681, 23516 ^ [_1202679, _1202681, _1202683])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202683)), 23525 ^ _776545 : [(23526 ^ _776545) ^ [_1202968] : [hBOOL(hAPP(_1202681, _1202968)), -(hBOOL(hAPP(_1202681, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202683), _1202679)))))]]], (46050 ^ _776545) ^ [_1701486, _1701488, _1701490] : [hAPP(c_List_Ofilter(_1701486, _1701488), _1701490) = _1701490, 46053 ^ _776545 : [(46054 ^ _776545) ^ [_1701577] : [hBOOL(hAPP(hAPP(c_member(_1701486), _1701577), hAPP(c_List_Oset(_1701486), _1701490))), -(hBOOL(hAPP(_1701488, _1701577)))]]], (50959 ^ _776545) ^ [_1808599, _1808601, _1808603] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1808599), _1808601)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1808599), _1808603))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1808599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1808601), _1808603)))], (28139 ^ _776545) ^ [_1281861] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1281861), c_Int_OMin) = c_Int_Opred(_1281861))], (25109 ^ _776545) ^ [_1231025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231025)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1231025))], (38556 ^ _776545) ^ [_1516102, _1516104] : [-(c_Divides_Odivmod__nat(_1516102, _1516104) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1516102, _1516104)))], (52481 ^ _776545) ^ [_1831262, _1831264] : [_1831262 = _1831264, -(hBOOL(hAPP(hAPP(c_fequal, _1831262), _1831264)))], (39143 ^ _776545) ^ [_1531517, _1531519, _1531521, _1531523, _1531525] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531517, _1531519), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531517, tc_HOL_Obool)), _1531521), _1531523)), _1531525) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1531517, _1531519), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531517, _1531519), _1531521), _1531525)), hAPP(hAPP(c_Product__Type_OSigma(_1531517, _1531519), _1531523), _1531525)))], (27409 ^ _776545) ^ [_1269502, _1269504] : [class_Groups_Oordered__ab__group__add__abs(_1269502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269502), c_Groups_Ozero__class_Ozero(_1269502)), _1269504)), -(hAPP(c_Groups_Oabs__class_Oabs(_1269502), _1269504) = _1269504)], (21291 ^ _776545) ^ [_1161886, _1161888] : [class_Int_Onumber__ring(_1161886), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161886), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161888)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1161886), hAPP(c_Int_Onumber__class_Onumber__of(_1161886), _1161888)))], (47341 ^ _776545) ^ [_1728318] : [-(c_List_Oembed__list(_1728318) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1728318))], (39595 ^ _776545) ^ [_1544483, _1544485, _1544487, _1544489] : [c_Relation_Orefl__on(_1544483, _1544485, _1544487), hBOOL(hAPP(hAPP(c_member(_1544483), _1544489), _1544485)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544483, _1544483)), hAPP(hAPP(c_Product__Type_OPair(_1544483, _1544483), _1544489), _1544489)), _1544487)))], (43242 ^ _776545) ^ [_1638031, _1638033, _1638035, _1638037] : [_1638031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1638033), _1638031), hAPP(hAPP(c_List_Olist_OCons(_1638033), _1638035), _1638037)) = c_List_Olist_ONil(_1638033))], (44723 ^ _776545) ^ [_1670605, _1670607, _1670609, _1670611, _1670613] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1670605), tc_List_Olist(_1670607), tc_List_Olist(_1670609), hAPP(c_List_Omap(_1670605, _1670607), _1670611)), hAPP(c_List_Omap(_1670609, _1670605), _1670613)) = hAPP(c_List_Omap(_1670609, _1670607), hAPP(c_Fun_Ocomp(_1670605, _1670607, _1670609, _1670611), _1670613)))], (22245 ^ _776545) ^ [_1179974, _1179976, _1179978, _1179980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179974), _1179976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179978), _1179980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179974), _1179978)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179976), _1179980))))], (34725 ^ _776545) ^ [_1423707, _1423709] : [-(c_Divides_Odivmod__nat(_1423707, _1423709) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1423707), _1423709)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1423707, _1423709)))], (13430 ^ _776545) ^ [_1015209, _1015211, _1015213, _1015215] : [class_Lattices_Osemilattice__sup(_1015209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015209), _1015211)), 13440 ^ _776545 : [(13443 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015209), 13439 ^ [_1015209, _1015211, _1015213, _1015215]), _1015213))], (13441 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1015209), 13439 ^ [_1015209, _1015211, _1015213, _1015215]), _1015211)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015209), hAPP(hAPP(c_Finite__Set_Ofold(_1015209, _1015209, c_Lattices_Osemilattice__sup__class_Osup(_1015209)), _1015215), _1015211)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1015209), _1015213), _1015215))))], (49818 ^ _776545) ^ [_1782942, _1782944] : [c_Relation_Osym(_1782942, hAPP(c_Set_OCollect(tc_prod(_1782942, _1782942)), hAPP(c_Product__Type_Oprod_Oprod__case(_1782942, _1782942, tc_HOL_Obool), _1782944))), -(c_Predicate_Osymp(_1782942, _1782944))], (7560 ^ _776545) ^ [_901451, _901453, _901455, _901457] : [7562 ^ _776545 : [(7565 ^ _776545) ^ [] : [hBOOL(hAPP(_901457, 7561 ^ [_901451, _901453, _901455, _901457]))], (7563 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901451), 7561 ^ [_901451, _901453, _901455, _901457]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901451, tc_HOL_Obool)), _901453), _901455))))]], 7566 ^ _776545 : [(7573 ^ _776545) ^ [_901768] : [hBOOL(hAPP(hAPP(c_member(_901451), _901768), _901455)), -(hBOOL(hAPP(_901457, _901768)))], (7567 ^ _776545) ^ [_901671] : [hBOOL(hAPP(hAPP(c_member(_901451), _901671), _901453)), -(hBOOL(hAPP(_901457, _901671)))]]], (52525 ^ _776545) ^ [_1831817, _1831819] : [hBOOL(_1831817), -(hBOOL(hAPP(hAPP(c_fdisj, _1831817), _1831819)))], (29121 ^ _776545) ^ [_1298443, _1298445] : [class_Int_Onumber__ring(_1298443), -(hAPP(c_Int_Onumber__class_Onumber__of(_1298443), c_Int_OBit0(_1298445)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298443), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1298443), c_Groups_Ozero__class_Ozero(_1298443)), hAPP(c_Int_Onumber__class_Onumber__of(_1298443), _1298445))), hAPP(c_Int_Onumber__class_Onumber__of(_1298443), _1298445)))], (29922 ^ _776545) ^ [_1313143, _1313145, _1313147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1313143), _1313145))), -(c_Random_Ominus__shift(_1313147, _1313143, _1313145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1313143), _1313145))], (34976 ^ _776545) ^ [_1429011, _1429013] : [-(_1429011 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34979 ^ _776545 : [(34986 ^ _776545) ^ [] : [-(_1429013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1429011, _1429013) = 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, _1429013))), 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, _1429011)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1429013))), c_Divides_Opdivmod(_1429011, _1429013)), 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), _1429013))))), c_Divides_Opdivmod(_1429011, _1429013)))))], (34980 ^ _776545) ^ [] : [_1429013 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1429011, _1429013) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1429011))]]], (22853 ^ _776545) ^ [_1190557, _1190559, _1190561, _1190563] : [class_Rings_Olinordered__semidom(_1190557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190559), _1190561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190557), c_Groups_Oone__class_Oone(_1190557)), _1190563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190557), hAPP(hAPP(c_Power_Opower__class_Opower(_1190557), _1190563), _1190559)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190557), _1190563), _1190561))))], (25243 ^ _776545) ^ [_1233531, _1233533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233531)), 25246 ^ _776545 : [(25249 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233533, _1233531)), _1233531)))], (25247 ^ _776545) ^ [] : [-(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, _1233533, _1233531))))]]], (34729 ^ _776545) ^ [_1423882, _1423884, _1423886, _1423888, _1423890, _1423892, _1423894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1423882, _1423884)), hAPP(hAPP(c_Product__Type_OPair(_1423882, _1423884), _1423886), _1423888)), _1423890)), -(hBOOL(hAPP(hAPP(c_member(_1423892), hAPP(hAPP(_1423894, _1423886), _1423888)), hAPP(c_Set_Oimage(tc_prod(_1423882, _1423884), _1423892, hAPP(c_Product__Type_Oprod_Oprod__case(_1423882, _1423884, _1423892), _1423894)), _1423890))))], (43703 ^ _776545) ^ [_1648354, _1648356, _1648358] : [-(c_List_Obutlast(_1648354, hAPP(hAPP(c_List_Oappend(_1648354), _1648356), hAPP(hAPP(c_List_Olist_OCons(_1648354), _1648358), c_List_Olist_ONil(_1648354)))) = _1648356)], (48215 ^ _776545) ^ [_1747797, _1747799, _1747801, _1747803] : [-(c_List_Olist__all(_1747797, _1747799, hAPP(hAPP(c_List_Oappend(_1747797), _1747801), _1747803))), c_List_Olist__all(_1747797, _1747799, _1747801), c_List_Olist__all(_1747797, _1747799, _1747803)], (47404 ^ _776545) ^ [_1729729, _1729731, _1729733, _1729735] : [hBOOL(hAPP(_1729729, _1729731)), -(c_List_OdropWhile(_1729733, _1729729, hAPP(hAPP(c_List_Olist_OCons(_1729733), _1729731), _1729735)) = c_List_OdropWhile(_1729733, _1729729, _1729735))], (42301 ^ _776545) ^ [_1615952, _1615954] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1615952), hAPP(c_List_Oset(_1615952), _1615954))))], (48500 ^ _776545) ^ [_1753826, _1753828, _1753830, _1753832, _1753834] : [hBOOL(hAPP(hAPP(_1753830, _1753834), _1753832)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753826, _1753828, _1753830), _1753832), _1753834)))], (11004 ^ _776545) ^ [_966671, _966673] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966671, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966671, tc_HOL_Obool)), _966673)) = _966673)], (13688 ^ _776545) ^ [_1020312, _1020314, _1020316, _1020318] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1020312), 13691 ^ _776545 : [(13698 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020312), _1020314), _1020318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020312), _1020314), _1020316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020312), _1020318), _1020316))))], (13692 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020312), _1020314), _1020316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020312), _1020318), _1020316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020312), _1020314), _1020318)))]]], (15316 ^ _776545) ^ [_1052868, _1052870, _1052872] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052868), _1052870)), -(hAPP(c_Finite__Set_Ocard(_1052868), hAPP(hAPP(c_Set_Oinsert(_1052868), _1052872), _1052870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1052868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052868, tc_HOL_Obool)), _1052870), hAPP(hAPP(c_Set_Oinsert(_1052868), _1052872), c_Orderings_Obot__class_Obot(tc_fun(_1052868, tc_HOL_Obool)))))))], (42976 ^ _776545) ^ [_1633163, _1633165, _1633167, _1633169] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633163) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1633165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1633163)), hAPP(hAPP(c_List_Olist_OCons(_1633165), _1633167), _1633169)) = c_List_Olist_ONil(_1633165))], (34956 ^ _776545) ^ [_1428720, _1428722] : [-(c_Divides_Opdivmod(_1428720, _1428722) = 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), _1428720)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428722))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428720), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1428722))))], (39483 ^ _776545) ^ [_1541907, _1541909, _1541911, _1541913] : [c_Wellfounded_Owf(_1541907, _1541909), c_Fun_Oinj__on(_1541907, _1541911, _1541913, c_Orderings_Otop__class_Otop(tc_fun(_1541907, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1541911, hAPP(c_Set_Oimage(tc_prod(_1541907, _1541907), tc_prod(_1541911, _1541911), c_Product__Type_Omap__pair(_1541907, _1541911, _1541907, _1541911, _1541913, _1541913)), _1541909)))], (8002 ^ _776545) ^ [_912126, _912128, _912130, _912132] : [hBOOL(hAPP(hAPP(c_member(_912126), _912128), _912130)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912126, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912126), _912128), _912132)), _912130) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912126, tc_HOL_Obool)), _912132), _912130))], (11672 ^ _776545) ^ [_980739, _980741, _980743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980739), _980741)), 11675 ^ _776545 : [(11682 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980739), _980743)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980739, tc_HOL_Obool)), _980743), _980741))))], (11676 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980739, tc_HOL_Obool)), _980743), _980741))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980739), _980743)))]]], (45924 ^ _776545) ^ [_1697724, _1697726, _1697728] : [-(c_List_Oconcat(_1697724, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697724)), _1697726), _1697728)) = hAPP(hAPP(c_List_Oappend(_1697724), _1697726), c_List_Oconcat(_1697724, _1697728)))], (48570 ^ _776545) ^ [_1755807, _1755809, _1755811, _1755813] : [-(hAPP(hAPP(c_List_Oappend(_1755807), c_List_Oreplicate(_1755807, _1755809, _1755811)), hAPP(hAPP(c_List_Olist_OCons(_1755807), _1755811), _1755813)) = hAPP(hAPP(c_List_Olist_OCons(_1755807), _1755811), hAPP(hAPP(c_List_Oappend(_1755807), c_List_Oreplicate(_1755807, _1755809, _1755811)), _1755813)))], (45866 ^ _776545) ^ [_1696567, _1696569] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696567)), c_List_Oremdups(_1696567, _1696569)) = hAPP(c_Finite__Set_Ocard(_1696567), hAPP(c_List_Oset(_1696567), _1696569)))], (40559 ^ _776545) ^ [_1568430, _1568432] : [-(c_Wellfounded_Owf(_1568430, _1568432)), 40562 ^ _776545 : [(40565 ^ _776545) ^ [_1568650] : [hBOOL(hAPP(hAPP(c_member(_1568430), _1568650), 40560 ^ [_1568430, _1568432])), 40569 ^ _776545 : [(40572 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568430), 40568 ^ [_1568430, _1568432, _1568650]), 40560 ^ [_1568430, _1568432])))], (40570 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568430, _1568430)), hAPP(hAPP(c_Product__Type_OPair(_1568430, _1568430), 40568 ^ [_1568430, _1568432, _1568650]), _1568650)), _1568432)))]]], (40563 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568430), 40561 ^ [_1568430, _1568432]), 40560 ^ [_1568430, _1568432])))]]], (46113 ^ _776545) ^ [_1702759] : [-(c_List_Otranspose(_1702759, c_List_Olist_ONil(tc_List_Olist(_1702759))) = c_List_Olist_ONil(tc_List_Olist(_1702759)))], (18172 ^ _776545) ^ [_1103217, _1103219] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1103217, _1103219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1103219), hAPP(c_Nat_OSuc, _1103217)))], (37913 ^ _776545) ^ [_1499287, _1499289, _1499291] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1499287, hAPP(hAPP(c_COMBC(_1499287, tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_fun(_1499287, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499287, tc_fun(tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_fun(_1499287, tc_HOL_Obool)), _1499287), c_COMBC(_1499287, tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499287, tc_prod(_1499287, _1499287)), tc_fun(_1499287, tc_fun(tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_HOL_Obool)), _1499287), hAPP(c_COMBB(tc_prod(_1499287, _1499287), tc_fun(tc_fun(tc_prod(_1499287, _1499287), tc_HOL_Obool), tc_HOL_Obool), _1499287), c_member(tc_prod(_1499287, _1499287)))), c_Product__Type_OPair(_1499287, _1499287)))), _1499289)), _1499291)), -(hBOOL(hAPP(hAPP(c_member(_1499287), _1499291), c_Wellfounded_Oacc(_1499287, _1499289))))], (51329 ^ _776545) ^ [_1815589, _1815591, _1815593] : [class_Rings_Odvd(_1815589), class_Rings_Osemiring__0(_1815589), 51336 ^ _776545 : [(51346 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1815591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815589), _1815593), 51353 ^ [_1815589, _1815591, _1815593])))), 51347 ^ _776545 : [(51348 ^ _776545) ^ [_1815918] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815589), _1815593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815589), _1815918), c_Groups_Ozero__class_Ozero(_1815589)))), hBOOL(hAPP(_1815591, _1815918))]]], (51337 ^ _776545) ^ [] : [51338 ^ _776545 : [(51339 ^ _776545) ^ [_1815781] : [hBOOL(hAPP(_1815591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815589), _1815593), _1815781)))]], 51341 ^ _776545 : [(51344 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1815591, 51340 ^ [_1815589, _1815591, _1815593])))], (51342 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815589), _1815593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815589), 51340 ^ [_1815589, _1815591, _1815593]), c_Groups_Ozero__class_Ozero(_1815589)))))]]]]], (10178 ^ _776545) ^ [_951210, _951212, _951214, _951216] : [class_Orderings_Olinorder(_951210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951210), _951212), _951214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951210), _951214), _951216)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951210, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_951210, _951212, _951214)), c_SetInterval_Oord__class_OgreaterThanLessThan(_951210, _951214, _951216)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951210, _951212), _951216))], (13576 ^ _776545) ^ [_1018185, _1018187, _1018189, _1018191] : [class_Groups_Ocancel__semigroup__add(_1018185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018185), _1018187), _1018189) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018185), _1018187), _1018191), -(_1018189 = _1018191)], (16598 ^ _776545) ^ [_1075111] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1075111)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1075111), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1075111)))], (52095 ^ _776545) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (45140 ^ _776545) ^ [_1680532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1680532)), _1680532 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45110 ^ _776545) ^ [_1679990, _1679992, _1679994, _1679996, _1679998] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679990)), _1679992) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679994)), _1679996), 45113 ^ _776545 : [(45122 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1679990, _1679994), _1679992), _1679996) = _1679998), hAPP(hAPP(c_List_Omap(tc_prod(_1679990, _1679994), _1679990), c_Product__Type_Ofst(_1679990, _1679994)), _1679998) = _1679992, hAPP(hAPP(c_List_Omap(tc_prod(_1679990, _1679994), _1679994), c_Product__Type_Osnd(_1679990, _1679994)), _1679998) = _1679996], (45114 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Ozip(_1679990, _1679994), _1679992), _1679996) = _1679998, 45117 ^ _776545 : [(45120 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1679990, _1679994), _1679994), c_Product__Type_Osnd(_1679990, _1679994)), _1679998) = _1679996)], (45118 ^ _776545) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1679990, _1679994), _1679990), c_Product__Type_Ofst(_1679990, _1679994)), _1679998) = _1679992)]]]]], (52423 ^ _776545) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (7998 ^ _776545) ^ [_912005, _912007] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_912005, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_912005, tc_HOL_Obool))), _912007) = _912007)], (33354 ^ _776545) ^ [_1388757, _1388759] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1388757, tc_HOL_Obool), _1388759) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1388757, tc_HOL_Obool), tc_fun(_1388757, tc_HOL_Obool)), _1388759), c_COMBI(tc_fun(_1388757, tc_HOL_Obool))))], (14266 ^ _776545) ^ [_1033386, _1033388, _1033390] : [class_Rings_Ocomm__semiring__1(_1033386), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033386), _1033388), _1033390) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033386), _1033390), _1033388))], (34221 ^ _776545) ^ [_1412846, _1412848] : [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(_1412846))), 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)), _1412848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412846)), hAPP(c_Nat_OSuc, _1412848))))], (25052 ^ _776545) ^ [_1230139, _1230141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230141, _1230139)), _1230139)))], (32111 ^ _776545) ^ [_1353411, _1353413, _1353415] : [class_Orderings_Olinorder(_1353411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353411), _1353413)), 32118 ^ _776545 : [(32125 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353411, tc_HOL_Obool)), _1353413), hAPP(hAPP(c_Set_Oinsert(_1353411), _1353415), c_Orderings_Obot__class_Obot(tc_fun(_1353411, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353411, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1353411, c_Orderings_Oord__class_Omax(_1353411), hAPP(hAPP(c_Set_Oinsert(_1353411), _1353415), _1353413)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353411), _1353415), c_Big__Operators_Olattice_OSup__fin(_1353411, c_Orderings_Oord__class_Omax(_1353411), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353411, tc_HOL_Obool)), _1353413), hAPP(hAPP(c_Set_Oinsert(_1353411), _1353415), c_Orderings_Obot__class_Obot(tc_fun(_1353411, tc_HOL_Obool)))))))], (32119 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353411, tc_HOL_Obool)), _1353413), hAPP(hAPP(c_Set_Oinsert(_1353411), _1353415), c_Orderings_Obot__class_Obot(tc_fun(_1353411, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1353411, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1353411, c_Orderings_Oord__class_Omax(_1353411), hAPP(hAPP(c_Set_Oinsert(_1353411), _1353415), _1353413)) = _1353415)]]], (23187 ^ _776545) ^ [_1196524, _1196526, _1196528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196524)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196526), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1196528)), 23194 ^ _776545 : [(23195 ^ _776545) ^ [_1196732] : [23197 ^ _776545 : [(23203 ^ _776545) ^ [] : [-(_1196732 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23199 ^ [_1196524, _1196526, _1196528, _1196732]), 23196 ^ [_1196524, _1196526, _1196528, _1196732]))], (23201 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23199 ^ [_1196524, _1196526, _1196528, _1196732]), _1196528)))], (23198 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23196 ^ [_1196524, _1196526, _1196528, _1196732]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1196524))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196732), _1196526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196732), _1196524)), _1196526)))]]], (43922 ^ _776545) ^ [_1654255, _1654257, _1654259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1654255, tc_HOL_Obool)), hAPP(c_List_Oset(_1654255), hAPP(hAPP(c_List_Odrop(_1654255), _1654257), _1654259))), hAPP(c_List_Oset(_1654255), _1654259))))], (8179 ^ _776545) ^ [_916174, _916176, _916178] : [class_Orderings_Oorder(_916174), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916174, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_916174), _916176)), c_SetInterval_Oord__class_OgreaterThanLessThan(_916174, _916176, _916178)) = c_Orderings_Obot__class_Obot(tc_fun(_916174, tc_HOL_Obool)))], (22839 ^ _776545) ^ [_1190292, _1190294, _1190296, _1190298] : [class_Rings_Olinordered__semidom(_1190292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190292), c_Groups_Oone__class_Oone(_1190292)), _1190294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190292), hAPP(hAPP(c_Power_Opower__class_Opower(_1190292), _1190294), _1190296)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190292), _1190294), _1190298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190296), _1190298)))], (9228 ^ _776545) ^ [_935723, _935725, _935727] : [class_Orderings_Olinorder(_935723), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935723), _935725), _935727))), 9235 ^ _776545 : [(9242 ^ _776545) ^ [] : [_935727 = _935725, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935723), _935727), _935725))], (9236 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935723), _935727), _935725))), -(_935727 = _935725)]]], (43381 ^ _776545) ^ [_1641391, _1641393, _1641395, _1641397, _1641399] : [-(hAPP(hAPP(c_List_Oappend(_1641391), _1641393), _1641395) = hAPP(hAPP(c_List_Olist_OCons(_1641391), _1641397), _1641399)), 43382 ^ _776545 : [(43389 ^ _776545) ^ [_1641574] : [_1641393 = hAPP(hAPP(c_List_Olist_OCons(_1641391), _1641397), _1641574), hAPP(hAPP(c_List_Oappend(_1641391), _1641574), _1641395) = _1641399], (43383 ^ _776545) ^ [] : [_1641393 = c_List_Olist_ONil(_1641391), _1641395 = hAPP(hAPP(c_List_Olist_OCons(_1641391), _1641397), _1641399)]]], (41098 ^ _776545) ^ [_1582410, _1582412, _1582414, _1582416] : [-(hAPP(c_Relation_Oconverse(_1582410, _1582410), hAPP(hAPP(c_Relation_Oinv__image(_1582412, _1582410), _1582414), _1582416)) = hAPP(hAPP(c_Relation_Oinv__image(_1582412, _1582410), hAPP(c_Relation_Oconverse(_1582412, _1582412), _1582414)), _1582416))], (6322 ^ _776545) ^ [_878408, _878410, _878412] : [_878408 = _878410, 6325 ^ _776545 : [(6328 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878412, tc_HOL_Obool)), _878410), _878408)))], (6326 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878412, tc_HOL_Obool)), _878408), _878410)))]]], (13222 ^ _776545) ^ [_1010516, _1010518, _1010520, _1010522] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1010516), _1010518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010516, tc_HOL_Obool)), _1010518), _1010520)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010516, tc_Nat_Onat), _1010522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010516, tc_HOL_Obool)), _1010520), _1010518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010516, tc_Nat_Onat), _1010522), _1010520)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010516, tc_Nat_Onat), _1010522), _1010518)))], (48456 ^ _776545) ^ [_1752767, _1752769, _1752771] : [-(hAPP(c_New__DSequence_Oneg__single(_1752767, _1752769), _1752771) = c_Lazy__Sequence_Ohb__single(_1752767, _1752769))], (16340 ^ _776545) ^ [_1071385, _1071387] : [class_Groups_Ogroup__add(_1071385), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071385), _1071387), c_Groups_Ozero__class_Ozero(_1071385)) = _1071387)], (44745 ^ _776545) ^ [_1671139, _1671141, _1671143, _1671145] : [-(hAPP(hAPP(c_List_Omap(_1671139, _1671141), _1671143), c_List_Obutlast(_1671139, _1671145)) = c_List_Obutlast(_1671141, hAPP(hAPP(c_List_Omap(_1671139, _1671141), _1671143), _1671145)))], (21149 ^ _776545) ^ [_1159133] : [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), _1159133))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159133) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1159133)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (38320 ^ _776545) ^ [_1510544, _1510546] : [c_FunDef_Oreduction__pair(_1510544, _1510546), 38323 ^ _776545 : [(38326 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510544, _1510544, _1510544), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool), tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool)), _1510546)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool), tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool)), _1510546))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool), tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool)), _1510546))))], (38324 ^ _776545) ^ [] : [-(c_Wellfounded_Owf(_1510544, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool), tc_fun(tc_prod(_1510544, _1510544), tc_HOL_Obool)), _1510546)))]]], (28095 ^ _776545) ^ [_1281231, _1281233] : [class_Rings_Osemiring__1(_1281231), 28098 ^ _776545 : [(28105 ^ _776545) ^ [] : [_1281233 = c_Groups_Ozero__class_Ozero(_1281231), -(c_Int_Oiszero(_1281231, _1281233))], (28099 ^ _776545) ^ [] : [c_Int_Oiszero(_1281231, _1281233), -(_1281233 = c_Groups_Ozero__class_Ozero(_1281231))]]], (48728 ^ _776545) ^ [_1758646, _1758648, _1758650, _1758652] : [-(hBOOL(hAPP(hAPP(c_member(_1758646), _1758648), hAPP(c_List_Oset(_1758646), c_List_Oreplicate(_1758646, _1758650, _1758652))))), _1758648 = _1758652, -(_1758650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47878 ^ _776545) ^ [_1740622, _1740624, _1740626, _1740628, _1740630] : [-(hAPP(c_List_Ofilter(_1740622, _1740624), _1740626) = hAPP(hAPP(c_List_Olist_OCons(_1740622), _1740628), _1740630)), 47879 ^ _776545 : [(47880 ^ _776545) ^ [_1740750, _1740752] : [_1740626 = hAPP(hAPP(c_List_Oappend(_1740622), _1740752), hAPP(hAPP(c_List_Olist_OCons(_1740622), _1740628), _1740750)), 47886 ^ _776545 : [(47889 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1740624, 47885 ^ [_1740622, _1740624, _1740626, _1740628, _1740630, _1740750, _1740752])))], (47887 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740622), 47885 ^ [_1740622, _1740624, _1740626, _1740628, _1740630, _1740750, _1740752]), hAPP(c_List_Oset(_1740622), _1740752))))]], hBOOL(hAPP(_1740624, _1740628)), _1740630 = hAPP(c_List_Ofilter(_1740622, _1740624), _1740750)]]], (47263 ^ _776545) ^ [_1726842, _1726844, _1726846, _1726848] : [hBOOL(hAPP(_1726842, _1726844)), -(c_List_OtakeWhile(_1726846, _1726842, hAPP(hAPP(c_List_Olist_OCons(_1726846), _1726844), _1726848)) = hAPP(hAPP(c_List_Olist_OCons(_1726846), _1726844), c_List_OtakeWhile(_1726846, _1726842, _1726848)))], (44605 ^ _776545) ^ [_1668536, _1668538, _1668540] : [_1668536 = c_List_Olist_ONil(_1668538), -(c_List_Olast(_1668538, hAPP(hAPP(c_List_Oappend(_1668538), _1668540), _1668536)) = c_List_Olast(_1668538, _1668540))], (7174 ^ _776545) ^ [_893414, _893416, _893418] : [hBOOL(hAPP(hAPP(c_member(_893414), _893416), _893418)), -(hAPP(hAPP(c_Set_Oinsert(_893414), _893416), _893418) = _893418)], (40136 ^ _776545) ^ [_1558516, _1558518, _1558520, _1558522, _1558524, _1558526] : [c_Finite__Set_Ofolding(_1558516, _1558518, _1558520, _1558522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558516), _1558524)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558516), _1558526)), -(hAPP(c_Fun_Ocomp(_1558518, _1558518, _1558518, hAPP(_1558522, _1558526)), hAPP(_1558522, _1558524)) = hAPP(c_Fun_Ocomp(_1558518, _1558518, _1558518, hAPP(_1558522, _1558524)), hAPP(_1558522, _1558526)))], (7041 ^ _776545) ^ [_891074, _891076, _891078, _891080, _891082] : [class_Complete__Lattice_Ocomplete__lattice(_891074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891076, tc_HOL_Obool)), _891078), _891080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891074), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891076, _891074), _891080), _891082)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891076, _891074), _891078), _891082))))], (26507 ^ _776545) ^ [_1254993, _1254995] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1254993) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1254995), 26510 ^ _776545 : [(26513 ^ _776545) ^ [] : [-(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), _1254995))))], (26511 ^ _776545) ^ [] : [-(_1254993 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1254995)))]]], (40120 ^ _776545) ^ [_1558114, _1558116, _1558118, _1558120, _1558122, _1558124, _1558126] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1558114, _1558116, _1558118), hAPP(c_Fun_Ocomp(_1558120, tc_fun(_1558116, _1558118), _1558114, _1558122), _1558124)), _1558126) = hAPP(hAPP(_1558122, hAPP(_1558124, hAPP(c_Product__Type_Ofst(_1558114, _1558116), _1558126))), hAPP(c_Product__Type_Osnd(_1558114, _1558116), _1558126)))], (4432 ^ _776545) ^ [_843836, _843838] : [_843838 = _843836, -(c_Lazy__Sequence_Osingle(_843838) = c_Lazy__Sequence_Osingle(_843836))], (25257 ^ _776545) ^ [_1233761] : [class_Int_Onumber__ring(_1233761), -(hAPP(c_Int_Onumber__class_Onumber__of(_1233761), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233761), c_Groups_Oone__class_Oone(_1233761)))], (28865 ^ _776545) ^ [_1294046, _1294048] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1294046)), c_Int_OBit0(_1294048)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1294046), _1294048)))], (51851 ^ _776545) ^ [_1824543, _1824545] : [class_Lattices_Obounded__lattice(_1824543), -(class_Lattices_Obounded__lattice(tc_fun(_1824545, _1824543)))], (47064 ^ _776545) ^ [_1722565, _1722567, _1722569] : [_1722567 = _1722569, -(hAPP(c_List_Orev(_1722565), _1722567) = hAPP(c_List_Orev(_1722565), _1722569))], (25018 ^ _776545) ^ [_1229613, _1229615, _1229617] : [_1229613 = 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), _1229613), _1229615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229613), _1229617)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38356 ^ _776545) ^ [_1511555, _1511557] : [c_Wellfounded_Owf(_1511555, _1511557), -(c_Wellfounded_Owf(tc_List_Olist(_1511555), c_List_Olenlex(_1511555, _1511557)))], (14219 ^ _776545) ^ [_1032325] : [14221 ^ _776545 : [(14224 ^ _776545) ^ [_1032435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14220 ^ [_1032325, _1032435]), _1032435))], (14222 ^ _776545) ^ [_1032401] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14220 ^ [_1032325, _1032401]), _1032325)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1032325)))], (5052 ^ _776545) ^ [_853558, _853560, _853562, _853564, _853566, _853568] : [-(c_Product__Type_Oprod_Oprod__case(_853568, _853564, _853560) = c_Product__Type_Oprod_Oprod__case(_853566, _853562, _853558)), _853568 = _853566, _853564 = _853562, _853560 = _853558], (45688 ^ _776545) ^ [_1693147, _1693149] : [-(c_Enum_On__lists(_1693147, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1693149) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1693147)), c_List_Olist_ONil(_1693147)), c_List_Olist_ONil(tc_List_Olist(_1693147))))], (2956 ^ _776545) ^ [_820420, _820422, _820424, _820426] : [-(c_Nitpick_Oinverse__frac(_820426, _820422) = c_Nitpick_Oinverse__frac(_820424, _820420)), _820426 = _820424, _820422 = _820420], (52465 ^ _776545) ^ [_1830946, _1830948] : [-(hAPP(c_COMBI(_1830946), _1830948) = _1830948)], (30012 ^ _776545) ^ [_1314802] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1314802) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16188 ^ _776545) ^ [_1069101, _1069103] : [class_Groups_Omonoid__add(_1069101), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069101), _1069103), c_Groups_Ozero__class_Ozero(_1069101)) = _1069103)], (44848 ^ _776545) ^ [_1673783, _1673785, _1673787] : [-(hAPP(hAPP(c_List_Omap(_1673783, _1673785), _1673787), c_List_Olist_ONil(_1673783)) = c_List_Olist_ONil(_1673785))], (25311 ^ _776545) ^ [_1234680, _1234682] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1234680), _1234682) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1234680 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1234680 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35858 ^ _776545) ^ [_1446753, _1446755, _1446757] : [class_Orderings_Olinorder(_1446753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446753), _1446755)), -(_1446755 = c_Orderings_Obot__class_Obot(tc_fun(_1446753, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446753), _1446757)), -(_1446757 = c_Orderings_Obot__class_Obot(tc_fun(_1446753, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1446753), c_Big__Operators_Olattice_OInf__fin(_1446753, c_Orderings_Oord__class_Omin(_1446753), _1446755)), c_Big__Operators_Olattice_OInf__fin(_1446753, c_Orderings_Oord__class_Omin(_1446753), _1446757)) = c_Big__Operators_Olattice_OInf__fin(_1446753, c_Orderings_Oord__class_Omin(_1446753), hAPP(c_Set_OCollect(_1446753), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_HOL_Obool), tc_HOL_Obool, _1446753), c_HOL_OEx(_1446753)), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool)), tc_fun(_1446753, tc_HOL_Obool), _1446753), hAPP(c_COMBB(tc_fun(_1446753, tc_HOL_Obool), tc_HOL_Obool, _1446753), c_HOL_OEx(_1446753))), hAPP(hAPP(c_COMBC(_1446753, tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool)), tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_fun(tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool))), tc_fun(tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool)), tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool))), _1446753), c_COMBS(_1446753, tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_fun(_1446753, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1446753, tc_fun(tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool))), _1446753), hAPP(c_COMBB(tc_fun(_1446753, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool)), _1446753), c_COMBS(_1446753, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool)), tc_fun(_1446753, tc_fun(_1446753, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1446753), hAPP(c_COMBB(tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1446753), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1446753), c_fconj))), hAPP(hAPP(c_COMBC(_1446753, tc_fun(_1446753, tc_fun(_1446753, _1446753)), tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1446753, _1446753), tc_fun(_1446753, tc_HOL_Obool)), tc_fun(tc_fun(_1446753, tc_fun(_1446753, _1446753)), tc_fun(_1446753, tc_fun(_1446753, tc_HOL_Obool))), _1446753), c_COMBB(tc_fun(_1446753, _1446753), tc_fun(_1446753, tc_HOL_Obool), _1446753)), hAPP(hAPP(c_COMBB(tc_fun(_1446753, tc_HOL_Obool), tc_fun(tc_fun(_1446753, _1446753), tc_fun(_1446753, tc_HOL_Obool)), _1446753), c_COMBB(_1446753, tc_HOL_Obool, _1446753)), c_fequal))), c_Orderings_Oord__class_Omax(_1446753)))))), hAPP(hAPP(c_COMBC(_1446753, tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1446753, tc_HOL_Obool), tc_fun(_1446753, tc_HOL_Obool)), _1446753), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1446753)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1446753), c_fconj), hAPP(hAPP(c_COMBC(_1446753, tc_fun(_1446753, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446753)), _1446755)))), hAPP(hAPP(c_COMBC(_1446753, tc_fun(_1446753, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446753)), _1446757))))))))], (20013 ^ _776545) ^ [_1137862, _1137864, _1137866, _1137868] : [class_Fields_Olinordered__field__inverse__zero(_1137862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137862), _1137864), _1137866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137862), _1137868), c_Groups_Ozero__class_Ozero(_1137862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137862), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137862), _1137866), _1137868)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137862), _1137864), _1137868))))], (52121 ^ _776545) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (25875 ^ _776545) ^ [_1244591, _1244593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244591, _1244593)), _1244591)))], (49448 ^ _776545) ^ [_1776253, _1776255] : [c_Equiv__Relations_Oequivp(_1776253, _1776255), 49451 ^ _776545 : [(49456 ^ _776545) ^ [] : [-(c_Predicate_Otransp(_1776253, _1776255))], (49454 ^ _776545) ^ [] : [-(c_Predicate_Osymp(_1776253, _1776255))], (49452 ^ _776545) ^ [] : [-(c_Predicate_Oreflp(_1776253, _1776255))]]], (43002 ^ _776545) ^ [_1633707, _1633709] : [-(_1633707 = c_List_Olist_ONil(_1633709)), hBOOL(hAPP(c_List_Odistinct(_1633709), _1633707)), -(hBOOL(hAPP(c_List_Odistinct(_1633709), c_List_Obutlast(_1633709, _1633707))))], (52519 ^ _776545) ^ [_1831730, _1831732] : [hBOOL(hAPP(hAPP(c_fconj, _1831730), _1831732)), -(hBOOL(_1831732))], (3718 ^ _776545) ^ [_832293, _832295] : [_832295 = _832293, -(c_List_Omonoid__add__class_Olistsum(_832295) = c_List_Omonoid__add__class_Olistsum(_832293))], (33605 ^ _776545) ^ [_1395404, _1395406, _1395408, _1395410, _1395412, _1395414] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395404, tc_fun(_1395406, tc_fun(_1395408, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1395404, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_fun(_1395406, tc_fun(_1395408, tc_HOL_Obool)), _1395404), hAPP(c_COMBC(_1395406, tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_fun(_1395408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395408, tc_fun(tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_fun(_1395408, tc_HOL_Obool)), _1395406), c_COMBC(_1395408, tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395408, tc_prod(_1395406, _1395408)), tc_fun(_1395408, tc_fun(tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_HOL_Obool)), _1395406), hAPP(c_COMBB(tc_prod(_1395406, _1395408), tc_fun(tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool), tc_HOL_Obool), _1395408), c_member(tc_prod(_1395406, _1395408)))), c_Product__Type_OPair(_1395406, _1395408))))), _1395410)), _1395412), _1395414)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1395406, _1395408)), hAPP(hAPP(c_Product__Type_OPair(_1395406, _1395408), _1395412), _1395414)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1395404, tc_fun(tc_prod(_1395406, _1395408), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1395404, tc_HOL_Obool))), _1395410))))], (15164 ^ _776545) ^ [_1050211, _1050213] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050211), _1050213) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1050211 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1050213 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (41729 ^ _776545) ^ [_1598292, _1598294, _1598296, _1598298, _1598300] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598292), tc_List_Olist(_1598292))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598292), tc_List_Olist(_1598292)), _1598294), _1598296)), hAPP(c_List_Olexn(_1598292, _1598298), _1598300))), 41732 ^ _776545 : [(41735 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598292)), _1598296) = _1598300)], (41733 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598292)), _1598294) = _1598300)]]], (15476 ^ _776545) ^ [_1056463, _1056465, _1056467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056463), _1056465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1056463), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056463, tc_HOL_Obool)), _1056465), hAPP(hAPP(c_Set_Oinsert(_1056463), _1056467), c_Orderings_Obot__class_Obot(tc_fun(_1056463, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1056463), _1056465))))], (45189 ^ _776545) ^ [_1681768] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1681768)) = _1681768)], (22687 ^ _776545) ^ [_1187599, _1187601] : [22688 ^ _776545 : [(22691 ^ _776545) ^ [] : [_1187599 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22689 ^ _776545) ^ [] : [_1187601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187599), _1187601) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52569 ^ _776545) ^ [_1832347, _1832349] : [v_P(_1832349, _1832347), -(v_P_H(_1832349, _1832347))], (30406 ^ _776545) ^ [_1322042, _1322044, _1322046] : [class_Orderings_Olinorder(_1322042), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322042), _1322044)), -(_1322044 = c_Orderings_Obot__class_Obot(tc_fun(_1322042, tc_HOL_Obool))), 30417 ^ _776545 : [(30418 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322042), _1322046), hAPP(c_Finite__Set_Ofold1(_1322042, c_Orderings_Oord__class_Omin(_1322042)), _1322044))), 30421 ^ _776545 : [(30422 ^ _776545) ^ [_1322335] : [hBOOL(hAPP(hAPP(c_member(_1322042), _1322335), _1322044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322042), _1322046), _1322335)))]]], (30428 ^ _776545) ^ [] : [30430 ^ _776545 : [(30433 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322042), _1322046), 30429 ^ [_1322042, _1322044, _1322046]))], (30431 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322042), 30429 ^ [_1322042, _1322044, _1322046]), _1322044)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322042), _1322046), hAPP(c_Finite__Set_Ofold1(_1322042, c_Orderings_Oord__class_Omin(_1322042)), _1322044))))]]], (36938 ^ _776545) ^ [_1477902, _1477904, _1477906, _1477908, _1477910, _1477912] : [c_Equiv__Relations_Oequiv(_1477902, _1477904, _1477906), c_Equiv__Relations_Ocongruent(_1477902, tc_fun(_1477908, tc_HOL_Obool), _1477906, _1477910), hBOOL(hAPP(hAPP(c_member(_1477902), _1477912), _1477904)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477902, tc_fun(_1477908, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1477902, _1477902, _1477906), hAPP(hAPP(c_Set_Oinsert(_1477902), _1477912), c_Orderings_Obot__class_Obot(tc_fun(_1477902, tc_HOL_Obool))))), _1477910) = hAPP(_1477910, _1477912))], (28999 ^ _776545) ^ [_1296387, _1296389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296387)), c_Int_OBit0(_1296389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296387), _1296389)))], (11570 ^ _776545) ^ [_978851, _978853] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_978851, _978853)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_978851, _978853), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978851), c_Orderings_Otop__class_Otop(tc_fun(_978851, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978853), c_Orderings_Otop__class_Otop(tc_fun(_978853, tc_HOL_Obool))))], (23161 ^ _776545) ^ [] : [-(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))))], (44493 ^ _776545) ^ [_1666549, _1666551, _1666553, _1666555, _1666557] : [class_Orderings_Olinorder(_1666549), hBOOL(hAPP(c_List_Odistinct(_1666551), _1666553)), -(hBOOL(hAPP(c_List_Odistinct(_1666551), c_List_Olinorder__class_Oinsort__insert__key(_1666551, _1666549, _1666555, _1666557, _1666553))))], (45579 ^ _776545) ^ [_1690488, _1690490, _1690492, _1690494, _1690496] : [c_List_Olist__all2(_1690488, _1690490, _1690492, _1690494, _1690496), 45582 ^ _776545 : [(45585 ^ _776545) ^ [_1690651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690651), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690488)), _1690494))), -(hBOOL(hAPP(hAPP(_1690492, hAPP(hAPP(c_List_Onth(_1690488), _1690494), _1690651)), hAPP(hAPP(c_List_Onth(_1690490), _1690496), _1690651))))], (45583 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690488)), _1690494) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690490)), _1690496))]]], (13360 ^ _776545) ^ [_1013664, _1013666, _1013668, _1013670, _1013672] : [class_Groups_Ocomm__monoid__add(_1013664), class_Groups_Oordered__cancel__ab__semigroup__add(_1013664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013666), _1013668)), -(_1013668 = c_Orderings_Obot__class_Obot(tc_fun(_1013666, tc_HOL_Obool))), 13378 ^ _776545 : [(13381 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013664), hAPP(_1013670, 13377 ^ [_1013664, _1013666, _1013668, _1013670, _1013672])), hAPP(_1013672, 13377 ^ [_1013664, _1013666, _1013668, _1013670, _1013672])))], (13379 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013666), 13377 ^ [_1013664, _1013666, _1013668, _1013670, _1013672]), _1013668)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013664), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013666, _1013664), _1013670), _1013668)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013666, _1013664), _1013672), _1013668))))], (33763 ^ _776545) ^ [] : [-(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)))], (8829 ^ _776545) ^ [_928425, _928427, _928429, _928431, _928433] : [class_Groups_Oordered__ab__group__add(_928425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928425), _928427), _928429) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_928425), _928431), _928433), 8836 ^ _776545 : [(8843 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928425), _928431), _928433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928425), _928427), _928429)))], (8837 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928425), _928427), _928429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_928425), _928431), _928433)))]]], (5116 ^ _776545) ^ [_854602, _854604] : [_854604 = _854602, -(c_Orderings_Otop__class_Otop(_854604) = c_Orderings_Otop__class_Otop(_854602))], (35024 ^ _776545) ^ [_1430161, _1430163, _1430165, _1430167] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430161, _1430163), _1430165)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430161, _1430163), _1430167)), -(_1430165 = _1430167)], (13015 ^ _776545) ^ [_1006127, _1006129, _1006131, _1006133, _1006135, _1006137] : [c_Finite__Set_Ofun__left__comm(_1006127, _1006129, _1006131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006127), _1006133)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1006127, _1006129, _1006131), _1006135), hAPP(hAPP(c_Set_Oinsert(_1006127), _1006137), _1006133)) = hAPP(hAPP(_1006131, _1006137), hAPP(hAPP(c_Finite__Set_Ofold(_1006127, _1006129, _1006131), _1006135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006127, tc_HOL_Obool)), _1006133), hAPP(hAPP(c_Set_Oinsert(_1006127), _1006137), c_Orderings_Obot__class_Obot(tc_fun(_1006127, tc_HOL_Obool)))))))], (7846 ^ _776545) ^ [_908620, _908622] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908620, tc_HOL_Obool)), _908622), c_Orderings_Obot__class_Obot(tc_fun(_908620, tc_HOL_Obool))) = _908622)], (30634 ^ _776545) ^ [_1326228, _1326230] : [class_Orderings_Olinorder(_1326228), -(c_Big__Operators_Olattice_OInf__fin(_1326228, c_Orderings_Oord__class_Omin(_1326228), hAPP(hAPP(c_Set_Oinsert(_1326228), _1326230), c_Orderings_Obot__class_Obot(tc_fun(_1326228, tc_HOL_Obool)))) = _1326230)], (44383 ^ _776545) ^ [_1664167, _1664169, _1664171, _1664173, _1664175] : [class_Orderings_Olinorder(_1664167), 44386 ^ _776545 : [(44395 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664169), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1664169, _1664167, _1664171), _1664173), _1664175)))), -(hBOOL(hAPP(hAPP(c_member(_1664169), _1664173), hAPP(c_List_Oset(_1664169), _1664175)))), hBOOL(hAPP(c_List_Odistinct(_1664169), _1664175))], (44387 ^ _776545) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1664169), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1664169, _1664167, _1664171), _1664173), _1664175))), 44390 ^ _776545 : [(44393 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664169), _1664175)))], (44391 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1664169), _1664173), hAPP(c_List_Oset(_1664169), _1664175)))]]]]], (37961 ^ _776545) ^ [_1501580, _1501582, _1501584, _1501586] : [hAPP(hAPP(c_Relation_Orel__comp(_1501580, _1501580, _1501580), _1501582), _1501584) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501580, _1501580), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501580, _1501580, _1501580), _1501582), _1501586) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501580, _1501580), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1501580, _1501580, _1501580), _1501582), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501580, _1501580), tc_HOL_Obool)), _1501584), _1501586)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501580, _1501580), tc_HOL_Obool)))], (13544 ^ _776545) ^ [_1017655, _1017657, _1017659, _1017661] : [class_Groups_Ocancel__semigroup__add(_1017655), 13547 ^ _776545 : [(13554 ^ _776545) ^ [] : [_1017659 = _1017661, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017655), _1017657), _1017659) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017655), _1017657), _1017661))], (13548 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017655), _1017657), _1017659) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017655), _1017657), _1017661), -(_1017659 = _1017661)]]], (14536 ^ _776545) ^ [_1038723, _1038725, _1038727] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038723), _1038725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038723), _1038727), -(_1038725 = _1038727)], (19995 ^ _776545) ^ [_1137427, _1137429, _1137431, _1137433, _1137435] : [class_Fields_Ofield__inverse__zero(_1137427), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137427), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137427), _1137429), _1137431)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137427), _1137433), _1137435)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137427), _1137429), _1137433)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137427), _1137431), _1137435)))], (2128 ^ _776545) ^ [_807418, _807420, _807422, _807424] : [-(c_Nat__Transfer_Otsub(_807424, _807420) = c_Nat__Transfer_Otsub(_807422, _807418)), _807424 = _807422, _807420 = _807418], (6404 ^ _776545) ^ [_879946, _879948, _879950] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_879946, tc_HOL_Obool)), _879948), _879950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879946, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_879946, tc_HOL_Obool), _879950)), _879948)))], (7928 ^ _776545) ^ [_910474, _910476, _910478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910474, tc_HOL_Obool)), _910476), _910478)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910474, tc_HOL_Obool)), _910478), _910476) = _910478)], (2814 ^ _776545) ^ [_818219, _818221, _818223, _818225, _818227, _818229, _818231, _818233] : [-(c_Product__Type_Oapfst(_818233, _818229, _818225, _818221) = c_Product__Type_Oapfst(_818231, _818227, _818223, _818219)), _818233 = _818231, _818229 = _818227, _818225 = _818223, _818221 = _818219], (3164 ^ _776545) ^ [_823648, _823650, _823652, _823654] : [-(c_Finite__Set_Ofold1(_823654, _823650) = c_Finite__Set_Ofold1(_823652, _823648)), _823654 = _823652, _823650 = _823648], (38283 ^ _776545) ^ [_1509883, _1509885] : [38285 ^ _776545 : [(38286 ^ _776545) ^ [_1509908] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509883, _1509883)), hAPP(hAPP(c_Product__Type_OPair(_1509883, _1509883), hAPP(38284 ^ [_1509883, _1509885], hAPP(c_Nat_OSuc, _1509908))), hAPP(38284 ^ [_1509883, _1509885], _1509908))), _1509885)))]], -(c_Wellfounded_Owf(_1509883, _1509885))], (16889 ^ _776545) ^ [_1080439, _1080441, _1080443, _1080445] : [class_Groups_Oordered__comm__monoid__add(_1080439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080439), c_Groups_Ozero__class_Ozero(_1080439)), _1080441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080439), _1080443), _1080445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080439), _1080443), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080439), _1080445), _1080441))))], (22151 ^ _776545) ^ [_1178233, _1178235] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178233)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178235)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178233), _1178235)))], (34085 ^ _776545) ^ [_1409413, _1409415, _1409417, _1409419] : [class_Groups_Ocomm__monoid__add(_1409413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1409415), _1409417)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409413), _1409419), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1409415, _1409417)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409413), hAPP(_1409419, _1409415)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409413), _1409419), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1409415, _1409417))))], (14196 ^ _776545) ^ [_1031906] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1031906))))], (49379 ^ _776545) ^ [_1773942, _1773944, _1773946, _1773948] : [class_Complete__Lattice_Ocomplete__lattice(_1773942), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1773944, _1773942), _1773946), _1773948) = c_Complete__Lattice_OSup__class_OSup(_1773942, hAPP(c_Set_OCollect(_1773942), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool), tc_HOL_Obool, _1773942), c_HOL_OEx(tc_fun(_1773944, _1773942))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool), tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool), _1773942), hAPP(c_COMBS(tc_fun(_1773944, _1773942), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1773944, _1773942)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1773944, _1773942), tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1773944, _1773942))), _1773946)))), hAPP(hAPP(c_COMBC(_1773942, tc_fun(tc_fun(_1773944, _1773942), _1773942), tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1773942, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1773944, _1773942), _1773942), tc_fun(tc_fun(_1773944, _1773942), tc_HOL_Obool)), _1773942), c_COMBB(_1773942, tc_HOL_Obool, tc_fun(_1773944, _1773942))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1773944, _1773942), _1773944, _1773942), c_COMBI(tc_fun(_1773944, _1773942))), _1773948)))))))], (33208 ^ _776545) ^ [_1385048, _1385050, _1385052, _1385054, _1385056] : [-(hAPP(hAPP(c_Set_Oinsert(_1385048), _1385050), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385052, tc_fun(_1385048, tc_HOL_Obool)), _1385054), _1385056)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1385052, tc_fun(_1385048, tc_HOL_Obool)), _1385054), hAPP(hAPP(c_COMBB(tc_fun(_1385048, tc_HOL_Obool), tc_fun(_1385048, tc_HOL_Obool), _1385052), hAPP(c_Set_Oinsert(_1385048), _1385050)), _1385056)))], (6748 ^ _776545) ^ [_885716, _885718, _885720] : [class_Orderings_Opreorder(_885716), _885718 = _885720, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885716), _885718), _885720)))], (48710 ^ _776545) ^ [_1758307, _1758309, _1758311] : [_1758309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1758307) = c_List_Oreplicate(_1758307, _1758309, _1758311))], (36065 ^ _776545) ^ [_1455358, _1455360, _1455362] : [class_Orderings_Olinorder(_1455358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455358), _1455360)), -(_1455360 = c_Orderings_Obot__class_Obot(tc_fun(_1455358, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1455358), _1455362), c_Big__Operators_Olattice_OSup__fin(_1455358, c_Orderings_Oord__class_Omax(_1455358), _1455360)) = c_Big__Operators_Olattice_OSup__fin(_1455358, c_Orderings_Oord__class_Omax(_1455358), hAPP(c_Set_OCollect(_1455358), hAPP(hAPP(c_COMBB(tc_fun(_1455358, tc_HOL_Obool), tc_HOL_Obool, _1455358), c_HOL_OEx(_1455358)), hAPP(hAPP(c_COMBC(_1455358, tc_fun(_1455358, tc_HOL_Obool), tc_fun(_1455358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455358, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1455358, tc_HOL_Obool), tc_fun(_1455358, tc_HOL_Obool)), _1455358), c_COMBS(_1455358, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455358, tc_HOL_Obool), tc_fun(_1455358, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1455358), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1455358), c_fconj)), hAPP(hAPP(c_COMBC(_1455358, tc_fun(_1455358, _1455358), tc_fun(_1455358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455358, tc_HOL_Obool), tc_fun(tc_fun(_1455358, _1455358), tc_fun(_1455358, tc_HOL_Obool)), _1455358), c_COMBB(_1455358, tc_HOL_Obool, _1455358)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1455358), _1455362))))), hAPP(hAPP(c_COMBC(_1455358, tc_fun(_1455358, tc_HOL_Obool), tc_HOL_Obool), c_member(_1455358)), _1455360))))))], (10691 ^ _776545) ^ [_960569, _960571] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960569, tc_HOL_Obool)), _960571), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960569, tc_HOL_Obool)), _960571)) = c_Orderings_Otop__class_Otop(tc_fun(_960569, tc_HOL_Obool)))], (50101 ^ _776545) ^ [_1788679, _1788681, _1788683, _1788685, _1788687] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1788679, _1788681, _1788683, _1788685), _1788687) = c_Hilbert__Choice_OEps(_1788679, hAPP(hAPP(c_COMBS(_1788679, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1788679), c_fconj), hAPP(hAPP(c_COMBC(_1788679, tc_fun(_1788679, tc_HOL_Obool), tc_HOL_Obool), c_member(_1788679)), _1788683))), hAPP(hAPP(c_COMBC(_1788679, _1788681, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1788681, tc_fun(_1788681, tc_HOL_Obool), _1788679), c_fequal), _1788685)), _1788687))))], (52427 ^ _776545) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (41720 ^ _776545) ^ [_1598024, _1598026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41721 ^ [_1598024, _1598026]), hAPP(_1598024, 41721 ^ [_1598024, _1598026]))), -(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)), _1598024)), _1598026)))))], (7548 ^ _776545) ^ [_901036, _901038, _901040, _901042] : [hBOOL(hAPP(_901036, _901038)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901040, tc_HOL_Obool)), _901036), _901042), _901038)))], (30282 ^ _776545) ^ [_1319729, _1319731, _1319733, _1319735] : [class_Orderings_Olinorder(_1319729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319729), _1319731), _1319733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319729), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319729), _1319731), _1319735)), _1319733)))], (34397 ^ _776545) ^ [_1416822, _1416824] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416822), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 34400 ^ _776545 : [(34409 ^ _776545) ^ [] : [-(c_Nitpick_Onorm__frac(_1416824, _1416822) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1416824), _1416822)), 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), _1416824))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1416822)))), -(_1416824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1416822 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34401 ^ _776545) ^ [] : [34402 ^ _776545 : [(34405 ^ _776545) ^ [] : [_1416822 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (34403 ^ _776545) ^ [] : [_1416824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1416824, _1416822) = 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)))]]], (44749 ^ _776545) ^ [_1671257, _1671259] : [-(hAPP(hAPP(c_List_Omap(_1671257, _1671257), c_COMBI(_1671257)), _1671259) = _1671259)], (1494 ^ _776545) ^ [_798084, _798086] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_798084)), _798086 = _798084, class_Groups_Oordered__cancel__ab__semigroup__add(_798086)], (1434 ^ _776545) ^ [_797334, _797336] : [-(class_Orderings_Otop(_797334)), _797336 = _797334, class_Orderings_Otop(_797336)], (10861 ^ _776545) ^ [_963925, _963927, _963929] : [class_Orderings_Olinorder(_963925), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963925), _963927), _963929)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963925, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_963925), _963927)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963925, _963927), _963929)) = hAPP(c_SetInterval_Oord__class_OlessThan(_963925), _963929))], (40755 ^ _776545) ^ [_1573922, _1573924] : [-(c_Transitive__Closure_Ortrancl(_1573922, _1573924) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573922, _1573922), tc_HOL_Obool)), c_Relation_OId(_1573922)), hAPP(hAPP(c_Relation_Orel__comp(_1573922, _1573922, _1573922), c_Transitive__Closure_Ortrancl(_1573922, _1573924)), _1573924)))], (39806 ^ _776545) ^ [_1550743, _1550745, _1550747, _1550749, _1550751, _1550753] : [hBOOL(hAPP(hAPP(c_member(_1550743), _1550745), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550747, _1550749, tc_fun(_1550743, tc_HOL_Obool)), _1550751), _1550753))), 39811 ^ _776545 : [(39814 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550743), _1550745), hAPP(hAPP(_1550751, 39809 ^ [_1550743, _1550745, _1550747, _1550749, _1550751, _1550753]), 39810 ^ [_1550743, _1550745, _1550747, _1550749, _1550751, _1550753]))))], (39812 ^ _776545) ^ [] : [-(_1550753 = hAPP(hAPP(c_Product__Type_OPair(_1550747, _1550749), 39809 ^ [_1550743, _1550745, _1550747, _1550749, _1550751, _1550753]), 39810 ^ [_1550743, _1550745, _1550747, _1550749, _1550751, _1550753]))]]], (44599 ^ _776545) ^ [_1668470, _1668472, _1668474] : [-(_1668470 = c_List_Olist_ONil(_1668472)), -(c_List_Olast(_1668472, hAPP(hAPP(c_List_Oappend(_1668472), _1668474), _1668470)) = c_List_Olast(_1668472, _1668470))], (41502 ^ _776545) ^ [_1592195, _1592197] : [-(c_Transitive__Closure_Ortrancl(_1592195, _1592197) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1592195, _1592195), 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(_1592195, _1592195), tc_HOL_Obool), tc_fun(tc_prod(_1592195, _1592195), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1592195, _1592195), tc_HOL_Obool)), _1592197)))], (48698 ^ _776545) ^ [_1758109, _1758111, _1758113] : [_1758111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1758109, _1758111, _1758113) = c_List_Olist_ONil(_1758109))], (47104 ^ _776545) ^ [_1723411, _1723413, _1723415, _1723417] : [_1723413 = hAPP(hAPP(c_List_Oappend(_1723411), hAPP(c_List_Orev(_1723411), _1723417)), hAPP(hAPP(c_List_Olist_OCons(_1723411), _1723415), c_List_Olist_ONil(_1723411))), -(hAPP(c_List_Orev(_1723411), _1723413) = hAPP(hAPP(c_List_Olist_OCons(_1723411), _1723415), _1723417))], (52241 ^ _776545) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (26040 ^ _776545) ^ [_1247183, _1247185, _1247187] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247183, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247185), _1247187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247185), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1247183), _1247185), _1247187))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247183, _1247185)))], (36456 ^ _776545) ^ [_1465768, _1465770, _1465772, _1465774, _1465776] : [hBOOL(hAPP(hAPP(c_member(_1465768), _1465770), hAPP(c_Relation_OImage(_1465772, _1465768, _1465774), hAPP(hAPP(c_Set_Oinsert(_1465772), _1465776), c_Orderings_Obot__class_Obot(tc_fun(_1465772, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465772, _1465768)), hAPP(hAPP(c_Product__Type_OPair(_1465772, _1465768), _1465776), _1465770)), _1465774)))], (34105 ^ _776545) ^ [_1410015, _1410017, _1410019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1410015), _1410017)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410015, tc_HOL_Obool)), _1410019), _1410017) = hAPP(hAPP(c_Finite__Set_Ofold(_1410015, tc_fun(_1410015, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1410015, tc_HOL_Obool), tc_fun(tc_fun(_1410015, tc_HOL_Obool), tc_fun(_1410015, tc_HOL_Obool)), _1410015), hAPP(c_COMBC(tc_fun(_1410015, tc_HOL_Obool), tc_fun(_1410015, tc_HOL_Obool), tc_fun(_1410015, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1410015, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1410015, tc_fun(_1410015, tc_HOL_Obool), tc_fun(_1410015, tc_HOL_Obool)), c_Set_Oinsert(_1410015)), c_Orderings_Obot__class_Obot(tc_fun(_1410015, tc_HOL_Obool))))), _1410019), _1410017))], (20137 ^ _776545) ^ [_1140118, _1140120, _1140122] : [class_Fields_Olinordered__field(_1140118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140118), _1140120), c_Groups_Ozero__class_Ozero(_1140118))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140118), _1140122), c_Groups_Ozero__class_Ozero(_1140118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140118), c_Groups_Ozero__class_Ozero(_1140118)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140118), _1140120), _1140122))))], (41445 ^ _776545) ^ [_1590620, _1590622, _1590624, _1590626] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590620, _1590620), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1590622), _1590624)), _1590626) = hAPP(hAPP(c_Relation_Orel__comp(_1590620, _1590620, _1590620), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590620, _1590620), tc_HOL_Obool), _1590622), _1590626)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590620, _1590620), tc_HOL_Obool), _1590624), _1590626)))], (52355 ^ _776545) ^ [_1829923, _1829925] : [-(class_Nat_Osize(tc_prod(_1829923, _1829925)))], (50528 ^ _776545) ^ [_1797870, _1797872, _1797874, _1797876] : [c_Fun_Obij__betw(_1797870, _1797872, _1797874, c_Orderings_Obot__class_Obot(tc_fun(_1797870, tc_HOL_Obool)), _1797876), -(_1797876 = c_Orderings_Obot__class_Obot(tc_fun(_1797872, tc_HOL_Obool)))], (40377 ^ _776545) ^ [_1563779, _1563781] : [40378 ^ _776545 : [(40379 ^ _776545) ^ [_1563825] : [hBOOL(hAPP(_1563779, _1563825))]], -(hBOOL(hAPP(_1563779, c_Hilbert__Choice_OEps(_1563781, _1563779))))], (24272 ^ _776545) ^ [] : [-(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))], (28207 ^ _776545) ^ [_1283031] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1283031)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1283031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37478 ^ _776545) ^ [_1489865, _1489867, _1489869, _1489871] : [-(_1489865 = c_Orderings_Obot__class_Obot(tc_fun(_1489867, tc_HOL_Obool))), 37481 ^ _776545 : [(37482 ^ _776545) ^ [] : [-(hAPP(c_Set_Oimage(_1489869, _1489867, 37489 ^ [_1489865, _1489867, _1489869, _1489871]), _1489871) = _1489865), 37483 ^ _776545 : [(37484 ^ _776545) ^ [_1490006] : [c_Fun_Oinj__on(_1489867, _1489869, _1490006, _1489865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489869, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489867, _1489869, _1490006), _1489865)), _1489871))]]], (37493 ^ _776545) ^ [] : [37494 ^ _776545 : [(37495 ^ _776545) ^ [_1490198] : [hAPP(c_Set_Oimage(_1489869, _1489867, _1490198), _1489871) = _1489865]], 37497 ^ _776545 : [(37500 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489869, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1489867, _1489869, 37496 ^ [_1489865, _1489867, _1489869, _1489871]), _1489865)), _1489871)))], (37498 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1489867, _1489869, 37496 ^ [_1489865, _1489867, _1489869, _1489871], _1489865))]]]]], (844 ^ _776545) ^ [_789163, _789165, _789167, _789169] : [-(c_Equiv__Relations_Opart__equivp(_789167, _789163)), c_Equiv__Relations_Opart__equivp(_789169, _789165), _789169 = _789167, _789165 = _789163], (25540 ^ _776545) ^ [_1238595, _1238597] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238595) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238597), 25543 ^ _776545 : [(25550 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238595)))), 25553 ^ _776545 : [(25560 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238597)))), -(_1238595 = _1238597)], (25554 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238597))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238595) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25544 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1238597)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28195 ^ _776545) ^ [_1282787, _1282789] : [class_Rings_Osemiring__1(_1282787), -(hBOOL(hAPP(hAPP(c_member(_1282787), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1282787), _1282789)), c_Nat_Osemiring__1__class_ONats(_1282787))))], (24646 ^ _776545) ^ [_1222455, _1222457, _1222459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222455)), 24649 ^ _776545 : [(24650 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1222457, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222459), _1222455)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222459, _1222455))), 24653 ^ _776545 : [(24654 ^ _776545) ^ [_1222656, _1222658] : [-(hBOOL(hAPP(hAPP(_1222457, _1222658), _1222656))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222656), _1222455)), _1222459 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222455), _1222658)), _1222656)]]], (24668 ^ _776545) ^ [] : [24671 ^ _776545 : [(24674 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24670 ^ [_1222455, _1222457, _1222459]), _1222455)))], (24676 ^ _776545) ^ [] : [-(_1222459 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222455), 24669 ^ [_1222455, _1222457, _1222459])), 24670 ^ [_1222455, _1222457, _1222459]))], (24678 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1222457, 24669 ^ [_1222455, _1222457, _1222459]), 24670 ^ [_1222455, _1222457, _1222459]))], (24672 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24670 ^ [_1222455, _1222457, _1222459])))]], -(hBOOL(hAPP(hAPP(_1222457, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222459), _1222455)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1222459, _1222455))))]]], (24050 ^ _776545) ^ [_1211937, _1211939] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211937), _1211939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1211939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24059 ^ _776545 : [(24062 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211937), _1211939)))], (24060 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211937)))]], 24063 ^ _776545 : [(24066 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211939), _1211937)))], (24064 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211937), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (4750 ^ _776545) ^ [_848845, _848847, _848849, _848851] : [-(c_Product__Type_Osnd(_848851, _848847) = c_Product__Type_Osnd(_848849, _848845)), _848851 = _848849, _848847 = _848845], (46409 ^ _776545) ^ [_1709819, _1709821] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1709819, _1709821) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1709819), _1709821)))], (38193 ^ _776545) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38558 ^ _776545) ^ [_1516136, _1516138, _1516140, _1516142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516136, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1516138, _1516136), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516138, _1516136), tc_HOL_Obool)), _1516140), _1516142))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516136, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1516138, _1516136), _1516140)), hAPP(c_Relation_ORange(_1516138, _1516136), _1516142)))))], (21815 ^ _776545) ^ [_1171840, _1171842] : [_1171840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171842), _1171840) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (42413 ^ _776545) ^ [_1618515, _1618517, _1618519] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618515)), _1618517), c_List_Olists(_1618515, _1618519))), 42416 ^ _776545 : [(42417 ^ _776545) ^ [_1618623] : [hBOOL(hAPP(hAPP(c_member(_1618515), _1618623), hAPP(c_List_Oset(_1618515), _1618517))), -(hBOOL(hAPP(hAPP(c_member(_1618515), _1618623), _1618519)))]]], (7374 ^ _776545) ^ [_897473, _897475, _897477, _897479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897473, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897473, tc_HOL_Obool)), _897475), hAPP(hAPP(c_Set_Oinsert(_897473), _897477), c_Orderings_Obot__class_Obot(tc_fun(_897473, tc_HOL_Obool))))), _897479)), hBOOL(hAPP(hAPP(c_member(_897473), _897477), _897475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897473, tc_HOL_Obool)), _897475), hAPP(hAPP(c_Set_Oinsert(_897473), _897477), _897479))))], (20743 ^ _776545) ^ [_1151054, _1151056, _1151058, _1151060] : [class_Fields_Ofield__inverse__zero(_1151054), -(_1151056 = c_Groups_Ozero__class_Ozero(_1151054)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151054), _1151058), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151054), _1151060), _1151056)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151054), _1151060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151054), _1151058), _1151056))), _1151056))], (23730 ^ _776545) ^ [_1206322] : [23731 ^ _776545 : [(23732 ^ _776545) ^ [_1206379] : [hBOOL(hAPP(_1206322, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206379)))]], 23734 ^ _776545 : [(23737 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1206322, 23733 ^ [_1206322])))], (23735 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23733 ^ [_1206322])))]]], (23811 ^ _776545) ^ [_1207841, _1207843, _1207845] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207841)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207843)), _1207845)) = 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), _1207841), _1207843))), _1207845))], (43476 ^ _776545) ^ [_1643527, _1643529, _1643531, _1643533, _1643535, _1643537] : [hAPP(hAPP(c_List_Oappend(_1643527), _1643529), _1643531) = _1643533, _1643535 = hAPP(hAPP(c_List_Oappend(_1643527), _1643531), _1643537), -(hAPP(hAPP(c_List_Oappend(_1643527), _1643529), _1643535) = hAPP(hAPP(c_List_Oappend(_1643527), _1643533), _1643537))], (33024 ^ _776545) ^ [_1379590, _1379592, _1379594, _1379596] : [_1379590 = c_Orderings_Obot__class_Obot(tc_fun(_1379592, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1379592, _1379594, hAPP(c_COMBK(_1379594, _1379592), _1379596)), _1379590) = c_Orderings_Obot__class_Obot(tc_fun(_1379594, tc_HOL_Obool)))], (42988 ^ _776545) ^ [_1633375, _1633377] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633375)), c_List_Olist_ONil(_1633375)), c_List_Olists(_1633375, _1633377))))], (46349 ^ _776545) ^ [_1708704, _1708706] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1708704, _1708706))))], (44876 ^ _776545) ^ [_1674918, _1674920, _1674922, _1674924, _1674926] : [-(hAPP(c_List_Orotate(_1674918, _1674920), hAPP(hAPP(c_List_Omap(_1674922, _1674918), _1674924), _1674926)) = hAPP(hAPP(c_List_Omap(_1674922, _1674918), _1674924), hAPP(c_List_Orotate(_1674922, _1674920), _1674926)))], (29251 ^ _776545) ^ [_1300827, _1300829] : [class_Rings_Oring__1__no__zero__divisors(_1300827), 29254 ^ _776545 : [(29261 ^ _776545) ^ [] : [_1300829 = c_Groups_Ozero__class_Ozero(_1300827), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1300827), _1300829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300827))], (29255 ^ _776545) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1300827), _1300829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1300827), -(_1300829 = c_Groups_Ozero__class_Ozero(_1300827))]]], (52031 ^ _776545) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (42467 ^ _776545) ^ [_1619872, _1619874, _1619876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1619872), _1619874)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1619872)), hAPP(c_Set_OCollect(tc_List_Olist(_1619872)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1619872), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1619872)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619872), tc_fun(_1619872, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1619872, tc_HOL_Obool), tc_fun(tc_fun(_1619872, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1619872)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1619872, tc_HOL_Obool))), c_List_Oset(_1619872))), _1619874))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1619872), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1619872)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1619872)))), _1619876))))))], (5895 ^ _776545) ^ [_870286, _870288, _870290] : [hBOOL(hAPP(_870290, _870288)), -(hBOOL(hAPP(hAPP(c_member(_870286), _870288), _870290)))], (51253 ^ _776545) ^ [_1814301, _1814303, _1814305, _1814307] : [class_Rings_Ocomm__semiring__1(_1814301), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814301), _1814303), _1814305)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814301), _1814303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814301), _1814307), _1814305))))], (4534 ^ _776545) ^ [_845403, _845405, _845407, _845409] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_845409, _845405) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_845407, _845403)), _845409 = _845407, _845405 = _845403], (41422 ^ _776545) ^ [_1589993, _1589995, _1589997] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589993, _1589993, _1589993), _1589995), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589993, _1589993), tc_HOL_Obool), _1589997), _1589995)) = hAPP(hAPP(c_Relation_Orel__comp(_1589993, _1589993, _1589993), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589993, _1589993), tc_HOL_Obool), _1589997), _1589995)), _1589995))], (48438 ^ _776545) ^ [_1752113, _1752115, _1752117, _1752119, _1752121, _1752123, _1752125] : [-(c_New__Random__Sequence_Opos__decr__bind(_1752113, _1752115, _1752117, _1752119, _1752121, _1752123, _1752125) = c_New__DSequence_Opos__decr__bind(_1752113, _1752115, hAPP(hAPP(hAPP(_1752117, _1752121), _1752123), _1752125), hAPP(hAPP(c_COMBC(_1752113, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1752115))), hAPP(hAPP(c_COMBC(_1752113, 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(_1752115)))), hAPP(hAPP(c_COMBC(_1752113, 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(_1752115))))), _1752119), _1752121)), _1752123)), _1752125)))], (44878 ^ _776545) ^ [_1674979, _1674981, _1674983, _1674985, _1674987, _1674989, _1674991] : [-(hAPP(c_List_Ofoldl(_1674979, _1674981, _1674983, _1674985), hAPP(hAPP(c_List_Omap(_1674987, _1674981), _1674989), _1674991)) = hAPP(c_List_Ofoldl(_1674979, _1674987, hAPP(hAPP(c_COMBC(_1674979, tc_fun(_1674987, _1674981), tc_fun(_1674987, _1674979)), hAPP(hAPP(c_COMBB(tc_fun(_1674981, _1674979), tc_fun(tc_fun(_1674987, _1674981), tc_fun(_1674987, _1674979)), _1674979), c_COMBB(_1674981, _1674979, _1674987)), _1674983)), _1674989), _1674985), _1674991))], (6573 ^ _776545) ^ [_882796, _882798] : [class_Orderings_Obot(_882796), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882796), c_Orderings_Obot__class_Obot(_882796)), _882798)))], (50269 ^ _776545) ^ [_1792693, _1792695, _1792697, _1792699, _1792701, _1792703] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1792693, _1792695, _1792697, _1792699), _1792701), _1792703) = hAPP(_1792699, hAPP(hAPP(c_Product__Type_OPair(_1792693, _1792695), _1792701), _1792703)))], (33150 ^ _776545) ^ [_1382929, _1382931, _1382933, _1382935] : [hAPP(hAPP(c_COMBC(_1382929, tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_fun(_1382931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382931, tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_fun(_1382931, tc_HOL_Obool)), _1382929), c_COMBC(_1382931, tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382931, tc_prod(_1382929, _1382931)), tc_fun(_1382931, tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), _1382929), hAPP(c_COMBB(tc_prod(_1382929, _1382931), tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool), _1382931), c_member(tc_prod(_1382929, _1382931)))), c_Product__Type_OPair(_1382929, _1382931)))), _1382933) = hAPP(hAPP(c_COMBC(_1382929, tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_fun(_1382931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382931, tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_fun(_1382931, tc_HOL_Obool)), _1382929), c_COMBC(_1382931, tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382931, tc_prod(_1382929, _1382931)), tc_fun(_1382931, tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool)), _1382929), hAPP(c_COMBB(tc_prod(_1382929, _1382931), tc_fun(tc_fun(tc_prod(_1382929, _1382931), tc_HOL_Obool), tc_HOL_Obool), _1382931), c_member(tc_prod(_1382929, _1382931)))), c_Product__Type_OPair(_1382929, _1382931)))), _1382935), -(_1382933 = _1382935)], (16116 ^ _776545) ^ [_1067883, _1067885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067883), _1067885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067883)), hAPP(c_Nat_OSuc, _1067885))))], (52169 ^ _776545) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (45497 ^ _776545) ^ [_1688845, _1688847, _1688849, _1688851, _1688853] : [c_List_Olist__all2(_1688845, _1688847, _1688849, _1688851, _1688853), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688845)), _1688851) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688847)), _1688853))], (37400 ^ _776545) ^ [_1488311, _1488313, _1488315, _1488317, _1488319] : [c_Fun_Oinj__on(_1488311, _1488313, _1488315, c_Orderings_Otop__class_Otop(tc_fun(_1488311, tc_HOL_Obool))), 37403 ^ _776545 : [(37410 ^ _776545) ^ [] : [_1488317 = _1488319, -(hAPP(c_Set_Oimage(_1488311, _1488313, _1488315), _1488317) = hAPP(c_Set_Oimage(_1488311, _1488313, _1488315), _1488319))], (37404 ^ _776545) ^ [] : [hAPP(c_Set_Oimage(_1488311, _1488313, _1488315), _1488317) = hAPP(c_Set_Oimage(_1488311, _1488313, _1488315), _1488319), -(_1488317 = _1488319)]]], (17043 ^ _776545) ^ [_1083352, _1083354, _1083356, _1083358] : [class_Rings_Oordered__semiring(_1083352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083352), _1083354), _1083356)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083352), c_Groups_Ozero__class_Ozero(_1083352)), _1083358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083352), _1083358), _1083354)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083352), _1083358), _1083356))))], (51489 ^ _776545) ^ [_1818548, _1818550] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818550), _1818548)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818548), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818550))))], (26667 ^ _776545) ^ [_1257851, _1257853] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257851)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257851)), _1257853) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257851)), _1257853)))], (31072 ^ _776545) ^ [_1334213, _1334215, _1334217] : [class_Orderings_Olinorder(_1334213), hAPP(_1334215, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334213), 31077 ^ [_1334213, _1334215, _1334217]), 31078 ^ [_1334213, _1334215, _1334217])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1334213), hAPP(_1334215, 31077 ^ [_1334213, _1334215, _1334217])), hAPP(_1334215, 31078 ^ [_1334213, _1334215, _1334217])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334213), _1334217)), -(_1334217 = c_Orderings_Obot__class_Obot(tc_fun(_1334213, tc_HOL_Obool))), -(hAPP(_1334215, c_Big__Operators_Olinorder__class_OMin(_1334213, _1334217)) = c_Big__Operators_Olinorder__class_OMin(_1334213, hAPP(c_Set_Oimage(_1334213, _1334213, _1334215), _1334217)))], (27353 ^ _776545) ^ [_1268668, _1268670] : [class_Rings_Olinordered__idom(_1268668), -(hAPP(c_Groups_Oabs__class_Oabs(_1268668), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268668), _1268670)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268668), _1268670))], (39345 ^ _776545) ^ [_1538270, _1538272] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1538270, _1538272, tc_prod(_1538270, _1538272)), c_Product__Type_OPair(_1538270, _1538272)) = c_Fun_Oid(tc_prod(_1538270, _1538272)))], (39681 ^ _776545) ^ [_1547103, _1547105] : [39683 ^ _776545 : [(39686 ^ _776545) ^ [] : [hBOOL(hAPP(_1547103, hAPP(c_Int_OAbs__Integ, 39682 ^ [_1547103, _1547105])))], (39684 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39682 ^ [_1547103, _1547105]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1547103, _1547105)))], (16815 ^ _776545) ^ [_1079177, _1079179] : [class_Groups_Olinordered__ab__group__add(_1079177), 16818 ^ _776545 : [(16825 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079177), _1079179), c_Groups_Ozero__class_Ozero(_1079177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079177), _1079179), _1079179)), c_Groups_Ozero__class_Ozero(_1079177))))], (16819 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079177), _1079179), _1079179)), c_Groups_Ozero__class_Ozero(_1079177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079177), _1079179), c_Groups_Ozero__class_Ozero(_1079177))))]]], (18382 ^ _776545) ^ [_1107223, _1107225, _1107227, _1107229, _1107231] : [class_Rings_Olinordered__semiring__strict(_1107223), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107223), _1107225), _1107227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107223), _1107229), _1107231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107223), c_Groups_Ozero__class_Ozero(_1107223)), _1107225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107223), c_Groups_Ozero__class_Ozero(_1107223)), _1107229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107223), _1107225), _1107229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107223), _1107227), _1107231))))], (31255 ^ _776545) ^ [_1337450, _1337452, _1337454] : [class_Orderings_Olinorder(_1337450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337450), _1337452)), -(hBOOL(hAPP(hAPP(c_member(_1337450), _1337454), _1337452))), -(c_Big__Operators_Olinorder__class_OMax(_1337450, hAPP(hAPP(c_Set_Oinsert(_1337450), _1337454), _1337452)) = hAPP(hAPP(c_Finite__Set_Ofold(_1337450, _1337450, c_Orderings_Oord__class_Omax(_1337450)), _1337454), _1337452))], (34329 ^ _776545) ^ [_1415423, _1415425, _1415427] : [-(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), _1415423)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1415425))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1415427))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1415427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1415423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1415423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1415427), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1415425)))))], (31137 ^ _776545) ^ [_1335380, _1335382, _1335384] : [class_Orderings_Olinorder(_1335380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335380), _1335382)), 31147 ^ _776545 : [(31150 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335380), _1335384), 31146 ^ [_1335380, _1335382, _1335384]))], (31148 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335380), 31146 ^ [_1335380, _1335382, _1335384]), _1335382)))]], hBOOL(hAPP(hAPP(c_member(_1335380), _1335384), _1335382)), -(c_Big__Operators_Olinorder__class_OMin(_1335380, _1335382) = _1335384)], (36543 ^ _776545) ^ [_1468459, _1468461, _1468463, _1468465] : [-(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), _1468459), _1468461)), 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), _1468463), _1468465)), 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), _1468459), _1468463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468461), _1468465))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468459), _1468465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1468461), _1468463)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (40370 ^ _776545) ^ [_1563680, _1563682] : [hBOOL(hAPP(_1563680, c_Hilbert__Choice_OEps(_1563682, _1563680))), -(hBOOL(hAPP(_1563680, 40373 ^ [_1563680, _1563682])))], (29063 ^ _776545) ^ [_1297525] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1297525)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1297525), c_Int_OPls)))], (39105 ^ _776545) ^ [_1530178, _1530180, _1530182, _1530184, _1530186] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530178, _1530180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530178, tc_HOL_Obool)), _1530182), _1530184)), _1530186) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530178, _1530180), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530178, _1530180), _1530182), _1530186)), hAPP(hAPP(c_Product__Type_OSigma(_1530178, _1530180), _1530184), _1530186)))], (29633 ^ _776545) ^ [_1307651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1307651)), -(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), _1307651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19344 ^ _776545) ^ [_1125797, _1125799, _1125801] : [class_Rings_Oring__1(_1125797), hBOOL(hAPP(hAPP(c_member(_1125797), _1125799), c_Int_Oring__1__class_OInts(_1125797))), hBOOL(hAPP(hAPP(c_member(_1125797), _1125801), c_Int_Oring__1__class_OInts(_1125797))), -(hBOOL(hAPP(hAPP(c_member(_1125797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125797), _1125799), _1125801)), c_Int_Oring__1__class_OInts(_1125797))))], (13932 ^ _776545) ^ [_1025502, _1025504, _1025506, _1025508, _1025510, _1025512] : [class_Rings_Oordered__ring(_1025502), 13935 ^ _776545 : [(13942 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025502), _1025508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025502), _1025510), _1025504)), _1025506)), _1025512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), _1025504), _1025506)), _1025508)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), _1025510), _1025506)), _1025512))))], (13936 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), _1025504), _1025506)), _1025508)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), _1025510), _1025506)), _1025512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025502), _1025508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025502), _1025510), _1025504)), _1025506)), _1025512))))]]], (38919 ^ _776545) ^ [_1525511, _1525513] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525511, _1525511)), _1525513)), 38922 ^ _776545 : [(38929 ^ _776545) ^ [] : [c_Wellfounded_Oacyclic(_1525511, _1525513), -(c_Wellfounded_Owf(_1525511, _1525513))], (38923 ^ _776545) ^ [] : [c_Wellfounded_Owf(_1525511, _1525513), -(c_Wellfounded_Oacyclic(_1525511, _1525513))]]], (25079 ^ _776545) ^ [_1230577, _1230579] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230577), _1230579) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230577, _1230579) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8713 ^ _776545) ^ [_926281, _926283, _926285] : [class_Lattices_Osemilattice__inf(_926281), 8716 ^ _776545 : [(8723 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926281), _926283), _926285) = _926283, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926281), _926283), _926285)))], (8717 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926281), _926283), _926285)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926281), _926283), _926285) = _926283)]]], (9102 ^ _776545) ^ [_933853, _933855, _933857, _933859] : [class_Orderings_Oord(_933853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933853), _933855), _933857)), _933857 = _933859, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933853), _933855), _933859)))], (14098 ^ _776545) ^ [_1029490, _1029492, _1029494] : [class_Rings_Ocomm__ring__1(_1029490), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029490), _1029492), _1029494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029490), _1029492), hAPP(c_Groups_Ouminus__class_Ouminus(_1029490), _1029494)))], (39751 ^ _776545) ^ [_1549147, _1549149] : [class_Complete__Lattice_Ocomplete__lattice(_1549147), -(c_Complete__Lattice_OSup__class_OSup(_1549147, _1549149) = c_Complete__Lattice_OInf__class_OInf(_1549147, hAPP(c_Set_OCollect(_1549147), hAPP(hAPP(c_COMBB(tc_fun(_1549147, tc_HOL_Obool), tc_HOL_Obool, _1549147), c_HOL_OAll(_1549147)), hAPP(hAPP(c_COMBB(tc_fun(_1549147, tc_HOL_Obool), tc_fun(_1549147, tc_HOL_Obool), _1549147), hAPP(c_COMBS(_1549147, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549147), c_fimplies), hAPP(hAPP(c_COMBC(_1549147, tc_fun(_1549147, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549147)), _1549149)))), hAPP(c_COMBC(_1549147, _1549147, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1549147)))))))], (24371 ^ _776545) ^ [_1217311] : [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), _1217311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217311)))], (50253 ^ _776545) ^ [_1792382, _1792384] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1792382), _1792384))), -(c_Quickcheck_Obeyond(_1792382, _1792384) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (51857 ^ _776545) ^ [_1824622, _1824624] : [class_Complete__Lattice_Ocomplete__lattice(_1824622), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1824624, _1824622)))], (7994 ^ _776545) ^ [_911916, _911918, _911920] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911916, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911916, tc_HOL_Obool)), _911918), _911920)), _911918)))], (26272 ^ _776545) ^ [_1251014] : [-(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)), _1251014)) = hAPP(c_Int_Onat, _1251014))], (29597 ^ _776545) ^ [_1306944, _1306946, _1306948] : [class_Rings_Ocomm__semiring__1(_1306944), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1306944), _1306946), 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)))), _1306948))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306944), _1306946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306944), hAPP(hAPP(c_Power_Opower__class_Opower(_1306944), _1306946), _1306948)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306944), _1306946), _1306948))))], (41060 ^ _776545) ^ [_1581259, _1581261] : [-(c_Transitive__Closure_Ortrancl(_1581259, hAPP(c_Relation_Oconverse(_1581259, _1581259), _1581261)) = hAPP(c_Relation_Oconverse(_1581259, _1581259), c_Transitive__Closure_Ortrancl(_1581259, _1581261)))], (25883 ^ _776545) ^ [_1244760, _1244762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244762)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244760), hAPP(c_Int_Onat, _1244762)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244760, _1244762)))], (26282 ^ _776545) ^ [_1251186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1251186))))], (52125 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (16957 ^ _776545) ^ [_1081699, _1081701, _1081703, _1081705, _1081707] : [class_Rings_Oordered__semiring(_1081699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081699), _1081701), _1081703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081699), _1081705), _1081707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081699), c_Groups_Ozero__class_Ozero(_1081699)), _1081703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081699), c_Groups_Ozero__class_Ozero(_1081699)), _1081705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081699), _1081701), _1081705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081699), _1081703), _1081707))))], (17869 ^ _776545) ^ [_1097970, _1097972, _1097974] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097970), _1097972)), 17872 ^ _776545 : [(17873 ^ _776545) ^ [] : [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(_1097970, tc_Nat_Onat), _1097974), _1097972))), 17876 ^ _776545 : [(17877 ^ _776545) ^ [_1098138] : [hBOOL(hAPP(hAPP(c_member(_1097970), _1098138), _1097972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1097974, _1098138))))]]], (17883 ^ _776545) ^ [] : [17885 ^ _776545 : [(17888 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1097974, 17884 ^ [_1097970, _1097972, _1097974])))], (17886 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097970), 17884 ^ [_1097970, _1097972, _1097974]), _1097972)))]], -(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(_1097970, tc_Nat_Onat), _1097974), _1097972))))]]], (33849 ^ _776545) ^ [_1403690] : [class_Orderings_Olinorder(_1403690), -(c_Orderings_Oord_Omin(_1403690, hAPP(c_COMBC(_1403690, _1403690, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1403690))) = c_Orderings_Oord__class_Omax(_1403690))], (25227 ^ _776545) ^ [_1233275, _1233277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233275), 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, _1233277, _1233275)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49700 ^ _776545) ^ [_1781163, _1781165] : [c_Relation_Osym(_1781163, _1781165), -(hAPP(c_Relation_Oconverse(_1781163, _1781163), _1781165) = _1781165)], (26649 ^ _776545) ^ [_1257550, _1257552] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1257550))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257550)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1257552)) = 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), _1257552)))], (36330 ^ _776545) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (35917 ^ _776545) ^ [_1449016, _1449018, _1449020, _1449022] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449016), hAPP(c_Set_OCollect(_1449016), _1449018))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1449020), hAPP(c_Set_OCollect(_1449020), hAPP(hAPP(c_COMBB(tc_fun(_1449016, tc_HOL_Obool), tc_HOL_Obool, _1449020), c_HOL_OEx(_1449016)), hAPP(hAPP(c_COMBC(_1449020, tc_fun(_1449016, tc_HOL_Obool), tc_fun(_1449016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449016, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1449016, tc_HOL_Obool), tc_fun(_1449016, tc_HOL_Obool)), _1449020), c_COMBS(_1449016, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449016, tc_HOL_Obool), tc_fun(_1449016, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1449020), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1449016), c_fconj)), hAPP(hAPP(c_COMBC(_1449020, tc_fun(_1449016, _1449020), tc_fun(_1449016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449020, tc_HOL_Obool), tc_fun(tc_fun(_1449016, _1449020), tc_fun(_1449016, tc_HOL_Obool)), _1449020), c_COMBB(_1449020, tc_HOL_Obool, _1449016)), c_fequal)), _1449022)))), _1449018))))))], (45561 ^ _776545) ^ [_1690097, _1690099, _1690101, _1690103, _1690105, _1690107, _1690109] : [c_List_Olist__all2(_1690097, _1690099, _1690101, _1690103, _1690105), c_List_Olist__all2(_1690097, _1690099, _1690101, _1690107, _1690109), -(c_List_Olist__all2(_1690097, _1690099, _1690101, hAPP(hAPP(c_List_Oappend(_1690097), _1690103), _1690107), hAPP(hAPP(c_List_Oappend(_1690099), _1690105), _1690109)))], (46996 ^ _776545) ^ [_1721172, _1721174] : [c_List_Olist_ONil(_1721172) = hAPP(c_List_Orev(_1721172), _1721174), -(_1721174 = c_List_Olist_ONil(_1721172))], (33310 ^ _776545) ^ [_1387548, _1387550, _1387552, _1387554, _1387556] : [class_Rings_Osemiring__0(_1387548), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387548), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387550, _1387548), _1387552), _1387554)), _1387556) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387550, _1387548), hAPP(hAPP(c_COMBC(_1387550, _1387548, _1387548), hAPP(hAPP(c_COMBB(_1387548, tc_fun(_1387548, _1387548), _1387550), c_Groups_Otimes__class_Otimes(_1387548)), _1387552)), _1387556)), _1387554))], (43551 ^ _776545) ^ [_1645231, _1645233, _1645235, _1645237, _1645239, _1645241] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645231)), _1645233) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645235)), _1645237), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645231)), _1645239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645235)), _1645241), -(hAPP(hAPP(c_List_Ozip(_1645231, _1645235), hAPP(hAPP(c_List_Oappend(_1645231), _1645233), _1645239)), hAPP(hAPP(c_List_Oappend(_1645235), _1645237), _1645241)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1645231, _1645235)), hAPP(hAPP(c_List_Ozip(_1645231, _1645235), _1645233), _1645237)), hAPP(hAPP(c_List_Ozip(_1645231, _1645235), _1645239), _1645241)))], (4976 ^ _776545) ^ [_852358, _852360, _852362, _852364, _852366, _852368, _852370, _852372, _852374, _852376] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852376, _852372, _852368, _852364, _852360) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_852374, _852370, _852366, _852362, _852358)), _852376 = _852374, _852372 = _852370, _852368 = _852366, _852364 = _852362, _852360 = _852358], (2290 ^ _776545) ^ [_809903, _809905, _809907, _809909] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_809909, _809905) = c_Code__Numeral_Odiv__mod__code__numeral(_809907, _809903)), _809909 = _809907, _809905 = _809903], (33380 ^ _776545) ^ [_1389502, _1389504, _1389506, _1389508, _1389510, _1389512] : [-(c_Nitpick_Opair__box_OPairBox(_1389502, _1389504, _1389506, _1389508) = c_Nitpick_Opair__box_OPairBox(_1389502, _1389504, _1389510, _1389512)), _1389506 = _1389510, _1389508 = _1389512], (5234 ^ _776545) ^ [_856409, _856411, _856413, _856415, _856417, _856419] : [-(c_Lazy__Sequence_Oappend(_856419, _856415, _856411) = c_Lazy__Sequence_Oappend(_856417, _856413, _856409)), _856419 = _856417, _856415 = _856413, _856411 = _856409], (31485 ^ _776545) ^ [_1341870, _1341872, _1341874, _1341876] : [class_Orderings_Olinorder(_1341870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341870), _1341872), _1341874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341870), _1341872), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341870), _1341876), _1341874))))], (40787 ^ _776545) ^ [_1574712, _1574714, _1574716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574712, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1574712, _1574712, _1574714), _1574716)), _1574716)), -(hAPP(c_Relation_OImage(_1574712, _1574712, c_Transitive__Closure_Ortrancl(_1574712, _1574714)), _1574716) = _1574716)], (30272 ^ _776545) ^ [_1319550, _1319552, _1319554, _1319556] : [class_Orderings_Olinorder(_1319550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319550), _1319552), _1319554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319550), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319550), _1319556), _1319552)), _1319554)))], (36468 ^ _776545) ^ [_1466116, _1466118, _1466120, _1466122] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1466116, _1466118), _1466120), _1466122) = hAPP(c_Set_OCollect(tc_prod(_1466118, _1466118)), hAPP(c_Product__Type_Oprod_Oprod__case(_1466118, _1466118, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1466118, tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_fun(_1466118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466118, tc_fun(tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_fun(_1466118, tc_HOL_Obool)), _1466118), c_COMBC(_1466118, tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466118, tc_prod(_1466116, _1466116)), tc_fun(_1466118, tc_fun(tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_HOL_Obool)), _1466118), hAPP(c_COMBB(tc_prod(_1466116, _1466116), tc_fun(tc_fun(tc_prod(_1466116, _1466116), tc_HOL_Obool), tc_HOL_Obool), _1466118), c_member(tc_prod(_1466116, _1466116)))), hAPP(hAPP(c_COMBC(_1466118, tc_fun(_1466118, _1466116), tc_fun(_1466118, tc_prod(_1466116, _1466116))), hAPP(hAPP(c_COMBB(tc_fun(_1466116, tc_prod(_1466116, _1466116)), tc_fun(tc_fun(_1466118, _1466116), tc_fun(_1466118, tc_prod(_1466116, _1466116))), _1466118), c_COMBB(_1466116, tc_prod(_1466116, _1466116), _1466118)), hAPP(hAPP(c_COMBB(_1466116, tc_fun(_1466116, tc_prod(_1466116, _1466116)), _1466118), c_Product__Type_OPair(_1466116, _1466116)), _1466122))), _1466122)))), _1466120))))], (44667 ^ _776545) ^ [_1669519, _1669521, _1669523] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669519)), _1669521), c_List_Olists(_1669519, _1669523))), -(_1669521 = c_List_Olist_ONil(_1669519)), 44676 ^ _776545 : [(44681 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1669519)), 44675 ^ [_1669519, _1669521, _1669523]), c_List_Olists(_1669519, _1669523))))], (44679 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1669519), 44674 ^ [_1669519, _1669521, _1669523]), _1669523)))], (44677 ^ _776545) ^ [] : [-(_1669521 = hAPP(hAPP(c_List_Olist_OCons(_1669519), 44674 ^ [_1669519, _1669521, _1669523]), 44675 ^ [_1669519, _1669521, _1669523]))]]], (29203 ^ _776545) ^ [_1299937] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299937)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1299937)))], (18332 ^ _776545) ^ [_1106262, _1106264, _1106266, _1106268] : [class_Rings_Olinordered__semiring__strict(_1106262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106262), _1106264), _1106266)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106262), _1106268), _1106266))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106262), c_Groups_Ozero__class_Ozero(_1106262)), _1106266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106262), _1106264), _1106268)))], (23087 ^ _776545) ^ [_1194820] : [-(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)), _1194820))))], (34493 ^ _776545) ^ [_1418518, _1418520, _1418522, _1418524, _1418526] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418518, tc_fun(_1418520, tc_HOL_Obool)), _1418522), _1418524), _1418526)), 34496 ^ _776545 : [(34497 ^ _776545) ^ [_1418627] : [hBOOL(hAPP(hAPP(c_member(_1418518), _1418627), _1418522)), -(hBOOL(hAPP(hAPP(_1418524, _1418627), _1418526)))]]], (27615 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41150 ^ _776545) ^ [_1583421, _1583423, _1583425] : [c_Equiv__Relations_Oequiv(_1583421, _1583423, _1583425), -(hAPP(hAPP(c_Relation_Orel__comp(_1583421, _1583421, _1583421), hAPP(c_Relation_Oconverse(_1583421, _1583421), _1583425)), _1583425) = _1583425)], (32928 ^ _776545) ^ [_1376846, _1376848, _1376850, _1376852, _1376854] : [_1376846 = c_Orderings_Obot__class_Obot(tc_fun(_1376848, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1376848, tc_fun(_1376850, tc_HOL_Obool)), _1376846), hAPP(hAPP(c_COMBC(_1376848, tc_fun(_1376850, tc_HOL_Obool), tc_fun(_1376850, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376850, tc_HOL_Obool), tc_fun(tc_fun(_1376850, tc_HOL_Obool), tc_fun(_1376850, tc_HOL_Obool)), _1376848), c_Groups_Ominus__class_Ominus(tc_fun(_1376850, tc_HOL_Obool))), _1376852)), _1376854)) = c_Orderings_Otop__class_Otop(tc_fun(_1376850, tc_HOL_Obool)))], (47144 ^ _776545) ^ [_1724342, _1724344, _1724346, _1724348] : [class_Orderings_Olinorder(_1724342), c_List_Olinorder__class_Osorted(_1724342, hAPP(c_List_Orev(_1724342), _1724344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724346), _1724348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724348), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724342)), _1724344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724342), hAPP(hAPP(c_List_Onth(_1724342), _1724344), _1724348)), hAPP(hAPP(c_List_Onth(_1724342), _1724344), _1724346))))], (34331 ^ _776545) ^ [_1415504, _1415506, _1415508] : [class_Int_Onumber__ring(_1415504), 34334 ^ _776545 : [(34341 ^ _776545) ^ [] : [-(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), _1415506)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1415504), hAPP(c_Int_Onumber__class_Onumber__of(_1415504), _1415508)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1415506))) = c_Groups_Oone__class_Oone(_1415504))], (34335 ^ _776545) ^ [] : [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), _1415506))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1415504), hAPP(c_Int_Onumber__class_Onumber__of(_1415504), _1415508)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1415506))) = hAPP(hAPP(c_HOL_OLet(_1415504, _1415504), hAPP(hAPP(c_Power_Opower__class_Opower(_1415504), hAPP(c_Int_Onumber__class_Onumber__of(_1415504), _1415508)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415506))), hAPP(hAPP(c_COMBS(_1415504, _1415504, _1415504), hAPP(hAPP(c_COMBB(_1415504, tc_fun(_1415504, _1415504), _1415504), c_Groups_Otimes__class_Otimes(_1415504)), hAPP(c_Groups_Otimes__class_Otimes(_1415504), hAPP(c_Int_Onumber__class_Onumber__of(_1415504), _1415508)))), c_COMBI(_1415504))))]]], (9730 ^ _776545) ^ [_943131, _943133, _943135, _943137] : [class_Lattices_Osemilattice__sup(_943131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943131), _943133), _943135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943131), _943133), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943131), _943137), _943135))))], (43446 ^ _776545) ^ [_1642818, _1642820, _1642822, _1642824] : [-(hAPP(hAPP(c_List_Oappend(_1642818), hAPP(hAPP(c_List_Olist_OCons(_1642818), _1642820), _1642822)), _1642824) = hAPP(hAPP(c_List_Olist_OCons(_1642818), _1642820), hAPP(hAPP(c_List_Oappend(_1642818), _1642822), _1642824)))], (51307 ^ _776545) ^ [_1815231, _1815233, _1815235, _1815237] : [class_Rings_Oidom(_1815231), 51310 ^ _776545 : [(51311 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815231), _1815233), _1815235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815231), _1815237), _1815235))), -(_1815235 = c_Groups_Ozero__class_Ozero(_1815231)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815231), _1815233), _1815237)))], (51321 ^ _776545) ^ [] : [51322 ^ _776545 : [(51325 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815231), _1815233), _1815237))], (51323 ^ _776545) ^ [] : [_1815235 = c_Groups_Ozero__class_Ozero(_1815231)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815231), _1815233), _1815235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815231), _1815237), _1815235))))]]], (43541 ^ _776545) ^ [_1644969, _1644971, _1644973, _1644975] : [-(hAPP(hAPP(c_List_Oappend(_1644969), hAPP(hAPP(c_List_Oappend(_1644969), _1644971), _1644973)), _1644975) = hAPP(hAPP(c_List_Oappend(_1644969), _1644971), hAPP(hAPP(c_List_Oappend(_1644969), _1644973), _1644975)))], (48466 ^ _776545) ^ [_1753043, _1753045] : [-(c_List_Osplice(_1753043, _1753045, c_List_Olist_ONil(_1753043)) = _1753045)], (1744 ^ _776545) ^ [_801209, _801211] : [-(class_Orderings_Opreorder(_801209)), _801211 = _801209, class_Orderings_Opreorder(_801211)], (2688 ^ _776545) ^ [_816260, _816262, _816264, _816266] : [-(c_Divides_Odivmod__nat__rel(_816266, _816262) = c_Divides_Odivmod__nat__rel(_816264, _816260)), _816266 = _816264, _816262 = _816260], (39151 ^ _776545) ^ [_1531884, _1531886, _1531888, _1531890, _1531892] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1531884, _1531886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1531884, tc_HOL_Obool)), _1531888), _1531890)), _1531892) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1531884, _1531886), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531884, _1531886), _1531888), _1531892)), hAPP(hAPP(c_Product__Type_OSigma(_1531884, _1531886), _1531890), _1531892)))], (52155 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (41674 ^ _776545) ^ [_1597137, _1597139, _1597141] : [-(c_Nitpick_Oof__frac(_1597139, _1597137, _1597141) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1597137), hAPP(c_Int_Oring__1__class_Oof__int(_1597137), hAPP(c_Nitpick_Onum(_1597139), _1597141))), hAPP(c_Int_Oring__1__class_Oof__int(_1597137), hAPP(c_Nitpick_Odenom(_1597139), _1597141)))), class_Rings_Oinverse(_1597137), class_Rings_Oring__1(_1597137)], (50184 ^ _776545) ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782] : [class_Groups_Ocomm__monoid__mult(_1790772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1790774), _1790776)), 50194 ^ _776545 : [(50197 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790778), hAPP(_1790780, 50193 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782])))], (50195 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790774), 50193 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782]), _1790776)))]], 50201 ^ _776545 : [(50205 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790774), 50203 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782]), _1790776)))], (50207 ^ _776545) ^ [] : [50200 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782] = 50203 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782]], (50209 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1790778, tc_HOL_Obool)), hAPP(_1790780, 50200 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782])), hAPP(_1790780, 50203 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782])) = c_Orderings_Obot__class_Obot(tc_fun(_1790778, tc_HOL_Obool))], (50202 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790774), 50200 ^ [_1790772, _1790774, _1790776, _1790778, _1790780, _1790782]), _1790776)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1790772, _1790778, c_Groups_Otimes__class_Otimes(_1790772)), _1790782), c_Groups_Oone__class_Oone(_1790772)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1790774, tc_fun(_1790778, tc_HOL_Obool)), _1790776), _1790780)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1790772, _1790774, c_Groups_Otimes__class_Otimes(_1790772)), hAPP(hAPP(c_COMBB(tc_fun(_1790778, tc_HOL_Obool), _1790772, _1790774), hAPP(hAPP(c_Finite__Set_Ofold__image(_1790772, _1790778, c_Groups_Otimes__class_Otimes(_1790772)), _1790782), c_Groups_Oone__class_Oone(_1790772))), _1790780)), c_Groups_Oone__class_Oone(_1790772)), _1790776))], (11894 ^ _776545) ^ [_985464, _985466, _985468, _985470, _985472] : [c_Finite__Set_Ofolding__one__idem(_985464, _985466, _985468), hBOOL(hAPP(c_Finite__Set_Ofinite(_985464), _985470)), -(_985470 = c_Orderings_Obot__class_Obot(tc_fun(_985464, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_985464), _985472)), -(_985472 = c_Orderings_Obot__class_Obot(tc_fun(_985464, tc_HOL_Obool))), -(hAPP(_985468, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985464, tc_HOL_Obool)), _985470), _985472)) = hAPP(hAPP(_985466, hAPP(_985468, _985470)), hAPP(_985468, _985472)))], (21303 ^ _776545) ^ [_1162108, _1162110, _1162112, _1162114] : [class_Rings_Ocomm__semiring__1(_1162108), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1162108), hAPP(hAPP(c_Power_Opower__class_Opower(_1162108), _1162110), _1162112)), _1162114) = hAPP(hAPP(c_Power_Opower__class_Opower(_1162108), _1162110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162112), _1162114)))], (7904 ^ _776545) ^ [_909868, _909870, _909872, _909874] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909868, tc_HOL_Obool)), _909870), hAPP(hAPP(c_Set_Oinsert(_909868), _909872), _909874)) = hAPP(hAPP(c_Set_Oinsert(_909868), _909872), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909868, tc_HOL_Obool)), _909870), _909874)))], (47422 ^ _776545) ^ [_1730007, _1730009, _1730011, _1730013, _1730015] : [-(c_List_OdropWhile(_1730007, _1730009, hAPP(hAPP(c_List_Omap(_1730011, _1730007), _1730013), _1730015)) = hAPP(hAPP(c_List_Omap(_1730011, _1730007), _1730013), c_List_OdropWhile(_1730011, hAPP(c_Fun_Ocomp(_1730007, tc_HOL_Obool, _1730011, _1730009), _1730013), _1730015)))], (50546 ^ _776545) ^ [_1798193, _1798195, _1798197, _1798199, _1798201] : [c_Fun_Obij__betw(_1798193, _1798195, _1798197, _1798199, _1798201), -(c_Fun_Obij__betw(_1798195, _1798193, c_Fun_Othe__inv__into(_1798193, _1798195, _1798199, _1798197), _1798201, _1798199))], (45884 ^ _776545) ^ [_1697019, _1697021] : [-(c_List_Oconcat(_1697019, _1697021) = hAPP(c_List_Ofoldl(tc_List_Olist(_1697019), tc_List_Olist(_1697019), c_List_Oappend(_1697019), c_List_Olist_ONil(_1697019)), _1697021))], (7579 ^ _776545) ^ [_901873, _901875, _901877, _901879] : [7583 ^ _776545 : [(7586 ^ _776545) ^ [] : [hBOOL(hAPP(_901879, 7582 ^ [_901873, _901875, _901877, _901879]))], (7584 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901873), 7582 ^ [_901873, _901875, _901877, _901879]), _901875)))]], 7588 ^ _776545 : [(7591 ^ _776545) ^ [] : [hBOOL(hAPP(_901879, 7587 ^ [_901873, _901875, _901877, _901879]))], (7589 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901873), 7587 ^ [_901873, _901875, _901877, _901879]), _901877)))]], 7592 ^ _776545 : [(7593 ^ _776545) ^ [_902206] : [hBOOL(hAPP(hAPP(c_member(_901873), _902206), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901873, tc_HOL_Obool)), _901875), _901877))), -(hBOOL(hAPP(_901879, _902206)))]]], (620 ^ _776545) ^ [_785913, _785915, _785917, _785919] : [-(c_List_Olinorder__class_Osorted(_785917, _785913)), c_List_Olinorder__class_Osorted(_785919, _785915), _785919 = _785917, _785915 = _785913], (28577 ^ _776545) ^ [_1289274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1289274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289274))))], (5034 ^ _776545) ^ [_853303, _853305] : [_853305 = _853303, -(c_Lattices_Osemilattice__inf__class_Oinf(_853305) = c_Lattices_Osemilattice__inf__class_Oinf(_853303))], (30640 ^ _776545) ^ [_1326341, _1326343] : [class_Orderings_Olinorder(_1326341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326341), _1326343)), -(_1326343 = c_Orderings_Obot__class_Obot(tc_fun(_1326341, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1326341), c_Big__Operators_Olinorder__class_OMin(_1326341, _1326343)), _1326343)))], (42677 ^ _776545) ^ [_1626230, _1626232, _1626234] : [-(hAPP(hAPP(c_List_Olist__update(_1626230, _1626232), _1626234), hAPP(hAPP(c_List_Onth(_1626230), _1626232), _1626234)) = _1626232)], (28295 ^ _776545) ^ [_1284549] : [c_Int_OMin = _1284549, -(c_Int_OMin = c_Int_OBit1(_1284549))], (24746 ^ _776545) ^ [_1224223] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224223)))], (45088 ^ _776545) ^ [_1679476, _1679478] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679476)), hAPP(c_Code__Numeral_Oof__nat, _1679478)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1679476), _1679478)))], (15134 ^ _776545) ^ [_1049761] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1049761) = _1049761)], (23962 ^ _776545) ^ [_1210578, _1210580, _1210582] : [class_Divides_Osemiring__div(_1210578), -(_1210580 = c_Groups_Ozero__class_Ozero(_1210578)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210578), _1210582), _1210580)), _1210580) = _1210582)], (40939 ^ _776545) ^ [_1578388] : [-(c_Relation_Orefl__on(_1578388, c_Orderings_Otop__class_Otop(tc_fun(_1578388, tc_HOL_Obool)), c_Relation_OId(_1578388)))], (25087 ^ _776545) ^ [_1230692] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230692, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1230692)], (16284 ^ _776545) ^ [_1070511, _1070513] : [class_Rings_Omult__zero(_1070511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070511), c_Groups_Ozero__class_Ozero(_1070511)), _1070513) = c_Groups_Ozero__class_Ozero(_1070511))], (43298 ^ _776545) ^ [_1639077, _1639079, _1639081] : [-(_1639077 = c_List_Olist_ONil(_1639079)), -(hBOOL(hAPP(hAPP(c_member(_1639079), hAPP(c_Product__Type_Ofst(_1639079, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1639079, _1639077), _1639081))), hAPP(c_List_Oset(_1639079), _1639077))))], (45836 ^ _776545) ^ [_1696082, _1696084, _1696086] : [hBOOL(hAPP(c_List_Odistinct(_1696082), _1696084)), -(c_List_Oremove1(_1696082, _1696086, c_List_Oremdups(_1696082, _1696084)) = c_List_Oremdups(_1696082, c_List_Oremove1(_1696082, _1696086, _1696084)))], (52233 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (18015 ^ _776545) ^ [_1100472, _1100474, _1100476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100472), _1100474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1100472), _1100476))), 18018 ^ _776545 : [(18021 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100474), _1100476)))], (18019 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100472)))]]], (6346 ^ _776545) ^ [_878853, _878855, _878857] : [_878853 = _878855, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878857, tc_HOL_Obool)), _878853), _878855)))], (43597 ^ _776545) ^ [_1646213, _1646215, _1646217] : [_1646213 = hAPP(hAPP(c_List_Oappend(_1646215), _1646217), _1646213), -(_1646217 = c_List_Olist_ONil(_1646215))], (11284 ^ _776545) ^ [_972627, _972629] : [class_Groups_Oordered__ab__group__add(_972627), -(hAPP(c_Set_Oimage(_972627, _972627, c_Groups_Ouminus__class_Ouminus(_972627)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_972627), _972629)) = hAPP(c_SetInterval_Oord__class_OlessThan(_972627), hAPP(c_Groups_Ouminus__class_Ouminus(_972627), _972629)))], (16779 ^ _776545) ^ [_1078439, _1078441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078439), hAPP(c_Nat_OSuc, _1078441)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1078439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1078439), _1078441)))], (41094 ^ _776545) ^ [_1582294, _1582296, _1582298, _1582300] : [-(hAPP(c_Relation_Oconverse(_1582294, _1582296), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582294, _1582296), tc_HOL_Obool)), _1582298), _1582300)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1582296, _1582294), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1582294, _1582296), _1582298)), hAPP(c_Relation_Oconverse(_1582294, _1582296), _1582300)))], (52433 ^ _776545) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (38507 ^ _776545) ^ [_1514771, _1514773, _1514775] : [-(hAPP(c_Relation_ORange(_1514771, _1514773), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1514771, _1514773), tc_HOL_Obool), _1514775)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1514771, _1514773), tc_HOL_Obool), tc_fun(_1514773, tc_HOL_Obool)), _1514775), c_Relation_ORange(_1514771, _1514773)))], (20123 ^ _776545) ^ [_1139849, _1139851, _1139853, _1139855] : [class_Fields_Olinordered__field(_1139849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139849), _1139851), _1139853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139849), c_Groups_Ozero__class_Ozero(_1139849)), _1139855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139849), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139849), _1139851), _1139855)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139849), _1139853), _1139855))))], (16484 ^ _776545) ^ [_1073401] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073401) = _1073401)], (22789 ^ _776545) ^ [_1189454, _1189456] : [class_Power_Opower(_1189454), class_Rings_Osemiring__0(_1189454), 22796 ^ _776545 : [(22803 ^ _776545) ^ [] : [-(_1189456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189454), c_Groups_Ozero__class_Ozero(_1189454)), _1189456) = c_Groups_Ozero__class_Ozero(_1189454))], (22797 ^ _776545) ^ [] : [_1189456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189454), c_Groups_Ozero__class_Ozero(_1189454)), _1189456) = c_Groups_Oone__class_Oone(_1189454))]]], (37284 ^ _776545) ^ [_1486154, _1486156, _1486158, _1486160] : [37286 ^ _776545 : [(37290 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486154), 37288 ^ [_1486154, _1486156, _1486158, _1486160]), _1486160)))], (37292 ^ _776545) ^ [] : [-(hAPP(_1486158, 37285 ^ [_1486154, _1486156, _1486158, _1486160]) = hAPP(_1486158, 37288 ^ [_1486154, _1486156, _1486158, _1486160]))], (37294 ^ _776545) ^ [] : [37285 ^ [_1486154, _1486156, _1486158, _1486160] = 37288 ^ [_1486154, _1486156, _1486158, _1486160]], (37287 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486154), 37285 ^ [_1486154, _1486156, _1486158, _1486160]), _1486160)))]], -(c_Fun_Oinj__on(_1486154, _1486156, _1486158, _1486160))], (46448 ^ _776545) ^ [_1710900, _1710902, _1710904, _1710906, _1710908] : [class_Orderings_Olinorder(_1710900), hBOOL(hAPP(hAPP(c_member(_1710902), _1710904), hAPP(c_List_Oset(_1710902), _1710906))), c_List_Olinorder__class_Osorted(_1710900, hAPP(hAPP(c_List_Omap(_1710902, _1710900), _1710908), _1710906)), hAPP(c_List_Ohd(_1710902), hAPP(c_List_Ofilter(_1710902, hAPP(hAPP(c_COMBB(_1710900, tc_HOL_Obool, _1710902), hAPP(c_fequal, hAPP(_1710908, _1710904))), _1710908)), _1710906)) = _1710904, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710902, _1710900, _1710908), _1710904), c_List_Oremove1(_1710902, _1710904, _1710906)) = _1710906)], (20001 ^ _776545) ^ [_1137604, _1137606, _1137608] : [class_Fields_Ofield__inverse__zero(_1137604), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137604), hAPP(c_Groups_Ouminus__class_Ouminus(_1137604), _1137606)), hAPP(c_Groups_Ouminus__class_Ouminus(_1137604), _1137608)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137604), _1137606), _1137608))], (24377 ^ _776545) ^ [_1217396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217396)), -(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), _1217396))))], (42953 ^ _776545) ^ [_1632568, _1632570, _1632572, _1632574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632568), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632570)), _1632572))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1632568), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632570)), _1632574))), 42963 ^ _776545 : [(42966 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Onth(_1632570), _1632572), 42962 ^ [_1632568, _1632570, _1632572, _1632574]) = hAPP(hAPP(c_List_Onth(_1632570), _1632574), 42962 ^ [_1632568, _1632570, _1632572, _1632574])], (42964 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42962 ^ [_1632568, _1632570, _1632572, _1632574]), _1632568)))]], -(hAPP(hAPP(c_List_Otake(_1632570), _1632568), _1632572) = hAPP(hAPP(c_List_Otake(_1632570), _1632568), _1632574))], (25203 ^ _776545) ^ [_1232858, _1232860] : [class_Int_Onumber__ring(_1232858), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232858), hAPP(c_Int_Onumber__class_Onumber__of(_1232858), c_Int_OMin)), _1232860) = hAPP(c_Groups_Ouminus__class_Ouminus(_1232858), _1232860))], (33821 ^ _776545) ^ [_1402958, _1402960, _1402962, _1402964] : [class_Rings_Osemiring__1(_1402958), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1402960, _1402958), hAPP(c_COMBK(_1402958, _1402960), _1402962)), _1402964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402958), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1402958), hAPP(c_Finite__Set_Ocard(_1402960), _1402964))), _1402962))], (26933 ^ _776545) ^ [_1261662, _1261664, _1261666] : [class_Rings_Olinordered__idom(_1261662), 26936 ^ _776545 : [(26943 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261664), _1261666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261662), hAPP(c_Int_Oring__1__class_Oof__int(_1261662), _1261664)), hAPP(c_Int_Oring__1__class_Oof__int(_1261662), _1261666))))], (26937 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261662), hAPP(c_Int_Oring__1__class_Oof__int(_1261662), _1261664)), hAPP(c_Int_Oring__1__class_Oof__int(_1261662), _1261666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261664), _1261666)))]]], (46341 ^ _776545) ^ [_1708530, _1708532] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1708530), _1708532)) = c_List_Oupt(_1708530, _1708532))], (52017 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (44200 ^ _776545) ^ [_1660358, _1660360, _1660362] : [-(_1660358 = c_List_Olist_ONil(_1660360)), -(hAPP(c_List_Otl(_1660360), hAPP(hAPP(c_List_Oappend(_1660360), _1660358), _1660362)) = hAPP(hAPP(c_List_Oappend(_1660360), hAPP(c_List_Otl(_1660360), _1660358)), _1660362))], (49052 ^ _776545) ^ [_1765998, _1766000] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765998, _1766000), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1765998)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10951 ^ _776545) ^ [_965777, _965779, _965781, _965783, _965785, _965787, _965789] : [c_Finite__Set_Ofun__left__comm(_965777, _965779, _965781), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_965777, _965779, _965781, _965783, _965785), _965787)), hBOOL(hAPP(hAPP(c_member(_965777), _965789), _965785)), 10963 ^ _776545 : [(10966 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_965777, _965779, _965781, _965783, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965777, tc_HOL_Obool)), _965785), hAPP(hAPP(c_Set_Oinsert(_965777), _965789), c_Orderings_Obot__class_Obot(tc_fun(_965777, tc_HOL_Obool))))), 10962 ^ [_965777, _965779, _965781, _965783, _965785, _965787, _965789])))], (10964 ^ _776545) ^ [] : [-(_965787 = hAPP(hAPP(_965781, _965789), 10962 ^ [_965777, _965779, _965781, _965783, _965785, _965787, _965789]))]]], (46261 ^ _776545) ^ [_1707207, _1707209] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1707207, _1707209)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1707207), _1707209))], (9804 ^ _776545) ^ [_944504, _944506, _944508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944504, tc_HOL_Obool)), _944506), _944508)), 9807 ^ _776545 : [(9810 ^ _776545) ^ [] : [_944506 = _944508], (9808 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_944504, tc_HOL_Obool)), _944506), _944508)))]]], (29953 ^ _776545) ^ [_1313627, _1313629, _1313631] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313627), _1313629)), hBOOL(hAPP(_1313631, c_Orderings_Obot__class_Obot(tc_fun(_1313627, tc_HOL_Obool)))), 29964 ^ _776545 : [(29967 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1313627), 29962 ^ [_1313627, _1313629, _1313631]), 29963 ^ [_1313627, _1313629, _1313631]))], (29969 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1313631, 29963 ^ [_1313627, _1313629, _1313631])))], (29971 ^ _776545) ^ [] : [hBOOL(hAPP(_1313631, hAPP(hAPP(c_Set_Oinsert(_1313627), 29962 ^ [_1313627, _1313629, _1313631]), 29963 ^ [_1313627, _1313629, _1313631])))], (29965 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1313627), 29963 ^ [_1313627, _1313629, _1313631])))]], -(hBOOL(hAPP(_1313631, _1313629)))], (38669 ^ _776545) ^ [_1519548, _1519550, _1519552, _1519554, _1519556] : [-(hAPP(c_Set_Ovimage(_1519548, _1519550, _1519552), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519550, tc_HOL_Obool)), _1519554), _1519556)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1519548, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519548, _1519550, _1519552), _1519554)), hAPP(c_Set_Ovimage(_1519548, _1519550, _1519552), _1519556)))], (10877 ^ _776545) ^ [_964255, _964257, _964259, _964261] : [class_Orderings_Oorder(_964255), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964255, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964255, _964257, _964259)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964255, _964259), _964261)) = c_Orderings_Obot__class_Obot(tc_fun(_964255, tc_HOL_Obool)))], (44208 ^ _776545) ^ [_1660480, _1660482, _1660484] : [-(hAPP(c_List_Orotate(_1660480, _1660482), _1660484) = hAPP(c_List_Orotate(_1660480, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1660482, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660480)), _1660484))), _1660484))], (14046 ^ _776545) ^ [_1028250, _1028252, _1028254, _1028256, _1028258, _1028260, _1028262, _1028264] : [c_Finite__Set_Ofolding__image__simple__idem(_1028250, _1028252, _1028254, _1028256, _1028258, _1028260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028252), _1028262)), -(hAPP(_1028260, hAPP(hAPP(c_Set_Oinsert(_1028252), _1028264), _1028262)) = hAPP(hAPP(_1028254, hAPP(_1028258, _1028264)), hAPP(_1028260, _1028262)))], (42767 ^ _776545) ^ [_1628250, _1628252, _1628254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628250), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628252)), _1628254))), -(hAPP(hAPP(c_List_Otake(_1628252), _1628250), c_List_Obutlast(_1628252, _1628254)) = hAPP(hAPP(c_List_Otake(_1628252), _1628250), _1628254))], (36742 ^ _776545) ^ [_1473619, _1473621, _1473623, _1473625] : [c_Equiv__Relations_Oequiv(_1473619, _1473621, _1473623), hBOOL(hAPP(hAPP(c_member(_1473619), _1473625), _1473621)), -(hBOOL(hAPP(hAPP(c_member(_1473619), _1473625), hAPP(c_Relation_OImage(_1473619, _1473619, _1473623), hAPP(hAPP(c_Set_Oinsert(_1473619), _1473625), c_Orderings_Obot__class_Obot(tc_fun(_1473619, tc_HOL_Obool)))))))], (11704 ^ _776545) ^ [_981338, _981340, _981342, _981344] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_981338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981338, tc_HOL_Obool)), _981340), hAPP(hAPP(c_Set_Oinsert(_981338), _981342), _981344)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_981338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981338, tc_HOL_Obool)), _981340), _981344))))], (16504 ^ _776545) ^ [_1073716] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1073716) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7762 ^ _776545) ^ [_906880, _906882, _906884, _906886] : [hBOOL(hAPP(hAPP(c_member(_906880), _906882), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906880, tc_HOL_Obool)), _906884), _906886))), -(hBOOL(hAPP(hAPP(c_member(_906880), _906882), _906884))), -(hBOOL(hAPP(hAPP(c_member(_906880), _906882), _906886)))], (41047 ^ _776545) ^ [_1580780, _1580782, _1580784] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580780, _1580780), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580780, _1580780), _1580782)), c_Transitive__Closure_Ortrancl(_1580780, _1580782)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1580780, _1580780), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580780, _1580780)), hAPP(hAPP(c_Product__Type_OPair(_1580780, _1580780), _1580784), _1580784)), c_Transitive__Closure_Otrancl(_1580780, _1580782)))], (43076 ^ _776545) ^ [_1634886, _1634888] : [-(hAPP(hAPP(c_List_Otake(_1634886), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1634888) = c_List_Olist_ONil(_1634886))], (25307 ^ _776545) ^ [_1234558, _1234560, _1234562] : [-(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), _1234558), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234560), _1234558))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234560, _1234558))), _1234562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234560), _1234562))], (19017 ^ _776545) ^ [_1119123, _1119125] : [19019 ^ _776545 : [(19022 ^ _776545) ^ [] : [hBOOL(hAPP(_1119125, 19018 ^ [_1119123, _1119125]))], (19020 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19018 ^ [_1119123, _1119125]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1119123))))]], 19023 ^ _776545 : [(19024 ^ _776545) ^ [_1119278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119278), _1119123)), -(hBOOL(hAPP(_1119125, _1119278)))]]], (45792 ^ _776545) ^ [_1695308, _1695310, _1695312, _1695314] : [-(hAPP(c_List_OremoveAll(_1695308, _1695310), hAPP(hAPP(c_List_Oappend(_1695308), _1695312), _1695314)) = hAPP(hAPP(c_List_Oappend(_1695308), hAPP(c_List_OremoveAll(_1695308, _1695310), _1695312)), hAPP(c_List_OremoveAll(_1695308, _1695310), _1695314)))], (33076 ^ _776545) ^ [_1381055, _1381057, _1381059, _1381061] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1381055, tc_fun(_1381057, tc_HOL_Obool))), _1381059), _1381061)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381055, _1381057)), hAPP(hAPP(c_Product__Type_OPair(_1381055, _1381057), _1381059), _1381061)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1381055, _1381057), tc_HOL_Obool)))))], (3432 ^ _776545) ^ [_827800, _827802, _827804, _827806, _827808, _827810] : [-(c_Enum_On__lists(_827810, _827806, _827802) = c_Enum_On__lists(_827808, _827804, _827800)), _827810 = _827808, _827806 = _827804, _827802 = _827800], (51033 ^ _776545) ^ [_1809876, _1809878, _1809880, _1809882] : [class_Rings_Ocomm__ring(_1809876), class_Rings_Odvd(_1809876), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809876), _1809878), _1809880)), 51044 ^ _776545 : [(51051 ^ _776545) ^ [_1810302, _1810304] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809876), _1809878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1809876), _1810304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1809876), _1810302), _1809880))), _1809882))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809876), _1809878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809876), _1810304), _1809882))))], (51045 ^ _776545) ^ [_1810129, _1810131] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809876), _1809878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809876), _1810131), _1809882))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809876), _1809878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1809876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1809876), _1810131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1809876), _1810129), _1809880))), _1809882))))]]], (22369 ^ _776545) ^ [_1182093, _1182095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182093), _1182095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182093), _1182095)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38537 ^ _776545) ^ [_1515564, _1515566, _1515568, _1515570] : [hBOOL(hAPP(hAPP(c_member(_1515564), _1515566), hAPP(c_Relation_ORange(_1515568, _1515564), _1515570))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515568, _1515564)), hAPP(hAPP(c_Product__Type_OPair(_1515568, _1515564), 38540 ^ [_1515564, _1515566, _1515568, _1515570]), _1515566)), _1515570)))], (32984 ^ _776545) ^ [_1378485, _1378487, _1378489] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378485, tc_HOL_Obool)), _1378487), _1378489) = hAPP(c_Set_OCollect(_1378485), hAPP(hAPP(c_COMBS(_1378485, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1378485), c_fconj), hAPP(hAPP(c_COMBC(_1378485, tc_fun(_1378485, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378485)), _1378487))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1378485), c_fNot), hAPP(hAPP(c_COMBC(_1378485, tc_fun(_1378485, tc_HOL_Obool), tc_HOL_Obool), c_member(_1378485)), _1378489)))))], (22153 ^ _776545) ^ [_1178294, _1178296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178294)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178294), _1178296)))], (22343 ^ _776545) ^ [_1181611, _1181613, _1181615] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1181611), _1181613)), _1181615) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181611), _1181615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181613), _1181615)))], (14152 ^ _776545) ^ [_1030752, _1030754, _1030756, _1030758, _1030760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030752), _1030754)), -(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), _1030752), _1030756)), _1030758)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030754), _1030756)), _1030760)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1030758), 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), _1030754), _1030752)), _1030756)), _1030760)))], (29097 ^ _776545) ^ [_1298090, _1298092] : [class_Int_Onumber__ring(_1298090), class_Int_Oring__char__0(_1298090), 29104 ^ _776545 : [(29111 ^ _776545) ^ [] : [c_Int_Oiszero(_1298090, hAPP(c_Int_Onumber__class_Onumber__of(_1298090), _1298092)), -(c_Int_Oiszero(_1298090, hAPP(c_Int_Onumber__class_Onumber__of(_1298090), c_Int_OBit0(_1298092))))], (29105 ^ _776545) ^ [] : [c_Int_Oiszero(_1298090, hAPP(c_Int_Onumber__class_Onumber__of(_1298090), c_Int_OBit0(_1298092))), -(c_Int_Oiszero(_1298090, hAPP(c_Int_Onumber__class_Onumber__of(_1298090), _1298092)))]]], (39357 ^ _776545) ^ [_1538506, _1538508, _1538510, _1538512] : [class_Groups_Ocomm__monoid__mult(_1538506), c_Fun_Oinj__on(_1538508, _1538506, _1538510, _1538512), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538508, _1538506), _1538510), _1538512) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538506, _1538506), c_Fun_Oid(_1538506)), hAPP(c_Set_Oimage(_1538508, _1538506, _1538510), _1538512)))], (14740 ^ _776545) ^ [_1042214, _1042216, _1042218, _1042220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042214), _1042216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042218), _1042220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042214), _1042218)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042216), _1042220))))], (48995 ^ _776545) ^ [_1764723, _1764725, _1764727] : [-(c_FunDef_OTHE__default(_1764725, _1764727, _1764723) = c_HOL_OThe(_1764725, _1764723)), 48996 ^ _776545 : [(48997 ^ _776545) ^ [_1764787] : [hBOOL(hAPP(_1764723, _1764787)), 49001 ^ _776545 : [(49004 ^ _776545) ^ [] : [49000 ^ [_1764723, _1764725, _1764727, _1764787] = _1764787], (49002 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1764723, 49000 ^ [_1764723, _1764725, _1764727, _1764787])))]]]]], (17947 ^ _776545) ^ [_1099402, _1099404] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1099402, _1099404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1099404)), _1099402))], (38642 ^ _776545) ^ [_1518930, _1518932, _1518934, _1518936, _1518938] : [hBOOL(hAPP(_1518936, hAPP(_1518934, _1518938))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1518930, _1518932, _1518934), _1518936), _1518938)))], (38953 ^ _776545) ^ [_1526155, _1526157, _1526159] : [-(hAPP(c_Relation_ODomain(_1526155, _1526157), hAPP(c_Set_OCollect(tc_prod(_1526155, _1526157)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526155, _1526157, tc_HOL_Obool), _1526159))) = hAPP(c_Set_OCollect(_1526155), hAPP(hAPP(c_COMBB(tc_fun(_1526157, tc_HOL_Obool), tc_HOL_Obool, _1526155), c_HOL_OEx(_1526157)), _1526159)))], (45591 ^ _776545) ^ [_1690804, _1690806, _1690808, _1690810, _1690812] : [-(c_List_Olist__all2(_1690804, _1690806, _1690808, _1690810, _1690812)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690804)), _1690810) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690806)), _1690812), 45597 ^ _776545 : [(45600 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1690808, hAPP(hAPP(c_List_Onth(_1690804), _1690810), 45596 ^ [_1690804, _1690806, _1690808, _1690810, _1690812])), hAPP(hAPP(c_List_Onth(_1690806), _1690812), 45596 ^ [_1690804, _1690806, _1690808, _1690810, _1690812])))], (45598 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45596 ^ [_1690804, _1690806, _1690808, _1690810, _1690812]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690804)), _1690810))))]]], (15360 ^ _776545) ^ [_1053911, _1053913, _1053915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053911), _1053913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1053911), _1053913)), hAPP(c_Finite__Set_Ocard(_1053911), hAPP(hAPP(c_Set_Oinsert(_1053911), _1053915), _1053913)))))], (49307 ^ _776545) ^ [_1771998, _1772000, _1772002] : [c_Relation_Otrans(_1771998, _1772000), c_Relation_Otrans(_1771998, _1772002), -(c_Relation_Otrans(_1771998, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1771998, _1771998), tc_HOL_Obool)), _1772000), _1772002)))], (47591 ^ _776545) ^ [_1733605, _1733607, _1733609] : [-(c_List_Oinsert(_1733605, _1733607, c_List_Oremdups(_1733605, _1733609)) = c_List_Oremdups(_1733605, c_List_Oinsert(_1733605, _1733607, _1733609)))], (34692 ^ _776545) ^ [_1422902, _1422904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1422902, _1422902)), hAPP(hAPP(c_Product__Type_OPair(_1422902, _1422902), 34693 ^ [_1422902, _1422904]), 34693 ^ [_1422902, _1422904])), _1422904)), -(c_Nitpick_Orefl_H(_1422902, _1422904))], (10607 ^ _776545) ^ [_958938, _958940, _958942, _958944, _958946] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_958938, _958940, _958942, _958944, c_Orderings_Obot__class_Obot(tc_fun(_958938, tc_HOL_Obool))), _958946)), -(_958946 = _958944)], (42303 ^ _776545) ^ [_1615986, _1615988, _1615990] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1615986, tc_HOL_Obool)), hAPP(c_List_Oset(_1615986), _1615988)), hAPP(c_List_Oset(_1615986), hAPP(hAPP(c_List_Olist_OCons(_1615986), _1615990), _1615988)))))], (29847 ^ _776545) ^ [_1311677, _1311679, _1311681, _1311683] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1311677, _1311679, _1311681, c_Code__Numeral_OSuc__code__numeral(_1311683)) = hAPP(_1311681, _1311683))], (38636 ^ _776545) ^ [_1518823, _1518825, _1518827, _1518829, _1518831] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1518823, _1518825, _1518827), _1518829), _1518831)), -(hBOOL(hAPP(_1518829, hAPP(_1518827, _1518831))))], (27249 ^ _776545) ^ [_1266831] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266831), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1266831)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1266831)))], (45750 ^ _776545) ^ [_1694549, _1694551] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694549)), c_List_Oremdups(_1694549, _1694551))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694549)), _1694551))))], (23707 ^ _776545) ^ [_1205983] : [_1205983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205983) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29315 ^ _776545) ^ [_1301851, _1301853] : [class_Rings_Olinordered__idom(_1301851), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301851), hAPP(c_Groups_Oabs__class_Oabs(_1301851), _1301853)), 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(_1301851), _1301853), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (48804 ^ _776545) ^ [_1760220, _1760222, _1760224, _1760226, _1760228, _1760230] : [-(c_New__Random__Sequence_Opos__union(_1760220, _1760222, _1760224, _1760226, _1760228, _1760230) = c_New__DSequence_Opos__union(_1760220, hAPP(hAPP(hAPP(_1760222, _1760226), _1760228), _1760230), hAPP(hAPP(hAPP(_1760224, _1760226), _1760228), _1760230)))], (43591 ^ _776545) ^ [_1646094, _1646096, _1646098] : [_1646098 = c_List_Olist_ONil(_1646096), -(_1646094 = hAPP(hAPP(c_List_Oappend(_1646096), _1646094), _1646098))], (45257 ^ _776545) ^ [_1682915] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682915), 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, _1682915)) = _1682915)], (45515 ^ _776545) ^ [_1689148, _1689150, _1689152, _1689154, _1689156, _1689158] : [c_List_Olist__all2(_1689148, _1689150, _1689152, _1689154, _1689156), -(c_List_Olist__all2(_1689148, _1689150, _1689152, hAPP(hAPP(c_List_Otake(_1689148), _1689158), _1689154), hAPP(hAPP(c_List_Otake(_1689150), _1689158), _1689156)))], (45822 ^ _776545) ^ [_1695846, _1695848] : [c_List_Oremdups(_1695846, _1695848) = c_List_Olist_ONil(_1695846), -(_1695848 = c_List_Olist_ONil(_1695846))], (46596 ^ _776545) ^ [_1713276, _1713278] : [class_Orderings_Olinorder(_1713276), -(_1713278 = c_List_Olist_ONil(_1713276)), c_List_Olinorder__class_Osorted(_1713276, _1713278), -(c_List_Olinorder__class_Osorted(_1713276, c_List_Obutlast(_1713276, _1713278)))], (15636 ^ _776545) ^ [_1060183] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060183)))], (32268 ^ _776545) ^ [_1356680, _1356682, _1356684] : [-(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), _1356680)), 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))), _1356682))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1356684))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1356684)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356680), 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), _1356684), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1356682)))))], (47664 ^ _776545) ^ [_1735521, _1735523, _1735525, _1735527, _1735529] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1735521, _1735521)), hAPP(hAPP(c_Product__Type_OPair(_1735521, _1735521), _1735523), _1735525)), c_List_Omeasures(_1735521, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735521, tc_Nat_Onat)), _1735527), _1735529)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1735527, _1735523)), hAPP(_1735527, _1735525)))), 47671 ^ _776545 : [(47674 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735521, _1735521)), hAPP(hAPP(c_Product__Type_OPair(_1735521, _1735521), _1735523), _1735525)), c_List_Omeasures(_1735521, _1735529))))], (47672 ^ _776545) ^ [] : [-(hAPP(_1735527, _1735523) = hAPP(_1735527, _1735525))]]], (44154 ^ _776545) ^ [_1659462, _1659464] : [hBOOL(hAPP(c_List_Odistinct(_1659462), _1659464)), -(hBOOL(hAPP(c_List_Odistinct(_1659462), hAPP(c_List_Otl(_1659462), _1659464))))], (46091 ^ _776545) ^ [_1702247, _1702249, _1702251] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1702247), tc_List_Olist(_1702247)), c_List_Opartition(_1702247, _1702249, _1702251)) = hAPP(c_List_Ofilter(_1702247, _1702249), _1702251))], (36142 ^ _776545) ^ [_1457941, _1457943, _1457945, _1457947, _1457949, _1457951, _1457953] : [hBOOL(hAPP(_1457941, _1457943)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457945, _1457945)), hAPP(hAPP(c_Product__Type_OPair(_1457945, _1457945), _1457947), _1457949)), hAPP(_1457951, _1457943))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1457953, _1457945), tc_prod(_1457953, _1457945))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1457953, _1457945), tc_prod(_1457953, _1457945)), hAPP(hAPP(c_Product__Type_OPair(_1457953, _1457945), _1457943), _1457947)), hAPP(hAPP(c_Product__Type_OPair(_1457953, _1457945), _1457943), _1457949))), c_Recdef_Osame__fst(_1457953, _1457945, _1457941, _1457951))))], (45014 ^ _776545) ^ [_1678086, _1678088, _1678090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678086), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678088)), _1678090))), -(hAPP(c_Random_Opick(_1678088, hAPP(hAPP(c_List_Omap(_1678088, tc_prod(tc_Code__Numeral_Ocode__numeral, _1678088)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1678088), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1678090)), hAPP(c_Code__Numeral_Oof__nat, _1678086)) = hAPP(hAPP(c_List_Onth(_1678088), _1678090), _1678086))], (46399 ^ _776545) ^ [_1709615] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1709615) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1709615)))], (38713 ^ _776545) ^ [_1520661, _1520663, _1520665, _1520667] : [-(hAPP(c_Set_Ovimage(_1520661, _1520663, _1520665), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1520663, tc_HOL_Obool), _1520667)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1520663, tc_HOL_Obool), tc_fun(_1520661, tc_HOL_Obool)), _1520667), c_Set_Ovimage(_1520661, _1520663, _1520665)))], (20903 ^ _776545) ^ [_1153999, _1154001, _1154003, _1154005] : [class_Fields_Olinordered__field__inverse__zero(_1153999), 20906 ^ _776545 : [(20907 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153999), _1154001), _1154003)), _1154005)), 20910 ^ _776545 : [(20917 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154003))), 20920 ^ _776545 : [(20927 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), _1154003), c_Groups_Ozero__class_Ozero(_1153999)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154005)))], (20921 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), _1154003), c_Groups_Ozero__class_Ozero(_1153999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153999), _1154005), _1154003)), _1154001)))]]], (20911 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), _1154001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153999), _1154005), _1154003))))]]], (20933 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153999), _1154001), _1154003)), _1154005))), 20936 ^ _776545 : [(20939 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), _1154001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153999), _1154005), _1154003)))], (20937 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154003)))]], 20940 ^ _776545 : [(20943 ^ _776545) ^ [] : [20944 ^ _776545 : [(20947 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153999), _1154005), _1154003)), _1154001))], (20945 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), _1154003), c_Groups_Ozero__class_Ozero(_1153999))))]], 20948 ^ _776545 : [(20951 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154005))], (20949 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), _1154003), c_Groups_Ozero__class_Ozero(_1153999)))]]], (20941 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153999), c_Groups_Ozero__class_Ozero(_1153999)), _1154003))]]]]], (4544 ^ _776545) ^ [_845552, _845554, _845556, _845558] : [-(c_HOL_OThe(_845558, _845554) = c_HOL_OThe(_845556, _845552)), _845558 = _845556, _845554 = _845552], (14284 ^ _776545) ^ [_1033781, _1033783, _1033785, _1033787] : [class_Rings_Ocomm__semiring__1(_1033781), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033781), _1033783), _1033785)), _1033787) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033781), _1033783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033781), _1033785), _1033787)))], (30040 ^ _776545) ^ [_1315244, _1315246, _1315248] : [class_Orderings_Olinorder(_1315244), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315244), _1315246), _1315248) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315244), _1315248), _1315246))], (50103 ^ _776545) ^ [_1788779, _1788781, _1788783, _1788785] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1788779, _1788781, c_Orderings_Otop__class_Otop(tc_fun(_1788779, tc_HOL_Obool)), _1788783), _1788785) = c_Hilbert__Choice_OEps(_1788779, hAPP(hAPP(c_COMBC(_1788779, _1788781, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1788781, tc_fun(_1788781, tc_HOL_Obool), _1788779), c_fequal), _1788783)), _1788785)))], (32616 ^ _776545) ^ [_1367984, _1367986, _1367988, _1367990, _1367992] : [-(_1367984 = c_Orderings_Obot__class_Obot(tc_fun(_1367986, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367988, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367986, tc_fun(_1367988, tc_HOL_Obool)), _1367984), _1367990)), _1367992) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367986, tc_fun(_1367988, tc_HOL_Obool)), _1367984), hAPP(hAPP(c_COMBC(_1367986, tc_fun(_1367988, tc_HOL_Obool), tc_fun(_1367988, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1367988, tc_HOL_Obool), tc_fun(tc_fun(_1367988, tc_HOL_Obool), tc_fun(_1367988, tc_HOL_Obool)), _1367986), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367988, tc_HOL_Obool))), _1367990)), _1367992)))], (44172 ^ _776545) ^ [_1659795, _1659797, _1659799, _1659801] : [-(hAPP(c_List_Orotate(_1659795, _1659797), hAPP(c_List_Orotate(_1659795, _1659799), _1659801)) = hAPP(c_List_Orotate(_1659795, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659797), _1659799)), _1659801))], (7876 ^ _776545) ^ [_909195, _909197] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909195, tc_HOL_Obool)), _909197), c_Orderings_Obot__class_Obot(tc_fun(_909195, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_909195, tc_HOL_Obool)))], (52069 ^ _776545) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (36689 ^ _776545) ^ [_1472326, _1472328, _1472330, _1472332] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472326, _1472326)), hAPP(hAPP(c_Product__Type_OPair(_1472326, _1472326), _1472328), _1472330)), c_Relation_OId__on(_1472326, _1472332)))), _1472328 = _1472330, hBOOL(hAPP(hAPP(c_member(_1472326), _1472328), _1472332))], (1124 ^ _776545) ^ [_793459, _793461] : [-(class_Rings_Oring__1__no__zero__divisors(_793459)), _793461 = _793459, class_Rings_Oring__1__no__zero__divisors(_793461)], (10301 ^ _776545) ^ [_953535, _953537, _953539] : [class_Groups_Ogroup__add(_953535), 10304 ^ _776545 : [(10311 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953535), _953539) = _953537, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953535), _953537) = _953539)], (10305 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_953535), _953537) = _953539, -(hAPP(c_Groups_Ouminus__class_Ouminus(_953535), _953539) = _953537)]]], (7722 ^ _776545) ^ [_905827, _905829, _905831] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_905827, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_905827, tc_HOL_Obool), tc_HOL_Obool)), _905829), _905831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905827, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905827, tc_HOL_Obool), _905829)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_905827, tc_HOL_Obool), _905831)))], (33667 ^ _776545) ^ [_1398406, _1398408, _1398410] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398406, tc_Nat_Onat), _1398408), _1398410) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1398406, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1398406), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1398408)), _1398410)))], (29157 ^ _776545) ^ [_1299150, _1299152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299150), _1299152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1299150)), c_Int_OBit0(_1299152))))], (37822 ^ _776545) ^ [_1497520] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1497520))], (12726 ^ _776545) ^ [_1000980, _1000982, _1000984, _1000986] : [class_Lattices_Osemilattice__inf(_1000980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000980), _1000982)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1000980, _1000980, c_Lattices_Osemilattice__inf__class_Oinf(_1000980)), _1000984), hAPP(hAPP(c_Set_Oinsert(_1000980), _1000986), _1000982)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1000980), _1000986), hAPP(hAPP(c_Finite__Set_Ofold(_1000980, _1000980, c_Lattices_Osemilattice__inf__class_Oinf(_1000980)), _1000984), _1000982)))], (48268 ^ _776545) ^ [_1748752, _1748754, _1748756] : [c_List_Olist__all(_1748752, _1748754, hAPP(c_List_Orev(_1748752), _1748756)), -(c_List_Olist__all(_1748752, _1748754, _1748756))], (34273 ^ _776545) ^ [_1414251, _1414253, _1414255] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414251), _1414253))), 34276 ^ _776545 : [(34283 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414255), _1414253))), -(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)), _1414251)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414255), _1414253)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34277 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1414255), _1414253)), -(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)), _1414251)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1414255), _1414253)) = 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))))]]], (26050 ^ _776545) ^ [_1247434] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1247434) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1247434)))], (44539 ^ _776545) ^ [_1667385, _1667387, _1667389] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667385), tc_List_Olist(_1667385))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667385), tc_List_Olist(_1667385)), c_List_Olist_ONil(_1667385)), _1667387)), c_List_Olexord(_1667385, _1667389))), -(_1667387 = hAPP(hAPP(c_List_Olist_OCons(_1667385), 44542 ^ [_1667385, _1667387, _1667389]), 44543 ^ [_1667385, _1667387, _1667389]))], (32914 ^ _776545) ^ [_1376550, _1376552, _1376554, _1376556, _1376558] : [class_Complete__Lattice_Ocomplete__lattice(_1376550), hBOOL(hAPP(hAPP(c_member(_1376552), _1376554), _1376556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376550), hAPP(_1376558, _1376554)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376552, _1376550), _1376556), _1376558))))], (37634 ^ _776545) ^ [_1493113, _1493115, _1493117, _1493119, _1493121, _1493123] : [c_Fun_Oinj__on(_1493113, _1493115, _1493117, _1493119), -(hBOOL(hAPP(hAPP(c_member(_1493115), _1493121), hAPP(c_Set_Oimage(_1493113, _1493115, _1493117), _1493119)))), -(c_Fun_Oinj__on(_1493113, _1493115, c_Fun_Ofun__upd(_1493113, _1493115, _1493117, _1493123, _1493121), _1493119))], (40781 ^ _776545) ^ [_1574569, _1574571, _1574573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574569, _1574569), tc_HOL_Obool)), _1574571), _1574573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574569, _1574569), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574569, _1574571)), c_Transitive__Closure_Ortrancl(_1574569, _1574573))))], (22325 ^ _776545) ^ [_1181175, _1181177] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181175), _1181177) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181177), _1181175))], (45436 ^ _776545) ^ [_1687342, _1687344, _1687346, _1687348, _1687350] : [-(c_List_Olist__all2(_1687342, _1687344, _1687346, _1687348, _1687350)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687342)), _1687348) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687344)), _1687350), 45442 ^ _776545 : [(45445 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687342, _1687344, tc_HOL_Obool), _1687346), 45441 ^ [_1687342, _1687344, _1687346, _1687348, _1687350]))], (45443 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687342, _1687344)), 45441 ^ [_1687342, _1687344, _1687346, _1687348, _1687350]), hAPP(c_List_Oset(tc_prod(_1687342, _1687344)), hAPP(hAPP(c_List_Ozip(_1687342, _1687344), _1687348), _1687350)))))]]], (37536 ^ _776545) ^ [_1490944, _1490946] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490944), c_Orderings_Otop__class_Otop(tc_fun(_1490944, tc_HOL_Obool)))), c_Fun_Oinj__on(_1490944, _1490944, _1490946, c_Orderings_Otop__class_Otop(tc_fun(_1490944, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1490944, _1490944, _1490946), c_Orderings_Otop__class_Otop(tc_fun(_1490944, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1490944, tc_HOL_Obool)))], (7416 ^ _776545) ^ [_898519, _898521, _898523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898519, tc_HOL_Obool)), _898521), _898523) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_898519, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898519, tc_HOL_Obool)), _898521), hAPP(hAPP(c_Set_Oinsert(tc_fun(_898519, tc_HOL_Obool)), _898523), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_898519, tc_HOL_Obool), tc_HOL_Obool))))))], (51669 ^ _776545) ^ [_1821626] : [_1821626 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821626), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9666 ^ _776545) ^ [_942016, _942018, _942020, _942022] : [class_Orderings_Oorder(_942016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942016), _942018), _942020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942016), _942022), _942018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942016), _942022), _942020)))], (15694 ^ _776545) ^ [_1061163] : [_1061163 = hAPP(c_Nat_OSuc, _1061163)], (39966 ^ _776545) ^ [_1554599, _1554601, _1554603, _1554605, _1554607, _1554609, _1554611, _1554613] : [class_Groups_Ocomm__monoid__mult(_1554599), c_Fun_Oinj__on(_1554601, _1554603, _1554605, _1554607), _1554609 = hAPP(c_Set_Oimage(_1554601, _1554603, _1554605), _1554607), _1554611 = hAPP(c_Fun_Ocomp(_1554603, _1554599, _1554601, _1554613), _1554605), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554603, _1554599), _1554613), _1554609) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1554601, _1554599), _1554611), _1554607))], (49576 ^ _776545) ^ [_1778381, _1778383] : [c_Relation_Oantisym(_1778381, hAPP(c_Relation_Oconverse(_1778381, _1778381), _1778383)), -(c_Relation_Oantisym(_1778381, _1778383))], (1134 ^ _776545) ^ [_793584, _793586] : [-(class_Rings_Olinordered__ring__strict(_793584)), _793586 = _793584, class_Rings_Olinordered__ring__strict(_793586)], (20109 ^ _776545) ^ [_1139580, _1139582, _1139584, _1139586] : [class_Fields_Olinordered__field(_1139580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139580), _1139582), _1139584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139580), _1139586), c_Groups_Ozero__class_Ozero(_1139580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139580), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139580), _1139584), _1139586)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139580), _1139582), _1139586))))], (30770 ^ _776545) ^ [_1328492, _1328494, _1328496] : [class_Orderings_Olinorder(_1328492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328492), _1328494)), -(_1328494 = c_Orderings_Obot__class_Obot(tc_fun(_1328492, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1328492, hAPP(hAPP(c_Set_Oinsert(_1328492), _1328496), _1328494)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328492), _1328496), c_Big__Operators_Olinorder__class_OMin(_1328492, _1328494)))], (52157 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (5286 ^ _776545) ^ [_857229, _857231, _857233, _857235, _857237, _857239] : [-(c_Lazy__Sequence_Obind(_857239, _857235, _857231) = c_Lazy__Sequence_Obind(_857237, _857233, _857229)), _857239 = _857237, _857235 = _857233, _857231 = _857229], (9954 ^ _776545) ^ [_946990, _946992, _946994] : [class_Orderings_Oorder(_946990), 9957 ^ _776545 : [(9964 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946990), _946992), _946994))), -(c_SetInterval_Oord__class_OatLeastAtMost(_946990, _946992, _946994) = c_Orderings_Obot__class_Obot(tc_fun(_946990, tc_HOL_Obool)))], (9958 ^ _776545) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_946990, _946992, _946994) = c_Orderings_Obot__class_Obot(tc_fun(_946990, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946990), _946992), _946994))]]], (49210 ^ _776545) ^ [_1769968, _1769970] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1769968, tc_HOL_Obool), _1769970) = hAPP(c_Set_OCollect(_1769968), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769968, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1769968), c_HOL_OEx(tc_fun(_1769968, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769968, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1769968, tc_HOL_Obool), tc_HOL_Obool), _1769968), hAPP(c_COMBS(tc_fun(_1769968, 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(_1769968, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769968, tc_HOL_Obool), tc_fun(tc_fun(_1769968, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769968, tc_HOL_Obool))), _1769970)))), c_member(_1769968)))))], (41102 ^ _776545) ^ [_1582508, _1582510, _1582512, _1582514] : [-(hAPP(c_Relation_Oconverse(_1582508, _1582510), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1582508, _1582510), tc_HOL_Obool)), _1582512), _1582514)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1582510, _1582508), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1582508, _1582510), _1582512)), hAPP(c_Relation_Oconverse(_1582508, _1582510), _1582514)))], (36780 ^ _776545) ^ [_1474405, _1474407, _1474409, _1474411, _1474413, _1474415, _1474417] : [c_Equiv__Relations_Oequiv(_1474405, _1474407, _1474409), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474405, tc_HOL_Obool)), _1474411), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474405), _1474407), _1474409))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1474405, tc_HOL_Obool)), _1474413), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1474405), _1474407), _1474409))), hBOOL(hAPP(hAPP(c_member(_1474405), _1474415), _1474411)), hBOOL(hAPP(hAPP(c_member(_1474405), _1474417), _1474413)), 36799 ^ _776545 : [(36806 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1474405, _1474405)), hAPP(hAPP(c_Product__Type_OPair(_1474405, _1474405), _1474415), _1474417)), _1474409)), -(_1474411 = _1474413)], (36800 ^ _776545) ^ [] : [_1474411 = _1474413, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474405, _1474405)), hAPP(hAPP(c_Product__Type_OPair(_1474405, _1474405), _1474415), _1474417)), _1474409)))]]], (25594 ^ _776545) ^ [_1239531, _1239533, _1239535] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239531)))), 25597 ^ _776545 : [(25604 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239533)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239533)), _1239535)) = 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), _1239531), _1239533))), _1239535))], (25598 ^ _776545) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239533))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239533)), _1239535)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239531)), _1239535))]]], (45848 ^ _776545) ^ [_1696249, _1696251, _1696253] : [hBOOL(hAPP(c_List_Odistinct(_1696249), _1696251)), -(c_List_Oremove1(_1696249, _1696253, _1696251) = hAPP(c_List_OremoveAll(_1696249, _1696253), _1696251))], (23785 ^ _776545) ^ [_1207348, _1207350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207348)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1207350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207348), _1207350)))], (2358 ^ _776545) ^ [_810957, _810959, _810961, _810963, _810965, _810967, _810969, _810971] : [-(c_Nitpick_Oprod(_810971, _810967, _810963, _810959) = c_Nitpick_Oprod(_810969, _810965, _810961, _810957)), _810971 = _810969, _810967 = _810965, _810963 = _810961, _810959 = _810957], (25127 ^ _776545) ^ [_1231299] : [-(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, _1231299))))))], (49141 ^ _776545) ^ [_1768102, _1768104, _1768106, _1768108] : [-(hAPP(c_Relation_OImage(_1768102, _1768104, hAPP(c_Set_OCollect(tc_prod(_1768102, _1768104)), hAPP(c_Product__Type_Oprod_Oprod__case(_1768102, _1768104, tc_HOL_Obool), _1768106))), _1768108) = hAPP(c_Set_OCollect(_1768104), hAPP(hAPP(c_COMBB(tc_fun(_1768102, tc_HOL_Obool), tc_HOL_Obool, _1768104), c_HOL_OEx(_1768102)), hAPP(hAPP(c_COMBB(tc_fun(_1768102, tc_HOL_Obool), tc_fun(_1768102, tc_HOL_Obool), _1768104), hAPP(c_COMBS(_1768102, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768102), c_fconj), hAPP(hAPP(c_COMBC(_1768102, tc_fun(_1768102, tc_HOL_Obool), tc_HOL_Obool), c_member(_1768102)), _1768108)))), hAPP(c_COMBC(_1768102, _1768104, tc_HOL_Obool), _1768106)))))], (2022 ^ _776545) ^ [_805671, _805673, _805675, _805677, _805679, _805681, _805683, _805685, _805687, _805689] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_805689, _805685, _805681, _805677, _805673) = c_SetInterval_Oord_OgreaterThanAtMost(_805687, _805683, _805679, _805675, _805671)), _805689 = _805687, _805685 = _805683, _805681 = _805679, _805677 = _805675, _805673 = _805671], (33843 ^ _776545) ^ [_1403589] : [class_Orderings_Olinorder(_1403589), -(c_Orderings_Oord_Omax(_1403589, hAPP(c_COMBC(_1403589, _1403589, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1403589))) = c_Orderings_Oord__class_Omin(_1403589))], (51989 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (40597 ^ _776545) ^ [_1569224, _1569226, _1569228, _1569230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569224, _1569224)), hAPP(hAPP(c_Product__Type_OPair(_1569224, _1569224), _1569226), _1569228)), _1569230)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569224, _1569224)), hAPP(hAPP(c_Product__Type_OPair(_1569224, _1569224), _1569226), _1569228)), c_Transitive__Closure_Otrancl(_1569224, _1569230))))], (17743 ^ _776545) ^ [_1095947, _1095949] : [class_Groups_Olinordered__ab__group__add(_1095947), 17746 ^ _776545 : [(17753 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095947), c_Groups_Ozero__class_Ozero(_1095947)), _1095949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095947), hAPP(c_Groups_Ouminus__class_Ouminus(_1095947), _1095949)), _1095949)))], (17747 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095947), hAPP(c_Groups_Ouminus__class_Ouminus(_1095947), _1095949)), _1095949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095947), c_Groups_Ozero__class_Ozero(_1095947)), _1095949)))]]], (4160 ^ _776545) ^ [_839562, _839564, _839566, _839568, _839570, _839572, _839574, _839576] : [-(c_New__Random__Sequence_Opos__bind(_839576, _839572, _839568, _839564) = c_New__Random__Sequence_Opos__bind(_839574, _839570, _839566, _839562)), _839576 = _839574, _839572 = _839570, _839568 = _839566, _839564 = _839562], (6025 ^ _776545) ^ [_872711, _872713, _872715, _872717] : [hBOOL(hAPP(hAPP(_872715, _872713), _872717)), -(hBOOL(hAPP(hAPP(c_member(_872711), _872713), c_SetInterval_Oord_OlessThan(_872711, _872715, _872717))))], (31603 ^ _776545) ^ [_1343944, _1343946, _1343948, _1343950] : [class_Orderings_Olinorder(_1343944), 31606 ^ _776545 : [(31615 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343944), _1343946), _1343948)), _1343950))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), _1343946), _1343950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), _1343948), _1343950))], (31607 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1343944), _1343946), _1343948)), _1343950)), 31610 ^ _776545 : [(31613 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), _1343948), _1343950)))], (31611 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343944), _1343946), _1343950)))]]]]], (10140 ^ _776545) ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264] : [c_Nitpick_Ofold__graph_H(_950252, _950254, _950256, _950258, _950260, hAPP(hAPP(_950256, _950262), _950264)), 10145 ^ _776545 : [(10148 ^ _776545) ^ [] : [-(hAPP(hAPP(_950256, _950262), _950264) = _950258)], (10146 ^ _776545) ^ [] : [-(_950260 = c_Orderings_Obot__class_Obot(tc_fun(_950252, tc_HOL_Obool)))]], 10151 ^ _776545 : [(10156 ^ _776545) ^ [] : [-(c_Nitpick_Ofold__graph_H(_950252, _950254, _950256, _950258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950252, tc_HOL_Obool)), _950260), hAPP(hAPP(c_Set_Oinsert(_950252), 10149 ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264]), c_Orderings_Obot__class_Obot(tc_fun(_950252, tc_HOL_Obool)))), 10150 ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264]))], (10154 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_950252), 10149 ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264]), _950260)))], (10152 ^ _776545) ^ [] : [-(hAPP(hAPP(_950256, _950262), _950264) = hAPP(hAPP(_950256, 10149 ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264]), 10150 ^ [_950252, _950254, _950256, _950258, _950260, _950262, _950264]))]]], (24118 ^ _776545) ^ [_1212954, _1212956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212954)), 24121 ^ _776545 : [(24130 ^ _776545) ^ [] : [-(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), _1212954), _1212956)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212956), _1212954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212956))], (24122 ^ _776545) ^ [] : [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), _1212954), _1212956))), 24125 ^ _776545 : [(24128 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212956)))], (24126 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212956), _1212954)))]]]]], (11167 ^ _776545) ^ [_969892, _969894, _969896, _969898, _969900] : [-(hAPP(c_Set_Oimage(_969892, _969894, _969896), hAPP(hAPP(c_Set_Oinsert(_969892), _969898), _969900)) = hAPP(hAPP(c_Set_Oinsert(_969894), hAPP(_969896, _969898)), hAPP(c_Set_Oimage(_969892, _969894, _969896), _969900)))], (34850 ^ _776545) ^ [_1426861, _1426863, _1426865, _1426867, _1426869, _1426871] : [_1426861 = _1426863, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1426865, _1426867, _1426869), _1426871), _1426861) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1426865, _1426867, _1426869), _1426871), _1426863))], (16482 ^ _776545) ^ [_1073372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073372), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1073372)], (23573 ^ _776545) ^ [_1203824, _1203826] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203826)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1203824), _1203826)))], (33324 ^ _776545) ^ [_1387947, _1387949, _1387951, _1387953] : [class_Groups_Ouminus(_1387947), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1387949, _1387947)), _1387951), _1387953) = hAPP(c_Groups_Ouminus__class_Ouminus(_1387947), hAPP(_1387951, _1387953)))], (20007 ^ _776545) ^ [_1137733, _1137735, _1137737] : [class_Fields_Ofield__inverse__zero(_1137733), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1137733), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137733), _1137735), _1137737)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137733), _1137735), hAPP(c_Groups_Ouminus__class_Ouminus(_1137733), _1137737)))], (2584 ^ _776545) ^ [_814634, _814636] : [_814636 = _814634, -(c_Int_Oint__ge__less__than(_814636) = c_Int_Oint__ge__less__than(_814634))], (52101 ^ _776545) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (9060 ^ _776545) ^ [_933168, _933170, _933172, _933174] : [class_Orderings_Oorder(_933168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933168), _933170), _933172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933168), _933174), _933170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933168), _933174), _933172)))], (16520 ^ _776545) ^ [_1073971, _1073973, _1073975] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073971), _1073973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073975), _1073973), -(_1073971 = _1073975), -(_1073973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37032 ^ _776545) ^ [_1480237, _1480239] : [-(c_Equiv__Relations_Oequivp(_1480237, _1480239)), 37037 ^ _776545 : [(37040 ^ _776545) ^ [] : [hAPP(_1480239, 37033 ^ [_1480237, _1480239]) = hAPP(_1480239, 37034 ^ [_1480237, _1480239])], (37038 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1480239, 37033 ^ [_1480237, _1480239]), 37034 ^ [_1480237, _1480239])))]], 37041 ^ _776545 : [(37044 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1480239, 37033 ^ [_1480237, _1480239]), 37034 ^ [_1480237, _1480239]))], (37042 ^ _776545) ^ [] : [-(hAPP(_1480239, 37033 ^ [_1480237, _1480239]) = hAPP(_1480239, 37034 ^ [_1480237, _1480239]))]]], (34761 ^ _776545) ^ [_1424980, _1424982] : [class_Rings_Osemiring__1(_1424980), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1424980), _1424982) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1424980, hAPP(hAPP(c_COMBC(_1424980, _1424980, _1424980), c_Groups_Oplus__class_Oplus(_1424980)), c_Groups_Oone__class_Oone(_1424980)), _1424982, c_Groups_Ozero__class_Ozero(_1424980)))], (43020 ^ _776545) ^ [_1633990] : [-(c_List_Obutlast(_1633990, c_List_Olist_ONil(_1633990)) = c_List_Olist_ONil(_1633990))], (47162 ^ _776545) ^ [_1724679, _1724681, _1724683] : [class_Orderings_Olinorder(_1724679), c_List_Olinorder__class_Osorted(_1724679, hAPP(c_List_Orev(_1724679), _1724681)), 47169 ^ _776545 : [(47176 ^ _776545) ^ [] : [-(_1724681 = c_List_Olist_ONil(_1724679)), -(c_List_Ofoldr(_1724679, _1724679, c_Orderings_Oord__class_Omax(_1724679), _1724681, _1724683) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1724679), hAPP(hAPP(c_List_Onth(_1724679), _1724681), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1724683))], (47170 ^ _776545) ^ [] : [_1724681 = c_List_Olist_ONil(_1724679), -(c_List_Ofoldr(_1724679, _1724679, c_Orderings_Oord__class_Omax(_1724679), _1724681, _1724683) = _1724683)]]], (43092 ^ _776545) ^ [_1635180] : [class_Groups_Omonoid__add(_1635180), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1635180), c_List_Olist_ONil(_1635180)) = c_Groups_Ozero__class_Ozero(_1635180))], (14278 ^ _776545) ^ [_1033638, _1033640, _1033642, _1033644] : [class_Rings_Ocomm__semiring__1(_1033638), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033638), _1033640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033638), _1033642), _1033644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033638), _1033640), _1033642)), _1033644))], (24307 ^ _776545) ^ [_1216132] : [-(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), _1216132))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20585 ^ _776545) ^ [_1148117, _1148119, _1148121, _1148123] : [class_Fields_Olinordered__field(_1148117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148117), c_Groups_Ozero__class_Ozero(_1148117)), _1148119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148117), _1148121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148117), _1148123), _1148119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148117), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148117), _1148121), _1148119)), _1148123)))], (1624 ^ _776545) ^ [_799709, _799711] : [-(class_Groups_Oab__semigroup__mult(_799709)), _799711 = _799709, class_Groups_Oab__semigroup__mult(_799711)], (42875 ^ _776545) ^ [_1630758, _1630760, _1630762, _1630764] : [hBOOL(hAPP(c_List_Odistinct(_1630758), _1630760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630762), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630758)), _1630760))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1630764), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630758)), _1630760))), 42886 ^ _776545 : [(42893 ^ _776545) ^ [] : [_1630762 = _1630764, -(hAPP(hAPP(c_List_Onth(_1630758), _1630760), _1630762) = hAPP(hAPP(c_List_Onth(_1630758), _1630760), _1630764))], (42887 ^ _776545) ^ [] : [hAPP(hAPP(c_List_Onth(_1630758), _1630760), _1630762) = hAPP(hAPP(c_List_Onth(_1630758), _1630760), _1630764), -(_1630762 = _1630764)]]], (13148 ^ _776545) ^ [_1009011, _1009013, _1009015, _1009017, _1009019] : [class_Groups_Oab__group__add(_1009011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009013), _1009015)), 13155 ^ _776545 : [(13162 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009013), _1009017), _1009015))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009013, _1009011), _1009019), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009013, tc_HOL_Obool)), _1009015), hAPP(hAPP(c_Set_Oinsert(_1009013), _1009017), c_Orderings_Obot__class_Obot(tc_fun(_1009013, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009013, _1009011), _1009019), _1009015))], (13156 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1009013), _1009017), _1009015)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009013, _1009011), _1009019), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009013, tc_HOL_Obool)), _1009015), hAPP(hAPP(c_Set_Oinsert(_1009013), _1009017), c_Orderings_Obot__class_Obot(tc_fun(_1009013, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009011), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009013, _1009011), _1009019), _1009015)), hAPP(_1009019, _1009017)))]]], (8952 ^ _776545) ^ [_931075, _931077, _931079, _931081, _931083, _931085, _931087] : [hBOOL(hAPP(hAPP(c_member(_931075), _931077), _931079)), c_Nitpick_Ofold__graph_H(_931075, _931081, _931083, _931085, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931075, tc_HOL_Obool)), _931079), hAPP(hAPP(c_Set_Oinsert(_931075), _931077), c_Orderings_Obot__class_Obot(tc_fun(_931075, tc_HOL_Obool)))), _931087), -(c_Nitpick_Ofold__graph_H(_931075, _931081, _931083, _931085, _931079, hAPP(hAPP(_931083, _931077), _931087)))], (52221 ^ _776545) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (39936 ^ _776545) ^ [_1553958, _1553960, _1553962] : [-(hAPP(c_Fun_Ocomp(_1553958, _1553960, _1553958, _1553962), c_Fun_Oid(_1553958)) = _1553962)], (37722 ^ _776545) ^ [_1495145, _1495147, _1495149, _1495151, _1495153] : [c_Fun_Oinj__on(_1495145, _1495147, _1495149, _1495151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495147, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495145, _1495147, _1495149), _1495151)), _1495153)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495147), _1495153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1495145), _1495151)), hAPP(c_Finite__Set_Ocard(_1495147), _1495153))))], (43212 ^ _776545) ^ [_1637451, _1637453, _1637455] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637451), tc_List_Olist(_1637451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637451), tc_List_Olist(_1637451)), c_List_Olist_ONil(_1637451)), _1637453)), c_List_Olex(_1637451, _1637455)))], (3012 ^ _776545) ^ [_821258, _821260] : [_821260 = _821258, -(c_Nitpick_Onum(_821260) = c_Nitpick_Onum(_821258))], (28725 ^ _776545) ^ [_1291485, _1291487] : [class_Int_Onumber__ring(_1291485), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1291485), c_Groups_Oone__class_Oone(_1291485)), hAPP(c_Int_Onumber__class_Onumber__of(_1291485), _1291487)) = hAPP(c_Int_Onumber__class_Onumber__of(_1291485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1291487)))], (49196 ^ _776545) ^ [_1769655, _1769657, _1769659, _1769661, _1769663] : [c_Relation_Otrans(_1769655, _1769657), hBOOL(hAPP(hAPP(c_member(tc_prod(_1769655, _1769655)), hAPP(hAPP(c_Product__Type_OPair(_1769655, _1769655), _1769659), _1769661)), _1769657)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1769655, _1769655)), hAPP(hAPP(c_Product__Type_OPair(_1769655, _1769655), _1769661), _1769663)), _1769657)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769655, _1769655)), hAPP(hAPP(c_Product__Type_OPair(_1769655, _1769655), _1769659), _1769663)), _1769657)))], (19947 ^ _776545) ^ [_1136508, _1136510, _1136512, _1136514] : [class_Fields_Olinordered__field(_1136508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136508), _1136510), c_Groups_Ozero__class_Ozero(_1136508))), 19954 ^ _776545 : [(19961 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136508), _1136514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136508), _1136512), _1136510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136508), _1136512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136508), _1136514), _1136510))))], (19955 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136508), _1136512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136508), _1136514), _1136510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136508), _1136514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136508), _1136512), _1136510))))]]], (43312 ^ _776545) ^ [_1639486, _1639488, _1639490] : [-(c_List_Olistset(_1639486, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1639486, tc_HOL_Obool)), _1639488), _1639490)) = c_List_Oset__Cons(_1639486, _1639488, c_List_Olistset(_1639486, _1639490)))], (3184 ^ _776545) ^ [_823946, _823948, _823950, _823952] : [-(c_Big__Operators_Olattice__class_OInf__fin(_823952, _823948) = c_Big__Operators_Olattice__class_OInf__fin(_823950, _823946)), _823952 = _823950, _823948 = _823946], (48754 ^ _776545) ^ [_1759099, _1759101, _1759103] : [-(_1759099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1759101), c_List_Oreplicate(_1759101, _1759099, _1759103)) = hAPP(hAPP(c_Set_Oinsert(_1759101), _1759103), c_Orderings_Obot__class_Obot(tc_fun(_1759101, tc_HOL_Obool))))], (19259 ^ _776545) ^ [_1124098, _1124100, _1124102] : [-(hAPP(c_Finite__Set_Ocard(_1124098), _1124100) = hAPP(c_Nat_OSuc, _1124102)), 19260 ^ _776545 : [(19261 ^ _776545) ^ [_1124198, _1124200] : [_1124100 = hAPP(hAPP(c_Set_Oinsert(_1124098), _1124200), _1124198), -(hBOOL(hAPP(hAPP(c_member(_1124098), _1124200), _1124198))), hAPP(c_Finite__Set_Ocard(_1124098), _1124198) = _1124102, 19272 ^ _776545 : [(19275 ^ _776545) ^ [] : [_1124198 = c_Orderings_Obot__class_Obot(tc_fun(_1124098, tc_HOL_Obool))], (19273 ^ _776545) ^ [] : [-(_1124102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (41929 ^ _776545) ^ [_1605131, _1605133, _1605135, _1605137] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605131), tc_List_Olist(_1605131))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605131), tc_List_Olist(_1605131)), _1605133), _1605135)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1605131), tc_List_Olist(_1605131)), c_List_Olistrel1(_1605131, _1605137)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605131), tc_List_Olist(_1605131))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605131), tc_List_Olist(_1605131)), _1605133), _1605135)), c_List_Olistrel1(_1605131, hAPP(c_Relation_Oconverse(_1605131, _1605131), _1605137)))))], (49900 ^ _776545) ^ [_1784301, _1784303] : [-(c_Equiv__Relations_Opart__equivp(_1784301, _1784303)), 49903 ^ _776545 : [(49904 ^ _776545) ^ [_1784421] : [hBOOL(hAPP(hAPP(_1784303, _1784421), _1784421))]], 49921 ^ _776545 : [(49924 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1784303, 49906 ^ [_1784301, _1784303]), 49906 ^ [_1784301, _1784303])))], (49926 ^ _776545) ^ [] : [-(hAPP(_1784303, 49905 ^ [_1784301, _1784303]) = hAPP(_1784303, 49906 ^ [_1784301, _1784303]))], (49928 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1784303, 49905 ^ [_1784301, _1784303]), 49906 ^ [_1784301, _1784303]))], (49922 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1784303, 49905 ^ [_1784301, _1784303]), 49905 ^ [_1784301, _1784303])))]], 49909 ^ _776545 : [(49912 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1784303, 49905 ^ [_1784301, _1784303]), 49905 ^ [_1784301, _1784303])), hBOOL(hAPP(hAPP(_1784303, 49906 ^ [_1784301, _1784303]), 49906 ^ [_1784301, _1784303])), hAPP(_1784303, 49905 ^ [_1784301, _1784303]) = hAPP(_1784303, 49906 ^ [_1784301, _1784303])], (49910 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1784303, 49905 ^ [_1784301, _1784303]), 49906 ^ [_1784301, _1784303])))]]], (39075 ^ _776545) ^ [_1529315, _1529317, _1529319] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529315, _1529317), _1529319), hAPP(c_COMBK(tc_fun(_1529317, tc_HOL_Obool), _1529315), c_Orderings_Obot__class_Obot(tc_fun(_1529317, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529315, _1529317), tc_HOL_Obool)))], (30292 ^ _776545) ^ [_1319908, _1319910, _1319912, _1319914] : [class_Orderings_Olinorder(_1319908), 30295 ^ _776545 : [(30296 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319908), _1319910), _1319912)), _1319914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), _1319910), _1319914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), _1319912), _1319914)))], (30306 ^ _776545) ^ [] : [30307 ^ _776545 : [(30310 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), _1319912), _1319914))], (30308 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), _1319910), _1319914))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319908), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319908), _1319910), _1319912)), _1319914)))]]], (24948 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (13560 ^ _776545) ^ [_1017920, _1017922, _1017924, _1017926] : [class_Groups_Ocancel__semigroup__add(_1017920), 13563 ^ _776545 : [(13570 ^ _776545) ^ [] : [_1017922 = _1017926, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017920), _1017922), _1017924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017920), _1017926), _1017924))], (13564 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017920), _1017922), _1017924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017920), _1017926), _1017924), -(_1017922 = _1017926)]]], (47617 ^ _776545) ^ [_1734142, _1734144] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1734142)), _1734144)), 47623 ^ _776545 : [(47626 ^ _776545) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1734142), 47622 ^ [_1734142, _1734144]))], (47624 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734142)), 47622 ^ [_1734142, _1734144]), hAPP(c_List_Oset(tc_List_Olist(_1734142)), _1734144))))]], 47630 ^ _776545 : [(47634 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734142)), 47632 ^ [_1734142, _1734144]), hAPP(c_List_Oset(tc_List_Olist(_1734142)), _1734144))))], (47636 ^ _776545) ^ [] : [47629 ^ [_1734142, _1734144] = 47632 ^ [_1734142, _1734144]], (47638 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1734142, tc_HOL_Obool)), hAPP(c_List_Oset(_1734142), 47629 ^ [_1734142, _1734144])), hAPP(c_List_Oset(_1734142), 47632 ^ [_1734142, _1734144])) = c_Orderings_Obot__class_Obot(tc_fun(_1734142, tc_HOL_Obool))], (47631 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734142)), 47629 ^ [_1734142, _1734144]), hAPP(c_List_Oset(tc_List_Olist(_1734142)), _1734144))))]], -(hBOOL(hAPP(c_List_Odistinct(_1734142), c_List_Oconcat(_1734142, _1734144))))], (7504 ^ _776545) ^ [_900189, _900191, _900193, _900195] : [hBOOL(hAPP(hAPP(c_member(_900189), _900191), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_900189, tc_HOL_Obool)), _900193), _900195))), 7507 ^ _776545 : [(7510 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900189), _900191), _900195)))], (7508 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900189), _900191), _900193)))]]], (4998 ^ _776545) ^ [_852747, _852749] : [_852749 = _852747, -(c_Set_OCollect(_852749) = c_Set_OCollect(_852747))], (51367 ^ _776545) ^ [_1816282, _1816284, _1816286, _1816288, _1816290] : [class_Rings_Ocomm__semiring__1(_1816282), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816282), _1816284), _1816286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1816288), _1816290)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816282), hAPP(hAPP(c_Power_Opower__class_Opower(_1816282), _1816284), _1816288)), hAPP(hAPP(c_Power_Opower__class_Opower(_1816282), _1816286), _1816290))))], (46028 ^ _776545) ^ [_1700684, _1700686, _1700688, _1700690] : [-(c_List_Otranspose(_1700684, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700684)), hAPP(hAPP(c_List_Olist_OCons(_1700684), _1700686), _1700688)), _1700690)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700684)), hAPP(hAPP(c_List_Olist_OCons(_1700684), _1700686), c_List_Oconcat(_1700684, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700684), tc_List_Olist(_1700684)), c_List_Olist_Olist__case(tc_List_Olist(_1700684), _1700684, c_List_Olist_ONil(_1700684), hAPP(hAPP(c_COMBB(tc_List_Olist(_1700684), tc_fun(tc_List_Olist(_1700684), tc_List_Olist(_1700684)), _1700684), c_COMBK(tc_List_Olist(_1700684), tc_List_Olist(_1700684))), hAPP(hAPP(c_COMBC(_1700684, tc_List_Olist(_1700684), tc_List_Olist(_1700684)), c_List_Olist_OCons(_1700684)), c_List_Olist_ONil(_1700684))))), _1700690)))), c_List_Otranspose(_1700684, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700684)), _1700688), c_List_Oconcat(tc_List_Olist(_1700684), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700684), tc_List_Olist(tc_List_Olist(_1700684))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1700684)), _1700684, c_List_Olist_ONil(tc_List_Olist(_1700684)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1700684), tc_List_Olist(tc_List_Olist(_1700684))), _1700684), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700684), tc_List_Olist(tc_List_Olist(_1700684)), tc_List_Olist(tc_List_Olist(_1700684))), c_List_Olist_OCons(tc_List_Olist(_1700684))), c_List_Olist_ONil(tc_List_Olist(_1700684)))))), _1700690))))))], (30366 ^ _776545) ^ [_1321252, _1321254, _1321256, _1321258] : [class_Orderings_Olinorder(_1321252), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321252, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1321252, _1321254, _1321256)), hAPP(c_SetInterval_Oord__class_OatMost(_1321252), _1321258)) = c_SetInterval_Oord__class_OatLeastAtMost(_1321252, _1321254, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321252), _1321256), _1321258)))], (27771 ^ _776545) ^ [_1275972, _1275974] : [-(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), _1275972)), _1275974))))], (52311 ^ _776545) ^ [_1829356] : [class_Enum_Oenum(_1829356), -(class_Enum_Oenum(tc_Option_Ooption(_1829356)))], (48584 ^ _776545) ^ [_1756056, _1756058, _1756060, _1756062] : [-(hAPP(hAPP(c_List_Odrop(_1756056), _1756058), c_List_Oreplicate(_1756056, _1756060, _1756062)) = c_List_Oreplicate(_1756056, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1756060), _1756058), _1756062))], (10701 ^ _776545) ^ [_960862, _960864, _960866] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960862, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960862, tc_HOL_Obool)), _960864), _960866)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960862, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960862, tc_HOL_Obool)), _960864)), _960866))], (7902 ^ _776545) ^ [_909801, _909803, _909805, _909807] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909801, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909801), _909803), _909805)), _909807) = hAPP(hAPP(c_Set_Oinsert(_909801), _909803), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909801, tc_HOL_Obool)), _909805), _909807)))], (10841 ^ _776545) ^ [_963525, _963527, _963529, _963531] : [class_Orderings_Olinorder(_963525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963525), _963527), _963529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963525), _963529), _963531)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963525, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963525, _963527), _963529)), c_SetInterval_Oord__class_OatLeastAtMost(_963525, _963529, _963531)) = c_SetInterval_Oord__class_OatLeastAtMost(_963525, _963527, _963531))], (41993 ^ _776545) ^ [_1607074, _1607076, _1607078] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607074), tc_List_Olist(_1607074))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607074), tc_List_Olist(_1607074)), _1607076), _1607076)), c_List_Olistrel(_1607074, c_Transitive__Closure_Ortrancl(_1607074, _1607078)))))], (30194 ^ _776545) ^ [_1318192, _1318194, _1318196, _1318198] : [class_Orderings_Olinorder(_1318192), 30197 ^ _776545 : [(30206 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318192), _1318196), _1318198)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), _1318196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), _1318198))], (30198 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318192), _1318196), _1318198))), 30201 ^ _776545 : [(30204 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), _1318198)))], (30202 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318192), _1318194), _1318196)))]]]]], (23940 ^ _776545) ^ [_1210137, _1210139, _1210141] : [class_Rings_Osemiring__1(_1210137), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210139), _1210141)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210137), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210137), _1210139)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210137), _1210141)))], (43671 ^ _776545) ^ [_1647487, _1647489, _1647491, _1647493] : [-(hAPP(hAPP(c_List_Onth(_1647487), hAPP(hAPP(c_List_Oappend(_1647487), _1647489), _1647491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647487)), _1647489)), _1647493)) = hAPP(hAPP(c_List_Onth(_1647487), _1647491), _1647493))], (22097 ^ _776545) ^ [_1177205, _1177207, _1177209, _1177211] : [class_Rings_Olinordered__semidom(_1177205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177205), c_Groups_Oone__class_Oone(_1177205)), _1177207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177205), hAPP(hAPP(c_Power_Opower__class_Opower(_1177205), _1177207), _1177209)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177205), _1177207), _1177211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177209), _1177211)))], (50979 ^ _776545) ^ [_1808926, _1808928] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808926), _1808928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1808928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1808926), _1808928)))], (28395 ^ _776545) ^ [_1286271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286271), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1286271)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43633 ^ _776545) ^ [_1646832, _1646834, _1646836] : [_1646836 = c_List_Olist_ONil(_1646832), -(hAPP(hAPP(c_List_Oappend(_1646832), _1646834), _1646836) = _1646834)], (50451 ^ _776545) ^ [_1796502, _1796504, _1796506, _1796508] : [c_Fun_Obij__betw(_1796502, _1796504, _1796506, _1796508, c_Orderings_Otop__class_Otop(tc_fun(_1796504, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1796502, _1796504, _1796506), c_Orderings_Otop__class_Otop(tc_fun(_1796502, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1796504, tc_HOL_Obool)))], (4044 ^ _776545) ^ [_837674, _837676, _837678, _837680, _837682, _837684, _837686, _837688] : [-(c_New__DSequence_Oneg__bind(_837688, _837684, _837680, _837676) = c_New__DSequence_Oneg__bind(_837686, _837682, _837678, _837674)), _837688 = _837686, _837684 = _837682, _837680 = _837678, _837676 = _837674], (30536 ^ _776545) ^ [_1324385, _1324387, _1324389] : [class_Orderings_Olinorder(_1324385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324385), _1324387)), hBOOL(hAPP(hAPP(c_member(_1324385), _1324389), _1324387)), 30547 ^ _776545 : [(30554 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324385, tc_HOL_Obool)), _1324387), hAPP(hAPP(c_Set_Oinsert(_1324385), _1324389), c_Orderings_Obot__class_Obot(tc_fun(_1324385, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324385, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1324385, _1324387) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1324385), _1324389), c_Big__Operators_Olinorder__class_OMin(_1324385, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324385, tc_HOL_Obool)), _1324387), hAPP(hAPP(c_Set_Oinsert(_1324385), _1324389), c_Orderings_Obot__class_Obot(tc_fun(_1324385, tc_HOL_Obool)))))))], (30548 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324385, tc_HOL_Obool)), _1324387), hAPP(hAPP(c_Set_Oinsert(_1324385), _1324389), c_Orderings_Obot__class_Obot(tc_fun(_1324385, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1324385, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1324385, _1324387) = _1324389)]]], (39217 ^ _776545) ^ [_1533686, _1533688, _1533690, _1533692] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1533686, _1533688)), hAPP(hAPP(c_Product__Type_OSigma(_1533686, _1533688), _1533690), hAPP(c_COMBK(tc_fun(_1533688, tc_HOL_Obool), _1533686), _1533692)))), -(_1533692 = c_Orderings_Obot__class_Obot(tc_fun(_1533688, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533686), _1533690)))], (48631 ^ _776545) ^ [_1756963, _1756965, _1756967, _1756969] : [48639 ^ _776545 : [(48642 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1756969, 48638 ^ [_1756963, _1756965, _1756967, _1756969])))], (48640 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756963), 48638 ^ [_1756963, _1756965, _1756967, _1756969]), hAPP(c_List_Oset(_1756963), c_List_Oreplicate(_1756963, _1756965, _1756967)))))]], hBOOL(hAPP(_1756969, _1756967)), -(_1756965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17809 ^ _776545) ^ [_1097054, _1097056, _1097058] : [class_Groups_Ogroup__add(_1097054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097054), _1097056), _1097058) = c_Groups_Ozero__class_Ozero(_1097054), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097054), _1097056) = _1097058)], (44174 ^ _776545) ^ [_1659848] : [-(c_List_Orotate(_1659848, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1659848)))], (37205 ^ _776545) ^ [_1484653, _1484655, _1484657] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484653, _1484653)), _1484655), c_Relation_OId__on(_1484653, _1484657))), 37209 ^ _776545 : [(37212 ^ _776545) ^ [] : [-(_1484655 = hAPP(hAPP(c_Product__Type_OPair(_1484653, _1484653), 37208 ^ [_1484653, _1484655, _1484657]), 37208 ^ [_1484653, _1484655, _1484657]))], (37210 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484653), 37208 ^ [_1484653, _1484655, _1484657]), _1484657)))]]], (19967 ^ _776545) ^ [_1136889, _1136891, _1136893, _1136895] : [class_Fields_Olinordered__field(_1136889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136889), c_Groups_Ozero__class_Ozero(_1136889)), _1136891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136889), _1136893), _1136891)), _1136895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136889), _1136893), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136889), _1136895), _1136891))))], (19681 ^ _776545) ^ [_1132018, _1132020, _1132022] : [class_Rings_Odivision__ring(_1132018), -(_1132020 = c_Groups_Ozero__class_Ozero(_1132018)), 19688 ^ _776545 : [(19695 ^ _776545) ^ [] : [_1132022 = _1132020, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132018), _1132022), _1132020) = c_Groups_Oone__class_Oone(_1132018))], (19689 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132018), _1132022), _1132020) = c_Groups_Oone__class_Oone(_1132018), -(_1132022 = _1132020)]]], (26246 ^ _776545) ^ [_1250598, _1250600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250598)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250598), _1250600)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1250598)), hAPP(c_Int_Onat, _1250600)))], (6210 ^ _776545) ^ [_876332, _876334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876332, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_876332, tc_HOL_Obool))), _876334)))], (32308 ^ _776545) ^ [_1357543, _1357545, _1357547, _1357549, _1357551, _1357553] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357543, tc_fun(_1357545, tc_HOL_Obool)), _1357547), _1357549), _1357551)), -(hBOOL(hAPP(hAPP(_1357549, _1357553), _1357551))), hBOOL(hAPP(hAPP(c_member(_1357543), _1357553), _1357547))], (35696 ^ _776545) ^ [_1442970, _1442972, _1442974, _1442976, _1442978, _1442980] : [hBOOL(hAPP(_1442970, _1442972)), hBOOL(hAPP(_1442974, _1442976)), 35703 ^ _776545 : [(35706 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1442974, hAPP(c_Product__Type_Osnd(_1442978, _1442980), hAPP(hAPP(c_Product__Type_OPair(_1442978, _1442980), _1442972), _1442976)))))], (35704 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1442970, hAPP(c_Product__Type_Ofst(_1442978, _1442980), hAPP(hAPP(c_Product__Type_OPair(_1442978, _1442980), _1442972), _1442976)))))]]], (43990 ^ _776545) ^ [_1655809, _1655811, _1655813, _1655815] : [-(_1655809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1655811), _1655809), hAPP(hAPP(c_List_Olist_OCons(_1655811), _1655813), _1655815)) = hAPP(hAPP(c_List_Odrop(_1655811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655809), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655815))], (38416 ^ _776545) ^ [_1512977, _1512979, _1512981, _1512983] : [38418 ^ _776545 : [(38421 ^ _776545) ^ [] : [c_Wellfounded_Owf(_1512979, hAPP(_1512981, 38417 ^ [_1512977, _1512979, _1512981, _1512983]))], (38419 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1512977, 38417 ^ [_1512977, _1512979, _1512981, _1512983])))]], -(c_Wellfounded_Owf(tc_prod(_1512983, _1512979), c_Recdef_Osame__fst(_1512983, _1512979, _1512977, _1512981)))], (15775 ^ _776545) ^ [_1062441] : [_1062441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062441), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (27985 ^ _776545) ^ [_1279451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1279451)), -(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), _1279451))))], (3680 ^ _776545) ^ [_831740, _831742] : [_831742 = _831740, -(c_Orderings_Oord__class_Omax(_831742) = c_Orderings_Oord__class_Omax(_831740))], (41542 ^ _776545) ^ [_1593178, _1593180, _1593182, _1593184, _1593186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593178, _1593178)), hAPP(hAPP(c_Product__Type_OPair(_1593178, _1593178), _1593180), _1593182)), c_Transitive__Closure_Ortrancl(_1593178, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593178, _1593178), tc_HOL_Obool)), _1593184), _1593186)))), 41548 ^ _776545 : [(41554 ^ _776545) ^ [] : [41547 ^ [_1593178, _1593180, _1593182, _1593184, _1593186] = 41550 ^ [_1593178, _1593180, _1593182, _1593184, _1593186]], (41552 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593178, _1593178)), hAPP(hAPP(c_Product__Type_OPair(_1593178, _1593178), 41547 ^ [_1593178, _1593180, _1593182, _1593184, _1593186]), 41550 ^ [_1593178, _1593180, _1593182, _1593184, _1593186])), _1593186)))], (41549 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593178, _1593178)), hAPP(hAPP(c_Product__Type_OPair(_1593178, _1593178), _1593180), 41547 ^ [_1593178, _1593180, _1593182, _1593184, _1593186])), c_Transitive__Closure_Ortrancl(_1593178, _1593184))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593178, _1593178)), hAPP(hAPP(c_Product__Type_OPair(_1593178, _1593178), _1593180), _1593182)), c_Transitive__Closure_Ortrancl(_1593178, _1593184))))], (37945 ^ _776545) ^ [_1501056, _1501058, _1501060, _1501062, _1501064, _1501066] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501056, _1501058, _1501060), _1501062), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501058, _1501060), tc_HOL_Obool)), _1501064), _1501066)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501056, _1501060), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501056, _1501058, _1501060), _1501062), _1501064)), hAPP(hAPP(c_Relation_Orel__comp(_1501056, _1501058, _1501060), _1501062), _1501066)))], (47247 ^ _776545) ^ [_1726414, _1726416, _1726418, _1726420] : [hBOOL(hAPP(hAPP(c_member(_1726414), _1726416), hAPP(c_List_Oset(_1726414), c_List_OtakeWhile(_1726414, _1726418, _1726420)))), 47250 ^ _776545 : [(47253 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1726418, _1726416)))], (47251 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726414), _1726416), hAPP(c_List_Oset(_1726414), _1726420))))]]], (5352 ^ _776545) ^ [_858294, _858296, _858298, _858300, _858302, _858304, _858306, _858308] : [-(c_Lazy__Sequence_Omap(_858308, _858304, _858300, _858296) = c_Lazy__Sequence_Omap(_858306, _858302, _858298, _858294)), _858308 = _858306, _858304 = _858302, _858300 = _858298, _858296 = _858294], (34031 ^ _776545) ^ [_1408350, _1408352] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1408350))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1408352)), hAPP(c_Int_Onat, _1408350)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1408352), _1408350)), 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)))], (15808 ^ _776545) ^ [_1062930, _1062932] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1062930), _1062932)), 15809 ^ _776545 : [(15816 ^ _776545) ^ [] : [_1062930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1062932 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15810 ^ _776545) ^ [] : [_1062930 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48594 ^ _776545) ^ [_1756241, _1756243, _1756245, _1756247] : [48596 ^ _776545 : [(48599 ^ _776545) ^ [] : [hBOOL(hAPP(_1756247, 48595 ^ [_1756241, _1756243, _1756245, _1756247]))], (48597 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756241), 48595 ^ [_1756241, _1756243, _1756245, _1756247]), hAPP(c_List_Oset(_1756241), c_List_Oreplicate(_1756241, _1756243, _1756245)))))]], -(hBOOL(hAPP(_1756247, _1756245))), -(_1756243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46413 ^ _776545) ^ [_1709892, _1709894] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1709892), hAPP(c_List_Onth(_1709892), _1709894)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709892)), _1709894))) = _1709894)], (24952 ^ _776545) ^ [_1228365, _1228367, _1228369] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228365), _1228367), _1228369) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228365), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228367, _1228369)), _1228369))], (27637 ^ _776545) ^ [_1273464, _1273466, _1273468] : [class_Rings_Olinordered__idom(_1273464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273464), c_Groups_Ozero__class_Ozero(_1273464)), _1273466)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273464), hAPP(c_Groups_Oabs__class_Oabs(_1273464), _1273468)), _1273466) = hAPP(c_Groups_Oabs__class_Oabs(_1273464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273464), _1273468), _1273466)))], (25903 ^ _776545) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52403 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (28075 ^ _776545) ^ [_1280944] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1280944), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1280944)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1280944)))], (34385 ^ _776545) ^ [_1416634, _1416636] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416634), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416636)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416634)) = 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), _1416636), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416634)))), 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)))], (11169 ^ _776545) ^ [_969956, _969958, _969960, _969962, _969964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969956, tc_HOL_Obool)), _969958), _969960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969962, tc_HOL_Obool)), hAPP(c_Set_Oimage(_969956, _969962, _969964), _969958)), hAPP(c_Set_Oimage(_969956, _969962, _969964), _969960))))], (31777 ^ _776545) ^ [_1347548, _1347550, _1347552] : [class_Orderings_Olinorder(_1347548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347548), _1347550)), -(_1347550 = c_Orderings_Obot__class_Obot(tc_fun(_1347548, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1347548, hAPP(hAPP(c_Set_Oinsert(_1347548), _1347552), _1347550)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1347548), _1347552), c_Big__Operators_Olinorder__class_OMax(_1347548, _1347550)))], (38671 ^ _776545) ^ [_1519646, _1519648, _1519650, _1519652, _1519654] : [hBOOL(hAPP(hAPP(c_member(_1519646), _1519648), hAPP(c_Set_Ovimage(_1519646, _1519650, _1519652), _1519654))), -(hBOOL(hAPP(hAPP(c_member(_1519650), hAPP(_1519652, _1519648)), _1519654)))], (42256 ^ _776545) ^ [_1614505, _1614507, _1614509, _1614511] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614505) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1614507), hAPP(hAPP(c_List_Olist_OCons(_1614507), _1614509), _1614511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614505)) = hAPP(hAPP(c_List_Onth(_1614507), _1614511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614505)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46610 ^ _776545) ^ [_1713468, _1713470] : [class_Orderings_Olinorder(_1713468), c_List_Olinorder__class_Osorted(_1713468, _1713470), -(c_List_Olinorder__class_Osorted(_1713468, c_List_Oremdups(_1713468, _1713470)))], (31753 ^ _776545) ^ [_1347124, _1347126] : [class_Orderings_Olinorder(_1347124), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347124), _1347126)), -(c_Big__Operators_Olinorder__class_OMax(_1347124, _1347126) = hAPP(c_Finite__Set_Ofold1(_1347124, c_Orderings_Oord__class_Omax(_1347124)), _1347126))], (22867 ^ _776545) ^ [_1190822, _1190824, _1190826, _1190828] : [class_Rings_Olinordered__semidom(_1190822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190824), _1190826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190822), c_Groups_Oone__class_Oone(_1190822)), _1190828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190822), hAPP(hAPP(c_Power_Opower__class_Opower(_1190822), _1190828), _1190824)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190822), _1190828), _1190826))))], (13529 ^ _776545) ^ [_1017333] : [13531 ^ _776545 : [(13534 ^ _776545) ^ [_1017443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 13530 ^ [_1017333, _1017443]), _1017443))], (13532 ^ _776545) ^ [_1017409] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13530 ^ [_1017333, _1017409]), _1017333)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1017333)))], (11628 ^ _776545) ^ [_979954, _979956, _979958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979954), _979956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979954, tc_HOL_Obool)), _979958), _979956)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_979954), _979958)))], (14554 ^ _776545) ^ [_1039044, _1039046, _1039048] : [_1039044 = _1039048, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039044), _1039046) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039048), _1039046))], (41198 ^ _776545) ^ [_1584829, _1584831, _1584833] : [c_Relation_Orefl__on(_1584829, _1584831, _1584833), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584829, _1584829), tc_HOL_Obool)), _1584833), hAPP(hAPP(c_Relation_Orel__comp(_1584829, _1584829, _1584829), hAPP(c_Relation_Oconverse(_1584829, _1584829), _1584833)), _1584833))))], (17531 ^ _776545) ^ [_1092281, _1092283, _1092285, _1092287] : [class_Rings_Olinordered__ring__strict(_1092281), 17534 ^ _776545 : [(17549 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092281), _1092283), _1092285)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092281), _1092287), _1092285)))), 17550 ^ _776545 : [(17557 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092285), c_Groups_Ozero__class_Ozero(_1092281))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092287), _1092283))], (17551 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), c_Groups_Ozero__class_Ozero(_1092281)), _1092285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092283), _1092287))]]], (17535 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092281), _1092283), _1092285)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092281), _1092287), _1092285))), 17540 ^ _776545 : [(17543 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092283), _1092287)))], (17541 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), c_Groups_Ozero__class_Ozero(_1092281)), _1092285)))]], 17544 ^ _776545 : [(17547 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092287), _1092283)))], (17545 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092281), _1092285), c_Groups_Ozero__class_Ozero(_1092281))))]]]]], (25907 ^ _776545) ^ [_1245147, _1245149] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1245147, _1245149)) = _1245149, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245147), _1245149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5731 ^ _776545) ^ [_866902] : [class_HOL_Oequal(_866902), -(c_fequal = c_HOL_Oequal__class_Oequal(_866902))], (18644 ^ _776545) ^ [_1112170, _1112172, _1112174] : [18645 ^ _776545 : [(18648 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112170), _1112174))], (18646 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1112172)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112170), _1112172)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112174), _1112172))))], (46241 ^ _776545) ^ [_1706519, _1706521, _1706523, _1706525, _1706527, _1706529, _1706531] : [-(c_List_Ofoldr(_1706519, _1706521, _1706523, hAPP(hAPP(c_List_Omap(_1706525, _1706519), _1706527), _1706529), _1706531) = c_List_Ofoldr(_1706525, _1706521, hAPP(c_Fun_Ocomp(_1706519, tc_fun(_1706521, _1706521), _1706525, _1706523), _1706527), _1706529, _1706531))], (26797 ^ _776545) ^ [_1259732, _1259734] : [c_Nat__Transfer_Ois__nat(_1259732), c_Nat__Transfer_Ois__nat(_1259734), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259732), _1259734)))], (36671 ^ _776545) ^ [_1471949, _1471951, _1471953, _1471955] : [_1471949 = _1471951, hBOOL(hAPP(hAPP(c_member(_1471953), _1471949), _1471955)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1471953, _1471953)), hAPP(hAPP(c_Product__Type_OPair(_1471953, _1471953), _1471949), _1471951)), c_Relation_OId__on(_1471953, _1471955))))], (52359 ^ _776545) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (5783 ^ _776545) ^ [_868078, _868080, _868082, _868084, _868086, _868088, _868090] : [c_Typedef_Otype__definition(_868078, _868080, _868082, _868084, _868086), hBOOL(hAPP(hAPP(c_member(_868080), _868088), _868086)), hBOOL(hAPP(hAPP(c_member(_868080), _868090), _868086)), 5794 ^ _776545 : [(5801 ^ _776545) ^ [] : [_868088 = _868090, -(hAPP(_868084, _868088) = hAPP(_868084, _868090))], (5795 ^ _776545) ^ [] : [hAPP(_868084, _868088) = hAPP(_868084, _868090), -(_868088 = _868090)]]], (16438 ^ _776545) ^ [_1072775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1072775)), _1072775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32640 ^ _776545) ^ [_1369073, _1369075, _1369077] : [-(hAPP(c_Set_OCollect(_1369073), hAPP(hAPP(c_COMBS(_1369073, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369073), c_fconj), _1369075)), _1369077)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369073, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1369073), _1369075)), hAPP(c_Set_OCollect(_1369073), _1369077)))], (34215 ^ _776545) ^ [_1412719, _1412721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412719)), hAPP(c_Nat_OSuc, _1412721))), -(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(_1412719))), 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)), _1412721)))))], (4038 ^ _776545) ^ [_837589, _837591] : [_837591 = _837589, -(c_New__DSequence_Opos__empty(_837591) = c_New__DSequence_Opos__empty(_837589))], (41068 ^ _776545) ^ [_1581543, _1581545, _1581547, _1581549, _1581551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581543, _1581545)), hAPP(hAPP(c_Product__Type_OPair(_1581543, _1581545), _1581547), _1581549)), hAPP(c_Relation_Oconverse(_1581545, _1581543), _1581551))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581545, _1581543)), hAPP(hAPP(c_Product__Type_OPair(_1581545, _1581543), _1581549), _1581547)), _1581551)))], (42105 ^ _776545) ^ [_1610601, _1610603, _1610605, _1610607, _1610609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610601), tc_List_Olist(_1610601))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610601), tc_List_Olist(_1610601)), _1610603), hAPP(hAPP(c_List_Olist_OCons(_1610601), _1610605), _1610607))), c_List_Olistrel(_1610601, _1610609))), 42110 ^ _776545 : [(42115 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610601), tc_List_Olist(_1610601))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610601), tc_List_Olist(_1610601)), 42109 ^ [_1610601, _1610603, _1610605, _1610607, _1610609]), _1610607)), c_List_Olistrel(_1610601, _1610609))))], (42113 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610601, _1610601)), hAPP(hAPP(c_Product__Type_OPair(_1610601, _1610601), 42108 ^ [_1610601, _1610603, _1610605, _1610607, _1610609]), _1610605)), _1610609)))], (42111 ^ _776545) ^ [] : [-(_1610603 = hAPP(hAPP(c_List_Olist_OCons(_1610601), 42108 ^ [_1610601, _1610603, _1610605, _1610607, _1610609]), 42109 ^ [_1610601, _1610603, _1610605, _1610607, _1610609]))]]], (47082 ^ _776545) ^ [_1722880, _1722882] : [-(hAPP(c_List_Orev(_1722880), hAPP(c_List_Orev(_1722880), _1722882)) = _1722882)], (52247 ^ _776545) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (43058 ^ _776545) ^ [_1634631, _1634633, _1634635] : [hAPP(hAPP(c_List_Otake(_1634631), _1634633), _1634635) = c_List_Olist_ONil(_1634631), -(_1634633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1634635 = c_List_Olist_ONil(_1634631))], (15838 ^ _776545) ^ [_1063355, _1063357] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063355), _1063357) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 15839 ^ _776545 : [(15846 ^ _776545) ^ [] : [_1063355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1063357 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15840 ^ _776545) ^ [] : [_1063355 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15154 ^ _776545) ^ [_1050056] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050056), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1050056)], (28945 ^ _776545) ^ [_1295427, _1295429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295427), _1295429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295427)), c_Int_OBit1(_1295429))))], (38195 ^ _776545) ^ [_1507960, _1507962] : [c_Wellfounded_Owf(_1507960, _1507962), -(c_Wellfounded_Owf(tc_fun(_1507960, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1507960, _1507962)))], (39107 ^ _776545) ^ [_1530261, _1530263, _1530265, _1530267, _1530269] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530261, _1530263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530261, tc_HOL_Obool)), _1530265), _1530267)), hAPP(c_COMBK(tc_fun(_1530263, tc_HOL_Obool), _1530261), _1530269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530261, _1530263), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530261, _1530263), _1530265), hAPP(c_COMBK(tc_fun(_1530263, tc_HOL_Obool), _1530261), _1530269))), hAPP(hAPP(c_Product__Type_OSigma(_1530261, _1530263), _1530267), hAPP(c_COMBK(tc_fun(_1530263, tc_HOL_Obool), _1530261), _1530269))))], (47040 ^ _776545) ^ [_1722083, _1722085, _1722087, _1722089, _1722091] : [c_List_Olist__all2(_1722083, _1722085, _1722087, _1722089, hAPP(c_List_Orev(_1722085), _1722091)), -(c_List_Olist__all2(_1722083, _1722085, _1722087, hAPP(c_List_Orev(_1722083), _1722089), _1722091))], (42365 ^ _776545) ^ [_1617404, _1617406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1617404), hAPP(c_List_Oset(_1617404), _1617406))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617404)), _1617406))))], (8261 ^ _776545) ^ [_917801, _917803] : [class_Lattices_Obounded__lattice__top(_917801), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917801), _917803), c_Orderings_Otop__class_Otop(_917801)) = c_Orderings_Otop__class_Otop(_917801))], (40615 ^ _776545) ^ [_1569663, _1569665] : [-(hAPP(c_Relation_ORange(_1569663, _1569663), c_Transitive__Closure_Otrancl(_1569663, _1569665)) = hAPP(c_Relation_ORange(_1569663, _1569663), _1569665))], (42009 ^ _776545) ^ [_1607507, _1607509, _1607511, _1607513, _1607515] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607507), tc_List_Olist(_1607507))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607507), tc_List_Olist(_1607507)), _1607509), _1607511)), c_List_Olistrel(_1607507, c_Transitive__Closure_Ortrancl(_1607507, _1607513)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607507), tc_List_Olist(_1607507))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607507), tc_List_Olist(_1607507)), _1607511), _1607515)), c_List_Olistrel(_1607507, c_Transitive__Closure_Ortrancl(_1607507, _1607513)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607507), tc_List_Olist(_1607507))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607507), tc_List_Olist(_1607507)), _1607509), _1607515)), c_List_Olistrel(_1607507, c_Transitive__Closure_Ortrancl(_1607507, _1607513)))))], (9610 ^ _776545) ^ [_941263, _941265, _941267] : [class_Orderings_Oorder(_941263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941263), _941265), _941267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941263), _941265), _941267))), -(_941265 = _941267)], (16719 ^ _776545) ^ [_1077285, _1077287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077285), _1077287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077285)), _1077287)))], (44308 ^ _776545) ^ [_1662624] : [class_Orderings_Olinorder(_1662624), -(c_Finite__Set_Ofun__left__comm(_1662624, tc_List_Olist(_1662624), c_List_Olinorder__class_Oinsort__key(_1662624, _1662624, c_COMBI(_1662624))))], (20179 ^ _776545) ^ [_1140883, _1140885, _1140887] : [class_Fields_Olinordered__field(_1140883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140883), c_Groups_Ozero__class_Ozero(_1140883)), _1140885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140883), c_Groups_Ozero__class_Ozero(_1140883)), _1140887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140883), c_Groups_Ozero__class_Ozero(_1140883)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140883), _1140885), _1140887))))], (46249 ^ _776545) ^ [_1706719, _1706721] : [class_Groups_Omonoid__add(_1706719), -(hAPP(c_List_Ofoldl(_1706719, _1706719, c_Groups_Oplus__class_Oplus(_1706719), c_Groups_Ozero__class_Ozero(_1706719)), _1706721) = c_List_Ofoldr(_1706719, _1706719, c_Groups_Oplus__class_Oplus(_1706719), _1706721, c_Groups_Ozero__class_Ozero(_1706719)))], (35604 ^ _776545) ^ [_1441036, _1441038, _1441040, _1441042] : [hAPP(c_Product__Type_Ofst(_1441036, _1441038), _1441040) = hAPP(c_Product__Type_Ofst(_1441036, _1441038), _1441042), hAPP(c_Product__Type_Osnd(_1441036, _1441038), _1441040) = hAPP(c_Product__Type_Osnd(_1441036, _1441038), _1441042), -(_1441040 = _1441042)], (38410 ^ _776545) ^ [_1512866, _1512868] : [-(c_List_Olex(_1512866, _1512868) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1512866), tc_List_Olist(_1512866)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1512866, _1512868)))], (41749 ^ _776545) ^ [_1599499, _1599501, _1599503, _1599505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599499)), _1599501)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599499)), _1599503))), _1599501 = hAPP(hAPP(c_List_Olist_OCons(_1599499), _1599505), _1599503)], (22695 ^ _776545) ^ [_1187728, _1187730, _1187732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1187728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187728), _1187730)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187728), _1187732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1187730), _1187732)))], (3854 ^ _776545) ^ [_834425, _834427, _834429, _834431, _834433, _834435] : [-(c_List_OtakeWhile(_834435, _834431, _834427) = c_List_OtakeWhile(_834433, _834429, _834425)), _834435 = _834433, _834431 = _834429, _834427 = _834425], (51735 ^ _776545) ^ [_1822720, _1822722] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822720), _1822722))), 51736 ^ _776545 : [(51737 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822720), _1822722)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822722), _1822720)))], (51743 ^ _776545) ^ [] : [_1822720 = _1822722]]], (8173 ^ _776545) ^ [_916047, _916049, _916051] : [class_Orderings_Oorder(_916047), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916047, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_916047), _916049)), c_SetInterval_Oord__class_OgreaterThanAtMost(_916047, _916049, _916051)) = c_Orderings_Obot__class_Obot(tc_fun(_916047, tc_HOL_Obool)))], (634 ^ _776545) ^ [_786106, _786108, _786110, _786112] : [-(c_FunDef_Ois__measure(_786110, _786106)), c_FunDef_Ois__measure(_786112, _786108), _786112 = _786110, _786108 = _786106], (40590 ^ _776545) ^ [_1569150, _1569152] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569150, _1569150)), hAPP(hAPP(c_Product__Type_OPair(_1569150, _1569150), 40591 ^ [_1569150, _1569152]), 40591 ^ [_1569150, _1569152])), c_Transitive__Closure_Otrancl(_1569150, _1569152)))), -(c_Wellfounded_Oacyclic(_1569150, _1569152))], (39734 ^ _776545) ^ [_1548380, _1548382, _1548384, _1548386] : [39736 ^ _776545 : [(39739 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548380, _1548380, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548380, tc_fun(_1548380, _1548382), tc_fun(_1548380, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548382, tc_HOL_Obool), tc_fun(tc_fun(_1548380, _1548382), tc_fun(_1548380, tc_HOL_Obool)), _1548380), c_COMBB(_1548382, tc_HOL_Obool, _1548380)), hAPP(hAPP(c_COMBB(_1548382, tc_fun(_1548382, tc_HOL_Obool), _1548380), c_fequal), _1548386))), _1548386)), 39735 ^ [_1548380, _1548382, _1548384, _1548386]))], (39737 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548380, _1548380)), 39735 ^ [_1548380, _1548382, _1548384, _1548386]), _1548384)))]], -(c_Equiv__Relations_Ocongruent(_1548380, _1548382, _1548384, _1548386))], (33417 ^ _776545) ^ [_1390269, _1390271, _1390273, _1390275, _1390277, _1390279] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390269, tc_fun(_1390271, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390273, tc_fun(_1390269, tc_HOL_Obool)), _1390275), _1390277)), _1390279) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390273, tc_fun(_1390271, tc_HOL_Obool)), _1390275), hAPP(hAPP(c_COMBC(_1390273, tc_fun(_1390269, tc_fun(_1390271, tc_HOL_Obool)), tc_fun(_1390271, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390269, tc_HOL_Obool), tc_fun(tc_fun(_1390269, tc_fun(_1390271, tc_HOL_Obool)), tc_fun(_1390271, tc_HOL_Obool)), _1390273), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390269, tc_fun(_1390271, tc_HOL_Obool))), _1390277)), _1390279)))], (10659 ^ _776545) ^ [_959920, _959922] : [class_Lattices_Oboolean__algebra(_959920), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959920), hAPP(c_Groups_Ouminus__class_Ouminus(_959920), _959922)), _959922) = c_Orderings_Otop__class_Otop(_959920))], (27627 ^ _776545) ^ [] : [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)], (42644 ^ _776545) ^ [_1625480, _1625482, _1625484, _1625486] : [42646 ^ _776545 : [(42649 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1625484, 42645 ^ [_1625480, _1625482, _1625484, _1625486])), hAPP(_1625486, 42645 ^ [_1625480, _1625482, _1625484, _1625486])))], (42647 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625480), 42645 ^ [_1625480, _1625482, _1625484, _1625486]), hAPP(c_List_Oset(_1625480), _1625482))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1625480, _1625484, _1625482)), c_List_Olist_Olist__size(_1625480, _1625486, _1625482))))], (40811 ^ _776545) ^ [_1575337, _1575339, _1575341, _1575343, _1575345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575337, _1575337)), hAPP(hAPP(c_Product__Type_OPair(_1575337, _1575337), _1575339), _1575341)), c_Transitive__Closure_Ortrancl(_1575337, _1575343))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575337, _1575337)), hAPP(hAPP(c_Product__Type_OPair(_1575337, _1575337), _1575341), _1575345)), _1575343)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575337, _1575337)), hAPP(hAPP(c_Product__Type_OPair(_1575337, _1575337), _1575339), _1575345)), c_Transitive__Closure_Ortrancl(_1575337, _1575343))))], (40434 ^ _776545) ^ [_1565209, _1565211, _1565213, _1565215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1565209, tc_HOL_Obool), tc_fun(_1565209, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1565209, tc_HOL_Obool), tc_fun(_1565209, tc_HOL_Obool)), _1565211), _1565213)), c_Wellfounded_Omax__ext(_1565209, _1565215))), 40437 ^ _776545 : [(40440 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565209), _1565213)))], (40442 ^ _776545) ^ [] : [_1565213 = c_Orderings_Obot__class_Obot(tc_fun(_1565209, tc_HOL_Obool))], (40444 ^ _776545) ^ [_1565503] : [hBOOL(hAPP(hAPP(c_member(_1565209), _1565503), _1565211)), 40448 ^ _776545 : [(40451 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565209, _1565209)), hAPP(hAPP(c_Product__Type_OPair(_1565209, _1565209), _1565503), 40447 ^ [_1565209, _1565211, _1565213, _1565215, _1565503])), _1565215)))], (40449 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565209), 40447 ^ [_1565209, _1565211, _1565213, _1565215, _1565503]), _1565213)))]]], (40438 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565209), _1565211)))]]], (50035 ^ _776545) ^ [_1787372, _1787374, _1787376, _1787378, _1787380, _1787382] : [hAPP(c_Hilbert__Choice_Oinv__into(_1787372, _1787374, _1787376, _1787378), _1787380) = hAPP(c_Hilbert__Choice_Oinv__into(_1787372, _1787374, _1787376, _1787378), _1787382), hBOOL(hAPP(hAPP(c_member(_1787374), _1787380), hAPP(c_Set_Oimage(_1787372, _1787374, _1787378), _1787376))), hBOOL(hAPP(hAPP(c_member(_1787374), _1787382), hAPP(c_Set_Oimage(_1787372, _1787374, _1787378), _1787376))), -(_1787380 = _1787382)], (47269 ^ _776545) ^ [_1726969, _1726971, _1726973, _1726975] : [-(hBOOL(hAPP(_1726969, _1726971))), -(c_List_OtakeWhile(_1726973, _1726969, hAPP(hAPP(c_List_Olist_OCons(_1726973), _1726971), _1726975)) = c_List_Olist_ONil(_1726973))], (3460 ^ _776545) ^ [_828242, _828244, _828246, _828248] : [-(c_List_OremoveAll(_828248, _828244) = c_List_OremoveAll(_828246, _828242)), _828248 = _828246, _828244 = _828242], (12796 ^ _776545) ^ [_1002267, _1002269, _1002271, _1002273] : [class_Lattices_Osemilattice__sup(_1002267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002267), _1002269)), hBOOL(hAPP(hAPP(c_member(_1002267), _1002271), _1002269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002267), _1002271), _1002273)), hAPP(hAPP(c_Finite__Set_Ofold(_1002267, _1002267, c_Lattices_Osemilattice__sup__class_Osup(_1002267)), _1002273), _1002269))))], (38533 ^ _776545) ^ [_1515359, _1515361, _1515363] : [-(c_HOL_OThe(tc_prod(_1515359, _1515361), _1515363) = c_HOL_OThe(tc_prod(_1515359, _1515361), hAPP(c_Product__Type_Oprod_Oprod__case(_1515359, _1515361, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1515361, tc_prod(_1515359, _1515361)), tc_fun(_1515361, tc_HOL_Obool), _1515359), hAPP(c_COMBB(tc_prod(_1515359, _1515361), tc_HOL_Obool, _1515361), _1515363)), c_Product__Type_OPair(_1515359, _1515361)))))], (34129 ^ _776545) ^ [_1410687, _1410689] : [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(_1410687))), 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)), _1410689))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410687) = hAPP(c_Nat_OSuc, _1410689))], (14534 ^ _776545) ^ [_1038654, _1038656, _1038658] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038654), _1038656)), _1038658) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038654), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1038656), _1038658)))], (36229 ^ _776545) ^ [_1460100, _1460102, _1460104, _1460106, _1460108] : [-(hAPP(c_Product__Type_Osnd(_1460100, _1460102), hAPP(c_Product__Type_Oapfst(_1460104, _1460100, _1460102, _1460106), _1460108)) = hAPP(c_Product__Type_Osnd(_1460104, _1460102), _1460108))], (29849 ^ _776545) ^ [_1311716] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1311716)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1311716)], (47307 ^ _776545) ^ [_1727583, _1727585, _1727587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727583)), c_List_OtakeWhile(_1727583, _1727585, _1727587))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727583)), _1727587))), hBOOL(hAPP(_1727585, hAPP(hAPP(c_List_Onth(_1727583), _1727587), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727583)), c_List_OtakeWhile(_1727583, _1727585, _1727587)))))], (51983 ^ _776545) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (2646 ^ _776545) ^ [_815573, _815575, _815577, _815579] : [-(c_Set_Othe__elem(_815579, _815575) = c_Set_Othe__elem(_815577, _815573)), _815579 = _815577, _815575 = _815573], (33218 ^ _776545) ^ [_1385314] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1385314, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1385314), hAPP(c_COMBK(tc_HOL_Obool, _1385314), c_fFalse)))], (33937 ^ _776545) ^ [_1405675, _1405677, _1405679] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1405675, tc_HOL_Obool)), _1405679), hAPP(c_Set_OPow(_1405675), _1405677))), -(hBOOL(hAPP(c_Predicate_OPowp(_1405675, hAPP(hAPP(c_COMBC(_1405675, tc_fun(_1405675, tc_HOL_Obool), tc_HOL_Obool), c_member(_1405675)), _1405677)), _1405679)))], (1824 ^ _776545) ^ [_802209, _802211] : [-(class_Rings_Osemiring(_802209)), _802211 = _802209, class_Rings_Osemiring(_802211)], (48042 ^ _776545) ^ [_1744171, _1744173, _1744175] : [c_List_Olist__ex(_1744171, _1744173, _1744175), 48046 ^ _776545 : [(48049 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1744173, hAPP(hAPP(c_List_Onth(_1744171), _1744175), 48045 ^ [_1744171, _1744173, _1744175]))))], (48047 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48045 ^ [_1744171, _1744173, _1744175]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744171)), _1744175))))]]], (48205 ^ _776545) ^ [_1747623, _1747625] : [-(c_List_Olist__all(_1747623, _1747625, c_List_Olist_ONil(_1747623)))], (28737 ^ _776545) ^ [_1291738, _1291740] : [_1291738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1291740, _1291738) = _1291740)], (50010 ^ _776545) ^ [_1786712, _1786714, _1786716] : [hAPP(c_Set_Oimage(_1786712, _1786714, _1786716), c_Orderings_Otop__class_Otop(tc_fun(_1786712, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1786714, tc_HOL_Obool)), 50013 ^ _776545 : [(50014 ^ _776545) ^ [_1786823] : [-(hAPP(_1786716, hAPP(c_Hilbert__Choice_Oinv__into(_1786712, _1786714, c_Orderings_Otop__class_Otop(tc_fun(_1786712, tc_HOL_Obool)), _1786716), _1786823)) = _1786823)]]], (27074 ^ _776545) ^ [_1264051, _1264053] : [class_Rings_Olinordered__idom(_1264051), 27077 ^ _776545 : [(27084 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264051), c_Groups_Ozero__class_Ozero(_1264051)), hAPP(c_Int_Oring__1__class_Oof__int(_1264051), _1264053))))], (27078 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264051), c_Groups_Ozero__class_Ozero(_1264051)), hAPP(c_Int_Oring__1__class_Oof__int(_1264051), _1264053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264053)))]]], (32534 ^ _776545) ^ [_1364609, _1364611, _1364613] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364609, tc_HOL_Obool)), _1364611), _1364613) = hAPP(c_Set_OCollect(_1364609), hAPP(hAPP(c_COMBS(_1364609, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364609), c_fdisj), hAPP(hAPP(c_COMBC(_1364609, tc_fun(_1364609, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364609)), _1364611))), hAPP(hAPP(c_COMBC(_1364609, tc_fun(_1364609, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364609)), _1364613))))], (7674 ^ _776545) ^ [_904521, _904523, _904525] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904521, tc_HOL_Obool)), _904523), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904521, tc_HOL_Obool)), _904523), _904525)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_904521, tc_HOL_Obool)), _904523), _904525))], (27991 ^ _776545) ^ [_1279551, _1279553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279551), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279551)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279553)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279553))], (34934 ^ _776545) ^ [_1428237, _1428239] : [-(_1428237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34937 ^ _776545 : [(34944 ^ _776545) ^ [] : [-(_1428239 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1428237, _1428239) = 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, _1428239))), 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)), _1428239)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428237))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428239), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428237), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1428237, _1428239)), 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), _1428239))))), c_Divides_Opdivmod(_1428237, _1428239)))))], (34938 ^ _776545) ^ [] : [_1428239 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428237, _1428239) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428237))]]], (26575 ^ _776545) ^ [_1256242, _1256244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256244)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1256242)), hAPP(c_Int_Onat, _1256244)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1256242, _1256244)))], (49056 ^ _776545) ^ [_1766077, _1766079, _1766081] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1766077, _1766079, _1766081) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766077)], (6043 ^ _776545) ^ [_873095, _873097, _873099, _873101, _873103] : [hBOOL(hAPP(hAPP(c_member(_873095), _873097), c_SetInterval_Oord_OatLeastAtMost(_873095, _873099, _873101, _873103))), 6046 ^ _776545 : [(6049 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873099, _873097), _873103)))], (6047 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873099, _873101), _873097)))]]], (40735 ^ _776545) ^ [_1573423, _1573425] : [-(c_Transitive__Closure_Otrancl(_1573423, _1573425) = hAPP(hAPP(c_Relation_Orel__comp(_1573423, _1573423, _1573423), c_Transitive__Closure_Ortrancl(_1573423, _1573425)), _1573425))], (18360 ^ _776545) ^ [_1106800, _1106802, _1106804, _1106806, _1106808] : [class_Rings_Olinordered__semiring__strict(_1106800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106800), _1106802), _1106804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106800), _1106806), _1106808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106800), c_Groups_Ozero__class_Ozero(_1106800)), _1106802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106800), c_Groups_Ozero__class_Ozero(_1106800)), _1106806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106800), _1106802), _1106806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106800), _1106804), _1106808))))], (38979 ^ _776545) ^ [_1527087, _1527089] : [-(c_Nitpick_Owf_H(_1527087, _1527089)), c_Wellfounded_Oacyclic(_1527087, _1527089), 38984 ^ _776545 : [(38987 ^ _776545) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (38985 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1527087, _1527087)), _1527089))]]], (6790 ^ _776545) ^ [_886306, _886308, _886310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886306, tc_HOL_Obool)), _886308), _886310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_886306, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_886306, _886308)), c_Predicate_OPowp(_886306, _886310))))], (50916 ^ _776545) ^ [_1807768, _1807770, _1807772] : [c_List_Oall__interval__nat(_1807768, _1807770, _1807772), -(c_List_Olist__all(tc_Nat_Onat, _1807768, c_List_Oupt(_1807770, _1807772)))], (50671 ^ _776545) ^ [_1800808, _1800810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800808), _1800810)), -(c_Fun_Obij__betw(_1800808, tc_Nat_Onat, 50674 ^ [_1800808, _1800810], _1800810, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1800808), _1800810))))], (46397 ^ _776545) ^ [_1709577, _1709579] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1709577, _1709579) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1709577, hAPP(c_Nat_OSuc, _1709579))))], (24174 ^ _776545) ^ [_1213841, _1213843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213841), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24177 ^ _776545 : [(24184 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213843), 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), _1213843), _1213841))))], (24178 ^ _776545) ^ [] : [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), _1213843), _1213841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213843), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15005 ^ _776545) ^ [_1047338, _1047340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047338), _1047340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047338), _1047340)))], (30834 ^ _776545) ^ [_1329548, _1329550, _1329552] : [class_Orderings_Olinorder(_1329548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329548), _1329550)), -(hBOOL(hAPP(hAPP(c_member(_1329548), _1329552), _1329550))), -(_1329550 = c_Orderings_Obot__class_Obot(tc_fun(_1329548, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1329548, c_Orderings_Oord__class_Omin(_1329548), hAPP(hAPP(c_Set_Oinsert(_1329548), _1329552), _1329550)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329548), _1329552), c_Big__Operators_Olattice_OInf__fin(_1329548, c_Orderings_Oord__class_Omin(_1329548), _1329550)))], (25095 ^ _776545) ^ [_1230857] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1230857) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230857))], (20 ^ _776545) ^ [_776805, _776807, _776809, _776811, _776813, _776815, _776817, _776819, _776821, _776823, _776825, _776827] : [-(c_Nitpick_Ofold__graph_H(_776825, _776821, _776817, _776813, _776809, _776805)), c_Nitpick_Ofold__graph_H(_776827, _776823, _776819, _776815, _776811, _776807), _776827 = _776825, _776823 = _776821, _776819 = _776817, _776815 = _776813, _776811 = _776809, _776807 = _776805], (21433 ^ _776545) ^ [_1164952, _1164954] : [class_Int_Onumber__ring(_1164952), -(hBOOL(hAPP(hAPP(c_member(_1164952), hAPP(c_Int_Onumber__class_Onumber__of(_1164952), _1164954)), c_Int_Oring__1__class_OInts(_1164952))))], (41144 ^ _776545) ^ [_1583314, _1583316] : [c_Wellfounded_Owf(_1583314, hAPP(c_Relation_Oconverse(_1583314, _1583314), _1583316)), -(c_Wellfounded_Owf(_1583314, hAPP(c_Relation_Oconverse(_1583314, _1583314), c_Transitive__Closure_Otrancl(_1583314, _1583316))))], (39824 ^ _776545) ^ [_1551405, _1551407, _1551409, _1551411, _1551413] : [hAPP(c_Set_Oimage(_1551405, _1551407, _1551409), c_Orderings_Otop__class_Otop(tc_fun(_1551405, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551407, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1551407, _1551411, _1551413), c_Orderings_Otop__class_Otop(tc_fun(_1551407, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551411, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1551405, _1551411, hAPP(c_Fun_Ocomp(_1551407, _1551411, _1551405, _1551413), _1551409)), c_Orderings_Otop__class_Otop(tc_fun(_1551405, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1551411, tc_HOL_Obool)))], (29735 ^ _776545) ^ [_1309652, _1309654, _1309656] : [29737 ^ _776545 : [(29740 ^ _776545) ^ [] : [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(_1309654, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29736 ^ [_1309652, _1309654, _1309656]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1309654, 29736 ^ [_1309652, _1309654, _1309656])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29738 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29736 ^ [_1309652, _1309654, _1309656]), _1309652)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1309654, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1309656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309656), hAPP(_1309654, _1309652))), 29750 ^ _776545 : [(29753 ^ _776545) ^ [] : [-(hAPP(_1309654, 29749 ^ [_1309652, _1309654, _1309656]) = _1309656)], (29751 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29749 ^ [_1309652, _1309654, _1309656]), _1309652)))]]], (51979 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (43308 ^ _776545) ^ [_1639392, _1639394, _1639396, _1639398, _1639400, _1639402] : [-(hAPP(c_List_Olist_Olist__case(_1639392, _1639394, _1639396, _1639398), hAPP(hAPP(c_List_Olist_OCons(_1639394), _1639400), _1639402)) = hAPP(hAPP(_1639398, _1639400), _1639402))], (51565 ^ _776545) ^ [_1819848, _1819850, _1819852, _1819854] : [class_Divides_Osemiring__div(_1819848), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819848), _1819850), _1819852)), 51572 ^ _776545 : [(51579 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819848), _1819850), _1819854)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819848), _1819850), c_Divides_Odiv__class_Omod(_1819848, _1819854, _1819852))))], (51573 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819848), _1819850), c_Divides_Odiv__class_Omod(_1819848, _1819854, _1819852))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819848), _1819850), _1819854)))]]], (17831 ^ _776545) ^ [_1097452, _1097454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1097452), _1097454))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1097452), hAPP(c_Nat_OSuc, _1097454)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (48893 ^ _776545) ^ [_1762285, _1762287, _1762289, _1762291] : [hBOOL(hAPP(hAPP(c_List_Omember(_1762285), hAPP(hAPP(c_List_Olist_OCons(_1762285), _1762287), _1762289)), _1762291)), -(_1762287 = _1762291), -(hBOOL(hAPP(hAPP(c_List_Omember(_1762285), _1762289), _1762291)))], (46138 ^ _776545) ^ [_1703242, _1703244] : [-(c_List_OremoveAll(_1703242, _1703244) = c_List_Ofilter(_1703242, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1703242), c_fNot), hAPP(c_fequal, _1703244))))], (46201 ^ _776545) ^ [_1704897, _1704899, _1704901, _1704903] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1704897)), c_List_Otranspose__rel(_1704897)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704897)), hAPP(hAPP(c_List_Olist_OCons(_1704897), _1704899), _1704901)), _1704903))), -(c_List_Otranspose(_1704897, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704897)), hAPP(hAPP(c_List_Olist_OCons(_1704897), _1704899), _1704901)), _1704903)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704897)), hAPP(hAPP(c_List_Olist_OCons(_1704897), _1704899), c_List_Oconcat(_1704897, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704897), tc_List_Olist(_1704897)), c_List_Olist_Olist__case(tc_List_Olist(_1704897), _1704897, c_List_Olist_ONil(_1704897), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704897), tc_fun(tc_List_Olist(_1704897), tc_List_Olist(_1704897)), _1704897), c_COMBK(tc_List_Olist(_1704897), tc_List_Olist(_1704897))), hAPP(hAPP(c_COMBC(_1704897, tc_List_Olist(_1704897), tc_List_Olist(_1704897)), c_List_Olist_OCons(_1704897)), c_List_Olist_ONil(_1704897))))), _1704903)))), c_List_Otranspose(_1704897, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704897)), _1704901), c_List_Oconcat(tc_List_Olist(_1704897), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704897), tc_List_Olist(tc_List_Olist(_1704897))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704897)), _1704897, c_List_Olist_ONil(tc_List_Olist(_1704897)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704897), tc_List_Olist(tc_List_Olist(_1704897))), _1704897), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704897), tc_List_Olist(tc_List_Olist(_1704897)), tc_List_Olist(tc_List_Olist(_1704897))), c_List_Olist_OCons(tc_List_Olist(_1704897))), c_List_Olist_ONil(tc_List_Olist(_1704897)))))), _1704903))))))], (27881 ^ _776545) ^ [_1277831, _1277833] : [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), _1277831)), _1277833))), _1277831 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1277833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15240 ^ _776545) ^ [_1051628, _1051630] : [class_Rings_Oring__1__no__zero__divisors(_1051628), 15243 ^ _776545 : [(15244 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051628), _1051630), _1051630) = c_Groups_Oone__class_Oone(_1051628), -(_1051630 = c_Groups_Oone__class_Oone(_1051628)), -(_1051630 = hAPP(c_Groups_Ouminus__class_Ouminus(_1051628), c_Groups_Oone__class_Oone(_1051628)))], (15254 ^ _776545) ^ [] : [15255 ^ _776545 : [(15258 ^ _776545) ^ [] : [_1051630 = hAPP(c_Groups_Ouminus__class_Ouminus(_1051628), c_Groups_Oone__class_Oone(_1051628))], (15256 ^ _776545) ^ [] : [_1051630 = c_Groups_Oone__class_Oone(_1051628)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051628), _1051630), _1051630) = c_Groups_Oone__class_Oone(_1051628))]]], (45078 ^ _776545) ^ [_1679235, _1679237, _1679239, _1679241] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679235)), _1679237) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679239)), _1679241), -(hAPP(hAPP(c_List_Omap(tc_prod(_1679235, _1679239), _1679239), c_Product__Type_Osnd(_1679235, _1679239)), hAPP(hAPP(c_List_Ozip(_1679235, _1679239), _1679237), _1679241)) = _1679241)], (48494 ^ _776545) ^ [_1753719, _1753721, _1753723, _1753725, _1753727] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1753719, _1753721, _1753723), _1753725), _1753727)), -(hBOOL(hAPP(hAPP(_1753723, _1753727), _1753725)))], (10243 ^ _776545) ^ [_952578, _952580, _952582] : [class_Orderings_Oorder(_952578), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952578, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_952578, _952580), _952582)), hAPP(c_SetInterval_Oord__class_OatLeast(_952578), _952582)) = c_Orderings_Obot__class_Obot(tc_fun(_952578, tc_HOL_Obool)))], (42612 ^ _776545) ^ [_1624912, _1624914] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1624912, _1624914) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624912, _1624914)))], (27647 ^ _776545) ^ [_1273665, _1273667, _1273669] : [class_Rings_Oordered__ring__abs(_1273665), -(hAPP(c_Groups_Oabs__class_Oabs(_1273665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273665), _1273667), _1273669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273665), hAPP(c_Groups_Oabs__class_Oabs(_1273665), _1273667)), hAPP(c_Groups_Oabs__class_Oabs(_1273665), _1273669))), 27654 ^ _776545 : [(27657 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273665), _1273667), c_Groups_Ozero__class_Ozero(_1273665)))], (27655 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273665), c_Groups_Ozero__class_Ozero(_1273665)), _1273667))]], 27658 ^ _776545 : [(27661 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273665), _1273669), c_Groups_Ozero__class_Ozero(_1273665)))], (27659 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273665), c_Groups_Ozero__class_Ozero(_1273665)), _1273669))]]], (41817 ^ _776545) ^ [_1601700, _1601702, _1601704, _1601706] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1601700), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601702), _1601704)))), -(hAPP(c_Random_Opick(_1601702, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1601702)), _1601704), _1601706)), _1601700) = hAPP(c_Random_Opick(_1601702, _1601706), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1601700), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1601702), _1601704))))], (16725 ^ _776545) ^ [_1077388, _1077390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077388), _1077390)), 16728 ^ _776545 : [(16735 ^ _776545) ^ [] : [_1077390 = _1077388, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077390), hAPP(c_Nat_OSuc, _1077388))))], (16729 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077390), hAPP(c_Nat_OSuc, _1077388))), -(_1077390 = _1077388)]]], (21417 ^ _776545) ^ [_1164624, _1164626, _1164628] : [class_Int_Onumber__ring(_1164624), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164624), hAPP(c_Groups_Ouminus__class_Ouminus(_1164624), hAPP(c_Int_Onumber__class_Onumber__of(_1164624), _1164626))), _1164628) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164624), hAPP(c_Int_Onumber__class_Onumber__of(_1164624), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164626))), _1164628))], (2264 ^ _776545) ^ [_809520, _809522] : [_809522 = _809520, -(c_SetInterval_Oord__class_OgreaterThan(_809522) = c_SetInterval_Oord__class_OgreaterThan(_809520))], (42685 ^ _776545) ^ [_1626420, _1626422, _1626424, _1626426] : [-(_1626420 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626422)), _1626424)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1626422, hAPP(hAPP(c_List_Olist__update(_1626422, _1626424), _1626420), _1626426)) = hAPP(hAPP(c_List_Olist__update(_1626422, c_List_Obutlast(_1626422, _1626424)), _1626420), _1626426))], (1264 ^ _776545) ^ [_795209, _795211] : [-(class_Int_Oring__char__0(_795209)), _795211 = _795209, class_Int_Oring__char__0(_795211)], (1254 ^ _776545) ^ [_795084, _795086] : [-(class_Rings_Ocomm__ring(_795084)), _795086 = _795084, class_Rings_Ocomm__ring(_795086)], (50863 ^ _776545) ^ [_1806383, _1806385, _1806387, _1806389] : [50866 ^ _776545 : [(50869 ^ _776545) ^ [] : [hAPP(_1806387, 50864 ^ [_1806383, _1806385, _1806387, _1806389]) = hAPP(_1806387, 50865 ^ [_1806383, _1806385, _1806387, _1806389])], (50867 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1806383, _1806383)), hAPP(hAPP(c_Product__Type_OPair(_1806383, _1806383), 50864 ^ [_1806383, _1806385, _1806387, _1806389]), 50865 ^ [_1806383, _1806385, _1806387, _1806389])), _1806385)))]], -(c_Equiv__Relations_Ocongruent(_1806383, _1806389, _1806385, _1806387))], (3076 ^ _776545) ^ [_822296, _822298, _822300, _822302] : [-(c_Wellfounded_Oacc(_822302, _822298) = c_Wellfounded_Oacc(_822300, _822296)), _822302 = _822300, _822298 = _822296], (6330 ^ _776545) ^ [_878557, _878559, _878561, _878563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878557, tc_HOL_Obool)), _878559), _878561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878557, tc_HOL_Obool)), _878561), _878563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878557, tc_HOL_Obool)), _878559), _878563)))], (6469 ^ _776545) ^ [_881097, _881099] : [-(_881099 = c_Orderings_Obot__class_Obot(tc_fun(_881097, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_881097), 6472 ^ [_881097, _881099]), _881099)))], (26597 ^ _776545) ^ [_1256603, _1256605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256603)), 26600 ^ _776545 : [(26607 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256603), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1256603)), _1256605)))], (26601 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1256603)), _1256605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256603), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256605))))]]], (32678 ^ _776545) ^ [_1370099, _1370101, _1370103, _1370105] : [class_Groups_Ocomm__monoid__add(_1370099), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370099), _1370101), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1370103), hAPP(c_Nat_OSuc, _1370105))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1370099), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370099, tc_Nat_Onat), _1370101), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1370103, _1370105)))], (43681 ^ _776545) ^ [_1647810, _1647812, _1647814, _1647816, _1647818] : [-(hAPP(hAPP(c_List_Olist__update(_1647810, hAPP(hAPP(c_List_Oappend(_1647810), _1647812), hAPP(hAPP(c_List_Olist_OCons(_1647810), _1647814), _1647816))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647810)), _1647812)), _1647818) = hAPP(hAPP(c_List_Oappend(_1647810), _1647812), hAPP(hAPP(c_List_Olist_OCons(_1647810), _1647818), _1647816)))], (3158 ^ _776545) ^ [_823563, _823565] : [_823565 = _823563, -(c_List_Orotate1(_823565) = c_List_Orotate1(_823563))], (26973 ^ _776545) ^ [_1262397, _1262399, _1262401] : [class_Rings_Oring__1(_1262397), -(hAPP(c_Int_Oring__1__class_Oof__int(_1262397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262399), _1262401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262397), hAPP(c_Int_Oring__1__class_Oof__int(_1262397), _1262399)), hAPP(c_Int_Oring__1__class_Oof__int(_1262397), _1262401)))], (3984 ^ _776545) ^ [_836686, _836688, _836690, _836692, _836694, _836696, _836698, _836700] : [-(c_New__DSequence_Opos__decr__bind(_836700, _836696, _836692, _836688) = c_New__DSequence_Opos__decr__bind(_836698, _836694, _836690, _836686)), _836700 = _836698, _836696 = _836694, _836692 = _836690, _836688 = _836686], (48564 ^ _776545) ^ [_1755658, _1755660, _1755662] : [-(c_List_Oreplicate(_1755658, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755658)), hAPP(c_List_Ofilter(_1755658, hAPP(c_fequal, _1755660)), _1755662)), _1755660) = hAPP(c_List_Ofilter(_1755658, hAPP(c_fequal, _1755660)), _1755662))], (17959 ^ _776545) ^ [_1099568, _1099570] : [17960 ^ _776545 : [(17963 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099570))], (17961 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1099568))]], -(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), _1099568), _1099570))))], (48470 ^ _776545) ^ [_1753105, _1753107, _1753109] : [-(c_List_Osplice(_1753105, hAPP(hAPP(c_List_Olist_OCons(_1753105), _1753107), _1753109), c_List_Olist_ONil(_1753105)) = hAPP(hAPP(c_List_Olist_OCons(_1753105), _1753107), _1753109))], (33138 ^ _776545) ^ [_1382632, _1382634, _1382636] : [hAPP(hAPP(c_COMBC(_1382632, tc_fun(_1382632, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382632)), _1382634) = hAPP(hAPP(c_COMBC(_1382632, tc_fun(_1382632, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382632)), _1382636), -(_1382634 = _1382636)], (20753 ^ _776545) ^ [_1151232, _1151234, _1151236, _1151238] : [class_Fields_Ofield(_1151232), -(_1151234 = c_Groups_Ozero__class_Ozero(_1151232)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151232), _1151236), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151232), _1151238), _1151234)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151232), _1151234), _1151236)), _1151238)), _1151234))], (7824 ^ _776545) ^ [_908175, _908177] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908175, tc_HOL_Obool)), _908177), c_Orderings_Obot__class_Obot(tc_fun(_908175, tc_HOL_Obool))) = _908177)], (38751 ^ _776545) ^ [_1521624, _1521626, _1521628, _1521630] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521624), _1521626)), c_Fun_Oinj__on(_1521628, _1521624, _1521630, c_Orderings_Otop__class_Otop(tc_fun(_1521628, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521628), hAPP(c_Set_Ovimage(_1521628, _1521624, _1521630), _1521626))))], (43914 ^ _776545) ^ [_1654070, _1654072] : [-(hAPP(c_List_Oset(_1654070), hAPP(c_List_Orotate1(_1654070), _1654072)) = hAPP(c_List_Oset(_1654070), _1654072))], (36090 ^ _776545) ^ [_1456228] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1456228) = _1456228)], (42638 ^ _776545) ^ [_1625401] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1625401)), -(c_List_Onat__list(_1625401))], (44747 ^ _776545) ^ [_1671192, _1671194, _1671196, _1671198, _1671200] : [-(hAPP(hAPP(c_List_Otake(_1671192), _1671194), hAPP(hAPP(c_List_Omap(_1671196, _1671192), _1671198), _1671200)) = hAPP(hAPP(c_List_Omap(_1671196, _1671192), _1671198), hAPP(hAPP(c_List_Otake(_1671196), _1671194), _1671200)))], (29059 ^ _776545) ^ [_1297453] : [-(c_Int_Opred(c_Int_OBit0(_1297453)) = c_Int_OBit1(c_Int_Opred(_1297453)))], (31178 ^ _776545) ^ [_1336086, _1336088] : [class_Orderings_Olinorder(_1336086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336086), _1336088)), -(_1336088 = c_Orderings_Obot__class_Obot(tc_fun(_1336086, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1336086), c_Big__Operators_Olinorder__class_OMax(_1336086, _1336088)), _1336088)))], (38314 ^ _776545) ^ [_1510422] : [class_Orderings_Owellorder(_1510422), -(c_Wellfounded_Owf(_1510422, hAPP(c_Set_OCollect(tc_prod(_1510422, _1510422)), hAPP(c_Product__Type_Oprod_Oprod__case(_1510422, _1510422, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1510422)))))], (8811 ^ _776545) ^ [_927998, _928000, _928002, _928004] : [class_Lattices_Odistrib__lattice(_927998), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927998), _928000), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927998), _928002), _928004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927998), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927998), _928000), _928002)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927998), _928000), _928004)))], (38830 ^ _776545) ^ [_1523631, _1523633] : [c_Wellfounded_OwfP(_1523631, _1523633), -(c_Wellfounded_Oacyclic(_1523631, hAPP(c_Set_OCollect(tc_prod(_1523631, _1523631)), hAPP(c_Product__Type_Oprod_Oprod__case(_1523631, _1523631, tc_HOL_Obool), _1523633))))], (13399 ^ _776545) ^ [_1014520, _1014522, _1014524, _1014526, _1014528] : [class_Groups_Ocomm__monoid__add(_1014520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014522), _1014524)), hBOOL(hAPP(hAPP(c_member(_1014522), _1014526), _1014524)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014522, _1014520), _1014528), _1014524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014520), hAPP(_1014528, _1014526)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1014522, _1014520), _1014528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014522, tc_HOL_Obool)), _1014524), hAPP(hAPP(c_Set_Oinsert(_1014522), _1014526), c_Orderings_Obot__class_Obot(tc_fun(_1014522, tc_HOL_Obool)))))))], (41626 ^ _776545) ^ [_1595890, _1595892] : [-(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)))), _1595890)) = 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)))), _1595892))), 41628 ^ _776545 : [(41631 ^ _776545) ^ [] : [41632 ^ _776545 : [(41635 ^ _776545) ^ [] : [hBOOL(hAPP(_1595892, 41627 ^ [_1595890, _1595892]))], (41633 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1595890, 41627 ^ [_1595890, _1595892])))]], 41636 ^ _776545 : [(41639 ^ _776545) ^ [] : [hBOOL(hAPP(_1595890, 41627 ^ [_1595890, _1595892]))], (41637 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1595892, 41627 ^ [_1595890, _1595892])))]]], (41629 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41627 ^ [_1595890, _1595892])))]]], (49694 ^ 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hAPP(c_Set_Ovimage(_1521114, _1521116, _1521118), _1521120))), hAPP(c_Set_Oimage(_1521114, _1521116, _1521118), c_Orderings_Otop__class_Otop(tc_fun(_1521114, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1521116, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521116), _1521120)))], (22715 ^ _776545) ^ [_1188030, _1188032] : [22716 ^ _776545 : [(22719 ^ _776545) ^ [] : [_1188032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22717 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188030))]], -(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), _1188030), _1188032))))], (35628 ^ _776545) ^ [_1441523, _1441525, _1441527] : [-(_1441523 = hAPP(hAPP(c_Product__Type_OPair(_1441525, _1441527), hAPP(c_Product__Type_Ofst(_1441525, _1441527), _1441523)), hAPP(c_Product__Type_Osnd(_1441525, _1441527), _1441523)))], (7672 ^ _776545) ^ [_904461, _904463, _904465] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904461, tc_HOL_Obool)), _904463), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904461, tc_HOL_Obool)), _904465), _904463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904461, tc_HOL_Obool)), _904463), _904465))], (28761 ^ _776545) ^ [_1292157, _1292159] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1292157), _1292159) = 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), _1292157)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1292159)))))], (52175 ^ _776545) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (13204 ^ _776545) ^ [_1010279] : [class_Lattices_Oab__semigroup__idem__mult(_1010279), -(c_Finite__Set_Ofun__left__comm__idem(_1010279, _1010279, c_Groups_Otimes__class_Otimes(_1010279)))], (17099 ^ _776545) ^ [_1084400, _1084402, _1084404] : [class_Rings_Oordered__cancel__semiring(_1084400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084400), c_Groups_Ozero__class_Ozero(_1084400)), _1084402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084400), _1084404), c_Groups_Ozero__class_Ozero(_1084400))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084400), _1084404), _1084402)), c_Groups_Ozero__class_Ozero(_1084400))))], (52321 ^ _776545) ^ [_1829482, _1829484] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1829482, _1829484)))], (4784 ^ _776545) ^ [_849364, _849366, _849368, _849370, _849372, _849374, _849376, _849378] : [-(c_Wellfounded_Olex__prod(_849378, _849374, _849370, _849366) = c_Wellfounded_Olex__prod(_849376, _849372, _849368, _849364)), _849378 = _849376, _849374 = _849372, _849370 = _849368, _849366 = _849364], (14570 ^ _776545) ^ [_1039298, _1039300, _1039302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039298), _1039300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039300), _1039302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039298), _1039302)))], (44477 ^ _776545) ^ [_1666181, _1666183, _1666185, _1666187, _1666189] : [class_Orderings_Olinorder(_1666181), -(hBOOL(hAPP(hAPP(c_member(_1666181), hAPP(_1666183, _1666185)), hAPP(c_Set_Oimage(_1666187, _1666181, _1666183), hAPP(c_List_Oset(_1666187), _1666189))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1666187, _1666181, _1666183, _1666185, _1666189) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1666187, _1666181, _1666183), _1666185), _1666189))], (50735 ^ _776545) ^ [_1802041, _1802043, _1802045, _1802047] : [c_Equiv__Relations_Oequivp(_1802041, _1802043), 50741 ^ _776545 : [(50744 ^ _776545) ^ [] : [hBOOL(hAPP(_1802047, 50740 ^ [_1802041, _1802043, _1802045, _1802047]))], (50742 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1802045, 50740 ^ [_1802041, _1802043, _1802045, _1802047])))]], 50747 ^ _776545 : [(50748 ^ _776545) ^ [_1802300] : [hBOOL(hAPP(_1802045, _1802300))]], 50750 ^ _776545 : [(50753 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1802047, 50749 ^ [_1802041, _1802043, _1802045, _1802047])))], (50751 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802041), 50749 ^ [_1802041, _1802043, _1802045, _1802047]), c_Quotient_ORespects(_1802041, _1802043))))]]], (17929 ^ _776545) ^ [_1099072, _1099074, _1099076, _1099078] : [class_Rings_Ocomm__semiring__1(_1099072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099074), _1099076)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1099074, _1099072), _1099078), _1099076) = c_Groups_Ozero__class_Ozero(_1099072)), 17938 ^ _776545 : [(17939 ^ _776545) ^ [_1099253] : [hBOOL(hAPP(hAPP(c_member(_1099074), _1099253), _1099076)), hAPP(_1099078, _1099253) = c_Groups_Ozero__class_Ozero(_1099072)]]], (20995 ^ _776545) ^ [_1155714, _1155716] : [-(c_Sum__Type_OPlus(_1155714, _1155716, c_Orderings_Otop__class_Otop(tc_fun(_1155714, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1155716, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1155714, _1155716), tc_HOL_Obool)))], (17229 ^ _776545) ^ [_1086707, _1086709, _1086711] : [class_Groups_Oordered__comm__monoid__add(_1086707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086707), _1086709), c_Groups_Ozero__class_Ozero(_1086707))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086707), _1086711), c_Groups_Ozero__class_Ozero(_1086707))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086707), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086707), _1086709), _1086711)), c_Groups_Ozero__class_Ozero(_1086707))))], (41136 ^ _776545) ^ [_1583174, _1583176, _1583178] : [c_Relation_Orefl__on(_1583174, _1583176, _1583178), -(c_Relation_Orefl__on(_1583174, _1583176, hAPP(c_Relation_Oconverse(_1583174, _1583174), _1583178)))], (1814 ^ _776545) ^ [_802084, _802086] : [-(class_Orderings_Oorder(_802084)), _802086 = _802084, class_Orderings_Oorder(_802086)], (18972 ^ _776545) ^ [_1118262] : [-(hAPP(c_Nat_OSuc, _1118262) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1118262))], (32015 ^ _776545) ^ [_1351817, _1351819, _1351821] : [class_Orderings_Olinorder(_1351817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351817), _1351819)), -(_1351819 = c_Orderings_Obot__class_Obot(tc_fun(_1351817, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1351817, c_Orderings_Oord__class_Omax(_1351817), hAPP(hAPP(c_Set_Oinsert(_1351817), _1351821), _1351819)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1351817), _1351821), c_Big__Operators_Olattice_OSup__fin(_1351817, c_Orderings_Oord__class_Omax(_1351817), _1351819)))], (18804 ^ _776545) ^ [_1115322, _1115324] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1115322), _1115324)))), -(_1115324 = c_Orderings_Obot__class_Obot(tc_fun(_1115322, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115322), _1115324))], (39037 ^ _776545) ^ [_1528272, _1528274, _1528276, _1528278, _1528280, _1528282] : [hBOOL(hAPP(hAPP(c_member(_1528272), _1528274), _1528276)), hBOOL(hAPP(hAPP(c_member(_1528278), _1528280), hAPP(_1528282, _1528274))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528272, _1528278)), hAPP(hAPP(c_Product__Type_OPair(_1528272, _1528278), _1528274), _1528280)), hAPP(hAPP(c_Product__Type_OSigma(_1528272, _1528278), _1528276), _1528282))))], (40425 ^ _776545) ^ [_1564950, _1564952, _1564954] : [40427 ^ _776545 : [(40430 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1564950), 40426 ^ [_1564950, _1564952, _1564954]), c_Wellfounded_Oacc(_1564950, _1564954)))], (40428 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564950, _1564950)), hAPP(hAPP(c_Product__Type_OPair(_1564950, _1564950), 40426 ^ [_1564950, _1564952, _1564954]), _1564952)), _1564954)))]], -(hBOOL(hAPP(hAPP(c_member(_1564950), _1564952), c_Wellfounded_Oacc(_1564950, _1564954))))], (45193 ^ _776545) ^ [_1681841, _1681843] : [hAPP(c_Code__Numeral_Onat__of, _1681841) = hAPP(c_Code__Numeral_Onat__of, _1681843), -(_1681841 = _1681843)], (19779 ^ _776545) ^ [_1133509, _1133511, _1133513, _1133515] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133509, _1133511)), c_Sum__Type_OPlus(_1133509, _1133511, _1133513, _1133515))), 19782 ^ _776545 : [(19785 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1133511), _1133515)))], (19783 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1133509), _1133513)))]]], (2144 ^ _776545) ^ [_807652, _807654] : [_807654 = _807652, -(c_Nat_Osemiring__1__class_ONats(_807654) = c_Nat_Osemiring__1__class_ONats(_807652))], (25251 ^ _776545) ^ [_1233668, _1233670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233668)), -(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, _1233670, _1233668))))], (28933 ^ _776545) ^ [_1295210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295210), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1295210)), c_Int_OPls)))], (52365 ^ _776545) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (34179 ^ _776545) ^ [_1411822, _1411824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411822)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411824))), -(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(_1411824))), 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), _1411822)), c_Int_Onat))))))], (52079 ^ _776545) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (33633 ^ _776545) ^ [_1397465, _1397467, _1397469, _1397471, _1397473] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1397465), hAPP(c_Set_Oimage(_1397467, _1397465, _1397469), c_Orderings_Otop__class_Otop(tc_fun(_1397467, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1397471), hAPP(c_Set_Oimage(_1397467, _1397471, hAPP(hAPP(c_COMBB(_1397465, _1397471, _1397467), _1397473), _1397469)), c_Orderings_Otop__class_Otop(tc_fun(_1397467, tc_HOL_Obool))))))], (5715 ^ _776545) ^ [_866670, _866672, _866674] : [class_HOL_Oequal(_866670), 5718 ^ _776545 : [(5725 ^ _776545) ^ [] : [_866672 = _866674, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_866670), _866672), _866674)))], (5719 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_866670), _866672), _866674)), -(_866672 = _866674)]]], (1524 ^ _776545) ^ [_798459, _798461] : [-(class_Groups_Olinordered__ab__semigroup__add(_798459)), _798461 = _798459, class_Groups_Olinordered__ab__semigroup__add(_798461)], (42361 ^ _776545) ^ [_1617309, _1617311, _1617313] : [-(hAPP(c_List_Oset(_1617309), hAPP(hAPP(c_List_Olist_OCons(_1617309), _1617311), _1617313)) = hAPP(hAPP(c_Set_Oinsert(_1617309), _1617311), hAPP(c_List_Oset(_1617309), _1617313)))], (18736 ^ _776545) ^ [_1113901, _1113903, _1113905, _1113907, _1113909, _1113911] : [class_Rings_Olinordered__semiring__1(_1113901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113901), _1113903), _1113905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113901), _1113907), _1113905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113901), c_Groups_Ozero__class_Ozero(_1113901)), _1113909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113901), c_Groups_Ozero__class_Ozero(_1113901)), _1113911)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113901), _1113909), _1113911) = c_Groups_Oone__class_Oone(_1113901), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113901), _1113909), _1113903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113901), _1113911), _1113907))), _1113905)))], (15093 ^ _776545) ^ [_1049056, _1049058] : [class_Groups_Omonoid__mult(_1049056), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049056), _1049058), c_Groups_Oone__class_Oone(_1049056)) = _1049058)], (35125 ^ _776545) ^ [_1432101, _1432103, _1432105] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1432101, _1432103), _1432105)), 35128 ^ _776545 : [(35129 ^ _776545) ^ [_1432186] : [hBOOL(hAPP(hAPP(_1432103, _1432186), _1432105)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1432101, _1432103), _1432186)))]]], (49863 ^ _776545) ^ [_1783628, _1783630] : [c_Equiv__Relations_Oequivp(_1783628, _1783630), -(c_Equiv__Relations_Opart__equivp(_1783628, _1783630))], (38868 ^ _776545) ^ [_1524349, _1524351] : [c_Wellfounded_Owf(_1524349, _1524351), -(c_Wellfounded_Oacyclic(_1524349, _1524351))], (9262 ^ _776545) ^ [_936113, _936115, _936117] : [class_Orderings_Olinorder(_936113), 9265 ^ _776545 : [(9266 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936113), _936115), _936117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936113), _936117), _936115))), -(_936115 = _936117)], (9276 ^ _776545) ^ [] : [9277 ^ _776545 : [(9280 ^ _776545) ^ [] : [_936115 = _936117], (9278 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936113), _936117), _936115))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936113), _936115), _936117))]]], (3398 ^ _776545) ^ [_827281, _827283, _827285, _827287] : [-(c_Enum_Osublists(_827287, _827283) = c_Enum_Osublists(_827285, _827281)), _827287 = _827285, _827283 = _827281], (16412 ^ _776545) ^ [_1072425, _1072427] : [class_Groups_Olinordered__ab__group__add(_1072425), 16415 ^ _776545 : [(16422 ^ _776545) ^ [] : [_1072427 = c_Groups_Ozero__class_Ozero(_1072425), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072425), _1072427) = _1072427)], (16416 ^ _776545) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1072425), _1072427) = _1072427, -(_1072427 = c_Groups_Ozero__class_Ozero(_1072425))]]], (44813 ^ _776545) ^ [_1672901, _1672903, _1672905, _1672907] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672901)), hAPP(hAPP(c_List_Omap(_1672903, _1672901), _1672905), _1672907)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672903)), _1672907))], (45187 ^ _776545) ^ [_1681739] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1681739)) = _1681739)], (25879 ^ _776545) ^ [_1244678, _1244680, _1244682] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244678), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244680, _1244682)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244678), _1244680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244678), _1244682)))], (29837 ^ _776545) ^ [_1311522, _1311524] : [_1311522 = _1311524, -(c_Code__Numeral_OSuc__code__numeral(_1311522) = c_Code__Numeral_OSuc__code__numeral(_1311524))], (52385 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (38850 ^ _776545) ^ [_1524009, _1524011, _1524013, _1524015, _1524017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524009, _1524011)), hAPP(hAPP(c_Product__Type_OPair(_1524009, _1524011), _1524013), _1524015)), _1524017)), -(hBOOL(hAPP(hAPP(c_member(_1524009), _1524013), hAPP(c_Relation_ODomain(_1524009, _1524011), _1524017))))], (52077 ^ _776545) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (38175 ^ _776545) ^ [_1507641, _1507643, _1507645] : [c_Wellfounded_Owf(_1507641, _1507643), -(c_Wellfounded_Owf(_1507641, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1507641, _1507641), tc_HOL_Obool)), _1507645), _1507643)))], (7648 ^ _776545) ^ [_903569, _903571, _903573, _903575] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903569, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903569, tc_HOL_Obool)), _903571), _903573)), _903575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903569, tc_HOL_Obool)), _903571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903569, tc_HOL_Obool)), _903573), _903575)))], (23914 ^ _776545) ^ [] : [-(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))], (7430 ^ _776545) ^ [_898847, _898849, _898851] : [class_Orderings_Olinorder(_898847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898847), _898849), _898851)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898847, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_898847, _898849, _898851)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_898847), _898851)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_898847), _898849))], (48472 ^ _776545) ^ [_1753154, _1753156, _1753158] : [-(hAPP(c_New__DSequence_Opos__single(_1753154, _1753156), _1753158) = hAPP(c_Lazy__Sequence_Osingle(_1753154), _1753156))], (34069 ^ _776545) ^ [_1409088, _1409090, _1409092] : [class_Groups_Ocomm__monoid__add(_1409088), class_Groups_Ocomm__monoid__mult(_1409088), c_Nat__Transfer_Onat__set(_1409090), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1409088), _1409092), _1409090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1409088), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1409088, tc_Nat_Onat), _1409092), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1409090)))], (11948 ^ _776545) ^ [_986262, _986264, _986266, _986268, _986270] : [-(hAPP(c_Fun_Ofun__upd(_986262, _986264, _986266, _986268, _986270), _986268) = _986270)], (30802 ^ _776545) ^ [_1329014, _1329016, _1329018] : [class_Orderings_Olinorder(_1329014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329014), _1329016)), -(_1329016 = c_Orderings_Obot__class_Obot(tc_fun(_1329014, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329014), _1329018)), -(_1329018 = c_Orderings_Obot__class_Obot(tc_fun(_1329014, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1329014, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329014, tc_HOL_Obool)), _1329016), _1329018)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329014), c_Big__Operators_Olinorder__class_OMin(_1329014, _1329016)), c_Big__Operators_Olinorder__class_OMin(_1329014, _1329018)))], (13916 ^ _776545) ^ [_1025063, _1025065, _1025067, _1025069, _1025071, _1025073] : [class_Rings_Oordered__ring(_1025063), 13919 ^ _776545 : [(13926 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025063), _1025065), _1025071)), _1025067)), _1025069)), _1025073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), _1025065), _1025067)), _1025069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), _1025071), _1025067)), _1025073))))], (13920 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), _1025065), _1025067)), _1025069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), _1025071), _1025067)), _1025073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1025063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025063), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1025063), _1025065), _1025071)), _1025067)), _1025069)), _1025073)))]]], (41574 ^ _776545) ^ [_1594296, _1594298, _1594300, _1594302, _1594304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594296, _1594296)), hAPP(hAPP(c_Product__Type_OPair(_1594296, _1594296), _1594298), _1594300)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594296, _1594296), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594302)), _1594304))), 41578 ^ _776545 : [(41581 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594296, _1594296)), hAPP(hAPP(c_Product__Type_OPair(_1594296, _1594296), 41577 ^ [_1594296, _1594298, _1594300, _1594302, _1594304]), _1594300)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594296, _1594296), tc_HOL_Obool), _1594302), _1594304))))], (41579 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594296, _1594296)), hAPP(hAPP(c_Product__Type_OPair(_1594296, _1594296), _1594298), 41577 ^ [_1594296, _1594298, _1594300, _1594302, _1594304])), _1594304)))]]], (43104 ^ _776545) ^ [_1635377, _1635379] : [_1635379 = c_List_Olist_ONil(_1635377), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635377)), _1635379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23035 ^ _776545) ^ [_1193886, _1193888, _1193890, _1193892, _1193894, _1193896] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193886), _1193888)), _1193890) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193892), _1193894)), _1193896), 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), _1193892), _1193894)), _1193896))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193896), _1193892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193892), _1193886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193888), _1193894)))], (11296 ^ _776545) ^ [_972873, _972875] : [class_Groups_Oordered__ab__group__add(_972873), -(hAPP(c_Set_Oimage(_972873, _972873, c_Groups_Ouminus__class_Ouminus(_972873)), hAPP(c_SetInterval_Oord__class_OatMost(_972873), _972875)) = hAPP(c_SetInterval_Oord__class_OatLeast(_972873), hAPP(c_Groups_Ouminus__class_Ouminus(_972873), _972875)))], (28535 ^ _776545) ^ [_1288595, _1288597] : [class_Int_Onumber__ring(_1288595), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288595), hAPP(c_Int_Onumber__class_Onumber__of(_1288595), c_Int_OBit1(c_Int_OPls))), _1288597) = _1288597)], (45217 ^ _776545) ^ [] : [-(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))))], (43916 ^ _776545) ^ [_1654110, _1654112, _1654114, _1654116] : [hBOOL(hAPP(hAPP(c_member(_1654110), _1654112), hAPP(c_List_Oset(_1654110), hAPP(hAPP(c_List_Odrop(_1654110), _1654114), _1654116)))), -(hBOOL(hAPP(hAPP(c_member(_1654110), _1654112), hAPP(c_List_Oset(_1654110), _1654116))))], (41857 ^ _776545) ^ [_1602840, _1602842, _1602844, _1602846] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602840), tc_List_Olist(_1602840))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602840), tc_List_Olist(_1602840)), _1602842), _1602844)), c_List_Olex(_1602840, _1602846)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602840), tc_List_Olist(_1602840))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602840), tc_List_Olist(_1602840)), _1602842), _1602844)), c_List_Olexord(_1602840, _1602846))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602840)), _1602842) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602840)), _1602844)], (24395 ^ _776545) ^ [_1217723] : [-(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, _1217723)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50887 ^ _776545) ^ [_1807205, _1807207, _1807209] : [-(c_Lazy__Sequence_Oflat(_1807205, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1807205), _1807207, _1807209)) = c_Lazy__Sequence_Oappend(_1807205, _1807207, c_Lazy__Sequence_Oflat(_1807205, _1807209)))], (46225 ^ _776545) ^ [_1705985, _1705987] : [-(c_List_Ofoldr(tc_List_Olist(_1705985), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1705985)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1705985))), c_List_Otranspose(_1705985, _1705987), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705985))), hAPP(c_List_Ofilter(tc_List_Olist(_1705985), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1705985)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1705985), tc_List_Olist(_1705985), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1705985)))), _1705987)))], (10671 ^ _776545) ^ [_960145, _960147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960145, tc_HOL_Obool)), _960147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960145, tc_HOL_Obool)), _960147))), -(_960147 = c_Orderings_Obot__class_Obot(tc_fun(_960145, tc_HOL_Obool)))], (7906 ^ _776545) ^ [_909935, _909937, _909939, _909941] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909935, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909935), _909937), _909939)), hAPP(hAPP(c_Set_Oinsert(_909935), _909937), _909941)) = hAPP(hAPP(c_Set_Oinsert(_909935), _909937), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_909935, tc_HOL_Obool)), _909939), _909941)))], (52449 ^ _776545) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (8227 ^ _776545) ^ [_917280, _917282] : [class_Lattices_Obounded__lattice__top(_917280), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917280), _917282), c_Orderings_Otop__class_Otop(_917280)) = _917282)], (22221 ^ _776545) ^ [_1179584, _1179586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179586), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179584), _1179586))), -(_1179584 = _1179586)], (38582 ^ _776545) ^ [_1517084, _1517086, _1517088, _1517090] : [hBOOL(hAPP(c_Predicate_ORangeP(_1517084, _1517086, hAPP(hAPP(c_COMBC(_1517084, tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_fun(_1517086, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517086, tc_fun(tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_fun(_1517086, tc_HOL_Obool)), _1517084), c_COMBC(_1517086, tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517086, tc_prod(_1517084, _1517086)), tc_fun(_1517086, tc_fun(tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_HOL_Obool)), _1517084), hAPP(c_COMBB(tc_prod(_1517084, _1517086), tc_fun(tc_fun(tc_prod(_1517084, _1517086), tc_HOL_Obool), tc_HOL_Obool), _1517086), c_member(tc_prod(_1517084, _1517086)))), c_Product__Type_OPair(_1517084, _1517086)))), _1517088)), _1517090)), -(hBOOL(hAPP(hAPP(c_member(_1517086), _1517090), hAPP(c_Relation_ORange(_1517084, _1517086), _1517088))))], (6440 ^ _776545) ^ [_880612, _880614, _880616, _880618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880612, tc_HOL_Obool)), _880614), _880616)), hBOOL(hAPP(hAPP(c_member(_880612), _880618), _880614)), -(hBOOL(hAPP(hAPP(c_member(_880612), _880618), _880616)))], (43777 ^ _776545) ^ [_1650223, _1650225, _1650227, _1650229, _1650231, _1650233, _1650235, _1650237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650223, _1650223)), hAPP(hAPP(c_Product__Type_OPair(_1650223, _1650223), _1650225), _1650227)), _1650229)), _1650231 = hAPP(hAPP(c_List_Oappend(_1650223), _1650233), hAPP(hAPP(c_List_Olist_OCons(_1650223), _1650225), _1650235)), _1650237 = hAPP(hAPP(c_List_Oappend(_1650223), _1650233), hAPP(hAPP(c_List_Olist_OCons(_1650223), _1650227), _1650235)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650223), tc_List_Olist(_1650223))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650223), tc_List_Olist(_1650223)), _1650231), _1650237)), c_List_Olistrel1(_1650223, _1650229))))], (23759 ^ _776545) ^ [_1206840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206840)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5917 ^ _776545) ^ [_870646, _870648, _870650, _870652] : [_870646 = _870648, 5920 ^ _776545 : [(5927 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870650), _870648), _870652)), -(hBOOL(hAPP(hAPP(c_member(_870650), _870646), _870652)))], (5921 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870650), _870646), _870652)), -(hBOOL(hAPP(hAPP(c_member(_870650), _870648), _870652)))]]], (47058 ^ _776545) ^ [_1722470, _1722472, _1722474] : [hAPP(c_List_Orev(_1722470), _1722472) = hAPP(c_List_Orev(_1722470), _1722474), -(_1722472 = _1722474)], (15904 ^ _776545) ^ [_1064396, _1064398] : [-(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), _1064396), _1064398)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1064398))], (25065 ^ _776545) ^ [_1230358, _1230360] : [25066 ^ _776545 : [(25067 ^ _776545) ^ [_1230407] : [_1230358 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230360), _1230407)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230358, _1230360) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23713 ^ _776545) ^ [] : [-(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)))], (21161 ^ _776545) ^ [_1159375, _1159377, _1159379] : [class_Int_Onumber__ring(_1159375), class_Int_Oring__char__0(_1159375), 21168 ^ _776545 : [(21175 ^ _776545) ^ [] : [_1159377 = _1159379, -(hAPP(c_Int_Onumber__class_Onumber__of(_1159375), _1159377) = hAPP(c_Int_Onumber__class_Onumber__of(_1159375), _1159379))], (21169 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1159375), _1159377) = hAPP(c_Int_Onumber__class_Onumber__of(_1159375), _1159379), -(_1159377 = _1159379)]]], (51893 ^ _776545) ^ [_1825096, _1825098] : [class_Lattices_Oboolean__algebra(_1825096), -(class_Lattices_Oboolean__algebra(tc_fun(_1825098, _1825096)))], (37416 ^ _776545) ^ [_1488592, _1488594, _1488596, _1488598] : [c_Fun_Oinj__on(_1488592, _1488594, _1488596, _1488598), -(hAPP(c_Finite__Set_Ocard(_1488594), hAPP(c_Set_Oimage(_1488592, _1488594, _1488596), _1488598)) = hAPP(c_Finite__Set_Ocard(_1488592), _1488598))], (48738 ^ _776545) ^ [_1758820, _1758822, _1758824] : [-(hAPP(hAPP(c_List_Oappend(_1758820), c_List_Oreplicate(_1758820, _1758822, _1758824)), hAPP(hAPP(c_List_Olist_OCons(_1758820), _1758824), c_List_Olist_ONil(_1758820))) = hAPP(hAPP(c_List_Olist_OCons(_1758820), _1758824), c_List_Oreplicate(_1758820, _1758822, _1758824)))], (44872 ^ _776545) ^ [_1674690, _1674692, _1674694, _1674696, _1674698, _1674700, _1674702, _1674704] : [-(hAPP(hAPP(c_List_Ozip(_1674690, _1674692), hAPP(hAPP(c_List_Omap(_1674694, _1674690), _1674696), _1674698)), hAPP(hAPP(c_List_Omap(_1674700, _1674692), _1674702), _1674704)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674694, _1674700), tc_prod(_1674690, _1674692)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674694, _1674700, tc_prod(_1674690, _1674692)), hAPP(hAPP(c_COMBC(_1674694, tc_fun(_1674700, _1674692), tc_fun(_1674700, tc_prod(_1674690, _1674692))), hAPP(hAPP(c_COMBB(tc_fun(_1674692, tc_prod(_1674690, _1674692)), tc_fun(tc_fun(_1674700, _1674692), tc_fun(_1674700, tc_prod(_1674690, _1674692))), _1674694), c_COMBB(_1674692, tc_prod(_1674690, _1674692), _1674700)), hAPP(hAPP(c_COMBB(_1674690, tc_fun(_1674692, tc_prod(_1674690, _1674692)), _1674694), c_Product__Type_OPair(_1674690, _1674692)), _1674696))), _1674702))), hAPP(hAPP(c_List_Ozip(_1674694, _1674700), _1674698), _1674704)))], (42279 ^ _776545) ^ [_1615147, _1615149, _1615151, _1615153] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615147), tc_List_Olist(_1615147))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615147), tc_List_Olist(_1615147)), _1615149), _1615151)), c_List_Olexord(_1615147, _1615153)))), 42280 ^ _776545 : [(42287 ^ _776545) ^ [_1615454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1615454), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615147)), _1615149)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615147)), _1615151)))), hAPP(hAPP(c_List_Otake(_1615147), _1615454), _1615149) = hAPP(hAPP(c_List_Otake(_1615147), _1615454), _1615151), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615147, _1615147)), hAPP(hAPP(c_Product__Type_OPair(_1615147, _1615147), hAPP(hAPP(c_List_Onth(_1615147), _1615149), _1615454)), hAPP(hAPP(c_List_Onth(_1615147), _1615151), _1615454))), _1615153))], (42281 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615147)), _1615149)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615147)), _1615151))), hAPP(hAPP(c_List_Otake(_1615147), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615147)), _1615149)), _1615151) = _1615149]]], (9718 ^ _776545) ^ [_942912, _942914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942912, tc_HOL_Obool)), _942914), c_Orderings_Obot__class_Obot(tc_fun(_942912, tc_HOL_Obool))))], (42327 ^ _776545) ^ [_1616568, _1616570, _1616572, _1616574] : [-(hAPP(hAPP(c_List_Otake(_1616568), hAPP(c_Nat_OSuc, _1616570)), hAPP(hAPP(c_List_Olist_OCons(_1616568), _1616572), _1616574)) = hAPP(hAPP(c_List_Olist_OCons(_1616568), _1616572), hAPP(hAPP(c_List_Otake(_1616568), _1616570), _1616574)))], (27473 ^ _776545) ^ [_1270756, _1270758, _1270760] : [class_Groups_Oordered__ab__group__add__abs(_1270756), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270756), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270756), hAPP(c_Groups_Oabs__class_Oabs(_1270756), _1270758)), hAPP(c_Groups_Oabs__class_Oabs(_1270756), _1270760))), hAPP(c_Groups_Oabs__class_Oabs(_1270756), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270756), _1270760), _1270758)))))], (52251 ^ _776545) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (10707 ^ _776545) ^ [_961041, _961043] : [class_Orderings_Olinorder(_961041), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961041, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_961041), _961043)) = hAPP(c_SetInterval_Oord__class_OlessThan(_961041), _961043))], (41174 ^ _776545) ^ [_1584031, _1584033, _1584035, _1584037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584031, _1584031)), hAPP(hAPP(c_Product__Type_OPair(_1584031, _1584031), _1584033), _1584035)), c_Transitive__Closure_Otrancl(_1584031, hAPP(c_Relation_Oconverse(_1584031, _1584031), _1584037)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584031, _1584031)), hAPP(hAPP(c_Product__Type_OPair(_1584031, _1584031), _1584033), _1584035)), hAPP(c_Relation_Oconverse(_1584031, _1584031), c_Transitive__Closure_Otrancl(_1584031, _1584037)))))], (19927 ^ _776545) ^ [_1136127, _1136129, _1136131, _1136133] : [class_Fields_Olinordered__field(_1136127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136127), _1136129), c_Groups_Ozero__class_Ozero(_1136127))), 19934 ^ _776545 : [(19941 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136127), _1136133), _1136129)), _1136131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136127), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136127), _1136131), _1136129)), _1136133)))], (19935 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136127), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136127), _1136131), _1136129)), _1136133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136127), _1136133), _1136129)), _1136131)))]]], (9502 ^ _776545) ^ [_939713, _939715, _939717] : [class_Orderings_Olinorder(_939713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939713), _939715), _939717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939713), _939717), _939715)))], (51933 ^ _776545) ^ [_1825620, _1825622] : [class_Orderings_Oord(_1825620), -(class_Orderings_Oord(tc_fun(_1825622, _1825620)))], (42250 ^ _776545) ^ [_1614386, _1614388, _1614390, _1614392] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614386) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1614388), hAPP(hAPP(c_List_Olist_OCons(_1614388), _1614390), _1614392)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1614386)) = _1614390)], (18061 ^ _776545) ^ [_1101335, _1101337, _1101339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101335), _1101337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101339), _1101335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101339), _1101337))))], (39938 ^ _776545) ^ [_1553995, _1553997, _1553999] : [-(hAPP(c_Fun_Ocomp(_1553995, _1553995, _1553997, c_Fun_Oid(_1553995)), _1553999) = _1553999)], (52059 ^ _776545) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (27106 ^ _776545) ^ [_1264566, _1264568] : [class_Rings_Olinordered__idom(_1264566), 27109 ^ _776545 : [(27116 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264566), c_Groups_Ozero__class_Ozero(_1264566)), hAPP(c_Int_Oring__1__class_Oof__int(_1264566), _1264568))))], (27110 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264566), c_Groups_Ozero__class_Ozero(_1264566)), hAPP(c_Int_Oring__1__class_Oof__int(_1264566), _1264568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264568)))]]], (39121 ^ _776545) ^ [_1530845, _1530847, _1530849, _1530851] : [-(hAPP(c_Set_Oimage(tc_prod(_1530845, _1530847), tc_prod(_1530847, _1530845), hAPP(c_Product__Type_Oprod_Oprod__case(_1530845, _1530847, tc_prod(_1530847, _1530845)), hAPP(c_COMBC(_1530847, _1530845, tc_prod(_1530847, _1530845)), c_Product__Type_OPair(_1530847, _1530845)))), hAPP(hAPP(c_Product__Type_OSigma(_1530845, _1530847), _1530849), hAPP(c_COMBK(tc_fun(_1530847, tc_HOL_Obool), _1530845), _1530851))) = hAPP(hAPP(c_Product__Type_OSigma(_1530847, _1530845), _1530851), hAPP(c_COMBK(tc_fun(_1530845, tc_HOL_Obool), _1530847), _1530849)))], (25465 ^ _776545) ^ [_1237206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237206)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1237206) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (23469 ^ _776545) ^ [_1201932, _1201934, _1201936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201932)), 23472 ^ _776545 : [(23473 ^ _776545) ^ [_1202066] : [23475 ^ _776545 : [(23481 ^ _776545) ^ [] : [-(_1202066 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23477 ^ [_1201932, _1201934, _1201936, _1202066]), 23474 ^ [_1201932, _1201934, _1201936, _1202066]))], (23479 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23477 ^ [_1201932, _1201934, _1201936, _1202066]), _1201934)))], (23476 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23474 ^ [_1201932, _1201934, _1201936, _1202066]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201932))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202066), _1201936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202066), _1201932)), _1201936)))]]], (51927 ^ _776545) ^ [_1825541, _1825543] : [class_Orderings_Otop(_1825541), -(class_Orderings_Otop(tc_fun(_1825543, _1825541)))], (6246 ^ _776545) ^ [_876930] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_876930, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_876930, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_876930, tc_HOL_Obool)))], (11322 ^ _776545) ^ [_973447, _973449, _973451] : [hAPP(c_Set_Oimage(_973449, tc_fun(_973449, tc_HOL_Obool), _973447), _973451) = hAPP(c_Set_OPow(_973449), _973451)], (7726 ^ _776545) ^ [_905964, _905966, _905968] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_905964, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_905964, tc_HOL_Obool), tc_HOL_Obool)), _905966), _905968)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_905964, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_905964, tc_HOL_Obool), _905966)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_905964, tc_HOL_Obool), _905968)))], (22175 ^ _776545) ^ [_1178711, _1178713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178711), _1178713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178711)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1178713))))], (6961 ^ _776545) ^ [_889509, _889511] : [hAPP(c_Set_OPow(_889509), _889511) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_889509, tc_HOL_Obool), tc_HOL_Obool))], (42512 ^ _776545) ^ [_1622440, _1622442, _1622444] : [_1622440 = _1622442, 42515 ^ _776545 : [(42518 ^ _776545) ^ [_1622596] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622444, _1622444)), _1622596), hAPP(c_List_Oset(tc_prod(_1622444, _1622444)), hAPP(hAPP(c_List_Ozip(_1622444, _1622444), _1622440), _1622442)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622444, _1622444, tc_HOL_Obool), c_fequal), _1622596)))], (42516 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622444)), _1622440) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622444)), _1622442))]]], (30232 ^ _776545) ^ [_1318828, _1318830, _1318832] : [class_Orderings_Olinorder(_1318828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318828), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318828), _1318830), _1318832)), _1318832)))], (28469 ^ _776545) ^ [_1287493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1287493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1287493))))], (10529 ^ _776545) ^ [_957539, _957541, _957543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957539, tc_HOL_Obool)), _957543), _957541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957539, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957539, tc_HOL_Obool)), _957541)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957539, tc_HOL_Obool)), _957543))))], (50839 ^ _776545) ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325)), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), _1805327), _1805329)), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), _1805331), _1805333))), c_Transitive__Closure_Ortrancl(tc_prod(_1805323, _1805325), _1805335))), hBOOL(hAPP(hAPP(_1805337, _1805331), _1805333)), 50852 ^ _776545 : [(50855 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325)), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), 50850 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]), 50851 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337])), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), _1805331), _1805333))), c_Transitive__Closure_Ortrancl(tc_prod(_1805323, _1805325), _1805335))))], (50857 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1805337, 50850 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]), 50851 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337])))], (50859 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1805337, 50848 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]), 50849 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]))], (50853 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1805323, _1805325), tc_prod(_1805323, _1805325)), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), 50848 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]), 50849 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337])), hAPP(hAPP(c_Product__Type_OPair(_1805323, _1805325), 50850 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]), 50851 ^ [_1805323, _1805325, _1805327, _1805329, _1805331, _1805333, _1805335, _1805337]))), _1805335)))]], -(hBOOL(hAPP(hAPP(_1805337, _1805327), _1805329)))], (6630 ^ _776545) ^ [_883881, _883883, _883885] : [class_Orderings_Oorder(_883881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883881), _883883), _883885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883881), _883885), _883883)), -(_883885 = _883883)], (38124 ^ _776545) ^ [_1506688, _1506690] : [-(c_Wellfounded_Owf(_1506688, hAPP(c_Wellfounded_Omeasure(_1506688), _1506690)))], (38144 ^ _776545) ^ [_1507014] : [-(c_Wellfounded_Owf(tc_fun(_1507014, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1507014)))], (68 ^ _776545) ^ [_777619, _777621, _777623, _777625, _777627, _777629] : [-(c_Finite__Set_Ofolding__one(_777627, _777623, _777619)), c_Finite__Set_Ofolding__one(_777629, _777625, _777621), _777629 = _777627, _777625 = _777623, _777621 = _777619], (39611 ^ _776545) ^ [_1544804, _1544806] : [c_Relation_Orefl__on(_1544804, c_Orderings_Otop__class_Otop(tc_fun(_1544804, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544804, _1544804)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544804, _1544804, tc_HOL_Obool), _1544806))), -(c_Predicate_Oreflp(_1544804, _1544806))], (45225 ^ _776545) ^ [_1682346, _1682348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1682346)), hAPP(c_Code__Numeral_Onat__of, _1682348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1682346), _1682348)))], (46034 ^ _776545) ^ [_1701108, _1701110, _1701112, _1701114, _1701116] : [class_Orderings_Olinorder(_1701108), -(hAPP(c_List_Ofilter(_1701110, _1701112), c_List_Olinorder__class_Osort__key(_1701110, _1701108, _1701114, _1701116)) = c_List_Olinorder__class_Osort__key(_1701110, _1701108, _1701114, hAPP(c_List_Ofilter(_1701110, _1701112), _1701116)))], (7992 ^ _776545) ^ [_911868, _911870, _911872] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911868, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911868, tc_HOL_Obool)), _911870), _911872)), _911872)))], (12682 ^ _776545) ^ [_1000105, _1000107, _1000109, _1000111] : [_1000105 = c_Finite__Set_Ofold1(_1000107, _1000109), -(hAPP(_1000105, hAPP(hAPP(c_Set_Oinsert(_1000107), _1000111), c_Orderings_Obot__class_Obot(tc_fun(_1000107, tc_HOL_Obool)))) = _1000111)], (34699 ^ _776545) ^ [_1423069] : [-(c_Divides_Oadjust(_1423069) = 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)), _1423069))))), 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)), _1423069))))), 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))))))))], (17127 ^ _776545) ^ [_1084910, _1084912, _1084914] : [class_Rings_Oordered__cancel__semiring(_1084910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084910), c_Groups_Ozero__class_Ozero(_1084910)), _1084912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084910), c_Groups_Ozero__class_Ozero(_1084910)), _1084914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084910), c_Groups_Ozero__class_Ozero(_1084910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084910), _1084912), _1084914))))], (41867 ^ _776545) ^ [_1603127, _1603129, _1603131, _1603133, _1603135, _1603137] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603127, _1603127)), hAPP(hAPP(c_Product__Type_OPair(_1603127, _1603127), _1603129), _1603131)), c_Transitive__Closure_Ortrancl(_1603127, _1603133))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603127), tc_List_Olist(_1603127))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603127), tc_List_Olist(_1603127)), _1603135), _1603137)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603127), c_List_Olistrel1(_1603127, _1603133)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603127), tc_List_Olist(_1603127))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603127), tc_List_Olist(_1603127)), hAPP(hAPP(c_List_Olist_OCons(_1603127), _1603129), _1603135)), hAPP(hAPP(c_List_Olist_OCons(_1603127), _1603131), _1603137))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603127), c_List_Olistrel1(_1603127, _1603133)))))], (48762 ^ _776545) ^ [_1759213, _1759215] : [class_Lazy__Sequence_Osmall__lazy(_1759213), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1759213), _1759215) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1759213), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1759213)), c_List_Olist_ONil(_1759213)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759213))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1759215)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1759213, tc_List_Olist(_1759213)), tc_List_Olist(_1759213), c_Lazy__Sequence_Oproduct(_1759213, tc_List_Olist(_1759213), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1759213, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1759215), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1759213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1759215), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1759213, tc_List_Olist(_1759213), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759213))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1759213), tc_List_Olist(_1759213)), tc_fun(tc_List_Olist(_1759213), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759213))), _1759213), hAPP(c_COMBB(tc_List_Olist(_1759213), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1759213)), tc_List_Olist(_1759213)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1759213)))), c_List_Olist_OCons(_1759213))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1759213)))))], (6001 ^ _776545) ^ [_872221, _872223, _872225, _872227] : [hBOOL(hAPP(hAPP(_872225, _872223), _872227)), -(hBOOL(hAPP(hAPP(c_member(_872221), _872223), c_SetInterval_Oord_OatMost(_872221, _872225, _872227))))], (33330 ^ _776545) ^ [_1388064, _1388066, _1388068, _1388070] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388064, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388066, tc_fun(_1388064, tc_HOL_Obool)), _1388068), _1388070)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388066, tc_fun(_1388064, tc_HOL_Obool)), _1388068), hAPP(hAPP(c_COMBB(tc_fun(_1388064, tc_HOL_Obool), tc_fun(_1388064, tc_HOL_Obool), _1388066), c_Groups_Ouminus__class_Ouminus(tc_fun(_1388064, tc_HOL_Obool))), _1388070)))], (10871 ^ _776545) ^ [_964124, _964126, _964128] : [class_Orderings_Oorder(_964124), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964124, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_964124), _964126)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_964124, _964126), _964128)) = c_Orderings_Obot__class_Obot(tc_fun(_964124, tc_HOL_Obool)))], (43084 ^ _776545) ^ [_1635032, _1635034] : [-(c_List_Olistrelp(_1635032, _1635034, c_List_Olist_ONil(_1635032), c_List_Olist_ONil(_1635032)))], (51465 ^ _776545) ^ [_1818115, _1818117] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1818115), 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)))), _1818117))), 51468 ^ _776545 : [(51471 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818115), _1818117))], (51469 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818117), _1818115)))]]], (21703 ^ _776545) ^ [_1169648, _1169650, _1169652, _1169654] : [class_Fields_Olinordered__field__inverse__zero(_1169648), class_Int_Onumber(_1169648), 21710 ^ _776545 : [(21711 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169648), _1169650), _1169652)), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654))), 21714 ^ _776545 : [(21721 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), _1169652))), 21724 ^ _776545 : [(21731 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169652), c_Groups_Ozero__class_Ozero(_1169648)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654))))], (21725 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169652), c_Groups_Ozero__class_Ozero(_1169648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169648), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)), _1169652)), _1169650)))]]], (21715 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), _1169652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169648), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)), _1169652))))]]], (21737 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1169648), _1169650), _1169652)), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)))), 21740 ^ _776545 : [(21743 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169648), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)), _1169652)))], (21741 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), _1169652)))]], 21744 ^ _776545 : [(21747 ^ _776545) ^ [] : [21748 ^ _776545 : [(21751 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169648), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)), _1169652)), _1169650))], (21749 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169652), c_Groups_Ozero__class_Ozero(_1169648))))]], 21752 ^ _776545 : [(21755 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), hAPP(c_Int_Onumber__class_Onumber__of(_1169648), _1169654)))], (21753 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), _1169652), c_Groups_Ozero__class_Ozero(_1169648)))]]], (21745 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169648), c_Groups_Ozero__class_Ozero(_1169648)), _1169652))]]]]], (27503 ^ _776545) ^ [_1271335, _1271337, _1271339] : [class_Groups_Oordered__ab__group__add__abs(_1271335), 27506 ^ _776545 : [(27515 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), hAPP(c_Groups_Oabs__class_Oabs(_1271335), _1271337)), _1271339))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), _1271337), _1271339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), hAPP(c_Groups_Ouminus__class_Ouminus(_1271335), _1271337)), _1271339))], (27507 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), hAPP(c_Groups_Oabs__class_Oabs(_1271335), _1271337)), _1271339)), 27510 ^ _776545 : [(27513 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), hAPP(c_Groups_Ouminus__class_Ouminus(_1271335), _1271337)), _1271339)))], (27511 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271335), _1271337), _1271339)))]]]]], (38550 ^ _776545) ^ [_1515881, _1515883, _1515885, _1515887, _1515889] : [-(hAPP(c_Fun_Othe__inv__into(_1515881, _1515883, _1515885, _1515887), _1515889) = c_HOL_OThe(_1515881, hAPP(hAPP(c_COMBS(_1515881, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515881), c_fconj), hAPP(hAPP(c_COMBC(_1515881, tc_fun(_1515881, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515881)), _1515885))), hAPP(hAPP(c_COMBC(_1515881, _1515883, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1515883, tc_fun(_1515883, tc_HOL_Obool), _1515881), c_fequal), _1515887)), _1515889))))], (43663 ^ _776545) ^ [_1647363, _1647365, _1647367] : [-(_1647363 = c_List_Olist_ONil(_1647365)), -(c_List_Obutlast(_1647365, hAPP(hAPP(c_List_Oappend(_1647365), _1647367), _1647363)) = hAPP(hAPP(c_List_Oappend(_1647365), _1647367), c_List_Obutlast(_1647365, _1647363)))], (28987 ^ _776545) ^ [_1296164, _1296166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1296164)), c_Int_OBit0(_1296166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296164), _1296166)))], (5967 ^ _776545) ^ [_871578, _871580, _871582, _871584, _871586, _871588, _871590] : [c_Typedef_Otype__definition(_871578, _871580, _871582, _871584, _871586), hBOOL(hAPP(hAPP(c_member(_871580), _871588), _871586)), hBOOL(hAPP(_871590, hAPP(_871582, 5976 ^ [_871578, _871580, _871582, _871584, _871586, _871588, _871590]))), -(hBOOL(hAPP(_871590, _871588)))], (6420 ^ _776545) ^ [_880242, _880244, _880246, _880248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880242, tc_HOL_Obool)), _880244), _880246)), hBOOL(hAPP(hAPP(c_member(_880242), _880248), _880244)), -(hBOOL(hAPP(hAPP(c_member(_880242), _880248), _880246)))], (1284 ^ _776545) ^ [_795459, _795461] : [-(class_Groups_Osgn__if(_795459)), _795461 = _795459, class_Groups_Osgn__if(_795461)], (14821 ^ _776545) ^ [_1043808, _1043810] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043808), _1043810)), _1043810) = _1043808)], (18886 ^ _776545) ^ [_1116714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116714)), -(_1116714 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116714), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (29015 ^ _776545) ^ [_1296681] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1296681)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1296681)))], (14228 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (41767 ^ _776545) ^ [_1599896, _1599898, _1599900, _1599902, _1599904] : [-(hAPP(hAPP(c_List_Olist_OCons(_1599896), _1599898), _1599900) = hAPP(hAPP(c_List_Olist_OCons(_1599896), _1599902), _1599904)), _1599898 = _1599902, _1599900 = _1599904], (23982 ^ _776545) ^ [_1210834, _1210836, _1210838, _1210840] : [class_Divides_Osemiring__div(_1210834), -(_1210836 = c_Groups_Ozero__class_Ozero(_1210834)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210834), _1210838), _1210836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210834), _1210840), _1210836)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1210834), _1210838), _1210840))], (10623 ^ _776545) ^ [_959236, _959238] : [class_Lattices_Oboolean__algebra(_959236), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959236), _959238), hAPP(c_Groups_Ouminus__class_Ouminus(_959236), _959238)) = c_Orderings_Obot__class_Obot(_959236))], (8267 ^ _776545) ^ [_917900, _917902, _917904] : [class_Lattices_Olattice(_917900), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917900), _917902), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917900), _917902), _917904)) = _917902)], (47838 ^ _776545) ^ [_1739527, _1739529, _1739531, _1739533] : [47840 ^ _776545 : [(47843 ^ _776545) ^ [] : [hBOOL(hAPP(_1739531, 47839 ^ [_1739527, _1739529, _1739531, _1739533]))], (47841 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739527), 47839 ^ [_1739527, _1739529, _1739531, _1739533]), hAPP(c_List_Oset(_1739527), _1739529))))]], -(c_List_OtakeWhile(_1739527, _1739531, hAPP(hAPP(c_List_Oappend(_1739527), _1739529), _1739533)) = hAPP(hAPP(c_List_Oappend(_1739527), _1739529), c_List_OtakeWhile(_1739527, _1739531, _1739533)))], (35636 ^ _776545) ^ [_1441702, _1441704, _1441706, _1441708, _1441710, _1441712] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1441702, _1441704), _1441704, _1441706), hAPP(hAPP(c_COMBB(_1441708, tc_fun(_1441704, _1441706), tc_prod(_1441702, _1441704)), _1441710), hAPP(hAPP(c_COMBB(_1441702, _1441708, tc_prod(_1441702, _1441704)), _1441712), c_Product__Type_Ofst(_1441702, _1441704)))), c_Product__Type_Osnd(_1441702, _1441704)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1441702, _1441704, _1441706), hAPP(hAPP(c_COMBB(_1441708, tc_fun(_1441704, _1441706), _1441702), _1441710), _1441712)))], (48372 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28259 ^ _776545) ^ [_1283931, _1283933] : [class_Int_Onumber__ring(_1283931), 28262 ^ _776545 : [(28269 ^ _776545) ^ [] : [c_Int_Oiszero(_1283931, hAPP(c_Int_Onumber__class_Onumber__of(_1283931), 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), _1283933)))), -(c_Groups_Oone__class_Oone(_1283931) = hAPP(c_Int_Onumber__class_Onumber__of(_1283931), _1283933))], (28263 ^ _776545) ^ [] : [c_Groups_Oone__class_Oone(_1283931) = hAPP(c_Int_Onumber__class_Onumber__of(_1283931), _1283933), -(c_Int_Oiszero(_1283931, hAPP(c_Int_Onumber__class_Onumber__of(_1283931), 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), _1283933)))))]]], (11936 ^ _776545) ^ [_986107, _986109, _986111, _986113, _986115, _986117] : [_986107 = _986109, -(hAPP(c_Fun_Ofun__upd(_986111, _986113, _986115, _986109, _986117), _986107) = _986117)], (45696 ^ _776545) ^ [_1693316, _1693318] : [-(_1693316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1693318, _1693316, c_List_Olist_ONil(_1693318)) = c_List_Olist_ONil(tc_List_Olist(_1693318)))], (39026 ^ _776545) ^ [_1528090, _1528092] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1528090), c_Int_OInteg)), hBOOL(hAPP(_1528092, hAPP(c_Int_ORep__Integ, 39031 ^ [_1528090, _1528092]))), -(hBOOL(hAPP(_1528092, _1528090)))], (45491 ^ _776545) ^ [_1688748, _1688750, _1688752, _1688754] : [_1688754 = c_List_Olist_ONil(_1688750), -(c_List_Olist__all2(_1688748, _1688750, _1688752, c_List_Olist_ONil(_1688748), _1688754))], (22635 ^ _776545) ^ [_1186621, _1186623, _1186625] : [class_Groups_Omonoid__mult(_1186621), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186621), _1186623), hAPP(c_Nat_OSuc, _1186625)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186621), hAPP(hAPP(c_Power_Opower__class_Opower(_1186621), _1186623), _1186625)), _1186623))], (25363 ^ _776545) ^ [_1235430] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235430))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1235430)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46007 ^ _776545) ^ [_1699836, _1699838, _1699840] : [c_List_Oconcat(_1699836, _1699838) = c_List_Oconcat(_1699836, _1699840), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699836))), _1699838) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699836))), _1699840), 46017 ^ _776545 : [(46020 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1699836), tc_List_Olist(_1699836), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699836), tc_fun(tc_List_Olist(_1699836), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699836), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1699836), tc_Nat_Onat), tc_fun(tc_List_Olist(_1699836), tc_HOL_Obool)), tc_List_Olist(_1699836)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699836))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699836)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1699836))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1699836)))), 46016 ^ [_1699836, _1699838, _1699840]))], (46018 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699836), tc_List_Olist(_1699836))), 46016 ^ [_1699836, _1699838, _1699840]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1699836), tc_List_Olist(_1699836))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1699836), tc_List_Olist(_1699836)), _1699838), _1699840)))))]], -(_1699838 = _1699840)], (974 ^ _776545) ^ [_791162, _791164, _791166, _791168, _791170, _791172, _791174, _791176, _791178, _791180, _791182, _791184] : [-(c_Equiv__Relations_Ocongruent2(_791182, _791178, _791174, _791170, _791166, _791162)), c_Equiv__Relations_Ocongruent2(_791184, _791180, _791176, _791172, _791168, _791164), _791184 = _791182, _791180 = _791178, _791176 = _791174, _791172 = _791170, _791168 = _791166, _791164 = _791162], (8793 ^ _776545) ^ [_927581, _927583] : [class_Lattices_Obounded__lattice__bot(_927581), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927581), c_Orderings_Obot__class_Obot(_927581)), _927583) = c_Orderings_Obot__class_Obot(_927581))], (39924 ^ _776545) ^ [_1553595, _1553597, _1553599, _1553601, _1553603, _1553605, _1553607, _1553609, _1553611, _1553613, _1553615] : [hAPP(_1553595, hAPP(_1553597, _1553599)) = hAPP(_1553601, hAPP(_1553603, _1553605)), -(hAPP(hAPP(c_Fun_Ocomp(_1553607, _1553609, _1553611, _1553595), _1553597), _1553599) = hAPP(hAPP(c_Fun_Ocomp(_1553613, _1553609, _1553615, _1553601), _1553603), _1553605))], (33156 ^ _776545) ^ [_1383478, _1383480, _1383482, _1383484] : [_1383482 = _1383484, -(hAPP(hAPP(c_COMBC(_1383478, tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_fun(_1383480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383480, tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_fun(_1383480, tc_HOL_Obool)), _1383478), c_COMBC(_1383480, tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383480, tc_prod(_1383478, _1383480)), tc_fun(_1383480, tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), _1383478), hAPP(c_COMBB(tc_prod(_1383478, _1383480), tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool), _1383480), c_member(tc_prod(_1383478, _1383480)))), c_Product__Type_OPair(_1383478, _1383480)))), _1383482) = hAPP(hAPP(c_COMBC(_1383478, tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_fun(_1383480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383480, tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_fun(_1383480, tc_HOL_Obool)), _1383478), c_COMBC(_1383480, tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1383480, tc_prod(_1383478, _1383480)), tc_fun(_1383480, tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool)), _1383478), hAPP(c_COMBB(tc_prod(_1383478, _1383480), tc_fun(tc_fun(tc_prod(_1383478, _1383480), tc_HOL_Obool), tc_HOL_Obool), _1383480), c_member(tc_prod(_1383478, _1383480)))), c_Product__Type_OPair(_1383478, _1383480)))), _1383484))], (36725 ^ _776545) ^ [_1473264, _1473266, _1473268, _1473270] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1473264, tc_HOL_Obool)), _1473266), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1473264), _1473268), _1473270))), 36729 ^ _776545 : [(36732 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473264), 36728 ^ [_1473264, _1473266, _1473268, _1473270]), _1473268)))], (36730 ^ _776545) ^ [] : [-(_1473266 = hAPP(c_Relation_OImage(_1473264, _1473264, _1473270), hAPP(hAPP(c_Set_Oinsert(_1473264), 36728 ^ [_1473264, _1473266, _1473268, _1473270]), c_Orderings_Obot__class_Obot(tc_fun(_1473264, tc_HOL_Obool)))))]]], (3638 ^ _776545) ^ [_831053, _831055, _831057, _831059] : [-(c_List_Orotate(_831059, _831055) = c_List_Orotate(_831057, _831053)), _831059 = _831057, _831055 = _831053], (15688 ^ _776545) ^ [_1061046] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1061046)) = 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), _1061046))))], (38505 ^ _776545) ^ [_1514689, _1514691, _1514693, _1514695] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514689, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514689, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1514691, _1514689), _1514693)), hAPP(c_Relation_ORange(_1514691, _1514689), _1514695))), hAPP(c_Relation_ORange(_1514691, _1514689), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1514691, _1514689), tc_HOL_Obool)), _1514693), _1514695)))))], (22255 ^ _776545) ^ [_1180180, _1180182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180180), _1180182)), 22258 ^ _776545 : [(22261 ^ _776545) ^ [] : [_1180180 = _1180182], (22259 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180180), _1180182)))]]], (45249 ^ _776545) ^ [_1682769] : [-(hAPP(c_Code__Numeral_Onat__of, _1682769) = c_Code__Numeral_Onat__of__aux(_1682769, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30930 ^ _776545) ^ [_1331372, _1331374, _1331376] : [class_Orderings_Olinorder(_1331372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331372), _1331374)), -(hBOOL(hAPP(hAPP(c_member(_1331372), _1331376), _1331374))), -(_1331374 = c_Orderings_Obot__class_Obot(tc_fun(_1331372, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1331372, hAPP(hAPP(c_Set_Oinsert(_1331372), _1331376), _1331374)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331372), _1331376), c_Big__Operators_Olinorder__class_OMin(_1331372, _1331374)))], (50159 ^ _776545) ^ [_1790142, _1790144, _1790146] : [hAPP(c_Set_Oimage(_1790142, _1790144, _1790146), c_Orderings_Otop__class_Otop(tc_fun(_1790142, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790144, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1790142, _1790144, _1790144, _1790146), c_Hilbert__Choice_Oinv__into(_1790142, _1790144, c_Orderings_Otop__class_Otop(tc_fun(_1790142, tc_HOL_Obool)), _1790146)) = c_Fun_Oid(_1790144))], (43498 ^ _776545) ^ [_1644002, _1644004, _1644006, _1644008] : [hAPP(hAPP(c_List_Oappend(_1644002), _1644004), _1644006) = hAPP(hAPP(c_List_Oappend(_1644002), _1644004), _1644008), -(_1644006 = _1644008)], (46353 ^ _776545) ^ [_1708780, _1708782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708780)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708782))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708780), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708782)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708780)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708780)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1708782))))], (35925 ^ _776545) ^ [_1449657, _1449659, _1449661] : [class_Groups_Olinordered__ab__semigroup__add(_1449657), hBOOL(hAPP(c_Finite__Set_Ofinite(_1449657), _1449659)), -(_1449659 = c_Orderings_Obot__class_Obot(tc_fun(_1449657, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1449657), _1449661), c_Big__Operators_Olinorder__class_OMax(_1449657, _1449659)) = c_Big__Operators_Olinorder__class_OMax(_1449657, hAPP(c_Set_OCollect(_1449657), hAPP(hAPP(c_COMBB(tc_fun(_1449657, tc_HOL_Obool), tc_HOL_Obool, _1449657), c_HOL_OEx(_1449657)), hAPP(hAPP(c_COMBC(_1449657, tc_fun(_1449657, tc_HOL_Obool), tc_fun(_1449657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449657, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1449657, tc_HOL_Obool), tc_fun(_1449657, tc_HOL_Obool)), _1449657), c_COMBS(_1449657, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449657, tc_HOL_Obool), tc_fun(_1449657, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1449657), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1449657), c_fconj)), hAPP(hAPP(c_COMBC(_1449657, tc_fun(_1449657, _1449657), tc_fun(_1449657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449657, tc_HOL_Obool), tc_fun(tc_fun(_1449657, _1449657), tc_fun(_1449657, tc_HOL_Obool)), _1449657), c_COMBB(_1449657, tc_HOL_Obool, _1449657)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1449657), _1449661))))), hAPP(hAPP(c_COMBC(_1449657, tc_fun(_1449657, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449657)), _1449659))))))], (40719 ^ _776545) ^ [_1573046, _1573048] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573046, _1573046)), hAPP(hAPP(c_Product__Type_OPair(_1573046, _1573046), _1573048), _1573048)), c_Relation_OId(_1573046))))], (23651 ^ _776545) ^ [_1205160, _1205162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205160)), 23654 ^ _776545 : [(23661 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205162), 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), _1205162), _1205160)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23655 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1205162), _1205160)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10719 ^ _776545) ^ [_961263, _961265, _961267] : [class_Orderings_Oorder(_961263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961263), _961265), _961267)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_961263, _961267), _961265) = c_Orderings_Obot__class_Obot(tc_fun(_961263, tc_HOL_Obool)))], (32189 ^ _776545) ^ [_1354986, _1354988] : [class_Orderings_Olinorder(_1354986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354986), _1354988)), -(_1354988 = c_Orderings_Obot__class_Obot(tc_fun(_1354986, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1354986), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354986), 32202 ^ [_1354986, _1354988]), 32203 ^ [_1354986, _1354988])), hAPP(hAPP(c_Set_Oinsert(_1354986), 32202 ^ [_1354986, _1354988]), hAPP(hAPP(c_Set_Oinsert(_1354986), 32203 ^ [_1354986, _1354988]), c_Orderings_Obot__class_Obot(tc_fun(_1354986, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1354986), c_Big__Operators_Olattice_OSup__fin(_1354986, c_Orderings_Oord__class_Omax(_1354986), _1354988)), _1354988)))], (31945 ^ _776545) ^ [_1350554, _1350556] : [class_Orderings_Olinorder(_1350554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350554), _1350556)), -(_1350556 = c_Orderings_Obot__class_Obot(tc_fun(_1350554, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350554), c_Big__Operators_Olattice_OInf__fin(_1350554, c_Orderings_Oord__class_Omin(_1350554), _1350556)), c_Big__Operators_Olattice_OSup__fin(_1350554, c_Orderings_Oord__class_Omax(_1350554), _1350556))))], (14260 ^ _776545) ^ [_1033209, _1033211, _1033213, _1033215, _1033217] : [class_Rings_Ocomm__semiring__1(_1033209), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), _1033211), _1033213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), _1033215), _1033217)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), _1033211), _1033215)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033209), _1033213), _1033217)))], (14981 ^ _776545) ^ [_1046842, _1046844, _1046846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046842), _1046844)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046844), _1046842)), _1046846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046844), _1046846)), _1046842))], (15186 ^ _776545) ^ [_1050541, _1050543] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050541), c_Orderings_Otop__class_Otop(tc_fun(_1050541, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1050541), _1050543) = hAPP(c_Finite__Set_Ocard(_1050541), c_Orderings_Otop__class_Otop(tc_fun(_1050541, tc_HOL_Obool))), -(_1050543 = c_Orderings_Otop__class_Otop(tc_fun(_1050541, tc_HOL_Obool)))], (44453 ^ _776545) ^ [_1665595, _1665597, _1665599] : [class_Orderings_Olinorder(_1665595), -(c_Big__Operators_Olattice_OSup__fin(_1665595, c_Orderings_Oord__class_Omax(_1665595), hAPP(c_List_Oset(_1665595), hAPP(hAPP(c_List_Olist_OCons(_1665595), _1665597), _1665599))) = hAPP(c_List_Ofoldl(_1665595, _1665595, c_Orderings_Oord__class_Omax(_1665595), _1665597), _1665599))], (14857 ^ _776545) ^ [_1044513, _1044515, _1044517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044513), _1044515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044513), _1044517)), 14864 ^ _776545 : [(14871 ^ _776545) ^ [] : [_1044515 = _1044517, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044515), _1044513) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044517), _1044513))], (14865 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044515), _1044513) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044517), _1044513), -(_1044515 = _1044517)]]], (51783 ^ _776545) ^ [_1823510, _1823512] : [_1823510 = _1823512, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823510), _1823512)))], (44088 ^ _776545) ^ [_1658405, _1658407, _1658409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658405), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658407)), _1658409))), -(hAPP(hAPP(c_List_Oappend(_1658407), hAPP(hAPP(c_List_Otake(_1658407), _1658405), _1658409)), hAPP(hAPP(c_List_Olist_OCons(_1658407), hAPP(c_List_Ohd(_1658407), hAPP(hAPP(c_List_Odrop(_1658407), _1658405), _1658409))), c_List_Olist_ONil(_1658407))) = hAPP(hAPP(c_List_Otake(_1658407), hAPP(c_Nat_OSuc, _1658405)), _1658409))], (14428 ^ _776545) ^ [_1037066, _1037068, _1037070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037066), _1037068)), 14431 ^ _776545 : [(14438 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037070), _1037066)), _1037068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037068), _1037066))))], (14432 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037068), _1037066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037070), _1037066)), _1037068)))]]], (49030 ^ _776545) ^ [_1765500, _1765502, _1765504, _1765506, _1765508, _1765510, _1765512] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1765500, tc_fun(_1765502, tc_fun(_1765504, tc_HOL_Obool))), _1765506), _1765508), _1765510), _1765512)), 49034 ^ _776545 : [(49037 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1765508, 49033 ^ [_1765500, _1765502, _1765504, _1765506, _1765508, _1765510, _1765512]), _1765510), _1765512)))], (49035 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765500), 49033 ^ [_1765500, _1765502, _1765504, _1765506, _1765508, _1765510, _1765512]), _1765506)))]]], (49062 ^ _776545) ^ [_1766213, _1766215, _1766217] : [c_List_Olist__all(tc_Int_Oint, _1766213, c_List_Oupto(_1766215, _1766217)), -(c_List_Oall__interval__int(_1766213, _1766215, _1766217))], (51513 ^ _776545) ^ [_1818971] : [_1818971 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818971), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (1674 ^ _776545) ^ [_800334, _800336] : [-(class_Groups_Ocomm__monoid__add(_800334)), _800336 = _800334, class_Groups_Ocomm__monoid__add(_800336)], (29475 ^ _776545) ^ [_1304553, _1304555] : [class_Rings_Oring__1__no__zero__divisors(_1304553), 29478 ^ _776545 : [(29479 ^ _776545) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1304553), _1304555), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1304553), -(_1304555 = c_Groups_Oone__class_Oone(_1304553)), -(_1304555 = hAPP(c_Groups_Ouminus__class_Ouminus(_1304553), c_Groups_Oone__class_Oone(_1304553)))], (29489 ^ _776545) ^ [] : [29490 ^ _776545 : [(29493 ^ _776545) ^ [] : [_1304555 = hAPP(c_Groups_Ouminus__class_Ouminus(_1304553), c_Groups_Oone__class_Oone(_1304553))], (29491 ^ _776545) ^ [] : [_1304555 = c_Groups_Oone__class_Oone(_1304553)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1304553), _1304555), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1304553))]]], (52503 ^ _776545) ^ [_1831504, _1831506] : [hBOOL(_1831504), hBOOL(_1831506), -(hBOOL(hAPP(hAPP(c_fconj, _1831504), _1831506)))], (51817 ^ _776545) ^ [_1824023, _1824025] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824023), _1824025)), -(_1824023 = _1824025), 51824 ^ _776545 : [(51827 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824025), _1824023))], (51825 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824023), _1824025)))]]], (12389 ^ _776545) ^ [_994163, _994165, _994167] : [class_Lattices_Olattice(_994163), hBOOL(hAPP(c_Finite__Set_Ofinite(_994163), _994165)), hBOOL(hAPP(c_Finite__Set_Ofinite(_994163), _994167)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994163, tc_HOL_Obool)), _994165), _994167) = c_Orderings_Obot__class_Obot(tc_fun(_994163, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994163), c_Big__Operators_Olattice__class_OInf__fin(_994163, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_994163, tc_HOL_Obool)), _994165), _994167))), c_Big__Operators_Olattice__class_OInf__fin(_994163, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994163, tc_HOL_Obool)), _994165), _994167))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994163), c_Big__Operators_Olattice__class_OInf__fin(_994163, _994165)), c_Big__Operators_Olattice__class_OInf__fin(_994163, _994167)))], (35394 ^ _776545) ^ [_1436383, _1436385, _1436387, _1436389, _1436391, _1436393, _1436395] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436383, _1436385), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436387), _1436389))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1436391, _1436385), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1436393), _1436395))), -(_1436385 = 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), _1436383), _1436391), _1436385), 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), _1436387), _1436393)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436389), _1436395)), _1436385))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436389), _1436395), _1436385)))))], (50307 ^ _776545) ^ [_1793502, _1793504, _1793506, _1793508, _1793510] : [c_Fun_Obij__betw(_1793502, _1793504, _1793506, c_Orderings_Otop__class_Otop(tc_fun(_1793502, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793504, tc_HOL_Obool))), c_Fun_Obij__betw(_1793508, _1793502, _1793510, c_Orderings_Otop__class_Otop(tc_fun(_1793508, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793502, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1793508, _1793504, c_Orderings_Otop__class_Otop(tc_fun(_1793508, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1793502, _1793504, _1793508, _1793506), _1793510)) = hAPP(c_Fun_Ocomp(_1793502, _1793508, _1793504, c_Hilbert__Choice_Oinv__into(_1793508, _1793502, c_Orderings_Otop__class_Otop(tc_fun(_1793508, tc_HOL_Obool)), _1793510)), c_Hilbert__Choice_Oinv__into(_1793502, _1793504, c_Orderings_Otop__class_Otop(tc_fun(_1793502, tc_HOL_Obool)), _1793506)))], (23181 ^ _776545) ^ [_1196407, _1196409, _1196411, _1196413] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1196407, _1196409, _1196411), _1196413), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1196409)], (14622 ^ _776545) ^ [_1040226, _1040228, _1040230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040226), _1040228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040226), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040230), _1040228))))], (49726 ^ _776545) ^ [_1781537, _1781539, _1781541] : [c_Relation_Osym(_1781537, _1781539), c_Relation_Osym(_1781537, _1781541), -(c_Relation_Osym(_1781537, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1781537, _1781537), tc_HOL_Obool)), _1781539), _1781541)))], (16146 ^ _776545) ^ [_1068367, _1068369, _1068371] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068367)), _1068369)), hAPP(c_Nat_OSuc, _1068371)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1068367), _1068369)), _1068371))], (50323 ^ _776545) ^ [_1794000, _1794002, _1794004, _1794006, _1794008, _1794010, _1794012, _1794014] : [c_Fun_Obij__betw(_1794000, _1794002, _1794004, _1794006, _1794008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794000, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794010, _1794000, _1794012), _1794014)), _1794006)), 50330 ^ _776545 : [(50337 ^ _776545) ^ [] : [c_Fun_Obij__betw(_1794010, _1794002, hAPP(c_Fun_Ocomp(_1794000, _1794002, _1794010, _1794004), _1794012), _1794014, _1794008), -(c_Fun_Obij__betw(_1794010, _1794000, _1794012, _1794014, _1794006))], (50331 ^ _776545) ^ [] : [c_Fun_Obij__betw(_1794010, _1794000, _1794012, _1794014, _1794006), -(c_Fun_Obij__betw(_1794010, _1794002, hAPP(c_Fun_Ocomp(_1794000, _1794002, _1794010, _1794004), _1794012), _1794014, _1794008))]]], (38187 ^ _776545) ^ [_1507855, _1507857, _1507859] : [c_Wellfounded_Owf(_1507855, _1507857), -(c_Wellfounded_Owf(_1507855, c_Wellfounded_Omlex__prod(_1507855, _1507859, _1507857)))], (52473 ^ _776545) ^ [_1831118, _1831120, _1831122, _1831124, _1831126, _1831128] : [-(hAPP(hAPP(hAPP(c_COMBS(_1831118, _1831120, _1831122), _1831124), _1831126), _1831128) = hAPP(hAPP(_1831124, _1831128), hAPP(_1831126, _1831128)))], (44727 ^ _776545) ^ [_1670747] : [-(hAPP(c_List_Omap(_1670747, _1670747), c_Fun_Oid(_1670747)) = c_Fun_Oid(tc_List_Olist(_1670747)))], (43695 ^ _776545) ^ [_1648129, _1648131, _1648133, _1648135] : [43696 ^ _776545 : [(43699 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648129), _1648131), hAPP(c_List_Oset(_1648129), c_List_Obutlast(_1648129, _1648135))))], (43697 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648129), _1648131), hAPP(c_List_Oset(_1648129), c_List_Obutlast(_1648129, _1648133))))]], -(hBOOL(hAPP(hAPP(c_member(_1648129), _1648131), hAPP(c_List_Oset(_1648129), c_List_Obutlast(_1648129, hAPP(hAPP(c_List_Oappend(_1648129), _1648133), _1648135))))))], (35688 ^ _776545) ^ [_1442740, _1442742, _1442744, _1442746, _1442748] : [-(c_Product__Type_Oprod_Oprod__size(_1442740, _1442742, _1442744, _1442746, _1442748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1442744, hAPP(c_Product__Type_Ofst(_1442740, _1442742), _1442748))), hAPP(_1442746, hAPP(c_Product__Type_Osnd(_1442740, _1442742), _1442748)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26677 ^ _776545) ^ [_1257970, _1257972] : [c_Nat__Transfer_Ois__nat(_1257970), c_Nat__Transfer_Ois__nat(_1257972), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1257970, _1257972) = 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, _1257970), hAPP(c_Int_Onat, _1257972))))], (29269 ^ _776545) ^ [] : [-(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))))], (33066 ^ _776545) ^ [_1380694, _1380696, _1380698, _1380700, _1380702, _1380704] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380694, tc_fun(_1380696, tc_HOL_Obool)), _1380698), hAPP(hAPP(c_COMBB(_1380700, tc_fun(_1380696, tc_HOL_Obool), _1380694), _1380702), _1380704)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1380700, tc_fun(_1380696, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1380694, _1380700, _1380704), _1380698)), _1380702))], (43216 ^ _776545) ^ [_1637608, _1637610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1637608), _1637610)), -(c_List_Oupto(_1637608, _1637610) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1637608), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1637608), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1637610)))], (48095 ^ _776545) ^ [_1745232, _1745234, _1745236] : [c_List_Olist__ex(_1745232, _1745234, _1745236), 48099 ^ _776545 : [(48102 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1745234, 48098 ^ [_1745232, _1745234, _1745236])))], (48100 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745232), 48098 ^ [_1745232, _1745234, _1745236]), hAPP(c_List_Oset(_1745232), _1745236))))]]], (5939 ^ _776545) ^ [_871020, _871022, _871024] : [_871022 = _871024, -(hBOOL(hAPP(hAPP(c_member(_871020), _871022), hAPP(c_fequal, _871024))))], (34950 ^ _776545) ^ [_1428597, _1428599, _1428601, _1428603, _1428605, _1428607] : [-(hAPP(c_Product__Type_Oapsnd(_1428597, _1428599, _1428601, _1428603), hAPP(hAPP(c_Product__Type_OPair(_1428601, _1428597), _1428605), _1428607)) = hAPP(hAPP(c_Product__Type_OPair(_1428601, _1428599), _1428605), hAPP(_1428603, _1428607)))], (43138 ^ _776545) ^ [_1635971, _1635973] : [-(c_List_Olist_Olist__size(_1635971, _1635973, c_List_Olist_ONil(_1635971)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30336 ^ _776545) ^ [_1320637, _1320639, _1320641] : [class_Int_Onumber(_1320637), class_Orderings_Oord(_1320637), 30343 ^ _776545 : [(30350 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320637), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320639)), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320641)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320637), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320639)), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320641)) = hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320641))], (30344 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320637), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320639)), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320641))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1320637), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320639)), hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320641)) = hAPP(c_Int_Onumber__class_Onumber__of(_1320637), _1320639))]]], (13538 ^ _776545) ^ [_1017512, _1017514, _1017516, _1017518] : [class_Groups_Oab__semigroup__add(_1017512), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017512), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017512), _1017514), _1017516)), _1017518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017512), _1017514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017512), _1017516), _1017518)))], (33953 ^ _776545) ^ [_1406235, _1406237, _1406239, _1406241, _1406243] : [class_Groups_Ocomm__monoid__add(_1406235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406237), _1406239)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406237, _1406235), _1406241), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406237, tc_HOL_Obool)), _1406239), _1406243)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1406237, _1406235), hAPP(hAPP(c_COMBC(_1406237, _1406235, _1406235), hAPP(hAPP(c_COMBS(_1406237, _1406235, tc_fun(_1406235, _1406235)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1406235, tc_fun(_1406235, _1406235)), _1406237), c_If(_1406235)), hAPP(hAPP(c_COMBC(_1406237, tc_fun(_1406237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1406237)), _1406243))), _1406241)), c_Groups_Ozero__class_Ozero(_1406235))), _1406239))], (41477 ^ _776545) ^ [_1591567, _1591569, _1591571] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591567, _1591567), hAPP(c_Nat_OSuc, _1591569)), _1591571) = hAPP(c_Fun_Ocomp(_1591567, _1591567, _1591567, _1591571), hAPP(hAPP(c_Nat_Ocompow(_1591567, _1591567), _1591569), _1591571)))], (2490 ^ _776545) ^ [_813103, _813105, _813107, _813109] : [-(c_Divides_OposDivAlg(_813109, _813105) = c_Divides_OposDivAlg(_813107, _813103)), _813109 = _813107, _813105 = _813103], (31325 ^ _776545) ^ [_1338895] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338895) = _1338895)], (38155 ^ _776545) ^ [_1507262, _1507264, _1507266, _1507268, _1507270, _1507272, _1507274] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1507262, _1507264, _1507266, _1507268, _1507270), _1507272), _1507274))), 38156 ^ _776545 : [(38157 ^ _776545) ^ [_1507333] : [hBOOL(hAPP(hAPP(_1507268, _1507272), _1507333)), hBOOL(hAPP(hAPP(_1507270, _1507333), _1507274))]]], (48446 ^ _776545) ^ [_1752353, _1752355, _1752357, _1752359, _1752361, _1752363, _1752365] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1752353, _1752355, _1752357, _1752359), _1752361), _1752363), _1752365) = c_New__DSequence_Oneg__bind(_1752353, _1752355, hAPP(hAPP(hAPP(_1752357, _1752361), _1752363), _1752365), hAPP(hAPP(c_COMBC(_1752353, 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(_1752355)))), hAPP(hAPP(c_COMBC(_1752353, 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(_1752355))))), hAPP(hAPP(c_COMBC(_1752353, 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(_1752355)))))), _1752359), _1752361)), _1752363)), _1752365)))], (37870 ^ _776545) ^ [_1498378, _1498380, _1498382, _1498384] : [c_Fun_Oinj__on(_1498378, _1498380, _1498382, _1498384), -(c_Fun_Oinj__on(_1498380, _1498378, c_Fun_Othe__inv__into(_1498378, _1498380, _1498384, _1498382), hAPP(c_Set_Oimage(_1498378, _1498380, _1498382), _1498384)))], (11006 ^ _776545) ^ [_966730, _966732, _966734] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966730, tc_HOL_Obool)), _966732) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_966730, tc_HOL_Obool)), _966734), -(_966732 = _966734)], (48464 ^ _776545) ^ [_1752972, _1752974, _1752976, _1752978, _1752980] : [-(c_List_Osplice(_1752972, hAPP(hAPP(c_List_Olist_OCons(_1752972), _1752974), _1752976), hAPP(hAPP(c_List_Olist_OCons(_1752972), _1752978), _1752980)) = hAPP(hAPP(c_List_Olist_OCons(_1752972), _1752974), hAPP(hAPP(c_List_Olist_OCons(_1752972), _1752978), c_List_Osplice(_1752972, _1752976, _1752980))))], (48436 ^ _776545) ^ [_1751996, _1751998, _1752000, _1752002, _1752004, _1752006, _1752008] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1751996, _1751998, _1752000, _1752002, _1752004, _1752006, _1752008) = c_New__DSequence_Oneg__decr__bind(_1751996, _1751998, hAPP(hAPP(hAPP(_1752000, _1752004), _1752006), _1752008), hAPP(hAPP(c_COMBC(_1751996, 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(_1751998)))), hAPP(hAPP(c_COMBC(_1751996, 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(_1751998))))), hAPP(hAPP(c_COMBC(_1751996, 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(_1751998)))))), _1752002), _1752004)), _1752006)), _1752008)))], (46178 ^ _776545) ^ [_1704260, _1704262] : [c_List_Otranspose(_1704260, _1704262) = c_List_Olist_ONil(tc_List_Olist(_1704260)), 46181 ^ _776545 : [(46182 ^ _776545) ^ [_1704355] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704260)), _1704355), hAPP(c_List_Oset(tc_List_Olist(_1704260)), _1704262))), -(_1704355 = c_List_Olist_ONil(_1704260))]]], (24956 ^ _776545) ^ [_1228467, _1228469, _1228471] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228467), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228469, _1228471)), _1228471) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228467), _1228469), _1228471))], (39049 ^ _776545) ^ [_1528597, _1528599, _1528601, _1528603, _1528605, _1528607] : [hBOOL(hAPP(hAPP(c_member(_1528597), _1528599), _1528601)), 39052 ^ _776545 : [(39059 ^ _776545) ^ [] : [_1528605 = _1528607, -(hAPP(hAPP(c_Product__Type_OSigma(_1528603, _1528597), _1528605), hAPP(c_COMBK(tc_fun(_1528597, tc_HOL_Obool), _1528603), _1528601)) = hAPP(hAPP(c_Product__Type_OSigma(_1528603, _1528597), _1528607), hAPP(c_COMBK(tc_fun(_1528597, tc_HOL_Obool), _1528603), _1528601)))], (39053 ^ _776545) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1528603, _1528597), _1528605), hAPP(c_COMBK(tc_fun(_1528597, tc_HOL_Obool), _1528603), _1528601)) = hAPP(hAPP(c_Product__Type_OSigma(_1528603, _1528597), _1528607), hAPP(c_COMBK(tc_fun(_1528597, tc_HOL_Obool), _1528603), _1528601)), -(_1528605 = _1528607)]]], (22893 ^ _776545) ^ [_1191349, _1191351, _1191353] : [class_Rings_Olinordered__semidom(_1191349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191349), c_Groups_Ozero__class_Ozero(_1191349)), _1191351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191349), _1191351), c_Groups_Oone__class_Oone(_1191349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191349), _1191351), hAPP(hAPP(c_Power_Opower__class_Opower(_1191349), _1191351), _1191353))), hAPP(hAPP(c_Power_Opower__class_Opower(_1191349), _1191351), _1191353))))], (32249 ^ _776545) ^ [_1356254, _1356256, _1356258, _1356260] : [class_Orderings_Olinorder(_1356254), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356254), _1356256)), 32259 ^ _776545 : [(32262 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356254), 32258 ^ [_1356254, _1356256, _1356258, _1356260]), _1356258))], (32260 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356254), 32258 ^ [_1356254, _1356256, _1356258, _1356260]), _1356256)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356254), hAPP(hAPP(c_Finite__Set_Ofold(_1356254, _1356254, c_Orderings_Oord__class_Omax(_1356254)), _1356260), _1356256)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356254), _1356258), _1356260))))], (47365 ^ _776545) ^ [_1728976, _1728978, _1728980] : [-(c_List_OdropWhile(_1728976, _1728978, _1728980) = c_List_Olist_ONil(_1728976)), hBOOL(hAPP(_1728978, hAPP(c_List_Ohd(_1728976), c_List_OdropWhile(_1728976, _1728978, _1728980))))], (45976 ^ _776545) ^ [_1698908, _1698910, _1698912] : [-(c_List_Oconcat(_1698908, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1698908)), _1698910), _1698912)) = hAPP(hAPP(c_List_Oappend(_1698908), c_List_Oconcat(_1698908, _1698910)), c_List_Oconcat(_1698908, _1698912)))], (9204 ^ _776545) ^ [_935442, _935444, _935446] : [class_Orderings_Oorder(_935442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935442), _935444), _935446)), _935444 = _935446], (17243 ^ _776545) ^ [_1086962, _1086964, _1086966] : [class_Groups_Oordered__comm__monoid__add(_1086962), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086962), c_Groups_Ozero__class_Ozero(_1086962)), _1086964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086962), c_Groups_Ozero__class_Ozero(_1086962)), _1086966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086962), c_Groups_Ozero__class_Ozero(_1086962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1086962), _1086964), _1086966))))], (24068 ^ _776545) ^ [_1212168, _1212170] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1212168), _1212170) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24069 ^ _776545 : [(24078 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212168), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212170), _1212168))], (24072 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212168), _1212170))], (24070 ^ _776545) ^ [] : [_1212170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (20997 ^ _776545) ^ [_1155762, _1155764, _1155766, _1155768, _1155770] : [class_Fields_Ofield(_1155762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1155764), _1155766)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1155764), _1155768)), 21011 ^ _776545 : [(21014 ^ _776545) ^ [] : [-(hAPP(_1155770, 21010 ^ [_1155762, _1155764, _1155766, _1155768, _1155770]) = c_Groups_Ozero__class_Ozero(_1155762))], (21012 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1155764), 21010 ^ [_1155762, _1155764, _1155766, _1155768, _1155770]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1155764, tc_HOL_Obool)), _1155766), _1155768))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1155764, _1155762), _1155770), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1155764, tc_HOL_Obool)), _1155766), _1155768)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155762), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1155764, _1155762), _1155770), _1155766)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1155764, _1155762), _1155770), _1155768))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1155764, _1155762), _1155770), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1155764, tc_HOL_Obool)), _1155766), _1155768))))], (29903 ^ _776545) ^ [_1312720, _1312722, _1312724, _1312726] : [class_Rings_Olinordered__semidom(_1312720), 29909 ^ _776545 : [(29912 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312720), c_Groups_Ozero__class_Ozero(_1312720)), hAPP(_1312726, 29908 ^ [_1312720, _1312722, _1312724, _1312726])))], (29910 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1312722), 29908 ^ [_1312720, _1312722, _1312724, _1312726]), _1312724)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312720), c_Groups_Ozero__class_Ozero(_1312720)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1312722, _1312720), _1312726), _1312724))))], (20295 ^ _776545) ^ [_1142812, _1142814, _1142816, _1142818] : [class_Fields_Ofield__inverse__zero(_1142812), 20298 ^ _776545 : [(20299 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142812), _1142814), _1142816) = _1142818, 20302 ^ _776545 : [(20309 ^ _776545) ^ [] : [_1142816 = c_Groups_Ozero__class_Ozero(_1142812), -(_1142818 = c_Groups_Ozero__class_Ozero(_1142812))], (20303 ^ _776545) ^ [] : [-(_1142816 = c_Groups_Ozero__class_Ozero(_1142812)), -(_1142814 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142812), _1142818), _1142816))]]], (20315 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142812), _1142814), _1142816) = _1142818), 20318 ^ _776545 : [(20321 ^ _776545) ^ [] : [_1142814 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142812), _1142818), _1142816)], (20319 ^ _776545) ^ [] : [_1142816 = c_Groups_Ozero__class_Ozero(_1142812)]], 20322 ^ _776545 : [(20325 ^ _776545) ^ [] : [_1142818 = c_Groups_Ozero__class_Ozero(_1142812)], (20323 ^ _776545) ^ [] : [-(_1142816 = c_Groups_Ozero__class_Ozero(_1142812))]]]]], (11266 ^ _776545) ^ [_972234, _972236, _972238] : [class_Groups_Oordered__ab__group__add(_972234), -(hAPP(c_Set_Oimage(_972234, _972234, c_Groups_Ouminus__class_Ouminus(_972234)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_972234, _972236), _972238)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_972234, hAPP(c_Groups_Ouminus__class_Ouminus(_972234), _972238), hAPP(c_Groups_Ouminus__class_Ouminus(_972234), _972236)))], (49974 ^ _776545) ^ [_1785894, _1785896, _1785898] : [c_Fun_Oinj__on(_1785894, _1785896, _1785898, c_Orderings_Otop__class_Otop(tc_fun(_1785894, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785896, _1785894, _1785894, c_Hilbert__Choice_Oinv__into(_1785894, _1785896, c_Orderings_Otop__class_Otop(tc_fun(_1785894, tc_HOL_Obool)), _1785898)), _1785898) = c_Fun_Oid(_1785894))], (28243 ^ _776545) ^ [_1283672, _1283674] : [class_Int_Onumber__ring(_1283672), 28246 ^ _776545 : [(28253 ^ _776545) ^ [] : [c_Int_Oiszero(_1283672, hAPP(c_Int_Onumber__class_Onumber__of(_1283672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283674), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1283672), _1283674) = c_Groups_Oone__class_Oone(_1283672))], (28247 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1283672), _1283674) = c_Groups_Oone__class_Oone(_1283672), -(c_Int_Oiszero(_1283672, hAPP(c_Int_Onumber__class_Onumber__of(_1283672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1283674), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (40150 ^ _776545) ^ [_1558797, _1558799, _1558801, _1558803, _1558805, _1558807, _1558809, _1558811] : [c_Finite__Set_Ofolding(_1558797, _1558799, _1558801, _1558803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558797), _1558805)), -(hAPP(c_Fun_Ocomp(_1558799, _1558799, _1558807, hAPP(_1558801, _1558809)), hAPP(c_Fun_Ocomp(_1558799, _1558799, _1558807, hAPP(_1558803, _1558805)), _1558811)) = hAPP(c_Fun_Ocomp(_1558799, _1558799, _1558807, hAPP(_1558803, _1558805)), hAPP(c_Fun_Ocomp(_1558799, _1558799, _1558807, hAPP(_1558801, _1558809)), _1558811)))], (30372 ^ _776545) ^ [_1321395, _1321397, _1321399, _1321401] : [class_Orderings_Olinorder(_1321395), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321395, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1321395), _1321397)), c_SetInterval_Oord__class_OatLeastAtMost(_1321395, _1321399, _1321401)) = c_SetInterval_Oord__class_OatLeastAtMost(_1321395, _1321399, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321395), _1321397), _1321401)))], (4702 ^ _776545) ^ [_848073, _848075] : [_848075 = _848073, -(c_DSequence_Osingle(_848075) = c_DSequence_Osingle(_848073))], (51899 ^ _776545) ^ [_1825175, _1825177] : [class_Orderings_Opreorder(_1825175), -(class_Orderings_Opreorder(tc_fun(_1825177, _1825175)))], (16352 ^ _776545) ^ [_1071562] : [class_Rings_Ozero__neq__one(_1071562), c_Groups_Ozero__class_Ozero(_1071562) = c_Groups_Oone__class_Oone(_1071562)], (44581 ^ _776545) ^ [_1668208, _1668210, _1668212] : [_1668208 = c_List_Olist_ONil(_1668210), -(c_List_Olast(_1668210, hAPP(hAPP(c_List_Olist_OCons(_1668210), _1668212), _1668208)) = _1668212)], (30058 ^ _776545) ^ [_1315603, _1315605, _1315607, _1315609] : [class_Orderings_Olinorder(_1315603), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315603), _1315605), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315603), _1315607), _1315609)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315603), _1315607), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315603), _1315605), _1315609)))], (37834 ^ _776545) ^ [_1497702, _1497704, _1497706, _1497708, _1497710] : [c_Fun_Oinj__on(_1497702, _1497704, _1497706, _1497708), hBOOL(hAPP(hAPP(c_member(_1497702), _1497710), _1497708)), -(hAPP(c_Fun_Othe__inv__into(_1497702, _1497704, _1497708, _1497706), hAPP(_1497706, _1497710)) = _1497710)], (23063 ^ _776545) ^ [_1194416, _1194418] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1194416), _1194418))))], (16318 ^ _776545) ^ [_1071049, _1071051, _1071053] : [class_Groups_Oab__group__add(_1071049), 16321 ^ _776545 : [(16328 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071049), _1071051), _1071053) = c_Groups_Ozero__class_Ozero(_1071049), -(_1071051 = _1071053)], (16322 ^ _776545) ^ [] : [_1071051 = _1071053, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071049), _1071051), _1071053) = c_Groups_Ozero__class_Ozero(_1071049))]]], (52091 ^ _776545) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (47992 ^ _776545) ^ [_1743112, _1743114, _1743116] : [class_Enum_Oenum(_1743112), class_Enum_Oenum(_1743114), 47999 ^ _776545 : [(48006 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1743114), hAPP(hAPP(c_COMBB(tc_fun(_1743112, tc_HOL_Obool), tc_HOL_Obool, _1743114), c_Enum_Oenum__class_Oenum__all(_1743112)), hAPP(hAPP(c_COMBB(tc_fun(_1743112, tc_prod(_1743114, _1743112)), tc_fun(_1743112, tc_HOL_Obool), _1743114), hAPP(c_COMBB(tc_prod(_1743114, _1743112), tc_HOL_Obool, _1743112), _1743116)), c_Product__Type_OPair(_1743114, _1743112))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1743114, _1743112)), _1743116)))], (48000 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1743114, _1743112)), _1743116)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1743114), hAPP(hAPP(c_COMBB(tc_fun(_1743112, tc_HOL_Obool), tc_HOL_Obool, _1743114), c_Enum_Oenum__class_Oenum__all(_1743112)), hAPP(hAPP(c_COMBB(tc_fun(_1743112, tc_prod(_1743114, _1743112)), tc_fun(_1743112, tc_HOL_Obool), _1743114), hAPP(c_COMBB(tc_prod(_1743114, _1743112), tc_HOL_Obool, _1743112), _1743116)), c_Product__Type_OPair(_1743114, _1743112))))))]]], (50117 ^ _776545) ^ [_1789137, _1789139, _1789141, _1789143] : [c_Fun_Oinj__on(_1789137, _1789139, _1789141, c_Orderings_Otop__class_Otop(tc_fun(_1789137, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1789139, _1789137, c_Hilbert__Choice_Oinv__into(_1789137, _1789139, c_Orderings_Otop__class_Otop(tc_fun(_1789137, tc_HOL_Obool)), _1789141)), hAPP(c_Set_Oimage(_1789137, _1789139, _1789141), _1789143)) = _1789143)], (26080 ^ _776545) ^ [_1247893, _1247895] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1247893), _1247895) = 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)), _1247893)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1247895))))], (28343 ^ _776545) ^ [_1285320, _1285322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285320), _1285322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1285320)), c_Int_OBit1(_1285322))))], (49588 ^ _776545) ^ [_1778557, _1778559, _1778561, _1778563] : [c_Relation_Oantisym(_1778557, _1778559), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778557, _1778557)), hAPP(hAPP(c_Product__Type_OPair(_1778557, _1778557), _1778561), _1778563)), _1778559)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778557, _1778557)), hAPP(hAPP(c_Product__Type_OPair(_1778557, _1778557), _1778563), _1778561)), _1778559)), -(_1778561 = _1778563)], (16689 ^ _776545) ^ [_1076759, _1076761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076759), hAPP(c_Nat_OSuc, _1076761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076759), _1076761)))], (48120 ^ _776545) ^ [_1745689, _1745691, _1745693] : [c_List_Olist__ex(_1745689, _1745691, _1745693), -(c_List_Olist__ex(_1745689, _1745691, hAPP(c_List_Orev(_1745689), _1745693)))], (43186 ^ _776545) ^ [_1636819, _1636821, _1636823] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636819, tc_HOL_Obool)), hAPP(c_List_Oset(_1636819), c_List_Oremove1(_1636819, _1636821, _1636823))), hAPP(c_List_Oset(_1636819), _1636823))))], (1504 ^ _776545) ^ [_798209, _798211] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_798209)), _798211 = _798209, class_Groups_Oordered__ab__semigroup__add__imp__le(_798211)], (21155 ^ _776545) ^ [_1159248, _1159250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1159248), _1159250)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1159248, tc_HOL_Obool)), hAPP(c_Set_OPow(_1159248), _1159250)) = 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(_1159248), _1159250)))], (18626 ^ _776545) ^ [_1111813, _1111815, _1111817] : [18627 ^ _776545 : [(18630 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1111815), _1111817))], (18628 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1111813)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111813), _1111815)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1111813), _1111817))))], (34483 ^ _776545) ^ [_1418261, _1418263, _1418265, _1418267, _1418269, _1418271] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418261, tc_fun(_1418263, tc_HOL_Obool))), _1418265), _1418267), _1418269), _1418271)), 34486 ^ _776545 : [(34489 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1418267, _1418269), _1418271)))], (34487 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1418265, _1418269), _1418271)))]]], (39473 ^ _776545) ^ [_1541606, _1541608, _1541610, _1541612, _1541614, _1541616, _1541618, _1541620, _1541622, _1541624] : [hAPP(c_Set_Oimage(_1541606, _1541608, _1541610), _1541612) = _1541614, hAPP(c_Set_Oimage(_1541616, _1541618, _1541620), _1541622) = _1541624, -(hAPP(c_Set_Oimage(tc_prod(_1541606, _1541616), tc_prod(_1541608, _1541618), c_Product__Type_Omap__pair(_1541606, _1541608, _1541616, _1541618, _1541610, _1541620)), hAPP(hAPP(c_Product__Type_OSigma(_1541606, _1541616), _1541612), hAPP(c_COMBK(tc_fun(_1541616, tc_HOL_Obool), _1541606), _1541622))) = hAPP(hAPP(c_Product__Type_OSigma(_1541608, _1541618), _1541614), hAPP(c_COMBK(tc_fun(_1541618, tc_HOL_Obool), _1541608), _1541624)))], (24030 ^ _776545) ^ [_1211587, _1211589] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1211587), _1211589)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211587)), _1211589))], (38904 ^ _776545) ^ [_1525123, _1525125, _1525127, _1525129] : [hBOOL(hAPP(hAPP(c_member(_1525123), _1525125), hAPP(c_Relation_ODomain(_1525123, _1525127), _1525129))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525123, _1525127)), hAPP(hAPP(c_Product__Type_OPair(_1525123, _1525127), _1525125), 38907 ^ [_1525123, _1525125, _1525127, _1525129])), _1525129)))], (5823 ^ _776545) ^ [_868779, _868781, _868783] : [5825 ^ _776545 : [(5828 ^ _776545) ^ [] : [hBOOL(hAPP(_868781, hAPP(c_Hoare__Mirabelle_OAbs__triple(_868779), 5824 ^ [_868779, _868781, _868783])))], (5826 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_868779, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _868779)), tc_HOL_Obool)), 5824 ^ [_868779, _868781, _868783]), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_868779, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _868779)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_868779)))))]], -(hBOOL(hAPP(_868781, _868783)))], (6061 ^ _776545) ^ [_873455, _873457, _873459, _873461, _873463] : [hBOOL(hAPP(hAPP(c_member(_873455), _873457), c_SetInterval_Oord_OgreaterThanLessThan(_873455, _873459, _873461, _873463))), 6064 ^ _776545 : [(6067 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873459, _873457), _873463)))], (6065 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873459, _873461), _873457)))]]], (5490 ^ _776545) ^ [_860439, _860441] : [_860441 = _860439, -(c_Orderings_Oord__class_Oless(_860441) = c_Orderings_Oord__class_Oless(_860439))], (10263 ^ _776545) ^ [_952944, _952946, _952948] : [class_Orderings_Olinorder(_952944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952944), _952946), _952948)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952944, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_952944, _952946), _952948)), hAPP(c_SetInterval_Oord__class_OatLeast(_952944), _952948)) = hAPP(c_SetInterval_Oord__class_OatLeast(_952944), _952946))], (43884 ^ _776545) ^ [_1653367, _1653369] : [hBOOL(hAPP(c_List_Odistinct(_1653367), hAPP(c_List_Orotate1(_1653367), _1653369))), -(hBOOL(hAPP(c_List_Odistinct(_1653367), _1653369)))], (14993 ^ _776545) ^ [_1047116, _1047118, _1047120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047116), _1047118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047116), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047120), _1047118))))], (46158 ^ _776545) ^ [_1703746, _1703748, _1703750] : [-(hAPP(c_List_Oset(_1703746), hAPP(c_List_Ofilter(_1703746, _1703748), _1703750)) = hAPP(c_Set_OCollect(_1703746), hAPP(hAPP(c_COMBS(_1703746, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1703746), c_fconj), hAPP(hAPP(c_COMBC(_1703746, tc_fun(_1703746, tc_HOL_Obool), tc_HOL_Obool), c_member(_1703746)), hAPP(c_List_Oset(_1703746), _1703750)))), _1703748)))], (48674 ^ _776545) ^ [_1757672, _1757674, _1757676, _1757678] : [-(hAPP(hAPP(c_List_Oappend(_1757672), c_List_Oreplicate(_1757672, _1757674, _1757676)), c_List_Oreplicate(_1757672, _1757678, _1757676)) = hAPP(hAPP(c_List_Oappend(_1757672), c_List_Oreplicate(_1757672, _1757678, _1757676)), c_List_Oreplicate(_1757672, _1757674, _1757676)))], (44593 ^ _776545) ^ [_1668363, _1668365, _1668367] : [_1668363 = c_List_Olist_ONil(_1668365), -(c_List_Olast(_1668365, hAPP(hAPP(c_List_Oappend(_1668365), _1668367), _1668363)) = c_List_Olast(_1668365, _1668367))], (46172 ^ _776545) ^ [_1704090, _1704092, _1704094] : [hBOOL(hAPP(c_List_Odistinct(_1704090), _1704092)), -(hAPP(c_List_Ofilter(_1704090, hAPP(hAPP(c_COMBC(_1704090, tc_fun(_1704090, tc_HOL_Obool), tc_HOL_Obool), c_member(_1704090)), hAPP(c_List_Oset(_1704090), c_List_Osublist(_1704090, _1704092, _1704094)))), _1704092) = c_List_Osublist(_1704090, _1704092, _1704094))], (42423 ^ _776545) ^ [_1618742, _1618744, _1618746] : [42425 ^ _776545 : [(42428 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1618742), 42424 ^ [_1618742, _1618744, _1618746]), _1618746))], (42426 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618742), 42424 ^ [_1618742, _1618744, _1618746]), hAPP(c_List_Oset(_1618742), _1618744))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1618742)), _1618744), c_List_Olists(_1618742, _1618746))))], (45945 ^ _776545) ^ [_1698202, _1698204] : [c_List_Oconcat(_1698202, _1698204) = c_List_Olist_ONil(_1698202), 45948 ^ _776545 : [(45949 ^ _776545) ^ [_1698293] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698202)), _1698293), hAPP(c_List_Oset(tc_List_Olist(_1698202)), _1698204))), -(_1698293 = c_List_Olist_ONil(_1698202))]]], (32590 ^ _776545) ^ [_1366834, _1366836, _1366838, _1366840, _1366842, _1366844] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1366834, _1366836)), hAPP(hAPP(c_Product__Type_OPair(_1366834, _1366836), _1366842), _1366844)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool)), _1366838), _1366840))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366834, tc_fun(_1366836, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1366834, tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_fun(_1366836, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366836, tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_fun(_1366836, tc_HOL_Obool)), _1366834), c_COMBC(_1366836, tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366836, tc_prod(_1366834, _1366836)), tc_fun(_1366836, tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), _1366834), hAPP(c_COMBB(tc_prod(_1366834, _1366836), tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool), _1366836), c_member(tc_prod(_1366834, _1366836)))), c_Product__Type_OPair(_1366834, _1366836)))), _1366838)), hAPP(hAPP(c_COMBC(_1366834, tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_fun(_1366836, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366836, tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_fun(_1366836, tc_HOL_Obool)), _1366834), c_COMBC(_1366836, tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366836, tc_prod(_1366834, _1366836)), tc_fun(_1366836, tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool)), _1366834), hAPP(c_COMBB(tc_prod(_1366834, _1366836), tc_fun(tc_fun(tc_prod(_1366834, _1366836), tc_HOL_Obool), tc_HOL_Obool), _1366836), c_member(tc_prod(_1366834, _1366836)))), c_Product__Type_OPair(_1366834, _1366836)))), _1366840)), _1366842), _1366844)))], (32548 ^ _776545) ^ [_1365130, _1365132, _1365134, _1365136, _1365138] : [-(_1365130 = c_Orderings_Obot__class_Obot(tc_fun(_1365132, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365132, tc_fun(_1365134, tc_HOL_Obool)), _1365130), hAPP(hAPP(c_COMBC(_1365132, tc_fun(_1365134, tc_HOL_Obool), tc_fun(_1365134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1365134, tc_HOL_Obool), tc_fun(tc_fun(_1365134, tc_HOL_Obool), tc_fun(_1365134, tc_HOL_Obool)), _1365132), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365134, tc_HOL_Obool))), _1365136)), _1365138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365134, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1365132, tc_fun(_1365134, tc_HOL_Obool)), _1365130), _1365136)), _1365138))], (28975 ^ _776545) ^ [_1295977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1295977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1295977)))], (38570 ^ _776545) ^ [_1516439, _1516441] : [c_Wellfounded_OwfP(_1516439, hAPP(hAPP(c_COMBC(_1516439, tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_fun(_1516439, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516439, tc_fun(tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_fun(_1516439, tc_HOL_Obool)), _1516439), c_COMBC(_1516439, tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516439, tc_prod(_1516439, _1516439)), tc_fun(_1516439, tc_fun(tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_HOL_Obool)), _1516439), hAPP(c_COMBB(tc_prod(_1516439, _1516439), tc_fun(tc_fun(tc_prod(_1516439, _1516439), tc_HOL_Obool), tc_HOL_Obool), _1516439), c_member(tc_prod(_1516439, _1516439)))), c_Product__Type_OPair(_1516439, _1516439)))), _1516441)), -(c_Wellfounded_Owf(_1516439, _1516441))], (14975 ^ _776545) ^ [_1046705, _1046707, _1046709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046705), _1046707)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046707), _1046709)), _1046705) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046707), _1046705)), _1046709))], (13518 ^ _776545) ^ [_1017146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1017146)), 13522 ^ _776545 : [(13523 ^ _776545) ^ [_1017226] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1017226), _1017146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017226), 13521 ^ [_1017146])))]]], (40478 ^ _776545) ^ [_1566348, _1566350, _1566352] : [c_Wellfounded_Owf(_1566348, _1566350), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566348, _1566348)), hAPP(hAPP(c_Product__Type_OPair(_1566348, _1566348), hAPP(_1566352, hAPP(c_Nat_OSuc, 40481 ^ [_1566348, _1566350, _1566352]))), hAPP(_1566352, 40481 ^ [_1566348, _1566350, _1566352]))), _1566350))], (13826 ^ _776545) ^ [_1023132, _1023134, _1023136] : [class_Groups_Ogroup__add(_1023132), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023132), _1023134), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023132), hAPP(c_Groups_Ouminus__class_Ouminus(_1023132), _1023134)), _1023136)) = _1023136)], (51997 ^ _776545) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (5084 ^ _776545) ^ [_854080, _854082, _854084, _854086, _854088, _854090] : [-(c_Set_Ovimage(_854090, _854086, _854082) = c_Set_Ovimage(_854088, _854084, _854080)), _854090 = _854088, _854086 = _854084, _854082 = _854080], (50071 ^ _776545) ^ [_1788120, _1788122, _1788124, _1788126, _1788128, _1788130] : [c_Fun_Oinj__on(_1788120, _1788122, _1788124, _1788126), hBOOL(hAPP(hAPP(c_member(_1788120), _1788128), _1788126)), hAPP(_1788124, _1788128) = _1788130, -(hAPP(c_Hilbert__Choice_Oinv__into(_1788120, _1788122, _1788126, _1788124), _1788130) = _1788128)], (28571 ^ _776545) ^ [_1289191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1289191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1289191)))], (39818 ^ _776545) ^ [_1551126, _1551128, _1551130, _1551132, _1551134, _1551136, _1551138, _1551140, _1551142, _1551144] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1551126, _1551128), tc_prod(_1551130, _1551132), tc_prod(_1551134, _1551136), c_Product__Type_Omap__pair(_1551126, _1551130, _1551128, _1551132, _1551138, _1551140)), c_Product__Type_Omap__pair(_1551134, _1551126, _1551136, _1551128, _1551142, _1551144)) = c_Product__Type_Omap__pair(_1551134, _1551130, _1551136, _1551132, hAPP(c_Fun_Ocomp(_1551126, _1551130, _1551134, _1551138), _1551142), hAPP(c_Fun_Ocomp(_1551128, _1551132, _1551136, _1551140), _1551144)))], (37987 ^ _776545) ^ [_1502263, _1502265, _1502267, _1502269] : [hBOOL(hAPP(hAPP(c_member(_1502263), _1502265), c_Wellfounded_Oacc(_1502263, _1502267))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502263, _1502263)), hAPP(hAPP(c_Product__Type_OPair(_1502263, _1502263), _1502269), _1502265)), _1502267)), -(hBOOL(hAPP(hAPP(c_member(_1502263), _1502269), c_Wellfounded_Oacc(_1502263, _1502267))))], (15978 ^ _776545) ^ [_1065672, _1065674] : [15979 ^ _776545 : [(15982 ^ _776545) ^ [] : [_1065672 = _1065674], (15980 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065672), _1065674))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065672), hAPP(c_Nat_OSuc, _1065674))))], (16014 ^ _776545) ^ [_1066278, _1066280] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066278), _1066280))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066278), hAPP(c_Nat_OSuc, _1066280))), -(_1066280 = _1066278)], (15396 ^ _776545) ^ [_1054613, _1054615, _1054617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054613), _1054615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1054613, tc_HOL_Obool)), _1054617), _1054615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054613), _1054617)), hAPP(c_Finite__Set_Ocard(_1054613), _1054615))))], (10939 ^ _776545) ^ [_965479, _965481] : [_965479 = c_Orderings_Obot__class_Obot(tc_fun(_965481, tc_HOL_Obool)), 10940 ^ _776545 : [(10941 ^ _776545) ^ [_965548, _965550] : [_965479 = hAPP(hAPP(c_Set_Oinsert(_965481), _965550), _965548), -(hBOOL(hAPP(hAPP(c_member(_965481), _965550), _965548)))]]], (1334 ^ _776545) ^ [_796084, _796086] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796084)), _796086 = _796084, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796086)], (35022 ^ _776545) ^ [_1430119, _1430121, _1430123, _1430125] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1430119, _1430121)), c_Nitpick_Opair__box_OPairBox(_1430119, _1430121, _1430123, _1430125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50317 ^ _776545) ^ [_1793787, _1793789, _1793791, _1793793, _1793795, _1793797] : [c_Fun_Obij__betw(_1793787, _1793789, _1793791, c_Orderings_Otop__class_Otop(tc_fun(_1793787, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793789, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793787, _1793789, _1793791), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793793, tc_fun(_1793787, tc_HOL_Obool)), _1793795), _1793797)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793793, tc_fun(_1793789, tc_HOL_Obool)), _1793795), hAPP(hAPP(c_COMBB(tc_fun(_1793787, tc_HOL_Obool), tc_fun(_1793789, tc_HOL_Obool), _1793793), c_Set_Oimage(_1793787, _1793789, _1793791)), _1793797)))], (36639 ^ _776545) ^ [_1471170, _1471172, _1471174] : [_1471172 = c_Orderings_Obot__class_Obot(tc_fun(_1471170, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471170), _1471172), _1471174) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1471170, tc_HOL_Obool), tc_HOL_Obool)))], (15196 ^ _776545) ^ [_1050728, _1050730] : [class_Rings_Olinordered__semidom(_1050728), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1050728), _1050730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050728), _1050730), c_Groups_Oone__class_Oone(_1050728)))))], (10024 ^ _776545) ^ [_948096, _948098, _948100, _948102] : [class_Orderings_Oorder(_948096), 10027 ^ _776545 : [(10036 ^ _776545) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_948096, _948098, _948100) = hAPP(hAPP(c_Set_Oinsert(_948096), _948102), c_Orderings_Obot__class_Obot(tc_fun(_948096, tc_HOL_Obool)))), _948098 = _948100, _948100 = _948102], (10028 ^ _776545) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_948096, _948098, _948100) = hAPP(hAPP(c_Set_Oinsert(_948096), _948102), c_Orderings_Obot__class_Obot(tc_fun(_948096, tc_HOL_Obool))), 10031 ^ _776545 : [(10034 ^ _776545) ^ [] : [-(_948100 = _948102)], (10032 ^ _776545) ^ [] : [-(_948098 = _948100)]]]]], (45834 ^ _776545) ^ [_1696026, _1696028, _1696030, _1696032] : [-(c_List_Oremdups(_1696026, hAPP(hAPP(c_List_Omap(_1696028, _1696026), _1696030), c_List_Oremdups(_1696028, _1696032))) = c_List_Oremdups(_1696026, hAPP(hAPP(c_List_Omap(_1696028, _1696026), _1696030), _1696032)))], (43316 ^ _776545) ^ [_1639761, _1639763, _1639765] : [class_Orderings_Olinorder(_1639761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1639761), _1639763)), -(c_List_Olinorder__class_Osorted__list__of__set(_1639761, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639761, tc_HOL_Obool)), _1639763), hAPP(hAPP(c_Set_Oinsert(_1639761), _1639765), c_Orderings_Obot__class_Obot(tc_fun(_1639761, tc_HOL_Obool))))) = c_List_Oremove1(_1639761, _1639765, c_List_Olinorder__class_Osorted__list__of__set(_1639761, _1639763)))], (1394 ^ _776545) ^ [_796834, _796836] : [-(class_Lattices_Osemilattice__inf(_796834)), _796836 = _796834, class_Lattices_Osemilattice__inf(_796836)], (17997 ^ _776545) ^ [_1100176, _1100178] : [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), _1100176), _1100178))), 18000 ^ _776545 : [(18003 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100178)))], (18001 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100176)))]]], (17647 ^ _776545) ^ [_1094315, _1094317] : [class_Groups_Oordered__ab__group__add(_1094315), 17650 ^ _776545 : [(17657 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094315), _1094317), c_Groups_Ozero__class_Ozero(_1094315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094315), c_Groups_Ozero__class_Ozero(_1094315)), hAPP(c_Groups_Ouminus__class_Ouminus(_1094315), _1094317))))], (17651 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094315), c_Groups_Ozero__class_Ozero(_1094315)), hAPP(c_Groups_Ouminus__class_Ouminus(_1094315), _1094317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094315), _1094317), c_Groups_Ozero__class_Ozero(_1094315))))]]], (3568 ^ _776545) ^ [_829908, _829910] : [_829910 = _829908, -(c_SetInterval_Oord__class_OatMost(_829910) = c_SetInterval_Oord__class_OatMost(_829908))], (28149 ^ _776545) ^ [_1282003] : [class_Rings_Osemiring__1(_1282003), -(hBOOL(hAPP(hAPP(c_member(_1282003), c_Groups_Ozero__class_Ozero(_1282003)), c_Nat_Osemiring__1__class_ONats(_1282003))))], (42809 ^ _776545) ^ [_1629437, _1629439, _1629441, _1629443] : [hBOOL(hAPP(c_List_Odistinct(_1629437), _1629439)), -(hBOOL(hAPP(hAPP(c_member(_1629437), _1629441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629437, tc_HOL_Obool)), hAPP(c_List_Oset(_1629437), _1629439)), hAPP(hAPP(c_Set_Oinsert(_1629437), hAPP(hAPP(c_List_Onth(_1629437), _1629439), _1629443)), c_Orderings_Obot__class_Obot(tc_fun(_1629437, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1629437), hAPP(hAPP(c_List_Olist__update(_1629437, _1629439), _1629443), _1629441))))], (34025 ^ _776545) ^ [_1408245, _1408247] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1408245)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1408247)), hAPP(c_Int_Onat, _1408245)) = hAPP(c_Int_Onat, _1408247))], (17015 ^ _776545) ^ [_1082814, _1082816, _1082818, _1082820] : [class_Rings_Oordered__ring(_1082814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082814), _1082816), _1082818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082814), _1082820), c_Groups_Ozero__class_Ozero(_1082814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082814), _1082818), _1082820)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082814), _1082816), _1082820))))], (39111 ^ _776545) ^ [_1530486, _1530488, _1530490, _1530492, _1530494, _1530496, _1530498, _1530500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530486, _1530488), tc_HOL_Obool)), _1530490), hAPP(hAPP(c_Product__Type_OSigma(_1530486, _1530488), _1530492), hAPP(c_COMBK(tc_fun(_1530488, tc_HOL_Obool), _1530486), _1530494)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530488, _1530496), tc_HOL_Obool)), _1530498), hAPP(hAPP(c_Product__Type_OSigma(_1530488, _1530496), _1530494), hAPP(c_COMBK(tc_fun(_1530496, tc_HOL_Obool), _1530488), _1530500)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530486, _1530496), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530486, _1530488, _1530496), _1530490), _1530498)), hAPP(hAPP(c_Product__Type_OSigma(_1530486, _1530496), _1530492), hAPP(c_COMBK(tc_fun(_1530496, tc_HOL_Obool), _1530486), _1530500)))))], (48025 ^ _776545) ^ [_1743837, _1743839, _1743841] : [class_Orderings_Olinorder(_1743837), 48031 ^ _776545 : [(48034 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743837), _1743841), 48030 ^ [_1743837, _1743839, _1743841]))], (48032 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743837), 48030 ^ [_1743837, _1743839, _1743841]), hAPP(c_List_Oset(_1743837), _1743839))))]], c_List_Olinorder__class_Osorted(_1743837, _1743839), -(c_List_Olinorder__class_Osorted(_1743837, hAPP(hAPP(c_List_Olist_OCons(_1743837), _1743841), _1743839)))], (1904 ^ _776545) ^ [_803209, _803211] : [-(class_HOL_Oequal(_803209)), _803211 = _803209, class_HOL_Oequal(_803211)], (5556 ^ _776545) ^ [_861404, _861406, _861408, _861410] : [-(tc_sum(_861410, _861406) = tc_sum(_861408, _861404)), _861410 = _861408, _861406 = _861404], (32450 ^ _776545) ^ [_1360699, _1360701, _1360703, _1360705, _1360707] : [_1360699 = c_Orderings_Obot__class_Obot(tc_fun(_1360701, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360701, tc_fun(_1360703, tc_HOL_Obool)), _1360699), hAPP(hAPP(c_COMBC(_1360701, tc_fun(_1360703, tc_HOL_Obool), tc_fun(_1360703, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1360703, tc_HOL_Obool), tc_fun(tc_fun(_1360703, tc_HOL_Obool), tc_fun(_1360703, tc_HOL_Obool)), _1360701), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360703, tc_HOL_Obool))), _1360705)), _1360707)) = c_Orderings_Obot__class_Obot(tc_fun(_1360703, tc_HOL_Obool)))], (5634 ^ _776545) ^ [_862561, _862563, _862565, _862567, _862569, _862571] : [-(c_COMBC(_862571, _862567, _862563) = c_COMBC(_862569, _862565, _862561)), _862571 = _862569, _862567 = _862565, _862563 = _862561], (5224 ^ _776545) ^ [_856260, _856262, _856264, _856266] : [-(c_Product__Type_OPair(_856266, _856262) = c_Product__Type_OPair(_856264, _856260)), _856266 = _856264, _856262 = _856260], (14174 ^ _776545) ^ [_1031344, _1031346, _1031348, _1031350, _1031352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031344), _1031346)), 14177 ^ _776545 : [(14184 ^ _776545) ^ [] : [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), _1031346), _1031344)), _1031348)), _1031350) = _1031352, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031346), _1031348)), _1031350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031344), _1031348)), _1031352))], (14178 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031346), _1031348)), _1031350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031344), _1031348)), _1031352), -(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), _1031346), _1031344)), _1031348)), _1031350) = _1031352)]]], (33372 ^ _776545) ^ [_1389375, _1389377, _1389379, _1389381, _1389383, _1389385] : [c_Nitpick_Opair__box_OPairBox(_1389375, _1389377, _1389379, _1389381) = c_Nitpick_Opair__box_OPairBox(_1389375, _1389377, _1389383, _1389385), 33375 ^ _776545 : [(33378 ^ _776545) ^ [] : [-(_1389381 = _1389385)], (33376 ^ _776545) ^ [] : [-(_1389379 = _1389383)]]], (47442 ^ _776545) ^ [_1730451, _1730453, _1730455, _1730457, _1730459] : [-(c_List_OdropWhile(_1730451, _1730453, _1730455) = hAPP(hAPP(c_List_Olist_OCons(_1730451), _1730457), _1730459)), _1730455 = hAPP(hAPP(c_List_Oappend(_1730451), c_List_OtakeWhile(_1730451, _1730453, _1730455)), hAPP(hAPP(c_List_Olist_OCons(_1730451), _1730457), _1730459)), -(hBOOL(hAPP(_1730453, _1730457)))], (37949 ^ _776545) ^ [_1501238, _1501240, _1501242, _1501244, _1501246, _1501248, _1501250] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1501238, _1501240, _1501242), hAPP(hAPP(c_Relation_Orel__comp(_1501238, _1501244, _1501240), _1501246), _1501248)), _1501250) = hAPP(hAPP(c_Relation_Orel__comp(_1501238, _1501244, _1501242), _1501246), hAPP(hAPP(c_Relation_Orel__comp(_1501244, _1501240, _1501242), _1501248), _1501250)))], (43110 ^ _776545) ^ [_1635474] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635474)), c_List_Olist_ONil(_1635474)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45158 ^ _776545) ^ [_1680900, _1680902, _1680904] : [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, _1680900), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1680900)), _1680902)))), -(hBOOL(hAPP(hAPP(c_member(_1680900), hAPP(c_Product__Type_Ofst(_1680900, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1680900, _1680902), _1680904))), hAPP(c_List_Oset(_1680900), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1680900), _1680900), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1680900)), _1680902)))))], (22131 ^ _776545) ^ [_1177845, _1177847, _1177849, _1177851] : [class_Rings_Olinordered__semidom(_1177845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177847), _1177849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177845), c_Groups_Ozero__class_Ozero(_1177845)), _1177851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177845), _1177851), c_Groups_Oone__class_Oone(_1177845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177845), hAPP(hAPP(c_Power_Opower__class_Opower(_1177845), _1177851), _1177849)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177845), _1177851), _1177847))))], (7970 ^ _776545) ^ [_911407, _911409, _911411, _911413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911407, tc_HOL_Obool)), _911409), _911411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911407, tc_HOL_Obool)), _911409), _911413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911407, tc_HOL_Obool)), _911409), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_911407, tc_HOL_Obool)), _911411), _911413))))], (19891 ^ _776545) ^ [_1135409, _1135411, _1135413, _1135415] : [class_Fields_Olinordered__field__inverse__zero(_1135409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135409), _1135411), _1135413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135409), _1135415), c_Groups_Ozero__class_Ozero(_1135409))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135409), c_Groups_Ozero__class_Ozero(_1135409)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135409), _1135411), _1135413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135409), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135409), _1135415), _1135411)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135409), _1135415), _1135413))))], (52117 ^ _776545) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (40389 ^ _776545) ^ [_1563989, _1563991, _1563993] : [40390 ^ _776545 : [(40391 ^ _776545) ^ [_1564043] : [hBOOL(hAPP(_1563989, _1564043))]], _1563991 = c_Hilbert__Choice_OEps(_1563993, _1563989), -(hBOOL(hAPP(_1563989, _1563991)))], (28541 ^ _776545) ^ [_1288696, _1288698] : [class_Int_Onumber__ring(_1288696), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288696), _1288698), hAPP(c_Int_Onumber__class_Onumber__of(_1288696), c_Int_OBit1(c_Int_OPls))) = _1288698)], (47301 ^ _776545) ^ [_1727430, _1727432, _1727434, _1727436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727430), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727432)), c_List_OtakeWhile(_1727432, _1727434, _1727436)))), -(hAPP(hAPP(c_List_Onth(_1727432), c_List_OtakeWhile(_1727432, _1727434, _1727436)), _1727430) = hAPP(hAPP(c_List_Onth(_1727432), _1727436), _1727430))], (51789 ^ _776545) ^ [_1823597, _1823599] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823597), _1823599)), 51792 ^ _776545 : [(51799 ^ _776545) ^ [] : [_1823599 = _1823597, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823599), _1823597)))], (51793 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823599), _1823597)), -(_1823599 = _1823597)]]], (46069 ^ _776545) ^ [_1701878, _1701880, _1701882] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701878, tc_HOL_Obool)), hAPP(c_List_Oset(_1701878), hAPP(c_List_Ofilter(_1701878, _1701880), _1701882))), hAPP(c_List_Oset(_1701878), _1701882))))], (52387 ^ _776545) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (41280 ^ _776545) ^ [_1586479, _1586481, _1586483] : [c_Relation_Ototal__on(_1586479, _1586481, _1586483), -(c_Relation_Ototal__on(_1586479, _1586481, hAPP(c_Relation_Oconverse(_1586479, _1586479), _1586483)))], (7619 ^ _776545) ^ [_902757, _902759, _902761, _902763] : [7633 ^ _776545 : [(7636 ^ _776545) ^ [] : [-(hBOOL(hAPP(_902763, 7632 ^ [_902757, _902759, _902761, _902763])))], (7634 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902757), 7632 ^ [_902757, _902759, _902761, _902763]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902757, tc_HOL_Obool)), _902759), _902761))))]], 7620 ^ _776545 : [(7627 ^ _776545) ^ [_902966] : [hBOOL(hAPP(hAPP(c_member(_902757), _902966), _902761)), hBOOL(hAPP(_902763, _902966))], (7621 ^ _776545) ^ [_902870] : [hBOOL(hAPP(hAPP(c_member(_902757), _902870), _902759)), hBOOL(hAPP(_902763, _902870))]]], (36025 ^ _776545) ^ [_1453817, _1453819, _1453821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1453817, tc_HOL_Obool), tc_fun(_1453817, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1453817, tc_HOL_Obool), tc_fun(_1453817, tc_HOL_Obool)), _1453819), _1453821)), c_Wellfounded_Ofinite__psubset(_1453817))), 36028 ^ _776545 : [(36031 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1453817), _1453821)))], (36029 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1453817, tc_HOL_Obool)), _1453819), _1453821)))]]], (40054 ^ _776545) ^ [_1556485, _1556487, _1556489, _1556491, _1556493, _1556495, _1556497, _1556499] : [c_Finite__Set_Ofolding__image(_1556485, _1556487, _1556489, _1556491, _1556493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556487), _1556495)), c_Fun_Oinj__on(_1556487, _1556487, _1556497, _1556495), -(hAPP(hAPP(_1556493, _1556499), hAPP(c_Set_Oimage(_1556487, _1556487, _1556497), _1556495)) = hAPP(hAPP(_1556493, hAPP(c_Fun_Ocomp(_1556487, _1556485, _1556487, _1556499), _1556497)), _1556495))], (20531 ^ _776545) ^ [_1147086, _1147088, _1147090, _1147092] : [class_Fields_Olinordered__field(_1147086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147086), _1147088), c_Groups_Ozero__class_Ozero(_1147086))), 20538 ^ _776545 : [(20545 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147086), _1147092), _1147088)), _1147090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147086), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147086), _1147090), _1147088)), _1147092)))], (20539 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147086), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147086), _1147090), _1147088)), _1147092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147086), _1147092), _1147088)), _1147090)))]]], (5550 ^ _776545) ^ [_861319, _861321] : [_861321 = _861319, -(tc_List_Olist(_861321) = tc_List_Olist(_861319))], (35150 ^ _776545) ^ [_1432610, _1432612] : [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), _1432610), _1432612))), 35153 ^ _776545 : [(35162 ^ _776545) ^ [] : [-(c_Divides_OposDivAlg(_1432610, _1432612) = hAPP(c_Divides_Oadjust(_1432612), c_Divides_OposDivAlg(_1432610, 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)))), _1432612)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432610), _1432612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1432612), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35154 ^ _776545) ^ [] : [35155 ^ _776545 : [(35158 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1432612), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35156 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432610), _1432612))]], -(c_Divides_OposDivAlg(_1432610, _1432612) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1432610))]]], (29197 ^ _776545) ^ [_1299836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299836), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1299836)), c_Int_OMin)))], (27190 ^ _776545) ^ [_1265852, _1265854] : [c_Nat__Transfer_Onat__set(_1265852), c_Nat__Transfer_Onat__set(_1265854), 27197 ^ _776545 : [(27204 ^ _776545) ^ [] : [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), _1265852)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265852), _1265854)))], (27198 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265852), _1265854)), -(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), _1265852)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265854))))]]], (11964 ^ _776545) ^ [_986577, _986579, _986581, _986583] : [c_Finite__Set_Ofolding__one__idem(_986577, _986579, _986581), -(hAPP(hAPP(_986579, _986583), _986583) = _986583)], (25873 ^ _776545) ^ [_1244508, _1244510, _1244512] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244508), _1244510)), _1244512) = 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), _1244508), _1244512)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244510), _1244512))), 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, _1244508, _1244512)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244510, _1244512))), _1244512)))], (18005 ^ _776545) ^ [_1100299, _1100301] : [-(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), _1100299), _1100301)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1100301))], (34600 ^ _776545) ^ [_1421032, _1421034, _1421036] : [-(c_Nat_Onat_Onat__case(_1421032, _1421034, _1421036, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1421034)], (14410 ^ _776545) ^ [_1036695, _1036697, _1036699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036695), _1036697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036699), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036697), _1036699)), _1036695))))], (28885 ^ _776545) ^ [_1294371] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1294371)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1294371)))], (4246 ^ _776545) ^ [_840879, _840881] : [_840881 = _840879, -(c_List_Odrop(_840881) = c_List_Odrop(_840879))], (46988 ^ _776545) ^ [_1720994, _1720996, _1720998] : [_1720998 = hAPP(hAPP(c_List_Olist_OCons(_1720994), _1720996), c_List_Olist_ONil(_1720994)), -(hAPP(hAPP(c_List_Olist_OCons(_1720994), _1720996), c_List_Olist_ONil(_1720994)) = hAPP(c_List_Orev(_1720994), _1720998))], (39794 ^ _776545) ^ [_1550290, _1550292] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1550290, tc_HOL_Obool), _1550292) = hAPP(c_Set_OCollect(_1550290), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550290, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1550290), c_HOL_OAll(tc_fun(_1550290, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550290, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1550290, tc_HOL_Obool), tc_HOL_Obool), _1550290), hAPP(c_COMBS(tc_fun(_1550290, 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(_1550290, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1550290, tc_HOL_Obool), tc_fun(tc_fun(_1550290, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1550290, tc_HOL_Obool))), _1550292)))), c_member(_1550290)))))], (5833 ^ _776545) ^ [_869039, _869041] : [-(_869039 = hAPP(c_Hoare__Mirabelle_OAbs__triple(_869041), 5831 ^ [_869039, _869041]))], (86 ^ _776545) ^ [_777888, _777890, _777892, _777894, _777896, _777898] : [-(c_Big__Operators_Osemilattice__big(_777896, _777892, _777888)), c_Big__Operators_Osemilattice__big(_777898, _777894, _777890), _777898 = _777896, _777894 = _777892, _777890 = _777888], (5456 ^ _776545) ^ [_859912, _859914, _859916, _859918, _859920, _859922] : [-(c_SetInterval_Oord_OatLeast(_859922, _859918, _859914) = c_SetInterval_Oord_OatLeast(_859920, _859916, _859912)), _859922 = _859920, _859918 = _859916, _859914 = _859912], (46795 ^ _776545) ^ [_1716895, _1716897, _1716899] : [class_Orderings_Olinorder(_1716895), 46798 ^ _776545 : [(46811 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716895, hAPP(hAPP(c_List_Olist_OCons(_1716895), _1716897), _1716899))), 46815 ^ _776545 : [(46818 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716895), _1716897), 46814 ^ [_1716895, _1716897, _1716899]))], (46816 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1716895), 46814 ^ [_1716895, _1716897, _1716899]), hAPP(c_List_Oset(_1716895), _1716899))))]], c_List_Olinorder__class_Osorted(_1716895, _1716899)], (46799 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1716895, hAPP(hAPP(c_List_Olist_OCons(_1716895), _1716897), _1716899)), 46802 ^ _776545 : [(46803 ^ _776545) ^ [_1717063] : [hBOOL(hAPP(hAPP(c_member(_1716895), _1717063), hAPP(c_List_Oset(_1716895), _1716899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716895), _1716897), _1717063)))], (46809 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716895, _1716899))]]]]], (38588 ^ _776545) ^ [_1517435, _1517437, _1517439, _1517441] : [hBOOL(hAPP(hAPP(c_member(_1517437), _1517441), hAPP(c_Relation_ORange(_1517435, _1517437), _1517439))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1517435, _1517437, hAPP(hAPP(c_COMBC(_1517435, tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_fun(_1517437, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517437, tc_fun(tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_fun(_1517437, tc_HOL_Obool)), _1517435), c_COMBC(_1517437, tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517437, tc_prod(_1517435, _1517437)), tc_fun(_1517437, tc_fun(tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_HOL_Obool)), _1517435), hAPP(c_COMBB(tc_prod(_1517435, _1517437), tc_fun(tc_fun(tc_prod(_1517435, _1517437), tc_HOL_Obool), tc_HOL_Obool), _1517437), c_member(tc_prod(_1517435, _1517437)))), c_Product__Type_OPair(_1517435, _1517437)))), _1517439)), _1517441)))], (11872 ^ _776545) ^ [_984939, _984941, _984943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_984939), _984941)), hBOOL(hAPP(_984943, _984941)), 11883 ^ _776545 : [(11886 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_984939), 11881 ^ [_984939, _984941, _984943]), 11882 ^ [_984939, _984941, _984943])))], (11888 ^ _776545) ^ [] : [-(hBOOL(hAPP(_984943, 11882 ^ [_984939, _984941, _984943])))], (11890 ^ _776545) ^ [] : [hBOOL(hAPP(_984943, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984939, tc_HOL_Obool)), 11882 ^ [_984939, _984941, _984943]), hAPP(hAPP(c_Set_Oinsert(_984939), 11881 ^ [_984939, _984941, _984943]), c_Orderings_Obot__class_Obot(tc_fun(_984939, tc_HOL_Obool))))))], (11884 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_984939), 11882 ^ [_984939, _984941, _984943])))]], -(hBOOL(hAPP(_984943, c_Orderings_Obot__class_Obot(tc_fun(_984939, tc_HOL_Obool)))))], (43086 ^ _776545) ^ [_1635063, _1635065] : [-(c_List_Olistrelp(_1635063, _1635065, c_List_Olist_ONil(_1635063), c_List_Olist_ONil(_1635063)))], (16458 ^ _776545) ^ [_1073014, _1073016] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1073014), _1073016) = _1073014, -(_1073016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8139 ^ _776545) ^ [_915254, _915256, _915258] : [hBOOL(hAPP(hAPP(c_member(_915254), _915256), _915258)), -(hAPP(hAPP(c_Set_Oinsert(_915254), _915256), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915254, tc_HOL_Obool)), _915258), hAPP(hAPP(c_Set_Oinsert(_915254), _915256), c_Orderings_Obot__class_Obot(tc_fun(_915254, tc_HOL_Obool))))) = _915258)], (49486 ^ _776545) ^ [_1776740, _1776742, _1776744, _1776746] : [c_Predicate_Osymp(_1776740, _1776742), hBOOL(hAPP(hAPP(_1776742, _1776744), _1776746)), -(hBOOL(hAPP(hAPP(_1776742, _1776746), _1776744)))], (29225 ^ _776545) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (4178 ^ _776545) ^ [_839863, _839865] : [_839865 = _839863, -(c_New__Random__Sequence_Opos__single(_839865) = c_New__Random__Sequence_Opos__single(_839863))], (36914 ^ _776545) ^ [_1477348, _1477350, _1477352, _1477354, _1477356] : [c_Equiv__Relations_Oequiv(_1477348, _1477350, _1477352), hBOOL(hAPP(hAPP(c_member(_1477348), _1477354), _1477350)), hBOOL(hAPP(hAPP(c_member(_1477348), _1477356), _1477350)), 36925 ^ _776545 : [(36932 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477348, _1477348)), hAPP(hAPP(c_Product__Type_OPair(_1477348, _1477348), _1477354), _1477356)), _1477352)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477348), hAPP(hAPP(c_Set_Oinsert(_1477348), _1477354), c_Orderings_Obot__class_Obot(tc_fun(_1477348, tc_HOL_Obool)))), _1477352) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477348), hAPP(hAPP(c_Set_Oinsert(_1477348), _1477356), c_Orderings_Obot__class_Obot(tc_fun(_1477348, tc_HOL_Obool)))), _1477352))], (36926 ^ _776545) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477348), hAPP(hAPP(c_Set_Oinsert(_1477348), _1477354), c_Orderings_Obot__class_Obot(tc_fun(_1477348, tc_HOL_Obool)))), _1477352) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1477348), hAPP(hAPP(c_Set_Oinsert(_1477348), _1477356), c_Orderings_Obot__class_Obot(tc_fun(_1477348, tc_HOL_Obool)))), _1477352), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477348, _1477348)), hAPP(hAPP(c_Product__Type_OPair(_1477348, _1477348), _1477354), _1477356)), _1477352)))]]], (36986 ^ _776545) ^ [_1479449, _1479451, _1479453, _1479455, _1479457] : [c_Equiv__Relations_Oequivp(_1479449, _1479451), hBOOL(hAPP(hAPP(_1479451, _1479453), _1479455)), hBOOL(hAPP(hAPP(_1479451, _1479455), _1479457)), -(hBOOL(hAPP(hAPP(_1479451, _1479453), _1479457)))], (11592 ^ _776545) ^ [_979279, _979281] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_979279), _979281)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_979279, tc_HOL_Obool)), hAPP(c_Set_OPow(_979279), _979281))))], (51977 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (1574 ^ _776545) ^ [_799084, _799086] : [-(class_Rings_Oordered__cancel__semiring(_799084)), _799086 = _799084, class_Rings_Oordered__cancel__semiring(_799086)], (49169 ^ _776545) ^ [_1768793, _1768795] : [c_Relation_Otrans(_1768793, _1768795), 49172 ^ _776545 : [(49173 ^ _776545) ^ [_1768929, _1768931] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768793, _1768793)), hAPP(hAPP(c_Product__Type_OPair(_1768793, _1768793), _1768931), _1768929)), _1768795)), 49176 ^ _776545 : [(49177 ^ _776545) ^ [_1769072] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768793, _1768793)), hAPP(hAPP(c_Product__Type_OPair(_1768793, _1768793), _1768929), _1769072)), _1768795)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768793, _1768793)), hAPP(hAPP(c_Product__Type_OPair(_1768793, _1768793), _1768931), _1769072)), _1768795)))]]]]], (44896 ^ _776545) ^ [_1675406, _1675408, _1675410, _1675412, _1675414] : [hAPP(hAPP(c_List_Omap(_1675406, _1675408), _1675410), _1675412) = hAPP(hAPP(c_List_Omap(_1675406, _1675408), _1675410), _1675414), c_Fun_Oinj__on(_1675406, _1675408, _1675410, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1675406, tc_HOL_Obool)), hAPP(c_List_Oset(_1675406), _1675412)), hAPP(c_List_Oset(_1675406), _1675414))), -(_1675412 = _1675414)], (29711 ^ _776545) ^ [_1309298] : [_1309298 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1309298) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5248 ^ _776545) ^ [_856630, _856632, _856634, _856636] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_856636, _856632) = c_SetInterval_Oord__class_OatLeastLessThan(_856634, _856630)), _856636 = _856634, _856632 = _856630], (11141 ^ _776545) ^ [_969371, _969373, _969375, _969377] : [hAPP(c_Set_Oimage(_969371, _969373, _969375), _969377) = c_Orderings_Obot__class_Obot(tc_fun(_969373, tc_HOL_Obool)), -(_969377 = c_Orderings_Obot__class_Obot(tc_fun(_969371, tc_HOL_Obool)))], (43240 ^ _776545) ^ [_1637966] : [-(c_List_Olists(_1637966, c_Orderings_Obot__class_Obot(tc_fun(_1637966, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1637966)), c_List_Olist_ONil(_1637966)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1637966), tc_HOL_Obool))))], (10130 ^ _776545) ^ [_950027, _950029, _950031] : [class_Orderings_Olinorder(_950027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950027), _950029), _950031)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950027, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_950027), _950029)), c_SetInterval_Oord__class_OgreaterThanLessThan(_950027, _950029, _950031)) = hAPP(c_SetInterval_Oord__class_OlessThan(_950027), _950031))], (33577 ^ _776545) ^ [_1394625] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1394625, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1394625), hAPP(c_COMBK(tc_HOL_Obool, _1394625), c_fTrue)))], (11054 ^ _776545) ^ [_967686] : [class_Groups_Oab__semigroup__mult(_967686), -(c_Finite__Set_Ofun__left__comm(_967686, _967686, c_Groups_Otimes__class_Otimes(_967686)))], (43868 ^ _776545) ^ [_1653011, _1653013, _1653015] : [-(hAPP(hAPP(c_List_Odrop(_1653011), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1653011), _1653013), _1653015)) = _1653015)], (33425 ^ _776545) ^ [_1390745, _1390747, _1390749, _1390751, _1390753, _1390755] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390745, tc_fun(_1390747, tc_HOL_Obool)), _1390749), hAPP(hAPP(c_COMBC(_1390745, tc_fun(_1390751, tc_fun(_1390747, tc_HOL_Obool)), tc_fun(_1390747, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390751, tc_HOL_Obool), tc_fun(tc_fun(_1390751, tc_fun(_1390747, tc_HOL_Obool)), tc_fun(_1390747, tc_HOL_Obool)), _1390745), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390751, tc_fun(_1390747, tc_HOL_Obool))), _1390753)), _1390755)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1390751, tc_fun(_1390747, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390745, tc_fun(_1390751, tc_HOL_Obool)), _1390749), _1390753)), _1390755))], (37997 ^ _776545) ^ [_1502496, _1502498, _1502500] : [hBOOL(hAPP(hAPP(c_member(_1502496), _1502498), c_Wellfounded_Oacc(_1502496, _1502500))), 38000 ^ _776545 : [(38001 ^ _776545) ^ [_1502610] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502496, _1502496)), hAPP(hAPP(c_Product__Type_OPair(_1502496, _1502496), _1502610), _1502498)), _1502500)), -(hBOOL(hAPP(hAPP(c_member(_1502496), _1502610), c_Wellfounded_Oacc(_1502496, _1502500))))]]], (35622 ^ _776545) ^ [_1441380, _1441382, _1441384, _1441386] : [-(hAPP(c_Product__Type_Ofst(_1441380, _1441382), hAPP(hAPP(c_Product__Type_OPair(_1441380, _1441382), _1441384), _1441386)) = _1441384)], (35923 ^ _776545) ^ [_1449377, _1449379] : [-(hAPP(c_Set_OPow(_1449377), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449377, tc_HOL_Obool)), _1449379)) = hAPP(c_Set_OCollect(tc_fun(_1449377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449377, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1449377, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1449377, tc_HOL_Obool), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1449377, tc_HOL_Obool)), c_COMBS(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1449377, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1449377, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1449377, tc_HOL_Obool), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_fun(_1449377, tc_HOL_Obool)), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_fun(_1449377, tc_HOL_Obool)), tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1449377, tc_HOL_Obool)), c_COMBB(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449377, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1449377, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1449377, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1449377, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1449377, tc_HOL_Obool)), _1449379)), c_Set_OPow(_1449377))))))], (7100 ^ _776545) ^ [_892188, _892190, _892192, _892194] : [class_Orderings_Oord(_892188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892188), hAPP(_892190, 7105 ^ [_892188, _892190, _892192, _892194])), hAPP(_892192, 7105 ^ [_892188, _892190, _892192, _892194]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892194, _892188)), _892190), _892192)))], (20599 ^ _776545) ^ [_1148386, _1148388, _1148390, _1148392] : [class_Fields_Olinordered__field(_1148386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), c_Groups_Ozero__class_Ozero(_1148386)), _1148388)), 20606 ^ _776545 : [(20613 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), _1148390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148386), _1148392), _1148388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148386), _1148390), _1148388)), _1148392)))], (20607 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148386), _1148390), _1148388)), _1148392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148386), _1148390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148386), _1148392), _1148388))))]]], (47676 ^ _776545) ^ [_1735800, _1735802, _1735804, _1735806, _1735808] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1735800, _1735800)), hAPP(hAPP(c_Product__Type_OPair(_1735800, _1735800), _1735802), _1735804)), c_List_Omeasures(_1735800, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1735800, tc_Nat_Onat)), _1735806), _1735808))))), 47677 ^ _776545 : [(47680 ^ _776545) ^ [] : [hAPP(_1735806, _1735802) = hAPP(_1735806, _1735804), hBOOL(hAPP(hAPP(c_member(tc_prod(_1735800, _1735800)), hAPP(hAPP(c_Product__Type_OPair(_1735800, _1735800), _1735802), _1735804)), c_List_Omeasures(_1735800, _1735808)))], (47678 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1735806, _1735802)), hAPP(_1735806, _1735804)))]]], (10683 ^ _776545) ^ [_960389] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960389, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_960389, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_960389, tc_HOL_Obool)))], (22263 ^ _776545) ^ [_1180307, _1180309] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180307), _1180309))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180307), _1180309)), -(_1180307 = _1180309)], (42628 ^ _776545) ^ [_1625232, _1625234] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1625232), _1625234) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1625232, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1625234), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33370 ^ _776545) ^ [_1389258, _1389260, _1389262, _1389264] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1389258, tc_HOL_Obool), tc_fun(_1389260, tc_HOL_Obool)), _1389262), hAPP(hAPP(c_COMBC(tc_fun(_1389258, tc_HOL_Obool), tc_fun(_1389258, tc_fun(_1389260, tc_HOL_Obool)), tc_fun(_1389260, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389258, tc_fun(_1389260, tc_HOL_Obool))), _1389264)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1389258, tc_fun(_1389260, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1389258, tc_HOL_Obool), _1389262)), _1389264))], (48440 ^ _776545) ^ [_1752224, _1752226, _1752228, _1752230, _1752232] : [-(hAPP(c_New__DSequence_Oneg__bind(_1752224, _1752226, _1752228, _1752230), _1752232) = c_Lazy__Sequence_Ohb__bind(_1752224, _1752226, hAPP(_1752228, _1752232), hAPP(hAPP(c_COMBC(_1752224, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1752226))), _1752230), _1752232)))], (37674 ^ _776545) ^ [_1493845, _1493847, _1493849, _1493851] : [c_Fun_Oinj__on(_1493845, _1493847, _1493849, c_Orderings_Otop__class_Otop(tc_fun(_1493845, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493847, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493845, _1493847, _1493849), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493845, tc_HOL_Obool)), _1493851))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493847, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1493845, _1493847, _1493849), _1493851)))))], (41757 ^ _776545) ^ [_1599700, _1599702, _1599704] : [hAPP(hAPP(c_List_Olist_OCons(_1599700), _1599702), _1599704) = _1599704], (25588 ^ _776545) ^ [_1239393, _1239395, _1239397] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1239393))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239393)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239395)), _1239397)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1239395)), _1239397))], (38338 ^ _776545) ^ [_1511154, _1511156, _1511158, _1511160] : [c_FunDef_Oreduction__pair(_1511154, _1511156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool)), _1511158), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool), tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool)), _1511156))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool)), _1511160), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool), tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool)), _1511156))), c_Wellfounded_Owf(_1511154, _1511160), -(c_Wellfounded_Owf(_1511154, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1511154, _1511154), tc_HOL_Obool)), _1511158), _1511160)))], (44767 ^ _776545) ^ [_1671586, _1671588, _1671590, _1671592, _1671594] : [hAPP(hAPP(c_List_Omap(_1671586, _1671588), _1671590), _1671592) = hAPP(hAPP(c_List_Omap(_1671586, _1671588), _1671590), _1671594), c_Fun_Oinj__on(_1671586, _1671588, _1671590, c_Orderings_Otop__class_Otop(tc_fun(_1671586, tc_HOL_Obool))), -(_1671592 = _1671594)], (6831 ^ _776545) ^ [_887192, _887194, _887196] : [class_Complete__Lattice_Ocomplete__lattice(_887192), 6837 ^ _776545 : [(6840 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887192), 6836 ^ [_887192, _887194, _887196]), _887196))], (6838 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887192), 6836 ^ [_887192, _887194, _887196]), _887194)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887192), c_Complete__Lattice_OSup__class_OSup(_887192, _887194)), _887196)))], (14654 ^ _776545) ^ [_1040832, _1040834, _1040836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040832), _1040834)), _1040836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040832), _1040836)))], (24214 ^ _776545) ^ [_1214507, _1214509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214507), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214509), _1214507)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214507), _1214509) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27575 ^ _776545) ^ [_1272598] : [class_Int_Onumber__ring(_1272598), -(hAPP(c_Int_Onumber__class_Onumber__of(_1272598), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1272598))], (52177 ^ _776545) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (10014 ^ _776545) ^ [_947931, _947933, _947935] : [class_Orderings_Oorder(_947931), _947933 = _947935, -(c_SetInterval_Oord__class_OatLeastAtMost(_947931, _947933, _947935) = hAPP(hAPP(c_Set_Oinsert(_947931), _947933), c_Orderings_Obot__class_Obot(tc_fun(_947931, tc_HOL_Obool))))], (1734 ^ _776545) ^ [_801084, _801086] : [-(class_Rings_Ozero__neq__one(_801084)), _801086 = _801084, class_Rings_Ozero__neq__one(_801086)], (49788 ^ _776545) ^ [_1782502, _1782504, _1782506] : [c_Equiv__Relations_Oequiv(_1782502, _1782504, _1782506), 49791 ^ _776545 : [(49796 ^ _776545) ^ [] : [-(c_Relation_Otrans(_1782502, _1782506))], (49794 ^ _776545) ^ [] : [-(c_Relation_Osym(_1782502, _1782506))], (49792 ^ _776545) ^ [] : [-(c_Relation_Orefl__on(_1782502, _1782504, _1782506))]]], (7822 ^ _776545) ^ [_908134, _908136] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908134, tc_HOL_Obool)), _908136), _908136) = c_Orderings_Obot__class_Obot(tc_fun(_908134, tc_HOL_Obool)))], (19549 ^ _776545) ^ [_1129678, _1129680] : [class_Rings_Odivision__ring__inverse__zero(_1129678), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129678), _1129680), c_Groups_Ozero__class_Ozero(_1129678)) = c_Groups_Ozero__class_Ozero(_1129678))], (27359 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (51875 ^ _776545) ^ [_1824859, _1824861] : [class_Lattices_Olattice(_1824859), -(class_Lattices_Osemilattice__sup(tc_fun(_1824861, _1824859)))], (13288 ^ _776545) ^ [_1012006, _1012008, _1012010, _1012012] : [hBOOL(hAPP(hAPP(c_member(_1012006), _1012008), _1012010)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012006, tc_Nat_Onat), _1012012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012006, tc_HOL_Obool)), _1012010), hAPP(hAPP(c_Set_Oinsert(_1012006), _1012008), c_Orderings_Obot__class_Obot(tc_fun(_1012006, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012006, tc_Nat_Onat), _1012012), _1012010)), hAPP(_1012012, _1012008)))], (2726 ^ _776545) ^ [_816851, _816853, _816855, _816857, _816859, _816861] : [-(c_Partial__Function_Oflat__lub(_816861, _816857, _816853) = c_Partial__Function_Oflat__lub(_816859, _816855, _816851)), _816861 = _816859, _816857 = _816855, _816853 = _816851], (45168 ^ _776545) ^ [_1681269, _1681271, _1681273, _1681275, _1681277] : [class_Groups_Omonoid__add(_1681269), class_Groups_Oordered__ab__semigroup__add(_1681269), 45178 ^ _776545 : [(45181 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681269), hAPP(_1681275, 45177 ^ [_1681269, _1681271, _1681273, _1681275, _1681277])), hAPP(_1681277, 45177 ^ [_1681269, _1681271, _1681273, _1681275, _1681277])))], (45179 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1681271), 45177 ^ [_1681269, _1681271, _1681273, _1681275, _1681277]), hAPP(c_List_Oset(_1681271), _1681273))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681269), hAPP(c_List_Omonoid__add__class_Olistsum(_1681269), hAPP(hAPP(c_List_Omap(_1681271, _1681269), _1681275), _1681273))), hAPP(c_List_Omonoid__add__class_Olistsum(_1681269), hAPP(hAPP(c_List_Omap(_1681271, _1681269), _1681277), _1681273)))))], (35348 ^ _776545) ^ [_1435762, _1435764, _1435766, _1435768] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1435762, _1435764), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1435766), _1435768))), -(_1435764 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1435762, _1435764) = _1435768)], (43950 ^ _776545) ^ [_1654850, _1654852, _1654854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654850)), _1654854)), _1654852)), -(hAPP(hAPP(c_List_Odrop(_1654850), _1654852), _1654854) = c_List_Olist_ONil(_1654850))], (23425 ^ _776545) ^ [_1201074, _1201076, _1201078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201074)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1201076), _1201078)), 23432 ^ _776545 : [(23433 ^ _776545) ^ [_1201264] : [23435 ^ _776545 : [(23441 ^ _776545) ^ [] : [-(_1201264 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 23437 ^ [_1201074, _1201076, _1201078, _1201264]), 23434 ^ [_1201074, _1201076, _1201078, _1201264]))], (23439 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23437 ^ [_1201074, _1201076, _1201078, _1201264]), _1201078)))], (23436 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23434 ^ [_1201074, _1201076, _1201078, _1201264]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201074))))]], -(_1201264 = _1201076), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201264), _1201074) = _1201076]]], (7730 ^ _776545) ^ [_906114, _906116, _906118] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906114, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906114, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906114, tc_HOL_Obool), _906116)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906114, tc_HOL_Obool), _906118))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_906114, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_906114, tc_HOL_Obool), tc_HOL_Obool)), _906116), _906118)))))], (26288 ^ _776545) ^ [_1251277, _1251279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251277)), 26291 ^ _776545 : [(26298 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251277), _1251279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251277)), hAPP(c_Int_Onat, _1251279))))], (26292 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1251277)), hAPP(c_Int_Onat, _1251279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251277), _1251279)))]]], (45461 ^ _776545) ^ [_1688027, _1688029, _1688031, _1688033, _1688035, _1688037, _1688039] : [c_List_Olist__all2(_1688027, _1688029, _1688031, _1688033, hAPP(hAPP(c_List_Omap(_1688035, _1688029), _1688037), _1688039)), -(c_List_Olist__all2(_1688027, _1688035, hAPP(hAPP(c_COMBC(_1688027, tc_fun(_1688035, _1688029), tc_fun(_1688035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1688029, tc_HOL_Obool), tc_fun(tc_fun(_1688035, _1688029), tc_fun(_1688035, tc_HOL_Obool)), _1688027), c_COMBB(_1688029, tc_HOL_Obool, _1688035)), _1688031)), _1688037), _1688033, _1688039))], (44178 ^ _776545) ^ [_1659934, _1659936, _1659938] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659934)), hAPP(c_List_Orotate(_1659934, _1659936), _1659938)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659934)), _1659938))], (41686 ^ _776545) ^ [_1597376, _1597378] : [-(c_Nitpick_Ouminus__frac(_1597376, _1597378) = c_Nitpick_OAbs__Frac(_1597376, 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(_1597376), _1597378))), hAPP(c_Nitpick_Odenom(_1597376), _1597378))))], (14945 ^ _776545) ^ [_1046165, _1046167, _1046169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046165), _1046167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046165), _1046169)), 14952 ^ _776545 : [(14959 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046167), _1046169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046167), _1046165)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046169), _1046165))))], (14953 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046167), _1046165)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046169), _1046165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046167), _1046169)))]]], (32596 ^ _776545) ^ [_1367497, _1367499, _1367501, _1367503, _1367505] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367497, tc_fun(_1367499, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1367497), _1367501), _1367503)), _1367505) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367499, tc_HOL_Obool)), hAPP(_1367505, _1367501)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367497, tc_fun(_1367499, tc_HOL_Obool)), _1367503), _1367505)))], (27419 ^ _776545) ^ [_1269657, _1269659] : [class_Groups_Oordered__ab__group__add__abs(_1269657), 27422 ^ _776545 : [(27429 ^ _776545) ^ [] : [-(_1269659 = c_Groups_Ozero__class_Ozero(_1269657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269657), c_Groups_Ozero__class_Ozero(_1269657)), hAPP(c_Groups_Oabs__class_Oabs(_1269657), _1269659))))], (27423 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269657), c_Groups_Ozero__class_Ozero(_1269657)), hAPP(c_Groups_Oabs__class_Oabs(_1269657), _1269659))), _1269659 = c_Groups_Ozero__class_Ozero(_1269657)]]], (49496 ^ _776545) ^ [_1776897, _1776899] : [c_Equiv__Relations_Oequivp(_1776897, _1776899), 49499 ^ _776545 : [(49504 ^ _776545) ^ [] : [-(c_Predicate_Otransp(_1776897, _1776899))], (49502 ^ _776545) ^ [] : [-(c_Predicate_Osymp(_1776897, _1776899))], (49500 ^ _776545) ^ [] : [-(c_Predicate_Oreflp(_1776897, _1776899))]]], (40623 ^ _776545) ^ [_1569825, _1569827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569825, _1569825)), _1569827)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569825, _1569825)), c_Transitive__Closure_Otrancl(_1569825, _1569827))))], (39133 ^ _776545) ^ [_1531149, _1531151, _1531153] : [c_Equiv__Relations_Oequiv(_1531149, _1531151, _1531153), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531149, _1531149), tc_HOL_Obool)), _1531153), hAPP(hAPP(c_Product__Type_OSigma(_1531149, _1531149), _1531151), hAPP(c_COMBK(tc_fun(_1531149, tc_HOL_Obool), _1531149), _1531151)))))], (21018 ^ _776545) ^ [_1156279, _1156281, _1156283, _1156285] : [c_Sum__Type_OPlus(_1156279, _1156281, _1156283, _1156285) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1156279, _1156281), tc_HOL_Obool)), 21021 ^ _776545 : [(21024 ^ _776545) ^ [] : [-(_1156285 = c_Orderings_Obot__class_Obot(tc_fun(_1156281, tc_HOL_Obool)))], (21022 ^ _776545) ^ [] : [-(_1156283 = c_Orderings_Obot__class_Obot(tc_fun(_1156279, tc_HOL_Obool)))]]], (42236 ^ _776545) ^ [_1614122, _1614124, _1614126, _1614128] : [-(hAPP(hAPP(c_List_Onth(_1614122), hAPP(hAPP(c_List_Olist_OCons(_1614122), _1614124), _1614126)), _1614128) = c_Nat_Onat_Onat__case(_1614122, _1614124, hAPP(c_List_Onth(_1614122), _1614126), _1614128))], (24980 ^ _776545) ^ [_1228918, _1228920, _1228922] : [class_Divides_Osemiring__div(_1228918), -(c_Divides_Odiv__class_Omod(_1228918, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1228918), _1228920), _1228922), _1228922) = c_Groups_Ozero__class_Ozero(_1228918))], (44296 ^ _776545) ^ [_1662298, _1662300, _1662302, _1662304] : [class_Groups_Osemigroup__add(_1662298), -(hAPP(c_List_Ofoldl(_1662298, _1662298, c_Groups_Oplus__class_Oplus(_1662298), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1662298), _1662300), _1662302)), _1662304) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1662298), _1662300), hAPP(c_List_Ofoldl(_1662298, _1662298, c_Groups_Oplus__class_Oplus(_1662298), _1662302), _1662304)))], (16072 ^ _776545) ^ [_1067152, _1067154] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067152)), _1067154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067152), hAPP(c_Nat_OSuc, _1067154)))], (3148 ^ _776545) ^ [_823414, _823416, _823418, _823420] : [-(c_Nat_Ocompow(_823420, _823416) = c_Nat_Ocompow(_823418, _823414)), _823420 = _823418, _823416 = _823414], (14348 ^ _776545) ^ [_1035328, _1035330, _1035332, _1035334, _1035336] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1035328), 14351 ^ _776545 : [(14352 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035330), _1035334)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035332), _1035336)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035330), _1035336)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035332), _1035334)), -(_1035330 = _1035332), -(_1035334 = _1035336)], (14362 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035330), _1035334)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035332), _1035336)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035330), _1035336)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035328), _1035332), _1035334))), 14365 ^ _776545 : [(14368 ^ _776545) ^ [] : [_1035334 = _1035336], (14366 ^ _776545) ^ [] : [_1035330 = _1035332]]]]], (14774 ^ _776545) ^ [_1042887, _1042889, _1042891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042889), _1042891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042887), _1042889)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042887), _1042891))))], (42699 ^ _776545) ^ [_1626790, _1626792, _1626794, _1626796, _1626798, _1626800] : [-(_1626790 = _1626792), -(hAPP(hAPP(c_List_Olist__update(_1626794, hAPP(hAPP(c_List_Olist__update(_1626794, _1626796), _1626790), _1626798)), _1626792), _1626800) = hAPP(hAPP(c_List_Olist__update(_1626794, hAPP(hAPP(c_List_Olist__update(_1626794, _1626796), _1626792), _1626800)), _1626790), _1626798))], (42795 ^ _776545) ^ [_1629004, _1629006, _1629008, _1629010] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629004), tc_List_Olist(_1629004))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629004), tc_List_Olist(_1629004)), _1629006), _1629008)), c_List_Olistrel1(_1629004, _1629010)))), 42796 ^ _776545 : [(42797 ^ _776545) ^ [_1629137, _1629139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629004, _1629004)), hAPP(hAPP(c_Product__Type_OPair(_1629004, _1629004), hAPP(hAPP(c_List_Onth(_1629004), _1629006), _1629137)), _1629139)), _1629010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629137), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629004)), _1629006))), _1629008 = hAPP(hAPP(c_List_Olist__update(_1629004, _1629006), _1629137), _1629139)]]], (46333 ^ _776545) ^ [_1708386, _1708388, _1708390] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1708386), c_List_Oupt(_1708388, _1708390)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1708388), _1708386), _1708390))], (24397 ^ _776545) ^ [_1217760, _1217762] : [class_Rings_Olinordered__semidom(_1217760), 24400 ^ _776545 : [(24407 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217760), c_Groups_Ozero__class_Ozero(_1217760)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217760), _1217762))))], (24401 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217760), c_Groups_Ozero__class_Ozero(_1217760)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217760), _1217762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217762)))]]], (44717 ^ _776545) ^ [_1670413, _1670415, _1670417, _1670419, _1670421] : [-(c_List_Olist_Olist__size(_1670413, _1670415, hAPP(hAPP(c_List_Omap(_1670417, _1670413), _1670419), _1670421)) = c_List_Olist_Olist__size(_1670417, hAPP(c_Fun_Ocomp(_1670413, tc_Nat_Onat, _1670417, _1670415), _1670419), _1670421))], (42151 ^ _776545) ^ [_1611808, _1611810, _1611812, _1611814] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611808)), hAPP(hAPP(c_List_Olist_OCons(_1611808), _1611810), _1611812)), c_List_Olists(_1611808, _1611814)))), hBOOL(hAPP(hAPP(c_member(_1611808), _1611810), _1611814)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611808)), _1611812), c_List_Olists(_1611808, _1611814)))], (8291 ^ _776545) ^ [_918438, _918440, _918442, _918444] : [class_Lattices_Osemilattice__sup(_918438), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918438), _918440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918438), _918442), _918444)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918438), _918442), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918438), _918440), _918444)))], (51623 ^ _776545) ^ [_1820844, _1820846] : [class_Rings_Ocomm__semiring__1(_1820844), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820844), c_Groups_Oone__class_Oone(_1820844)), _1820846)))], (2544 ^ _776545) ^ [_814030, _814032, _814034, _814036] : [-(c_FunDef_Orp__inv__image(_814036, _814032) = c_FunDef_Orp__inv__image(_814034, _814030)), _814036 = _814034, _814032 = _814030], (44741 ^ _776545) ^ [_1671016, _1671018, _1671020, _1671022, _1671024] : [-(hAPP(hAPP(c_List_Omap(_1671016, _1671018), _1671020), hAPP(hAPP(c_List_Olist_OCons(_1671016), _1671022), _1671024)) = hAPP(hAPP(c_List_Olist_OCons(_1671018), hAPP(_1671020, _1671022)), hAPP(hAPP(c_List_Omap(_1671016, _1671018), _1671020), _1671024)))], (42393 ^ _776545) ^ [_1618099, _1618101, _1618103, _1618105, _1618107] : [hBOOL(hAPP(hAPP(c_member(_1618099), _1618101), hAPP(c_List_Oset(_1618099), _1618103))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618105), hAPP(_1618107, _1618101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618105), c_List_Olist_Olist__size(_1618099, _1618107, _1618103))))], (26775 ^ _776545) ^ [_1259441, _1259443] : [c_Nat__Transfer_Onat__set(_1259441), c_Nat__Transfer_Onat__set(_1259443), 26782 ^ _776545 : [(26789 ^ _776545) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259441) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259443), -(_1259441 = _1259443)], (26783 ^ _776545) ^ [] : [_1259441 = _1259443, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259441) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1259443))]]], (18914 ^ _776545) ^ [_1117186, _1117188, _1117190] : [class_Rings_Olinordered__ring(_1117186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117186), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117186), _1117188), _1117188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117186), _1117190), _1117190))), c_Groups_Ozero__class_Ozero(_1117186)))], (28241 ^ _776545) ^ [_1283629, _1283631] : [-(c_Nitpick_Onat__lcm(_1283629, _1283631) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1283629), _1283631)), c_Nitpick_Onat__gcd(_1283629, _1283631)))], (37941 ^ _776545) ^ [_1500946, _1500948, _1500950, _1500952] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500946, _1500948, _1500950), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500946, _1500948), tc_HOL_Obool))), _1500952) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500946, _1500950), tc_HOL_Obool)))], (47723 ^ _776545) ^ [_1737012, _1737014, _1737016] : [class_Enum_Oenum(_1737012), class_Enum_Oenum(_1737014), 47730 ^ _776545 : [(47737 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737014), hAPP(hAPP(c_COMBB(tc_fun(_1737012, tc_HOL_Obool), tc_HOL_Obool, _1737014), c_Enum_Oenum__class_Oenum__ex(_1737012)), hAPP(hAPP(c_COMBB(tc_fun(_1737012, tc_prod(_1737014, _1737012)), tc_fun(_1737012, tc_HOL_Obool), _1737014), hAPP(c_COMBB(tc_prod(_1737014, _1737012), tc_HOL_Obool, _1737012), _1737016)), c_Product__Type_OPair(_1737014, _1737012))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1737014, _1737012)), _1737016)))], (47731 ^ _776545) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1737014, _1737012)), _1737016)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1737014), hAPP(hAPP(c_COMBB(tc_fun(_1737012, tc_HOL_Obool), tc_HOL_Obool, _1737014), c_Enum_Oenum__class_Oenum__ex(_1737012)), hAPP(hAPP(c_COMBB(tc_fun(_1737012, tc_prod(_1737014, _1737012)), tc_fun(_1737012, tc_HOL_Obool), _1737014), hAPP(c_COMBB(tc_prod(_1737014, _1737012), tc_HOL_Obool, _1737012), _1737016)), c_Product__Type_OPair(_1737014, _1737012))))))]]], (4122 ^ _776545) ^ [_838963, _838965, _838967, _838969] : [-(c_New__DSequence_Oneg__single(_838969, _838965) = c_New__DSequence_Oneg__single(_838967, _838963)), _838969 = _838967, _838965 = _838963], (24710 ^ _776545) ^ [_1223616, _1223618] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223616) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223618), -(_1223616 = _1223618)], (30154 ^ _776545) ^ [_1317512, _1317514, _1317516] : [class_Orderings_Olinorder(_1317512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317512), _1317514), _1317516)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1317512), _1317516), _1317514) = _1317514)], (42299 ^ _776545) ^ [_1615808, _1615810, _1615812] : [-(hAPP(c_List_Oset(_1615808), c_List_Osublist(_1615808, _1615810, _1615812)) = hAPP(c_Set_OCollect(_1615808), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1615808), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1615808, 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)), _1615808), 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)), _1615808), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1615808, tc_fun(tc_Nat_Onat, _1615808), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615808, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1615808), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1615808), c_COMBB(_1615808, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1615808), _1615810))))), 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(_1615808)), _1615810)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1615812))))))], (3382 ^ _776545) ^ [_827047, _827049] : [_827049 = _827047, -(c_Set_OPow(_827049) = c_Set_OPow(_827047))], (21411 ^ _776545) ^ [_1164469, _1164471, _1164473, _1164475] : [class_Rings_Ocomm__semiring__1(_1164469), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164469), hAPP(hAPP(c_Power_Opower__class_Opower(_1164469), _1164471), _1164473)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164469), _1164471), _1164475)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1164469), _1164471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164473), _1164475)))], (52167 ^ _776545) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (34610 ^ _776545) ^ [_1421241, _1421243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421241)), _1421243)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1421241), _1421243)))], (48542 ^ _776545) ^ [_1754633, _1754635, _1754637, _1754639, _1754641] : [-(c_Predicate_Oconversep(_1754633, _1754635, c_Predicate_Opred__comp(_1754633, _1754637, _1754635, _1754639, _1754641)) = c_Predicate_Opred__comp(_1754635, _1754637, _1754633, c_Predicate_Oconversep(_1754637, _1754635, _1754641), c_Predicate_Oconversep(_1754633, _1754637, _1754639)))], (4278 ^ _776545) ^ [_841347, _841349] : [_841349 = _841347, -(c_List_Onth(_841349) = c_List_Onth(_841347))], (48576 ^ _776545) ^ [_1755962, _1755964, _1755966, _1755968] : [-(hAPP(hAPP(c_List_Otake(_1755962), _1755964), c_List_Oreplicate(_1755962, _1755966, _1755968)) = c_List_Oreplicate(_1755962, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1755964), _1755966), _1755968))], (15986 ^ _776545) ^ [_1065830, _1065832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1065830)), hAPP(c_Nat_OSuc, _1065832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1065830), _1065832)))], (28883 ^ _776545) ^ [_1294346] : [c_Int_OMin = c_Int_OBit0(_1294346)], (38554 ^ _776545) ^ [_1516031, _1516033, _1516035, _1516037, _1516039] : [-(hAPP(c_Relation_ORange(_1516031, _1516033), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1516031, _1516033)), hAPP(hAPP(c_Product__Type_OPair(_1516031, _1516033), _1516035), _1516037)), _1516039)) = hAPP(hAPP(c_Set_Oinsert(_1516033), _1516037), hAPP(c_Relation_ORange(_1516031, _1516033), _1516039)))], (32700 ^ _776545) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49550 ^ _776545) ^ [_1777962, _1777964] : [c_Relation_Otrans(_1777962, _1777964), c_Relation_Oantisym(_1777962, _1777964), -(c_Relation_Otrans(_1777962, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1777962, _1777962), tc_HOL_Obool)), _1777964), c_Relation_OId(_1777962))))], (18117 ^ _776545) ^ [_1102298, _1102300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102298), _1102300)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102298), _1102300) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47491 ^ _776545) ^ [_1731664, _1731666, _1731668] : [47493 ^ _776545 : [(47496 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1731666, 47492 ^ [_1731664, _1731666, _1731668])))], (47494 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731664), 47492 ^ [_1731664, _1731666, _1731668]), hAPP(c_List_Oset(_1731664), c_List_OdropWhile(_1731664, _1731666, _1731668)))))]], -(c_List_OtakeWhile(_1731664, _1731666, _1731668) = hAPP(c_List_Ofilter(_1731664, _1731666), _1731668))], (40821 ^ _776545) ^ [_1575604, _1575606, _1575608, _1575610, _1575612] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575604, _1575604)), hAPP(hAPP(c_Product__Type_OPair(_1575604, _1575604), _1575606), _1575608)), c_Transitive__Closure_Ortrancl(_1575604, _1575610))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575604, _1575604)), hAPP(hAPP(c_Product__Type_OPair(_1575604, _1575604), _1575608), _1575612)), c_Transitive__Closure_Ortrancl(_1575604, _1575610))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575604, _1575604)), hAPP(hAPP(c_Product__Type_OPair(_1575604, _1575604), _1575606), _1575612)), c_Transitive__Closure_Ortrancl(_1575604, _1575610))))], (44519 ^ _776545) ^ [_1667016, _1667018, _1667020, _1667022, _1667024] : [class_Orderings_Olinorder(_1667016), hBOOL(hAPP(hAPP(c_member(_1667016), hAPP(_1667018, _1667020)), hAPP(c_Set_Oimage(_1667022, _1667016, _1667018), hAPP(c_List_Oset(_1667022), _1667024)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1667022, _1667016, _1667018, _1667020, _1667024) = _1667024)], (44072 ^ _776545) ^ [_1657891, _1657893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657891)), _1657893)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1657891), _1657893) = _1657893)], (28613 ^ _776545) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (52425 ^ _776545) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (17407 ^ _776545) ^ [_1090019, _1090021, _1090023] : [class_Rings_Olinordered__semiring__strict(_1090019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090019), c_Groups_Ozero__class_Ozero(_1090019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090019), _1090021), _1090023))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090019), c_Groups_Ozero__class_Ozero(_1090019)), _1090023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090019), c_Groups_Ozero__class_Ozero(_1090019)), _1090021)))], (46217 ^ _776545) ^ [_1705795, _1705797] : [-(c_Random_Oselect__weight(_1705795, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1705795), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1705795, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1705795, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1705795)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1705797)) = c_Random_Oselect__weight(_1705795, _1705797))], (23934 ^ _776545) ^ [_1210002, _1210004, _1210006] : [class_Rings_Osemiring__1(_1210002), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210004), _1210006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1210002), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210002), _1210004)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210002), _1210006)))], (27979 ^ _776545) ^ [_1279366] : [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), _1279366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1279366)))], (5993 ^ _776545) ^ [] : [c_HOL_Oinduct__false], (40399 ^ _776545) ^ [_1564149, _1564151, _1564153] : [-(c_Hilbert__Choice_OEps(tc_prod(_1564149, _1564151), _1564153) = c_Hilbert__Choice_OEps(tc_prod(_1564149, _1564151), hAPP(c_Product__Type_Oprod_Oprod__case(_1564149, _1564151, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1564151, tc_prod(_1564149, _1564151)), tc_fun(_1564151, tc_HOL_Obool), _1564149), hAPP(c_COMBB(tc_prod(_1564149, _1564151), tc_HOL_Obool, _1564151), _1564153)), c_Product__Type_OPair(_1564149, _1564151)))))], (49835 ^ _776545) ^ [_1783218, _1783220] : [-(c_Equiv__Relations_Opart__equivp(_1783218, _1783220)), 49838 ^ _776545 : [(49839 ^ _776545) ^ [_1783295] : [hBOOL(hAPP(hAPP(_1783220, _1783295), _1783295))]], c_Predicate_Osymp(_1783218, _1783220), c_Predicate_Otransp(_1783218, _1783220)], (27461 ^ _776545) ^ [_1270440, _1270442, _1270444] : [class_Groups_Oordered__ab__group__add__abs(_1270440), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270440), hAPP(c_Groups_Oabs__class_Oabs(_1270440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270440), hAPP(c_Groups_Oabs__class_Oabs(_1270440), _1270442)), hAPP(c_Groups_Oabs__class_Oabs(_1270440), _1270444)))), hAPP(c_Groups_Oabs__class_Oabs(_1270440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270440), _1270442), _1270444)))))], (52023 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (30890 ^ _776545) ^ [_1330657, _1330659, _1330661] : [class_Orderings_Olinorder(_1330657), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330657), _1330659)), -(_1330659 = c_Orderings_Obot__class_Obot(tc_fun(_1330657, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330657), _1330661)), -(_1330661 = c_Orderings_Obot__class_Obot(tc_fun(_1330657, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330657, tc_HOL_Obool)), _1330659), _1330661) = c_Orderings_Obot__class_Obot(tc_fun(_1330657, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1330657, c_Orderings_Oord__class_Omin(_1330657), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330657, tc_HOL_Obool)), _1330659), _1330661)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330657), c_Big__Operators_Olattice_OInf__fin(_1330657, c_Orderings_Oord__class_Omin(_1330657), _1330659)), c_Big__Operators_Olattice_OInf__fin(_1330657, c_Orderings_Oord__class_Omin(_1330657), _1330661)))], (17273 ^ _776545) ^ [_1087500, _1087502] : [class_Groups_Olinordered__ab__group__add(_1087500), 17276 ^ _776545 : [(17283 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087500), c_Groups_Ozero__class_Ozero(_1087500)), _1087502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087500), c_Groups_Ozero__class_Ozero(_1087500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087500), _1087502), _1087502))))], (17277 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087500), c_Groups_Ozero__class_Ozero(_1087500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087500), _1087502), _1087502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087500), c_Groups_Ozero__class_Ozero(_1087500)), _1087502)))]]], (4510 ^ _776545) ^ [_845063, _845065] : [_845065 = _845063, -(c_Lazy__Sequence_Oyield(_845065) = c_Lazy__Sequence_Oyield(_845063))], (26809 ^ _776545) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38489 ^ _776545) ^ [_1514427, _1514429] : [-(c_HOL_OThe(_1514427, hAPP(hAPP(c_COMBC(_1514427, _1514427, tc_HOL_Obool), c_fequal), _1514429)) = _1514429)], (46954 ^ _776545) ^ [_1720267, _1720269] : [-(c_Fun_Oinj__on(tc_List_Olist(_1720267), tc_List_Olist(_1720267), c_List_Orev(_1720267), _1720269))], (24309 ^ _776545) ^ [_1216166, _1216168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216166), _1216168)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216168)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216166)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216168), _1216166)))], (3734 ^ _776545) ^ [_832527, _832529, _832531, _832533, _832535, _832537] : [-(c_List_Oinsert(_832537, _832533, _832529) = c_List_Oinsert(_832535, _832531, _832527)), _832537 = _832535, _832533 = _832531, _832529 = _832527], (26807 ^ _776545) ^ [_1259867] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259867)))], (47014 ^ _776545) ^ [_1721466, _1721468] : [_1721468 = c_List_Olist_ONil(_1721466), -(hAPP(c_List_Orev(_1721466), _1721468) = c_List_Olist_ONil(_1721466))], (4340 ^ _776545) ^ [_842270, _842272] : [_842272 = _842270, -(c_If(_842272) = c_If(_842270))], (52123 ^ _776545) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (26553 ^ _776545) ^ [_1255824, _1255826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1255824)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1255824), _1255826)), _1255824) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19131 ^ _776545) ^ [_1121274, _1121276, _1121278, _1121280, _1121282, _1121284, _1121286] : [c_Big__Operators_Ocomm__monoid__big(_1121274, _1121276, _1121278, _1121280, _1121282), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1121276), _1121284))), -(hAPP(hAPP(_1121282, _1121286), _1121284) = _1121280)], (17663 ^ _776545) ^ [_1094589, _1094591] : [class_Groups_Olinordered__ab__group__add(_1094589), 17666 ^ _776545 : [(17673 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094589), _1094591), c_Groups_Ozero__class_Ozero(_1094589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094589), _1094591), hAPP(c_Groups_Ouminus__class_Ouminus(_1094589), _1094591))))], (17667 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094589), _1094591), hAPP(c_Groups_Ouminus__class_Ouminus(_1094589), _1094591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094589), _1094591), c_Groups_Ozero__class_Ozero(_1094589))))]]], (24383 ^ _776545) ^ [_1217487, _1217489, _1217491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217487), _1217489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217491)), -(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), _1217491)), _1217487)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217491)), _1217489))))], (27611 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (40943 ^ _776545) ^ [_1578436, _1578438, _1578440, _1578442] : [-(hBOOL(hAPP(hAPP(c_member(_1578436), _1578438), hAPP(c_Relation_ODomain(_1578436, _1578436), _1578440)))), 40946 ^ _776545 : [(40953 ^ _776545) ^ [] : [_1578438 = _1578442, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578436, _1578436)), hAPP(hAPP(c_Product__Type_OPair(_1578436, _1578436), _1578438), _1578442)), c_Transitive__Closure_Ortrancl(_1578436, _1578440))))], (40947 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578436, _1578436)), hAPP(hAPP(c_Product__Type_OPair(_1578436, _1578436), _1578438), _1578442)), c_Transitive__Closure_Ortrancl(_1578436, _1578440))), -(_1578438 = _1578442)]]], (18051 ^ _776545) ^ [_1101154, _1101156, _1101158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101154), _1101156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101158)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101154), _1101158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101156), _1101158))))], (31543 ^ _776545) ^ [_1342864, _1342866, _1342868] : [class_Orderings_Olinorder(_1342864), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342864), _1342866), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342864), _1342868), _1342866))))], (39932 ^ _776545) ^ [_1553824, _1553826, _1553828, _1553830, _1553832, _1553834, _1553836] : [-(hAPP(c_Product__Type_Oapsnd(_1553824, _1553826, _1553828, _1553830), hAPP(c_Product__Type_Oapsnd(_1553832, _1553824, _1553828, _1553834), _1553836)) = hAPP(c_Product__Type_Oapsnd(_1553832, _1553826, _1553828, hAPP(c_Fun_Ocomp(_1553824, _1553826, _1553832, _1553830), _1553834)), _1553836))], (35823 ^ _776545) ^ [_1445505, _1445507, _1445509, _1445511, _1445513, _1445515] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445505), _1445507)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445509), _1445511)), 35833 ^ _776545 : [(35836 ^ _776545) ^ [] : [hAPP(c_Finite__Set_Ocard(_1445505), hAPP(c_Set_OCollect(_1445505), hAPP(hAPP(c_COMBS(_1445505, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1445505), c_fconj), hAPP(hAPP(c_COMBC(_1445505, tc_fun(_1445505, tc_HOL_Obool), tc_HOL_Obool), c_member(_1445505)), _1445507))), hAPP(hAPP(c_COMBC(_1445505, _1445509, tc_HOL_Obool), _1445513), 35832 ^ [_1445505, _1445507, _1445509, _1445511, _1445513, _1445515])))) = _1445515], (35834 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445509), 35832 ^ [_1445505, _1445507, _1445509, _1445511, _1445513, _1445515]), _1445511)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1445505, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1445509, tc_HOL_Obool), tc_Nat_Onat, _1445505), c_Finite__Set_Ocard(_1445509)), hAPP(hAPP(c_COMBB(tc_fun(_1445509, tc_HOL_Obool), tc_fun(_1445509, tc_HOL_Obool), _1445505), c_Set_OCollect(_1445509)), hAPP(hAPP(c_COMBB(tc_fun(_1445509, tc_HOL_Obool), tc_fun(_1445509, tc_HOL_Obool), _1445505), hAPP(c_COMBS(_1445509, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1445509), c_fconj), hAPP(hAPP(c_COMBC(_1445509, tc_fun(_1445509, tc_HOL_Obool), tc_HOL_Obool), c_member(_1445509)), _1445511)))), _1445513)))), _1445507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1445515), hAPP(c_Finite__Set_Ocard(_1445509), _1445511)))], (36974 ^ _776545) ^ [_1478801, _1478803] : [c_Equiv__Relations_Oequiv(_1478801, c_Orderings_Otop__class_Otop(tc_fun(_1478801, tc_HOL_Obool)), _1478803), -(c_Equiv__Relations_Oequivp(_1478801, hAPP(hAPP(c_COMBC(_1478801, tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_fun(_1478801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478801, tc_fun(tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_fun(_1478801, tc_HOL_Obool)), _1478801), c_COMBC(_1478801, tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478801, tc_prod(_1478801, _1478801)), tc_fun(_1478801, tc_fun(tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_HOL_Obool)), _1478801), hAPP(c_COMBB(tc_prod(_1478801, _1478801), tc_fun(tc_fun(tc_prod(_1478801, _1478801), tc_HOL_Obool), tc_HOL_Obool), _1478801), c_member(tc_prod(_1478801, _1478801)))), c_Product__Type_OPair(_1478801, _1478801)))), _1478803)))], (33523 ^ _776545) ^ [] : [-(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)))], (34842 ^ _776545) ^ [_1426710, _1426712, _1426714, _1426716, _1426718, _1426720] : [hAPP(hAPP(c_Product__Type_OPair(_1426710, _1426712), _1426714), _1426716) = hAPP(hAPP(c_Product__Type_OPair(_1426710, _1426712), _1426718), _1426720), 34845 ^ _776545 : [(34848 ^ _776545) ^ [] : [-(_1426716 = _1426720)], (34846 ^ _776545) ^ [] : [-(_1426714 = _1426718)]]], (33885 ^ _776545) ^ [_1404452] : [-(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)))), _1404452)) = 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), _1404452), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (52399 ^ _776545) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (49157 ^ _776545) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (6844 ^ _776545) ^ [_887448, _887450, _887452] : [6846 ^ _776545 : [(6849 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887448), 6845 ^ [_887448, _887450, _887452]), _887452))], (6847 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887448), 6845 ^ [_887448, _887450, _887452]), _887450)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887448, tc_HOL_Obool)), _887450), _887452)))], (34622 ^ _776545) ^ [_1421453, _1421455] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1421453), hAPP(c_Nat_OSuc, _1421455)) = 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), _1421453), _1421455)))], (29145 ^ _776545) ^ [_1298927, _1298929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1298927), _1298929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1298927)), c_Int_OBit1(_1298929))))], (38258 ^ _776545) ^ [_1509130, _1509132] : [hAPP(hAPP(c_Relation_Orel__comp(_1509130, _1509130, _1509130), _1509132), _1509132) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509130, _1509130), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1509130, _1509132))], (24244 ^ _776545) ^ [_1215036, _1215038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1215038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215036), _1215038)), _1215036)))], (51209 ^ _776545) ^ [_1813507, _1813509, _1813511, _1813513] : [class_Rings_Ocomm__semiring__1(_1813507), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1813507), _1813509), _1813511)), _1813513)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813507), _1813511), _1813513)))], (13168 ^ _776545) ^ [_1009481, _1009483, _1009485, _1009487, _1009489] : [class_Groups_Ocomm__monoid__mult(_1009481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009483), _1009485)), hBOOL(hAPP(hAPP(c_member(_1009483), _1009487), _1009485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009483, _1009481), _1009489), _1009485) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009481), hAPP(_1009489, _1009487)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009483, _1009481), _1009489), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009483, tc_HOL_Obool)), _1009485), hAPP(hAPP(c_Set_Oinsert(_1009483), _1009487), c_Orderings_Obot__class_Obot(tc_fun(_1009483, tc_HOL_Obool)))))))], (21647 ^ _776545) ^ [_1168579, _1168581, _1168583, _1168585] : [class_Fields_Olinordered__field__inverse__zero(_1168579), class_Int_Onumber(_1168579), 21654 ^ _776545 : [(21655 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168579), _1168583), _1168585))), 21658 ^ _776545 : [(21665 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), c_Groups_Ozero__class_Ozero(_1168579)), _1168585))), 21668 ^ _776545 : [(21675 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168585), c_Groups_Ozero__class_Ozero(_1168579)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), c_Groups_Ozero__class_Ozero(_1168579))))], (21669 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168585), c_Groups_Ozero__class_Ozero(_1168579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), _1168585))))]]], (21659 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), c_Groups_Ozero__class_Ozero(_1168579)), _1168585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), _1168585)), _1168583)))]]], (21681 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1168579), _1168583), _1168585)))), 21684 ^ _776545 : [(21687 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), _1168585)), _1168583))], (21685 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), c_Groups_Ozero__class_Ozero(_1168579)), _1168585)))]], 21688 ^ _776545 : [(21691 ^ _776545) ^ [] : [21692 ^ _776545 : [(21695 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), _1168585)))], (21693 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168585), c_Groups_Ozero__class_Ozero(_1168579))))]], 21696 ^ _776545 : [(21699 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), hAPP(c_Int_Onumber__class_Onumber__of(_1168579), _1168581)), c_Groups_Ozero__class_Ozero(_1168579)))], (21697 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), _1168585), c_Groups_Ozero__class_Ozero(_1168579)))]]], (21689 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168579), c_Groups_Ozero__class_Ozero(_1168579)), _1168585))]]]]], (36711 ^ _776545) ^ [_1472911, _1472913, _1472915, _1472917, _1472919] : [c_Equiv__Relations_Oequiv(_1472911, _1472913, _1472915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472911, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1472911, _1472911, _1472915), hAPP(hAPP(c_Set_Oinsert(_1472911), _1472917), c_Orderings_Obot__class_Obot(tc_fun(_1472911, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1472911, _1472911, _1472915), hAPP(hAPP(c_Set_Oinsert(_1472911), _1472919), c_Orderings_Obot__class_Obot(tc_fun(_1472911, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1472911), _1472917), _1472913)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472911, _1472911)), hAPP(hAPP(c_Product__Type_OPair(_1472911, _1472911), _1472919), _1472917)), _1472915)))], (52099 ^ _776545) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (44182 ^ _776545) ^ [_1660024] : [-(hAPP(c_List_Otl(_1660024), c_List_Olist_ONil(_1660024)) = c_List_Olist_ONil(_1660024))], (49054 ^ _776545) ^ [_1766031, _1766033] : [-(c_Lazy__Sequence_Oappend(_1766031, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1766031), _1766033) = _1766033)], (45652 ^ _776545) ^ [_1692196, _1692198, _1692200, _1692202] : [hBOOL(hAPP(c_List_Odistinct(_1692196), _1692198)), hBOOL(hAPP(c_List_Odistinct(_1692200), _1692202)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1692196, _1692200)), c_Enum_Oproduct(_1692196, _1692200, _1692198, _1692202))))], (31647 ^ _776545) ^ [_1344673, _1344675, _1344677] : [class_Int_Onumber(_1344673), class_Orderings_Oord(_1344673), 31654 ^ _776545 : [(31661 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344673), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344675)), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344677)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344673), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344675)), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344677)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344675))], (31655 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344673), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344675)), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344677))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344673), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344675)), hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344677)) = hAPP(c_Int_Onumber__class_Onumber__of(_1344673), _1344677))]]], (48247 ^ _776545) ^ [_1748318, _1748320, _1748322] : [48249 ^ _776545 : [(48252 ^ _776545) ^ [] : [hBOOL(hAPP(_1748320, 48248 ^ [_1748318, _1748320, _1748322]))], (48250 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748318), 48248 ^ [_1748318, _1748320, _1748322]), hAPP(c_List_Oset(_1748318), _1748322))))]], -(c_List_Olist__all(_1748318, _1748320, _1748322))], (688 ^ _776545) ^ [_786921, _786923, _786925, _786927, _786929, _786931] : [-(c_List_Oall__interval__int(_786929, _786925, _786921)), c_List_Oall__interval__int(_786931, _786927, _786923), _786931 = _786929, _786927 = _786925, _786923 = _786921], (21439 ^ _776545) ^ [_1165055, _1165057, _1165059, _1165061] : [class_Fields_Ofield__inverse__zero(_1165055), class_Int_Onumber(_1165055), 21446 ^ _776545 : [(21447 ^ _776545) ^ [] : [_1165057 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165055), _1165059), hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061)), 21450 ^ _776545 : [(21457 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061) = c_Groups_Ozero__class_Ozero(_1165055), -(_1165057 = c_Groups_Ozero__class_Ozero(_1165055))], (21451 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061) = c_Groups_Ozero__class_Ozero(_1165055)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165055), _1165057), hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061)) = _1165059)]]], (21463 ^ _776545) ^ [] : [-(_1165057 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165055), _1165059), hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061))), 21466 ^ _776545 : [(21469 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165055), _1165057), hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061)) = _1165059], (21467 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061) = c_Groups_Ozero__class_Ozero(_1165055)]], 21470 ^ _776545 : [(21473 ^ _776545) ^ [] : [_1165057 = c_Groups_Ozero__class_Ozero(_1165055)], (21471 ^ _776545) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1165055), _1165061) = c_Groups_Ozero__class_Ozero(_1165055))]]]]], (7348 ^ _776545) ^ [_896896, _896898] : [class_Complete__Lattice_Ocomplete__lattice(_896896), -(c_Complete__Lattice_OInf__class_OInf(_896896, hAPP(hAPP(c_Set_Oinsert(_896896), _896898), c_Orderings_Obot__class_Obot(tc_fun(_896896, tc_HOL_Obool)))) = _896898)], (39796 ^ _776545) ^ [_1550418, _1550420, _1550422, _1550424, _1550426, _1550428] : [39799 ^ _776545 : [(39802 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550424), _1550426), hAPP(hAPP(_1550428, 39797 ^ [_1550418, _1550420, _1550422, _1550424, _1550426, _1550428]), 39798 ^ [_1550418, _1550420, _1550422, _1550424, _1550426, _1550428])))], (39800 ^ _776545) ^ [] : [-(_1550418 = hAPP(hAPP(c_Product__Type_OPair(_1550420, _1550422), 39797 ^ [_1550418, _1550420, _1550422, _1550424, _1550426, _1550428]), 39798 ^ [_1550418, _1550420, _1550422, _1550424, _1550426, _1550428]))]], -(hBOOL(hAPP(hAPP(c_member(_1550424), _1550426), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550420, _1550422, tc_fun(_1550424, tc_HOL_Obool)), _1550428), _1550418))))], (14120 ^ _776545) ^ [_1030000, _1030002, _1030004, _1030006, _1030008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030000), _1030002)), 14123 ^ _776545 : [(14130 ^ _776545) ^ [] : [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), _1030002), _1030000)), _1030004)), _1030006)), _1030008)), -(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), _1030002), _1030004)), _1030006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030000), _1030004)), _1030008))))], (14124 ^ _776545) ^ [] : [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), _1030002), _1030004)), _1030006)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030000), _1030004)), _1030008))), -(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), _1030002), _1030000)), _1030004)), _1030006)), _1030008)))]]], (20481 ^ _776545) ^ [_1146113, _1146115, _1146117] : [class_Fields_Olinordered__field(_1146113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146113), _1146115), c_Groups_Ozero__class_Ozero(_1146113))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146113), _1146117), c_Groups_Ozero__class_Ozero(_1146113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146113), c_Groups_Ozero__class_Ozero(_1146113)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146113), _1146115), _1146117))))], (2118 ^ _776545) ^ [_807269, _807271, _807273, _807275] : [-(c_Int_Onat__aux(_807275, _807271) = c_Int_Onat__aux(_807273, _807269)), _807275 = _807273, _807271 = _807269], (4812 ^ _776545) ^ [_849814, _849816] : [_849816 = _849814, -(c_Wellfounded_Ofinite__psubset(_849816) = c_Wellfounded_Ofinite__psubset(_849814))], (47393 ^ _776545) ^ [_1729489, _1729491, _1729493] : [47395 ^ _776545 : [(47398 ^ _776545) ^ [] : [hBOOL(hAPP(_1729491, 47394 ^ [_1729489, _1729491, _1729493]))], (47396 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729489), 47394 ^ [_1729489, _1729491, _1729493]), hAPP(c_List_Oset(_1729489), _1729493))))]], -(c_List_OdropWhile(_1729489, _1729491, _1729493) = c_List_Olist_ONil(_1729489))], (36253 ^ _776545) ^ [_1460814, _1460816, _1460818, _1460820, _1460822] : [class_Groups_Ocomm__monoid__add(_1460814), class_Groups_Ocomm__monoid__mult(_1460814), _1460816 = _1460818, c_Nat__Transfer_Onat__set(_1460818), 36271 ^ _776545 : [(36274 ^ _776545) ^ [] : [hAPP(_1460820, 36270 ^ [_1460814, _1460816, _1460818, _1460820, _1460822]) = hAPP(_1460822, 36270 ^ [_1460814, _1460816, _1460818, _1460820, _1460822])], (36272 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36270 ^ [_1460814, _1460816, _1460818, _1460820, _1460822])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1460814), _1460820), _1460816) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1460814), _1460822), _1460818))], (26765 ^ _776545) ^ [_1259285, _1259287] : [class_Int_Onumber__ring(_1259285), -(hAPP(c_Int_Onumber__class_Onumber__of(_1259285), _1259287) = hAPP(c_Int_Oring__1__class_Oof__int(_1259285), _1259287))], (28789 ^ _776545) ^ [_1292771, _1292773] : [c_Int_OBit0(_1292771) = c_Int_OBit1(_1292773)], (52379 ^ _776545) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (16066 ^ _776545) ^ [_1067043, _1067045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1067043)), hAPP(c_Nat_OSuc, _1067045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067043), _1067045)))], (50910 ^ _776545) ^ [_1807683, _1807685, _1807687] : [c_List_Olist__all(tc_Nat_Onat, _1807683, c_List_Oupt(_1807685, _1807687)), -(c_List_Oall__interval__nat(_1807683, _1807685, _1807687))], (23717 ^ _776545) ^ [_1206112] : [-(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), _1206112))))], (50889 ^ _776545) ^ [_1807266, _1807268, _1807270] : [c_List_Oall__interval__nat(_1807266, _1807268, _1807270), 50892 ^ _776545 : [(50893 ^ _776545) ^ [_1807346] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807346), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1807268), _1807270))), -(hBOOL(hAPP(_1807266, _1807346)))]]], (52163 ^ _776545) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (42479 ^ _776545) ^ [_1620499, _1620501, _1620503, _1620505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1620499), tc_List_Olist(_1620499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1620499), tc_List_Olist(_1620499)), _1620501), _1620503)), c_List_Olistrel(_1620499, _1620505))), 42482 ^ _776545 : [(42485 ^ _776545) ^ [_1620835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620499, _1620499)), _1620835), hAPP(c_List_Oset(tc_prod(_1620499, _1620499)), hAPP(hAPP(c_List_Ozip(_1620499, _1620499), _1620501), _1620503)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1620499, _1620499, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1620499, tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_fun(_1620499, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620499, tc_fun(tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_fun(_1620499, tc_HOL_Obool)), _1620499), c_COMBC(_1620499, tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620499, tc_prod(_1620499, _1620499)), tc_fun(_1620499, tc_fun(tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_HOL_Obool)), _1620499), hAPP(c_COMBB(tc_prod(_1620499, _1620499), tc_fun(tc_fun(tc_prod(_1620499, _1620499), tc_HOL_Obool), tc_HOL_Obool), _1620499), c_member(tc_prod(_1620499, _1620499)))), c_Product__Type_OPair(_1620499, _1620499)))), _1620505)), _1620835)))], (42483 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620499)), _1620501) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620499)), _1620503))]]], (48012 ^ _776545) ^ [_1743551, _1743553, _1743555, _1743557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743553)), _1743555))), 48018 ^ _776545 : [(48021 ^ _776545) ^ [] : [hBOOL(hAPP(_1743557, 48017 ^ [_1743551, _1743553, _1743555, _1743557]))], (48019 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743553), 48017 ^ [_1743551, _1743553, _1743555, _1743557]), hAPP(c_List_Oset(_1743553), _1743555))))]], -(hBOOL(hAPP(_1743557, hAPP(hAPP(c_List_Onth(_1743553), _1743555), _1743551))))], (30916 ^ _776545) ^ [_1331152, _1331154, _1331156] : [class_Orderings_Olinorder(_1331152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331152), _1331154)), -(hBOOL(hAPP(hAPP(c_member(_1331152), _1331156), _1331154))), -(c_Big__Operators_Olattice_OInf__fin(_1331152, c_Orderings_Oord__class_Omin(_1331152), hAPP(hAPP(c_Set_Oinsert(_1331152), _1331156), _1331154)) = hAPP(hAPP(c_Finite__Set_Ofold(_1331152, _1331152, c_Orderings_Oord__class_Omin(_1331152)), _1331156), _1331154))], (42506 ^ _776545) ^ [_1622191, _1622193, _1622195, _1622197, _1622199] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1622191, _1622193)), _1622195), hAPP(hAPP(c_List_Ozip(_1622191, _1622193), _1622197), _1622199)) = hAPP(hAPP(c_List_Ozip(_1622191, _1622193), hAPP(hAPP(c_List_Otake(_1622191), _1622195), _1622197)), hAPP(hAPP(c_List_Otake(_1622193), _1622195), _1622199)))], (25181 ^ _776545) ^ [_1232483, _1232485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232483)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232485), _1232483)), _1232483) = _1232485)], (27170 ^ _776545) ^ [_1265549, _1265551] : [c_Nat__Transfer_Onat__set(_1265549), c_Nat__Transfer_Onat__set(_1265551), 27177 ^ _776545 : [(27184 ^ _776545) ^ [] : [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), _1265549)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265549), _1265551)))], (27178 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1265549), _1265551)), -(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), _1265549)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1265551))))]]], (3592 ^ _776545) ^ [_830294, _830296, _830298, _830300, _830302, _830304, _830306, _830308, _830310, _830312] : [-(c_List_Olinorder__class_Oinsort__insert__key(_830312, _830308, _830304, _830300, _830296) = c_List_Olinorder__class_Oinsort__insert__key(_830310, _830306, _830302, _830298, _830294)), _830312 = _830310, _830308 = _830306, _830304 = _830302, _830300 = _830298, _830296 = _830294], (36523 ^ _776545) ^ [_1467925, _1467927, _1467929, _1467931, _1467933] : [-(hBOOL(hAPP(hAPP(c_member(_1467925), _1467927), hAPP(c_Relation_OImage(_1467929, _1467925, _1467931), _1467933)))), 36524 ^ _776545 : [(36525 ^ _776545) ^ [_1468011] : [hBOOL(hAPP(hAPP(c_member(_1467929), _1468011), _1467933)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1467929, _1467925)), hAPP(hAPP(c_Product__Type_OPair(_1467929, _1467925), _1468011), _1467927)), _1467931))]]], (33014 ^ _776545) ^ [_1379271, _1379273] : [-(hAPP(c_Set_OCollect(_1379271), hAPP(hAPP(c_COMBC(_1379271, _1379271, tc_HOL_Obool), c_fequal), _1379273)) = hAPP(hAPP(c_Set_Oinsert(_1379271), _1379273), c_Orderings_Obot__class_Obot(tc_fun(_1379271, tc_HOL_Obool))))], (35668 ^ _776545) ^ [_1442364, _1442366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1442366), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1442364), _1442366) = 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), _1442364), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1442366)))))], (50592 ^ _776545) ^ [_1799195, _1799197, _1799199] : [-(c_Fun_Obij__betw(_1799195, _1799197, _1799199, c_Orderings_Otop__class_Otop(tc_fun(_1799195, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799197, tc_HOL_Obool)))), c_Fun_Oinj__on(_1799195, _1799197, _1799199, c_Orderings_Otop__class_Otop(tc_fun(_1799195, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1799195, _1799197, _1799199), c_Orderings_Otop__class_Otop(tc_fun(_1799195, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799197, tc_HOL_Obool))], (37526 ^ _776545) ^ [_1490749, _1490751] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490749), c_Orderings_Otop__class_Otop(tc_fun(_1490749, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1490749, _1490749, _1490751), c_Orderings_Otop__class_Otop(tc_fun(_1490749, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1490749, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1490749, _1490749, _1490751, c_Orderings_Otop__class_Otop(tc_fun(_1490749, tc_HOL_Obool))))], (22641 ^ _776545) ^ [_1186752, _1186754, _1186756] : [class_Power_Opower(_1186752), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1186752), _1186754), hAPP(c_Nat_OSuc, _1186756)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186752), _1186754), hAPP(hAPP(c_Power_Opower__class_Opower(_1186752), _1186754), _1186756)))], (32970 ^ _776545) ^ [_1378038, _1378040, _1378042, _1378044, _1378046] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378038, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378040, tc_fun(_1378038, tc_HOL_Obool)), _1378042), _1378044)), _1378046) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378040, tc_fun(_1378038, tc_HOL_Obool)), _1378042), hAPP(hAPP(c_COMBC(_1378040, tc_fun(_1378038, tc_HOL_Obool), tc_fun(_1378038, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378038, tc_HOL_Obool), tc_fun(tc_fun(_1378038, tc_HOL_Obool), tc_fun(_1378038, tc_HOL_Obool)), _1378040), c_Groups_Ominus__class_Ominus(tc_fun(_1378038, tc_HOL_Obool))), _1378044)), _1378046)))], (34928 ^ _776545) ^ [_1428159, _1428161] : [_1428159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1428159, _1428161) = 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)))], (42863 ^ _776545) ^ [_1630520, _1630522] : [hBOOL(hAPP(c_List_Odistinct(_1630520), _1630522)), -(hAPP(c_Finite__Set_Ocard(_1630520), hAPP(c_List_Oset(_1630520), _1630522)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630520)), _1630522))], (6240 ^ _776545) ^ [_876837] : [class_Complete__Lattice_Ocomplete__lattice(_876837), -(c_Complete__Lattice_OInf__class_OInf(_876837, c_Orderings_Otop__class_Otop(tc_fun(_876837, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_876837))], (50171 ^ _776545) ^ [_1790446, _1790448, _1790450, _1790452, _1790454] : [c_Fun_Oinj__on(_1790446, _1790448, _1790450, c_Orderings_Otop__class_Otop(tc_fun(_1790446, tc_HOL_Obool))), 50177 ^ _776545 : [(50180 ^ _776545) ^ [] : [hBOOL(hAPP(_1790452, hAPP(c_Hilbert__Choice_Oinv__into(_1790446, _1790448, c_Orderings_Otop__class_Otop(tc_fun(_1790446, tc_HOL_Obool)), _1790450), 50176 ^ [_1790446, _1790448, _1790450, _1790452, _1790454])))], (50178 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790448), 50176 ^ [_1790446, _1790448, _1790450, _1790452, _1790454]), hAPP(c_Set_Oimage(_1790446, _1790448, _1790450), c_Orderings_Otop__class_Otop(tc_fun(_1790446, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1790452, _1790454)))], (34015 ^ _776545) ^ [_1408021, _1408023, _1408025, _1408027] : [class_Complete__Lattice_Ocomplete__lattice(_1408021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408023), _1408025)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408023, _1408021), _1408025), _1408027) = hAPP(hAPP(c_Finite__Set_Ofold(_1408023, _1408021, hAPP(hAPP(c_COMBB(_1408021, tc_fun(_1408021, _1408021), _1408023), c_Lattices_Osemilattice__inf__class_Oinf(_1408021)), _1408027)), c_Orderings_Otop__class_Otop(_1408021)), _1408025))], (21385 ^ _776545) ^ [_1163888, _1163890, _1163892, _1163894] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163888), hAPP(c_Int_Onumber__class_Onumber__of(_1163888), _1163890)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163888), _1163892), _1163894)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163888), hAPP(c_Int_Onumber__class_Onumber__of(_1163888), _1163890)), _1163892)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163888), hAPP(c_Int_Onumber__class_Onumber__of(_1163888), _1163890)), _1163894))), class_Int_Onumber(_1163888), class_Rings_Oring(_1163888)], (26857 ^ _776545) ^ [_1260525, _1260527] : [c_Nat__Transfer_Ois__nat(_1260525), c_Nat__Transfer_Onat__set(_1260527), 26864 ^ _776545 : [(26871 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1260525)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1260527))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1260525), _1260527)))], (26865 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1260525), _1260527)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1260525)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1260527))))]]], (33304 ^ _776545) ^ [_1387209, _1387211, _1387213, _1387215, _1387217, _1387219, _1387221] : [class_Rings_Osemiring__0(_1387209), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387209), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387211, _1387209), _1387213), _1387215)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387217, _1387209), _1387219), _1387221)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387211, _1387209), hAPP(hAPP(c_COMBC(_1387211, tc_fun(_1387217, tc_HOL_Obool), _1387209), hAPP(hAPP(c_COMBB(tc_fun(_1387217, _1387209), tc_fun(tc_fun(_1387217, tc_HOL_Obool), _1387209), _1387211), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1387217, _1387209)), hAPP(hAPP(c_COMBC(_1387211, tc_fun(_1387217, _1387209), tc_fun(_1387217, _1387209)), hAPP(hAPP(c_COMBB(tc_fun(_1387209, _1387209), tc_fun(tc_fun(_1387217, _1387209), tc_fun(_1387217, _1387209)), _1387211), c_COMBB(_1387209, _1387209, _1387217)), hAPP(hAPP(c_COMBB(_1387209, tc_fun(_1387209, _1387209), _1387211), c_Groups_Otimes__class_Otimes(_1387209)), _1387213))), _1387219))), _1387221)), _1387215))], (36659 ^ _776545) ^ [_1471597, _1471599] : [-(c_Relation_OId__on(_1471597, _1471599) = hAPP(c_Product__Type_Oprod_Oprod__case(_1471597, _1471597, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1471597, tc_HOL_Obool, tc_fun(_1471597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471597, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1471597, tc_HOL_Obool)), _1471597), c_COMBC(_1471597, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471597, tc_HOL_Obool), tc_fun(_1471597, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1471597), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471597), c_fconj)), c_fequal))), _1471599)))], (18206 ^ _776545) ^ [_1103915, _1103917, _1103919] : [class_Groups_Oordered__comm__monoid__add(_1103915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103915), _1103917), c_Groups_Ozero__class_Ozero(_1103915))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103915), _1103919), c_Groups_Ozero__class_Ozero(_1103915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103915), _1103917), _1103919)), c_Groups_Ozero__class_Ozero(_1103915))))], (11644 ^ _776545) ^ [_980214, _980216, _980218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_980214), _980216)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980214), _980218)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_980214), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980214, tc_HOL_Obool)), _980216), _980218))))], (10693 ^ _776545) ^ [_960618, _960620] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960618, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960618, tc_HOL_Obool)), _960620)), _960620) = c_Orderings_Otop__class_Otop(tc_fun(_960618, tc_HOL_Obool)))], (16917 ^ _776545) ^ [_1080947, _1080949, _1080951] : [class_Rings_Oordered__cancel__semiring(_1080947), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080947), _1080949), _1080951)), c_Groups_Ozero__class_Ozero(_1080947)))), 16922 ^ _776545 : [(16929 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080947), _1080949), c_Groups_Ozero__class_Ozero(_1080947))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080947), c_Groups_Ozero__class_Ozero(_1080947)), _1080951))], (16923 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080947), c_Groups_Ozero__class_Ozero(_1080947)), _1080949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080947), _1080951), c_Groups_Ozero__class_Ozero(_1080947)))]]], (10104 ^ _776545) ^ [_949508, _949510, _949512, _949514] : [class_Orderings_Oorder(_949508), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949508, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949508, _949510, _949512)), c_SetInterval_Oord__class_OgreaterThanLessThan(_949508, _949512, _949514)) = c_Orderings_Obot__class_Obot(tc_fun(_949508, tc_HOL_Obool)))], (45668 ^ _776545) ^ [_1692549] : [-(c_Enum_Osublists(_1692549, c_List_Olist_ONil(_1692549)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692549)), c_List_Olist_ONil(_1692549)), c_List_Olist_ONil(tc_List_Olist(_1692549))))], (35288 ^ _776545) ^ [_1434965, _1434967, _1434969] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434965, _1434965), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1434967), _1434969))), -(_1434965 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1434969 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24351 ^ _776545) ^ [_1216971, _1216973, _1216975] : [class_Divides_Osemiring__div(_1216971), -(_1216973 = c_Groups_Ozero__class_Ozero(_1216971)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216971), _1216973), _1216975)), _1216973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216971), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1216971), _1216975), _1216973)), c_Groups_Oone__class_Oone(_1216971)))], (6658 ^ _776545) ^ [_884327, _884329, _884331] : [class_Orderings_Oorder(_884327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884327), _884329), _884331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884327), _884331), _884329)), -(_884329 = _884331)], (8255 ^ _776545) ^ [_917702, _917704] : [class_Lattices_Obounded__lattice__top(_917702), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917702), c_Orderings_Otop__class_Otop(_917702)), _917704) = c_Orderings_Otop__class_Otop(_917702))], (47339 ^ _776545) ^ [_1728275, _1728277] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1728275), _1728277) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1728275)), c_List_Oembed__list(_1728277))))], (52389 ^ _776545) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (36533 ^ _776545) ^ [_1468191, _1468193, _1468195, _1468197] : [-(hAPP(c_Relation_OImage(_1468191, _1468193, _1468195), _1468197) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468191, tc_fun(_1468193, tc_HOL_Obool)), _1468197), hAPP(hAPP(c_COMBB(tc_fun(_1468191, tc_HOL_Obool), tc_fun(_1468193, tc_HOL_Obool), _1468191), c_Relation_OImage(_1468191, _1468193, _1468195)), hAPP(hAPP(c_COMBC(_1468191, tc_fun(_1468191, tc_HOL_Obool), tc_fun(_1468191, tc_HOL_Obool)), c_Set_Oinsert(_1468191)), c_Orderings_Obot__class_Obot(tc_fun(_1468191, tc_HOL_Obool))))))], (45036 ^ _776545) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10273 ^ _776545) ^ [_953139, _953141, _953143] : [-(hBOOL(hAPP(hAPP(c_member(_953139), _953141), _953143))), -(hBOOL(hAPP(hAPP(c_member(_953139), _953141), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953139, tc_HOL_Obool)), _953143))))], (43583 ^ _776545) ^ [_1645946, _1645948] : [-(hAPP(hAPP(c_List_Oappend(_1645946), _1645948), c_List_Olist_ONil(_1645946)) = _1645948)], (31505 ^ _776545) ^ [_1342228, _1342230, _1342232, _1342234] : [class_Orderings_Olinorder(_1342228), 31508 ^ _776545 : [(31517 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342228), _1342230), _1342232)), _1342234))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), _1342230), _1342234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), _1342232), _1342234))], (31509 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342228), _1342230), _1342232)), _1342234)), 31512 ^ _776545 : [(31515 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), _1342232), _1342234)))], (31513 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342228), _1342230), _1342234)))]]]]], (45662 ^ _776545) ^ [_1692373, _1692375, _1692377, _1692379] : [-(hAPP(c_List_Oset(tc_prod(_1692373, _1692375)), c_Enum_Oproduct(_1692373, _1692375, _1692377, _1692379)) = hAPP(hAPP(c_Product__Type_OSigma(_1692373, _1692375), hAPP(c_List_Oset(_1692373), _1692377)), hAPP(c_COMBK(tc_fun(_1692375, tc_HOL_Obool), _1692373), hAPP(c_List_Oset(_1692375), _1692379))))], (11024 ^ _776545) ^ [_967101, _967103, _967105] : [class_Lattices_Oab__semigroup__idem__mult(_967101), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967101), _967103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967101), _967103), _967105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967101), _967103), _967105))], (38034 ^ _776545) ^ [_1504396, _1504398, _1504400, _1504402, _1504404, _1504406, _1504408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504396, _1504400)), hAPP(hAPP(c_Product__Type_OPair(_1504396, _1504400), _1504406), _1504408)), hAPP(hAPP(c_Relation_Orel__comp(_1504396, _1504398, _1504400), _1504402), _1504404))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1504396, _1504398, _1504400, hAPP(hAPP(c_COMBC(_1504396, tc_fun(tc_prod(_1504396, 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_1504400), tc_HOL_Obool), tc_fun(_1504400, tc_HOL_Obool)), _1504398), c_COMBC(_1504400, tc_fun(tc_prod(_1504398, _1504400), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504400, tc_prod(_1504398, _1504400)), tc_fun(_1504400, tc_fun(tc_fun(tc_prod(_1504398, _1504400), tc_HOL_Obool), tc_HOL_Obool)), _1504398), hAPP(c_COMBB(tc_prod(_1504398, _1504400), tc_fun(tc_fun(tc_prod(_1504398, _1504400), tc_HOL_Obool), tc_HOL_Obool), _1504400), c_member(tc_prod(_1504398, _1504400)))), c_Product__Type_OPair(_1504398, _1504400)))), _1504404)), _1504406), _1504408)))], (9332 ^ _776545) ^ [_937071, _937073, _937075] : [class_Orderings_Olinorder(_937071), 9335 ^ _776545 : [(9342 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937071), _937073), _937075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937071, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_937071), _937073)), hAPP(c_SetInterval_Oord__class_OlessThan(_937071), _937075))))], (9336 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937071, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_937071), _937073)), hAPP(c_SetInterval_Oord__class_OlessThan(_937071), _937075))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937071), _937073), _937075)))]]], (5685 ^ _776545) ^ [_866191, _866193, _866195] : [_866193 = _866195, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(_866191)), _866193), _866195)))], (23916 ^ _776545) ^ [] : [-(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)))], (8321 ^ _776545) ^ [_919117, _919119, _919121] : [class_Lattices_Osemilattice__sup(_919117), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919117), _919119), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919117), _919119), _919121)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919117), _919119), _919121))], (35042 ^ _776545) ^ [_1430446, _1430448, _1430450, _1430452] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430446, _1430448), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1430450), _1430452))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1430446, _1430448) = _1430452)], (44942 ^ _776545) ^ [_1676368, _1676370, _1676372, _1676374] : [class_Groups_Oab__group__add(_1676368), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1676368), hAPP(c_List_Omonoid__add__class_Olistsum(_1676368), hAPP(hAPP(c_List_Omap(_1676370, _1676368), _1676372), _1676374))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1676368), hAPP(hAPP(c_List_Omap(_1676370, _1676368), hAPP(c_Fun_Ocomp(_1676368, _1676368, _1676370, c_Groups_Ouminus__class_Ouminus(_1676368)), _1676372)), _1676374)))], (40753 ^ _776545) ^ [_1573878, _1573880] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573878, _1573878, _1573878), c_Transitive__Closure_Ortrancl(_1573878, _1573880)), c_Transitive__Closure_Ortrancl(_1573878, _1573880)) = c_Transitive__Closure_Ortrancl(_1573878, _1573880))], (8131 ^ _776545) ^ [_915120, _915122, _915124] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_915120, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_915120, tc_HOL_Obool)), _915122), _915124)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915120, tc_HOL_Obool)), _915122), c_Complete__Lattice_OInf__class_OInf(tc_fun(_915120, tc_HOL_Obool), _915124)))], (49967 ^ _776545) ^ [_1785515, _1785517] : [c_Equiv__Relations_Opart__equivp(_1785515, _1785517), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1785515, tc_HOL_Obool)), 49970 ^ [_1785515, _1785517]), hAPP(hAPP(c_COMBB(tc_fun(_1785515, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1785515, tc_HOL_Obool)), c_HOL_OEx(_1785515)), hAPP(hAPP(c_COMBB(tc_fun(_1785515, tc_HOL_Obool), tc_fun(_1785515, tc_HOL_Obool), tc_fun(_1785515, tc_HOL_Obool)), hAPP(c_COMBS(_1785515, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785515), c_fconj), hAPP(hAPP(c_COMBS(_1785515, _1785515, tc_HOL_Obool), _1785517), c_COMBI(_1785515))))), hAPP(hAPP(c_COMBC(tc_fun(_1785515, tc_HOL_Obool), tc_fun(_1785515, tc_fun(_1785515, tc_HOL_Obool)), tc_fun(_1785515, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1785515, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1785515, tc_fun(_1785515, tc_HOL_Obool)), tc_fun(_1785515, tc_HOL_Obool)), tc_fun(_1785515, tc_HOL_Obool)), c_COMBB(tc_fun(_1785515, tc_HOL_Obool), tc_HOL_Obool, _1785515)), c_fequal)), _1785517))))))], (31893 ^ _776545) ^ [_1349546, _1349548, _1349550] : [class_Orderings_Olinorder(_1349546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349546), _1349548)), -(_1349548 = c_Orderings_Obot__class_Obot(tc_fun(_1349546, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349546), _1349550)), -(_1349550 = c_Orderings_Obot__class_Obot(tc_fun(_1349546, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349546, tc_HOL_Obool)), _1349548), _1349550) = c_Orderings_Obot__class_Obot(tc_fun(_1349546, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1349546, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349546, tc_HOL_Obool)), _1349548), _1349550)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1349546), c_Big__Operators_Olinorder__class_OMax(_1349546, _1349548)), c_Big__Operators_Olinorder__class_OMax(_1349546, _1349550)))], (29473 ^ _776545) ^ [] : [-(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))))], (38727 ^ _776545) ^ [_1521030, _1521032, _1521034, _1521036, _1521038] : [-(hAPP(c_Set_Ovimage(_1521030, _1521032, _1521034), hAPP(hAPP(c_Set_Oinsert(_1521032), _1521036), _1521038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521030, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521030, _1521032, _1521034), hAPP(hAPP(c_Set_Oinsert(_1521032), _1521036), c_Orderings_Obot__class_Obot(tc_fun(_1521032, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1521030, _1521032, _1521034), _1521038)))], (45808 ^ _776545) ^ [_1695616, _1695618] : [c_List_Olist_ONil(_1695616) = c_List_Oremdups(_1695616, _1695618), -(_1695618 = c_List_Olist_ONil(_1695616))], (23501 ^ _776545) ^ [_1202494, _1202496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202494)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202496)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1202496), _1202494)), _1202496) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1202496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202494), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (4062 ^ _776545) ^ [_837975, _837977, _837979, _837981, _837983, _837985, _837987, _837989] : [-(c_New__Random__Sequence_Oneg__map(_837989, _837985, _837981, _837977) = c_New__Random__Sequence_Oneg__map(_837987, _837983, _837979, _837975)), _837989 = _837987, _837985 = _837983, _837981 = _837979, _837977 = _837975], (22605 ^ _776545) ^ [_1186127, _1186129] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1186127), c_Groups_Ozero__class_Ozero(_1186127)), hAPP(c_Nat_OSuc, _1186129)) = c_Groups_Ozero__class_Ozero(_1186127)), class_Power_Opower(_1186127), class_Rings_Osemiring__0(_1186127)], (6079 ^ _776545) ^ [_873818, _873820, _873822, _873824, _873826, _873828] : [hBOOL(hAPP(hAPP(c_member(_873818), _873820), c_SetInterval_Oord_OgreaterThanAtMost(_873818, _873822, _873824, _873826, _873828))), 6082 ^ _776545 : [(6085 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873822, _873820), _873828)))], (6083 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_873824, _873826), _873820)))]]], (5739 ^ _776545) ^ [_867014, _867016] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867014, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867014)), tc_HOL_Obool)), hAPP(c_Hoare__Mirabelle_ORep__triple(_867014), _867016)), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_867014, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _867014)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_867014)))))], (28169 ^ _776545) ^ [_1282353, _1282355, _1282357] : [class_Rings_Osemiring__1(_1282353), hBOOL(hAPP(hAPP(c_member(_1282353), _1282355), c_Nat_Osemiring__1__class_ONats(_1282353))), hBOOL(hAPP(hAPP(c_member(_1282353), _1282357), c_Nat_Osemiring__1__class_ONats(_1282353))), -(hBOOL(hAPP(hAPP(c_member(_1282353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282353), _1282355), _1282357)), c_Nat_Osemiring__1__class_ONats(_1282353))))], (33052 ^ _776545) ^ [_1380220, _1380222, _1380224, _1380226] : [-(hAPP(c_Set_Oimage(_1380220, _1380222, _1380224), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1380220, tc_HOL_Obool), _1380226)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1380220, tc_HOL_Obool), tc_fun(_1380222, tc_HOL_Obool)), _1380226), c_Set_Oimage(_1380220, _1380222, _1380224)))], (42853 ^ _776545) ^ [_1630326, _1630328, _1630330] : [-(hBOOL(hAPP(c_List_Odistinct(_1630326), hAPP(hAPP(c_List_Olist_OCons(_1630326), _1630328), _1630330)))), -(hBOOL(hAPP(hAPP(c_member(_1630326), _1630328), hAPP(c_List_Oset(_1630326), _1630330)))), hBOOL(hAPP(c_List_Odistinct(_1630326), _1630330))], (39047 ^ _776545) ^ [_1528507, _1528509, _1528511, _1528513] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528507, _1528509), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1528507, tc_HOL_Obool), _1528511)), _1528513) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1528507, tc_HOL_Obool), tc_fun(tc_prod(_1528507, _1528509), tc_HOL_Obool)), _1528511), hAPP(hAPP(c_COMBC(tc_fun(_1528507, tc_HOL_Obool), tc_fun(_1528507, tc_fun(_1528509, tc_HOL_Obool)), tc_fun(tc_prod(_1528507, _1528509), tc_HOL_Obool)), c_Product__Type_OSigma(_1528507, _1528509)), _1528513)))], (22887 ^ _776545) ^ [_1191252, _1191254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1191252)), -(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), _1191252), _1191254))))], (21261 ^ _776545) ^ [_1161171, _1161173, _1161175] : [class_Int_Onumber__ring(_1161171), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1161173), _1161175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161171), hAPP(c_Int_Onumber__class_Onumber__of(_1161171), _1161173)), hAPP(c_Int_Onumber__class_Onumber__of(_1161171), _1161175)))], (40176 ^ _776545) ^ [_1559368, _1559370, _1559372, _1559374, _1559376, _1559378] : [c_Finite__Set_Ofolding(_1559368, _1559370, _1559372, _1559374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559368), _1559376)), -(hAPP(hAPP(_1559374, _1559376), _1559378) = hAPP(hAPP(c_Finite__Set_Ofold(_1559368, _1559370, _1559372), _1559378), _1559376))], (34711 ^ _776545) ^ [_1423341, _1423343, _1423345, _1423347, _1423349] : [-(hAPP(c_Nat_Onat_Onat__rec(_1423341, _1423343, _1423345), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1423347)), _1423349)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1423341), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1423347))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423341, _1423341), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1423341, tc_fun(_1423341, _1423341)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1423341, tc_fun(_1423341, _1423341)), tc_Int_Oint), c_If(_1423341)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1423341, _1423343, _1423345), _1423349))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1423341, _1423341), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1423341, _1423341), tc_Int_Oint), _1423345), 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)), _1423349))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1423341, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1423341, _1423343, _1423345)), 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)), _1423349))))))], (49434 ^ _776545) ^ [_1776009, _1776011, _1776013, _1776015, _1776017] : [c_Predicate_Otransp(_1776009, _1776011), hBOOL(hAPP(hAPP(_1776011, _1776013), _1776015)), hBOOL(hAPP(hAPP(_1776011, _1776015), _1776017)), -(hBOOL(hAPP(hAPP(_1776011, _1776013), _1776017)))], (48468 ^ _776545) ^ [_1753074, _1753076] : [-(c_List_Osplice(_1753074, c_List_Olist_ONil(_1753074), _1753076) = _1753076)], (33144 ^ _776545) ^ [_1382767, _1382769, _1382771] : [_1382769 = _1382771, -(hAPP(hAPP(c_COMBC(_1382767, tc_fun(_1382767, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382767)), _1382769) = hAPP(hAPP(c_COMBC(_1382767, tc_fun(_1382767, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382767)), _1382771))], (13724 ^ _776545) ^ [_1021009, _1021011, _1021013, _1021015, _1021017] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1021009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021009), _1021011), _1021013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021009), _1021015), _1021017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1021009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021009), _1021011), _1021015)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1021009), _1021013), _1021017))))], (28859 ^ _776545) ^ [_1293939, _1293941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293939), _1293941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293939)), c_Int_OBit0(_1293941))))], (46026 ^ _776545) ^ [_1700564, _1700566, _1700568] : [-(c_Enum_On__lists(_1700564, hAPP(c_Nat_OSuc, _1700566), _1700568) = c_List_Oconcat(tc_List_Olist(_1700564), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700564), tc_List_Olist(tc_List_Olist(_1700564))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700564), tc_List_Olist(_1700564), tc_List_Olist(tc_List_Olist(_1700564))), hAPP(hAPP(c_COMBB(tc_fun(_1700564, tc_List_Olist(_1700564)), tc_fun(tc_List_Olist(_1700564), tc_List_Olist(tc_List_Olist(_1700564))), tc_List_Olist(_1700564)), c_List_Omap(_1700564, tc_List_Olist(_1700564))), hAPP(c_COMBC(_1700564, tc_List_Olist(_1700564), tc_List_Olist(_1700564)), c_List_Olist_OCons(_1700564)))), _1700568)), c_Enum_On__lists(_1700564, _1700566, _1700568))))], (1094 ^ _776545) ^ [_793084, _793086] : [-(class_Rings_Olinordered__semiring__1__strict(_793084)), _793086 = _793084, class_Rings_Olinordered__semiring__1__strict(_793086)], (42585 ^ _776545) ^ [_1624396, _1624398] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1624396, _1624398) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1624396), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1624398), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (34209 ^ _776545) ^ [_1412553, _1412555] : [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(_1412555))), 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), _1412553)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412553)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412555))))], (48786 ^ _776545) ^ [_1759940, _1759942, _1759944, _1759946, _1759948] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1759940, _1759942, _1759944) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1759940, _1759946, _1759948), 48789 ^ _776545 : [(48792 ^ _776545) ^ [] : [-(_1759944 = _1759948)], (48790 ^ _776545) ^ [] : [-(_1759942 = _1759946)]]], (28481 ^ _776545) ^ [_1287689] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1287689))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1287689)))))], (43797 ^ _776545) ^ [_1650851, _1650853, _1650855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1650851), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650853)), _1650855))), -(hAPP(hAPP(c_List_Otake(_1650853), hAPP(c_Nat_OSuc, _1650851)), _1650855) = hAPP(hAPP(c_List_Oappend(_1650853), hAPP(hAPP(c_List_Otake(_1650853), _1650851), _1650855)), hAPP(hAPP(c_List_Olist_OCons(_1650853), hAPP(hAPP(c_List_Onth(_1650853), _1650855), _1650851)), c_List_Olist_ONil(_1650853))))], (32506 ^ _776545) ^ [_1363468, _1363470, _1363472, _1363474, _1363476] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363468, tc_fun(_1363470, tc_HOL_Obool)), _1363472), hAPP(hAPP(c_COMBB(tc_fun(_1363470, tc_HOL_Obool), tc_fun(_1363470, tc_HOL_Obool), _1363468), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363470, tc_HOL_Obool)), _1363474)), _1363476)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363470, tc_HOL_Obool)), _1363474), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1363468, tc_fun(_1363470, tc_HOL_Obool)), _1363472), _1363476)))], (29087 ^ _776545) ^ [_1297917, _1297919] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1297917)), c_Int_OBit0(_1297919)))], (40012 ^ _776545) ^ [_1555498, _1555500, _1555502, _1555504, _1555506, _1555508, _1555510] : [c_Fun_Oinj__on(_1555498, _1555500, _1555502, hAPP(c_Set_Oimage(_1555504, _1555498, _1555506), _1555508)), c_Fun_Oinj__on(_1555504, _1555498, _1555506, _1555508), hBOOL(hAPP(hAPP(c_member(_1555500), _1555510), hAPP(c_Set_Oimage(_1555498, _1555500, _1555502), hAPP(c_Set_Oimage(_1555504, _1555498, _1555506), _1555508)))), -(hAPP(c_Fun_Othe__inv__into(_1555504, _1555500, _1555508, hAPP(c_Fun_Ocomp(_1555498, _1555500, _1555504, _1555502), _1555506)), _1555510) = hAPP(hAPP(c_Fun_Ocomp(_1555498, _1555504, _1555500, c_Fun_Othe__inv__into(_1555504, _1555498, _1555508, _1555506)), c_Fun_Othe__inv__into(_1555498, _1555500, hAPP(c_Set_Oimage(_1555504, _1555498, _1555506), _1555508), _1555502)), _1555510))], (8495 ^ _776545) ^ [_922485, _922487, _922489] : [class_Lattices_Osemilattice__sup(_922485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922485), _922487), _922489)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922485), _922489), _922487) = _922489)], (41116 ^ _776545) ^ [_1582837, _1582839] : [-(hAPP(c_Relation_Oconverse(_1582837, _1582837), c_Relation_OId__on(_1582837, _1582839)) = c_Relation_OId__on(_1582837, _1582839))], (6672 ^ _776545) ^ [_884540, _884542, _884544, _884546] : [class_Orderings_Oorder(_884540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884540), _884542), _884544)), _884542 = _884546, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884540), _884546), _884544)))], (43817 ^ _776545) ^ [_1651481, _1651483, _1651485, _1651487, _1651489, _1651491] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651481), tc_List_Olist(_1651481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651481), tc_List_Olist(_1651481)), hAPP(hAPP(c_List_Oappend(_1651481), _1651483), hAPP(hAPP(c_List_Olist_OCons(_1651481), _1651485), c_List_Olist_ONil(_1651481)))), hAPP(hAPP(c_List_Oappend(_1651481), _1651487), hAPP(hAPP(c_List_Olist_OCons(_1651481), _1651489), c_List_Olist_ONil(_1651481))))), c_List_Olistrel1(_1651481, _1651491)))), 43818 ^ _776545 : [(43825 ^ _776545) ^ [] : [_1651483 = _1651487, hBOOL(hAPP(hAPP(c_member(tc_prod(_1651481, _1651481)), hAPP(hAPP(c_Product__Type_OPair(_1651481, _1651481), _1651485), _1651489)), _1651491))], (43819 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651481), tc_List_Olist(_1651481))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651481), tc_List_Olist(_1651481)), _1651483), _1651487)), c_List_Olistrel1(_1651481, _1651491))), _1651485 = _1651489]]], (47363 ^ _776545) ^ [_1728934, _1728936, _1728938] : [-(hAPP(hAPP(c_List_Oappend(_1728934), c_List_OtakeWhile(_1728934, _1728936, _1728938)), c_List_OdropWhile(_1728934, _1728936, _1728938)) = _1728938)], (33340 ^ _776545) ^ [_1388379, _1388381, _1388383, _1388385, _1388387] : [class_Fields_Ofield(_1388379), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388379), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388381, _1388379), _1388383), _1388385)), _1388387) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1388381, _1388379), hAPP(hAPP(c_COMBC(_1388381, _1388379, _1388379), hAPP(hAPP(c_COMBB(_1388379, tc_fun(_1388379, _1388379), _1388381), c_Rings_Oinverse__class_Odivide(_1388379)), _1388383)), _1388387)), _1388385))], (1194 ^ _776545) ^ [_794334, _794336] : [-(class_Rings_Olinordered__idom(_794334)), _794336 = _794334, class_Rings_Olinordered__idom(_794336)], (48452 ^ _776545) ^ [_1752602, _1752604, _1752606, _1752608, _1752610] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1752602), _1752604), _1752606), _1752608), _1752610) = c_New__DSequence_Oneg__single(_1752602, _1752604))], (15222 ^ _776545) ^ [_1051237, _1051239, _1051241] : [class_Rings_Ocomm__semiring__1(_1051237), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051237), _1051239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051237), _1051241), _1051239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051237), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051237), _1051241), c_Groups_Oone__class_Oone(_1051237))), _1051239))], (38219 ^ _776545) ^ [_1508399, _1508401, _1508403, _1508405] : [c_Wellfounded_Owf(_1508399, _1508401), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508399, _1508399)), hAPP(hAPP(c_Product__Type_OPair(_1508399, _1508399), _1508403), _1508405)), _1508401)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508399, _1508399)), hAPP(hAPP(c_Product__Type_OPair(_1508399, _1508399), _1508405), _1508403)), _1508401))], (44044 ^ _776545) ^ [_1657183, _1657185, _1657187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657183), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657185)), _1657187))), -(hAPP(hAPP(c_List_Olist_OCons(_1657185), hAPP(hAPP(c_List_Onth(_1657185), _1657187), _1657183)), hAPP(hAPP(c_List_Odrop(_1657185), hAPP(c_Nat_OSuc, _1657183)), _1657187)) = hAPP(hAPP(c_List_Odrop(_1657185), _1657183), _1657187))], (27361 ^ _776545) ^ [_1268797] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1268797), c_Int_OPls) = _1268797)], (49297 ^ _776545) ^ [_1771862, _1771864] : [c_Relation_Otrans(_1771862, _1771864), -(c_Transitive__Closure_Otrancl(_1771862, _1771864) = _1771864)], (5877 ^ _776545) ^ [_869980, _869982] : [-(hAPP(c_Set_OCollect(_869980), _869982) = _869982)], (52471 ^ _776545) ^ [_1831066, _1831068, _1831070, _1831072, _1831074, _1831076] : [-(hAPP(hAPP(hAPP(c_COMBC(_1831066, _1831068, _1831070), _1831072), _1831074), _1831076) = hAPP(hAPP(_1831072, _1831076), _1831074))], (7400 ^ _776545) ^ [_898081, _898083, _898085, _898087] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898081, tc_HOL_Obool)), _898083), hAPP(hAPP(c_Set_Oinsert(_898081), _898085), _898087)))), 7403 ^ _776545 : [(7406 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898081, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898081, tc_HOL_Obool)), _898083), hAPP(hAPP(c_Set_Oinsert(_898081), _898085), c_Orderings_Obot__class_Obot(tc_fun(_898081, tc_HOL_Obool))))), _898087))], (7404 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898081), _898085), _898083)))]], 7407 ^ _776545 : [(7410 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898081, tc_HOL_Obool)), _898083), _898087))], (7408 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898081), _898085), _898083))]]], (566 ^ _776545) ^ [_785074, _785076, _785078, _785080, _785082, _785084] : [-(c_Finite__Set_Ofun__left__comm(_785082, _785078, _785074)), c_Finite__Set_Ofun__left__comm(_785084, _785080, _785076), _785084 = _785082, _785080 = _785078, _785076 = _785074], (7940 ^ _776545) ^ [_910734, _910736, _910738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910734, tc_HOL_Obool)), _910736), _910738)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910734, tc_HOL_Obool)), _910736), _910738) = _910738)], (52011 ^ _776545) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (7890 ^ _776545) ^ [_909508, _909510, _909512, _909514, _909516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909508, tc_HOL_Obool)), _909510), _909512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909508, tc_HOL_Obool)), _909514), _909516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909508, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909508, tc_HOL_Obool)), _909510), _909516)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909508, tc_HOL_Obool)), _909512), _909514))))], (35708 ^ _776545) ^ [_1443217, _1443219] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1443217), _1443219) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1443217, _1443219)))], (46321 ^ _776545) ^ [_1708208, _1708210] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1708208), _1708210))), -(c_List_Oupt(_1708208, hAPP(c_Nat_OSuc, _1708210)) = c_List_Olist_ONil(tc_Nat_Onat))], (25748 ^ _776545) ^ [_1242505, _1242507, _1242509, _1242511] : [_1242505 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242507), _1242509)), _1242511), -(_1242507 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242505, _1242507) = _1242511), 25755 ^ _776545 : [(25758 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242511), _1242507))], (25756 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242507)))]], 25763 ^ _776545 : [(25766 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242507), _1242511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242511), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25764 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242507))]]], (33453 ^ _776545) ^ [_1391575, _1391577, _1391579, _1391581] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1391575, tc_HOL_Obool), tc_fun(_1391577, tc_HOL_Obool)), _1391579), hAPP(hAPP(c_COMBC(tc_fun(_1391575, tc_HOL_Obool), tc_fun(_1391575, tc_fun(_1391577, tc_HOL_Obool)), tc_fun(_1391577, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391575, tc_fun(_1391577, tc_HOL_Obool))), _1391581)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391575, tc_fun(_1391577, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1391575, tc_HOL_Obool), _1391579)), _1391581))], (28081 ^ _776545) ^ [_1280999, _1281001] : [class_Int_Onumber__ring(_1280999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1281001)), -(hBOOL(hAPP(hAPP(c_member(_1280999), hAPP(c_Int_Onumber__class_Onumber__of(_1280999), _1281001)), c_Nat_Osemiring__1__class_ONats(_1280999))))], (48838 ^ _776545) ^ [_1760788, _1760790, _1760792] : [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), _1760788), _1760790))), -(hBOOL(hAPP(hAPP(_1760792, _1760788), _1760790))), 48845 ^ _776545 : [(48848 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48843 ^ [_1760788, _1760790, _1760792]), 48844 ^ [_1760788, _1760790, _1760792]))), -(hBOOL(hAPP(hAPP(_1760792, 48843 ^ [_1760788, _1760790, _1760792]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48844 ^ [_1760788, _1760790, _1760792]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48854 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1760792, 48843 ^ [_1760788, _1760790, _1760792]), 48844 ^ [_1760788, _1760790, _1760792]))], (48846 ^ _776545) ^ [] : [-(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), 48843 ^ [_1760788, _1760790, _1760792]), 48844 ^ [_1760788, _1760790, _1760792]))))]]], (45723 ^ _776545) ^ [_1693891, _1693893, _1693895, _1693897] : [45725 ^ _776545 : [(45728 ^ _776545) ^ [] : [hBOOL(hAPP(_1693895, hAPP(hAPP(c_List_Onth(_1693891), _1693893), 45724 ^ [_1693891, _1693893, _1693895, _1693897])))], (45726 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45724 ^ [_1693891, _1693893, _1693895, _1693897]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693891)), _1693893))))]], hBOOL(hAPP(hAPP(c_member(_1693891), _1693897), hAPP(c_List_Oset(_1693891), _1693893))), -(hBOOL(hAPP(_1693895, _1693897)))], (35642 ^ _776545) ^ [_1441921, _1441923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1441921), 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)), _1441923)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441921), _1441923) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1441921, _1441923)))], (29351 ^ _776545) ^ [_1302512, _1302514] : [class_Fields_Olinordered__field__inverse__zero(_1302512), class_Int_Onumber__ring(_1302512), 29358 ^ _776545 : [(29365 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302512), c_Groups_Ozero__class_Ozero(_1302512)), _1302514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302512), c_Groups_Ozero__class_Ozero(_1302512)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302512), _1302514), hAPP(c_Int_Onumber__class_Onumber__of(_1302512), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29359 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302512), c_Groups_Ozero__class_Ozero(_1302512)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302512), _1302514), hAPP(c_Int_Onumber__class_Onumber__of(_1302512), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302512), c_Groups_Ozero__class_Ozero(_1302512)), _1302514)))]]], (33743 ^ _776545) ^ [_1400517, _1400519, _1400521, _1400523, _1400525] : [hBOOL(hAPP(hAPP(c_member(_1400517), _1400519), _1400521)), -(hAPP(c_Set_Oimage(_1400517, _1400523, hAPP(c_COMBK(_1400523, _1400517), _1400525)), _1400521) = hAPP(hAPP(c_Set_Oinsert(_1400523), _1400525), c_Orderings_Obot__class_Obot(tc_fun(_1400523, tc_HOL_Obool))))], (28281 ^ _776545) ^ [_1284317, _1284319] : [class_Int_Onumber__ring(_1284317), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1284317), c_Groups_Oone__class_Oone(_1284317)), hAPP(c_Int_Onumber__class_Onumber__of(_1284317), _1284319)) = hAPP(c_Int_Onumber__class_Onumber__of(_1284317), 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), _1284319))))], (36602 ^ _776545) ^ [_1470106, _1470108] : [-(hAPP(c_Relation_OField(_1470106), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1470106, _1470106), tc_HOL_Obool), _1470108)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1470106, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1470106, _1470106), tc_HOL_Obool), tc_fun(_1470106, tc_HOL_Obool), c_Relation_OField(_1470106)), _1470108)))], (1634 ^ _776545) ^ [_799834, _799836] : [-(class_Groups_Ocomm__monoid__mult(_799834)), _799836 = _799834, class_Groups_Ocomm__monoid__mult(_799836)], (46227 ^ _776545) ^ [_1706082, _1706084, _1706086, _1706088] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706082)), _1706084))), c_List_Ofoldr(tc_List_Olist(_1706086), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706086)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706086))), _1706088, 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(_1706082)), _1706084)), c_List_Ofoldr(tc_List_Olist(_1706086), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706086)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706086), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1706086)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706086)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1706086), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1706086)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706086), tc_List_Olist(_1706086), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1706086)))), _1706088), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (27090 ^ _776545) ^ [_1264304, _1264306] : [class_Rings_Olinordered__idom(_1264304), 27093 ^ _776545 : [(27100 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264304), hAPP(c_Int_Oring__1__class_Oof__int(_1264304), _1264306)), c_Groups_Ozero__class_Ozero(_1264304))))], (27094 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264304), hAPP(c_Int_Oring__1__class_Oof__int(_1264304), _1264306)), c_Groups_Ozero__class_Ozero(_1264304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1264306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (52475 ^ _776545) ^ [_1831173, _1831175] : [hBOOL(hAPP(hAPP(c_fequal, _1831173), _1831175)), -(_1831173 = _1831175)], (40576 ^ _776545) ^ [_1568906, _1568908] : [c_Wellfounded_Owf(_1568906, _1568908), -(c_Wellfounded_Owf(_1568906, c_Transitive__Closure_Otrancl(_1568906, _1568908)))], (45424 ^ _776545) ^ [_1687017, _1687019, _1687021, _1687023, _1687025] : [c_List_Olist__all2(_1687017, _1687019, _1687021, _1687023, _1687025), 45427 ^ _776545 : [(45430 ^ _776545) ^ [_1687183] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1687017, _1687019)), _1687183), hAPP(c_List_Oset(tc_prod(_1687017, _1687019)), hAPP(hAPP(c_List_Ozip(_1687017, _1687019), _1687023), _1687025)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687017, _1687019, tc_HOL_Obool), _1687021), _1687183)))], (45428 ^ _776545) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687017)), _1687023) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687019)), _1687025))]]], (29081 ^ _776545) ^ [_1297816] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1297816)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1297816))))], (43956 ^ _776545) ^ [_1654975, _1654977, _1654979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654975)), _1654977)), _1654979)), -(hAPP(hAPP(c_List_Odrop(_1654975), _1654979), _1654977) = c_List_Olist_ONil(_1654975))], (5837 ^ _776545) ^ [_869151, _869153, _869155] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869151, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869151)), tc_HOL_Obool)), _869153), hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom, tc_fun(_869151, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_sum(tc_Com_Ostate, _869151)), tc_HOL_Obool)), c_Hoare__Mirabelle_Otriple_Otriple__rep__set(_869151)))), hBOOL(hAPP(_869155, hAPP(c_Hoare__Mirabelle_ORep__triple(_869151), 5842 ^ [_869151, _869153, _869155]))), -(hBOOL(hAPP(_869155, _869153)))], (8090 ^ _776545) ^ [_914136, _914138, _914140] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914136, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_914136, tc_HOL_Obool), _914138)), _914140) = c_Orderings_Obot__class_Obot(tc_fun(_914136, tc_HOL_Obool)), 8093 ^ _776545 : [(8094 ^ _776545) ^ [_914271] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_914136, tc_HOL_Obool)), _914271), _914138)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_914136, tc_HOL_Obool)), _914271), _914140) = c_Orderings_Obot__class_Obot(tc_fun(_914136, tc_HOL_Obool)))]]], (31164 ^ _776545) ^ [_1335859, _1335861, _1335863] : [class_Orderings_Olinorder(_1335859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335859), _1335861)), hBOOL(hAPP(hAPP(c_member(_1335859), _1335863), _1335861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335859), _1335863), c_Big__Operators_Olinorder__class_OMax(_1335859, _1335861))))], (20513 ^ _776545) ^ [_1146727, _1146729, _1146731, _1146733] : [class_Fields_Olinordered__field(_1146727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146727), _1146729), _1146731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146727), c_Groups_Ozero__class_Ozero(_1146727)), _1146733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146727), c_Groups_Ozero__class_Ozero(_1146727)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146727), _1146731), _1146729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146727), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146727), _1146733), _1146731)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146727), _1146733), _1146729))))], (10767 ^ _776545) ^ [_961991, _961993] : [class_Orderings_Olinorder(_961991), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961991, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_961991), _961993)) = hAPP(c_SetInterval_Oord__class_OatMost(_961991), _961993))], (34858 ^ _776545) ^ [_1427030, _1427032, _1427034, _1427036, _1427038, _1427040] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1427030, _1427032, _1427034), _1427036), hAPP(hAPP(c_Product__Type_OPair(_1427030, _1427032), _1427038), _1427040)) = hAPP(hAPP(_1427036, _1427038), _1427040))], (24966 ^ _776545) ^ [_1228696, _1228698, _1228700] : [-(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, _1228696, _1228698)), _1228700), _1228698) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1228696), _1228700), _1228698))], (35811 ^ _776545) ^ [_1445307, _1445309] : [_1445307 = _1445309, -(hAPP(c_Int_ORep__Integ, _1445307) = hAPP(c_Int_ORep__Integ, _1445309))], (43018 ^ _776545) ^ [_1633961] : [-(hBOOL(hAPP(c_List_Odistinct(_1633961), c_List_Olist_ONil(_1633961))))], (27305 ^ _776545) ^ [_1267835, _1267837] : [class_Groups_Oordered__ab__group__add__abs(_1267835), -(hAPP(c_Groups_Oabs__class_Oabs(_1267835), hAPP(c_Groups_Ouminus__class_Ouminus(_1267835), _1267837)) = hAPP(c_Groups_Oabs__class_Oabs(_1267835), _1267837))], (22239 ^ _776545) ^ [_1179851, _1179853, _1179855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179851), _1179853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179855), _1179851)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179855), _1179853))))], (35461 ^ _776545) ^ [_1437949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1437949)), 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), _1437949)) = 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), _1437949))))))], (43525 ^ _776545) ^ [_1644581, _1644583, _1644585, _1644587, _1644589] : [-(hAPP(hAPP(c_List_Oappend(_1644581), _1644583), _1644585) = hAPP(hAPP(c_List_Oappend(_1644581), _1644587), _1644589)), 43526 ^ _776545 : [(43533 ^ _776545) ^ [_1644805] : [hAPP(hAPP(c_List_Oappend(_1644581), _1644583), _1644805) = _1644587, _1644585 = hAPP(hAPP(c_List_Oappend(_1644581), _1644805), _1644589)], (43527 ^ _776545) ^ [_1644693] : [_1644583 = hAPP(hAPP(c_List_Oappend(_1644581), _1644587), _1644693), hAPP(hAPP(c_List_Oappend(_1644581), _1644693), _1644585) = _1644589]]], (19813 ^ _776545) ^ [_1134121, _1134123, _1134125, _1134127] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1134121, _1134123)), c_Sum__Type_OPlus(_1134121, _1134123, _1134125, _1134127))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1134123), _1134127)))], (32318 ^ _776545) ^ [_1357744, _1357746, _1357748, _1357750, _1357752, _1357754] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357744, tc_fun(_1357746, tc_HOL_Obool)), _1357748), _1357750), _1357752)), hBOOL(hAPP(hAPP(c_member(_1357744), _1357754), _1357748)), -(hBOOL(hAPP(hAPP(_1357750, _1357754), _1357752)))], (28367 ^ _776545) ^ [_1285766, _1285768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1285766), _1285768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1285766)), c_Int_OBit1(_1285768))))], (16498 ^ _776545) ^ [_1073629] : [_1073629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073629), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44459 ^ _776545) ^ [_1665730, _1665732, _1665734, _1665736] : [class_Complete__Lattice_Ocomplete__lattice(_1665730), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1665732, _1665730), hAPP(c_List_Oset(_1665732), _1665734)), _1665736) = hAPP(c_List_Ofoldl(_1665730, _1665732, hAPP(c_COMBC(_1665732, _1665730, _1665730), hAPP(hAPP(c_COMBB(_1665730, tc_fun(_1665730, _1665730), _1665732), c_Lattices_Osemilattice__sup__class_Osup(_1665730)), _1665736)), c_Orderings_Obot__class_Obot(_1665730)), _1665734))], (10535 ^ _776545) ^ [_957692, _957694, _957696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957692, tc_HOL_Obool)), _957694), _957696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957692, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957692, tc_HOL_Obool)), _957696)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957692, tc_HOL_Obool)), _957694))))], (14084 ^ _776545) ^ [_1029129, _1029131, _1029133, _1029135, _1029137] : [class_Groups_Oab__group__add(_1029129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029131), _1029133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029131), _1029135)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029131, _1029129), _1029137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029131, tc_HOL_Obool)), _1029133), _1029135)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1029129), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029131, _1029129), _1029137), _1029133)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029131, _1029129), _1029137), _1029135))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029131, _1029129), _1029137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1029131, tc_HOL_Obool)), _1029133), _1029135))))], (39902 ^ _776545) ^ [_1553056, _1553058, _1553060, _1553062, _1553064, _1553066, _1553068, _1553070] : [hAPP(c_Fun_Ocomp(_1553056, _1553058, _1553060, _1553062), _1553064) = hAPP(c_Fun_Ocomp(_1553066, _1553058, _1553060, _1553068), _1553070), 39905 ^ _776545 : [(39906 ^ _776545) ^ [_1553171] : [-(hAPP(_1553062, hAPP(_1553064, _1553171)) = hAPP(_1553068, hAPP(_1553070, _1553171)))]]], (11278 ^ _776545) ^ [_972504, _972506] : [class_Groups_Oordered__ab__group__add(_972504), -(hAPP(c_Set_Oimage(_972504, _972504, c_Groups_Ouminus__class_Ouminus(_972504)), hAPP(c_SetInterval_Oord__class_OlessThan(_972504), _972506)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_972504), hAPP(c_Groups_Ouminus__class_Ouminus(_972504), _972506)))], (34832 ^ _776545) ^ [_1426527, _1426529, _1426531, _1426533, _1426535, _1426537] : [-(hAPP(hAPP(c_Product__Type_OPair(_1426527, _1426529), _1426531), _1426533) = hAPP(hAPP(c_Product__Type_OPair(_1426527, _1426529), _1426535), _1426537)), _1426531 = _1426535, _1426533 = _1426537], (26531 ^ _776545) ^ [_1255414, _1255416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255416)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1255414)), hAPP(c_Int_Onat, _1255416)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255414), _1255416)))], (49143 ^ _776545) ^ [_1768228, _1768230, _1768232, _1768234, _1768236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768228), tc_List_Olist(_1768228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768228), tc_List_Olist(_1768228)), _1768230), _1768232)), c_List_Olexord(_1768228, _1768234))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768228), tc_List_Olist(_1768228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768228), tc_List_Olist(_1768228)), _1768232), _1768236)), c_List_Olexord(_1768228, _1768234))), c_Relation_Otrans(_1768228, _1768234), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1768228), tc_List_Olist(_1768228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1768228), tc_List_Olist(_1768228)), _1768230), _1768236)), c_List_Olexord(_1768228, _1768234))))], (34686 ^ _776545) ^ [_1422782, _1422784] : [c_Nitpick_Orefl_H(_1422782, _1422784), 34689 ^ _776545 : [(34690 ^ _776545) ^ [_1422860] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1422782, _1422782)), hAPP(hAPP(c_Product__Type_OPair(_1422782, _1422782), _1422860), _1422860)), _1422784)))]]], (19555 ^ _776545) ^ [_1129777, _1129779, _1129781, _1129783] : [class_Rings_Odivision__ring(_1129777), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129777), _1129779), _1129781)), _1129783) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129777), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129777), _1129779), _1129783)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129777), _1129781), _1129783)))], (4952 ^ _776545) ^ [_851988, _851990, _851992, _851994, _851996, _851998] : [-(c_Finite__Set_Ofold__image(_851998, _851994, _851990) = c_Finite__Set_Ofold__image(_851996, _851992, _851988)), _851998 = _851996, _851994 = _851992, _851990 = _851988], (27789 ^ _776545) ^ [_1276262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1276262), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10192 ^ _776545) ^ [_951479, _951481, _951483] : [class_Orderings_Olinorder(_951479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951479), _951481), _951483)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951479, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_951479), _951481), c_Orderings_Obot__class_Obot(tc_fun(_951479, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_951479, _951481, _951483)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_951479, _951481), _951483))], (52413 ^ _776545) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (46267 ^ _776545) ^ [_1707322, _1707324] : [c_List_Oupt(_1707322, _1707324) = c_List_Olist_ONil(tc_Nat_Onat), -(_1707324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1707324), _1707322)))], (33539 ^ _776545) ^ [_1393686, _1393688, _1393690, _1393692] : [c_Orderings_Otop__class_Otop(tc_fun(_1393686, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1393688, tc_fun(_1393686, tc_HOL_Obool)), _1393690), _1393692), 33542 ^ _776545 : [(33543 ^ _776545) ^ [_1393802] : [hBOOL(hAPP(hAPP(c_member(_1393688), _1393802), _1393690)), -(hAPP(_1393692, _1393802) = c_Orderings_Otop__class_Otop(tc_fun(_1393686, tc_HOL_Obool)))]]], (24806 ^ _776545) ^ [_1225293, _1225295, _1225297, _1225299] : [class_Divides_Osemiring__div(_1225293), -(c_Divides_Odiv__class_Omod(_1225293, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225293), _1225295), c_Divides_Odiv__class_Omod(_1225293, _1225297, _1225299)), _1225299) = c_Divides_Odiv__class_Omod(_1225293, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225293), _1225295), _1225297), _1225299))], (10994 ^ _776545) ^ [_966478, _966480, _966482, _966484, _966486, _966488] : [_966478 = hAPP(_966480, _966482), hBOOL(hAPP(hAPP(c_member(_966484), _966482), _966486)), -(hBOOL(hAPP(hAPP(c_member(_966488), _966478), hAPP(c_Set_Oimage(_966484, _966488, _966480), _966486))))], (3030 ^ _776545) ^ [_821513, _821515, _821517, _821519] : [-(c_List_Olenlex(_821519, _821515) = c_List_Olenlex(_821517, _821513)), _821519 = _821517, _821515 = _821513], (34203 ^ _776545) ^ [_1412408, _1412410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412408)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412410))), -(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(_1412410))), 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), _1412408)), c_Int_Onat))))))], (28841 ^ _776545) ^ [_1293615, _1293617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1293615)), c_Int_OBit0(_1293617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293615), _1293617)))], (34701 ^ _776545) ^ [_1423130, _1423132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1423130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1423130), _1423132)), -(c_Divides_Odivmod__nat(_1423132, _1423130) = 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), _1423132), _1423130)), _1423130))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1423132), _1423130), _1423130)))], (33865 ^ _776545) ^ [_1403990, _1403992, _1403994, _1403996, _1403998] : [class_Complete__Lattice_Ocomplete__lattice(_1403990), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403992), _1403994)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1403990), _1403996), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403992, _1403990), _1403994), _1403998)) = hAPP(hAPP(c_Finite__Set_Ofold(_1403992, _1403990, hAPP(hAPP(c_COMBB(_1403990, tc_fun(_1403990, _1403990), _1403992), c_Lattices_Osemilattice__sup__class_Osup(_1403990)), _1403998)), _1403996), _1403994))], (43352 ^ _776545) ^ [_1640570, _1640572, _1640574, _1640576, _1640578] : [_1640570 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1640572, _1640574, _1640576), _1640570), _1640578) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640574), _1640572), c_List_Olist_ONil(_1640574)), _1640578))], (1464 ^ _776545) ^ [_797709, _797711] : [-(class_Lazy__Sequence_Osmall__lazy(_797709)), _797711 = _797709, class_Lazy__Sequence_Osmall__lazy(_797711)], (34672 ^ _776545) ^ [_1422447, _1422449, _1422451, _1422453, _1422455] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1422447, _1422449, _1422451), _1422453), _1422455)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1422447, _1422449)), hAPP(hAPP(c_Product__Type_OPair(_1422447, _1422449), _1422453), _1422455)), _1422451)))], (11556 ^ _776545) ^ [_978550] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_978550), c_Orderings_Otop__class_Otop(tc_fun(_978550, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_978550)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_978550), tc_HOL_Obool)))))], (16194 ^ _776545) ^ [_1069196, _1069198] : [class_Groups_Ocomm__monoid__add(_1069196), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1069196), _1069198), c_Groups_Ozero__class_Ozero(_1069196)) = _1069198)], (40731 ^ _776545) ^ [_1573329, _1573331] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573329, _1573329), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1573329, _1573331)), c_Relation_OId(_1573329)) = c_Transitive__Closure_Ortrancl(_1573329, _1573331))], (26060 ^ _776545) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (49738 ^ _776545) ^ [_1781723, _1781725] : [c_Relation_Osym(_1781723, _1781725), -(c_Relation_Osym(_1781723, c_Transitive__Closure_Ortrancl(_1781723, _1781725)))], (706 ^ _776545) ^ [_787190, _787192, _787194, _787196] : [-(c_Predicate_Oreflp(_787194, _787190)), c_Predicate_Oreflp(_787196, _787192), _787196 = _787194, _787192 = _787190], (13796 ^ _776545) ^ [_1022477, _1022479, _1022481, _1022483] : [class_Rings_Ocomm__semiring(_1022477), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022477), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022477), _1022479), _1022481)), _1022483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022477), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022477), _1022479), _1022483)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1022477), _1022481), _1022483)))], (39862 ^ _776545) ^ [_1552205, _1552207, _1552209, _1552211, _1552213, _1552215] : [c_Fun_Oinj__on(_1552205, _1552207, hAPP(c_Fun_Ocomp(_1552209, _1552207, _1552205, _1552211), _1552213), _1552215), -(c_Fun_Oinj__on(_1552209, _1552207, _1552211, hAPP(c_Set_Oimage(_1552205, _1552209, _1552213), _1552215)))], (38069 ^ _776545) ^ [_1505679, _1505681, _1505683, _1505685] : [-(c_Wellfounded_Omax__extp(_1505679, _1505681, _1505683, _1505685)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505679), _1505683)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505679), _1505685)), -(_1505685 = c_Orderings_Obot__class_Obot(tc_fun(_1505679, tc_HOL_Obool))), 38083 ^ _776545 : [(38086 ^ _776545) ^ [_1506024] : [hBOOL(hAPP(hAPP(c_member(_1505679), _1506024), _1505685)), hBOOL(hAPP(hAPP(_1505681, 38082 ^ [_1505679, _1505681, _1505683, _1505685]), _1506024))], (38084 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505679), 38082 ^ [_1505679, _1505681, _1505683, _1505685]), _1505683)))]]], (48424 ^ _776545) ^ [_1751819, _1751821, _1751823, _1751825, _1751827] : [_1751819 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1751821, _1751823, _1751825, _1751827), _1751819) = c_Lazy__Sequence_Oempty(_1751823))], (40835 ^ _776545) ^ [_1575947, _1575949] : [-(hAPP(c_Relation_ORange(_1575947, _1575947), c_Transitive__Closure_Ortrancl(_1575947, _1575949)) = c_Orderings_Otop__class_Otop(tc_fun(_1575947, tc_HOL_Obool)))], (50277 ^ _776545) ^ [_1792874, _1792876] : [-(c_Fun_Obij__betw(_1792874, _1792874, c_Fun_Oid(_1792874), _1792876, _1792876))], (52261 ^ _776545) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (47343 ^ _776545) ^ [_1728346, _1728348, _1728350] : [hBOOL(hAPP(c_List_Odistinct(_1728346), _1728348)), hBOOL(hAPP(hAPP(c_member(_1728346), _1728350), hAPP(c_List_Oset(_1728346), _1728348))), -(c_List_OtakeWhile(_1728346, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728346), c_fNot), hAPP(hAPP(c_COMBC(_1728346, _1728346, tc_HOL_Obool), c_fequal), _1728350)), hAPP(c_List_Orev(_1728346), _1728348)) = hAPP(c_List_Orev(_1728346), hAPP(c_List_Otl(_1728346), c_List_OdropWhile(_1728346, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1728346), c_fNot), hAPP(hAPP(c_COMBC(_1728346, _1728346, tc_HOL_Obool), c_fequal), _1728350)), _1728348))))], (32566 ^ _776545) ^ [_1365573, _1365575, _1365577, _1365579] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365573, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1365573, tc_fun(_1365573, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365573)), _1365575)), hAPP(hAPP(c_COMBC(_1365573, tc_fun(_1365573, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365573)), _1365577)), _1365579)), -(hBOOL(hAPP(hAPP(c_member(_1365573), _1365579), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365573, tc_HOL_Obool)), _1365575), _1365577))))], (15380 ^ _776545) ^ [_1054289, _1054291, _1054293] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054289), _1054291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1054289, tc_HOL_Obool)), _1054293), _1054291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1054289), _1054293)), hAPP(c_Finite__Set_Ocard(_1054289), _1054291))))], (11018 ^ _776545) ^ [_966950, _966952, _966954, _966956, _966958] : [hAPP(c_Set_Oimage(_966950, _966952, _966954), _966956) = _966958, -(hAPP(c_Set_Oimage(tc_fun(_966950, tc_HOL_Obool), tc_fun(_966952, tc_HOL_Obool), c_Set_Oimage(_966950, _966952, _966954)), hAPP(c_Set_OPow(_966950), _966956)) = hAPP(c_Set_OPow(_966952), _966958))], (33487 ^ _776545) ^ [_1392495, _1392497, _1392499, _1392501, _1392503] : [class_Groups_Ocomm__monoid__mult(_1392495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392497), _1392499)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392497, _1392495), hAPP(hAPP(c_COMBS(_1392497, _1392495, _1392495), hAPP(hAPP(c_COMBB(_1392495, tc_fun(_1392495, _1392495), _1392497), c_Groups_Otimes__class_Otimes(_1392495)), _1392501)), _1392503)), _1392499) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392495), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392497, _1392495), _1392501), _1392499)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392497, _1392495), _1392503), _1392499)))], (48568 ^ _776545) ^ [_1755752, _1755754, _1755756, _1755758] : [-(hAPP(hAPP(c_List_Omap(_1755752, _1755754), hAPP(c_COMBK(_1755754, _1755752), _1755756)), _1755758) = c_List_Oreplicate(_1755754, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755752)), _1755758), _1755756))], (35626 ^ _776545) ^ [_1441475, _1441477, _1441479] : [-(hAPP(hAPP(c_Product__Type_OPair(_1441475, _1441477), hAPP(c_Product__Type_Ofst(_1441475, _1441477), _1441479)), hAPP(c_Product__Type_Osnd(_1441475, _1441477), _1441479)) = _1441479)], (50792 ^ _776545) ^ [_1803351, _1803353, _1803355, _1803357, _1803359] : [50794 ^ _776545 : [(50797 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803355, tc_HOL_Obool)), _1803357), hAPP(_1803359, 50793 ^ [_1803351, _1803353, _1803355, _1803357, _1803359])))], (50795 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803351), 50793 ^ [_1803351, _1803353, _1803355, _1803357, _1803359]), _1803353)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803355, tc_HOL_Obool)), _1803357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1803351, tc_fun(_1803355, tc_HOL_Obool)), _1803353), _1803359))))], (33332 ^ _776545) ^ [_1388146, _1388148, _1388150, _1388152] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388146, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1388148, tc_fun(_1388146, tc_HOL_Obool)), _1388150), _1388152)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1388148, tc_fun(_1388146, tc_HOL_Obool)), _1388150), hAPP(hAPP(c_COMBB(tc_fun(_1388146, tc_HOL_Obool), tc_fun(_1388146, tc_HOL_Obool), _1388148), c_Groups_Ouminus__class_Ouminus(tc_fun(_1388146, tc_HOL_Obool))), _1388152)))], (24610 ^ _776545) ^ [_1221722, _1221724, _1221726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221722), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24613 ^ _776545 : [(24614 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1221724, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221726), _1221722)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221726, _1221722))), 24617 ^ _776545 : [(24618 ^ _776545) ^ [_1221932, _1221934] : [-(hBOOL(hAPP(hAPP(_1221724, _1221934), _1221932))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221722), _1221932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221932), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1221726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221722), _1221934)), _1221932)]]], (24632 ^ _776545) ^ [] : [24635 ^ _776545 : [(24638 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24634 ^ [_1221722, _1221724, _1221726]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24640 ^ _776545) ^ [] : [-(_1221726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1221722), 24633 ^ [_1221722, _1221724, _1221726])), 24634 ^ [_1221722, _1221724, _1221726]))], (24642 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1221724, 24633 ^ [_1221722, _1221724, _1221726]), 24634 ^ [_1221722, _1221724, _1221726]))], (24636 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1221722), 24634 ^ [_1221722, _1221724, _1221726])))]], -(hBOOL(hAPP(hAPP(_1221724, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1221726), _1221722)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221726, _1221722))))]]], (14793 ^ _776545) ^ [_1043248, _1043250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043248), _1043250))))], (22521 ^ _776545) ^ [_1184726, _1184728] : [class_Groups_Omonoid__mult(_1184726), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184726), _1184728), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1184728)], (32229 ^ _776545) ^ [_1355851, _1355853, _1355855] : [class_Orderings_Olinorder(_1355851), hAPP(_1355853, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355851), 32234 ^ [_1355851, _1355853, _1355855]), 32235 ^ [_1355851, _1355853, _1355855])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1355851), hAPP(_1355853, 32234 ^ [_1355851, _1355853, _1355855])), hAPP(_1355853, 32235 ^ [_1355851, _1355853, _1355855])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355851), _1355855)), -(_1355855 = c_Orderings_Obot__class_Obot(tc_fun(_1355851, tc_HOL_Obool))), -(hAPP(_1355853, c_Big__Operators_Olinorder__class_OMax(_1355851, _1355855)) = c_Big__Operators_Olinorder__class_OMax(_1355851, hAPP(c_Set_Oimage(_1355851, _1355851, _1355853), _1355855)))], (40322 ^ _776545) ^ [_1562613, _1562615, _1562617, _1562619, _1562621, _1562623, _1562625, _1562627] : [class_Groups_Ocomm__monoid__mult(_1562613), c_Fun_Oinj__on(_1562615, _1562617, _1562619, _1562621), _1562623 = hAPP(c_Set_Oimage(_1562615, _1562617, _1562619), _1562621), 40336 ^ _776545 : [(40339 ^ _776545) ^ [] : [hAPP(_1562625, 40335 ^ [_1562613, _1562615, _1562617, _1562619, _1562621, _1562623, _1562625, _1562627]) = hAPP(hAPP(c_Fun_Ocomp(_1562617, _1562613, _1562615, _1562627), _1562619), 40335 ^ [_1562613, _1562615, _1562617, _1562619, _1562621, _1562623, _1562625, _1562627])], (40337 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562615), 40335 ^ [_1562613, _1562615, _1562617, _1562619, _1562621, _1562623, _1562625, _1562627]), _1562621)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562617, _1562613), _1562627), _1562623) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1562615, _1562613), _1562625), _1562621))], (2338 ^ _776545) ^ [_810659, _810661, _810663, _810665] : [-(c_Groups_Osgn__class_Osgn(_810665, _810661) = c_Groups_Osgn__class_Osgn(_810663, _810659)), _810665 = _810663, _810661 = _810659], (12197 ^ _776545) ^ [_990649, _990651, _990653] : [class_Lattices_Olattice(_990649), hBOOL(hAPP(c_Finite__Set_Ofinite(_990649), _990651)), -(_990651 = c_Orderings_Obot__class_Obot(tc_fun(_990649, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_990649), _990653)), -(_990653 = c_Orderings_Obot__class_Obot(tc_fun(_990649, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_990649, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_990649, tc_HOL_Obool)), _990651), _990653)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_990649), c_Big__Operators_Olattice__class_OSup__fin(_990649, _990651)), c_Big__Operators_Olattice__class_OSup__fin(_990649, _990653)))], (37876 ^ _776545) ^ [_1498491, _1498493] : [-(c_Fun_Oinj__on(tc_fun(_1498491, _1498493), tc_fun(tc_prod(_1498491, _1498493), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1498491, _1498493), tc_HOL_Obool), tc_fun(tc_prod(_1498491, _1498493), tc_HOL_Obool), tc_fun(_1498491, _1498493)), c_Set_OCollect(tc_prod(_1498491, _1498493))), hAPP(hAPP(c_COMBB(tc_fun(_1498491, tc_fun(_1498493, tc_HOL_Obool)), tc_fun(tc_prod(_1498491, _1498493), tc_HOL_Obool), tc_fun(_1498491, _1498493)), c_Product__Type_Oprod_Oprod__case(_1498491, _1498493, tc_HOL_Obool)), hAPP(c_COMBB(_1498493, tc_fun(_1498493, tc_HOL_Obool), _1498491), hAPP(c_COMBC(_1498493, _1498493, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1498491, _1498493), tc_HOL_Obool))))], (17071 ^ _776545) ^ [_1083890, _1083892, _1083894] : [class_Rings_Oordered__ring(_1083890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083890), _1083892), c_Groups_Ozero__class_Ozero(_1083890))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083890), _1083894), c_Groups_Ozero__class_Ozero(_1083890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083890), c_Groups_Ozero__class_Ozero(_1083890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083890), _1083892), _1083894))))], (14628 ^ _776545) ^ [_1040337, _1040339, _1040341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040337), _1040339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040337), _1040341)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040339), _1040341))))], (41684 ^ _776545) ^ [_1597330, _1597332] : [-(c_Nitpick_Oinverse__frac(_1597330, _1597332) = hAPP(hAPP(c_Nitpick_Ofrac(_1597330), hAPP(c_Nitpick_Odenom(_1597330), _1597332)), hAPP(c_Nitpick_Onum(_1597330), _1597332)))], (16334 ^ _776545) ^ [_1071290, _1071292] : [class_Groups_Ogroup__add(_1071290), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1071290), _1071292), _1071292) = c_Groups_Ozero__class_Ozero(_1071290))], (41019 ^ _776545) ^ [_1580234, _1580236] : [-(c_Relation_Oirrefl(_1580234, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1580234, _1580234), tc_HOL_Obool)), _1580236), c_Relation_OId(_1580234))))], (48393 ^ _776545) ^ [_1751177, _1751179, _1751181] : [-(c_List_Olist__ex1(_1751177, _1751179, _1751181)), 48394 ^ _776545 : [(48395 ^ _776545) ^ [_1751271] : [hBOOL(hAPP(hAPP(c_member(_1751177), _1751271), hAPP(c_List_Oset(_1751177), _1751181))), hBOOL(hAPP(_1751179, _1751271)), 48403 ^ _776545 : [(48408 ^ _776545) ^ [] : [48402 ^ [_1751177, _1751179, _1751181, _1751271] = _1751271], (48406 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1751179, 48402 ^ [_1751177, _1751179, _1751181, _1751271])))], (48404 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751177), 48402 ^ [_1751177, _1751179, _1751181, _1751271]), hAPP(c_List_Oset(_1751177), _1751181))))]]]]], (34512 ^ _776545) ^ [_1418989, _1418991, _1418993, _1418995, _1418997, _1418999, _1419001] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418989, tc_fun(_1418991, tc_fun(_1418993, tc_HOL_Obool))), _1418995), _1418997), _1418999), _1419001)), 34515 ^ _776545 : [(34516 ^ _776545) ^ [_1419117] : [hBOOL(hAPP(hAPP(c_member(_1418989), _1419117), _1418995)), -(hBOOL(hAPP(hAPP(hAPP(_1418997, _1419117), _1418999), _1419001)))]]], (45090 ^ _776545) ^ [_1679537, _1679539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1679537)), hAPP(c_Code__Numeral_Oof__nat, _1679539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679537), _1679539)))], (39852 ^ _776545) ^ [_1552018, _1552020, _1552022, _1552024, _1552026, _1552028] : [c_Fun_Oinj__on(_1552018, _1552020, _1552022, _1552024), c_Fun_Oinj__on(_1552020, _1552026, _1552028, hAPP(c_Set_Oimage(_1552018, _1552020, _1552022), _1552024)), -(c_Fun_Oinj__on(_1552018, _1552026, hAPP(c_Fun_Ocomp(_1552020, _1552026, _1552018, _1552028), _1552022), _1552024))], (15482 ^ _776545) ^ [_1056628, _1056630, _1056632, _1056634, _1056636] : [class_Groups_Ocomm__monoid__mult(_1056628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056630), _1056632)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056630), _1056634)), 15496 ^ _776545 : [(15499 ^ _776545) ^ [] : [hAPP(_1056636, 15495 ^ [_1056628, _1056630, _1056632, _1056634, _1056636]) = c_Groups_Oone__class_Oone(_1056628)], (15497 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1056630), 15495 ^ [_1056628, _1056630, _1056632, _1056634, _1056636]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056630, tc_HOL_Obool)), _1056632), _1056634))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056630, _1056628), _1056636), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056630, tc_HOL_Obool)), _1056632), _1056634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056628), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056630, _1056628), _1056636), _1056632)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1056630, _1056628), _1056636), _1056634)))], (33809 ^ _776545) ^ [_1402681, _1402683, _1402685, _1402687, _1402689] : [_1402681 = c_Orderings_Obot__class_Obot(tc_fun(_1402683, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1402683, tc_fun(_1402685, tc_HOL_Obool)), _1402681), hAPP(hAPP(c_COMBB(tc_fun(_1402685, tc_HOL_Obool), tc_fun(_1402685, tc_HOL_Obool), _1402683), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1402685, tc_HOL_Obool)), _1402687)), _1402689)) = c_Orderings_Otop__class_Otop(tc_fun(_1402685, tc_HOL_Obool)))], (33629 ^ _776545) ^ [_1397375, _1397377, _1397379, _1397381, _1397383] : [-(hAPP(c_Set_Oimage(_1397375, _1397377, hAPP(hAPP(c_COMBB(_1397379, _1397377, _1397375), _1397381), _1397383)), c_Orderings_Otop__class_Otop(tc_fun(_1397375, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1397379, _1397377, _1397381), hAPP(c_Set_Oimage(_1397375, _1397379, _1397383), c_Orderings_Otop__class_Otop(tc_fun(_1397375, tc_HOL_Obool)))))], (12447 ^ _776545) ^ [_995204, _995206, _995208, _995210, _995212] : [c_Finite__Set_Ofolding__one__idem(_995204, _995206, _995208), hBOOL(hAPP(c_Finite__Set_Ofinite(_995204), _995210)), -(_995212 = c_Orderings_Obot__class_Obot(tc_fun(_995204, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_995204, tc_HOL_Obool)), _995212), _995210)), -(hAPP(hAPP(_995206, hAPP(_995208, _995212)), hAPP(_995208, _995210)) = hAPP(_995208, _995210))], (42616 ^ _776545) ^ [_1624982, _1624984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624982), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1624984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1624984), _1624982)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1624984))))], (38396 ^ _776545) ^ [] : [-(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))))], (38695 ^ _776545) ^ [_1520168, _1520170, _1520172, _1520174, _1520176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520168, tc_HOL_Obool)), _1520170), _1520172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520174, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1520174, _1520168, _1520176), _1520170)), hAPP(c_Set_Ovimage(_1520174, _1520168, _1520176), _1520172))))], (26402 ^ _776545) ^ [_1253029, _1253031] : [hBOOL(hAPP(_1253029, hAPP(c_Int_Onat, _1253031))), 26405 ^ _776545 : [(26412 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253031), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1253029, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26406 ^ _776545) ^ [_1253129] : [_1253031 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1253129), -(hBOOL(hAPP(_1253029, _1253129)))]]], (34363 ^ _776545) ^ [_1416250, _1416252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416250)), 34366 ^ _776545 : [(34373 ^ _776545) ^ [] : [-(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), _1416252), _1416250)))), -(c_Divides_OnegDivAlg(_1416252, _1416250) = hAPP(c_Divides_Oadjust(_1416250), c_Divides_OnegDivAlg(_1416252, 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)))), _1416250))))], (34367 ^ _776545) ^ [] : [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), _1416252), _1416250))), -(c_Divides_OnegDivAlg(_1416252, _1416250) = 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), _1416252), _1416250)))]]], (15914 ^ _776545) ^ [_1064551, _1064553, _1064555] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064551), _1064553)), 15917 ^ _776545 : [(15937 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064551, tc_Nat_Onat), _1064555), _1064553) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 15938 ^ _776545 : [(15939 ^ _776545) ^ [_1065032] : [hBOOL(hAPP(hAPP(c_member(_1064551), _1065032), _1064553)), hAPP(_1064555, _1065032) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15947 ^ _776545 : [(15952 ^ _776545) ^ [] : [hAPP(_1064555, 15946 ^ [_1064551, _1064553, _1064555, _1065032]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15950 ^ _776545) ^ [] : [_1065032 = 15946 ^ [_1064551, _1064553, _1064555, _1065032]], (15948 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1064551), 15946 ^ [_1064551, _1064553, _1064555, _1065032]), _1064553)))]]]]], (15918 ^ _776545) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064551, tc_Nat_Onat), _1064555), _1064553) = hAPP(c_Nat_OSuc, 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_1707004)), hAPP(hAPP(c_List_Ozip(_1707002, tc_Nat_Onat), _1707006), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707002)), _1707006))))))], (42504 ^ _776545) ^ [_1621966, _1621968, _1621970, _1621972] : [-(hAPP(c_List_Oset(tc_prod(_1621966, _1621968)), hAPP(hAPP(c_List_Ozip(_1621966, _1621968), _1621970), _1621972)) = hAPP(c_Set_OCollect(tc_prod(_1621966, _1621968)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1621966, _1621968)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1621966, _1621968), 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(_1621966, _1621968)), 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, 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hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621966)), _1621970)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621968)), _1621972)))))))], (38050 ^ _776545) ^ [_1505279, _1505281, _1505283, _1505285] : [c_Wellfounded_Omax__extp(_1505279, _1505281, _1505283, _1505285), 38053 ^ _776545 : [(38056 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505279), _1505285)))], (38058 ^ _776545) ^ [] : [_1505285 = c_Orderings_Obot__class_Obot(tc_fun(_1505279, tc_HOL_Obool))], (38060 ^ _776545) ^ [_1505495] : [hBOOL(hAPP(hAPP(c_member(_1505279), _1505495), _1505283)), 38064 ^ _776545 : [(38067 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1505281, _1505495), 38063 ^ [_1505279, _1505281, _1505283, _1505285, _1505495])))], (38065 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505279), 38063 ^ [_1505279, _1505281, _1505283, _1505285, _1505495]), _1505285)))]]], (38054 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505279), _1505283)))]]], (52265 ^ _776545) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (8817 ^ _776545) ^ [_928157, _928159, _928161, _928163] : [class_Lattices_Odistrib__lattice(_928157), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928157), _928159), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928157), _928161), _928163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928157), _928159), _928161)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928157), _928159), _928163)))], (16644 ^ _776545) ^ [_1075869, _1075871, _1075873, _1075875] : [class_Groups_Ocomm__monoid__add(_1075869), 16647 ^ _776545 : [(16654 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1075871), _1075873))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075869), _1075875), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075873), hAPP(c_Nat_OSuc, _1075871))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075869), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075869), _1075875), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075873), _1075871))), hAPP(_1075875, _1075871)))], (16648 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1075871), _1075873)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1075869), _1075875), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1075873), hAPP(c_Nat_OSuc, _1075871))) = c_Groups_Ozero__class_Ozero(_1075869))]]], (47452 ^ _776545) ^ [_1730665, _1730667, _1730669] : [-(c_List_OdropWhile(_1730665, _1730667, _1730669) = hAPP(hAPP(c_List_Odrop(_1730665), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730665)), c_List_OtakeWhile(_1730665, _1730667, _1730669))), _1730669))], (8357 ^ _776545) ^ [_919751, _919753, _919755, _919757] : [class_Lattices_Osemilattice__inf(_919751), 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[_1134008, _1134010, _1134012, _1134014] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1134008, _1134010)), c_Sum__Type_OPlus(_1134008, _1134010, _1134012, _1134014))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1134008), _1134012)))], (36661 ^ _776545) ^ [_1471691] : [-(c_Relation_OId__on(_1471691, c_Orderings_Obot__class_Obot(tc_fun(_1471691, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1471691, _1471691), tc_HOL_Obool)))], (13832 ^ _776545) ^ [_1023251, _1023253, _1023255] : [class_Groups_Ogroup__add(_1023251), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023251), hAPP(c_Groups_Ouminus__class_Ouminus(_1023251), _1023253)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1023251), _1023253), _1023255)) = _1023255)], (13662 ^ _776545) ^ [_1019810, _1019812, _1019814, _1019816] : [class_Groups_Oordered__ab__semigroup__add(_1019810), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019810), _1019812), _1019814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019810), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019810), _1019812), _1019816)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019810), _1019814), _1019816))))], (49183 ^ _776545) ^ [_1769235, _1769237] : [49186 ^ _776545 : [(49192 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769235, _1769235)), hAPP(hAPP(c_Product__Type_OPair(_1769235, _1769235), 49184 ^ [_1769235, _1769237]), 49188 ^ [_1769235, _1769237])), _1769237))], (49190 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769235, _1769235)), hAPP(hAPP(c_Product__Type_OPair(_1769235, _1769235), 49185 ^ [_1769235, _1769237]), 49188 ^ [_1769235, _1769237])), _1769237)))], (49187 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769235, _1769235)), hAPP(hAPP(c_Product__Type_OPair(_1769235, _1769235), 49184 ^ [_1769235, _1769237]), 49185 ^ [_1769235, _1769237])), _1769237)))]], -(c_Relation_Otrans(_1769235, _1769237))], (6262 ^ _776545) ^ [_877200] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_877200, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_877200, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_877200, tc_HOL_Obool)))], (16076 ^ _776545) ^ [_1067238, _1067240] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067238), hAPP(c_Nat_OSuc, _1067240)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1067238), _1067240)))], (41260 ^ _776545) ^ [_1586143, _1586145, _1586147, _1586149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586143, _1586145), tc_HOL_Obool)), _1586147), _1586149)), c_Relation_Osingle__valued(_1586143, _1586145, _1586149), -(c_Relation_Osingle__valued(_1586143, _1586145, _1586147))], (34862 ^ _776545) ^ [_1427155, _1427157] : [34863 ^ _776545 : [(34866 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1427157), _1427155))], (34864 ^ _776545) ^ [] : [_1427155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1427157, _1427155) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1427157))], (7918 ^ _776545) ^ [_910255, _910257, _910259, _910261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910255, tc_HOL_Obool)), _910257), _910259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910255, tc_HOL_Obool)), _910261), _910259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910255, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910255, tc_HOL_Obool)), _910257), _910261)), _910259)))], (29301 ^ _776545) ^ [_1301617] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1301617), 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), _1301617), _1301617))], (32005 ^ _776545) ^ [_1351654, _1351656] : [class_Orderings_Olinorder(_1351654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351654), _1351656)), -(c_Big__Operators_Olattice_OSup__fin(_1351654, c_Orderings_Oord__class_Omax(_1351654), _1351656) = hAPP(c_Finite__Set_Ofold1(_1351654, c_Orderings_Oord__class_Omax(_1351654)), _1351656))], (3508 ^ _776545) ^ [_828990, _828992] : [_828992 = _828990, -(c_List_Otranspose__rel(_828992) = c_List_Otranspose__rel(_828990))], (38362 ^ _776545) ^ [_1511642, _1511644, _1511646, _1511648] : [38364 ^ _776545 : [(38367 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1511644, hAPP(_1511646, 38363 ^ [_1511642, _1511644, _1511646, _1511648]))), hAPP(_1511644, 38363 ^ [_1511642, _1511644, _1511646, _1511648])))], (38365 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1511642, 38363 ^ [_1511642, _1511644, _1511646, _1511648])))]], -(c_Wellfounded_Owf(_1511648, hAPP(c_Set_OCollect(tc_prod(_1511648, _1511648)), hAPP(c_Product__Type_Oprod_Oprod__case(_1511648, _1511648, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1511648, tc_HOL_Obool), tc_fun(_1511648, tc_HOL_Obool), _1511648), hAPP(c_COMBS(_1511648, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511648), c_fconj), _1511642))), hAPP(hAPP(c_COMBC(_1511648, tc_fun(_1511648, _1511648), tc_fun(_1511648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511648, tc_HOL_Obool), tc_fun(tc_fun(_1511648, _1511648), tc_fun(_1511648, tc_HOL_Obool)), _1511648), c_COMBB(_1511648, tc_HOL_Obool, _1511648)), c_fequal)), _1511646))))))], (39984 ^ _776545) ^ [_1554948, _1554950, _1554952, _1554954, _1554956] : [class_Groups_Ocomm__monoid__add(_1554948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554950), _1554952)), c_Fun_Oinj__on(_1554950, _1554950, _1554954, _1554952), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554950, _1554948), _1554956), hAPP(c_Set_Oimage(_1554950, _1554950, _1554954), _1554952)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1554950, _1554948), hAPP(c_Fun_Ocomp(_1554950, _1554948, _1554950, _1554956), _1554954)), _1554952))], (41192 ^ _776545) ^ [_1584632, _1584634, _1584636, _1584638, _1584640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584634, tc_HOL_Obool)), _1584638), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584634, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584632, _1584634, hAPP(c_Relation_Oconverse(_1584634, _1584632), _1584636)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1584632, tc_HOL_Obool)), _1584640))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584632, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1584634, _1584632, _1584636), _1584638)), _1584640)))], (11260 ^ _776545) ^ [_972130, _972132, _972134, _972136] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_972130, _972132, _972134), _972136)), _972134 = c_Orderings_Obot__class_Obot(tc_fun(_972130, tc_HOL_Obool))], (50614 ^ _776545) ^ [_1799652, _1799654, _1799656, _1799658] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1799652, _1799654, _1799656), c_Product__Type_Ocurry(_1799652, _1799654, _1799656, _1799658)) = _1799658)], (30499 ^ _776545) ^ [_1323720, _1323722, _1323724] : [class_Orderings_Olinorder(_1323720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323720), _1323722)), -(_1323722 = c_Orderings_Obot__class_Obot(tc_fun(_1323720, tc_HOL_Obool))), 30510 ^ _776545 : [(30511 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323720), _1323724), hAPP(c_Finite__Set_Ofold1(_1323720, c_Orderings_Oord__class_Omin(_1323720)), _1323722))), 30514 ^ _776545 : [(30515 ^ _776545) ^ [_1324013] : [hBOOL(hAPP(hAPP(c_member(_1323720), _1324013), _1323722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323720), _1323724), _1324013)))]]], (30521 ^ _776545) ^ [] : [30523 ^ _776545 : [(30526 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323720), _1323724), 30522 ^ [_1323720, _1323722, _1323724]))], (30524 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323720), 30522 ^ [_1323720, _1323722, _1323724]), _1323722)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323720), _1323724), hAPP(c_Finite__Set_Ofold1(_1323720, c_Orderings_Oord__class_Omin(_1323720)), _1323722))))]]], (13820 ^ _776545) ^ [_1022993, _1022995, _1022997] : [class_Groups_Ogroup__add(_1022993), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1022993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022993), _1022995), _1022997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022993), hAPP(c_Groups_Ouminus__class_Ouminus(_1022993), _1022997)), hAPP(c_Groups_Ouminus__class_Ouminus(_1022993), _1022995)))], (8038 ^ _776545) ^ [_913103, _913105, _913107, _913109] : [-(hBOOL(hAPP(hAPP(c_member(_913103), _913105), _913107))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913103, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_913103), _913105), _913109)), _913107) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_913103, tc_HOL_Obool)), _913109), _913107))], (15436 ^ _776545) ^ [_1055543, _1055545, _1055547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055543), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055543, tc_HOL_Obool)), _1055545), _1055547))), -(hAPP(c_Finite__Set_Ocard(_1055543), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055543, tc_HOL_Obool)), _1055545), _1055547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055543), _1055545)), hAPP(c_Finite__Set_Ocard(_1055543), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055543, tc_HOL_Obool)), _1055545), _1055547))))], (22669 ^ _776545) ^ [_1187311, _1187313, _1187315] : [class_Fields_Ofield__inverse__zero(_1187311), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187311), c_Groups_Oone__class_Oone(_1187311)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187311), _1187313), _1187315)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1187311), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187311), c_Groups_Oone__class_Oone(_1187311)), _1187313)), _1187315))], (6007 ^ _776545) ^ [_872357, _872359, _872361, _872363] : [hBOOL(hAPP(hAPP(c_member(_872357), _872359), c_SetInterval_Oord_OatLeast(_872357, _872361, _872363))), -(hBOOL(hAPP(hAPP(_872361, _872363), _872359)))], (21073 ^ _776545) ^ [_1157405, _1157407, _1157409] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1157405, tc_HOL_Obool)), _1157407)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1157405), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1157405, tc_HOL_Obool), _1157407))), 21083 ^ _776545 : [(21086 ^ _776545) ^ [] : [hAPP(c_Finite__Set_Ocard(_1157405), 21082 ^ [_1157405, _1157407, _1157409]) = _1157409], (21084 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157405, tc_HOL_Obool)), 21082 ^ [_1157405, _1157407, _1157409]), _1157407)))]], 21090 ^ _776545 : [(21094 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157405, tc_HOL_Obool)), 21092 ^ [_1157405, _1157407, _1157409]), _1157407)))], (21096 ^ _776545) ^ [] : [21089 ^ [_1157405, _1157407, _1157409] = 21092 ^ [_1157405, _1157407, _1157409]], (21098 ^ _776545) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1157405, tc_HOL_Obool)), 21089 ^ [_1157405, _1157407, _1157409]), 21092 ^ [_1157405, _1157407, _1157409]) = c_Orderings_Obot__class_Obot(tc_fun(_1157405, tc_HOL_Obool))], (21091 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1157405, tc_HOL_Obool)), 21089 ^ [_1157405, _1157407, _1157409]), _1157407)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157409), hAPP(c_Finite__Set_Ocard(tc_fun(_1157405, tc_HOL_Obool)), _1157407)) = hAPP(c_Finite__Set_Ocard(_1157405), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1157405, tc_HOL_Obool), _1157407)))], (44280 ^ _776545) ^ [_1661971, _1661973, _1661975] : [class_Groups_Omonoid__add(_1661971), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1661971), _1661973), hAPP(c_List_Ofoldl(_1661971, _1661971, c_Groups_Oplus__class_Oplus(_1661971), c_Groups_Ozero__class_Ozero(_1661971)), _1661975)) = hAPP(c_List_Ofoldl(_1661971, _1661971, c_Groups_Oplus__class_Oplus(_1661971), _1661973), _1661975))], (15037 ^ _776545) ^ [_1048012, _1048014, _1048016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048012), _1048014)), hBOOL(hAPP(hAPP(c_member(_1048012), _1048016), _1048014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1048012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048012, tc_HOL_Obool)), _1048014), hAPP(hAPP(c_Set_Oinsert(_1048012), _1048016), c_Orderings_Obot__class_Obot(tc_fun(_1048012, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1048012), _1048014))))], (7810 ^ _776545) ^ [_907872, _907874, _907876, _907878] : [hBOOL(hAPP(hAPP(c_member(_907872), _907874), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_907872, tc_HOL_Obool)), _907876), _907878))), -(hBOOL(hAPP(hAPP(c_member(_907872), _907874), _907876)))], (20165 ^ _776545) ^ [_1140628, _1140630, _1140632] : [class_Fields_Olinordered__field(_1140628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140628), c_Groups_Ozero__class_Ozero(_1140628)), _1140630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140628), _1140632), c_Groups_Ozero__class_Ozero(_1140628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140628), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140628), _1140630), _1140632)), c_Groups_Ozero__class_Ozero(_1140628))))], (2950 ^ _776545) ^ [_820335, _820337] : [_820337 = _820335, -(c_Int_Oring__1__class_Oof__int(_820337) = c_Int_Oring__1__class_Oof__int(_820335))], (52005 ^ _776545) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12786 ^ _776545) ^ [_1002110, _1002112] : [class_Lattices_Olattice(_1002110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002110), _1002112)), -(c_Big__Operators_Olattice__class_OInf__fin(_1002110, _1002112) = hAPP(c_Finite__Set_Ofold1(_1002110, c_Lattices_Osemilattice__inf__class_Oinf(_1002110)), _1002112))], (23449 ^ _776545) ^ [_1201524, _1201526, _1201528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201524)), 23452 ^ _776545 : [(23453 ^ _776545) ^ [_1201658] : [23455 ^ _776545 : [(23461 ^ _776545) ^ [] : [-(_1201658 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 23457 ^ [_1201524, _1201526, _1201528, _1201658]), 23454 ^ [_1201524, _1201526, _1201528, _1201658]))], (23459 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23457 ^ [_1201524, _1201526, _1201528, _1201658]), _1201526)))], (23456 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 23454 ^ [_1201524, _1201526, _1201528, _1201658]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1201524))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201528), _1201658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201658), _1201524))))]]], (28753 ^ _776545) ^ [_1291959, _1291961] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291959, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1291961)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1291959, 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)))), _1291961)))], (5510 ^ _776545) ^ [_860745, _860747] : [_860747 = _860745, -(c_Groups_Ozero__class_Ozero(_860747) = c_Groups_Ozero__class_Ozero(_860745))], (14913 ^ _776545) ^ [_1045549, _1045551, _1045553, _1045555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045549), _1045551)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045553), _1045555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045549), _1045553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045551), _1045555))))], (44631 ^ _776545) ^ [_1668946, _1668948, _1668950, _1668952] : [hAPP(hAPP(c_List_Oappend(_1668946), _1668948), hAPP(hAPP(c_List_Olist_OCons(_1668946), _1668950), c_List_Olist_ONil(_1668946))) = _1668952, 44634 ^ _776545 : [(44639 ^ _776545) ^ [] : [-(c_List_Olast(_1668946, _1668952) = _1668950)], (44637 ^ _776545) ^ [] : [-(c_List_Obutlast(_1668946, _1668952) = _1668948)], (44635 ^ _776545) ^ [] : [_1668952 = c_List_Olist_ONil(_1668946)]]], (52277 ^ _776545) ^ [_1828921] : [-(class_Nat_Osize(tc_List_Olist(_1828921)))], (27959 ^ _776545) ^ [_1279040, _1279042] : [class_Int_Onumber__ring(_1279040), class_Rings_Olinordered__idom(_1279040), 27966 ^ _776545 : [(27973 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279042), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279040), hAPP(c_Int_Onumber__class_Onumber__of(_1279040), _1279042)), c_Groups_Ozero__class_Ozero(_1279040))))], (27967 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279040), hAPP(c_Int_Onumber__class_Onumber__of(_1279040), _1279042)), c_Groups_Ozero__class_Ozero(_1279040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1279042), c_Int_OPls)))]]], (25893 ^ _776545) ^ [_1244931, _1244933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244933)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244931, _1244933)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1244931), hAPP(c_Int_Onat, _1244933)))], (52067 ^ _776545) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (12951 ^ _776545) ^ [_1005050, _1005052, _1005054] : [class_Lattices_Oab__semigroup__idem__mult(_1005050), -(_1005052 = c_Orderings_Obot__class_Obot(tc_fun(_1005050, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1005050), _1005052)), -(hAPP(c_Finite__Set_Ofold1(_1005050, c_Groups_Otimes__class_Otimes(_1005050)), hAPP(hAPP(c_Set_Oinsert(_1005050), _1005054), _1005052)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005050), _1005054), hAPP(c_Finite__Set_Ofold1(_1005050, c_Groups_Otimes__class_Otimes(_1005050)), _1005052)))], (37820 ^ _776545) ^ [_1497490, _1497492] : [-(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)), _1497490), _1497492))], (16172 ^ _776545) ^ [_1068860, _1068862] : [class_Groups_Olinordered__ab__group__add(_1068860), 16175 ^ _776545 : [(16182 ^ _776545) ^ [] : [_1068862 = c_Groups_Ozero__class_Ozero(_1068860), -(c_Groups_Ozero__class_Ozero(_1068860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068860), _1068862), _1068862))], (16176 ^ _776545) ^ [] : [c_Groups_Ozero__class_Ozero(_1068860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1068860), _1068862), _1068862), -(_1068862 = c_Groups_Ozero__class_Ozero(_1068860))]]], (33002 ^ _776545) ^ [_1379037, _1379039, _1379041] : [hBOOL(hAPP(_1379037, _1379039)), -(hAPP(c_Set_OCollect(_1379041), hAPP(hAPP(c_COMBS(_1379041, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1379041), c_fconj), hAPP(c_fequal, _1379039))), _1379037)) = hAPP(hAPP(c_Set_Oinsert(_1379041), _1379039), c_Orderings_Obot__class_Obot(tc_fun(_1379041, tc_HOL_Obool))))], (21279 ^ _776545) ^ [_1161610, _1161612, _1161614] : [class_Int_Onumber__ring(_1161610), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1161610), hAPP(c_Int_Onumber__class_Onumber__of(_1161610), _1161612)), hAPP(c_Int_Onumber__class_Onumber__of(_1161610), _1161614)) = hAPP(c_Int_Onumber__class_Onumber__of(_1161610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1161612), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1161614))))], (45886 ^ _776545) ^ [_1697063, _1697065, _1697067] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1697063), tc_List_Olist(_1697063), c_List_Oappend(_1697063), _1697065), _1697067) = hAPP(hAPP(c_List_Oappend(_1697063), _1697065), c_List_Oconcat(_1697063, _1697067)))], (15111 ^ _776545) ^ [_1049341, _1049343, _1049345] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049341), _1049343)), 15114 ^ _776545 : [(15115 ^ _776545) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049341, tc_Nat_Onat), _1049345), _1049343) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15118 ^ _776545 : [(15119 ^ _776545) ^ [_1049503] : [hBOOL(hAPP(hAPP(c_member(_1049341), _1049503), _1049343)), -(hAPP(_1049345, _1049503) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (15125 ^ _776545) ^ [] : [15127 ^ _776545 : [(15130 ^ _776545) ^ [] : [hAPP(_1049345, 15126 ^ [_1049341, _1049343, _1049345]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (15128 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049341), 15126 ^ [_1049341, _1049343, _1049345]), _1049343)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049341, tc_Nat_Onat), _1049345), _1049343) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4496 ^ _776545) ^ [_844842, _844844, _844846, _844848, _844850, _844852] : [-(c_Lazy__Sequence_Oanamorph(_844852, _844848, _844844) = c_Lazy__Sequence_Oanamorph(_844850, _844846, _844842)), _844852 = _844850, _844848 = _844846, _844844 = _844842], (52373 ^ _776545) ^ [_1830100] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1830100)))], (17985 ^ _776545) ^ [_1099957, _1099959] : [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), _1099957), _1099959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1099959), _1099957)))], (25877 ^ _776545) ^ [_1244625, _1244627, _1244629] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1244625, _1244627)), _1244629) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244625), _1244629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244627), _1244629)))], (35036 ^ _776545) ^ [_1430351, _1430353, _1430355] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1430351, _1430353), _1430355)), -(c_Divides_Odivmod__nat(_1430351, _1430353) = _1430355)], (26673 ^ _776545) ^ [_1257915, _1257917] : [-(c_Int_Onat__aux(_1257915, _1257917) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1257915)), _1257917))], (3696 ^ _776545) ^ [_831974, _831976, _831978, _831980] : [-(c_List_Obutlast(_831980, _831976) = c_List_Obutlast(_831978, _831974)), _831980 = _831978, _831976 = _831974], (43068 ^ _776545) ^ [_1634743, _1634745, _1634747] : [43069 ^ _776545 : [(43072 ^ _776545) ^ [] : [_1634747 = c_List_Olist_ONil(_1634743)], (43070 ^ _776545) ^ [] : [_1634745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1634743), _1634745), _1634747) = c_List_Olist_ONil(_1634743))], (26841 ^ _776545) ^ [_1260311, _1260313] : [c_Nat__Transfer_Ois__nat(_1260311), 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_776545) ^ [_875942, _875944, _875946, _875948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875942, tc_HOL_Obool)), _875944), _875946)), hBOOL(hAPP(hAPP(c_member(_875942), _875948), _875944)), -(hBOOL(hAPP(hAPP(c_member(_875942), _875948), _875946)))], (25091 ^ _776545) ^ [_1230756, _1230758, _1230760] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230756), _1230758)), _1230760) = 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), _1230756), _1230760)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230758), _1230760))), 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, _1230756, _1230760)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1230758, _1230760))), _1230760)))], (16845 ^ _776545) ^ [_1079715, _1079717, 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_1752916)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752914)), _1752918)))], (16024 ^ _776545) ^ [_1066426, _1066428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066426), _1066428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1066426), hAPP(c_Nat_OSuc, _1066428))))], (23888 ^ _776545) ^ [_1209237, _1209239, _1209241] : [class_Rings_Olinordered__semidom(_1209237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209239), _1209241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209237), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209237), _1209239)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209237), _1209241))))], (14895 ^ _776545) ^ [_1045193, _1045195] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045193), _1045195)), _1045193)))], (24868 ^ _776545) ^ [_1226680, _1226682, _1226684, _1226686, _1226688, _1226690] : 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(34594 ^ _776545) ^ [_1420899, _1420901, _1420903, _1420905, _1420907, _1420909] : [hBOOL(hAPP(hAPP(_1420899, _1420901), _1420903)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420905, tc_fun(_1420907, tc_HOL_Obool))), _1420899), _1420909), _1420901), _1420903)))], (35776 ^ _776545) ^ [_1444417] : [-(hAPP(c_Int_Onat, _1444417) = 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, _1444417)), 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)))))))], (21515 ^ _776545) ^ [_1166260, _1166262, _1166264, _1166266] : [class_Fields_Ofield__inverse__zero(_1166260), class_Int_Onumber(_1166260), 21522 ^ _776545 : [(21523 ^ _776545) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166260), _1166262), _1166264) = hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266), 21526 ^ _776545 : [(21533 ^ _776545) ^ [] : [_1166264 = c_Groups_Ozero__class_Ozero(_1166260), -(hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266) = c_Groups_Ozero__class_Ozero(_1166260))], (21527 ^ _776545) ^ [] : [-(_1166264 = c_Groups_Ozero__class_Ozero(_1166260)), -(_1166262 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166260), hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266)), _1166264))]]], (21539 ^ _776545) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166260), _1166262), _1166264) = hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266)), 21542 ^ _776545 : [(21545 ^ _776545) ^ [] : [_1166262 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166260), hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266)), _1166264)], (21543 ^ _776545) ^ [] : [_1166264 = c_Groups_Ozero__class_Ozero(_1166260)]], 21546 ^ _776545 : [(21549 ^ _776545) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1166260), _1166266) = c_Groups_Ozero__class_Ozero(_1166260)], (21547 ^ _776545) ^ [] : [-(_1166264 = c_Groups_Ozero__class_Ozero(_1166260))]]]]], (40110 ^ _776545) ^ [_1557853, _1557855, _1557857, _1557859, _1557861, _1557863, _1557865, _1557867] : [c_Finite__Set_Ofolding__image(_1557853, _1557855, _1557857, _1557859, _1557861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557855), _1557863)), -(hAPP(hAPP(_1557861, hAPP(hAPP(c_COMBS(_1557855, _1557853, _1557853), hAPP(hAPP(c_COMBB(_1557853, tc_fun(_1557853, _1557853), _1557855), _1557857), _1557865)), _1557867)), _1557863) = hAPP(hAPP(_1557857, hAPP(hAPP(_1557861, _1557865), _1557863)), hAPP(hAPP(_1557861, _1557867), _1557863)))], (1004 ^ _776545) ^ [_791707, _791709, _791711, _791713, _791715, _791717] : [-(c_List_Olist__all(_791715, _791711, _791707)), c_List_Olist__all(_791717, _791713, _791709), _791717 = _791715, _791713 = _791711, _791709 = _791707], (45678 ^ _776545) ^ [_1692864, _1692866, _1692868] : [-(hAPP(c_List_Oset(tc_List_Olist(_1692864)), c_Enum_On__lists(_1692864, _1692866, _1692868)) = hAPP(c_Set_OCollect(tc_List_Olist(_1692864)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1692864), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1692864)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692864), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1692864)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1692864)))), _1692866))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1692864), tc_fun(_1692864, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1692864, tc_HOL_Obool), tc_fun(tc_fun(_1692864, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1692864)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1692864, tc_HOL_Obool))), c_List_Oset(_1692864))), hAPP(c_List_Oset(_1692864), _1692868)))))], (34912 ^ _776545) ^ [_1427922, _1427924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427922))), 34915 ^ _776545 : [(34922 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427924))), -(c_Divides_Odivmod__int(_1427922, _1427924) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427922), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427924))))], (34916 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1427924)), -(c_Divides_Odivmod__int(_1427922, _1427924) = c_Divides_OnegDivAlg(_1427922, _1427924))]]], (45680 ^ _776545) ^ [_1693009, _1693011] : [-(c_Enum_Oenum__the(_1693009, _1693011) = c_HOL_OThe(_1693009, _1693011))], (44870 ^ _776545) ^ [_1674586, _1674588, _1674590, _1674592, _1674594, _1674596] : [-(hAPP(hAPP(c_List_Ozip(_1674586, _1674588), hAPP(hAPP(c_List_Omap(_1674590, _1674586), _1674592), _1674594)), _1674596) = hAPP(hAPP(c_List_Omap(tc_prod(_1674590, _1674588), tc_prod(_1674586, _1674588)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674590, _1674588, tc_prod(_1674586, _1674588)), hAPP(hAPP(c_COMBB(_1674586, tc_fun(_1674588, tc_prod(_1674586, _1674588)), _1674590), c_Product__Type_OPair(_1674586, _1674588)), _1674592))), hAPP(hAPP(c_List_Ozip(_1674590, _1674588), _1674594), _1674596)))], (12518 ^ _776545) ^ [_996681, _996683, _996685] : [class_Lattices_Olattice(_996681), hAPP(_996683, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996681), 12523 ^ [_996681, _996683, _996685]), 12524 ^ [_996681, _996683, _996685])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_996681), hAPP(_996683, 12523 ^ [_996681, _996683, _996685])), hAPP(_996683, 12524 ^ [_996681, _996683, _996685])), hBOOL(hAPP(c_Finite__Set_Ofinite(_996681), _996685)), -(_996685 = c_Orderings_Obot__class_Obot(tc_fun(_996681, tc_HOL_Obool))), -(hAPP(_996683, c_Big__Operators_Olattice__class_OInf__fin(_996681, _996685)) = c_Big__Operators_Olattice__class_OInf__fin(_996681, hAPP(c_Set_Oimage(_996681, _996681, _996683), _996685)))], (48676 ^ _776545) ^ [_1757733, _1757735, _1757737, _1757739] : [-(c_List_Oreplicate(_1757733, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757735), _1757737), _1757739) = hAPP(hAPP(c_List_Oappend(_1757733), c_List_Oreplicate(_1757733, _1757735, _1757739)), c_List_Oreplicate(_1757733, _1757737, _1757739)))], (50485 ^ _776545) ^ [_1797170, _1797172, _1797174] : [_1797172 = _1797174, -(c_Fun_Obij__betw(_1797170, _1797170, c_Fun_Oid(_1797170), _1797172, _1797174))], (52047 ^ _776545) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (2740 ^ _776545) ^ [_817072, _817074] : [_817074 = _817072, -(c_Equiv__Relations_Oquotient(_817074) = c_Equiv__Relations_Oquotient(_817072))], (18262 ^ _776545) ^ [_1104931, _1104933, _1104935] : [class_Groups_Oordered__comm__monoid__add(_1104931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104931), c_Groups_Ozero__class_Ozero(_1104931)), _1104933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104931), c_Groups_Ozero__class_Ozero(_1104931)), _1104935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104931), c_Groups_Ozero__class_Ozero(_1104931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104931), _1104933), _1104935))))], (38902 ^ _776545) ^ [_1525056, _1525058, _1525060] : [-(hAPP(c_Set_Oimage(tc_prod(_1525056, _1525058), _1525056, c_Product__Type_Ofst(_1525056, _1525058)), _1525060) = hAPP(c_Relation_ODomain(_1525056, _1525058), _1525060))], (36598 ^ _776545) ^ [_1469964] : [-(_1469964 = 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), 36595 ^ [_1469964]), 36596 ^ [_1469964])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (14795 ^ _776545) ^ [_1043284, _1043286] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043286), _1043284))))], (3498 ^ _776545) ^ [_828841, _828843, _828845, _828847] : [-(c_Random_Oselect__weight(_828847, _828843) = c_Random_Oselect__weight(_828845, _828841)), _828847 = _828845, _828843 = _828841], (20831 ^ _776545) ^ [_1152616, _1152618, _1152620] : [class_Fields_Olinordered__field(_1152616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152616), _1152618), _1152620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152616), _1152618), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152616), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152616), _1152618), _1152620)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152616), c_Groups_Oone__class_Oone(_1152616)), c_Groups_Oone__class_Oone(_1152616))))))], (15714 ^ _776545) ^ [_1061494] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1061494)], (35624 ^ _776545) ^ [_1441424, _1441426, _1441428, _1441430, _1441432] : [-(hAPP(c_Product__Type_Ofst(_1441424, _1441426), hAPP(c_Product__Type_Oapsnd(_1441428, _1441426, _1441424, _1441430), _1441432)) = hAPP(c_Product__Type_Ofst(_1441424, _1441428), _1441432))], (32704 ^ _776545) ^ [_1370686] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1370686)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370686)), 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))))], (26262 ^ _776545) ^ [_1250894] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1250894)))), -(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), _1250894)) = 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), _1250894))))], (31377 ^ _776545) ^ [_1339839, _1339841, _1339843, _1339845] : [class_Orderings_Olinorder(_1339839), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339839), _1339841), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339839), _1339843), _1339845)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339839), _1339843), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339839), _1339841), _1339845)))], (36003 ^ _776545) ^ [_1452700, _1452702, _1452704] : [class_Lattices_Odistrib__lattice(_1452700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452700), _1452702)), -(_1452702 = c_Orderings_Obot__class_Obot(tc_fun(_1452700, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452700), _1452704)), -(_1452704 = c_Orderings_Obot__class_Obot(tc_fun(_1452700, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1452700), c_Big__Operators_Olattice__class_OSup__fin(_1452700, _1452702)), c_Big__Operators_Olattice__class_OSup__fin(_1452700, _1452704)) = c_Big__Operators_Olattice__class_OSup__fin(_1452700, hAPP(c_Set_OCollect(_1452700), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_HOL_Obool), tc_HOL_Obool, _1452700), c_HOL_OEx(_1452700)), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool)), tc_fun(_1452700, tc_HOL_Obool), _1452700), hAPP(c_COMBB(tc_fun(_1452700, tc_HOL_Obool), tc_HOL_Obool, _1452700), c_HOL_OEx(_1452700))), hAPP(hAPP(c_COMBC(_1452700, tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool)), tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_fun(tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool))), tc_fun(tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool)), tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool))), _1452700), c_COMBS(_1452700, tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_fun(_1452700, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1452700, tc_fun(tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool))), _1452700), hAPP(c_COMBB(tc_fun(_1452700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool)), _1452700), c_COMBS(_1452700, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool)), tc_fun(_1452700, tc_fun(_1452700, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1452700), hAPP(c_COMBB(tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1452700), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452700), c_fconj))), hAPP(hAPP(c_COMBC(_1452700, tc_fun(_1452700, tc_fun(_1452700, _1452700)), tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1452700, _1452700), tc_fun(_1452700, tc_HOL_Obool)), tc_fun(tc_fun(_1452700, tc_fun(_1452700, _1452700)), tc_fun(_1452700, tc_fun(_1452700, tc_HOL_Obool))), _1452700), c_COMBB(tc_fun(_1452700, _1452700), tc_fun(_1452700, tc_HOL_Obool), _1452700)), hAPP(hAPP(c_COMBB(tc_fun(_1452700, tc_HOL_Obool), tc_fun(tc_fun(_1452700, _1452700), tc_fun(_1452700, tc_HOL_Obool)), _1452700), c_COMBB(_1452700, tc_HOL_Obool, _1452700)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1452700)))))), hAPP(hAPP(c_COMBC(_1452700, tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1452700, tc_HOL_Obool), tc_fun(_1452700, tc_HOL_Obool)), _1452700), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1452700)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452700), c_fconj), hAPP(hAPP(c_COMBC(_1452700, tc_fun(_1452700, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452700)), _1452702)))), hAPP(hAPP(c_COMBC(_1452700, tc_fun(_1452700, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452700)), _1452704))))))))], (22111 ^ _776545) ^ [_1177470, _1177472, _1177474, _1177476] : [class_Rings_Olinordered__semidom(_1177470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177470), c_Groups_Oone__class_Oone(_1177470)), _1177472)), 22118 ^ _776545 : [(22125 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177474), _1177476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177470), hAPP(hAPP(c_Power_Opower__class_Opower(_1177470), _1177472), _1177474)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177470), _1177472), _1177476))))], (22119 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177470), hAPP(hAPP(c_Power_Opower__class_Opower(_1177470), _1177472), _1177474)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177470), _1177472), _1177476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1177474), _1177476)))]]], (37516 ^ _776545) ^ [_1490570, _1490572, _1490574] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490570), _1490572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490570, tc_HOL_Obool)), _1490572), hAPP(c_Set_Oimage(_1490570, _1490570, _1490574), _1490572))), -(c_Fun_Oinj__on(_1490570, _1490570, _1490574, _1490572))], (40757 ^ _776545) ^ [_1573979, _1573981, _1573983] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573979, _1573979), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573979, _1573979), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573979, _1573981)), c_Transitive__Closure_Ortrancl(_1573979, _1573983))), c_Transitive__Closure_Ortrancl(_1573979, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573979, _1573979), tc_HOL_Obool)), _1573981), _1573983)))))], (49325 ^ _776545) ^ [_1772296, _1772298, _1772300, _1772302] : [c_Relation_Otrans(_1772296, _1772298), -(c_Relation_Otrans(_1772300, hAPP(hAPP(c_Relation_Oinv__image(_1772296, _1772300), _1772298), _1772302)))], (26541 ^ _776545) ^ [_1255593, _1255595] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1255593), _1255595) = 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)), _1255593)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1255595))))], (19500 ^ _776545) ^ [_1128773, _1128775, _1128777, _1128779, _1128781] : [class_Groups_Ocomm__monoid__add(_1128773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1128775), _1128777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128775, tc_HOL_Obool)), _1128779), _1128777)), 19514 ^ _776545 : [(19517 ^ _776545) ^ [] : [hAPP(_1128781, 19513 ^ [_1128773, _1128775, _1128777, _1128779, _1128781]) = c_Groups_Ozero__class_Ozero(_1128773)], (19515 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1128775), 19513 ^ [_1128773, _1128775, _1128777, _1128779, _1128781]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1128775, tc_HOL_Obool)), _1128777), _1128779))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128775, _1128773), _1128781), _1128779) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1128775, _1128773), _1128781), _1128777))], (41759 ^ _776545) ^ [_1599759, _1599761, _1599763, _1599765, _1599767] : [hAPP(hAPP(c_List_Olist_OCons(_1599759), _1599761), _1599763) = hAPP(hAPP(c_List_Olist_OCons(_1599759), _1599765), _1599767), 41762 ^ _776545 : [(41765 ^ _776545) ^ [] : [-(_1599763 = _1599767)], (41763 ^ _776545) ^ [] : [-(_1599761 = _1599765)]]], (6809 ^ _776545) ^ [_886705, _886707, _886709] : [6811 ^ _776545 : [(6814 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886705, tc_HOL_Obool)), 6810 ^ [_886705, _886707, _886709]), _886709))], (6812 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_886705, tc_HOL_Obool)), 6810 ^ [_886705, _886707, _886709]), _886707)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886705, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_886705, tc_HOL_Obool), _886707)), _886709)))], (36606 ^ _776545) ^ [_1470210, _1470212, _1470214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1470210, _1470210), tc_HOL_Obool)), _1470212), _1470214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470210, tc_HOL_Obool)), hAPP(c_Relation_OField(_1470210), _1470212)), hAPP(c_Relation_OField(_1470210), _1470214))))], (48512 ^ _776545) ^ [_1754070, _1754072, _1754074, _1754076, _1754078] : [hBOOL(hAPP(hAPP(_1754074, _1754078), _1754076)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1754070, _1754072, _1754074), _1754076), _1754078)))], (4132 ^ _776545) ^ [_839112, _839114, _839116, _839118] : [-(c_Lazy__Sequence_Ohb__single(_839118, _839114) = c_Lazy__Sequence_Ohb__single(_839116, _839112)), _839118 = _839116, _839114 = _839112], (11924 ^ _776545) ^ [_985964, _985966, _985968, _985970, _985972, _985974] : [-(_985964 = _985966), -(hAPP(c_Fun_Ofun__upd(_985968, _985970, _985972, _985966, _985974), _985964) = hAPP(_985972, _985964))], (23699 ^ _776545) ^ [] : [-(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))], (14600 ^ _776545) ^ [_1039769, _1039771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039769), _1039771)), _1039769))], (47642 ^ _776545) ^ [_1734859, _1734861, _1734863, _1734865, _1734867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1734859, _1734861)), hAPP(_1734859, _1734863))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1734865, _1734865)), hAPP(hAPP(c_Product__Type_OPair(_1734865, _1734865), _1734861), _1734863)), c_List_Omeasures(_1734865, _1734867))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1734865, _1734865)), hAPP(hAPP(c_Product__Type_OPair(_1734865, _1734865), _1734861), _1734863)), c_List_Omeasures(_1734865, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1734865, tc_Nat_Onat)), _1734859), _1734867)))))], (27735 ^ _776545) ^ [_1275439] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1275439), hAPP(c_Int_Onumber__class_Onumber__of(_1275439), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1275439)), class_Int_Onumber__ring(_1275439), class_Rings_Olinordered__idom(_1275439)], (26745 ^ _776545) ^ [_1259015, _1259017] : [c_Nat__Transfer_Onat__set(_1259015), c_Nat__Transfer_Onat__set(_1259017), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1259015), _1259017)))], (32958 ^ _776545) ^ [_1377641, _1377643, _1377645, _1377647, _1377649] : [-(_1377641 = c_Orderings_Obot__class_Obot(tc_fun(_1377643, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377645, tc_HOL_Obool)), _1377647), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377643, tc_fun(_1377645, tc_HOL_Obool)), _1377641), _1377649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1377643, tc_fun(_1377645, tc_HOL_Obool)), _1377641), hAPP(hAPP(c_COMBB(tc_fun(_1377645, tc_HOL_Obool), tc_fun(_1377645, tc_HOL_Obool), _1377643), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377645, tc_HOL_Obool)), _1377647)), _1377649)))], (51951 ^ _776545) ^ [_1825857, _1825859] : [class_Groups_Ominus(_1825857), -(class_Groups_Ominus(tc_fun(_1825859, _1825857)))], (48668 ^ _776545) ^ [_1757557, _1757559, _1757561, _1757563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757557), _1757559)), -(hAPP(hAPP(c_List_Onth(_1757561), c_List_Oreplicate(_1757561, _1757559, _1757563)), _1757557) = _1757563)], (47132 ^ _776545) ^ [_1723966, _1723968, _1723970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723966), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723968)), _1723970))), -(hAPP(hAPP(c_List_Onth(_1723968), hAPP(c_List_Orev(_1723968), _1723970)), _1723966) = hAPP(hAPP(c_List_Onth(_1723968), _1723970), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723968)), _1723970)), hAPP(c_Nat_OSuc, _1723966))))], (48492 ^ _776545) ^ [_1753660, _1753662, _1753664] : [-(c_Predicate_Oconversep(_1753660, _1753662, c_Predicate_Oconversep(_1753662, _1753660, _1753664)) = _1753664)], (27821 ^ _776545) ^ [_1276783, _1276785] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276783)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1276785)))), 27824 ^ _776545 : [(27827 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1276785))], (27825 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276783), _1276785)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1276783), _1276785))], (13638 ^ _776545) ^ [_1019344, _1019346, _1019348, _1019350, _1019352] : [class_Groups_Oordered__ab__semigroup__add(_1019344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019344), _1019346), _1019348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019344), _1019350), _1019352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019344), _1019346), _1019350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019344), _1019348), _1019352))))], (44587 ^ _776545) ^ [_1668307, _1668309, _1668311] : [-(_1668307 = c_List_Olist_ONil(_1668309)), -(c_List_Olast(_1668309, hAPP(hAPP(c_List_Olist_OCons(_1668309), _1668311), _1668307)) = c_List_Olast(_1668309, _1668307))], (6963 ^ _776545) ^ [_889547, _889549] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_889547, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_889547, tc_HOL_Obool))), hAPP(c_Set_OPow(_889547), _889549))))], (43206 ^ _776545) ^ [_1637229, _1637231] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637229), tc_List_Olist(_1637229))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637229), tc_List_Olist(_1637229)), c_List_Olist_ONil(_1637229)), c_List_Olist_ONil(_1637229))), c_List_Olistrel(_1637229, _1637231))))], (41718 ^ _776545) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26158 ^ _776545) ^ [_1249200, _1249202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1249200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249202, _1249200)), _1249200)))], (12864 ^ _776545) ^ [_1003509, _1003511, _1003513, _1003515, _1003517, _1003519] : [c_Finite__Set_Ofun__left__comm(_1003509, _1003511, _1003513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003509), _1003515)), -(hBOOL(hAPP(hAPP(c_member(_1003509), _1003517), _1003515))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1003509, _1003511, _1003513), _1003519), hAPP(hAPP(c_Set_Oinsert(_1003509), _1003517), _1003515)) = hAPP(hAPP(c_Finite__Set_Ofold(_1003509, _1003511, _1003513), hAPP(hAPP(_1003513, _1003517), _1003519)), _1003515))], (49525 ^ _776545) ^ [_1777449, _1777451, _1777453, _1777455] : [-(c_Wellfounded_Omax__extp(_1777449, _1777451, _1777453, _1777455)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1777449), _1777453)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1777449), _1777455)), -(_1777455 = c_Orderings_Obot__class_Obot(tc_fun(_1777449, tc_HOL_Obool))), 49539 ^ _776545 : [(49542 ^ _776545) ^ [_1777794] : [hBOOL(hAPP(hAPP(c_member(_1777449), _1777794), _1777455)), hBOOL(hAPP(hAPP(_1777451, 49538 ^ [_1777449, _1777451, _1777453, _1777455]), _1777794))], (49540 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777449), 49538 ^ [_1777449, _1777451, _1777453, _1777455]), _1777453)))]]], (16380 ^ _776545) ^ [_1071967, _1071969] : [class_Groups_Olinordered__ab__group__add(_1071967), 16383 ^ _776545 : [(16390 ^ _776545) ^ [] : [_1071969 = c_Groups_Ozero__class_Ozero(_1071967), -(_1071969 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071967), _1071969))], (16384 ^ _776545) ^ [] : [_1071969 = hAPP(c_Groups_Ouminus__class_Ouminus(_1071967), _1071969), -(_1071969 = c_Groups_Ozero__class_Ozero(_1071967))]]], (8209 ^ _776545) ^ [_916911, _916913, _916915, _916917, _916919] : [class_Lattices_Olattice(_916911), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916913, _916911)), _916915), _916917), _916919) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916911), hAPP(_916915, _916919)), hAPP(_916917, _916919)))], (36438 ^ _776545) ^ [_1464814, _1464816] : [-(c_FunDef_Orp__inv__image(_1464814, _1464816) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))))), tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))), tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)), tc_fun(tc_fun(_1464816, _1464814), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool)), c_COMBS(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)), tc_fun(tc_fun(_1464816, _1464814), tc_fun(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), tc_fun(tc_prod(_1464814, _1464814), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool))), tc_fun(_1464816, _1464814)), c_Product__Type_OPair(tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool), tc_fun(tc_prod(_1464816, _1464816), tc_HOL_Obool)))), c_Relation_Oinv__image(_1464814, _1464816))))), c_Relation_Oinv__image(_1464814, _1464816))))], (15702 ^ _776545) ^ [_1061309, _1061311] : [hAPP(c_Nat_OSuc, _1061309) = hAPP(c_Nat_OSuc, _1061311), -(_1061309 = _1061311)], (19388 ^ _776545) ^ [_1126575, _1126577] : [class_Int_Oring__char__0(_1126575), hBOOL(hAPP(hAPP(c_member(_1126575), _1126577), c_Int_Oring__1__class_OInts(_1126575))), 19395 ^ _776545 : [(19402 ^ _776545) ^ [] : [_1126577 = c_Groups_Ozero__class_Ozero(_1126575), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126575), _1126577), _1126577) = c_Groups_Ozero__class_Ozero(_1126575))], (19396 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1126575), _1126577), _1126577) = c_Groups_Ozero__class_Ozero(_1126575), -(_1126577 = c_Groups_Ozero__class_Ozero(_1126575))]]], (50427 ^ _776545) ^ [_1796101, _1796103, _1796105, _1796107, _1796109] : [c_Fun_Obij__betw(_1796101, _1796103, _1796105, _1796107, _1796109), 50430 ^ _776545 : [(50433 ^ _776545) ^ [] : [-(hAPP(c_Set_Oimage(_1796101, _1796103, _1796105), _1796107) = _1796109)], (50431 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1796101, _1796103, _1796105, _1796107))]]], (32706 ^ _776545) ^ [_1370723, _1370725, _1370727, _1370729] : [_1370723 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1370725, _1370727), 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)), _1370729))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370725), _1370723)))], (29117 ^ _776545) ^ [_1298383] : [-(c_Int_Osucc(c_Int_OBit1(_1298383)) = c_Int_OBit0(c_Int_Osucc(_1298383)))], (26078 ^ _776545) ^ [_1247864] : [-(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)), _1247864)) = _1247864)], (43924 ^ _776545) ^ [_1654310, _1654312] : [-(hAPP(hAPP(c_List_Odrop(_1654310), _1654312), c_List_Olist_ONil(_1654310)) = c_List_Olist_ONil(_1654310))], (33985 ^ _776545) ^ [_1407397, _1407399, _1407401, _1407403] : [class_Complete__Lattice_Ocomplete__lattice(_1407397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407399), _1407401)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407399, _1407397), _1407401), _1407403) = hAPP(hAPP(c_Finite__Set_Ofold(_1407399, _1407397, hAPP(hAPP(c_COMBB(_1407397, tc_fun(_1407397, _1407397), _1407399), c_Lattices_Osemilattice__sup__class_Osup(_1407397)), _1407403)), c_Orderings_Obot__class_Obot(_1407397)), _1407401))], (28129 ^ _776545) ^ [_1281709, _1281711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1281709)), _1281711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1281709), _1281711)))], (17421 ^ _776545) ^ [_1090274, _1090276, _1090278] : [class_Rings_Olinordered__semiring__strict(_1090274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090274), c_Groups_Ozero__class_Ozero(_1090274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090274), _1090276), _1090278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090274), c_Groups_Ozero__class_Ozero(_1090274)), _1090276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090274), c_Groups_Ozero__class_Ozero(_1090274)), _1090278)))], (38721 ^ _776545) ^ [_1520885, _1520887, _1520889, _1520891, _1520893] : [hAPP(_1520891, _1520887) = _1520893, -(hBOOL(hAPP(hAPP(c_member(_1520885), _1520887), hAPP(c_Set_Ovimage(_1520885, _1520889, _1520891), hAPP(hAPP(c_Set_Oinsert(_1520889), _1520893), c_Orderings_Obot__class_Obot(tc_fun(_1520889, tc_HOL_Obool)))))))], (48051 ^ _776545) ^ [_1744341, _1744343, _1744345] : [-(c_List_Olist__ex(_1744341, _1744343, _1744345)), 48052 ^ _776545 : [(48053 ^ _776545) ^ [_1744406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744406), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744341)), _1744345))), hBOOL(hAPP(_1744343, hAPP(hAPP(c_List_Onth(_1744341), _1744345), _1744406)))]]], (10445 ^ _776545) ^ [_955960, _955962, _955964] : [class_Groups_Oordered__ab__group__add(_955960), 10448 ^ _776545 : [(10455 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955960), _955964), _955962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955960), hAPP(c_Groups_Ouminus__class_Ouminus(_955960), _955962)), hAPP(c_Groups_Ouminus__class_Ouminus(_955960), _955964))))], (10449 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955960), hAPP(c_Groups_Ouminus__class_Ouminus(_955960), _955962)), hAPP(c_Groups_Ouminus__class_Ouminus(_955960), _955964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955960), _955964), _955962)))]]], (5422 ^ _776545) ^ [_859385, _859387] : [_859387 = _859385, -(c_Orderings_Oord__class_Oless__eq(_859387) = c_Orderings_Oord__class_Oless__eq(_859385))], (46838 ^ _776545) ^ [_1717642, _1717644, _1717646] : [class_Orderings_Olinorder(_1717642), hBOOL(hAPP(hAPP(c_member(_1717642), _1717644), hAPP(c_List_Oset(_1717642), _1717646))), c_List_Olinorder__class_Osorted(_1717642, _1717646), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1717642, _1717642, c_COMBI(_1717642)), _1717644), c_List_Oremove1(_1717642, _1717644, _1717646)) = _1717646)], (52147 ^ _776545) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (39011 ^ _776545) ^ [_1527670, _1527672, _1527674, _1527676] : [39012 ^ _776545 : [(39013 ^ _776545) ^ [_1527724] : [hBOOL(hAPP(hAPP(_1527674, _1527676), _1527724))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1527670, _1527672, _1527674), _1527676)))], (3446 ^ _776545) ^ [_828021, _828023, _828025, _828027, _828029, _828031] : [-(c_List_Opartition(_828031, _828027, _828023) = c_List_Opartition(_828029, _828025, _828021)), _828031 = _828029, _828027 = _828025, _828023 = _828021], (34391 ^ _776545) ^ [_1416716, _1416718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416716), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1416718, _1416716) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416718), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416716)))], (49774 ^ _776545) ^ [_1782293, _1782295, _1782297] : [c_Relation_Orefl__on(_1782293, _1782295, _1782297), c_Relation_Osym(_1782293, _1782297), c_Relation_Otrans(_1782293, _1782297), -(c_Equiv__Relations_Oequiv(_1782293, _1782295, _1782297))], (42524 ^ _776545) ^ [_1622751, _1622753, _1622755] : [-(_1622751 = _1622753), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622755)), _1622751) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622755)), _1622753), 42530 ^ _776545 : [(42533 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1622755, _1622755, tc_HOL_Obool), c_fequal), 42529 ^ [_1622751, _1622753, _1622755]))], (42531 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622755, _1622755)), 42529 ^ [_1622751, _1622753, _1622755]), hAPP(c_List_Oset(tc_prod(_1622755, _1622755)), hAPP(hAPP(c_List_Ozip(_1622755, _1622755), _1622751), _1622753)))))]]], (27347 ^ _776545) ^ [_1268539, _1268541, _1268543] : [class_Rings_Olinordered__idom(_1268539), -(hAPP(c_Groups_Oabs__class_Oabs(_1268539), hAPP(hAPP(c_Power_Opower__class_Opower(_1268539), _1268541), _1268543)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1268539), hAPP(c_Groups_Oabs__class_Oabs(_1268539), _1268541)), _1268543))], (49105 ^ _776545) ^ [_1766920, _1766922, _1766924, _1766926] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1766920, _1766922, _1766924, c_Code__Numeral_OSuc__code__numeral(_1766926)) = hAPP(hAPP(_1766924, _1766926), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1766920, _1766922, _1766924, _1766926)))], (52279 ^ _776545) ^ [_1828945, _1828947] : [-(class_Finite__Set_Ofinite(tc_sum(_1828945, _1828947))), class_Finite__Set_Ofinite(_1828945), class_Finite__Set_Ofinite(_1828947)], (47697 ^ _776545) ^ [_1736492, _1736494, _1736496, _1736498] : [class_Orderings_Oorder(_1736492), class_Enum_Oenum(_1736494), 47704 ^ _776545 : [(47713 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1736494, _1736492)), _1736496), _1736498))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736494, _1736492)), _1736496), _1736498)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1736494), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1736494), c_fNot), hAPP(hAPP(c_COMBS(_1736494, _1736492, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736492, tc_fun(_1736492, tc_HOL_Obool), _1736494), c_fequal), _1736496)), _1736498))))], (47705 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1736494, _1736492)), _1736496), _1736498)), 47708 ^ _776545 : [(47711 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1736494), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1736494), c_fNot), hAPP(hAPP(c_COMBS(_1736494, _1736492, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736492, tc_fun(_1736492, tc_HOL_Obool), _1736494), c_fequal), _1736496)), _1736498)))))], (47709 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736494, _1736492)), _1736496), _1736498)))]]]]], (44918 ^ _776545) ^ [_1675889, _1675891, _1675893, _1675895] : [hBOOL(hAPP(c_List_Odistinct(_1675889), hAPP(hAPP(c_List_Omap(_1675891, _1675889), _1675893), _1675895))), 44921 ^ _776545 : [(44924 ^ _776545) ^ [] : [-(c_Fun_Oinj__on(_1675891, _1675889, _1675893, hAPP(c_List_Oset(_1675891), _1675895)))], (44922 ^ _776545) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1675891), _1675895)))]]], (47899 ^ _776545) ^ [_1741172, _1741174, _1741176, _1741178, _1741180] : [hAPP(hAPP(c_List_Olist_OCons(_1741172), _1741174), _1741176) = hAPP(c_List_Ofilter(_1741172, _1741178), _1741180), 47904 ^ _776545 : [(47913 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1741178, _1741174)))], (47915 ^ _776545) ^ [] : [-(_1741176 = hAPP(c_List_Ofilter(_1741172, _1741178), 47903 ^ [_1741172, _1741174, _1741176, _1741178, _1741180]))], (47907 ^ _776545) ^ [_1741486] : [hBOOL(hAPP(hAPP(c_member(_1741172), _1741486), hAPP(c_List_Oset(_1741172), 47902 ^ [_1741172, _1741174, _1741176, _1741178, _1741180]))), hBOOL(hAPP(_1741178, _1741486))], (47905 ^ _776545) ^ [] : [-(_1741180 = hAPP(hAPP(c_List_Oappend(_1741172), 47902 ^ [_1741172, _1741174, _1741176, _1741178, _1741180]), hAPP(hAPP(c_List_Olist_OCons(_1741172), _1741174), 47903 ^ [_1741172, _1741174, _1741176, _1741178, _1741180])))]]], (26675 ^ _776545) ^ [] : [-(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))))], (48374 ^ _776545) ^ [_1750744, _1750746, _1750748] : [c_List_Olist__ex1(_1750744, _1750746, _1750748), 48378 ^ _776545 : [(48383 ^ _776545) ^ [_1750990] : [-(_1750990 = 48377 ^ [_1750744, _1750746, _1750748]), hBOOL(hAPP(hAPP(c_member(_1750744), _1750990), hAPP(c_List_Oset(_1750744), _1750748))), hBOOL(hAPP(_1750746, _1750990))], (48381 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1750746, 48377 ^ [_1750744, _1750746, _1750748])))], (48379 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750744), 48377 ^ [_1750744, _1750746, _1750748]), hAPP(c_List_Oset(_1750744), _1750748))))]]], (16660 ^ _776545) ^ [_1076199, _1076201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076199), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076199), _1076201)))))], (49616 ^ _776545) ^ [_1779166, _1779168] : [49619 ^ _776545 : [(49624 ^ _776545) ^ [] : [49617 ^ [_1779166, _1779168] = 49618 ^ [_1779166, _1779168]], (49622 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779166, _1779166)), hAPP(hAPP(c_Product__Type_OPair(_1779166, _1779166), 49618 ^ [_1779166, _1779168]), 49617 ^ [_1779166, _1779168])), _1779168)))], (49620 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779166, _1779166)), hAPP(hAPP(c_Product__Type_OPair(_1779166, _1779166), 49617 ^ [_1779166, _1779168]), 49618 ^ [_1779166, _1779168])), _1779168)))]], -(c_Relation_Oantisym(_1779166, _1779168))], (16508 ^ _776545) ^ [_1073771] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073771), _1073771) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28475 ^ _776545) ^ [_1287594] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1287594)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1287594))))], (21423 ^ _776545) ^ [_1164769, _1164771, _1164773] : [class_Rings_Oring__1(_1164769), hBOOL(hAPP(hAPP(c_member(_1164769), _1164771), c_Int_Oring__1__class_OInts(_1164769))), -(hBOOL(hAPP(hAPP(c_member(_1164769), hAPP(hAPP(c_Power_Opower__class_Opower(_1164769), _1164771), _1164773)), c_Int_Oring__1__class_OInts(_1164769))))], (43872 ^ _776545) ^ [_1653110, _1653112, _1653114, _1653116, _1653118] : [hAPP(hAPP(c_List_Odrop(_1653110), _1653112), _1653114) = hAPP(hAPP(c_List_Olist_OCons(_1653110), _1653116), _1653118), -(hAPP(hAPP(c_List_Onth(_1653110), _1653114), _1653112) = _1653116)], (17587 ^ _776545) ^ [_1093280, _1093282, _1093284] : [class_Groups_Oordered__ab__group__add(_1093280), 17590 ^ _776545 : [(17597 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093280), _1093282), _1093284)), c_Groups_Ozero__class_Ozero(_1093280))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093280), _1093282), _1093284)))], (17591 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093280), _1093282), _1093284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093280), _1093282), _1093284)), c_Groups_Ozero__class_Ozero(_1093280))))]]], (19797 ^ _776545) ^ [_1133831, _1133833, _1133835, _1133837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1133831), _1133833)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133835), _1133837)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1133831, _1133835)), c_Sum__Type_OPlus(_1133831, _1133835, _1133833, _1133837))))], (46882 ^ _776545) ^ [_1718607, _1718609, _1718611, _1718613] : [class_Orderings_Olinorder(_1718607), c_List_Olinorder__class_Osorted(_1718607, _1718609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718611), _1718613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718613), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718607)), _1718609))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718607), hAPP(hAPP(c_List_Onth(_1718607), _1718609), _1718611)), hAPP(hAPP(c_List_Onth(_1718607), _1718609), _1718613))))], (29179 ^ _776545) ^ [_1299557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1299557)))], (30530 ^ _776545) ^ [_1324298] : [class_Orderings_Oord(_1324298), -(c_Orderings_Oord__class_Omin(_1324298) = c_Orderings_Oord_Omin(_1324298, c_Orderings_Oord__class_Oless__eq(_1324298)))], (32604 ^ _776545) ^ [_1367725, _1367727, _1367729, _1367731, _1367733] : [-(_1367725 = c_Orderings_Obot__class_Obot(tc_fun(_1367727, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367729, tc_HOL_Obool)), _1367731), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367727, tc_fun(_1367729, tc_HOL_Obool)), _1367725), _1367733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1367727, tc_fun(_1367729, tc_HOL_Obool)), _1367725), hAPP(hAPP(c_COMBB(tc_fun(_1367729, tc_HOL_Obool), tc_fun(_1367729, tc_HOL_Obool), _1367727), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1367729, tc_HOL_Obool)), _1367731)), _1367733)))], (26062 ^ _776545) ^ [_1247657, _1247659] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247657, _1247659)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247657), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1247659)))], (11106 ^ _776545) ^ [_968624, _968626, _968628, _968630, _968632] : [hBOOL(hAPP(hAPP(c_member(_968624), _968626), hAPP(c_Set_Oimage(_968628, _968624, _968630), _968632))), 11110 ^ _776545 : [(11113 ^ _776545) ^ [] : [-(_968626 = hAPP(_968630, 11109 ^ [_968624, _968626, _968628, _968630, _968632]))], (11111 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968628), 11109 ^ [_968624, _968626, _968628, _968630, _968632]), _968632)))]]], (34491 ^ _776545) ^ [_1418452, _1418454, _1418456, _1418458] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1418452, tc_fun(_1418454, tc_HOL_Obool))), _1418456), _1418458))], (23609 ^ _776545) ^ [_1204418, _1204420] : [class_Divides_Osemiring__div(_1204418), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1204418), _1204420), c_Groups_Oone__class_Oone(_1204418)) = _1204420)], (45040 ^ _776545) ^ [_1678565, _1678567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1678565)), hAPP(c_Code__Numeral_Oof__nat, _1678567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678565), _1678567)))], (4522 ^ _776545) ^ [_845233, _845235] : [_845235 = _845233, -(c_List_Olist_OCons(_845235) = c_List_Olist_OCons(_845233))], (50687 ^ _776545) ^ [_1801195, _1801197, _1801199] : [c_Equiv__Relations_Oequivp(_1801195, _1801197), 50690 ^ _776545 : [(50691 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1801199, 50698 ^ [_1801195, _1801197, _1801199]))), 50692 ^ _776545 : [(50693 ^ _776545) ^ [_1801317] : [hBOOL(hAPP(hAPP(c_member(_1801195), _1801317), c_Quotient_ORespects(_1801195, _1801197))), hBOOL(hAPP(_1801199, _1801317))]]], (50702 ^ _776545) ^ [] : [50703 ^ _776545 : [(50704 ^ _776545) ^ [_1801484] : [hBOOL(hAPP(_1801199, _1801484))]], 50706 ^ _776545 : [(50709 ^ _776545) ^ [] : [-(hBOOL(hAPP(_1801199, 50705 ^ [_1801195, _1801197, _1801199])))], (50707 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801195), 50705 ^ [_1801195, _1801197, _1801199]), c_Quotient_ORespects(_1801195, _1801197))))]]]]], (9970 ^ _776545) ^ [_947209, _947211, _947213] : [class_Orderings_Oorder(_947209), 9973 ^ _776545 : [(9980 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947209), _947211), _947213))), -(c_Orderings_Obot__class_Obot(tc_fun(_947209, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_947209, _947211, _947213))], (9974 ^ _776545) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_947209, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_947209, _947211, _947213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947209), _947211), _947213))]]], (45978 ^ _776545) ^ [_1698962, _1698964] : [class_Orderings_Olinorder(_1698962), -(c_List_Olinorder__class_Osort__key(_1698962, _1698962, c_COMBI(_1698962), _1698964) = hAPP(c_List_Ofoldl(tc_List_Olist(_1698962), _1698962, hAPP(c_COMBC(_1698962, tc_List_Olist(_1698962), tc_List_Olist(_1698962)), c_List_Olinorder__class_Oinsort__key(_1698962, _1698962, c_COMBI(_1698962))), c_List_Olist_ONil(_1698962)), _1698964))], (33298 ^ _776545) ^ [_1387008, _1387010, _1387012, _1387014, _1387016] : [class_Groups_Ocomm__monoid__mult(_1387008), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387010, _1387008), hAPP(hAPP(c_COMBS(_1387010, _1387008, _1387008), hAPP(hAPP(c_COMBB(_1387008, tc_fun(_1387008, _1387008), _1387010), c_Groups_Otimes__class_Otimes(_1387008)), _1387012)), _1387014)), _1387016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387008), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387010, _1387008), _1387012), _1387016)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387010, _1387008), _1387014), _1387016)))], (35204 ^ _776545) ^ [_1433425, _1433427, _1433429] : [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), _1433425), _1433427))), -(hBOOL(hAPP(hAPP(_1433429, _1433425), _1433427))), 35211 ^ _776545 : [(35214 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(_1433429, 35209 ^ [_1433425, _1433427, _1433429]), 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)))), 35210 ^ [_1433425, _1433427, _1433429])))), -(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), 35209 ^ [_1433425, _1433427, _1433429]), 35210 ^ [_1433425, _1433427, _1433429])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 35210 ^ [_1433425, _1433427, _1433429]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35224 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(_1433429, 35209 ^ [_1433425, _1433427, _1433429]), 35210 ^ [_1433425, _1433427, _1433429]))], (35212 ^ _776545) ^ [] : [-(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), 35209 ^ [_1433425, _1433427, _1433429]), 35210 ^ [_1433425, _1433427, _1433429]))))]]], (43088 ^ _776545) ^ [_1635094, _1635096, _1635098] : [-(hAPP(hAPP(c_List_Ozip(_1635094, _1635096), c_List_Olist_ONil(_1635094)), _1635098) = c_List_Olist_ONil(tc_prod(_1635094, _1635096)))], (802 ^ _776545) ^ [_788584, _788586, _788588, _788590] : [-(c_Relation_Osym(_788588, _788584)), c_Relation_Osym(_788590, _788586), _788590 = _788588, _788586 = _788584], (39367 ^ _776545) ^ [_1538699, _1538701, _1538703, _1538705, _1538707, _1538709] : [class_Groups_Ocomm__monoid__mult(_1538699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538701), _1538703)), 39377 ^ _776545 : [(39380 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538705), hAPP(_1538707, 39376 ^ [_1538699, _1538701, _1538703, _1538705, _1538707, _1538709])))], (39378 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538701), 39376 ^ [_1538699, _1538701, _1538703, _1538705, _1538707, _1538709]), _1538703)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538701, _1538699), hAPP(hAPP(c_COMBS(_1538701, tc_fun(_1538705, tc_HOL_Obool), _1538699), hAPP(hAPP(c_COMBB(tc_fun(_1538705, _1538699), tc_fun(tc_fun(_1538705, tc_HOL_Obool), _1538699), _1538701), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538705, _1538699)), _1538709)), _1538707)), _1538703) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1538701, _1538705), _1538699), hAPP(c_Product__Type_Oprod_Oprod__case(_1538701, _1538705, _1538699), _1538709)), hAPP(hAPP(c_Product__Type_OSigma(_1538701, _1538705), _1538703), _1538707)))], (50393 ^ _776545) ^ [_1795408, _1795410, _1795412, _1795414] : [c_Fun_Obij__betw(_1795408, _1795410, _1795412, c_Orderings_Otop__class_Otop(tc_fun(_1795408, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1795410, tc_HOL_Obool))), 50396 ^ _776545 : [(50403 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795410), _1795414)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795408), hAPP(c_Set_Ovimage(_1795408, _1795410, _1795412), _1795414))))], (50397 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795408), hAPP(c_Set_Ovimage(_1795408, _1795410, _1795412), _1795414))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795410), _1795414)))]]], (32298 ^ _776545) ^ [_1357320, _1357322, _1357324, _1357326, _1357328, _1357330, _1357332, _1357334] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1357320, tc_fun(_1357322, tc_fun(_1357324, tc_HOL_Obool))), _1357326), _1357328), _1357330), _1357332)), hBOOL(hAPP(hAPP(c_member(_1357320), _1357334), _1357326)), -(hBOOL(hAPP(hAPP(hAPP(_1357328, _1357334), _1357330), _1357332)))], (48262 ^ _776545) ^ [_1748617, _1748619, _1748621] : [c_FunDef_Ois__measure(_1748617, _1748619), -(c_FunDef_Ois__measure(tc_prod(_1748617, _1748621), hAPP(hAPP(c_COMBB(_1748617, tc_Nat_Onat, tc_prod(_1748617, _1748621)), _1748619), c_Product__Type_Ofst(_1748617, _1748621))))], (38858 ^ _776545) ^ [_1524190, _1524192, _1524194] : [c_Wellfounded_Oacyclic(_1524190, _1524192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524190, _1524190), tc_HOL_Obool)), _1524194), _1524192)), -(c_Wellfounded_Oacyclic(_1524190, _1524194))], (44405 ^ _776545) ^ [_1664569, _1664571, _1664573, _1664575, _1664577] : [c_Finite__Set_Ofun__left__comm__idem(_1664569, _1664571, _1664573), -(hAPP(hAPP(c_Finite__Set_Ofold(_1664569, _1664571, _1664573), _1664575), hAPP(c_List_Oset(_1664569), _1664577)) = hAPP(c_List_Ofoldl(_1664571, _1664569, hAPP(c_COMBC(_1664569, _1664571, _1664571), _1664573), _1664575), _1664577))], (21995 ^ _776545) ^ [_1175237, _1175239, _1175241, _1175243] : [class_Fields_Olinordered__field__inverse__zero(_1175237), class_Int_Onumber(_1175237), 22002 ^ _776545 : [(22003 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175237), _1175241), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)))), 22006 ^ _776545 : [(22013 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), c_Groups_Ozero__class_Ozero(_1175237)), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)))), 22016 ^ _776545 : [(22023 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)), c_Groups_Ozero__class_Ozero(_1175237)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175239), c_Groups_Ozero__class_Ozero(_1175237))))], (22017 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)), c_Groups_Ozero__class_Ozero(_1175237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175237), _1175239), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)))))]]], (22007 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), c_Groups_Ozero__class_Ozero(_1175237)), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175237), _1175239), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))), _1175241)))]]], (22029 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1175237), _1175241), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))))), 22032 ^ _776545 : [(22035 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175237), _1175239), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))), _1175241))], (22033 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), c_Groups_Ozero__class_Ozero(_1175237)), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))))]], 22036 ^ _776545 : [(22039 ^ _776545) ^ [] : [22040 ^ _776545 : [(22043 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175237), _1175239), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243))))], (22041 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)), c_Groups_Ozero__class_Ozero(_1175237))))]], 22044 ^ _776545 : [(22047 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175237), _1175239), c_Groups_Ozero__class_Ozero(_1175237)))], (22045 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)), c_Groups_Ozero__class_Ozero(_1175237)))]]], (22037 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175237), c_Groups_Ozero__class_Ozero(_1175237)), hAPP(c_Int_Onumber__class_Onumber__of(_1175237), _1175243)))]]]]], (952 ^ _776545) ^ [_790809, _790811, _790813, _790815, _790817, _790819, _790821, _790823] : [-(c_Equiv__Relations_Ocongruent(_790821, _790817, _790813, _790809)), c_Equiv__Relations_Ocongruent(_790823, _790819, _790815, _790811), _790823 = _790821, _790819 = _790817, _790815 = _790813, _790811 = _790809], (33973 ^ _776545) ^ [_1406967, _1406969, _1406971, _1406973] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1406967), _1406969)), -(hAPP(c_Set_Oimage(_1406967, _1406971, _1406973), _1406969) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1406971, tc_HOL_Obool), _1406967, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406971, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1406967, tc_fun(_1406971, tc_HOL_Obool), tc_fun(_1406971, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1406971, tc_fun(tc_fun(_1406971, tc_HOL_Obool), tc_fun(_1406971, tc_HOL_Obool)), _1406967), c_Set_Oinsert(_1406971)), _1406973)), c_Orderings_Obot__class_Obot(tc_fun(_1406971, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1406971, tc_HOL_Obool))), _1406969))], (25309 ^ _776545) ^ [_1234619, _1234621, _1234623] : [-(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), _1234619), _1234621)), _1234621)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234619, _1234621))), _1234623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234619), _1234623))], (7640 ^ _776545) ^ [_903244, _903246, _903248, _903250] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903244, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903244, tc_HOL_Obool)), _903246), _903248)), _903250) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903244, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903244, tc_HOL_Obool)), _903246), _903250)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_903244, tc_HOL_Obool)), _903248), _903250)))], (3804 ^ _776545) ^ [_833648, _833650] : [_833650 = _833648, -(c_Enum_Oenum__class_Oenum__ex(_833650) = c_Enum_Oenum__class_Oenum__ex(_833648))], (1164 ^ _776545) ^ [_793959, _793961] : [-(class_Groups_Oordered__ab__group__add(_793959)), _793961 = _793959, class_Groups_Oordered__ab__group__add(_793961)], (17837 ^ _776545) ^ [_1097504, _1097506, _1097508] : [class_Groups_Ocomm__monoid__add(_1097504), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1097506, _1097504), _1097508), c_Orderings_Obot__class_Obot(tc_fun(_1097506, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1097504))], (42077 ^ _776545) ^ [_1610025, _1610027, _1610029, _1610031, _1610033, _1610035] : [hBOOL(hAPP(hAPP(_1610025, _1610027), _1610029)), c_List_Olistrelp(_1610031, _1610025, _1610033, _1610035), -(c_List_Olistrelp(_1610031, _1610025, hAPP(hAPP(c_List_Olist_OCons(_1610031), _1610027), _1610033), hAPP(hAPP(c_List_Olist_OCons(_1610031), _1610029), _1610035)))], (34684 ^ _776545) ^ [_1422723, _1422725] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1422723, _1422725) = 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), _1422723), _1422725)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1422723, _1422725)))], (13802 ^ _776545) ^ [_1022636, _1022638, _1022640] : [class_Groups_Ogroup__add(_1022636), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1022636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1022636), _1022638), _1022640)), _1022640) = _1022638)], (46662 ^ _776545) ^ [_1714278, _1714280, _1714282, _1714284, _1714286] : [class_Orderings_Olinorder(_1714278), c_List_Olinorder__class_Osorted(_1714278, hAPP(hAPP(c_List_Omap(_1714280, _1714278), _1714282), _1714284)), -(c_List_Olinorder__class_Osorted(_1714278, hAPP(hAPP(c_List_Omap(_1714280, _1714278), _1714282), c_List_Oremove1(_1714280, _1714286, _1714284))))], (50602 ^ _776545) ^ [_1799404, _1799406, _1799408] : [c_Fun_Oinj__on(_1799404, _1799406, _1799408, c_Orderings_Otop__class_Otop(tc_fun(_1799404, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1799404, _1799406, _1799408), c_Orderings_Otop__class_Otop(tc_fun(_1799404, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799406, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1799404, _1799406, _1799408, c_Orderings_Otop__class_Otop(tc_fun(_1799404, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799406, tc_HOL_Obool))))], (4760 ^ _776545) ^ [_848994, _848996, _848998, _849000] : [-(c_Product__Type_Ofst(_849000, _848996) = c_Product__Type_Ofst(_848998, _848994)), _849000 = _848998, _848996 = _848994], (4936 ^ _776545) ^ [_851754, _851756] : [_851756 = _851754, -(c_HOL_OEx(_851756) = c_HOL_OEx(_851754))], (33585 ^ _776545) ^ [_1394779, _1394781, _1394783] : [class_Groups_Ocomm__monoid__add(_1394779), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1394781, _1394779), hAPP(c_COMBK(_1394779, _1394781), c_Groups_Ozero__class_Ozero(_1394779))), _1394783) = c_Groups_Ozero__class_Ozero(_1394779))], (52027 ^ _776545) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (39940 ^ _776545) ^ [_1554032, _1554034, _1554036, _1554038, _1554040, _1554042, _1554044] : [hAPP(c_Fun_Ocomp(_1554032, _1554034, _1554036, _1554038), _1554040) = hAPP(c_Fun_Ocomp(_1554034, _1554034, _1554036, c_Fun_Oid(_1554034)), _1554042), -(hAPP(_1554038, hAPP(_1554040, _1554044)) = hAPP(_1554042, _1554044))], (23715 ^ _776545) ^ [_1206084] : [-(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), _1206084))))], (41005 ^ _776545) ^ [_1579832, _1579834, _1579836, _1579838] : [-(c_Wellfounded_Oacyclic(_1579832, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1579832, _1579832)), hAPP(hAPP(c_Product__Type_OPair(_1579832, _1579832), _1579834), _1579836)), _1579838))), c_Wellfounded_Oacyclic(_1579832, _1579838), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579832, _1579832)), hAPP(hAPP(c_Product__Type_OPair(_1579832, _1579832), _1579836), _1579834)), c_Transitive__Closure_Ortrancl(_1579832, _1579838))))], (42727 ^ _776545) ^ [_1627455, _1627457, _1627459, _1627461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627455, tc_HOL_Obool)), hAPP(c_List_Oset(_1627455), hAPP(hAPP(c_List_Olist__update(_1627455, _1627457), _1627459), _1627461))), hAPP(hAPP(c_Set_Oinsert(_1627455), _1627461), hAPP(c_List_Oset(_1627455), _1627457)))))], (38446 ^ _776545) ^ [_1513556, _1513558, _1513560] : [-(hAPP(c_Relation_ORange(_1513556, _1513558), hAPP(c_Set_OCollect(tc_prod(_1513556, _1513558)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513556, _1513558, tc_HOL_Obool), _1513560))) = hAPP(c_Set_OCollect(_1513558), hAPP(hAPP(c_COMBB(tc_fun(_1513556, tc_HOL_Obool), tc_HOL_Obool, _1513558), c_HOL_OEx(_1513556)), hAPP(c_COMBC(_1513556, _1513558, tc_HOL_Obool), _1513560))))], (45894 ^ _776545) ^ [_1697210, _1697212, _1697214, _1697216] : [class_Orderings_Olinorder(_1697210), -(hAPP(c_List_Oset(_1697212), c_List_Olinorder__class_Osort__key(_1697212, _1697210, _1697214, _1697216)) = hAPP(c_List_Oset(_1697212), _1697216))], (44739 ^ _776545) ^ [_1670942, _1670944, _1670946, _1670948, _1670950] : [-(hAPP(hAPP(c_List_Omap(_1670942, _1670944), _1670946), hAPP(hAPP(c_List_Oappend(_1670942), _1670948), _1670950)) = hAPP(hAPP(c_List_Oappend(_1670944), hAPP(hAPP(c_List_Omap(_1670942, _1670944), _1670946), _1670948)), hAPP(hAPP(c_List_Omap(_1670942, _1670944), _1670946), _1670950)))], (32438 ^ _776545) ^ [_1360440, _1360442, _1360444, _1360446, _1360448] : [_1360440 = c_Orderings_Obot__class_Obot(tc_fun(_1360442, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360444, tc_HOL_Obool)), _1360446), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1360442, tc_fun(_1360444, tc_HOL_Obool)), _1360440), _1360448)) = _1360446)], (46568 ^ _776545) ^ [_1712813, _1712815, _1712817, _1712819] : [class_Orderings_Olinorder(_1712813), 46571 ^ _776545 : [(46580 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712813, hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712815), hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712817), _1712819)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712813), _1712815), _1712817)), c_List_Olinorder__class_Osorted(_1712813, hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712817), _1712819))], (46572 ^ _776545) ^ [] : [c_List_Olinorder__class_Osorted(_1712813, hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712815), hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712817), _1712819))), 46575 ^ _776545 : [(46578 ^ _776545) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712813, hAPP(hAPP(c_List_Olist_OCons(_1712813), _1712817), _1712819)))], (46576 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712813), _1712815), _1712817)))]]]]], (49238 ^ _776545) ^ [_1770603, _1770605, _1770607, _1770609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770603), _1770605)), 49241 ^ _776545 : [(49242 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770607), hAPP(c_Set_OCollect(_1770607), hAPP(hAPP(c_COMBB(tc_fun(_1770603, tc_HOL_Obool), tc_HOL_Obool, _1770607), c_HOL_OEx(_1770603)), hAPP(hAPP(c_COMBB(tc_fun(_1770603, tc_HOL_Obool), tc_fun(_1770603, tc_HOL_Obool), _1770607), hAPP(c_COMBS(_1770603, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1770603), c_fconj), hAPP(hAPP(c_COMBC(_1770603, tc_fun(_1770603, tc_HOL_Obool), tc_HOL_Obool), c_member(_1770603)), _1770605)))), _1770609))))), 49245 ^ _776545 : [(49246 ^ _776545) ^ [_1770911] : [hBOOL(hAPP(hAPP(c_member(_1770603), _1770911), _1770605)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1770607), hAPP(c_Set_OCollect(_1770607), hAPP(hAPP(c_COMBC(_1770607, _1770603, tc_HOL_Obool), _1770609), _1770911)))))]]], (49252 ^ _776545) ^ [] : [49254 ^ _776545 : [(49257 ^ _776545) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770607), hAPP(c_Set_OCollect(_1770607), hAPP(hAPP(c_COMBC(_1770607, _1770603, tc_HOL_Obool), _1770609), 49253 ^ [_1770603, _1770605, _1770607, _1770609]))))], (49255 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770603), 49253 ^ [_1770603, _1770605, _1770607, _1770609]), _1770605)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1770607), hAPP(c_Set_OCollect(_1770607), hAPP(hAPP(c_COMBB(tc_fun(_1770603, tc_HOL_Obool), tc_HOL_Obool, _1770607), c_HOL_OEx(_1770603)), hAPP(hAPP(c_COMBB(tc_fun(_1770603, tc_HOL_Obool), tc_fun(_1770603, tc_HOL_Obool), _1770607), hAPP(c_COMBS(_1770603, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1770603), c_fconj), hAPP(hAPP(c_COMBC(_1770603, tc_fun(_1770603, tc_HOL_Obool), tc_HOL_Obool), c_member(_1770603)), _1770605)))), _1770609))))))]]], (50899 ^ _776545) ^ [_1807453, _1807455, _1807457] : [50901 ^ _776545 : [(50904 ^ _776545) ^ [] : [hBOOL(hAPP(_1807453, 50900 ^ [_1807453, _1807455, _1807457]))], (50902 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50900 ^ [_1807453, _1807455, _1807457]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1807455), _1807457))))]], -(c_List_Oall__interval__nat(_1807453, _1807455, _1807457))], (8651 ^ _776545) ^ [_925221, _925223, _925225] : [class_Lattices_Osemilattice__inf(_925221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925221), _925223), _925225)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925221), _925225), _925223) = _925223)], (16604 ^ _776545) ^ [_1075219] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1075219)) = hAPP(c_Nat_OSuc, _1075219))], (25121 ^ _776545) ^ [_1231208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231208), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1231208)))], (6394 ^ _776545) ^ [_879781, _879783, _879785] : [class_Complete__Lattice_Ocomplete__lattice(_879781), hBOOL(hAPP(hAPP(c_member(_879781), _879783), _879785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879781), _879783), c_Complete__Lattice_OSup__class_OSup(_879781, _879785))))], (42185 ^ _776545) ^ [_1612740, _1612742, _1612744, _1612746] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612740), tc_List_Olist(_1612740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612740), tc_List_Olist(_1612740)), _1612742), _1612744)), c_List_Olistrel(_1612740, _1612746)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612740)), _1612742) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612740)), _1612744), 42191 ^ _776545 : [(42194 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612740, _1612740)), hAPP(hAPP(c_Product__Type_OPair(_1612740, _1612740), hAPP(hAPP(c_List_Onth(_1612740), _1612742), 42190 ^ [_1612740, _1612742, _1612744, _1612746])), hAPP(hAPP(c_List_Onth(_1612740), _1612744), 42190 ^ [_1612740, _1612742, _1612744, _1612746]))), _1612746))], (42192 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42190 ^ [_1612740, _1612742, _1612744, _1612746]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612740)), _1612742))))]]], (29585 ^ _776545) ^ [_1306674, _1306676, _1306678] : [class_Rings_Olinordered__idom(_1306674), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306674), c_Groups_Ozero__class_Ozero(_1306674)), hAPP(hAPP(c_Power_Opower__class_Opower(_1306674), _1306676), 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)))), _1306678)))))], (27255 ^ _776545) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14450 ^ _776545) ^ [_1037466, _1037468, _1037470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037466), _1037468)), 14453 ^ _776545 : [(14460 ^ _776545) ^ [] : [_1037468 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037470), _1037466), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037468), _1037466) = _1037470)], (14454 ^ _776545) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037468), _1037466) = _1037470, -(_1037468 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037470), _1037466))]]], (29185 ^ _776545) ^ [_1299640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1299640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1299640))))], (35268 ^ _776545) ^ [_1434624, _1434626, _1434628, _1434630, _1434632] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434624, _1434626), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1434628), _1434630))), -(_1434626 = 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)), _1434632)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1434624, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434626), _1434632)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1434628), _1434632)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434626), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1434628, _1434632))), _1434630)))))], (48174 ^ _776545) ^ [_1746893, _1746895, _1746897] : [-(hBOOL(hAPP(hAPP(c_member(_1746893), _1746895), hAPP(c_List_Oset(_1746893), _1746897)))), 48175 ^ _776545 : [(48176 ^ _776545) ^ [_1746982, _1746984] : [_1746897 = hAPP(hAPP(c_List_Oappend(_1746893), _1746984), hAPP(hAPP(c_List_Olist_OCons(_1746893), _1746895), _1746982)), -(hBOOL(hAPP(hAPP(c_member(_1746893), _1746895), hAPP(c_List_Oset(_1746893), _1746982))))]]], (44856 ^ _776545) ^ [_1673947, _1673949, _1673951, _1673953] : [_1673953 = c_List_Olist_ONil(_1673947), -(hAPP(hAPP(c_List_Omap(_1673947, _1673949), _1673951), _1673953) = c_List_Olist_ONil(_1673949))], (45710 ^ _776545) ^ [_1693552, _1693554, _1693556, _1693558, _1693560] : [45712 ^ _776545 : [(45715 ^ _776545) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1693552, _1693554, tc_HOL_Obool), _1693560), 45711 ^ [_1693552, _1693554, _1693556, _1693558, _1693560]))], (45713 ^ _776545) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1693552, _1693554)), 45711 ^ [_1693552, _1693554, _1693556, _1693558, _1693560]), hAPP(c_List_Oset(tc_prod(_1693552, _1693554)), hAPP(hAPP(c_List_Ozip(_1693552, _1693554), _1693556), _1693558)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693552)), _1693556) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693554)), _1693558), -(c_List_Olist__all2(_1693552, _1693554, _1693560, _1693556, _1693558))], (37195 ^ _776545) ^ [_1484304, _1484306, _1484308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1484304), _1484306)), c_Fun_Oinj__on(_1484304, tc_fun(tc_fun(_1484304, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1484304, tc_fun(tc_prod(_1484304, _1484304), tc_HOL_Obool), tc_fun(tc_fun(_1484304, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484304, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1484304, _1484304), tc_HOL_Obool), tc_fun(tc_fun(_1484304, tc_HOL_Obool), tc_HOL_Obool)), _1484304), c_Equiv__Relations_Oquotient(_1484304)), hAPP(hAPP(c_COMBC(_1484304, tc_fun(_1484304, tc_HOL_Obool), tc_fun(_1484304, tc_HOL_Obool)), c_Set_Oinsert(_1484304)), c_Orderings_Obot__class_Obot(tc_fun(_1484304, tc_HOL_Obool))))), _1484308), _1484306), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1484304, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1484304), _1484306), _1484308)) = hAPP(c_Finite__Set_Ocard(_1484304), _1484306))]], input).
% 45.26/43.96 ncf('1',plain,[v_P_H(52574 ^ [], 52575 ^ []), -(v_Q(52574 ^ [], 52578 ^ []))],start(52580 ^ 0,bind([[_2080080], [52574 ^ []]]))).
% 45.26/43.96 ncf('1.1',plain,[-(v_P_H(52574 ^ [], 52575 ^ [])), v_P(52574 ^ [], 52575 ^ [])],extension(52569 ^ 1,bind([[_1832347, _1832349], [52575 ^ [], 52574 ^ []]]))).
% 45.26/43.96 ncf('1.1.1',plain,[-(v_P(52574 ^ [], 52575 ^ []))],extension(52577 ^ 2)).
% 45.26/43.96 ncf('1.2',plain,[v_Q(52574 ^ [], 52578 ^ [])],extension(52586 ^ 1)).
% 45.26/43.96 %-----------------------------------------------------
% 45.26/43.96 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------