%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:59 EDT 2023

% Result   : Theorem 45.14s 43.93s
% Output   : Proof 45.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.14  % Command  : nanocop.sh %s %d
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 22:26:30 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 45.14/43.93  
% 45.14/43.93  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 45.14/43.93  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.14/43.93  %-----------------------------------------------------
% 45.14/43.93  ncf(matrix, plain, [(51645 ^ _2059947) ^ [] : [v_Q(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s1), hAPP(c_Natural_Ogetlocs, v_s_H))), v_X), hAPP(hAPP(c_Natural_Ogetlocs, v_s1), c_Com_ORes)))], !, (41760 ^ _777864) ^ [_1587175, _1587177, _1587179, _1587181, _1587183, _1587185] : [-(hAPP(hAPP(c_Fun_Ocomp(_1587175, _1587177, _1587179, _1587181), _1587183), _1587185) = hAPP(_1587181, hAPP(_1587183, _1587185)))], (50064 ^ _777864) ^ [_1785574, _1785576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785574), _1785576)), -(c_List_Oupt(_1785574, _1785576) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1785574), c_List_Oupt(hAPP(c_Nat_OSuc, _1785574), _1785576)))], (51289 ^ _777864) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (14101 ^ _777864) ^ [_1016366, _1016368] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1016366), _1016368) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016366, _1016368)), _1016368))], (8746 ^ _777864) ^ [_922995, _922997, _922999, _923001, _923003] : [class_Rings_Ocomm__semiring__1(_922995), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), _922997), _922999)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), _923001), _923003)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), _923001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922995), _922997), _922999)), _923003)))], (48614 ^ _777864) ^ [_1754675, _1754677, _1754679, _1754681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1754675), _1754677)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754679)), _1754681))), -(hAPP(hAPP(c_List_Onth(_1754679), hAPP(hAPP(c_List_Odrop(_1754679), _1754675), _1754681)), _1754677) = hAPP(hAPP(c_List_Onth(_1754679), _1754681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1754675), _1754677)))], (22851 ^ _777864) ^ [_1173753, _1173755] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1173753), _1173755) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1173753, _1173755)))], (36560 ^ _777864) ^ [_1458902, _1458904, _1458906, _1458908, _1458910, _1458912] : [class_Groups_Ocomm__monoid__add(_1458902), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458904, _1458902), hAPP(hAPP(c_COMBC(_1458904, tc_fun(_1458906, tc_HOL_Obool), _1458902), hAPP(hAPP(c_COMBB(tc_fun(_1458906, _1458902), tc_fun(tc_fun(_1458906, tc_HOL_Obool), _1458902), _1458904), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458906, _1458902)), _1458908)), _1458910)), _1458912) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458906, _1458902), hAPP(hAPP(c_COMBC(_1458906, tc_fun(_1458904, tc_HOL_Obool), _1458902), hAPP(hAPP(c_COMBB(tc_fun(_1458904, _1458902), tc_fun(tc_fun(_1458904, tc_HOL_Obool), _1458902), _1458906), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458904, _1458902)), hAPP(c_COMBC(_1458904, _1458906, _1458902), _1458908))), _1458912)), _1458910))], (6006 ^ _777864) ^ [_876630, _876632, _876634, _876636, _876638] : [c_Com_Ocom_OAss(_876630, _876632) = c_Com_Ocom_OLocal(_876634, _876636, _876638)], (45555 ^ _777864) ^ [_1677399, _1677401, _1677403, _1677405] : [-(c_Map_Omap__add(_1677399, _1677401, _1677403, c_Map_Omap__of(_1677399, _1677401, _1677405)) = c_List_Ofoldr(tc_prod(_1677399, _1677401), tc_fun(_1677399, tc_Option_Ooption(_1677401)), hAPP(c_Product__Type_Oprod_Oprod__case(_1677399, _1677401, tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), hAPP(hAPP(c_COMBC(_1677399, tc_fun(_1677401, tc_Option_Ooption(_1677401)), tc_fun(_1677401, tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1677401), tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), tc_fun(tc_fun(_1677401, tc_Option_Ooption(_1677401)), tc_fun(_1677401, tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401))))), _1677399), c_COMBB(tc_Option_Ooption(_1677401), tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401))), _1677401)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(tc_Option_Ooption(_1677401), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), tc_fun(tc_Option_Ooption(_1677401), tc_fun(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), _1677399), c_COMBC(tc_fun(_1677399, tc_Option_Ooption(_1677401)), tc_Option_Ooption(_1677401), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), hAPP(c_COMBC(tc_fun(_1677399, tc_Option_Ooption(_1677401)), _1677399, tc_fun(tc_Option_Ooption(_1677401), tc_fun(_1677399, tc_Option_Ooption(_1677401)))), c_Fun_Ofun__upd(_1677399, tc_Option_Ooption(_1677401)))))), c_Option_Ooption_OSome(_1677401))), _1677405, _1677403))], (41724 ^ _777864) ^ [_1586178, _1586180, _1586182, _1586184, _1586186] : [hAPP(c_Set_Oimage(_1586178, _1586180, _1586182), c_Orderings_Otop__class_Otop(tc_fun(_1586178, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1586180, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1586180, _1586184, _1586186), c_Orderings_Otop__class_Otop(tc_fun(_1586180, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1586184, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1586178, _1586184, hAPP(c_Fun_Ocomp(_1586180, _1586184, _1586178, _1586186), _1586182)), c_Orderings_Otop__class_Otop(tc_fun(_1586178, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1586184, tc_HOL_Obool)))], (11497 ^ _777864) ^ [_969550, _969552, _969554] : [class_Rings_Oordered__cancel__semiring(_969550), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969550), _969552), _969554)), c_Groups_Ozero__class_Ozero(_969550)))), 11502 ^ _777864 : [(11509 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), _969552), c_Groups_Ozero__class_Ozero(_969550))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), c_Groups_Ozero__class_Ozero(_969550)), _969554))], (11503 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), c_Groups_Ozero__class_Ozero(_969550)), _969552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969550), _969554), c_Groups_Ozero__class_Ozero(_969550)))]]], (45811 ^ _777864) ^ [_1683799, _1683801, _1683803, _1683805] : [-(hAPP(hAPP(c_Option_Omap(_1683799, _1683801), _1683803), hAPP(c_Option_Ooption_OSome(_1683799), _1683805)) = hAPP(c_Option_Ooption_OSome(_1683801), hAPP(_1683803, _1683805)))], (42760 ^ _777864) ^ [_1609469, _1609471, _1609473, _1609475] : [class_Orderings_Olinorder(_1609469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609469), _1609471)), hBOOL(hAPP(hAPP(c_member(_1609469), _1609473), _1609471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609469), hAPP(hAPP(c_Finite__Set_Ofold(_1609469, _1609469, c_Orderings_Oord__class_Omin(_1609469)), _1609475), _1609471)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1609469), _1609473), _1609475))))], (35212 ^ _777864) ^ [_1432553, _1432555, _1432557, _1432559] : [-(_1432553 = c_Orderings_Obot__class_Obot(tc_fun(_1432555, tc_HOL_Obool))), 35215 ^ _777864 : [(35216 ^ _777864) ^ [] : [-(hAPP(c_Set_Oimage(_1432557, _1432555, 35223 ^ [_1432553, _1432555, _1432557, _1432559]), _1432559) = _1432553), 35217 ^ _777864 : [(35218 ^ _777864) ^ [_1432694] : [c_Fun_Oinj__on(_1432555, _1432557, _1432694, _1432553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432557, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432555, _1432557, _1432694), _1432553)), _1432559))]]], (35227 ^ _777864) ^ [] : [35228 ^ _777864 : [(35229 ^ _777864) ^ [_1432886] : [hAPP(c_Set_Oimage(_1432557, _1432555, _1432886), _1432559) = _1432553]], 35231 ^ _777864 : [(35234 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432557, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432555, _1432557, 35230 ^ [_1432553, _1432555, _1432557, _1432559]), _1432553)), _1432559)))], (35232 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1432555, _1432557, 35230 ^ [_1432553, _1432555, _1432557, _1432559], _1432553))]]]]], (47592 ^ _777864) ^ [_1729221, _1729223, _1729225] : [-(hAPP(hAPP(c_List_Otake(_1729221), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1729221), _1729223), _1729225)) = hAPP(hAPP(c_List_Olist_OCons(_1729221), _1729223), c_List_Olist_ONil(_1729221)))], (27111 ^ _777864) ^ [_1257972, _1257974, _1257976] : [hBOOL(hAPP(hAPP(c_member(_1257972), _1257974), hAPP(hAPP(c_Set_Oinsert(_1257972), _1257976), c_Orderings_Obot__class_Obot(tc_fun(_1257972, tc_HOL_Obool))))), -(_1257974 = _1257976)], (44903 ^ _777864) ^ [_1662160, _1662162, _1662164] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662160, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1662160, tc_HOL_Obool)), _1662162), _1662164)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662160, tc_HOL_Obool)), _1662162), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662160, tc_HOL_Obool), _1662164)))], (24197 ^ _777864) ^ [_1201663, _1201665] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1201663)), _1201665) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1201663), 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), _1201663)), _1201665))], (1502 ^ _777864) ^ [_799407, _799409] : [-(class_Groups_Oab__semigroup__mult(_799407)), _799409 = _799407, class_Groups_Oab__semigroup__mult(_799409)], (38033 ^ _777864) ^ [_1491762, _1491764, _1491766, _1491768, _1491770] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1491762, _1491762, _1491764, _1491766, _1491768), _1491770)), -(hBOOL(hAPP(hAPP(c_member(_1491762), _1491766), _1491768))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1491762, _1491764, hAPP(hAPP(c_Set_Oinsert(_1491762), _1491766), _1491768)), _1491770)))], (51461 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (5018 ^ _777864) ^ [_854633, _854635, _854637, _854639] : [-(c_Product__Type_Osnd(_854639, _854635) = c_Product__Type_Osnd(_854637, _854633)), _854639 = _854637, _854635 = _854633], (51351 ^ _777864) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (40389 ^ _777864) ^ [_1547597, _1547599] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547597), _1547599)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1547597, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1547597, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1547597, tc_HOL_Obool), tc_fun(_1547597, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1547597, tc_HOL_Obool))), _1547599)))))], (14494 ^ _777864) ^ [_1022925, _1022927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022925)), 14497 ^ _777864 : [(14506 ^ _777864) ^ [] : [-(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), _1022925), _1022927)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022927), _1022925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022927))], (14498 ^ _777864) ^ [] : [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), _1022925), _1022927))), 14501 ^ _777864 : [(14504 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022927)))], (14502 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022927), _1022925)))]]]]], (29326 ^ _777864) ^ [_1309322, _1309324, _1309326, _1309328, _1309330] : [c_Finite__Set_Ofolding__one(_1309322, _1309324, _1309326), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309322), _1309328)), hBOOL(hAPP(hAPP(c_member(_1309322), _1309330), _1309328)), 29337 ^ _777864 : [(29344 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309322, tc_HOL_Obool)), _1309328), hAPP(hAPP(c_Set_Oinsert(_1309322), _1309330), c_Orderings_Obot__class_Obot(tc_fun(_1309322, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309322, tc_HOL_Obool))), -(hAPP(_1309326, _1309328) = hAPP(hAPP(_1309324, _1309330), hAPP(_1309326, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309322, tc_HOL_Obool)), _1309328), hAPP(hAPP(c_Set_Oinsert(_1309322), _1309330), c_Orderings_Obot__class_Obot(tc_fun(_1309322, tc_HOL_Obool)))))))], (29338 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309322, tc_HOL_Obool)), _1309328), hAPP(hAPP(c_Set_Oinsert(_1309322), _1309330), c_Orderings_Obot__class_Obot(tc_fun(_1309322, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309322, tc_HOL_Obool)), -(hAPP(_1309326, _1309328) = _1309330)]]], (38244 ^ _777864) ^ [_1495489, _1495491, _1495493] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1495489, _1495491, c_Orderings_Obot__class_Obot(tc_fun(_1495489, tc_HOL_Obool))), _1495493))], (14087 ^ _777864) ^ [_1016045, _1016047, _1016049] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016047), _1016049)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016047), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016045), _1016047), _1016049))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016045, _1016047)))], (42012 ^ _777864) ^ [_1592963, _1592965, _1592967, _1592969, _1592971, _1592973, _1592975, _1592977] : [c_Finite__Set_Ofolding(_1592963, _1592965, _1592967, _1592969), -(hAPP(c_Fun_Ocomp(_1592965, _1592965, _1592971, hAPP(_1592967, _1592973)), hAPP(c_Fun_Ocomp(_1592965, _1592965, _1592971, hAPP(_1592967, _1592975)), _1592977)) = hAPP(c_Fun_Ocomp(_1592965, _1592965, _1592971, hAPP(_1592967, _1592975)), hAPP(c_Fun_Ocomp(_1592965, _1592965, _1592971, hAPP(_1592967, _1592973)), _1592977)))], (39389 ^ _777864) ^ [_1522996, _1522998, _1523000, _1523002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522996), _1522998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522996, _1522996), tc_HOL_Obool)), _1523000), hAPP(hAPP(c_Product__Type_OSigma(_1522996, _1522996), _1522998), hAPP(c_COMBK(tc_fun(_1522996, tc_HOL_Obool), _1522996), _1522998)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1522996, tc_HOL_Obool)), _1523002), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1522996), _1522998), _1523000))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522996), _1523002)))], (51239 ^ _777864) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (23769 ^ _777864) ^ [_1193231, _1193233] : [-(c_Divides_Odivmod__nat(_1193233, _1193231) = 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), _1193233), _1193231), _1193231))), -(_1193231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1193233), _1193231)))], (24199 ^ _777864) ^ [_1201711, _1201713] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1201711), hAPP(c_Nat_OSuc, _1201713)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973513), c_Groups_Ozero__class_Ozero(_973513)), _973517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973513), c_Groups_Ozero__class_Ozero(_973513)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973513), _973515), _973517))))], (41352 ^ _777864) ^ [_1576519, _1576521] : [-(hAPP(c_Relation_OField(_1576519), _1576521) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1576519, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1576519, _1576519), _1576521)), hAPP(c_Relation_ORange(_1576519, _1576519), _1576521)))], (37705 ^ _777864) ^ [_1485147, _1485149, _1485151] : [class_Orderings_Oorder(_1485147), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485147, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1485147, _1485149), _1485151)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485147), _1485151)) = c_Orderings_Obot__class_Obot(tc_fun(_1485147, tc_HOL_Obool)))], (28984 ^ _777864) ^ [_1301799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1301799)), -(_1301799 = 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))), _1301799)), c_FunDef_Omax__strict)))], (7568 ^ _777864) ^ [_903396] : [-(c_Option_Ois__none(_903396, c_Option_Ooption_ONone(_903396)))], (26963 ^ _777864) ^ [_1254018, _1254020, _1254022, _1254024] : [hBOOL(hAPP(hAPP(c_member(_1254018), _1254020), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254018, tc_HOL_Obool)), _1254022), _1254024))), -(hBOOL(hAPP(hAPP(c_member(_1254018), _1254020), _1254022)))], (40624 ^ _777864) ^ 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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(_1798269)), _1798271)), _1798267)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1798273))], (32793 ^ _777864) ^ [_1378905, _1378907, _1378909] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378905, tc_Nat_Onat), _1378907), _1378909) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378905, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1378905), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378907)), _1378909)))], (24207 ^ _777864) ^ [_1201860] : [class_Orderings_Oord(_1201860), -(c_Orderings_Oord__class_Omax(_1201860) = c_Orderings_Oord_Omax(_1201860, c_Orderings_Oord__class_Oless__eq(_1201860)))], (6074 ^ _777864) ^ [_877861, _877863] : [c_Com_Ovname_OGlb(_877861) = c_Com_Ovname_OLoc(_877863)], (2246 ^ _777864) ^ [_810949, _810951, _810953, _810955] : [-(c_Divides_Odivmod__int__rel(_810955, _810951) = c_Divides_Odivmod__int__rel(_810953, _810949)), _810955 = _810953, _810951 = _810949], (40262 ^ _777864) ^ [_1542426, _1542428, _1542430] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1542426, tc_HOL_Obool)), _1542428), _1542430) = hAPP(c_Set_OCollect(_1542426), hAPP(hAPP(c_COMBS(_1542426, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542426), c_fconj), hAPP(hAPP(c_COMBC(_1542426, tc_fun(_1542426, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542426)), _1542428))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542426), c_fNot), hAPP(hAPP(c_COMBC(_1542426, tc_fun(_1542426, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542426)), _1542430)))))], (31885 ^ _777864) ^ [_1360750, _1360752] : [class_Orderings_Olinorder(_1360750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360750), _1360752)), -(_1360752 = c_Orderings_Obot__class_Obot(tc_fun(_1360750, tc_HOL_Obool))), 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969042), _969048), _969044))))], (50977 ^ _777864) ^ [_1806242, _1806244, _1806246, _1806248, _1806250] : [-(c_List_OdropWhile(_1806242, _1806244, hAPP(hAPP(c_List_Omap(_1806246, _1806242), _1806248), _1806250)) = hAPP(hAPP(c_List_Omap(_1806246, _1806242), _1806248), c_List_OdropWhile(_1806246, hAPP(c_Fun_Ocomp(_1806242, tc_HOL_Obool, _1806246, _1806244), _1806248), _1806250)))], (49446 ^ _777864) ^ [_1772812, _1772814, _1772816, _1772818] : [-(_1772812 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772814)), _1772816)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1772814, hAPP(hAPP(c_List_Olist__update(_1772814, _1772816), _1772812), _1772818)) = hAPP(hAPP(c_List_Olist__update(_1772814, c_List_Obutlast(_1772814, _1772816)), _1772812), _1772818))], (27285 ^ _777864) ^ [_1262782, _1262784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1262782, _1262782)), hAPP(hAPP(c_Product__Type_OPair(_1262782, _1262782), 27286 ^ [_1262782, _1262784]), 27286 ^ [_1262782, _1262784])), _1262784)), -(c_Nitpick_Orefl_H(_1262782, _1262784))], (10952 ^ _777864) ^ [_960209] : [_960209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960209), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5478 ^ _777864) ^ [_861649, _861651] : [_861651 = _861649, -(c_Option_Othe(_861651) = c_Option_Othe(_861649))], (36778 ^ _777864) ^ [_1464664, _1464666, _1464668, _1464670, _1464672] : [class_Groups_Ocomm__monoid__add(_1464664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464666), _1464668)), -(hBOOL(hAPP(hAPP(c_member(_1464666), _1464670), _1464668))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464666, _1464664), _1464672), hAPP(hAPP(c_Set_Oinsert(_1464666), _1464670), _1464668)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464664), hAPP(_1464672, _1464670)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464666, _1464664), _1464672), _1464668)))], (3250 ^ _777864) ^ [_827055, _827057] : [_827057 = _827055, -(c_Int_OBit1(_827057) = c_Int_OBit1(_827055))], (50722 ^ _777864) ^ [_1801142, _1801144, _1801146, _1801148, _1801150] : [-(c_List_OtakeWhile(_1801142, _1801144, hAPP(hAPP(c_List_Omap(_1801146, _1801142), _1801148), _1801150)) = hAPP(hAPP(c_List_Omap(_1801146, _1801142), _1801148), c_List_OtakeWhile(_1801146, hAPP(c_Fun_Ocomp(_1801142, tc_HOL_Obool, _1801146, _1801144), _1801148), _1801150)))], (49107 ^ _777864) ^ [_1765697, _1765699, _1765701, _1765703] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765697)), hAPP(hAPP(c_List_Olist_OCons(_1765697), _1765699), _1765701)), c_List_Olists(_1765697, _1765703))), 49110 ^ _777864 : [(49113 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765697)), _1765701), c_List_Olists(_1765697, _1765703))))], (49111 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765697), _1765699), _1765703)))]]], (9398 ^ _777864) ^ [_934609, _934611, _934613, _934615] : [class_Rings_Olinordered__ring__strict(_934609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934609), _934611), c_Groups_Ozero__class_Ozero(_934609))), 9405 ^ _777864 : [(9412 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934609), _934615), _934613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934609), _934611), _934613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934609), _934611), _934615))))], (9406 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934609), _934611), _934613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934609), _934611), _934615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934609), _934615), _934613)))]]], (28801 ^ _777864) ^ [_1298373, _1298375, _1298377] : [-(hAPP(c_Relation_OField(_1298373), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1298373, _1298373), tc_HOL_Obool)), _1298375), _1298377)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298373, tc_HOL_Obool)), hAPP(c_Relation_OField(_1298373), _1298375)), hAPP(c_Relation_OField(_1298373), _1298377)))], (15898 ^ _777864) ^ [_1050254, _1050256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050254), _1050256)), -(c_Nat__Transfer_Otsub(_1050256, _1050254) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050256), _1050254))], (26901 ^ _777864) ^ [_1252800, _1252802, _1252804, _1252806] : [hBOOL(hAPP(hAPP(c_member(_1252800), _1252802), _1252804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252800, tc_HOL_Obool)), _1252804), _1252806)), -(hBOOL(hAPP(hAPP(c_member(_1252800), _1252802), _1252806)))], (23721 ^ _777864) ^ [_1192233, _1192235, _1192237, _1192239, _1192241, _1192243] : [hAPP(c_Product__Type_Oapsnd(_1192233, _1192235, _1192237, _1192239), _1192241) = hAPP(c_Product__Type_Oapsnd(_1192233, _1192235, _1192237, _1192243), _1192241), -(hAPP(_1192239, hAPP(c_Product__Type_Osnd(_1192237, _1192233), _1192241)) = hAPP(_1192243, hAPP(c_Product__Type_Osnd(_1192237, _1192233), _1192241)))], (36678 ^ _777864) ^ [_1462350, _1462352, _1462354, _1462356, _1462358] : [class_Groups_Oab__group__add(_1462350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462352), _1462354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462354), _1462356)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1462350), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462350), _1462358), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462352), _1462356))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462350), _1462358), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462352), _1462354))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462350), _1462358), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462354), _1462356)))], (48015 ^ _777864) ^ [_1739403, _1739405, _1739407, _1739409, _1739411] : [-(hAPP(hAPP(c_List_Oappend(_1739403), _1739405), _1739407) = hAPP(hAPP(c_List_Oappend(_1739403), _1739409), _1739411)), 48016 ^ _777864 : [(48023 ^ _777864) ^ [_1739627] : [hAPP(hAPP(c_List_Oappend(_1739403), _1739405), _1739627) = _1739409, _1739407 = hAPP(hAPP(c_List_Oappend(_1739403), _1739627), _1739411)], (48017 ^ _777864) ^ [_1739515] : [_1739405 = hAPP(hAPP(c_List_Oappend(_1739403), _1739409), _1739515), hAPP(hAPP(c_List_Oappend(_1739403), _1739515), _1739407) = _1739411]]], (43311 ^ _777864) ^ [_1621349, _1621351] : [-(c_Transitive__Closure_Otrancl(_1621349, _1621351) = hAPP(hAPP(c_Relation_Orel__comp(_1621349, _1621349, _1621349), _1621351), c_Transitive__Closure_Ortrancl(_1621349, _1621351)))], (46617 ^ _777864) ^ [_1705108, _1705110, _1705112, _1705114, _1705116, _1705118] : [hBOOL(hAPP(hAPP(_1705108, _1705110), _1705112)), c_List_Olistrelp(_1705114, _1705108, _1705116, _1705118), -(c_List_Olistrelp(_1705114, _1705108, hAPP(hAPP(c_List_Olist_OCons(_1705114), _1705110), _1705116), hAPP(hAPP(c_List_Olist_OCons(_1705114), _1705112), _1705118)))], (16380 ^ _777864) ^ [_1058769, _1058771, _1058773] : [class_Groups_Oordered__ab__group__add__abs(_1058769), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058769), hAPP(c_Groups_Oabs__class_Oabs(_1058769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058769), _1058771), _1058773))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058769), hAPP(c_Groups_Oabs__class_Oabs(_1058769), _1058771)), hAPP(c_Groups_Oabs__class_Oabs(_1058769), _1058773)))))], (24337 ^ _777864) ^ [_1203991, _1203993] : [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), _1203991), _1203993))), 24340 ^ _777864 : [(24347 ^ _777864) ^ [] : [-(_1203993 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1203991, _1203993) = c_Nitpick_Onat__gcd(_1203993, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1203991, _1203993)))], (24341 ^ _777864) ^ [] : [_1203993 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1203991, _1203993) = _1203991)]]], (9092 ^ _777864) ^ [_928839, _928841, _928843, _928845] : [class_Rings_Ocomm__semiring__1(_928839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928839), _928841), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928839), _928843), _928845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928839), _928841), _928843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928839), _928841), _928845)))], (36746 ^ _777864) ^ [_1463957, _1463959, _1463961, _1463963] : [class_Rings_Osemiring__1(_1463957), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463959, _1463957), hAPP(c_COMBK(_1463957, _1463959), _1463961)), _1463963) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1463957), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1463957), hAPP(c_Finite__Set_Ocard(_1463959), _1463963))), _1463961))], (30891 ^ _777864) ^ [_1342694, _1342696, _1342698] : [class_Lattices_Olattice(_1342694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342694), _1342696)), hBOOL(hAPP(hAPP(c_member(_1342694), _1342698), _1342696)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1342694), _1342698), c_Big__Operators_Olattice__class_OSup__fin(_1342694, _1342696)) = _1342698)], (50666 ^ _777864) ^ [_1799204, _1799206, _1799208, _1799210] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1799204)), c_List_Otranspose__rel(_1799204)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1799204)), hAPP(hAPP(c_List_Olist_OCons(_1799204), _1799206), _1799208)), _1799210))), -(c_List_Otranspose(_1799204, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1799204)), hAPP(hAPP(c_List_Olist_OCons(_1799204), _1799206), _1799208)), _1799210)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1799204)), hAPP(hAPP(c_List_Olist_OCons(_1799204), _1799206), c_List_Oconcat(_1799204, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1799204), tc_List_Olist(_1799204)), c_List_Olist_Olist__case(tc_List_Olist(_1799204), _1799204, c_List_Olist_ONil(_1799204), hAPP(hAPP(c_COMBB(tc_List_Olist(_1799204), tc_fun(tc_List_Olist(_1799204), tc_List_Olist(_1799204)), _1799204), c_COMBK(tc_List_Olist(_1799204), tc_List_Olist(_1799204))), hAPP(hAPP(c_COMBC(_1799204, tc_List_Olist(_1799204), tc_List_Olist(_1799204)), c_List_Olist_OCons(_1799204)), c_List_Olist_ONil(_1799204))))), _1799210)))), c_List_Otranspose(_1799204, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1799204)), _1799208), c_List_Oconcat(tc_List_Olist(_1799204), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1799204), tc_List_Olist(tc_List_Olist(_1799204))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1799204)), _1799204, c_List_Olist_ONil(tc_List_Olist(_1799204)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1799204), tc_List_Olist(tc_List_Olist(_1799204))), _1799204), hAPP(hAPP(c_COMBC(tc_List_Olist(_1799204), tc_List_Olist(tc_List_Olist(_1799204)), tc_List_Olist(tc_List_Olist(_1799204))), c_List_Olist_OCons(tc_List_Olist(_1799204))), c_List_Olist_ONil(tc_List_Olist(_1799204)))))), _1799210))))))], (14960 ^ _777864) ^ [_1031480, _1031482, _1031484] : [class_Rings_Oring__1(_1031480), -(hAPP(c_Int_Oring__1__class_Oof__int(_1031480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1031482), _1031484)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031480), hAPP(c_Int_Oring__1__class_Oof__int(_1031480), _1031482)), hAPP(c_Int_Oring__1__class_Oof__int(_1031480), _1031484)))], (40685 ^ _777864) ^ [_1559315, _1559317] : [-(c_Product__Type_Omap__pair(_1559315, _1559315, _1559317, _1559317, c_COMBI(_1559315), c_COMBI(_1559317)) = c_Fun_Oid(tc_prod(_1559315, _1559317)))], (30062 ^ _777864) ^ [_1324826, _1324828, _1324830] : [class_Lattices_Osemilattice__inf(_1324826), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324826), _1324828), _1324830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324826), _1324830), _1324828))], (19052 ^ _777864) ^ [_1105365, _1105367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105365)), c_Int_OBit0(_1105367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105365), _1105367)))], (47340 ^ _777864) ^ [_1724243, _1724245, _1724247] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724243)), hAPP(hAPP(c_List_Otake(_1724243), _1724245), _1724247)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724243)), _1724247)), _1724245))], (10103 ^ _777864) ^ [_946566, _946568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946566), _946568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946568), _946566)), -(_946566 = _946568)], (51325 ^ _777864) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (26911 ^ _777864) ^ [_1252985, _1252987, _1252989, _1252991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252985, tc_HOL_Obool)), _1252987), _1252989)), hBOOL(hAPP(hAPP(c_member(_1252985), _1252991), _1252987)), -(hBOOL(hAPP(hAPP(c_member(_1252985), _1252991), _1252989)))], (12594 ^ _777864) ^ [_989327, _989329, _989331] : [class_Rings_Olinordered__ring(_989327), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989327), c_Groups_Ozero__class_Ozero(_989327)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_989327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989327), _989329), _989329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989327), _989331), _989331)))))], (28659 ^ _777864) ^ [_1295026, _1295028, _1295030] : [class_Rings_Oring__1(_1295026), -(hAPP(c_Int_Oring__1__class_Oof__int(_1295026), 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), _1295028), _1295030)), 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(_1295026), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295026), _1295028)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1295026), _1295030)))], (47712 ^ _777864) ^ [_1731646, _1731648, _1731650, _1731652] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1731648), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731646)), hAPP(hAPP(c_List_Olist_OCons(_1731648), _1731650), _1731652)) = hAPP(hAPP(c_List_Olist_OCons(_1731648), _1731650), hAPP(hAPP(c_List_Otake(_1731648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731646)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1731652)))], (50949 ^ _777864) ^ [_1805460, _1805462, _1805464, _1805466, _1805468] : [c_Finite__Set_Ofun__left__comm(_1805460, _1805462, _1805464), -(hAPP(hAPP(c_Finite__Set_Ofold(_1805460, _1805462, _1805464), _1805466), hAPP(c_List_Oset(_1805460), _1805468)) = hAPP(c_List_Ofoldl(_1805462, _1805460, hAPP(c_COMBC(_1805460, _1805462, _1805462), _1805464), _1805466), c_List_Oremdups(_1805460, _1805468)))], (27748 ^ _777864) ^ [_1272128, _1272130, _1272132, _1272134] : [27749 ^ _777864 : [(27752 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272128), _1272130), _1272134))], (27750 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272128), _1272130), _1272132))]], -(hBOOL(hAPP(hAPP(c_member(_1272128), _1272130), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272128, tc_HOL_Obool)), _1272134), _1272132))))], (5352 ^ _777864) ^ [_859744, _859746] : [_859746 = _859744, -(c_List_Ohd(_859746) = c_List_Ohd(_859744))], (28771 ^ _777864) ^ [_1297750, _1297752] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1297750, _1297750)), hAPP(hAPP(c_Product__Type_OPair(_1297750, _1297750), 28772 ^ [_1297750, _1297752]), 28772 ^ [_1297750, _1297752])), _1297752))), -(c_Relation_Oirrefl(_1297750, _1297752))], (40036 ^ _777864) ^ [_1537565] : [-(c_Finite__Set_Ofun__left__comm__idem(_1537565, tc_fun(_1537565, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1537565, tc_HOL_Obool), tc_fun(tc_fun(_1537565, tc_HOL_Obool), tc_fun(_1537565, tc_HOL_Obool)), _1537565), hAPP(c_COMBC(tc_fun(_1537565, tc_HOL_Obool), tc_fun(_1537565, tc_HOL_Obool), tc_fun(_1537565, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1537565, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1537565, tc_fun(_1537565, tc_HOL_Obool), tc_fun(_1537565, tc_HOL_Obool)), c_Set_Oinsert(_1537565)), c_Orderings_Obot__class_Obot(tc_fun(_1537565, tc_HOL_Obool))))))], (24699 ^ _777864) ^ [_1211135, _1211137] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1211135), _1211137) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211135)), hAPP(c_Code__Numeral_Onat__of, _1211137))))], (5090 ^ _777864) ^ [_855791, _855793, _855795, _855797, _855799, _855801] : [-(c_Map_Omap__of(_855801, _855797, _855793) = c_Map_Omap__of(_855799, _855795, _855791)), _855801 = _855799, _855797 = _855795, _855793 = _855791], (26814 ^ _777864) ^ [_1251267, _1251269] : [_1251269 = c_Orderings_Obot__class_Obot(tc_fun(_1251267, tc_HOL_Obool)), 26817 ^ _777864 : [(26818 ^ _777864) ^ [_1251347] : [hBOOL(hAPP(hAPP(c_member(_1251267), _1251347), _1251269))]]], (47534 ^ _777864) ^ [_1728212, _1728214] : [-(c_List_Olistrelp(_1728212, _1728214, c_List_Olist_ONil(_1728212), c_List_Olist_ONil(_1728212)))], (50861 ^ _777864) ^ [_1803969, _1803971] : [c_List_Olist_ONil(_1803969) = c_List_Oremdups(_1803969, _1803971), -(_1803971 = c_List_Olist_ONil(_1803969))], (14892 ^ _777864) ^ [_1030182, _1030184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030184)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1030182)), hAPP(c_Int_Onat, _1030184)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1030182, _1030184)))], (41984 ^ _777864) ^ [_1592361, _1592363, _1592365, _1592367, _1592369, _1592371] : [c_Finite__Set_Ofolding(_1592361, _1592363, _1592365, _1592367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592361), _1592369)), hBOOL(hAPP(hAPP(c_member(_1592361), _1592371), _1592369)), -(hAPP(_1592367, _1592369) = hAPP(c_Fun_Ocomp(_1592363, _1592363, _1592363, hAPP(_1592367, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1592361, tc_HOL_Obool)), _1592369), hAPP(hAPP(c_Set_Oinsert(_1592361), _1592371), c_Orderings_Obot__class_Obot(tc_fun(_1592361, tc_HOL_Obool)))))), hAPP(_1592365, _1592371)))], (40689 ^ _777864) ^ [_1559385] : [-(hAPP(c_Set_Oimage(_1559385, _1559385, c_Fun_Oid(_1559385)), c_Orderings_Otop__class_Otop(tc_fun(_1559385, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1559385, tc_HOL_Obool)))], (51233 ^ _777864) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (7758 ^ _777864) ^ [_906629, _906631, _906633] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_906629, _906631)), _906633), _906633))), 7759 ^ _777864 : [(7762 ^ _777864) ^ [_906729] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_906631), _906633), _906729)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_906629, _906631)), _906729), _906633))], (7760 ^ _777864) ^ [] : [-(hBOOL(hAPP(_906629, _906633)))]]], (49515 ^ _777864) ^ [_1774245, _1774247, _1774249] : [hAPP(c_List_Ofilter(_1774245, _1774247), _1774249) = _1774249, 49518 ^ _777864 : [(49519 ^ _777864) ^ [_1774336] : [hBOOL(hAPP(hAPP(c_member(_1774245), _1774336), hAPP(c_List_Oset(_1774245), _1774249))), -(hBOOL(hAPP(_1774247, _1774336)))]]], (38587 ^ _777864) ^ [_1503833, _1503835] : [-(hBOOL(hAPP(hAPP(c_member(_1503833), _1503835), c_Orderings_Otop__class_Otop(tc_fun(_1503833, tc_HOL_Obool)))))], (23411 ^ _777864) ^ [_1186432, _1186434] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1186432)), hAPP(c_Nat_OSuc, _1186434)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1186432), _1186434)))], (7708 ^ _777864) ^ [_905687, _905689, _905691, _905693] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905687, _905689)), _905691), _905693)), 7713 ^ _777864 : [(7716 ^ _777864) ^ [] : [hBOOL(hAPP(_905687, _905691))], (7714 ^ _777864) ^ [] : [-(_905693 = _905691)]], 7717 ^ _777864 : [(7723 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905687, _905689)), 7719 ^ [_905687, _905689, _905691, _905693]), _905693)))], (7721 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_905689), _905691), 7719 ^ [_905687, _905689, _905691, _905693])))], (7718 ^ _777864) ^ [] : [-(hBOOL(hAPP(_905687, _905691)))]]], (31933 ^ _777864) ^ [_1361555, _1361557] : [class_Orderings_Olinorder(_1361555), -(c_Big__Operators_Olattice_OSup__fin(_1361555, c_Orderings_Oord__class_Omax(_1361555), hAPP(hAPP(c_Set_Oinsert(_1361555), _1361557), c_Orderings_Obot__class_Obot(tc_fun(_1361555, tc_HOL_Obool)))) = _1361557)], (26249 ^ _777864) ^ [_1239525, _1239527, _1239529, _1239531] : [26250 ^ _777864 : [(26253 ^ _777864) ^ [] : [hBOOL(hAPP(_1239529, _1239531))], (26251 ^ _777864) ^ [] : [_1239527 = _1239531]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1239525), _1239527), _1239529), _1239531)))], (15184 ^ _777864) ^ [_1035512, _1035514, _1035516] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035512), _1035514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035516), _1035514)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035512), _1035516))], (16196 ^ _777864) ^ [_1055578, _1055580] : [class_Rings_Olinordered__idom(_1055578), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055578), hAPP(c_Groups_Oabs__class_Oabs(_1055578), _1055580)), hAPP(c_Groups_Oabs__class_Oabs(_1055578), _1055580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055578), _1055580), _1055580))], (16240 ^ _777864) ^ [_1056465, _1056467, _1056469, _1056471] : [class_Rings_Ocomm__semiring__1(_1056465), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1056465), hAPP(hAPP(c_Power_Opower__class_Opower(_1056465), _1056467), _1056469)), _1056471) = hAPP(hAPP(c_Power_Opower__class_Opower(_1056465), _1056467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1056469), _1056471)))], (51475 ^ _777864) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (2734 ^ _777864) ^ [_818561, _818563] : [_818563 = _818561, -(c_Code__Numeral_OSuc__code__numeral(_818563) = c_Code__Numeral_OSuc__code__numeral(_818561))], (48722 ^ _777864) ^ [_1757596, _1757598, _1757600] : [-(_1757596 = c_List_Olist_ONil(_1757598)), -(hAPP(c_List_Ohd(_1757598), hAPP(hAPP(c_List_Oappend(_1757598), _1757596), _1757600)) = hAPP(c_List_Ohd(_1757598), _1757596))], (3526 ^ _777864) ^ [_831423, _831425, _831427, _831429] : [-(c_Com_Ocom_OWhile(_831429, _831425) = c_Com_Ocom_OWhile(_831427, _831423)), _831429 = _831427, _831425 = _831423], (32295 ^ _777864) ^ [_1368448, _1368450, _1368452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368448), _1368450)), hBOOL(hAPP(hAPP(c_member(_1368448), _1368452), _1368450)), -(hAPP(c_Finite__Set_Ocard(_1368448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368448, tc_HOL_Obool)), _1368450), hAPP(hAPP(c_Set_Oinsert(_1368448), _1368452), c_Orderings_Obot__class_Obot(tc_fun(_1368448, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1368448), _1368450)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7496 ^ _777864) ^ [_901827, _901829, _901831, _901833] : [c_Com_Ocom_OAss(_901827, _901829) = c_Com_Ocom_OSemi(_901831, _901833)], (17554 ^ _777864) ^ [_1080916, _1080918] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080916))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080916)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080918)) = 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), _1080918)))], (2096 ^ _777864) ^ [_808502, _808504, _808506, _808508] : [-(c_Random_Oinc__shift(_808508, _808504) = c_Random_Oinc__shift(_808506, _808502)), _808508 = _808506, _808504 = _808502], (49418 ^ _777864) ^ [_1772106, _1772108, _1772110] : [-(hAPP(hAPP(c_List_Odrop(_1772106), _1772108), c_List_Obutlast(_1772106, _1772110)) = c_List_Obutlast(_1772106, hAPP(hAPP(c_List_Odrop(_1772106), _1772108), _1772110)))], (29309 ^ _777864) ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1308433), _1308435)), 29315 ^ _777864 : [(29318 ^ _777864) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1308437, _1308439, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1308437)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1308437), hAPP(_1308447, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449])), hAPP(_1308443, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449])), hAPP(_1308449, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1308437), tc_HOL_Obool))))], (29316 ^ _777864) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1308437, _1308439, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1308437)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1308437), hAPP(_1308441, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449])), hAPP(_1308443, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449])), hAPP(_1308445, 29314 ^ [_1308433, _1308435, _1308437, _1308439, _1308441, _1308443, _1308445, _1308447, _1308449]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1308437), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1308437, _1308439, hAPP(c_Set_Oimage(_1308433, tc_Hoare__Mirabelle_Otriple(_1308437), hAPP(hAPP(c_COMBS(_1308433, tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437)), hAPP(hAPP(c_COMBS(_1308433, tc_Com_Ocom, tc_fun(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437))), hAPP(hAPP(c_COMBB(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437))), _1308433), c_Hoare__Mirabelle_Otriple_Otriple(_1308437)), _1308441)), _1308443)), _1308445)), _1308435)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1308437, _1308439, hAPP(c_Set_Oimage(_1308433, tc_Hoare__Mirabelle_Otriple(_1308437), hAPP(hAPP(c_COMBS(_1308433, tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437)), hAPP(hAPP(c_COMBS(_1308433, tc_Com_Ocom, tc_fun(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437))), hAPP(hAPP(c_COMBB(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1308437, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1308437))), _1308433), c_Hoare__Mirabelle_Otriple_Otriple(_1308437)), _1308447)), _1308443)), _1308449)), _1308435)))], (37867 ^ _777864) ^ [_1488311, _1488313, _1488315, _1488317, _1488319] : [class_Groups_Ocomm__monoid__add(_1488311), class_Groups_Ocomm__monoid__mult(_1488311), _1488313 = _1488315, c_Nat__Transfer_Onat__set(_1488315), 37885 ^ _777864 : [(37888 ^ _777864) ^ [] : [hAPP(_1488317, 37884 ^ [_1488311, _1488313, _1488315, _1488317, _1488319]) = hAPP(_1488319, 37884 ^ [_1488311, _1488313, _1488315, _1488317, _1488319])], (37886 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37884 ^ [_1488311, _1488313, _1488315, _1488317, _1488319])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1488311), _1488317), _1488313) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1488311), _1488319), _1488315))], (24091 ^ _777864) ^ [_1199130] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1199130) = _1199130)], (40763 ^ _777864) ^ [_1561593, _1561595, _1561597, _1561599, _1561601, _1561603, _1561605] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561593, _1561595, _1561597), _1561599), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561601, tc_fun(tc_prod(_1561595, _1561597), tc_HOL_Obool)), _1561603), _1561605)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561601, tc_fun(tc_prod(_1561593, _1561597), tc_HOL_Obool)), _1561603), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1561595, _1561597), tc_HOL_Obool), tc_fun(tc_prod(_1561593, _1561597), tc_HOL_Obool), _1561601), hAPP(c_Relation_Orel__comp(_1561593, _1561595, _1561597), _1561599)), _1561605)))], (5908 ^ _777864) ^ [_874933, _874935, _874937, _874939, _874941] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_874933, _874935), _874937, _874939, _874941), -(_874941 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _874937), _874933), hAPP(_874935, _874937)))], (13620 ^ _777864) ^ [_1007329, _1007331] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007329, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1007331)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007329, _1007331) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (890 ^ _777864) ^ [_791573, _791575, _791577, _791579, _791581, _791583] : [-(c_Equiv__Relations_Oequiv(_791581, _791577, _791573)), c_Equiv__Relations_Oequiv(_791583, _791579, _791575), _791583 = _791581, _791579 = _791577, _791575 = _791573], (6554 ^ _777864) ^ [_886063, _886065] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886063), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886063), _886065)))))], (12015 ^ _777864) ^ [_978990, _978992] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978990)), _978992) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978990), _978992)))], (14460 ^ _777864) ^ [_1022366, _1022368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022366), _1022368)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022366), _1022368) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7788 ^ _777864) ^ [_907186, _907188, _907190] : [hAPP(c_Com_Ocom_OBODY, _907186) = c_Com_Ocom_OWhile(_907188, _907190)], (27003 ^ _777864) ^ [_1254752, _1254754, _1254756, _1254758] : [_1254752 = _1254754, 27006 ^ _777864 : [(27013 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254756), _1254754), _1254758)), -(hBOOL(hAPP(hAPP(c_member(_1254756), _1254752), _1254758)))], (27007 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254756), _1254752), _1254758)), -(hBOOL(hAPP(hAPP(c_member(_1254756), _1254754), _1254758)))]]], (31913 ^ _777864) ^ [_1361195, _1361197, _1361199] : [class_Orderings_Olinorder(_1361195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361195), _1361197)), hBOOL(hAPP(hAPP(c_member(_1361195), _1361199), _1361197)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361195), _1361199), c_Big__Operators_Olattice_OSup__fin(_1361195, c_Orderings_Oord__class_Omax(_1361195), _1361197)) = c_Big__Operators_Olattice_OSup__fin(_1361195, c_Orderings_Oord__class_Omax(_1361195), _1361197))], (25151 ^ _777864) ^ [_1219154, _1219156] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219154), _1219156)), -(_1219154 = _1219156), 25158 ^ _777864 : [(25161 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219156), _1219154))], (25159 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219154), _1219156)))]]], (19372 ^ _777864) ^ [_1110961, _1110963, _1110965] : [class_Rings_Olinordered__semidom(_1110961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110961), hAPP(hAPP(c_Power_Opower__class_Opower(_1110961), _1110963), 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(_1110961), _1110965), 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(_1110961), c_Groups_Ozero__class_Ozero(_1110961)), _1110965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110961), _1110963), _1110965)))], (44728 ^ _777864) ^ [_1657994, _1657996, _1657998] : [class_Complete__Lattice_Ocomplete__lattice(_1657994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1657994), _1657996)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1657994), _1657998), c_Complete__Lattice_OInf__class_OInf(_1657994, _1657996)) = hAPP(hAPP(c_Finite__Set_Ofold(_1657994, _1657994, c_Lattices_Osemilattice__inf__class_Oinf(_1657994)), _1657998), _1657996))], (8600 ^ _777864) ^ [_920505, _920507] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _920505)), _920507) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _920505), _920507)))], (33543 ^ _777864) ^ [_1395215, _1395217, _1395219, _1395221, _1395223, _1395225] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395215, tc_fun(_1395217, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395219, tc_fun(_1395215, tc_HOL_Obool)), _1395221), _1395223)), _1395225) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395219, tc_fun(_1395217, tc_HOL_Obool)), _1395221), hAPP(hAPP(c_COMBC(_1395219, tc_fun(_1395215, tc_fun(_1395217, tc_HOL_Obool)), tc_fun(_1395217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395215, tc_HOL_Obool), tc_fun(tc_fun(_1395215, tc_fun(_1395217, tc_HOL_Obool)), tc_fun(_1395217, tc_HOL_Obool)), _1395219), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395215, tc_fun(_1395217, tc_HOL_Obool))), _1395223)), _1395225)))], (10604 ^ _777864) ^ [_954700, _954702, _954704] : [class_Orderings_Olinorder(_954700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954700), _954702), _954704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954700), _954704), _954702))], (22548 ^ _777864) ^ [_1167653, _1167655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1167653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1167655), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1167653), _1167655) = 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), _1167653), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167655)))))], (47478 ^ _777864) ^ [_1727206] : [class_Orderings_Olinorder(_1727206), -(c_List_Olinorder__class_Osorted__list__of__set(_1727206, c_Orderings_Obot__class_Obot(tc_fun(_1727206, tc_HOL_Obool))) = c_List_Olist_ONil(_1727206))], (34777 ^ _777864) ^ [_1423525, _1423527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1423525), hAPP(c_Nat_OSuc, _1423527))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1423525, hAPP(c_Nat_OSuc, _1423527)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423527)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1423525, _1423527)))], (50518 ^ _777864) ^ [_1795417, _1795419, _1795421] : [_1795419 = _1795421, -(hAPP(c_List_Orev(_1795417), _1795419) = hAPP(c_List_Orev(_1795417), _1795421))], (19198 ^ _777864) ^ [_1107958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1107958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1107958)))], (51149 ^ _777864) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (25309 ^ _777864) ^ [_1221733, _1221735, _1221737, _1221739] : [class_Divides_Osemiring__div(_1221733), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221733), _1221735), _1221737)), -(c_Divides_Odiv__class_Omod(_1221733, c_Divides_Odiv__class_Omod(_1221733, _1221739, _1221737), _1221735) = c_Divides_Odiv__class_Omod(_1221733, _1221739, _1221735))], (46759 ^ _777864) ^ [_1709342, _1709344, _1709346] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709342)), c_List_Osublist(_1709342, _1709344, _1709346)) = 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(_1709342)), _1709344)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1709346)))))], (20832 ^ _777864) ^ [_1137149, _1137151, _1137153, _1137155] : [class_Fields_Ofield(_1137149), -(_1137151 = c_Groups_Ozero__class_Ozero(_1137149)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137149), _1137153), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137149), _1137155), _1137151)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137149), _1137151), _1137153)), _1137155)), _1137151))], (23109 ^ _777864) ^ [_1179042, _1179044] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179042) = hAPP(c_Nat_OSuc, _1179044), -(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(_1179042))), 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)), _1179044))))))], (11072 ^ _777864) ^ [_962279, _962281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962279), hAPP(c_Nat_OSuc, _962281))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962279), _962281))), -(_962279 = hAPP(c_Nat_OSuc, _962281))], (37346 ^ _777864) ^ [_1477830, _1477832, _1477834] : [-(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), _1477830)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1477832))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1477834))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1477834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1477830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1477834), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1477832)))))], (9760 ^ _777864) ^ [_940934, _940936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _940934)), hAPP(c_Int_Onat, _940936))), 9763 ^ _777864 : [(9766 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _940934), _940936)))], (9764 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _940936)))]]], (15680 ^ _777864) ^ [_1045559, _1045561, _1045563, _1045565, _1045567, _1045569] : [class_Rings_Oordered__ring(_1045559), 15683 ^ _777864 : [(15690 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045559), _1045565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045559), _1045567), _1045561)), _1045563)), _1045569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045559), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), _1045561), _1045563)), _1045565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), _1045567), _1045563)), _1045569))))], (15684 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045559), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), _1045561), _1045563)), _1045565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), _1045567), _1045563)), _1045569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045559), _1045565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045559), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045559), _1045567), _1045561)), _1045563)), _1045569))))]]], (51179 ^ _777864) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (36614 ^ _777864) ^ [_1460681, _1460683, _1460685, _1460687, _1460689] : [class_Groups_Oab__group__add(_1460681), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460683, _1460681), hAPP(hAPP(c_COMBS(_1460683, _1460681, _1460681), hAPP(hAPP(c_COMBB(_1460681, tc_fun(_1460681, _1460681), _1460683), c_Groups_Ominus__class_Ominus(_1460681)), _1460685)), _1460687)), _1460689) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1460681), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460683, _1460681), _1460685), _1460689)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460683, _1460681), _1460687), _1460689)))], (44524 ^ _777864) ^ [_1653539, _1653541] : [-(c_Transitive__Closure_Ortrancl(_1653539, _1653541) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1653539, _1653539), 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(_1653539, _1653539), tc_HOL_Obool), tc_fun(tc_prod(_1653539, _1653539), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1653539, _1653539), tc_HOL_Obool)), _1653541)))], (6996 ^ _777864) ^ [_892833, _892835] : [6997 ^ _777864 : [(6998 ^ _777864) ^ [_892881] : [_892833 = hAPP(c_Option_Ooption_OSome(_892835), _892881)]], _892833 = c_Option_Ooption_ONone(_892835)], (14253 ^ _777864) ^ [_1018866, _1018868] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018866, _1018868) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1018866 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018868), 14256 ^ [_1018866, _1018868]))], (18552 ^ _777864) ^ [_1096873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1096873))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1096873)))], (4478 ^ _777864) ^ [_846347, _846349] : [_846349 = _846347, -(c_Lattices_Osemilattice__inf__class_Oinf(_846349) = c_Lattices_Osemilattice__inf__class_Oinf(_846347))], (34157 ^ _777864) ^ [_1410779, _1410781, _1410783, _1410785] : [_1410779 = _1410781, hBOOL(hAPP(hAPP(c_member(_1410783), _1410779), _1410785)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1410783, _1410783)), hAPP(hAPP(c_Product__Type_OPair(_1410783, _1410783), _1410779), _1410781)), c_Relation_OId__on(_1410783, _1410785))))], (49438 ^ _777864) ^ [_1772617, _1772619] : [-(c_List_Obutlast(_1772617, _1772619) = hAPP(hAPP(c_List_Otake(_1772617), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772617)), _1772619)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1772619))], (26987 ^ _777864) ^ [_1254491, _1254493, _1254495, _1254497] : [_1254491 = _1254493, 26990 ^ _777864 : [(26997 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254495), _1254497), _1254493)), -(hBOOL(hAPP(hAPP(c_member(_1254495), _1254497), _1254491)))], (26991 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254495), _1254497), _1254491)), -(hBOOL(hAPP(hAPP(c_member(_1254495), _1254497), _1254493)))]]], (45973 ^ _777864) ^ [_1687522, _1687524, _1687526, _1687528] : [hBOOL(hAPP(c_List_Odistinct(_1687522), hAPP(hAPP(c_List_Omap(tc_prod(_1687522, _1687524), _1687522), c_Product__Type_Ofst(_1687522, _1687524)), _1687526))), hBOOL(hAPP(c_List_Odistinct(_1687522), hAPP(hAPP(c_List_Omap(tc_prod(_1687522, _1687524), _1687522), c_Product__Type_Ofst(_1687522, _1687524)), _1687528))), 45980 ^ _777864 : [(45987 ^ _777864) ^ [] : [hAPP(c_List_Oset(tc_prod(_1687522, _1687524)), _1687526) = hAPP(c_List_Oset(tc_prod(_1687522, _1687524)), _1687528), -(c_Map_Omap__of(_1687522, _1687524, _1687526) = c_Map_Omap__of(_1687522, _1687524, _1687528))], (45981 ^ _777864) ^ [] : [c_Map_Omap__of(_1687522, _1687524, _1687526) = c_Map_Omap__of(_1687522, _1687524, _1687528), -(hAPP(c_List_Oset(tc_prod(_1687522, _1687524)), _1687526) = hAPP(c_List_Oset(tc_prod(_1687522, _1687524)), _1687528))]]], (44372 ^ _777864) ^ [_1649580, _1649582] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1649580, _1649580), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1649582) = c_Relation_OId(_1649580))], (49683 ^ _777864) ^ [_1778785, _1778787] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1778785))), c_List_Otranspose(_1778785, _1778787)) = c_List_Ofoldr(tc_List_Olist(_1778785), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1778785)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1778785))), _1778787, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26523 ^ _777864) ^ [_1245175, _1245177] : [-(_1245175 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245177), _1245175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1245177)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1245175))))], (15148 ^ _777864) ^ [_1034943, _1034945, _1034947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034943), _1034945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1034943), _1034947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034947), _1034945)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034947), _1034943))))], (25045 ^ _777864) ^ [_1217466, _1217468] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217466), _1217468)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217468), _1217466))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217468), _1217466)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217466), _1217468)))], (46148 ^ _777864) ^ [_1691218, _1691220, _1691222, _1691224, _1691226, _1691228, _1691230, _1691232] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1691218, _1691220), _1691222), _1691224), hAPP(hAPP(c_List_Ozip(_1691218, _1691220), hAPP(hAPP(c_List_Omap(_1691226, _1691218), _1691228), _1691230)), _1691232)) = hAPP(hAPP(c_List_Omap(tc_prod(_1691226, _1691220), _1691222), hAPP(c_Product__Type_Oprod_Oprod__case(_1691226, _1691220, _1691222), hAPP(hAPP(c_COMBB(tc_fun(_1691220, tc_prod(_1691218, _1691220)), tc_fun(_1691220, _1691222), _1691226), hAPP(c_COMBB(tc_prod(_1691218, _1691220), _1691222, _1691220), _1691224)), hAPP(hAPP(c_COMBB(_1691218, tc_fun(_1691220, tc_prod(_1691218, _1691220)), _1691226), c_Product__Type_OPair(_1691218, _1691220)), _1691228)))), hAPP(hAPP(c_List_Ozip(_1691226, _1691220), _1691230), _1691232)))], (41333 ^ _777864) ^ [_1575967, _1575969, _1575971, _1575973] : [hBOOL(hAPP(hAPP(c_member(_1575967), _1575969), hAPP(c_Relation_ODomain(_1575967, _1575971), _1575973))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575967, _1575971)), hAPP(hAPP(c_Product__Type_OPair(_1575967, _1575971), _1575969), 41336 ^ [_1575967, _1575969, _1575971, _1575973])), _1575973)))], (30222 ^ _777864) ^ [_1328426, _1328428, _1328430] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328426, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328426, tc_HOL_Obool)), _1328428), _1328430)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328426, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328426, tc_HOL_Obool)), _1328428)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328426, tc_HOL_Obool)), _1328430)))], (11939 ^ _777864) ^ [_977530, _977532, _977534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977530), _977532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977530), _977534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977532), _977534))))], (43723 ^ _777864) ^ [_1630970, _1630972, _1630974, _1630976, _1630978] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630970, tc_HOL_Obool)), _1630972), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630974, tc_fun(_1630970, tc_HOL_Obool)), _1630976), _1630978)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630974, tc_fun(_1630970, tc_HOL_Obool)), _1630976), hAPP(hAPP(c_COMBB(tc_fun(_1630970, tc_HOL_Obool), tc_fun(_1630970, tc_HOL_Obool), _1630974), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630970, tc_HOL_Obool)), _1630972)), _1630978)))], (15396 ^ _777864) ^ [_1039748, _1039750, _1039752] : [class_Groups_Ogroup__add(_1039748), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039748), _1039750), _1039752) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039748), _1039750), hAPP(c_Groups_Ouminus__class_Ouminus(_1039748), _1039752)))], (1182 ^ _777864) ^ [_795407, _795409] : [-(class_Groups_Oabs__if(_795407)), _795409 = _795407, class_Groups_Oabs__if(_795409)], (4782 ^ _777864) ^ [_851009, _851011, _851013, _851015, _851017, _851019] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_851019, _851015, _851011) = c_SetInterval_Oord__class_OgreaterThanAtMost(_851017, _851013, _851009)), _851019 = _851017, _851015 = _851013, _851011 = _851009], (29035 ^ _777864) ^ [_1302873, _1302875, _1302877, _1302879] : [hBOOL(hAPP(hAPP(c_member(_1302873), _1302875), c_Wellfounded_Oacc(_1302873, _1302877))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1302873, _1302873)), hAPP(hAPP(c_Product__Type_OPair(_1302873, _1302873), _1302879), _1302875)), _1302877)), -(hBOOL(hAPP(hAPP(c_member(_1302873), _1302879), c_Wellfounded_Oacc(_1302873, _1302877))))], (50688 ^ _777864) ^ [_1800047, _1800049, _1800051] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800047), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1800047))), _1800049))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1800047))), _1800049))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1800047))), hAPP(c_List_Ofilter(tc_List_Olist(_1800047), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1800047)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800051)), c_Nat_Osize__class_Osize(tc_List_Olist(_1800047)))), c_List_Otranspose(_1800047, _1800049))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800047)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1800047)), _1800049), _1800051)))], (16162 ^ _777864) ^ [_1054997, _1054999] : [class_Groups_Oordered__ab__group__add__abs(_1054997), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054997), _1054999), hAPP(c_Groups_Oabs__class_Oabs(_1054997), _1054999))))], (35850 ^ _777864) ^ [_1444570, _1444572, _1444574] : [-(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)), _1444570)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444572), _1444574)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444572), _1444570)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444574), _1444570)))], (48133 ^ _777864) ^ [_1741759, _1741761, _1741763] : [_1741759 = hAPP(hAPP(c_List_Oappend(_1741761), _1741759), _1741763), -(_1741763 = c_List_Olist_ONil(_1741761))], (27546 ^ _777864) ^ [_1268405] : [class_Rings_Oring__1(_1268405), -(hBOOL(hAPP(hAPP(c_member(_1268405), c_Groups_Oone__class_Oone(_1268405)), c_Int_Oring__1__class_OInts(_1268405))))], (45894 ^ _777864) ^ [_1685675, _1685677, _1685679, _1685681, _1685683] : [hAPP(c_Map_Omap__of(_1685675, _1685677, _1685679), _1685681) = hAPP(c_Option_Ooption_OSome(_1685677), _1685683), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685675, _1685677)), hAPP(hAPP(c_Product__Type_OPair(_1685675, _1685677), _1685681), _1685683)), hAPP(c_List_Oset(tc_prod(_1685675, _1685677)), _1685679))))], (15604 ^ _777864) ^ [_1043658, _1043660, _1043662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043658), _1043660)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043662), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043660), _1043658)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043662), _1043658)), _1043660))], (42808 ^ _777864) ^ [_1610383, _1610385, _1610387] : [class_Lattices_Olattice(_1610383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610383), _1610385)), -(c_Big__Operators_Olattice__class_OInf__fin(_1610383, hAPP(hAPP(c_Set_Oinsert(_1610383), _1610387), _1610385)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610383, _1610383, c_Lattices_Osemilattice__inf__class_Oinf(_1610383)), _1610387), _1610385))], (28048 ^ _777864) ^ [_1277650, _1277652, _1277654, _1277656] : [class_Lattices_Osemilattice__sup(_1277650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277650), _1277652), _1277654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277650), _1277652), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277650), _1277654), _1277656))))], (33797 ^ _777864) ^ [_1402103, _1402105, _1402107, _1402109, _1402111] : [_1402103 = c_Orderings_Obot__class_Obot(tc_fun(_1402105, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402105, tc_fun(_1402107, tc_HOL_Obool)), _1402103), hAPP(hAPP(c_COMBB(tc_fun(_1402107, tc_HOL_Obool), tc_fun(_1402107, tc_HOL_Obool), _1402105), hAPP(c_Set_Oinsert(_1402107), _1402109)), _1402111)) = c_Orderings_Obot__class_Obot(tc_fun(_1402107, tc_HOL_Obool)))], (19762 ^ _777864) ^ [_1118228, _1118230] : [class_Rings_Odivision__ring(_1118228), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118228), c_Groups_Ozero__class_Ozero(_1118228)), _1118230) = c_Groups_Ozero__class_Ozero(_1118228))], (49707 ^ _777864) ^ [_1779454] : [class_Orderings_Olinorder(_1779454), -(c_List_Olinorder__class_Osorted(_1779454, c_List_Olist_ONil(_1779454)))], (16886 ^ _777864) ^ [_1068917, _1068919, _1068921, _1068923] : [class_Rings_Olinordered__semidom(_1068917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068917), c_Groups_Oone__class_Oone(_1068917)), _1068919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068917), hAPP(hAPP(c_Power_Opower__class_Opower(_1068917), _1068919), _1068921)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068917), _1068919), _1068923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068921), _1068923)))], (12129 ^ _777864) ^ [_980920] : [12131 ^ _777864 : [(12134 ^ _777864) ^ [] : [hBOOL(hAPP(_980920, 12130 ^ [_980920]))], (12132 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12130 ^ [_980920])))]], 12135 ^ _777864 : [(12136 ^ _777864) ^ [_981047] : [-(hBOOL(hAPP(_980920, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981047))))]]], (13607 ^ _777864) ^ [_1007113, _1007115] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007113, _1007115) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1007113 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007115), 13610 ^ [_1007113, _1007115]))], (48438 ^ _777864) ^ [_1750314, _1750316, _1750318, _1750320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750314), tc_List_Olist(_1750314))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750314), tc_List_Olist(_1750314)), _1750316), _1750318)), c_List_Olistrel1(_1750314, _1750320))), 48443 ^ _777864 : [(48448 ^ _777864) ^ [] : [-(_1750318 = hAPP(hAPP(c_List_Olist__update(_1750314, _1750316), 48442 ^ [_1750314, _1750316, _1750318, _1750320]), 48441 ^ [_1750314, _1750316, _1750318, _1750320]))], (48446 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48442 ^ [_1750314, _1750316, _1750318, _1750320]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750314)), _1750316))))], (48444 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1750314, _1750314)), hAPP(hAPP(c_Product__Type_OPair(_1750314, _1750314), hAPP(hAPP(c_List_Onth(_1750314), _1750316), 48442 ^ [_1750314, _1750316, _1750318, _1750320])), 48441 ^ [_1750314, _1750316, _1750318, _1750320])), _1750320)))]]], (10438 ^ _777864) ^ [_952179, _952181, _952183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952179), _952181)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952183), _952181))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952179), _952183)))], (26639 ^ _777864) ^ [_1247647, _1247649, _1247651, _1247653, _1247655, _1247657] : [c_Hoare__Mirabelle_Ohoare__derivs(_1247647, _1247649, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1247647)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1247647), _1247651), _1247653), _1247655)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1247647), tc_HOL_Obool)))), 26646 ^ _777864 : [(26649 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1247657, 26644 ^ [_1247647, _1247649, _1247651, _1247653, _1247655, _1247657]), 26645 ^ [_1247647, _1247649, _1247651, _1247653, _1247655, _1247657]))], (26647 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1247655, 26644 ^ [_1247647, _1247649, _1247651, _1247653, _1247655, _1247657]), 26645 ^ [_1247647, _1247649, _1247651, _1247653, _1247655, _1247657])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1247647, _1247649, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1247647)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1247647), _1247651), _1247653), _1247657)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1247647), tc_HOL_Obool)))))], (36406 ^ _777864) ^ [_1455577, _1455579, _1455581, _1455583, _1455585] : [hAPP(_1455577, _1455579) = hAPP(c_Option_Ooption_OSome(_1455581), _1455583), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1455585, tc_Option_Ooption(_1455581)), _1455577), _1455579), hAPP(c_Option_Ooption_OSome(_1455581), _1455583)) = _1455577)], (6008 ^ _777864) ^ [_876689, _876691, _876693, _876695, _876697] : [c_Com_Ocom_OCall(_876689, _876691, _876693) = c_Com_Ocom_OAss(_876695, _876697)], (49047 ^ _777864) ^ [_1764274, _1764276] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1764274), hAPP(c_List_Oset(tc_Nat_Onat), _1764276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764274), 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)), _1764276))))], (30026 ^ _777864) ^ [_1324090, _1324092, _1324094, _1324096] : [class_Lattices_Osemilattice__inf(_1324090), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324090), _1324092), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324090), _1324094), _1324096)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324090), _1324094), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324090), _1324092), _1324096)))], (28741 ^ _777864) ^ [_1296808, _1296810, _1296812, _1296814] : [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), _1296808), _1296810)), 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), _1296812), _1296814)), 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), _1296808), _1296814)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296812), _1296810))))], (49586 ^ _777864) ^ [_1775731, _1775733, _1775735, _1775737, _1775739] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775731)), hAPP(c_List_Ofilter(_1775731, _1775733), hAPP(hAPP(c_List_Omap(_1775735, _1775731), _1775737), _1775739))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775735)), hAPP(c_List_Ofilter(_1775735, hAPP(c_Fun_Ocomp(_1775731, tc_HOL_Obool, _1775735, _1775733), _1775737)), _1775739)))], (35752 ^ _777864) ^ [_1442862, _1442864] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442862), hAPP(c_Nat_OSuc, _1442864)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1442862, _1442864))], (30202 ^ _777864) ^ [_1327779, _1327781, _1327783, _1327785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327779, tc_HOL_Obool)), _1327785), _1327781)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327779, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327779, tc_HOL_Obool)), _1327781), _1327783)), _1327785) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327779, tc_HOL_Obool)), _1327781), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327779, tc_HOL_Obool)), _1327783), _1327785)))], (46054 ^ _777864) ^ [_1689384] : [c_List_Onat__list(_1689384), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1689384)))], (13419 ^ _777864) ^ [_1003308, _1003310, _1003312] : [class_Divides_Osemiring__div(_1003308), -(c_Divides_Odiv__class_Omod(_1003308, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003308), _1003310), _1003312), _1003310) = c_Divides_Odiv__class_Omod(_1003308, _1003312, _1003310))], (14860 ^ _777864) ^ [_1029590, _1029592] : [-(_1029590 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14863 ^ _777864 : [(14870 ^ _777864) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029592, _1029590) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029592), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029590)) = 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), _1029592), _1029590))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14864 ^ _777864) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029592, _1029590) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029592), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029590)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029592), _1029590)))]]], (9170 ^ _777864) ^ [_930601, _930603, _930605] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _930601), _930603)), _930605) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930601), _930605)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930603), _930605)))], (7834 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45922 ^ _777864) ^ [] : [c_Com_OWT__bodies, 45925 ^ _777864 : [(45926 ^ _777864) ^ [_1686405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1686405), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1686405)))]]], (32517 ^ _777864) ^ [_1372961, _1372963, _1372965] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372961), _1372963)), -(hBOOL(hAPP(hAPP(c_member(_1372961), _1372965), _1372963))), -(hAPP(c_Finite__Set_Ocard(_1372961), hAPP(hAPP(c_Set_Oinsert(_1372961), _1372965), _1372963)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1372961), _1372963)))], (49552 ^ _777864) ^ [_1774935, _1774937, _1774939, _1774941] : [-(hBOOL(hAPP(_1774935, _1774937))), -(c_List_Oremove1(_1774939, _1774937, hAPP(c_List_Ofilter(_1774939, _1774935), _1774941)) = hAPP(c_List_Ofilter(_1774939, _1774935), _1774941))], (15524 ^ _777864) ^ [_1042092, _1042094, _1042096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042092), _1042094)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042094), _1042092)), _1042096) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042094), _1042096)), _1042092))], (14662 ^ _777864) ^ [_1025820, _1025822, _1025824, _1025826] : [class_Divides_Osemiring__div(_1025820), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025820), _1025822), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025820), _1025824), _1025822))), c_Divides_Odiv__class_Omod(_1025820, _1025824, _1025822))), _1025826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025820), _1025824), _1025826))], (22813 ^ _777864) ^ [_1172906] : [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), _1172906))), -(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), _1172906)) = 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), _1172906))))], (6127 ^ _777864) ^ [_878644, _878646, _878648] : [class_Rings_Osemiring__1(_878644), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_878644, _878646, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _878648) = _878648)], (36644 ^ _777864) ^ [_1461560, _1461562, _1461564, _1461566] : [class_Groups_Ocomm__monoid__add(_1461560), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461560), _1461562), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1461564), hAPP(c_Nat_OSuc, _1461566))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461560), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1461560, tc_Nat_Onat), _1461562), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1461564, _1461566)))], (44937 ^ _777864) ^ [_1662821] : [class_Complete__Lattice_Ocomplete__lattice(_1662821), -(c_Complete__Lattice_OSup__class_OSup(_1662821, c_Orderings_Otop__class_Otop(tc_fun(_1662821, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1662821))], (12067 ^ _777864) ^ [_979884, _979886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979884), hAPP(c_Nat_OSuc, _979886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979884), _979886)))], (17686 ^ _777864) ^ [_1082738, _1082740] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1082738), _1082740) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 17687 ^ _777864 : [(17694 ^ _777864) ^ [] : [_1082738 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1082740 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (17688 ^ _777864) ^ [] : [_1082738 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1082740 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (972 ^ _777864) ^ [_792782, _792784] : [-(class_Lattices_Obounded__lattice(_792782)), _792784 = _792782, class_Lattices_Obounded__lattice(_792784)], (15518 ^ _777864) ^ [_1041955, _1041957, _1041959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041955), _1041957)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041957), _1041959)), _1041955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041957), _1041955)), _1041959))], (14300 ^ _777864) ^ [_1019709, _1019711, _1019713] : [class_Divides_Osemiring__div(_1019709), -(_1019711 = c_Groups_Ozero__class_Ozero(_1019709)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019709), _1019711), _1019713)), _1019711) = _1019713)], (23181 ^ _777864) ^ [_1180587, _1180589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180587)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180589))), -(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(_1180589))), 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), _1180587)), c_Int_Onat))))))], (17602 ^ _777864) ^ [_1081550] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1081550), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51249 ^ _777864) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (30693 ^ _777864) ^ [_1339088, _1339090, _1339092, _1339094] : [hBOOL(hAPP(hAPP(_1339092, _1339094), _1339090)), -(hBOOL(hAPP(hAPP(c_member(_1339088), _1339090), c_SetInterval_Oord_OatLeast(_1339088, _1339092, _1339094))))], (17968 ^ _777864) ^ [_1087526] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1087526), c_Int_OPls) = _1087526)], (46883 ^ _777864) ^ [_1712466, _1712468, _1712470, _1712472] : [class_Rings_Osemiring__1(_1712466), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1712466), hAPP(hAPP(c_List_Omap(_1712468, _1712466), hAPP(c_COMBK(_1712466, _1712468), _1712470)), _1712472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1712466), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1712466), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712468)), _1712472))), _1712470))], (16952 ^ _777864) ^ [_1070162, _1070164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070162), _1070164)))], (44925 ^ _777864) ^ [_1662593, _1662595] : [class_Complete__Lattice_Ocomplete__lattice(_1662593), -(c_Complete__Lattice_OSup__class_OSup(_1662593, hAPP(hAPP(c_Set_Oinsert(_1662593), _1662595), c_Orderings_Obot__class_Obot(tc_fun(_1662593, tc_HOL_Obool)))) = _1662595)], (47634 ^ _777864) ^ [_1730069, _1730071] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730069), tc_List_Olist(_1730069))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730069), tc_List_Olist(_1730069)), c_List_Olist_ONil(_1730069)), c_List_Olist_ONil(_1730069))), c_List_Olistrel(_1730069, _1730071))))], (42902 ^ _777864) ^ [_1612248, _1612250, _1612252] : [class_Lattices_Olattice(_1612248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612248), _1612250)), -(hBOOL(hAPP(hAPP(c_member(_1612248), _1612252), _1612250))), -(c_Big__Operators_Olattice__class_OSup__fin(_1612248, hAPP(hAPP(c_Set_Oinsert(_1612248), _1612252), _1612250)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612248, _1612248, c_Lattices_Osemilattice__sup__class_Osup(_1612248)), _1612252), _1612250))], (43219 ^ _777864) ^ [_1619067, _1619069, _1619071, _1619073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619067, _1619067)), hAPP(hAPP(c_Product__Type_OPair(_1619067, _1619067), _1619069), _1619071)), c_Transitive__Closure_Otrancl(_1619067, _1619073))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619067, _1619067)), hAPP(hAPP(c_Product__Type_OPair(_1619067, _1619067), _1619069), _1619071)), c_Transitive__Closure_Ortrancl(_1619067, _1619073))))], (34093 ^ _777864) ^ [_1409435, _1409437, _1409439, _1409441, _1409443, _1409445, _1409447] : [c_Finite__Set_Ofolding__image__simple(_1409435, _1409437, _1409439, _1409441, _1409443, _1409445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409437), _1409447)), -(hAPP(_1409445, _1409447) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1409435, _1409437, _1409439), _1409443), _1409441), _1409447))], (15264 ^ _777864) ^ [_1037005, _1037007, _1037009] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037005), _1037007)), _1037009) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037005), _1037009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1037007), _1037009)))], (33721 ^ _777864) ^ [_1399646, _1399648, _1399650, _1399652, _1399654] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399646, tc_fun(_1399648, tc_HOL_Obool)), _1399650), hAPP(hAPP(c_COMBS(_1399646, tc_fun(_1399648, tc_HOL_Obool), tc_fun(_1399648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399648, tc_HOL_Obool), tc_fun(tc_fun(_1399648, tc_HOL_Obool), tc_fun(_1399648, tc_HOL_Obool)), _1399646), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399648, tc_HOL_Obool))), _1399652)), _1399654)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399648, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399646, tc_fun(_1399648, tc_HOL_Obool)), _1399650), _1399652)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399646, tc_fun(_1399648, tc_HOL_Obool)), _1399650), _1399654)))], (44289 ^ _777864) ^ [_1647523, _1647525, _1647527] : [c_Relation_Osingle__valued(_1647523, _1647525, _1647527), 44292 ^ _777864 : [(44293 ^ _777864) ^ [_1647644, _1647646] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1647523, _1647525)), hAPP(hAPP(c_Product__Type_OPair(_1647523, _1647525), _1647646), _1647644)), _1647527)), 44296 ^ _777864 : [(44297 ^ _777864) ^ [_1647770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1647523, _1647525)), hAPP(hAPP(c_Product__Type_OPair(_1647523, _1647525), _1647646), _1647770)), _1647527)), -(_1647644 = _1647770)]]]]], (26826 ^ _777864) ^ [_1251507, _1251509] : [-(_1251509 = c_Orderings_Obot__class_Obot(tc_fun(_1251507, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1251507), 26829 ^ [_1251507, _1251509]), _1251509)))], (24107 ^ _777864) ^ [_1199403, _1199405, _1199407, _1199409] : [class_Orderings_Olinorder(_1199403), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199403), _1199405), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199403), _1199407), _1199409)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199403), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199403), _1199405), _1199407)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199403), _1199405), _1199409)))], (45900 ^ _777864) ^ [_1685836, _1685838, _1685840, _1685842, _1685844] : [hAPP(c_Map_Omap__of(_1685836, _1685838, _1685840), _1685842) = hAPP(c_Option_Ooption_OSome(_1685838), _1685844), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685836, _1685838)), hAPP(hAPP(c_Product__Type_OPair(_1685836, _1685838), _1685842), _1685844)), hAPP(c_List_Oset(tc_prod(_1685836, _1685838)), _1685840))))], (4550 ^ _777864) ^ [_847411, _847413, _847415, _847417] : [-(c_List_Olists(_847417, _847413) = c_List_Olists(_847415, _847411)), _847417 = _847415, _847413 = _847411], (47265 ^ _777864) ^ [_1722066, _1722068] : [-(c_Random_Oselect(_1722066, _1722068) = 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(_1722066, 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(_1722066)), _1722068)))), hAPP(hAPP(c_COMBB(_1722066, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1722066, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1722066, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1722066, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1722066), _1722068)), c_Code__Numeral_Onat__of))))], (1712 ^ _777864) ^ [_802032, _802034] : [-(class_Orderings_Oord(_802032)), _802034 = _802032, class_Orderings_Oord(_802034)], (49154 ^ _777864) ^ [_1766831, _1766833, _1766835, _1766837] : [49155 ^ _777864 : [(49156 ^ _777864) ^ [_1766928, _1766930] : [_1766831 = hAPP(hAPP(c_List_Olist_OCons(_1766833), _1766930), _1766928)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1766833), tc_List_Olist(_1766833))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1766833), tc_List_Olist(_1766833)), _1766835), hAPP(hAPP(c_List_Oappend(_1766833), _1766835), _1766831))), c_List_Olexord(_1766833, _1766837))))], (47980 ^ _777864) ^ [_1738422, _1738424, _1738426, _1738428, _1738430, _1738432] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738422)), _1738424) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738426)), _1738428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738422)), _1738430) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738426)), _1738432), -(hAPP(hAPP(c_List_Ozip(_1738422, _1738426), hAPP(hAPP(c_List_Oappend(_1738422), _1738424), _1738430)), hAPP(hAPP(c_List_Oappend(_1738426), _1738428), _1738432)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1738422, _1738426)), hAPP(hAPP(c_List_Ozip(_1738422, _1738426), _1738424), _1738428)), hAPP(hAPP(c_List_Ozip(_1738422, _1738426), _1738430), _1738432)))], (7068 ^ _777864) ^ [_893971, _893973, _893975] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_893971), 7071 ^ _777864 : [(7078 ^ _777864) ^ [] : [_893975 = c_Groups_Ozero__class_Ozero(_893971), -(_893973 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893971), _893973), _893975))], (7072 ^ _777864) ^ [] : [_893973 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893971), _893973), _893975), -(_893975 = c_Groups_Ozero__class_Ozero(_893971))]]], (36446 ^ _777864) ^ [_1456493, _1456495, _1456497, _1456499] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1456493, tc_Option_Ooption(_1456495)), hAPP(c_COMBK(tc_Option_Ooption(_1456495), _1456493), c_Option_Ooption_ONone(_1456495))), _1456497), c_Option_Ooption_ONone(_1456495)), _1456499) = c_Option_Ooption_ONone(_1456495))], (14145 ^ _777864) ^ [_1017197, _1017199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017199)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1017197)), hAPP(c_Int_Onat, _1017199)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017197), _1017199)))], (45768 ^ _777864) ^ [_1682596, _1682598, _1682600, _1682602] : [hAPP(c_List_Oset(_1682596), _1682598) = c_Map_Odom(_1682596, _1682600, _1682602), -(c_Map_Omap__of(_1682596, _1682600, hAPP(hAPP(c_List_Omap(_1682596, tc_prod(_1682596, _1682600)), hAPP(hAPP(c_COMBS(_1682596, _1682600, tc_prod(_1682596, _1682600)), c_Product__Type_OPair(_1682596, _1682600)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1682600), _1682600, _1682596), c_Option_Othe(_1682600)), _1682602))), _1682598)) = _1682602)], (51103 ^ _777864) ^ [_1808065, _1808067] : [class_Orderings_Oord(_1808065), -(class_Orderings_Oord(tc_fun(_1808067, _1808065)))], (51477 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (19458 ^ _777864) ^ [_1112345, _1112347] : [class_Rings_Oring__1__no__zero__divisors(_1112345), 19461 ^ _777864 : [(19462 ^ _777864) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1112345), _1112347), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1112345), -(_1112347 = c_Groups_Oone__class_Oone(_1112345)), -(_1112347 = hAPP(c_Groups_Ouminus__class_Ouminus(_1112345), c_Groups_Oone__class_Oone(_1112345)))], (19472 ^ _777864) ^ [] : [19473 ^ _777864 : [(19476 ^ _777864) ^ [] : [_1112347 = hAPP(c_Groups_Ouminus__class_Ouminus(_1112345), c_Groups_Oone__class_Oone(_1112345))], (19474 ^ _777864) ^ [] : [_1112347 = c_Groups_Oone__class_Oone(_1112345)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1112345), _1112347), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1112345))]]], (18482 ^ _777864) ^ [_1095752] : [_1095752 = c_Int_OMin, -(c_Int_OBit1(_1095752) = c_Int_OMin)], (15904 ^ _777864) ^ [_1050353, _1050355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050353), _1050355))), -(c_Nat__Transfer_Otsub(_1050355, _1050353) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38310 ^ _777864) ^ [_1496744, _1496746] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1496744), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1496746), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 38317 ^ _777864 : [(38324 ^ _777864) ^ [] : [_1496744 = _1496746, -(hAPP(c_Code__Numeral_Oof__nat, _1496744) = hAPP(c_Code__Numeral_Oof__nat, _1496746))], (38318 ^ _777864) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1496744) = hAPP(c_Code__Numeral_Oof__nat, _1496746), -(_1496744 = _1496746)]]], (11297 ^ _777864) ^ [_966099, _966101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _966099)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _966099), _966101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _966099)), hAPP(c_Int_Onat, _966101)))], (31817 ^ _777864) ^ [_1359216, _1359218, _1359220] : [class_Orderings_Olinorder(_1359216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359216), _1359218)), hBOOL(hAPP(hAPP(c_member(_1359216), _1359220), _1359218)), 31828 ^ _777864 : [(31835 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359216, tc_HOL_Obool)), _1359218), hAPP(hAPP(c_Set_Oinsert(_1359216), _1359220), c_Orderings_Obot__class_Obot(tc_fun(_1359216, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359216, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1359216, c_Orderings_Oord__class_Omax(_1359216), _1359218) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1359216), _1359220), c_Big__Operators_Olattice_OSup__fin(_1359216, c_Orderings_Oord__class_Omax(_1359216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359216, tc_HOL_Obool)), _1359218), hAPP(hAPP(c_Set_Oinsert(_1359216), _1359220), c_Orderings_Obot__class_Obot(tc_fun(_1359216, tc_HOL_Obool)))))))], (31829 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359216, tc_HOL_Obool)), _1359218), hAPP(hAPP(c_Set_Oinsert(_1359216), _1359220), c_Orderings_Obot__class_Obot(tc_fun(_1359216, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359216, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1359216, c_Orderings_Oord__class_Omax(_1359216), _1359218) = _1359220)]]], (51471 ^ _777864) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (15598 ^ _777864) ^ [_1043533, _1043535, _1043537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043537), _1043535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043533), _1043535)), _1043537)))], (6731 ^ _777864) ^ [_888738, _888740] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888738), _888740))), 6734 ^ _777864 : [(6741 ^ _777864) ^ [] : [_888738 = _888740, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888738), hAPP(c_Nat_OSuc, _888740))))], (6735 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888738), hAPP(c_Nat_OSuc, _888740))), -(_888738 = _888740)]]], (6292 ^ _777864) ^ [_881554, _881556, _881558, _881560] : [class_Groups_Ocancel__semigroup__add(_881554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881554), _881556), _881558) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881554), _881560), _881558), -(_881556 = _881560)], (28152 ^ _777864) ^ [_1279750, _1279752, _1279754, _1279756, _1279758] : [class_Lattices_Olattice(_1279750), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279752, _1279750)), _1279754), _1279756), _1279758) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279750), hAPP(_1279754, _1279758)), hAPP(_1279756, _1279758)))], (27292 ^ _777864) ^ [_1262961, _1262963, _1262965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262961, tc_HOL_Obool)), _1262963), hAPP(hAPP(c_Set_Oinsert(_1262961), _1262965), c_Orderings_Obot__class_Obot(tc_fun(_1262961, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1262961, _1262965, _1262963) = _1262965)], (42448 ^ _777864) ^ [_1602962, _1602964, _1602966, _1602968, _1602970, _1602972] : [class_Groups_Oab__semigroup__mult(_1602962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602964), _1602966)), 42458 ^ _777864 : [(42461 ^ _777864) ^ [] : [hAPP(_1602968, 42457 ^ [_1602962, _1602964, _1602966, _1602968, _1602970, _1602972]) = hAPP(_1602970, 42457 ^ [_1602962, _1602964, _1602966, _1602968, _1602970, _1602972])], (42459 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602964), 42457 ^ [_1602962, _1602964, _1602966, _1602968, _1602970, _1602972]), _1602966)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1602962, _1602964, c_Groups_Otimes__class_Otimes(_1602962)), _1602968), _1602972), _1602966) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1602962, _1602964, c_Groups_Otimes__class_Otimes(_1602962)), _1602970), _1602972), _1602966))], (15966 ^ _777864) ^ [_1051526, _1051528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051526)), 15969 ^ _777864 : [(15976 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051528), _1051526))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051528), _1051526) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051528), _1051526)), _1051526)))], (15970 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051528), _1051526)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051528), _1051526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44248 ^ _777864) ^ [_1646627, _1646629, _1646631, _1646633, _1646635, _1646637, _1646639, _1646641] : [c_Fun_Oinj__on(_1646627, _1646629, _1646631, _1646633), 44254 ^ _777864 : [(44257 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646627, tc_HOL_Obool)), hAPP(_1646639, 44253 ^ [_1646627, _1646629, _1646631, _1646633, _1646635, _1646637, _1646639, _1646641])), _1646633))], (44255 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646635), 44253 ^ [_1646627, _1646629, _1646631, _1646633, _1646635, _1646637, _1646639, _1646641]), _1646637)))]], hBOOL(hAPP(hAPP(c_member(_1646635), _1646641), _1646637)), -(hAPP(c_Set_Oimage(_1646627, _1646629, _1646631), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646635, tc_fun(_1646627, tc_HOL_Obool)), _1646637), _1646639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646635, tc_fun(_1646629, tc_HOL_Obool)), _1646637), hAPP(hAPP(c_COMBB(tc_fun(_1646627, tc_HOL_Obool), tc_fun(_1646629, tc_HOL_Obool), _1646635), c_Set_Oimage(_1646627, _1646629, _1646631)), _1646639)))], (28621 ^ _777864) ^ [_1293359, _1293361, _1293363, _1293365] : [-(_1293359 = c_Orderings_Obot__class_Obot(tc_fun(_1293361, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1293361, _1293363, hAPP(c_COMBK(_1293363, _1293361), _1293365)), _1293359) = hAPP(hAPP(c_Set_Oinsert(_1293363), _1293365), c_Orderings_Obot__class_Obot(tc_fun(_1293363, tc_HOL_Obool))))], (2740 ^ _777864) ^ [_818646, _818648, _818650, _818652, _818654, _818656, _818658, _818660, _818662, _818664, _818666, _818668, _818670, _818672] : [-(c_New__Random__Sequence_Opos__decr__bind(_818672, _818668, _818664, _818660, _818656, _818652, _818648) = c_New__Random__Sequence_Opos__decr__bind(_818670, _818666, _818662, _818658, _818654, _818650, _818646)), _818672 = _818670, _818668 = _818666, _818664 = _818662, _818660 = _818658, _818656 = _818654, _818652 = _818650, _818648 = _818646], (11425 ^ _777864) ^ [_968318, _968320, _968322] : [class_Groups_Oordered__comm__monoid__add(_968318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968318), c_Groups_Ozero__class_Ozero(_968318)), _968320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968318), c_Groups_Ozero__class_Ozero(_968318)), _968322)), 11436 ^ _777864 : [(11445 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968318), _968320), _968322) = c_Groups_Ozero__class_Ozero(_968318)), _968320 = c_Groups_Ozero__class_Ozero(_968318), _968322 = c_Groups_Ozero__class_Ozero(_968318)], (11437 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968318), _968320), _968322) = c_Groups_Ozero__class_Ozero(_968318), 11440 ^ _777864 : [(11443 ^ _777864) ^ [] : [-(_968322 = c_Groups_Ozero__class_Ozero(_968318))], (11441 ^ _777864) ^ [] : [-(_968320 = c_Groups_Ozero__class_Ozero(_968318))]]]]], (29688 ^ _777864) ^ [_1316884, _1316886, _1316888, _1316890] : [class_Lattices_Osemilattice__inf(_1316884), 29691 ^ _777864 : [(29700 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316884), _1316888), _1316890)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), _1316888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), _1316890))], (29692 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316884), _1316888), _1316890))), 29695 ^ _777864 : [(29698 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), _1316890)))], (29696 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316884), _1316886), _1316888)))]]]]], (44641 ^ _777864) ^ [_1656012, _1656014, _1656016] : [class_Complete__Lattice_Ocomplete__lattice(_1656012), 44644 ^ _777864 : [(44645 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656012), _1656014), c_Complete__Lattice_OInf__class_OInf(_1656012, _1656016))), 44648 ^ _777864 : [(44649 ^ _777864) ^ [_1656170] : [hBOOL(hAPP(hAPP(c_member(_1656012), _1656170), _1656016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656012), _1656014), _1656170)))]]], (44655 ^ _777864) ^ [] : [44657 ^ _777864 : [(44660 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656012), _1656014), 44656 ^ [_1656012, _1656014, _1656016]))], (44658 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656012), 44656 ^ [_1656012, _1656014, _1656016]), _1656016)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656012), _1656014), c_Complete__Lattice_OInf__class_OInf(_1656012, _1656016))))]]], (47304 ^ _777864) ^ [_1723376, _1723378, _1723380, _1723382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1723376), _1723378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1723380, tc_HOL_Obool)), hAPP(c_List_Oset(_1723380), hAPP(hAPP(c_List_Otake(_1723380), _1723376), _1723382))), hAPP(c_List_Oset(_1723380), hAPP(hAPP(c_List_Otake(_1723380), _1723378), _1723382)))))], (44812 ^ _777864) ^ [_1660242, _1660244, _1660246] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660242, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1660242, tc_HOL_Obool), _1660244)), _1660246) = c_Orderings_Obot__class_Obot(tc_fun(_1660242, tc_HOL_Obool)), 44815 ^ _777864 : [(44816 ^ _777864) ^ [_1660377] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1660242, tc_HOL_Obool)), _1660377), _1660244)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660242, tc_HOL_Obool)), _1660377), _1660246) = c_Orderings_Obot__class_Obot(tc_fun(_1660242, tc_HOL_Obool)))]]], (50885 ^ _777864) ^ [_1804344, _1804346] : [class_Orderings_Olinorder(_1804344), c_List_Olinorder__class_Osorted(_1804344, _1804346), -(c_List_Olinorder__class_Osorted(_1804344, c_List_Oremdups(_1804344, _1804346)))], (44224 ^ _777864) ^ [_1645956] : [-(c_Relation_OId(_1645956) = hAPP(c_Set_OCollect(tc_prod(_1645956, _1645956)), hAPP(hAPP(c_COMBB(tc_fun(_1645956, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1645956, _1645956)), c_HOL_OEx(_1645956)), hAPP(hAPP(c_COMBC(tc_prod(_1645956, _1645956), tc_fun(_1645956, tc_prod(_1645956, _1645956)), tc_fun(_1645956, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1645956, _1645956), tc_HOL_Obool), tc_fun(tc_fun(_1645956, tc_prod(_1645956, _1645956)), tc_fun(_1645956, tc_HOL_Obool)), tc_prod(_1645956, _1645956)), c_COMBB(tc_prod(_1645956, _1645956), tc_HOL_Obool, _1645956)), c_fequal)), hAPP(hAPP(c_COMBS(_1645956, _1645956, tc_prod(_1645956, _1645956)), c_Product__Type_OPair(_1645956, _1645956)), c_COMBI(_1645956))))))], (6647 ^ _777864) ^ [_887595] : [-(_887595 = 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)), _887595)))], (43737 ^ _777864) ^ [_1631675, _1631677] : [-(hAPP(c_Relation_OField(_1631675), hAPP(c_Relation_Oconverse(_1631675, _1631675), _1631677)) = hAPP(c_Relation_OField(_1631675), _1631677))], (41818 ^ _777864) ^ [_1588511, _1588513, _1588515, _1588517, _1588519, _1588521] : [c_Fun_Oinj__on(_1588511, _1588513, hAPP(c_Fun_Ocomp(_1588515, _1588513, _1588511, _1588517), _1588519), _1588521), -(c_Fun_Oinj__on(_1588511, _1588515, _1588519, _1588521))], (19654 ^ _777864) ^ [_1116274, _1116276] : [class_Int_Onumber__ring(_1116274), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1116274), hAPP(c_Int_Onumber__class_Onumber__of(_1116274), 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)))), _1116276)) = c_Groups_Oone__class_Oone(_1116274))], (13880 ^ _777864) ^ [_1011954, _1011956, _1011958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011954), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13883 ^ _777864 : [(13884 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1011956, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011958), _1011954)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011958, _1011954))), 13887 ^ _777864 : [(13888 ^ _777864) ^ [_1012164, _1012166] : [-(hBOOL(hAPP(hAPP(_1011956, _1012166), _1012164))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011954), _1012164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012164), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1011958 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011954), _1012166)), _1012164)]]], (13902 ^ _777864) ^ [] : [13905 ^ _777864 : [(13908 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13904 ^ [_1011954, _1011956, _1011958]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13910 ^ _777864) ^ [] : [-(_1011958 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011954), 13903 ^ [_1011954, _1011956, _1011958])), 13904 ^ [_1011954, _1011956, _1011958]))], (13912 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1011956, 13903 ^ [_1011954, _1011956, _1011958]), 13904 ^ [_1011954, _1011956, _1011958]))], (13906 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011954), 13904 ^ [_1011954, _1011956, _1011958])))]], -(hBOOL(hAPP(hAPP(_1011956, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011958), _1011954)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011958, _1011954))))]]], (43072 ^ _777864) ^ [_1615856, _1615858, _1615860, _1615862, _1615864, _1615866] : [c_Finite__Set_Ofun__left__comm(_1615856, _1615858, _1615860), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615856), _1615862)), hBOOL(hAPP(hAPP(c_member(_1615856), _1615864), _1615862)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1615856, _1615858, _1615860), _1615866), _1615862) = hAPP(hAPP(_1615860, _1615864), hAPP(hAPP(c_Finite__Set_Ofold(_1615856, _1615858, _1615860), _1615866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615856, tc_HOL_Obool)), _1615862), hAPP(hAPP(c_Set_Oinsert(_1615856), _1615864), c_Orderings_Obot__class_Obot(tc_fun(_1615856, tc_HOL_Obool)))))))], (44822 ^ _777864) ^ [_1660510, _1660512, _1660514] : [44824 ^ _777864 : [(44827 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660510, tc_HOL_Obool)), 44823 ^ [_1660510, _1660512, _1660514]), _1660514) = c_Orderings_Obot__class_Obot(tc_fun(_1660510, tc_HOL_Obool))], (44825 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1660510, tc_HOL_Obool)), 44823 ^ [_1660510, _1660512, _1660514]), _1660512)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1660510, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1660510, tc_HOL_Obool), _1660512)), _1660514) = c_Orderings_Obot__class_Obot(tc_fun(_1660510, tc_HOL_Obool)))], (9700 ^ _777864) ^ [_939954, _939956] : [class_Int_Oring__char__0(_939954), 9703 ^ _777864 : [(9710 ^ _777864) ^ [] : [_939956 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_939954) = hAPP(c_Int_Oring__1__class_Oof__int(_939954), _939956))], (9704 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(_939954) = hAPP(c_Int_Oring__1__class_Oof__int(_939954), _939956), -(_939956 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (39431 ^ _777864) ^ [_1524327, _1524329, _1524331] : [class_Lattices_Osemilattice__inf(_1524327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524327), _1524329)), -(_1524329 = c_Orderings_Obot__class_Obot(tc_fun(_1524327, tc_HOL_Obool))), 39442 ^ _777864 : [(39443 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1524327), _1524331), hAPP(c_Finite__Set_Ofold1(_1524327, c_Lattices_Osemilattice__inf__class_Oinf(_1524327)), _1524329))), 39446 ^ _777864 : [(39447 ^ _777864) ^ [_1524620] : [hBOOL(hAPP(hAPP(c_member(_1524327), _1524620), _1524329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1524327), _1524331), _1524620)))]]], (39453 ^ _777864) ^ [] : [39455 ^ _777864 : [(39458 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1524327), _1524331), 39454 ^ [_1524327, _1524329, _1524331]))], (39456 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524327), 39454 ^ [_1524327, _1524329, _1524331]), _1524329)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1524327), _1524331), hAPP(c_Finite__Set_Ofold1(_1524327, c_Lattices_Osemilattice__inf__class_Oinf(_1524327)), _1524329))))]]], (7480 ^ _777864) ^ [_901366, _901368, _901370, _901372, _901374] : [c_Com_Ocom_OAss(_901366, _901368) = c_Com_Ocom_OCond(_901370, _901372, _901374)], (30196 ^ _777864) ^ [_1327594, _1327596, _1327598, _1327600] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327594, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327594, tc_HOL_Obool)), _1327596), _1327598)), _1327600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327594, tc_HOL_Obool)), _1327596), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327594, tc_HOL_Obool)), _1327598), _1327600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327594, tc_HOL_Obool)), _1327600), _1327596)))], (29932 ^ _777864) ^ [_1321916, _1321918, _1321920] : [class_Lattices_Olattice(_1321916), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321916), _1321918), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321916), _1321918), _1321920)) = _1321918)], (28994 ^ _777864) ^ [_1301909, _1301911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1301909, _1301909)), _1301911)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1301909), hAPP(c_Relation_OField(_1301909), _1301911))))], (5358 ^ _777864) ^ [_859829, _859831, _859833, _859835, _859837, _859839] : [-(c_List_OdropWhile(_859839, _859835, _859831) = c_List_OdropWhile(_859837, _859833, _859829)), _859839 = _859837, _859835 = _859833, _859831 = _859829], (33851 ^ _777864) ^ [_1403444, _1403446, _1403448, _1403450, _1403452] : [-(_1403444 = c_Orderings_Obot__class_Obot(tc_fun(_1403446, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403446, tc_fun(_1403448, tc_HOL_Obool)), _1403444), hAPP(hAPP(c_COMBB(tc_fun(_1403448, tc_HOL_Obool), tc_fun(_1403448, tc_HOL_Obool), _1403446), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403448, tc_HOL_Obool)), _1403450)), _1403452)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403448, tc_HOL_Obool)), _1403450), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403446, tc_fun(_1403448, tc_HOL_Obool)), _1403444), _1403452)))], (46126 ^ _777864) ^ [_1690763, _1690765, _1690767, _1690769, _1690771] : [-(hBOOL(hAPP(hAPP(c_member(_1690763), _1690765), hAPP(c_List_Oset(_1690763), _1690767)))), -(hAPP(c_Map_Omap__of(_1690763, _1690769, hAPP(hAPP(c_List_Ozip(_1690763, _1690769), _1690767), hAPP(hAPP(c_List_Omap(_1690763, _1690769), _1690771), _1690767))), _1690765) = c_Option_Ooption_ONone(_1690769))], (36226 ^ _777864) ^ [_1452137, _1452139, _1452141, _1452143, _1452145, _1452147] : [c_Fun_Oinj__on(_1452137, _1452139, _1452141, _1452143), -(hBOOL(hAPP(hAPP(c_member(_1452139), _1452145), hAPP(c_Set_Oimage(_1452137, _1452139, _1452141), _1452143)))), -(c_Fun_Oinj__on(_1452137, _1452139, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1452137, _1452139), _1452141), _1452147), _1452145), _1452143))], (38842 ^ _777864) ^ [_1509739, _1509741, _1509743, _1509745, _1509747] : [c_Fun_Oinj__on(_1509739, _1509741, _1509743, c_Orderings_Otop__class_Otop(tc_fun(_1509739, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509741, tc_HOL_Obool)), _1509745), hAPP(c_Set_Oimage(_1509739, _1509741, _1509743), _1509747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509739, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1509739, _1509741, _1509743), _1509745)), _1509747)))], (23275 ^ _777864) ^ [_1182965, _1182967, _1182969, _1182971, _1182973] : [-(c_Nat_Onat_Onat__case(_1182965, _1182967, _1182969, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1182971)), _1182973)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1182965), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1182971))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1182965, _1182965), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1182965, tc_fun(_1182965, _1182965)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1182965, tc_fun(_1182965, _1182965)), tc_Int_Oint), c_If(_1182965)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1182965, _1182967, _1182969, _1182973))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1182965, tc_Int_Oint), _1182969), 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)), _1182973)))))], (7506 ^ _777864) ^ [_902110, _902112] : [c_Com_Ocom_OSemi(_902110, _902112) = c_Com_Ocom_OSKIP], (7552 ^ _777864) ^ [_903117, _903119, _903121, _903123, _903125] : [-(hAPP(c_Option_Ooption_Ooption__case(_903117, _903119, _903121, _903123), hAPP(c_Option_Ooption_OSome(_903119), _903125)) = hAPP(_903123, _903125))], (19322 ^ _777864) ^ [_1110067, _1110069, _1110071] : [class_Groups_Omonoid__mult(_1110067), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1110067), _1110069), 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)))), _1110071)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1110067), hAPP(hAPP(c_Power_Opower__class_Opower(_1110067), _1110069), _1110071)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (48600 ^ _777864) ^ [_1754389, _1754391, _1754393, _1754395] : [-(hAPP(hAPP(c_List_Odrop(_1754389), _1754391), hAPP(hAPP(c_List_Olist_OCons(_1754389), _1754393), _1754395)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1754389), hAPP(hAPP(c_List_Olist_OCons(_1754389), _1754393), _1754395), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1754389), tc_List_Olist(_1754389)), c_List_Odrop(_1754389)), _1754395), _1754391))], (39327 ^ _777864) ^ [_1521889, _1521891] : [class_Lattices_Olattice(_1521889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521889), _1521891)), -(c_Big__Operators_Olattice__class_OSup__fin(_1521889, _1521891) = hAPP(c_Finite__Set_Ofold1(_1521889, c_Lattices_Osemilattice__sup__class_Osup(_1521889)), _1521891))], (47157 ^ _777864) ^ [_1719064, _1719066, _1719068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719066)), _1719068))), -(hBOOL(hAPP(hAPP(c_member(_1719066), hAPP(hAPP(c_List_Onth(_1719066), _1719068), _1719064)), hAPP(c_List_Oset(_1719066), _1719068))))], (17714 ^ _777864) ^ [_1083188] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083188))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17394 ^ _777864) ^ [_1078062, _1078064, _1078066, _1078068] : [class_Rings_Olinordered__semidom(_1078062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078062), c_Groups_Oone__class_Oone(_1078062)), _1078064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078062), hAPP(hAPP(c_Power_Opower__class_Opower(_1078062), _1078064), _1078066)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078062), _1078064), _1078068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078066), _1078068)))], (26425 ^ _777864) ^ [_1243354, _1243356] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243354)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243356))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243354), _1243356)))], (25363 ^ _777864) ^ [_1222656, _1222658, _1222660] : [class_Rings_Ocomm__ring__1(_1222656), 25366 ^ _777864 : [(25373 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222656), _1222658), _1222660)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222656), hAPP(c_Groups_Ouminus__class_Ouminus(_1222656), _1222658)), _1222660)))], (25367 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222656), hAPP(c_Groups_Ouminus__class_Ouminus(_1222656), _1222658)), _1222660)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222656), _1222658), _1222660)))]]], (10113 ^ _777864) ^ [_946715, _946717, _946719, _946721] : [class_Orderings_Oord(_946715), 10116 ^ _777864 : [(10123 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946715), hAPP(_946719, 10124 ^ [_946715, _946717, _946719, _946721])), hAPP(_946721, 10124 ^ [_946715, _946717, _946719, _946721]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946717, _946715)), _946719), _946721)))], (10117 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946717, _946715)), _946719), _946721)), 10120 ^ _777864 : [(10121 ^ _777864) ^ [_946872] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946715), hAPP(_946719, _946872)), hAPP(_946721, _946872))))]]]]], (17134 ^ _777864) ^ [_1073372, _1073374, _1073376] : [class_Rings_Olinordered__idom(_1073372), -(hAPP(c_Groups_Oabs__class_Oabs(_1073372), hAPP(hAPP(c_Power_Opower__class_Opower(_1073372), _1073374), _1073376)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1073372), hAPP(c_Groups_Oabs__class_Oabs(_1073372), _1073374)), _1073376))], (4078 ^ _777864) ^ [_840151, _840153, _840155, _840157, _840159, _840161, _840163, _840165] : [-(c_Wellfounded_Olex__prod(_840165, _840161, _840157, _840153) = c_Wellfounded_Olex__prod(_840163, _840159, _840155, _840151)), _840165 = _840163, _840161 = _840159, _840157 = _840155, _840153 = _840151], (15508 ^ _777864) ^ [_1041768, _1041770, _1041772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041768), _1041770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041772), _1041768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041768), _1041772)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041770), _1041772))))], (49035 ^ _777864) ^ [_1763768, _1763770, _1763772, _1763774, _1763776] : [hBOOL(hAPP(hAPP(c_member(_1763768), _1763770), hAPP(c_List_Oset(_1763768), _1763772))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1763774), hAPP(_1763776, _1763770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1763774), c_List_Olist_Olist__size(_1763768, _1763776, _1763772))))], (19798 ^ _777864) ^ [_1119064, _1119066] : [class_Rings_Odivision__ring(_1119064), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119064), _1119066), c_Groups_Oone__class_Oone(_1119064)) = _1119066)], (44161 ^ _777864) ^ [_1644550, _1644552, _1644554, _1644556, _1644558, _1644560, _1644562] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644550, tc_fun(_1644552, tc_fun(_1644554, tc_HOL_Obool))), _1644556), _1644558), _1644560), _1644562)), 44164 ^ _777864 : [(44165 ^ _777864) ^ [_1644678] : [hBOOL(hAPP(hAPP(c_member(_1644550), _1644678), _1644556)), -(hBOOL(hAPP(hAPP(hAPP(_1644558, _1644678), _1644560), _1644562)))]]], (41844 ^ _777864) ^ [_1589032, _1589034, _1589036, _1589038, _1589040, _1589042, _1589044, _1589046] : [class_Groups_Ocomm__monoid__mult(_1589032), c_Fun_Oinj__on(_1589034, _1589036, _1589038, _1589040), _1589042 = hAPP(c_Set_Oimage(_1589034, _1589036, _1589038), _1589040), _1589044 = hAPP(c_Fun_Ocomp(_1589036, _1589032, _1589034, _1589046), _1589038), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589036, _1589032), _1589046), _1589042) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589034, _1589032), _1589044), _1589040))], (38348 ^ _777864) ^ [_1497673] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1497673)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (18800 ^ _777864) ^ [_1100797, _1100799] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1100797, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1100799)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1100797, 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)))), _1100799)))], (7972 ^ _777864) ^ [_910686] : [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), _910686))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _910686)))], (42040 ^ _777864) ^ [_1593713, _1593715, _1593717, _1593719, _1593721, _1593723] : [c_Finite__Set_Ofolding(_1593713, _1593715, _1593717, _1593719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593713), _1593721)), -(hAPP(c_Fun_Ocomp(_1593715, _1593715, _1593715, hAPP(_1593717, _1593723)), hAPP(_1593719, _1593721)) = hAPP(c_Fun_Ocomp(_1593715, _1593715, _1593715, hAPP(_1593719, _1593721)), hAPP(_1593717, _1593723)))], (37240 ^ _777864) ^ [_1475536, _1475538, _1475540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475536), _1475538)), 37243 ^ _777864 : [(37263 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475536, tc_Nat_Onat), _1475540), _1475538) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 37264 ^ _777864 : [(37265 ^ _777864) ^ [_1476017] : [hBOOL(hAPP(hAPP(c_member(_1475536), _1476017), _1475538)), hAPP(_1475540, _1476017) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37273 ^ _777864 : [(37278 ^ _777864) ^ [] : [hAPP(_1475540, 37272 ^ [_1475536, _1475538, _1475540, _1476017]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37276 ^ _777864) ^ [] : [_1476017 = 37272 ^ [_1475536, _1475538, _1475540, _1476017]], (37274 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475536), 37272 ^ [_1475536, _1475538, _1475540, _1476017]), _1475538)))]]]]], (37244 ^ _777864) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475536, tc_Nat_Onat), _1475540), _1475538) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37248 ^ _777864 : [(37253 ^ _777864) ^ [_1475856] : [hBOOL(hAPP(hAPP(c_member(_1475536), _1475856), _1475538)), -(37247 ^ [_1475536, _1475538, _1475540] = _1475856), -(hAPP(_1475540, _1475856) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37251 ^ _777864) ^ [] : [-(hAPP(_1475540, 37247 ^ [_1475536, _1475538, _1475540]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37249 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475536), 37247 ^ [_1475536, _1475538, _1475540]), _1475538)))]]]]], (17720 ^ _777864) ^ [_1083279] : [-(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, _1083279))))))], (27786 ^ _777864) ^ [_1272872, _1272874] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272872, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1272872, tc_HOL_Obool))), _1272874) = _1272874)], (50229 ^ _777864) ^ [_1788671, _1788673, _1788675] : [class_Orderings_Olinorder(_1788671), hBOOL(hAPP(hAPP(c_member(_1788671), _1788673), hAPP(c_List_Oset(_1788671), _1788675))), c_List_Olinorder__class_Osorted(_1788671, _1788675), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1788671, _1788671, c_COMBI(_1788671)), _1788673), c_List_Oremove1(_1788671, _1788673, _1788675)) = _1788675)], (43653 ^ _777864) ^ [_1628902, _1628904, _1628906, _1628908, _1628910] : [-(hAPP(c_Relation_Oconverse(_1628902, _1628904), hAPP(hAPP(c_Relation_Orel__comp(_1628902, _1628906, _1628904), _1628908), _1628910)) = hAPP(hAPP(c_Relation_Orel__comp(_1628904, _1628906, _1628902), hAPP(c_Relation_Oconverse(_1628906, _1628904), _1628910)), hAPP(c_Relation_Oconverse(_1628902, _1628906), _1628908)))], (204 ^ _777864) ^ [_780800, _780802, _780804, _780806, _780808, _780810, _780812, _780814, _780816, _780818, _780820, _780822] : [-(c_Nitpick_Ofold__graph_H(_780820, _780816, _780812, _780808, _780804, _780800)), c_Nitpick_Ofold__graph_H(_780822, _780818, _780814, _780810, _780806, _780802), _780822 = _780820, _780818 = _780816, _780814 = _780812, _780810 = _780808, _780806 = _780804, _780802 = _780800], (48522 ^ _777864) ^ [_1752597, _1752599] : [hBOOL(hAPP(c_List_Odistinct(_1752597), _1752599)), -(hBOOL(hAPP(c_List_Odistinct(_1752597), hAPP(c_List_Orotate1(_1752597), _1752599))))], (51209 ^ _777864) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (23473 ^ _777864) ^ [_1187629, _1187631, _1187633] : [class_Orderings_Olinorder(_1187629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187629), _1187631), _1187633)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187629), _1187633), _1187631) = _1187631)], (19828 ^ _777864) ^ [_1119705, _1119707, _1119709] : [class_Fields_Olinordered__field__inverse__zero(_1119705), -(hAPP(c_Groups_Oabs__class_Oabs(_1119705), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119705), _1119707), _1119709)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119705), hAPP(c_Groups_Oabs__class_Oabs(_1119705), _1119707)), hAPP(c_Groups_Oabs__class_Oabs(_1119705), _1119709)))], (4634 ^ _777864) ^ [_848707, _848709, _848711, _848713] : [-(c_Random_Oselect__weight(_848713, _848709) = c_Random_Oselect__weight(_848711, _848707)), _848713 = _848711, _848709 = _848707], (7794 ^ _777864) ^ [_907347, _907349, _907351, _907353, _907355] : [c_Com_Ocom_OCond(_907347, _907349, _907351) = c_Com_Ocom_OWhile(_907353, _907355)], (29193 ^ _777864) ^ [_1306106, _1306108, _1306110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1306106), hAPP(hAPP(c_Set_Oinsert(_1306106), _1306108), _1306110))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306106), _1306110)))], (20202 ^ _777864) ^ [_1126098, _1126100, _1126102, _1126104, _1126106] : [class_Fields_Ofield(_1126098), -(_1126100 = c_Groups_Ozero__class_Ozero(_1126098)), -(_1126102 = c_Groups_Ozero__class_Ozero(_1126098)), 20213 ^ _777864 : [(20220 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126098), _1126104), _1126102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126098), _1126106), _1126100), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126098), _1126104), _1126100) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126098), _1126106), _1126102))], (20214 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126098), _1126104), _1126100) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126098), _1126106), _1126102), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126098), _1126104), _1126102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126098), _1126106), _1126100))]]], (47360 ^ _777864) ^ [_1724688, _1724690, _1724692] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724688), tc_List_Olist(_1724688))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724688), tc_List_Olist(_1724688)), _1724690), c_List_Olist_ONil(_1724688))), c_List_Olistrel(_1724688, _1724692))), -(_1724690 = c_List_Olist_ONil(_1724688))], (4574 ^ _777864) ^ [_847781, _847783] : [_847783 = _847781, -(c_Set_Oinsert(_847783) = c_Set_Oinsert(_847781))], (24331 ^ _777864) ^ [_1203883, _1203885] : [-(c_Nitpick_Onat__lcm(_1203883, _1203885) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1203883), _1203885)), c_Nitpick_Onat__gcd(_1203883, _1203885)))], (48678 ^ _777864) ^ [_1756395, _1756397, _1756399, _1756401] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1756395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1756397), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1756395)), hAPP(hAPP(c_List_Olist_OCons(_1756397), _1756399), _1756401)) = hAPP(hAPP(c_List_Odrop(_1756397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1756395)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1756401))], (23337 ^ _777864) ^ [_1184860, _1184862, _1184864, _1184866] : [-(hAPP(c_Nat_Onat_Onat__rec(_1184860, _1184862, _1184864), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1184866)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1184860), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1184866))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1184860, _1184860), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1184860, tc_fun(_1184860, _1184860)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1184860, tc_fun(_1184860, _1184860)), tc_Int_Oint), c_If(_1184860)), c_Nat__Numeral_Oneg)), _1184862)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1184860, _1184860), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1184860, _1184860), tc_Int_Oint), _1184864), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1184860, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1184860, _1184862, _1184864)), c_Int_Onat)))))], (44041 ^ _777864) ^ [_1640858, _1640860, _1640862, _1640864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640858, _1640858)), hAPP(hAPP(c_Product__Type_OPair(_1640858, _1640858), _1640860), _1640862)), c_Transitive__Closure_Otrancl(_1640858, hAPP(c_Relation_Oconverse(_1640858, _1640858), _1640864)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640858, _1640858)), hAPP(hAPP(c_Product__Type_OPair(_1640858, _1640858), _1640860), _1640862)), hAPP(c_Relation_Oconverse(_1640858, _1640858), c_Transitive__Closure_Otrancl(_1640858, _1640864)))))], (16202 ^ _777864) ^ [_1055705, _1055707, _1055709] : [class_Rings_Olinordered__idom(_1055705), -(hAPP(c_Groups_Oabs__class_Oabs(_1055705), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055705), _1055707), _1055709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055705), hAPP(c_Groups_Oabs__class_Oabs(_1055705), _1055707)), hAPP(c_Groups_Oabs__class_Oabs(_1055705), _1055709)))], (36390 ^ _777864) ^ [_1455260, _1455262, _1455264, _1455266, _1455268, _1455270, _1455272] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1455260, tc_Option_Ooption(_1455262)), _1455264), _1455266), hAPP(c_Option_Ooption_OSome(_1455262), _1455268)), _1455270) = hAPP(c_Option_Ooption_OSome(_1455262), _1455272)), 36391 ^ _777864 : [(36398 ^ _777864) ^ [] : [-(_1455270 = _1455266), hAPP(_1455264, _1455270) = hAPP(c_Option_Ooption_OSome(_1455262), _1455272)], (36392 ^ _777864) ^ [] : [_1455270 = _1455266, _1455268 = _1455272]]], (43617 ^ _777864) ^ [_1628182, _1628184, _1628186] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628182, tc_fun(_1628184, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1628182, tc_HOL_Obool))), _1628186) = c_Orderings_Otop__class_Otop(tc_fun(_1628184, tc_HOL_Obool)))], (47946 ^ _777864) ^ [_1737593, _1737595, _1737597, _1737599, _1737601, _1737603] : [hAPP(hAPP(c_List_Olist_OCons(_1737593), _1737595), _1737597) = _1737599, _1737601 = hAPP(hAPP(c_List_Oappend(_1737593), _1737597), _1737603), -(hAPP(hAPP(c_List_Olist_OCons(_1737593), _1737595), _1737601) = hAPP(hAPP(c_List_Oappend(_1737593), _1737599), _1737603))], (38494 ^ _777864) ^ [_1500535, _1500537, _1500539, _1500541, _1500543] : [c_Fun_Oinj__on(_1500535, _1500537, _1500539, c_Orderings_Otop__class_Otop(tc_fun(_1500535, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1500535, _1500537, _1500539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500535, tc_HOL_Obool)), _1500541), _1500543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1500537, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1500535, _1500537, _1500539), _1500541)), hAPP(c_Set_Oimage(_1500535, _1500537, _1500539), _1500543)))], (28468 ^ _777864) ^ [_1289724, _1289726, _1289728, _1289730, _1289732, _1289734] : [hBOOL(hAPP(hAPP(_1289724, _1289726), _1289728)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289730, tc_fun(_1289732, tc_HOL_Obool))), _1289734), _1289724), _1289726), _1289728)))], (9676 ^ _777864) ^ [_939600, _939602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _939600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _939602), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _939600), _939602))), -(_939600 = _939602)], (11225 ^ _777864) ^ [_964847, _964849, _964851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964847), _964849)), _964851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964849), _964851)))], (27784 ^ _777864) ^ [_1272831, _1272833] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272831, tc_HOL_Obool)), _1272833), c_Orderings_Obot__class_Obot(tc_fun(_1272831, tc_HOL_Obool))) = _1272833)], (38230 ^ _777864) ^ [_1495245, _1495247] : [-(c_Sum__Type_OPlus(_1495245, _1495247, c_Orderings_Otop__class_Otop(tc_fun(_1495245, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1495247, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1495245, _1495247), tc_HOL_Obool)))], (22821 ^ _777864) ^ [_1173088, _1173090] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1173088, _1173090) = 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), _1173088), _1173090)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1173088, _1173090)))], (47994 ^ _777864) ^ [_1738871, _1738873, _1738875, _1738877, _1738879, _1738881] : [-(c_List_Ofoldr(_1738871, _1738873, _1738875, hAPP(hAPP(c_List_Oappend(_1738871), _1738877), _1738879), _1738881) = c_List_Ofoldr(_1738871, _1738873, _1738875, _1738877, c_List_Ofoldr(_1738871, _1738873, _1738875, _1738879, _1738881)))], (25637 ^ _777864) ^ [_1227568, _1227570, _1227572, _1227574, _1227576] : [class_Rings_Ocomm__semiring__1(_1227568), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227568), _1227570), _1227572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227574), _1227576)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227568), hAPP(hAPP(c_Power_Opower__class_Opower(_1227568), _1227570), _1227574)), hAPP(hAPP(c_Power_Opower__class_Opower(_1227568), _1227572), _1227576))))], (19804 ^ _777864) ^ [_1119159, _1119161, _1119163] : [class_Rings_Odivision__ring(_1119159), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1119159), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119159), _1119161), _1119163)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119159), hAPP(c_Groups_Ouminus__class_Ouminus(_1119159), _1119161)), _1119163))], (19694 ^ _777864) ^ [] : [-(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)))], (42094 ^ _777864) ^ [_1594890, _1594892, _1594894, _1594896, _1594898, _1594900, _1594902] : [c_Finite__Set_Ofolding__image(_1594890, _1594892, _1594894, _1594896, _1594898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594892), _1594900)), -(hAPP(hAPP(_1594898, _1594902), _1594900) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1594890, _1594892, _1594894), _1594902), _1594896), _1594900))], (4874 ^ _777864) ^ [_852395, _852397] : [_852397 = _852395, -(c_List_Odrop(_852397) = c_List_Odrop(_852395))], (44574 ^ _777864) ^ [_1654691, _1654693] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1654691), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654691, tc_HOL_Obool), _1654693)))), 44575 ^ _777864 : [(44576 ^ _777864) ^ [_1654755] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1654691, tc_HOL_Obool)), _1654755), _1654693)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1654691), _1654755))]]], (10560 ^ _777864) ^ [_954113, _954115, _954117] : [class_Orderings_Oorder(_954113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954113), _954115), _954117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954113), _954115), _954117))), -(_954115 = _954117)], (28074 ^ _777864) ^ [_1278099, _1278101] : [class_Lattices_Osemilattice__sup(_1278099), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278099), _1278101), _1278101) = _1278101)], (22713 ^ _777864) ^ [_1170876, _1170878, _1170880] : [-(_1170876 = _1170878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170880, tc_HOL_Obool)), _1170876), _1170878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170880, tc_HOL_Obool)), _1170878), _1170876))], (39367 ^ _777864) ^ [_1522517, _1522519] : [class_Orderings_Olinorder(_1522517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522517), _1522519)), -(c_Big__Operators_Olattice_OInf__fin(_1522517, c_Orderings_Oord__class_Omin(_1522517), _1522519) = hAPP(c_Finite__Set_Ofold1(_1522517, c_Orderings_Oord__class_Omin(_1522517)), _1522519))], (14646 ^ _777864) ^ [_1025489, _1025491, _1025493] : [class_Divides_Osemiring__div(_1025489), -(_1025491 = c_Groups_Ozero__class_Ozero(_1025489)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025489), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025489), _1025493), _1025491)), _1025491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025489), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025489), _1025493), _1025491)), c_Groups_Oone__class_Oone(_1025489)))], (38556 ^ _777864) ^ [_1502458, _1502460, _1502462, _1502464, _1502466, _1502468] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502460, _1502462)), hAPP(hAPP(c_Product__Type_OPair(_1502460, _1502462), _1502466), _1502468)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502458, tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1502458, tc_HOL_Obool))), _1502464))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502458, tc_fun(_1502460, tc_fun(_1502462, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1502458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_fun(_1502460, tc_fun(_1502462, tc_HOL_Obool)), _1502458), hAPP(c_COMBC(_1502460, tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_fun(_1502462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502462, tc_fun(tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_fun(_1502462, tc_HOL_Obool)), _1502460), c_COMBC(_1502462, tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502462, tc_prod(_1502460, _1502462)), tc_fun(_1502462, tc_fun(tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_HOL_Obool)), _1502460), hAPP(c_COMBB(tc_prod(_1502460, _1502462), tc_fun(tc_fun(tc_prod(_1502460, _1502462), tc_HOL_Obool), tc_HOL_Obool), _1502462), c_member(tc_prod(_1502460, _1502462)))), c_Product__Type_OPair(_1502460, _1502462))))), _1502464)), _1502466), _1502468)))], (5894 ^ _777864) ^ [_874630, _874632, _874634, _874636] : [-(c_Com_Ovname_Ovname__case(_874630, _874632, _874634, c_Com_Ovname_OLoc(_874636)) = hAPP(_874634, _874636))], (21088 ^ _777864) ^ [_1141455, _1141457] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141455), _1141457), hAPP(c_Int_Onumber__class_Onumber__of(_1141455), c_Int_OBit1(c_Int_OPls))) = _1141457), class_Fields_Ofield(_1141455), class_Int_Onumber__ring(_1141455)], (3610 ^ _777864) ^ [_832781, _832783, _832785, _832787, _832789, _832791, _832793, _832795] : [-(c_New__Random__Sequence_Oneg__bind(_832795, _832791, _832787, _832783) = c_New__Random__Sequence_Oneg__bind(_832793, _832789, _832785, _832781)), _832795 = _832793, _832791 = _832789, _832787 = _832785, _832783 = _832781], (41950 ^ _777864) ^ [_1591445, _1591447, _1591449, _1591451, _1591453, _1591455, _1591457] : [c_Hoare__Mirabelle_Ohoare__derivs(_1591445, _1591447, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1591445)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1591445), c_Hoare__Mirabelle_Opeek__and(_1591445, _1591449, _1591451)), _1591453), _1591455)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1591445), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1591445, _1591447, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1591445)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1591445), c_Hoare__Mirabelle_Opeek__and(_1591445, _1591449, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1591451))), _1591457), _1591455)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1591445), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1591445, _1591447, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1591445)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1591445), _1591449), c_Com_Ocom_OCond(_1591451, _1591453, _1591457)), _1591455)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1591445), tc_HOL_Obool)))))], (8060 ^ _777864) ^ [_912200, _912202, _912204] : [class_Orderings_Olinorder(_912200), 8063 ^ _777864 : [(8064 ^ _777864) ^ [] : [-(_912202 = _912204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912200), _912202), _912204))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912200), _912204), _912202)))], (8074 ^ _777864) ^ [] : [8075 ^ _777864 : [(8078 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912200), _912204), _912202))], (8076 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912200), _912202), _912204))]], _912202 = _912204]]], (41754 ^ _777864) ^ [_1587028, _1587030, _1587032, _1587034, _1587036, _1587038, _1587040, _1587042, _1587044] : [hAPP(c_Fun_Ocomp(_1587028, _1587030, _1587032, _1587034), _1587036) = hAPP(c_Fun_Ocomp(_1587038, _1587030, _1587032, _1587040), _1587042), -(hAPP(_1587034, hAPP(_1587036, _1587044)) = hAPP(_1587040, hAPP(_1587042, _1587044)))], (49570 ^ _777864) ^ [_1775333, _1775335, _1775337, _1775339] : [-(hBOOL(hAPP(_1775333, _1775335))), -(hAPP(c_List_Ofilter(_1775337, _1775333), hAPP(hAPP(c_List_Olist_OCons(_1775337), _1775335), _1775339)) = hAPP(c_List_Ofilter(_1775337, _1775333), _1775339))], (48712 ^ _777864) ^ [_1757401, _1757403, _1757405] : [-(_1757401 = c_List_Olist_ONil(_1757403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757405), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757403)), _1757401))), -(hAPP(c_List_Ohd(_1757403), hAPP(hAPP(c_List_Odrop(_1757403), _1757405), _1757401)) = hAPP(hAPP(c_List_Onth(_1757403), _1757401), _1757405))], (16298 ^ _777864) ^ [_1057499, _1057501] : [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), _1057499)), _1057501))), _1057499 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1057501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19040 ^ _777864) ^ [_1105142, _1105144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105142)), c_Int_OBit0(_1105144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105142), _1105144)))], (37112 ^ _777864) ^ [_1472808, _1472810, _1472812, _1472814, _1472816] : [class_Groups_Oordered__comm__monoid__add(_1472808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472810), _1472812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472810, tc_HOL_Obool)), _1472814), _1472812)), 37126 ^ _777864 : [(37129 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472808), c_Groups_Ozero__class_Ozero(_1472808)), hAPP(_1472816, 37125 ^ [_1472808, _1472810, _1472812, _1472814, _1472816])))], (37127 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472810), 37125 ^ [_1472808, _1472810, _1472812, _1472814, _1472816]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472810, tc_HOL_Obool)), _1472812), _1472814))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472808), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472810, _1472808), _1472816), _1472814)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472810, _1472808), _1472816), _1472812))))], (17070 ^ _777864) ^ [_1072113, _1072115] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1072113) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072115)), _1072113 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1072115)), 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), _1072115)))], (12466 ^ _777864) ^ [_986894, _986896, _986898, _986900, _986902] : [class_Rings_Olinordered__semiring__strict(_986894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986894), _986896), _986898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986894), _986900), _986902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986894), c_Groups_Ozero__class_Ozero(_986894)), _986896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986894), c_Groups_Ozero__class_Ozero(_986894)), _986900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986894), _986896), _986900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986894), _986898), _986902))))], (1002 ^ _777864) ^ [_793157, _793159] : [-(class_Groups_Olinordered__ab__group__add(_793157)), _793159 = _793157, class_Groups_Olinordered__ab__group__add(_793159)], (44366 ^ _777864) ^ [_1649369, _1649371, _1649373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649369, _1649369)), _1649371), c_Transitive__Closure_Ortrancl(_1649369, _1649373))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649369, _1649369)), _1649371), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1649369, _1649369), 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(_1649369, _1649369), tc_HOL_Obool), tc_fun(tc_prod(_1649369, _1649369), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1649369, _1649369), tc_HOL_Obool)), _1649373)))))], (28780 ^ _777864) ^ [_1297821] : [-(_1297821 = 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), 28777 ^ [_1297821]), 28778 ^ [_1297821])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (22723 ^ _777864) ^ [_1171051, _1171053, _1171055] : [_1171051 = _1171053, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171055, tc_HOL_Obool)), _1171051), _1171053)))], (19948 ^ _777864) ^ [_1121654, _1121656, _1121658] : [class_Fields_Olinordered__field__inverse__zero(_1121654), 19951 ^ _777864 : [(19966 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121654), _1121656), _1121658)))), 19967 ^ _777864 : [(19974 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), _1121656), c_Groups_Ozero__class_Ozero(_1121654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), _1121658), c_Groups_Ozero__class_Ozero(_1121654)))], (19968 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), _1121656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), _1121658))]]], (19952 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121654), _1121656), _1121658))), 19957 ^ _777864 : [(19960 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), _1121658)))], (19958 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), c_Groups_Ozero__class_Ozero(_1121654)), _1121656)))]], 19961 ^ _777864 : [(19964 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), _1121658), c_Groups_Ozero__class_Ozero(_1121654))))], (19962 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121654), _1121656), c_Groups_Ozero__class_Ozero(_1121654))))]]]]], (51547 ^ _777864) ^ [_1812512] : [hBOOL(hAPP(c_fNot, _1812512)), hBOOL(_1812512)], (30336 ^ _777864) ^ [_1331000, _1331002, _1331004, _1331006, _1331008, _1331010, _1331012] : [c_Equiv__Relations_Oequiv(_1331000, _1331002, _1331004), hBOOL(hAPP(hAPP(c_member(tc_fun(_1331000, tc_HOL_Obool)), _1331006), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1331000), _1331002), _1331004))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1331000, tc_HOL_Obool)), _1331008), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1331000), _1331002), _1331004))), hBOOL(hAPP(hAPP(c_member(_1331000), _1331010), _1331006)), hBOOL(hAPP(hAPP(c_member(_1331000), _1331012), _1331008)), 30355 ^ _777864 : [(30362 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1331000, _1331000)), hAPP(hAPP(c_Product__Type_OPair(_1331000, _1331000), _1331010), _1331012)), _1331004)), -(_1331006 = _1331008)], (30356 ^ _777864) ^ [] : [_1331006 = _1331008, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1331000, _1331000)), hAPP(hAPP(c_Product__Type_OPair(_1331000, _1331000), _1331010), _1331012)), _1331004)))]]], (27035 ^ _777864) ^ [_1255331, _1255333, _1255335] : [_1255333 = _1255335, -(hAPP(hAPP(c_COMBC(_1255331, tc_fun(_1255331, tc_HOL_Obool), tc_HOL_Obool), c_member(_1255331)), _1255333) = hAPP(hAPP(c_COMBC(_1255331, tc_fun(_1255331, tc_HOL_Obool), tc_HOL_Obool), c_member(_1255331)), _1255335))], (28966 ^ _777864) ^ [_1301016, _1301018, _1301020] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1301016, hAPP(hAPP(c_COMBC(_1301016, tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_fun(_1301016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1301016, tc_fun(tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_fun(_1301016, tc_HOL_Obool)), _1301016), c_COMBC(_1301016, tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1301016, tc_prod(_1301016, _1301016)), tc_fun(_1301016, tc_fun(tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_HOL_Obool)), _1301016), hAPP(c_COMBB(tc_prod(_1301016, _1301016), tc_fun(tc_fun(tc_prod(_1301016, _1301016), tc_HOL_Obool), tc_HOL_Obool), _1301016), c_member(tc_prod(_1301016, _1301016)))), c_Product__Type_OPair(_1301016, _1301016)))), _1301018)), _1301020)), -(hBOOL(hAPP(hAPP(c_member(_1301016), _1301020), c_Wellfounded_Oacc(_1301016, _1301018))))], (13555 ^ _777864) ^ [_1006196, _1006198, _1006200] : [class_Divides_Osemiring__div(_1006196), -(c_Divides_Odiv__class_Omod(_1006196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006196), _1006198), _1006200), _1006198) = c_Groups_Ozero__class_Ozero(_1006196))], (5900 ^ _777864) ^ [_874762, _874764, _874766, _874768] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_874762, _874764)), _874766), _874768)), -(_874768 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _874766), _874762), hAPP(_874764, _874766)))], (5238 ^ _777864) ^ [_858053, _858055] : [_858055 = _858053, -(c_List_Oreturn__list(_858055) = c_List_Oreturn__list(_858053))], (26575 ^ _777864) ^ [_1246021, _1246023] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246021), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1246023)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246021)), _1246023)))], (9883 ^ _777864) ^ [_943046, _943048] : [class_Rings_Olinordered__idom(_943046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943046), _943048), c_Groups_Ozero__class_Ozero(_943046))), -(c_Groups_Osgn__class_Osgn(_943046, _943048) = hAPP(c_Groups_Ouminus__class_Ouminus(_943046), c_Groups_Oone__class_Oone(_943046)))], (29233 ^ _777864) ^ [_1306829, _1306831, _1306833] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306829, tc_HOL_Obool)), _1306831), _1306833)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306829), _1306831)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306829), _1306833))], (41323 ^ _777864) ^ [_1575715, _1575717, _1575719, _1575721] : [-(hAPP(c_Relation_ODomain(_1575715, _1575717), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1575715, _1575717), tc_HOL_Obool)), _1575719), _1575721)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1575715, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1575715, _1575717), _1575719)), hAPP(c_Relation_ODomain(_1575715, _1575717), _1575721)))], (41155 ^ _777864) ^ [_1571695, _1571697] : [-(hAPP(c_Relation_ORange(_1571695, _1571695), c_Relation_OId__on(_1571695, _1571697)) = _1571697)], (23339 ^ _777864) ^ [_1185000, _1185002] : [_1185000 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185000, _1185002) = 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)))], (47486 ^ _777864) ^ [_1727342, _1727344, _1727346] : [-(hAPP(hAPP(c_List_Ozip(_1727342, _1727344), c_List_Olist_ONil(_1727342)), _1727346) = c_List_Olist_ONil(tc_prod(_1727342, _1727344)))], (6048 ^ _777864) ^ [_877459, _877461] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_877459, _877461)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1452 ^ _777864) ^ [_798782, _798784] : [-(class_Rings_Oordered__cancel__semiring(_798782)), _798784 = _798782, class_Rings_Oordered__cancel__semiring(_798784)], (25191 ^ _777864) ^ [_1219776, _1219778] : [_1219776 = _1219778, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219776), _1219778)))], (6807 ^ _777864) ^ [_889935, _889937, _889939] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_889935, _889937, _889939)], (33386 ^ _777864) ^ [_1391660, _1391662, _1391664] : [class_Orderings_Oorder(_1391660), 33389 ^ _777864 : [(33396 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391660), _1391662), _1391664))), -(c_Orderings_Obot__class_Obot(tc_fun(_1391660, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1391660, _1391662, _1391664))], (33390 ^ _777864) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1391660, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1391660, _1391662, _1391664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391660), _1391662), _1391664))]]], (28978 ^ _777864) ^ [_1301704] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1301704)), -(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))), _1301704)), c_FunDef_Omax__weak)))], (38890 ^ _777864) ^ [_1511092, _1511094, _1511096, _1511098, _1511100] : [c_Typedef_Otype__definition(_1511092, _1511094, _1511096, _1511098, _1511100), -(hAPP(c_Set_Oimage(_1511094, _1511092, _1511098), _1511100) = c_Orderings_Otop__class_Otop(tc_fun(_1511092, tc_HOL_Obool)))], (46837 ^ _777864) ^ [_1711414, _1711416] : [class_Groups_Oordered__ab__group__add__abs(_1711414), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711414), hAPP(c_Groups_Oabs__class_Oabs(_1711414), hAPP(c_List_Omonoid__add__class_Olistsum(_1711414), _1711416))), hAPP(c_List_Omonoid__add__class_Olistsum(_1711414), hAPP(hAPP(c_List_Omap(_1711414, _1711414), c_Groups_Oabs__class_Oabs(_1711414)), _1711416)))))], (50646 ^ _777864) ^ [_1798890, _1798892, _1798894] : [class_Orderings_Olinorder(_1798890), c_List_Olinorder__class_Osorted(_1798890, hAPP(c_List_Orev(_1798890), _1798892)), 50653 ^ _777864 : [(50660 ^ _777864) ^ [] : [-(_1798892 = c_List_Olist_ONil(_1798890)), -(c_List_Ofoldr(_1798890, _1798890, c_Orderings_Oord__class_Omax(_1798890), _1798892, _1798894) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1798890), hAPP(hAPP(c_List_Onth(_1798890), _1798892), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1798894))], (50654 ^ _777864) ^ [] : [_1798892 = c_List_Olist_ONil(_1798890), -(c_List_Ofoldr(_1798890, _1798890, c_Orderings_Oord__class_Omax(_1798890), _1798892, _1798894) = _1798894)]]], (30707 ^ _777864) ^ [_1339376, _1339378, _1339380, _1339382, _1339384] : [-(hBOOL(hAPP(hAPP(c_member(_1339376), _1339378), c_SetInterval_Oord_OatLeastAtMost(_1339376, _1339380, _1339382, _1339384)))), hBOOL(hAPP(hAPP(_1339380, _1339382), _1339378)), hBOOL(hAPP(hAPP(_1339380, _1339378), _1339384))], (27788 ^ _777864) ^ [_1272913, _1272915, _1272917] : [class_Lattices_Obounded__lattice__bot(_1272913), 27791 ^ _777864 : [(27800 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272913), _1272915), _1272917) = c_Orderings_Obot__class_Obot(_1272913)), _1272915 = c_Orderings_Obot__class_Obot(_1272913), _1272917 = c_Orderings_Obot__class_Obot(_1272913)], (27792 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272913), _1272915), _1272917) = c_Orderings_Obot__class_Obot(_1272913), 27795 ^ _777864 : [(27798 ^ _777864) ^ [] : [-(_1272917 = c_Orderings_Obot__class_Obot(_1272913))], (27796 ^ _777864) ^ [] : [-(_1272915 = c_Orderings_Obot__class_Obot(_1272913))]]]]], (25491 ^ _777864) ^ [_1224818, _1224820, _1224822, _1224824] : [class_Rings_Oidom(_1224818), 25494 ^ _777864 : [(25495 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224818), _1224820), _1224822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224818), _1224820), _1224824))), -(_1224820 = c_Groups_Ozero__class_Ozero(_1224818)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224818), _1224822), _1224824)))], (25505 ^ _777864) ^ [] : [25506 ^ _777864 : [(25509 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224818), _1224822), _1224824))], (25507 ^ _777864) ^ [] : [_1224820 = c_Groups_Ozero__class_Ozero(_1224818)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224818), _1224820), _1224822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224818), _1224820), _1224824))))]]], (5694 ^ _777864) ^ [_869725, _869727, _869729] : [5695 ^ _777864 : [(5696 ^ _777864) ^ [_869775] : [c_Natural_Oevaln(_869725, _869727, _869775, _869729)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869725), _869727), _869729)))], (19610 ^ _777864) ^ [_1115346] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1115346, 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, _1115346, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23295 ^ _777864) ^ [_1183745, _1183747, _1183749, _1183751, _1183753, _1183755, _1183757] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1183745, _1183747, _1183749, _1183751), _1183753), _1183755), _1183757) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183747, _1183749, _1183751), _1183755), hAPP(_1183753, _1183757)))], (36608 ^ _777864) ^ [_1460498, _1460500, _1460502, _1460504, _1460506] : [class_Fields_Ofield(_1460498), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1460498), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460500, _1460498), _1460502), _1460504)), _1460506) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460500, _1460498), hAPP(hAPP(c_COMBC(_1460500, _1460498, _1460498), hAPP(hAPP(c_COMBB(_1460498, tc_fun(_1460498, _1460498), _1460500), c_Rings_Oinverse__class_Odivide(_1460498)), _1460502)), _1460506)), _1460504))], (33845 ^ _777864) ^ [_1403275, _1403277, _1403279, _1403281, _1403283] : [_1403275 = c_Orderings_Obot__class_Obot(tc_fun(_1403277, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403277, tc_fun(_1403279, tc_HOL_Obool)), _1403275), hAPP(hAPP(c_COMBB(tc_fun(_1403279, tc_HOL_Obool), tc_fun(_1403279, tc_HOL_Obool), _1403277), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403279, tc_HOL_Obool)), _1403281)), _1403283)) = c_Orderings_Obot__class_Obot(tc_fun(_1403279, tc_HOL_Obool)))], (4032 ^ _777864) ^ [_839368, _839370, _839372, _839374] : [-(c_Relation_Oinv__image(_839374, _839370) = c_Relation_Oinv__image(_839372, _839368)), _839374 = _839372, _839370 = _839368], (17976 ^ _777864) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (15266 ^ _777864) ^ [_1037062, _1037064, _1037066] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037062), _1037064)), _1037066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037062), _1037066)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037064), _1037066)))], (50048 ^ _777864) ^ [_1785334, _1785336] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1785334, _1785336)))], (13449 ^ _777864) ^ [_1003965, _1003967, _1003969, _1003971] : [class_Divides_Osemiring__div(_1003965), -(c_Divides_Odiv__class_Omod(_1003965, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003965), c_Divides_Odiv__class_Omod(_1003965, _1003967, _1003969)), _1003971), _1003969) = c_Divides_Odiv__class_Omod(_1003965, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003965), _1003967), _1003971), _1003969))], (10031 ^ _777864) ^ [_945560, _945562] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945560), _945562) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _945560 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _945562 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (48608 ^ _777864) ^ [_1754603, _1754605, _1754607, _1754609] : [-(_1754603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1754605), _1754603), hAPP(hAPP(c_List_Olist_OCons(_1754605), _1754607), _1754609)) = hAPP(hAPP(c_List_Odrop(_1754605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1754603), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1754609))], (40126 ^ _777864) ^ [_1539437, _1539439] : [-(hAPP(c_Set_OCollect(_1539437), hAPP(hAPP(c_COMBC(_1539437, tc_fun(_1539437, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539437)), _1539439)) = _1539439)], (43505 ^ _777864) ^ [_1625845, _1625847, _1625849, _1625851, _1625853, _1625855, _1625857, _1625859] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625845, tc_fun(_1625847, tc_fun(_1625849, tc_HOL_Obool))), _1625851), _1625853), _1625855), _1625857)), -(hBOOL(hAPP(hAPP(hAPP(_1625853, _1625859), _1625855), _1625857))), hBOOL(hAPP(hAPP(c_member(_1625845), _1625859), _1625851))], (24985 ^ _777864) ^ [_1216502, _1216504, _1216506] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216502), _1216504)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216504), _1216502))), _1216504 = _1216506, 24996 ^ _777864 : [(24999 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216506), _1216502))], (24997 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216502), _1216506)))]]], (6400 ^ _777864) ^ [_883498, _883500, _883502] : [class_Groups_Oordered__comm__monoid__add(_883498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883498), _883500), c_Groups_Ozero__class_Ozero(_883498))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883498), _883502), c_Groups_Ozero__class_Ozero(_883498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883498), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883498), _883500), _883502)), c_Groups_Ozero__class_Ozero(_883498))))], (40336 ^ _777864) ^ [_1545165, _1545167, _1545169, _1545171] : [-(hAPP(c_Relation_OImage(_1545165, _1545167, _1545169), hAPP(hAPP(c_Set_Oinsert(_1545165), _1545171), c_Orderings_Obot__class_Obot(tc_fun(_1545165, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1545167), hAPP(hAPP(c_COMBC(_1545167, tc_fun(tc_prod(_1545165, _1545167), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1545165, _1545167), tc_fun(tc_fun(tc_prod(_1545165, _1545167), tc_HOL_Obool), tc_HOL_Obool), _1545167), c_member(tc_prod(_1545165, _1545167))), hAPP(c_Product__Type_OPair(_1545165, _1545167), _1545171))), _1545169)))], (36424 ^ _777864) ^ [_1456036, _1456038, _1456040] : [class_Orderings_Olinorder(_1456036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456036), _1456038), _1456040)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456036, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1456036), _1456038)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456036, _1456038), _1456040)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1456036), _1456040))], (31159 ^ _777864) ^ [_1347001, _1347003, _1347005, _1347007] : [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), _1347001, _1347003)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347005, _1347007))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347001), _1347003)), 31166 ^ _777864 : [(31169 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347003), _1347007)))], (31167 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347005), _1347001)))]]], (27832 ^ _777864) ^ [_1273661, _1273663, _1273665] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273661, tc_HOL_Obool)), _1273663), _1273665) = _1273665, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273661, tc_HOL_Obool)), _1273663), _1273665)))], (43619 ^ _777864) ^ [_1628231, _1628233, _1628235, _1628237] : [class_Complete__Lattice_Ocomplete__lattice(_1628231), -(_1628233 = c_Orderings_Obot__class_Obot(tc_fun(_1628235, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628235, _1628231), _1628233), hAPP(c_COMBK(_1628231, _1628235), _1628237)) = _1628237)], (47802 ^ _777864) ^ [_1734130, _1734132, _1734134, _1734136] : [-(c_Map_Omap__upds(_1734130, _1734132, _1734134, _1734136, c_List_Olist_ONil(_1734132)) = _1734134)], (23335 ^ _777864) ^ [_1184745, _1184747] : 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hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1184747)))))), 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)), _1184747))), 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)), _1184747))))), 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)), _1184747)))), 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), _1184747))), 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))))))))], (43641 ^ _777864) ^ [_1628661, _1628663, _1628665, _1628667, _1628669] : [_1628661 = c_Orderings_Obot__class_Obot(tc_fun(_1628663, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628665, tc_HOL_Obool)), _1628667), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628663, tc_fun(_1628665, tc_HOL_Obool)), _1628661), _1628669)) = _1628667)], (49870 ^ _777864) ^ [_1782480, _1782482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1782480), _1782482))), -(c_List_Oupt(_1782480, hAPP(c_Nat_OSuc, _1782482)) = c_List_Olist_ONil(tc_Nat_Onat))], (28384 ^ _777864) ^ [_1286912, _1286914, _1286916, _1286918] : [c_Wellfounded_Omax__extp(_1286912, hAPP(hAPP(c_COMBC(_1286912, tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_fun(_1286912, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286912, tc_fun(tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_fun(_1286912, tc_HOL_Obool)), _1286912), c_COMBC(_1286912, tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1286912, tc_prod(_1286912, _1286912)), tc_fun(_1286912, tc_fun(tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_HOL_Obool)), _1286912), hAPP(c_COMBB(tc_prod(_1286912, _1286912), tc_fun(tc_fun(tc_prod(_1286912, _1286912), tc_HOL_Obool), tc_HOL_Obool), _1286912), c_member(tc_prod(_1286912, _1286912)))), c_Product__Type_OPair(_1286912, _1286912)))), _1286914), _1286916, _1286918), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286912, tc_HOL_Obool), tc_fun(_1286912, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286912, tc_HOL_Obool), tc_fun(_1286912, tc_HOL_Obool)), _1286916), _1286918)), c_Wellfounded_Omax__ext(_1286912, _1286914))))], (736 ^ _777864) ^ [_789232, _789234, _789236, _789238, _789240, _789242] : [-(c_Relation_Ototal__on(_789240, _789236, _789232)), c_Relation_Ototal__on(_789242, _789238, _789234), _789242 = _789240, _789238 = _789236, _789234 = _789232], (33731 ^ _777864) ^ [_1400146, _1400148, _1400150, _1400152, _1400154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400146, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400148, tc_fun(_1400146, tc_HOL_Obool)), _1400150), _1400152)), _1400154) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400148, tc_fun(_1400146, tc_HOL_Obool)), _1400150), hAPP(hAPP(c_COMBC(_1400148, tc_fun(_1400146, tc_HOL_Obool), tc_fun(_1400146, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400146, tc_HOL_Obool), tc_fun(tc_fun(_1400146, tc_HOL_Obool), tc_fun(_1400146, tc_HOL_Obool)), _1400148), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400146, tc_HOL_Obool))), _1400152)), _1400154)))], (46551 ^ _777864) ^ [_1703452, _1703454, _1703456] : [-(hAPP(c_List_Olexn(_1703452, _1703454), hAPP(c_Nat_OSuc, _1703456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1703452), tc_List_Olist(_1703452)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1703452, tc_List_Olist(_1703452)), tc_prod(_1703452, tc_List_Olist(_1703452))), tc_prod(tc_List_Olist(_1703452), tc_List_Olist(_1703452)), c_Product__Type_Omap__pair(tc_prod(_1703452, tc_List_Olist(_1703452)), tc_List_Olist(_1703452), tc_prod(_1703452, tc_List_Olist(_1703452)), tc_List_Olist(_1703452), hAPP(c_Product__Type_Oprod_Oprod__case(_1703452, tc_List_Olist(_1703452), tc_List_Olist(_1703452)), c_List_Olist_OCons(_1703452)), hAPP(c_Product__Type_Oprod_Oprod__case(_1703452, tc_List_Olist(_1703452), tc_List_Olist(_1703452)), c_List_Olist_OCons(_1703452)))), c_Wellfounded_Olex__prod(_1703452, tc_List_Olist(_1703452), _1703454, hAPP(c_List_Olexn(_1703452, _1703454), _1703456)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1703452), tc_List_Olist(_1703452))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1703452), tc_List_Olist(_1703452), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703452), tc_fun(tc_List_Olist(_1703452), tc_HOL_Obool), tc_fun(tc_List_Olist(_1703452), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1703452), tc_HOL_Obool), tc_fun(tc_List_Olist(_1703452), tc_HOL_Obool)), tc_List_Olist(_1703452)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1703452))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1703452)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703452), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703452)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703452)))), hAPP(c_Nat_OSuc, _1703456))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703452), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703452)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703452)))), hAPP(c_Nat_OSuc, _1703456)))))))], (21608 ^ _777864) ^ [_1151320, _1151322, _1151324, _1151326] : [class_Fields_Olinordered__field__inverse__zero(_1151320), class_Int_Onumber(_1151320), 21615 ^ _777864 : [(21616 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151322), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151320), _1151324), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)))), 21619 ^ _777864 : [(21626 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), c_Groups_Ozero__class_Ozero(_1151320)), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)))), 21629 ^ _777864 : [(21636 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)), c_Groups_Ozero__class_Ozero(_1151320)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151322), c_Groups_Ozero__class_Ozero(_1151320))))], (21630 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)), c_Groups_Ozero__class_Ozero(_1151320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151320), _1151322), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)))))]]], (21620 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), c_Groups_Ozero__class_Ozero(_1151320)), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151320), _1151322), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))), _1151324)))]]], (21642 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151322), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151320), _1151324), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))))), 21645 ^ _777864 : [(21648 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151320), _1151322), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))), _1151324))], (21646 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), c_Groups_Ozero__class_Ozero(_1151320)), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))))]], 21649 ^ _777864 : [(21652 ^ _777864) ^ [] : [21653 ^ _777864 : [(21656 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151320), _1151322), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326))))], (21654 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)), c_Groups_Ozero__class_Ozero(_1151320))))]], 21657 ^ _777864 : [(21660 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151320), _1151322), c_Groups_Ozero__class_Ozero(_1151320)))], (21658 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)), c_Groups_Ozero__class_Ozero(_1151320)))]]], (21650 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151320), c_Groups_Ozero__class_Ozero(_1151320)), hAPP(c_Int_Onumber__class_Onumber__of(_1151320), _1151326)))]]]]], (13170 ^ _777864) ^ [_999033, _999035] : [_999033 = _999035, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999033), _999035)))], (27716 ^ _777864) ^ [] : [-(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)))], (27069 ^ _777864) ^ [_1255997, _1255999] : [hBOOL(hAPP(hAPP(c_member(_1255997), _1255999), c_Orderings_Obot__class_Obot(tc_fun(_1255997, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1255997, tc_HOL_Obool)), _1255999)))], (40596 ^ _777864) ^ [_1555390, _1555392, _1555394] : [class_Orderings_Olinorder(_1555390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555390), _1555392)), -(_1555392 = c_Orderings_Obot__class_Obot(tc_fun(_1555390, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555390), _1555394)), -(_1555394 = 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tc_fun(_1555390, tc_HOL_Obool)), tc_fun(_1555390, tc_fun(_1555390, tc_HOL_Obool))), _1555390), c_COMBS(_1555390, tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1555390, tc_fun(_1555390, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1555390, tc_fun(tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_HOL_Obool))), _1555390), hAPP(c_COMBB(tc_fun(_1555390, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_HOL_Obool)), _1555390), c_COMBS(_1555390, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1555390, tc_fun(_1555390, tc_HOL_Obool)), tc_fun(_1555390, tc_fun(_1555390, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1555390), hAPP(c_COMBB(tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1555390), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555390), c_fconj))), hAPP(hAPP(c_COMBC(_1555390, tc_fun(_1555390, tc_fun(_1555390, _1555390)), tc_fun(_1555390, tc_fun(_1555390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1555390, _1555390), tc_fun(_1555390, tc_HOL_Obool)), tc_fun(tc_fun(_1555390, tc_fun(_1555390, _1555390)), tc_fun(_1555390, tc_fun(_1555390, tc_HOL_Obool))), _1555390), c_COMBB(tc_fun(_1555390, _1555390), tc_fun(_1555390, tc_HOL_Obool), _1555390)), hAPP(hAPP(c_COMBB(tc_fun(_1555390, tc_HOL_Obool), tc_fun(tc_fun(_1555390, _1555390), tc_fun(_1555390, tc_HOL_Obool)), _1555390), c_COMBB(_1555390, tc_HOL_Obool, _1555390)), c_fequal))), c_Orderings_Oord__class_Omax(_1555390)))))), hAPP(hAPP(c_COMBC(_1555390, tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555390, tc_HOL_Obool), tc_fun(_1555390, tc_HOL_Obool)), _1555390), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555390)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555390), c_fconj), hAPP(hAPP(c_COMBC(_1555390, tc_fun(_1555390, tc_HOL_Obool), tc_HOL_Obool), c_member(_1555390)), _1555392)))), hAPP(hAPP(c_COMBC(_1555390, tc_fun(_1555390, tc_HOL_Obool), tc_HOL_Obool), c_member(_1555390)), _1555394))))))))], (41196 ^ _777864) ^ [_1572663, _1572665, _1572667, _1572669] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572663, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1572665, _1572663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1572665, _1572663), tc_HOL_Obool)), _1572667), _1572669))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1572663, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1572665, _1572663), _1572667)), hAPP(c_Relation_ORange(_1572665, _1572663), _1572669)))))], (3310 ^ _777864) ^ [_828051, _828053] : [_828053 = _828051, -(c_Int_Oring__1__class_Oof__int(_828053) = c_Int_Oring__1__class_Oof__int(_828051))], (4796 ^ _777864) ^ [_851230, _851232, _851234, _851236, _851238, _851240] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_851240, _851236, _851232) = c_SetInterval_Oord__class_OgreaterThanLessThan(_851238, _851234, _851230)), _851240 = _851238, _851236 = _851234, _851232 = _851230], (41013 ^ _777864) ^ [_1568431, _1568433] : [c_Wellfounded_Owf(_1568431, _1568433), 41017 ^ _777864 : [(41018 ^ _777864) ^ [_1568567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568431, _1568431)), hAPP(hAPP(c_Product__Type_OPair(_1568431, _1568431), hAPP(_1568567, hAPP(c_Nat_OSuc, 41016 ^ [_1568431, _1568433, _1568567]))), hAPP(_1568567, 41016 ^ [_1568431, _1568433, _1568567]))), _1568433))]]], (35018 ^ _777864) ^ [_1428718, _1428720] : [class_Groups_Oordered__ab__group__add(_1428718), -(c_Fun_Oinj__on(_1428718, _1428718, c_Groups_Ouminus__class_Ouminus(_1428718), _1428720))], (44409 ^ _777864) ^ [_1650446, _1650448, _1650450, _1650452] : [-(hAPP(_1650446, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1650448, _1650448), _1650450), _1650446), _1650452)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1650448, _1650448), _1650450), _1650446), hAPP(_1650446, _1650452)))], (46986 ^ _777864) ^ [_1714629, _1714631, _1714633] : [class_Orderings_Olinorder(_1714629), -(hBOOL(hAPP(hAPP(c_member(_1714629), _1714631), hAPP(c_List_Oset(_1714629), _1714633)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1714629, _1714629, c_COMBI(_1714629), _1714631, _1714633) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714629, _1714629, c_COMBI(_1714629)), _1714631), _1714633))], (17508 ^ _777864) ^ [_1080170, _1080172] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080170))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080172)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15482 ^ _777864) ^ [_1041292, _1041294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041292), _1041294)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1041294)), _1041292) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041294), _1041292)))], (44700 ^ _777864) ^ [_1657242] : [class_Complete__Lattice_Ocomplete__lattice(_1657242), -(c_Complete__Lattice_OInf__class_OInf(_1657242, c_Orderings_Otop__class_Otop(tc_fun(_1657242, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1657242))], (13236 ^ _777864) ^ [_1000097, _1000099, _1000101, _1000103] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000097), _1000099)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000101), _1000099)), _1000103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1000097), _1000101)), _1000099)), _1000103))], (2072 ^ _777864) ^ [_808132, _808134, _808136, _808138] : [-(c_Random_Olog(_808138, _808134) = c_Random_Olog(_808136, _808132)), _808138 = _808136, _808134 = _808132], (24611 ^ _777864) ^ [_1209649] : [-(_1209649 = 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, _1209649)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1209649))))], (38472 ^ _777864) ^ [_1500011, _1500013, _1500015, _1500017, _1500019] : [c_Fun_Oinj__on(_1500011, _1500013, _1500015, c_Orderings_Otop__class_Otop(tc_fun(_1500011, tc_HOL_Obool))), 38475 ^ _777864 : [(38482 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500011, tc_HOL_Obool)), _1500017), _1500019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500013, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1500011, _1500013, _1500015), _1500017)), hAPP(c_Set_Oimage(_1500011, _1500013, _1500015), _1500019))))], (38476 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500013, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1500011, _1500013, _1500015), _1500017)), hAPP(c_Set_Oimage(_1500011, _1500013, _1500015), _1500019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500011, tc_HOL_Obool)), _1500017), _1500019)))]]], (22735 ^ _777864) ^ [_1171249, _1171251, _1171253, _1171255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171249, tc_HOL_Obool)), _1171251), _1171253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171249, tc_HOL_Obool)), _1171253), _1171255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171249, tc_HOL_Obool)), _1171251), _1171255)))], (29556 ^ _777864) ^ [_1314093, _1314095, _1314097, _1314099, _1314101] : [c_Equiv__Relations_Oequiv(_1314093, _1314095, _1314097), hBOOL(hAPP(hAPP(c_member(tc_fun(_1314093, tc_HOL_Obool)), _1314099), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314093), _1314095), _1314097))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1314093, tc_HOL_Obool)), _1314101), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314093), _1314095), _1314097))), -(_1314099 = _1314101), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314093, tc_HOL_Obool)), _1314099), _1314101) = c_Orderings_Obot__class_Obot(tc_fun(_1314093, tc_HOL_Obool)))], (43710 ^ _777864) ^ [_1630508, _1630510, _1630512, _1630514, _1630516] : [43712 ^ _777864 : [(43715 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630508, tc_HOL_Obool)), _1630510), hAPP(_1630516, 43711 ^ [_1630508, _1630510, _1630512, _1630514, _1630516])))], (43713 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630512), 43711 ^ [_1630508, _1630510, _1630512, _1630514, _1630516]), _1630514)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630508, tc_HOL_Obool)), _1630510), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630512, tc_fun(_1630508, tc_HOL_Obool)), _1630514), _1630516))))], (22238 ^ _777864) ^ [_1162179, _1162181, _1162183, _1162185] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162179, _1162181), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1162183), _1162185))), -(_1162181 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1162179, _1162181) = _1162185)], (34519 ^ _777864) ^ [_1418842, _1418844, _1418846] : [hBOOL(hAPP(c_Predicate_OPowp(_1418842, hAPP(hAPP(c_COMBC(_1418842, tc_fun(_1418842, tc_HOL_Obool), tc_HOL_Obool), c_member(_1418842)), _1418844)), _1418846)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418842, tc_HOL_Obool)), _1418846), hAPP(c_Set_OPow(_1418842), _1418844))))], (6974 ^ _777864) ^ [_892585, _892587] : [hAPP(c_Option_Ooption_OSome(_892585), _892587) = c_Option_Ooption_ONone(_892585)], (17040 ^ _777864) ^ [_1071601] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1071601) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071601)))], (25607 ^ _777864) ^ [_1226983, _1226985, _1226987] : [class_Divides_Oring__div(_1226983), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226983), _1226985), _1226987)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226983), hAPP(c_Groups_Ouminus__class_Ouminus(_1226983), _1226987)), _1226985) = hAPP(c_Groups_Ouminus__class_Ouminus(_1226983), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226983), _1226987), _1226985)))], (5647 ^ _777864) ^ [_868902, _868904, _868906, _868908, _868910, _868912, _868914] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_868902), _868904), _868906), _868908) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_868902), _868910), _868912), _868914), 5650 ^ _777864 : [(5655 ^ _777864) ^ [] : [-(_868908 = _868914)], (5653 ^ _777864) ^ [] : [-(_868906 = _868912)], (5651 ^ _777864) ^ [] : [-(_868904 = _868910)]]], (24715 ^ _777864) ^ [_1211544, _1211546, _1211548, _1211550, _1211552] : [-(_1211544 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1211546, _1211548, _1211550, _1211552), _1211544) = c_Lazy__Sequence_Ohb__bind(_1211546, _1211548, hAPP(_1211550, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1211544), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1211546, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1211548))), _1211552), _1211544)))], (1062 ^ _777864) ^ [_793907, _793909] : [-(class_Rings_Oordered__ring__abs(_793907)), _793909 = _793907, class_Rings_Oordered__ring__abs(_793909)], (22178 ^ _777864) ^ [_1161367, _1161369, _1161371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161367, tc_fun(_1161367, tc_HOL_Obool))), _1161369), _1161371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161367, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1161367, _1161371)), c_Wellfounded_Oaccp(_1161367, _1161369))))], (15664 ^ _777864) ^ [_1045120, _1045122, _1045124, _1045126, _1045128, _1045130] : [class_Rings_Oordered__ring(_1045120), 15667 ^ _777864 : [(15674 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045120), _1045122), _1045128)), _1045124)), _1045126)), _1045130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), _1045122), _1045124)), _1045126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), _1045128), _1045124)), _1045130))))], (15668 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), _1045122), _1045124)), _1045126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), _1045128), _1045124)), _1045130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045120), _1045122), _1045128)), _1045124)), _1045126)), _1045130)))]]], (3840 ^ _777864) ^ [_836296, _836298] : [_836298 = _836296, -(c_Set_OPow(_836298) = c_Set_OPow(_836296))], (24101 ^ _777864) ^ [_1199294, _1199296, _1199298] : [class_Orderings_Olinorder(_1199294), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199294), _1199296), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199294), _1199296), _1199298)) = _1199296)], (19792 ^ _777864) ^ [_1118905, _1118907, _1118909, _1118911] : [class_Rings_Odivision__ring(_1118905), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118905), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118905), _1118907), _1118909)), _1118911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118905), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118905), _1118907), _1118911)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118905), _1118909), _1118911)))], (51331 ^ _777864) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (14133 ^ _777864) ^ [_1016979, _1016981] : [class_Divides_Osemiring__div(_1016979), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1016979), _1016981), c_Groups_Oone__class_Oone(_1016979)) = _1016981)], (50807 ^ _777864) ^ [_1802749, _1802751, _1802753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802749)), c_List_OtakeWhile(_1802749, _1802751, _1802753))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802749)), _1802753))), hBOOL(hAPP(_1802751, hAPP(hAPP(c_List_Onth(_1802749), _1802753), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802749)), c_List_OtakeWhile(_1802749, _1802751, _1802753)))))], (15702 ^ _777864) ^ [_1046107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046107)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046107), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1046107)], (5892 ^ _777864) ^ [_874591, _874593, _874595, _874597] : [-(c_Com_Ovname_Ovname__rec(_874591, _874593, _874595, c_Com_Ovname_OLoc(_874597)) = hAPP(_874595, _874597))], (48868 ^ _777864) ^ [_1760175, _1760177] : [class_Lattices_Oab__semigroup__idem__mult(_1760175), -(_1760177 = c_List_Olist_ONil(_1760175)), -(hAPP(c_Finite__Set_Ofold1(_1760175, c_Groups_Otimes__class_Otimes(_1760175)), hAPP(c_List_Oset(_1760175), _1760177)) = hAPP(c_List_Ofoldl(_1760175, _1760175, c_Groups_Otimes__class_Otimes(_1760175), hAPP(c_List_Ohd(_1760175), _1760177)), hAPP(c_List_Otl(_1760175), _1760177)))], (47354 ^ _777864) ^ [_1724626, _1724628] : [-(_1724626 = c_List_Olist_ONil(_1724628)), -(c_Random_Oselect__weight(_1724628, hAPP(hAPP(c_List_Omap(_1724628, tc_prod(tc_Code__Numeral_Ocode__numeral, _1724628)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1724628), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1724626)) = c_Random_Oselect(_1724628, _1724626))], (46150 ^ _777864) ^ [_1691361, _1691363, _1691365, _1691367, _1691369, _1691371, _1691373, _1691375] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1691361, _1691363), _1691365), _1691367), hAPP(hAPP(c_List_Ozip(_1691361, _1691363), _1691369), hAPP(hAPP(c_List_Omap(_1691371, _1691363), _1691373), _1691375))) = hAPP(hAPP(c_List_Omap(tc_prod(_1691361, _1691371), _1691365), hAPP(c_Product__Type_Oprod_Oprod__case(_1691361, _1691371, _1691365), hAPP(hAPP(c_COMBB(tc_fun(_1691371, tc_prod(_1691361, _1691363)), tc_fun(_1691371, _1691365), _1691361), hAPP(c_COMBB(tc_prod(_1691361, _1691363), _1691365, _1691371), _1691367)), hAPP(hAPP(c_COMBC(_1691361, tc_fun(_1691371, _1691363), tc_fun(_1691371, tc_prod(_1691361, _1691363))), hAPP(hAPP(c_COMBB(tc_fun(_1691363, tc_prod(_1691361, _1691363)), tc_fun(tc_fun(_1691371, _1691363), tc_fun(_1691371, tc_prod(_1691361, _1691363))), _1691361), c_COMBB(_1691363, tc_prod(_1691361, _1691363), _1691371)), c_Product__Type_OPair(_1691361, _1691363))), _1691373)))), hAPP(hAPP(c_List_Ozip(_1691361, _1691371), _1691369), _1691375)))], (11823 ^ _777864) ^ [_975599] : [class_Rings_Olinordered__semidom(_975599), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975599), c_Groups_Ozero__class_Ozero(_975599)), c_Groups_Oone__class_Oone(_975599))))], (35612 ^ _777864) ^ [_1440270, _1440272, _1440274, _1440276] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1440270), _1440272)), 35615 ^ _777864 : [(35616 ^ _777864) ^ [_1440424] : [35618 ^ _777864 : [(35624 ^ _777864) ^ [] : [-(_1440424 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35620 ^ [_1440270, _1440272, _1440274, _1440276, _1440424]), 35617 ^ [_1440270, _1440272, _1440274, _1440276, _1440424]))], (35622 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35620 ^ [_1440270, _1440272, _1440274, _1440276, _1440424]), _1440274)))], (35619 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35617 ^ [_1440270, _1440272, _1440274, _1440276, _1440424]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1440272))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1440270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440424), _1440276))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1440270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1440424), _1440272)), _1440276))))]]], (18134 ^ _777864) ^ [_1089917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089917), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089917)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30240 ^ _777864) ^ [_1328871, _1328873, _1328875] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328871, tc_HOL_Obool)), _1328873), _1328875) = c_Orderings_Obot__class_Obot(tc_fun(_1328871, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328871, tc_HOL_Obool)), _1328873), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328871, tc_HOL_Obool)), _1328875))))], (24145 ^ _777864) ^ [_1200432, _1200434, _1200436, _1200438, _1200440] : [-(hAPP(c_Product__Type_Ofst(_1200432, _1200434), hAPP(c_Product__Type_Oapfst(_1200436, _1200432, _1200434, _1200438), _1200440)) = hAPP(_1200438, hAPP(c_Product__Type_Ofst(_1200436, _1200434), _1200440)))], (49428 ^ _777864) ^ [_1772380, _1772382, _1772384] : [-(c_List_Obutlast(_1772380, hAPP(hAPP(c_List_Oappend(_1772380), _1772382), hAPP(hAPP(c_List_Olist_OCons(_1772380), _1772384), c_List_Olist_ONil(_1772380)))) = _1772382)], (18132 ^ _777864) ^ [_1089880] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1089880), c_Int_OMin) = c_Int_Opred(_1089880))], (25819 ^ _777864) ^ [_1231184, _1231186, _1231188] : [class_Divides_Osemiring__div(_1231184), class_Int_Onumber(_1231184), 25826 ^ _777864 : [(25833 ^ _777864) ^ [] : [c_Divides_Odiv__class_Omod(_1231184, hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231188), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231186)) = c_Groups_Ozero__class_Ozero(_1231184), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231184), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231186)), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231188))))], (25827 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231184), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231186)), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231188))), -(c_Divides_Odiv__class_Omod(_1231184, hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231188), hAPP(c_Int_Onumber__class_Onumber__of(_1231184), _1231186)) = c_Groups_Ozero__class_Ozero(_1231184))]]], (18802 ^ _777864) ^ [_1100842, _1100844] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1100842))), _1100844) = 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)))), _1100842), _1100844))], (20642 ^ _777864) ^ [_1133714, _1133716, _1133718, _1133720] : [class_Fields_Olinordered__field(_1133714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133714), c_Groups_Ozero__class_Ozero(_1133714)), _1133716)), 20649 ^ _777864 : [(20656 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133714), _1133718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133714), _1133720), _1133716))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133714), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133714), _1133718), _1133716)), _1133720)))], (20650 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133714), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133714), _1133718), _1133716)), _1133720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133714), _1133718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133714), _1133720), _1133716))))]]], (39123 ^ _777864) ^ [_1516363, _1516365, _1516367, _1516369, _1516371] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516363, _1516365), _1516367), hAPP(hAPP(c_COMBS(_1516363, tc_fun(_1516365, tc_HOL_Obool), tc_fun(_1516365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516365, tc_HOL_Obool), tc_fun(tc_fun(_1516365, tc_HOL_Obool), tc_fun(_1516365, tc_HOL_Obool)), _1516363), c_Groups_Ominus__class_Ominus(tc_fun(_1516365, tc_HOL_Obool))), _1516369)), _1516371)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1516363, _1516365), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516363, _1516365), _1516367), _1516369)), hAPP(hAPP(c_Product__Type_OSigma(_1516363, _1516365), _1516367), _1516371)))], (15346 ^ _777864) ^ [_1038611, _1038613, _1038615, _1038617, _1038619, _1038621] : [class_Rings_Oring(_1038611), 15349 ^ _777864 : [(15356 ^ _777864) ^ [] : [_1038617 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038611), _1038619), _1038613)), _1038615)), _1038621), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), _1038613), _1038615)), _1038617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), _1038619), _1038615)), _1038621))], (15350 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), _1038613), _1038615)), _1038617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), _1038619), _1038615)), _1038621), -(_1038617 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038611), _1038619), _1038613)), _1038615)), _1038621))]]], (25209 ^ _777864) ^ [_1220068, _1220070] : [25216 ^ _777864 : [(25219 ^ _777864) ^ [] : [_1220068 = _1220070], (25217 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220068), _1220070)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220068), _1220070)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220070), _1220068)))], (19318 ^ _777864) ^ [_1110000] : [-(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)))), _1110000) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110000), _1110000))], (50714 ^ _777864) ^ [_1800931, _1800933] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800931), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1800931))), _1800933))), -(c_List_Otranspose(_1800931, c_List_Otranspose(_1800931, _1800933)) = c_List_OtakeWhile(tc_List_Olist(_1800931), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1800931)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1800931), tc_List_Olist(_1800931), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1800931))), _1800933))], (37104 ^ _777864) ^ [_1472383, _1472385, _1472387, _1472389, _1472391] : [-(c_Map_Orestrict__map(_1472383, _1472385, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472383, tc_Option_Ooption(_1472385)), _1472387), _1472389), hAPP(c_Option_Ooption_OSome(_1472385), _1472391)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472383, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1472383), _1472389), c_Orderings_Obot__class_Obot(tc_fun(_1472383, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1472383, _1472385, _1472387, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472383, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1472383), _1472389), c_Orderings_Obot__class_Obot(tc_fun(_1472383, tc_HOL_Obool))))))], (36484 ^ _777864) ^ [_1457392, _1457394, _1457396, _1457398, _1457400] : [hBOOL(hAPP(hAPP(c_member(_1457392), _1457394), _1457396)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1457392, tc_Option_Ooption(_1457398)), c_Map_Orestrict__map(_1457392, _1457398, _1457400, _1457396)), _1457394), c_Option_Ooption_ONone(_1457398)) = c_Map_Orestrict__map(_1457392, _1457398, _1457400, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1457392, tc_HOL_Obool)), _1457396), hAPP(hAPP(c_Set_Oinsert(_1457392), _1457394), c_Orderings_Obot__class_Obot(tc_fun(_1457392, tc_HOL_Obool))))))], (4928 ^ _777864) ^ [_853220, _853222] : [_853222 = _853220, -(c_Groups_Ominus__class_Ominus(_853222) = c_Groups_Ominus__class_Ominus(_853220))], (48127 ^ _777864) ^ [_1741640, _1741642, _1741644] : [_1741644 = c_List_Olist_ONil(_1741642), -(_1741640 = hAPP(hAPP(c_List_Oappend(_1741642), _1741644), _1741640))], (43999 ^ _777864) ^ [_1639710, _1639712, _1639714, _1639716, _1639718] : [_1639710 = c_Orderings_Obot__class_Obot(tc_fun(_1639712, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639712, tc_fun(_1639714, tc_HOL_Obool)), _1639710), hAPP(hAPP(c_COMBC(_1639712, tc_fun(_1639714, tc_HOL_Obool), tc_fun(_1639714, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639714, tc_HOL_Obool), tc_fun(tc_fun(_1639714, tc_HOL_Obool), tc_fun(_1639714, tc_HOL_Obool)), _1639712), c_Groups_Ominus__class_Ominus(tc_fun(_1639714, tc_HOL_Obool))), _1639716)), _1639718)) = c_Orderings_Otop__class_Otop(tc_fun(_1639714, tc_HOL_Obool)))], (49452 ^ _777864) ^ [_1772887, _1772889] : [-(_1772887 = c_List_Olist_ONil(_1772889)), -(hAPP(hAPP(c_List_Oappend(_1772889), c_List_Obutlast(_1772889, _1772887)), hAPP(hAPP(c_List_Olist_OCons(_1772889), c_List_Olast(_1772889, _1772887)), c_List_Olist_ONil(_1772889))) = _1772887)], (30074 ^ _777864) ^ [_1325026, _1325028] : [class_Lattices_Osemilattice__inf(_1325026), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325026), _1325028), _1325028) = _1325028)], (7250 ^ _777864) ^ [_897101, _897103, _897105, _897107, _897109] : [c_Com_Ocom_OCond(_897101, _897103, _897105) = c_Com_Ocom_OSemi(_897107, _897109)], (17350 ^ _777864) ^ [_1077334, _1077336] : [class_Power_Opower(_1077334), class_Rings_Osemiring__0(_1077334), 17357 ^ _777864 : [(17364 ^ _777864) ^ [] : [-(_1077336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077334), c_Groups_Ozero__class_Ozero(_1077334)), _1077336) = c_Groups_Ozero__class_Ozero(_1077334))], (17358 ^ _777864) ^ [] : [_1077336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077334), c_Groups_Ozero__class_Ozero(_1077334)), _1077336) = c_Groups_Oone__class_Oone(_1077334))]]], (44206 ^ _777864) ^ [_1645568, _1645570] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645568, _1645568), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1645568, _1645570)), c_Relation_OId(_1645568)) = c_Transitive__Closure_Ortrancl(_1645568, _1645570))], (19074 ^ _777864) ^ [_1105790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1105790)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105790), c_Int_OMin)))], (29838 ^ _777864) ^ [_1319567, _1319569] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319567, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1319567, tc_HOL_Obool))), _1319569) = c_Orderings_Obot__class_Obot(tc_fun(_1319567, tc_HOL_Obool)))], (27882 ^ _777864) ^ [_1274704, _1274706, _1274708] : [class_Lattices_Olattice(_1274704), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274704), _1274706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274704), _1274708), _1274706))))], (17792 ^ _777864) ^ [_1084514, _1084516, _1084518] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084514)))), 17795 ^ _777864 : [(17802 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084516)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084516)), _1084518)) = 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), _1084514), _1084516))), _1084518))], (17796 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084516))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084514)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084516)), _1084518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084514)), _1084518))]]], (22446 ^ _777864) ^ [_1165837] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1165837)], (12061 ^ _777864) ^ [_979764, _979766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979764), _979766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _979764)), _979766)))], (23639 ^ _777864) ^ [_1190639, _1190641, _1190643, _1190645] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1190639), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190639), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190639), _1190641), _1190643)), _1190645) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190639), _1190641), _1190645)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190639), _1190643), _1190645)))], (4904 ^ _777864) ^ [_852850, _852852, _852854, _852856, _852858, _852860] : [-(c_Product__Type_Oprod_Oprod__case(_852860, _852856, _852852) = c_Product__Type_Oprod_Oprod__case(_852858, _852854, _852850)), _852860 = _852858, _852856 = _852854, _852852 = _852850], (4242 ^ _777864) ^ [_842733, _842735, _842737, _842739, _842741, _842743] : [-(c_List_Oset__Cons(_842743, _842739, _842735) = c_List_Oset__Cons(_842741, _842737, _842733)), _842743 = _842741, _842739 = _842737, _842735 = _842733], (23563 ^ _777864) ^ [_1189159, _1189161, _1189163, _1189165] : [class_Orderings_Olinorder(_1189159), 23566 ^ _777864 : [(23567 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189159), _1189161), _1189163)), _1189165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), _1189161), _1189165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), _1189163), _1189165)))], (23577 ^ _777864) ^ [] : [23578 ^ _777864 : [(23581 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), _1189163), _1189165))], (23579 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), _1189161), _1189165))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189159), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189159), _1189161), _1189163)), _1189165)))]]], (36300 ^ _777864) ^ [_1453685] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453685))))], (45591 ^ _777864) ^ [_1678252, _1678254, _1678256, _1678258] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1678254, _1678252)), _1678256), _1678258) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1678254), hAPP(hAPP(c_COMBC(_1678254, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1678252, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1678254), c_Smallcheck_Osmall__class_Osmall(_1678252)), hAPP(hAPP(c_COMBB(tc_fun(_1678252, tc_prod(_1678254, _1678252)), tc_fun(_1678252, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1678254), hAPP(c_COMBB(tc_prod(_1678254, _1678252), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1678252), _1678256)), c_Product__Type_OPair(_1678254, _1678252)))), _1678258)), _1678258)), class_Smallcheck_Osmall(_1678252), class_Smallcheck_Osmall(_1678254)], (3358 ^ _777864) ^ [_828761, _828763] : [_828763 = _828761, -(c_Int_Oint__ge__less__than2(_828763) = c_Int_Oint__ge__less__than2(_828761))], (24619 ^ _777864) ^ [_1209745, _1209747] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1209745, _1209747) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1209745), hAPP(c_Code__Numeral_Onat__of, _1209747))))], (46545 ^ _777864) ^ [_1703069, _1703071, _1703073, _1703075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703069), tc_List_Olist(_1703069))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1703069), tc_List_Olist(_1703069)), _1703073), _1703075)), c_List_Olistrel(_1703069, _1703071))), -(c_List_Olistrelp(_1703069, hAPP(hAPP(c_COMBC(_1703069, tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_fun(_1703069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1703069, tc_fun(tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_fun(_1703069, tc_HOL_Obool)), _1703069), c_COMBC(_1703069, tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1703069, tc_prod(_1703069, _1703069)), tc_fun(_1703069, tc_fun(tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_HOL_Obool)), _1703069), hAPP(c_COMBB(tc_prod(_1703069, _1703069), tc_fun(tc_fun(tc_prod(_1703069, _1703069), tc_HOL_Obool), tc_HOL_Obool), _1703069), c_member(tc_prod(_1703069, _1703069)))), c_Product__Type_OPair(_1703069, _1703069)))), _1703071), _1703073, _1703075))], (646 ^ _777864) ^ [_787879, _787881, _787883, _787885, _787887, _787889, _787891, _787893] : [-(c_Finite__Set_Ofolding(_787891, _787887, _787883, _787879)), c_Finite__Set_Ofolding(_787893, _787889, _787885, _787881), _787893 = _787891, _787889 = _787887, _787885 = _787883, _787881 = _787879], (32093 ^ _777864) ^ [_1364225, _1364227, _1364229] : [class_Orderings_Olinorder(_1364225), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364225), _1364227)), -(hBOOL(hAPP(hAPP(c_member(_1364225), _1364229), _1364227))), -(_1364227 = c_Orderings_Obot__class_Obot(tc_fun(_1364225, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1364225, c_Orderings_Oord__class_Omax(_1364225), hAPP(hAPP(c_Set_Oinsert(_1364225), _1364229), _1364227)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364225), _1364229), c_Big__Operators_Olattice_OSup__fin(_1364225, c_Orderings_Oord__class_Omax(_1364225), _1364227)))], (18058 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (39157 ^ _777864) ^ [_1517421, _1517423, _1517425] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1517421, _1517423), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517421, _1517423), c_Orderings_Otop__class_Otop(tc_fun(_1517421, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1517423, tc_HOL_Obool), _1517421), _1517425))) = hAPP(hAPP(c_Product__Type_OSigma(_1517421, _1517423), c_Orderings_Otop__class_Otop(tc_fun(_1517421, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1517423, tc_HOL_Obool), _1517421), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1517423, tc_HOL_Obool)), _1517425))))], (8860 ^ _777864) ^ [_925170] : [class_Groups_Ogroup__add(_925170), -(hAPP(c_Groups_Ouminus__class_Ouminus(_925170), c_Groups_Ozero__class_Ozero(_925170)) = c_Groups_Ozero__class_Ozero(_925170))], (1752 ^ _777864) ^ [_802532, _802534] : [-(class_Int_Onumber(_802532)), _802534 = _802532, class_Int_Onumber(_802534)], (28122 ^ _777864) ^ [_1279035, _1279037, _1279039, _1279041] : [class_Lattices_Olattice(_1279035), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279035), _1279037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279035), _1279039), _1279041)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279035), _1279039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279035), _1279037), _1279041)))], (244 ^ _777864) ^ [_781470, _781472] : [-(class_Fields_Ofield__inverse__zero(_781470)), _781472 = _781470, class_Fields_Ofield__inverse__zero(_781472)], (44694 ^ _777864) ^ [_1657149] : [class_Complete__Lattice_Ocomplete__lattice(_1657149), -(c_Complete__Lattice_OInf__class_OInf(_1657149, c_Orderings_Obot__class_Obot(tc_fun(_1657149, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1657149))], (33140 ^ _777864) ^ [_1386006, _1386008, _1386010, _1386012, _1386014] : [class_Orderings_Olinorder(_1386006), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386006, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1386006, _1386008, _1386010)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1386006, _1386012, _1386014)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1386006, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1386006), _1386008), _1386012), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1386006), _1386010), _1386014)))], (29900 ^ _777864) ^ [_1320944, _1320946, _1320948, _1320950] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320944, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320944, tc_HOL_Obool)), _1320946), _1320948)), _1320950) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320944, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320944, tc_HOL_Obool)), _1320946), _1320950)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320944, tc_HOL_Obool)), _1320948), _1320950)))], (6392 ^ _777864) ^ [_883373, _883375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883373), _883375)), _883375 = _883373], (24579 ^ _777864) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39121 ^ _777864) ^ [_1516314, _1516316, _1516318] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516314, _1516316), c_Orderings_Obot__class_Obot(tc_fun(_1516314, tc_HOL_Obool))), _1516318) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516314, _1516316), tc_HOL_Obool)))], (44949 ^ _777864) ^ [_1663197, _1663199, _1663201] : [class_Complete__Lattice_Ocomplete__lattice(_1663197), -(c_Complete__Lattice_OSup__class_OSup(_1663197, hAPP(hAPP(c_Set_Oinsert(_1663197), _1663199), hAPP(hAPP(c_Set_Oinsert(_1663197), _1663201), c_Orderings_Obot__class_Obot(tc_fun(_1663197, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1663197), _1663199), _1663201))], (16784 ^ _777864) ^ [_1066966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1066966)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1066966 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40140 ^ _777864) ^ [_1539712, _1539714, _1539716] : [hBOOL(hAPP(hAPP(c_member(_1539712), _1539714), hAPP(c_Set_OCollect(_1539712), _1539716))), -(hBOOL(hAPP(_1539716, _1539714)))], (18986 ^ _777864) ^ [_1104188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104188), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104188)), c_Int_OPls)))], (12105 ^ _777864) ^ [_980521] : [-(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), _980521))))], (13395 ^ _777864) ^ [_1002934, _1002936] : [class_Divides_Osemiring__div(_1002934), -(c_Divides_Odiv__class_Omod(_1002934, c_Groups_Ozero__class_Ozero(_1002934), _1002936) = c_Groups_Ozero__class_Ozero(_1002934))], (100 ^ _777864) ^ [_779238, _779240] : [-(class_Rings_Oinverse(_779238)), _779240 = _779238, class_Rings_Oinverse(_779240)], (28753 ^ _777864) ^ [_1297221, _1297223, _1297225, _1297227] : [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), _1297221), _1297223)), 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), _1297225), _1297227)), 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), _1297221), _1297227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297225), _1297223))))], (38788 ^ _777864) ^ [_1508543, _1508545, _1508547, _1508549, _1508551] : [-(hAPP(c_Set_Ovimage(_1508543, _1508545, _1508547), hAPP(hAPP(c_Set_Oinsert(_1508545), _1508549), _1508551)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1508543, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1508543, _1508545, _1508547), hAPP(hAPP(c_Set_Oinsert(_1508545), _1508549), c_Orderings_Obot__class_Obot(tc_fun(_1508545, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1508543, _1508545, _1508547), _1508551)))], (48620 ^ _777864) ^ [_1754876, _1754878, _1754880, _1754882, _1754884] : [hAPP(hAPP(c_List_Oappend(_1754876), _1754878), _1754880) = hAPP(hAPP(c_List_Oappend(_1754876), _1754882), _1754884), 48623 ^ _777864 : [(48632 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754878)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754882)))), 48635 ^ _777864 : [(48638 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1754876), hAPP(hAPP(c_List_Odrop(_1754876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754882)), _1754878)), _1754880) = _1754884)], (48636 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1754876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754882)), _1754878) = _1754882)]]], (48624 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754878)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754882))), 48627 ^ _777864 : [(48630 ^ _777864) ^ [] : [-(_1754880 = hAPP(hAPP(c_List_Oappend(_1754876), hAPP(hAPP(c_List_Odrop(_1754876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754878)), _1754882)), _1754884))], (48628 ^ _777864) ^ [] : [-(_1754878 = hAPP(hAPP(c_List_Otake(_1754876), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754876)), _1754878)), _1754882))]]]]], (13626 ^ _777864) ^ [_1007419, _1007421] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1007419), _1007421) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007419, _1007421) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (37357 ^ _777864) ^ [_1478141, _1478143, _1478145, _1478147, _1478149] : [class_Groups_Ocomm__monoid__add(_1478141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478143), _1478145)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478143), _1478147)), 37371 ^ _777864 : [(37374 ^ _777864) ^ [] : [hAPP(_1478149, 37370 ^ [_1478141, _1478143, _1478145, _1478147, _1478149]) = c_Groups_Ozero__class_Ozero(_1478141)], (37372 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478143), 37370 ^ [_1478141, _1478143, _1478145, _1478147, _1478149]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478143, tc_HOL_Obool)), _1478145), _1478147))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478143, _1478141), _1478149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478143, tc_HOL_Obool)), _1478145), _1478147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478141), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478143, _1478141), _1478149), _1478145)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478143, _1478141), _1478149), _1478147)))], (24395 ^ _777864) ^ [_1205194, _1205196, _1205198, _1205200, _1205202, _1205204] : [c_Nitpick_Opair__box_OPairBox(_1205194, _1205196, _1205198, _1205200) = c_Nitpick_Opair__box_OPairBox(_1205194, _1205196, _1205202, _1205204), 24398 ^ _777864 : [(24401 ^ _777864) ^ [] : [-(_1205200 = _1205204)], (24399 ^ _777864) ^ [] : [-(_1205198 = _1205202)]]], (34457 ^ _777864) ^ [_1417221, _1417223, _1417225, _1417227, _1417229] : [hAPP(c_Set_Oimage(_1417221, _1417223, _1417225), _1417227) = _1417229, -(hAPP(c_Set_Oimage(tc_fun(_1417221, tc_HOL_Obool), tc_fun(_1417223, tc_HOL_Obool), c_Set_Oimage(_1417221, _1417223, _1417225)), hAPP(c_Set_OPow(_1417221), _1417227)) = hAPP(c_Set_OPow(_1417223), _1417229))], (22703 ^ _777864) ^ [_1170682, _1170684] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170682, tc_HOL_Obool)), _1170684), _1170684)))], (50955 ^ _777864) ^ [_1805611, _1805613] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1805611), _1805613) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1805611)), c_List_Oembed__list(_1805613))))], (26047 ^ _777864) ^ [_1235401, _1235403, _1235405] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235401), _1235403)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235401), _1235405)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235401), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235403, _1235405))))], (33704 ^ _777864) ^ [_1399056, _1399058, _1399060, _1399062, _1399064] : [33706 ^ _777864 : [(33709 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1399056, tc_HOL_Obool)), hAPP(_1399062, 33705 ^ [_1399056, _1399058, _1399060, _1399062, _1399064])), _1399064))], (33707 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399058), 33705 ^ [_1399056, _1399058, _1399060, _1399062, _1399064]), _1399060)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1399056, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399058, tc_fun(_1399056, tc_HOL_Obool)), _1399060), _1399062)), _1399064)))], (34769 ^ _777864) ^ [_1423397, _1423399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1423397)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1423397, _1423399)))], (16980 ^ _777864) ^ [_1070701] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070701)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1070701)))], (38595 ^ _777864) ^ [_1504206, _1504208] : [c_Equiv__Relations_Oequivp(_1504206, hAPP(hAPP(c_COMBC(_1504206, tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_fun(_1504206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504206, tc_fun(tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_fun(_1504206, tc_HOL_Obool)), _1504206), c_COMBC(_1504206, tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504206, tc_prod(_1504206, _1504206)), tc_fun(_1504206, tc_fun(tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_HOL_Obool)), _1504206), hAPP(c_COMBB(tc_prod(_1504206, _1504206), tc_fun(tc_fun(tc_prod(_1504206, _1504206), tc_HOL_Obool), tc_HOL_Obool), _1504206), c_member(tc_prod(_1504206, _1504206)))), c_Product__Type_OPair(_1504206, _1504206)))), _1504208)), -(c_Equiv__Relations_Oequiv(_1504206, c_Orderings_Otop__class_Otop(tc_fun(_1504206, tc_HOL_Obool)), _1504208))], (47800 ^ _777864) ^ [_1734093, _1734095, _1734097, _1734099] : [-(c_Map_Omap__upds(_1734093, _1734095, _1734097, c_List_Olist_ONil(_1734093), _1734099) = _1734097)], (9082 ^ _777864) ^ [_928710] : [class_Rings_Ozero__neq__one(_928710), c_Groups_Ozero__class_Ozero(_928710) = c_Groups_Oone__class_Oone(_928710)], (20236 ^ _777864) ^ [_1126709, _1126711, _1126713, _1126715] : [class_Fields_Ofield__inverse__zero(_1126709), -(_1126711 = c_Groups_Ozero__class_Ozero(_1126709)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126709), _1126713), _1126711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126709), _1126715), _1126711)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126709), _1126713), _1126715))], (19774 ^ _777864) ^ [_1118426, _1118428, _1118430, _1118432] : [class_Rings_Odivision__ring(_1118426), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118426), _1118428), _1118430)), _1118432) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118426), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118426), _1118428), _1118432)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118426), _1118430), _1118432)))], (3846 ^ _777864) ^ [_836381, _836383] : [_836383 = _836381, -(c_Relation_OField(_836383) = c_Relation_OField(_836381))], (38762 ^ _777864) ^ [_1507837, _1507839, _1507841, _1507843, _1507845] : [-(hAPP(c_Set_Ovimage(_1507837, _1507839, _1507841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507839, tc_HOL_Obool)), _1507843), _1507845)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507837, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1507837, _1507839, _1507841), _1507843)), hAPP(c_Set_Ovimage(_1507837, _1507839, _1507841), _1507845)))], (48866 ^ _777864) ^ [_1760096, _1760098, _1760100] : [-(hAPP(c_List_Orotate(_1760096, _1760098), _1760100) = hAPP(hAPP(c_List_Oappend(_1760096), hAPP(hAPP(c_List_Odrop(_1760096), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1760098, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760096)), _1760100))), _1760100)), hAPP(hAPP(c_List_Otake(_1760096), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1760098, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760096)), _1760100))), _1760100)))], (45501 ^ _777864) ^ [_1676134, _1676136, _1676138, _1676140, _1676142] : [-(hBOOL(hAPP(hAPP(c_member(_1676134), _1676136), c_Map_Odom(_1676134, _1676138, _1676140)))), -(hAPP(c_Map_Omap__add(_1676134, _1676138, _1676142, _1676140), _1676136) = hAPP(_1676142, _1676136))], (35756 ^ _777864) ^ [_1442929, _1442931] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442929), _1442931)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1442931), _1442929))], (41722 ^ _777864) ^ [_1586116, _1586118, _1586120, _1586122, _1586124, _1586126] : [-(hAPP(c_Set_Oimage(_1586116, _1586118, hAPP(c_Fun_Ocomp(_1586120, _1586118, _1586116, _1586122), _1586124)), _1586126) = hAPP(c_Set_Oimage(_1586120, _1586118, _1586122), hAPP(c_Set_Oimage(_1586116, _1586120, _1586124), _1586126)))], (50957 ^ _777864) ^ [_1805654, _1805656, _1805658] : [hBOOL(hAPP(c_List_Odistinct(_1805654), _1805656)), hBOOL(hAPP(hAPP(c_member(_1805654), _1805658), hAPP(c_List_Oset(_1805654), _1805656))), -(c_List_OtakeWhile(_1805654, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1805654), c_fNot), hAPP(hAPP(c_COMBC(_1805654, _1805654, tc_HOL_Obool), c_fequal), _1805658)), hAPP(c_List_Orev(_1805654), _1805656)) = hAPP(c_List_Orev(_1805654), hAPP(c_List_Otl(_1805654), c_List_OdropWhile(_1805654, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1805654), c_fNot), hAPP(hAPP(c_COMBC(_1805654, _1805654, tc_HOL_Obool), c_fequal), _1805658)), _1805656))))], (18662 ^ _777864) ^ [_1098662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1098662))))], (2484 ^ _777864) ^ [_814584, _814586] : [_814586 = _814584, -(c_Nitpick_Ofrac(_814586) = c_Nitpick_Ofrac(_814584))], (47448 ^ _777864) ^ [_1726402, _1726404, _1726406, _1726408] : [_1726408 = c_List_Olist_ONil(_1726402), -(hAPP(hAPP(c_List_Omap(_1726402, _1726404), _1726406), _1726408) = c_List_Olist_ONil(_1726404))], (6038 ^ _777864) ^ [_877273, _877275, _877277, _877279] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_877273)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877273), _877275), _877277), _877279)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23445 ^ _777864) ^ [_1187131, _1187133, _1187135, _1187137] : [class_Orderings_Olinorder(_1187131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187131), _1187133), _1187135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187131), _1187133), _1187137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187131), _1187133), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187131), _1187135), _1187137))))], (43062 ^ _777864) ^ [_1615585, _1615587, _1615589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615585, _1615585), tc_HOL_Obool)), _1615587), _1615589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615585, _1615585), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1615585, _1615585, _1615585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1615585, _1615585), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615585, _1615587)), _1615589)), _1615587)), _1615589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615585, _1615585), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615585, _1615587)), _1615589)))], (40725 ^ _777864) ^ [_1560088, _1560090] : [40726 ^ _777864 : [(40727 ^ _777864) ^ [_1560152, _1560154] : [_1560090 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1560088, _1560152), 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)), _1560154)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560088), _1560090)))], (2678 ^ _777864) ^ [_817707, _817709] : [_817709 = _817707, -(c_DSequence_Osingle(_817709) = c_DSequence_Osingle(_817707))], (24531 ^ _777864) ^ [_1208372, _1208374, _1208376] : [-(c_Random__Sequence_Oempty(_1208372, _1208374, _1208376) = 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(_1208372)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1208372)))], (46569 ^ _777864) ^ [_1704037, _1704039, _1704041, _1704043, _1704045, _1704047] : [-(hAPP(hAPP(c_List_Ozip(_1704037, _1704039), hAPP(hAPP(c_List_Olist_OCons(_1704037), _1704041), _1704043)), hAPP(hAPP(c_List_Olist_OCons(_1704039), _1704045), _1704047)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1704037, _1704039)), hAPP(hAPP(c_Product__Type_OPair(_1704037, _1704039), _1704041), _1704045)), hAPP(hAPP(c_List_Ozip(_1704037, _1704039), _1704043), _1704047)))], (4096 ^ _777864) ^ [_840452, _840454, _840456, _840458] : [-(c_List_Olexn(_840458, _840454) = c_List_Olexn(_840456, _840452)), _840458 = _840456, _840454 = _840452], (19506 ^ _777864) ^ [_1113193, _1113195, _1113197] : [class_Rings_Olinordered__idom(_1113193), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113193), c_Groups_Ozero__class_Ozero(_1113193)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113193), hAPP(hAPP(c_Power_Opower__class_Opower(_1113193), _1113195), 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(_1113193), _1113197), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (10015 ^ _777864) ^ [_945260, _945262, _945264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945260), _945262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945260), _945264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945262), _945264))))], (33613 ^ _777864) ^ [_1396945, _1396947, _1396949, _1396951, _1396953] : [hBOOL(hAPP(hAPP(c_member(_1396945), _1396947), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396949, tc_fun(_1396945, tc_HOL_Obool)), _1396951), _1396953))), 33617 ^ _777864 : [(33620 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396945), _1396947), hAPP(_1396953, 33616 ^ [_1396945, _1396947, _1396949, _1396951, _1396953]))))], (33618 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396949), 33616 ^ [_1396945, _1396947, _1396949, _1396951, _1396953]), _1396951)))]]], (25617 ^ _777864) ^ [_1227180, _1227182, _1227184] : [class_Divides_Oring__div(_1227180), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227180), _1227182), _1227184)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1227180), _1227184), hAPP(c_Groups_Ouminus__class_Ouminus(_1227180), _1227182)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1227180), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1227180), _1227184), _1227182)))], (28334 ^ _777864) ^ [] : [-(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)))))], (28733 ^ _777864) ^ [] : [-(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))))))], (45275 ^ _777864) ^ [_1671155, _1671157] : [c_Wellfounded_Owf(_1671155, _1671157), 45278 ^ _777864 : [(45279 ^ _777864) ^ [_1671287] : [45280 ^ _777864 : [(45281 ^ _777864) ^ [_1671392] : [hBOOL(hAPP(hAPP(c_member(_1671155), _1671392), _1671287))]], 45283 ^ _777864 : [(45286 ^ _777864) ^ [_1671514] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1671155, _1671155)), hAPP(hAPP(c_Product__Type_OPair(_1671155, _1671155), _1671514), 45282 ^ [_1671155, _1671157, _1671287])), _1671157)), hBOOL(hAPP(hAPP(c_member(_1671155), _1671514), _1671287))], (45284 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671155), 45282 ^ [_1671155, _1671157, _1671287]), _1671287)))]]]]], (42160 ^ _777864) ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290] : [class_Groups_Ocomm__monoid__add(_1596280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596282), _1596284)), 42170 ^ _777864 : [(42171 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1596282), 42169 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290]), _1596284)))], (42176 ^ _777864) ^ [] : [42169 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290] = 42172 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290]], (42180 ^ _777864) ^ [] : [hAPP(_1596288, hAPP(_1596286, 42169 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290])) = c_Groups_Ozero__class_Ozero(_1596280)], (42178 ^ _777864) ^ [] : [-(hAPP(_1596286, 42169 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290]) = hAPP(_1596286, 42172 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290]))], (42174 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1596282), 42172 ^ [_1596280, _1596282, _1596284, _1596286, _1596288, _1596290]), _1596284)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1596290, _1596280), _1596288), hAPP(c_Set_Oimage(_1596282, _1596290, _1596286), _1596284)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1596282, _1596280), hAPP(c_Fun_Ocomp(_1596290, _1596280, _1596282, _1596288), _1596286)), _1596284))], (22683 ^ _777864) ^ [_1170288, _1170290, _1170292, _1170294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170288, tc_HOL_Obool)), _1170290), _1170292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170288, tc_HOL_Obool)), _1170292), _1170294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170288, tc_HOL_Obool)), _1170290), _1170294)))], (20852 ^ _777864) ^ [_1137505, _1137507, _1137509, _1137511] : [class_Fields_Ofield(_1137505), -(_1137507 = c_Groups_Ozero__class_Ozero(_1137505)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137505), _1137509), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137505), _1137511), _1137507)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137505), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137505), _1137507), _1137509)), _1137511)), _1137507))], (40972 ^ _777864) ^ [_1567504, _1567506] : [c_Wellfounded_Owf(_1567504, _1567506), 40975 ^ _777864 : [(40976 ^ _777864) ^ [_1567573] : [-(hBOOL(hAPP(hAPP(c_member(_1567504), _1567573), c_Wellfounded_Oacc(_1567504, _1567506))))]]], (4146 ^ _777864) ^ [_841221, _841223] : [_841223 = _841221, -(c_HOL_OEx(_841223) = c_HOL_OEx(_841221))], (18812 ^ _777864) ^ [_1101098, _1101100] : [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), _1101098))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1101100)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1101098))) = 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), _1101100), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1101098)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10774 ^ _777864) ^ [_957153, _957155, _957157] : [class_Orderings_Olinorder(_957153), 10777 ^ _777864 : [(10784 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957153), _957157), _957155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957153), _957155), _957157))], (10778 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957153), _957155), _957157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957153), _957157), _957155)))]]], (28146 ^ _777864) ^ [_1279607, _1279609, _1279611, _1279613] : [class_Lattices_Osemilattice__sup(_1279607), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279607), _1279609), _1279611)), _1279613) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279607), _1279609), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279607), _1279611), _1279613)))], (12814 ^ _777864) ^ [_992990, _992992] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992990)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992992))))), _992990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _992992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22098 ^ _777864) ^ [_1159875, _1159877] : [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), _1159875), _1159877))), 22101 ^ _777864 : [(22110 ^ _777864) ^ [] : [-(c_Divides_OposDivAlg(_1159875, _1159877) = hAPP(c_Divides_Oadjust(_1159877), c_Divides_OposDivAlg(_1159875, 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)))), _1159877)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159875), _1159877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159877), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22102 ^ _777864) ^ [] : [22103 ^ _777864 : [(22106 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159877), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22104 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159875), _1159877))]], -(c_Divides_OposDivAlg(_1159875, _1159877) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1159875))]]], (45251 ^ _777864) ^ [_1670634, _1670636, _1670638, _1670640] : [class_Lattices_Osemilattice__sup(_1670634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670634), _1670636)), 45261 ^ _777864 : [(45264 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670634), 45260 ^ [_1670634, _1670636, _1670638, _1670640]), _1670638))], (45262 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670634), 45260 ^ [_1670634, _1670636, _1670638, _1670640]), _1670636)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670634), hAPP(hAPP(c_Finite__Set_Ofold(_1670634, _1670634, c_Lattices_Osemilattice__sup__class_Osup(_1670634)), _1670640), _1670636)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1670634), _1670638), _1670640))))], (7562 ^ _777864) ^ [_903276, _903278] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_903276, _903278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_903278)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (562 ^ _777864) ^ [_786543, _786545, _786547, _786549, _786551, _786553] : [-(c_Hoare__Mirabelle_Ohoare__valids(_786551, _786547, _786543)), c_Hoare__Mirabelle_Ohoare__valids(_786553, _786549, _786545), _786553 = _786551, _786549 = _786547, _786545 = _786543], (28026 ^ _777864) ^ [_1277226, _1277228, _1277230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277226, tc_HOL_Obool)), _1277228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277226, tc_HOL_Obool)), _1277230), _1277228)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277226, tc_HOL_Obool)), _1277228), _1277230))], (16412 ^ _777864) ^ [_1059539, _1059541, _1059543] : [class_Groups_Oordered__ab__group__add__abs(_1059539), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059539), hAPP(c_Groups_Oabs__class_Oabs(_1059539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059539), hAPP(c_Groups_Oabs__class_Oabs(_1059539), _1059541)), hAPP(c_Groups_Oabs__class_Oabs(_1059539), _1059543)))), hAPP(c_Groups_Oabs__class_Oabs(_1059539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059539), _1059541), _1059543)))))], (45523 ^ _777864) ^ [_1676603, _1676605, _1676607, _1676609] : [c_Fun_Oinj__on(_1676603, tc_Option_Ooption(_1676605), _1676609, c_Map_Odom(_1676603, _1676605, _1676609)), -(c_Fun_Oinj__on(_1676603, tc_Option_Ooption(_1676605), c_Map_Omap__add(_1676603, _1676605, _1676607, _1676609), c_Map_Odom(_1676603, _1676605, _1676609)))], (38184 ^ _777864) ^ [_1494468] : [class_Finite__Set_Ofinite(_1494468), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494468), c_Orderings_Otop__class_Otop(tc_fun(_1494468, tc_HOL_Obool)))))], (50841 ^ _777864) ^ [_1803576] : [c_List_Onat__list(_1803576), -(c_List_Oembed__list(c_List_Oreturn__list(_1803576)) = _1803576)], (39193 ^ _777864) ^ [_1518627, _1518629, _1518631] : [c_Equiv__Relations_Oequiv(_1518627, _1518629, _1518631), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518627, _1518627), tc_HOL_Obool)), _1518631), hAPP(hAPP(c_Product__Type_OSigma(_1518627, _1518627), _1518629), hAPP(c_COMBK(tc_fun(_1518627, tc_HOL_Obool), _1518627), _1518629)))))], (17852 ^ _777864) ^ [_1085513, _1085515] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085513)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085513)), _1085515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1085513))), _1085515))], (42024 ^ _777864) ^ [_1593289, _1593291, _1593293, _1593295, _1593297, _1593299, _1593301, _1593303, _1593305, _1593307, _1593309] : [c_Finite__Set_Ofolding(_1593289, _1593291, _1593293, _1593295), -(hAPP(c_Fun_Ocomp(_1593297, _1593299, _1593301, _1593303), hAPP(c_Fun_Ocomp(_1593305, _1593297, _1593301, _1593307), _1593309)) = hAPP(c_Fun_Ocomp(_1593305, _1593299, _1593301, hAPP(c_Fun_Ocomp(_1593297, _1593299, _1593305, _1593303), _1593307)), _1593309))], (47101 ^ _777864) ^ [_1717737, _1717739] : [hBOOL(hAPP(c_List_Odistinct(_1717737), _1717739)), 47104 ^ _777864 : [(47105 ^ _777864) ^ [_1717869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717869), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717737)), _1717739))), 47108 ^ _777864 : [(47109 ^ _777864) ^ [_1717996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717996), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717737)), _1717739))), -(_1717869 = _1717996), hAPP(hAPP(c_List_Onth(_1717737), _1717739), _1717869) = hAPP(hAPP(c_List_Onth(_1717737), _1717739), _1717996)]]]]], (3686 ^ _777864) ^ [_834003, _834005, _834007, _834009] : [-(c_Lazy__Sequence_Ohb__single(_834009, _834005) = c_Lazy__Sequence_Ohb__single(_834007, _834003)), _834009 = _834007, _834005 = _834003], (48229 ^ _777864) ^ [_1743957, _1743959, _1743961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743957), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743959)), _1743961))), -(hAPP(hAPP(c_List_Otake(_1743959), hAPP(c_Nat_OSuc, _1743957)), _1743961) = hAPP(hAPP(c_List_Oappend(_1743959), hAPP(hAPP(c_List_Otake(_1743959), _1743957), _1743961)), hAPP(hAPP(c_List_Olist_OCons(_1743959), hAPP(hAPP(c_List_Onth(_1743959), _1743961), _1743957)), c_List_Olist_ONil(_1743959))))], (3052 ^ _777864) ^ [_823852, _823854, _823856, _823858] : [-(c_FunDef_Orp__inv__image(_823858, _823854) = c_FunDef_Orp__inv__image(_823856, _823852)), _823858 = _823856, _823854 = _823852], (47119 ^ _777864) ^ [_1718197, _1718199] : [47121 ^ _777864 : [(47125 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47123 ^ [_1718197, _1718199]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718197)), _1718199))))], (47127 ^ _777864) ^ [] : [47120 ^ [_1718197, _1718199] = 47123 ^ [_1718197, _1718199]], (47129 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1718197), _1718199), 47120 ^ [_1718197, _1718199]) = hAPP(hAPP(c_List_Onth(_1718197), _1718199), 47123 ^ [_1718197, _1718199]))], (47122 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47120 ^ [_1718197, _1718199]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718197)), _1718199))))]], -(hBOOL(hAPP(c_List_Odistinct(_1718197), _1718199)))], (5898 ^ _777864) ^ [_874713, _874715, _874717] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_874713, _874715)), _874717), hAPP(hAPP(hAPP(c_Natural_Oupdate, _874717), _874713), hAPP(_874715, _874717)))))], (45030 ^ _777864) ^ [_1664695, _1664697, _1664699] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1664695, tc_HOL_Obool)), _1664697), _1664699))), 45036 ^ _777864 : [(45040 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1664695, tc_HOL_Obool)), 45038 ^ [_1664695, _1664697, _1664699]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1664695, tc_HOL_Obool)), _1664697), _1664699))))], (45042 ^ _777864) ^ [] : [45035 ^ [_1664695, _1664697, _1664699] = 45038 ^ [_1664695, _1664697, _1664699]], (45044 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1664695, tc_HOL_Obool)), 45035 ^ [_1664695, _1664697, _1664699]), 45038 ^ [_1664695, _1664697, _1664699]) = c_Orderings_Obot__class_Obot(tc_fun(_1664695, tc_HOL_Obool))], (45037 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1664695, tc_HOL_Obool)), 45035 ^ [_1664695, _1664697, _1664699]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1664695, tc_HOL_Obool)), _1664697), _1664699))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1664695, tc_HOL_Obool)), _1664697), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1664695, tc_HOL_Obool), _1664699)) = c_Orderings_Obot__class_Obot(tc_fun(_1664695, tc_HOL_Obool)))], (43144 ^ _777864) ^ [_1617388, _1617390, _1617392, _1617394, _1617396, _1617398] : [c_Finite__Set_Ofun__left__comm(_1617388, _1617390, _1617392), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1617388, _1617390, _1617392, _1617394, _1617396), _1617398)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617388, _1617390, _1617392), _1617394), _1617396) = _1617398)], (50398 ^ _777864) ^ [_1792828, _1792830] : [hAPP(c_List_Orev(_1792828), _1792830) = c_List_Olist_ONil(_1792828), -(_1792830 = c_List_Olist_ONil(_1792828))], (43757 ^ _777864) ^ [_1632266, _1632268, _1632270, _1632272, _1632274] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632266, tc_fun(_1632268, tc_HOL_Obool)), _1632270), hAPP(hAPP(c_COMBS(_1632266, tc_fun(_1632268, tc_HOL_Obool), tc_fun(_1632268, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1632268, tc_HOL_Obool), tc_fun(tc_fun(_1632268, tc_HOL_Obool), tc_fun(_1632268, tc_HOL_Obool)), _1632266), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632268, tc_HOL_Obool))), _1632272)), _1632274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1632268, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632266, tc_fun(_1632268, tc_HOL_Obool)), _1632270), _1632272)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632266, tc_fun(_1632268, tc_HOL_Obool)), _1632270), _1632274)))], (18694 ^ _777864) ^ [] : [-(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))))))], (38960 ^ _777864) ^ [_1512309, _1512311, _1512313, _1512315] : [c_Wellfounded_Omax__extp(_1512309, _1512311, _1512313, _1512315), 38963 ^ _777864 : [(38966 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512309), _1512315)))], (38968 ^ _777864) ^ [] : [_1512315 = c_Orderings_Obot__class_Obot(tc_fun(_1512309, tc_HOL_Obool))], (38970 ^ _777864) ^ [_1512525] : [hBOOL(hAPP(hAPP(c_member(_1512309), _1512525), _1512313)), 38974 ^ _777864 : [(38977 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1512311, _1512525), 38973 ^ [_1512309, _1512311, _1512313, _1512315, _1512525])))], (38975 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512309), 38973 ^ [_1512309, _1512311, _1512313, _1512315, _1512525]), _1512315)))]]], (38964 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512309), _1512313)))]]], (7478 ^ _777864) ^ [_901307, _901309, _901311, _901313, _901315] : [c_Com_Ocom_OCond(_901307, _901309, _901311) = c_Com_Ocom_OAss(_901313, _901315)], (4152 ^ _777864) ^ [_841306, _841308, _841310, _841312, _841314, _841316, _841318, _841320] : [-(c_Product__Type_Oscomp(_841320, _841316, _841312, _841308) = c_Product__Type_Oscomp(_841318, _841314, _841310, _841306)), _841320 = _841318, _841316 = _841314, _841312 = _841310, _841308 = _841306], (44893 ^ _777864) ^ [_1661939, _1661941, _1661943] : [c_Equiv__Relations_Oequiv(_1661939, _1661941, _1661943), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661939, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1661939), _1661941), _1661943)) = _1661941)], (6398 ^ _777864) ^ [_883470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883470), _883470))], (12360 ^ _777864) ^ [_984863, _984865, _984867, _984869] : [class_Rings_Olinordered__ring__strict(_984863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984863), c_Groups_Ozero__class_Ozero(_984863)), _984865)), 12367 ^ _777864 : [(12374 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984863), _984867), _984869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984863), _984865), _984867)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984863), _984865), _984869))))], (12368 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984863), _984865), _984867)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984863), _984865), _984869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984863), _984867), _984869)))]]], (10272 ^ _777864) ^ [_949225, _949227, _949229, _949231] : [class_Orderings_Opreorder(_949225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949225), _949227), _949229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949225), _949229), _949231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949225), _949227), _949231)))], (27578 ^ _777864) ^ [_1268959, _1268961] : [class_Rings_Oring__1(_1268959), -(hBOOL(hAPP(hAPP(c_member(_1268959), hAPP(c_Int_Oring__1__class_Oof__int(_1268959), _1268961)), c_Int_Oring__1__class_OInts(_1268959))))], (26569 ^ _777864) ^ [_1245910, _1245912] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1245910)), _1245912)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1245910), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1245912)))))], (11829 ^ _777864) ^ [_975694] : [class_Rings_Olinordered__semidom(_975694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975694), c_Groups_Oone__class_Oone(_975694)), c_Groups_Ozero__class_Ozero(_975694)))], (37096 ^ _777864) ^ [_1472235, _1472237, _1472239, _1472241, _1472243, _1472245] : [-(hBOOL(hAPP(hAPP(c_member(_1472235), _1472237), _1472239))), -(c_Map_Orestrict__map(_1472235, _1472241, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472235, tc_Option_Ooption(_1472241)), _1472243), _1472237), _1472245), _1472239) = c_Map_Orestrict__map(_1472235, _1472241, _1472243, _1472239))], (50919 ^ _777864) ^ [_1804893, _1804895] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1804893)), c_List_Oremdups(_1804893, _1804895)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1804893)), _1804895), -(c_List_Oremdups(_1804893, _1804895) = _1804895)], (2986 ^ _777864) ^ [_822857, _822859, _822861, _822863] : [-(c_Com_Ocom_OAss(_822863, _822859) = c_Com_Ocom_OAss(_822861, _822857)), _822863 = _822861, _822859 = _822857], (21340 ^ _777864) ^ [_1146112, _1146114, _1146116, _1146118] : [class_Fields_Olinordered__field__inverse__zero(_1146112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146112), _1146114), _1146116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146112), _1146118), c_Groups_Ozero__class_Ozero(_1146112))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146112), c_Groups_Ozero__class_Ozero(_1146112)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146112), _1146114), _1146116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146112), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146112), _1146118), _1146114)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146112), _1146118), _1146116))))], (14119 ^ _777864) ^ [_1016738, _1016740] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016738)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016740)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016738), _1016740))], (34737 ^ _777864) ^ [_1422800, _1422802, _1422804, _1422806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422800), _1422802)), hAPP(c_Finite__Set_Ocard(_1422804), hAPP(c_Set_Oimage(_1422800, _1422804, _1422806), _1422802)) = hAPP(c_Finite__Set_Ocard(_1422800), _1422802), -(c_Fun_Oinj__on(_1422800, _1422804, _1422806, _1422802))], (23863 ^ _777864) ^ [_1194923, _1194925] : [class_Orderings_Olinorder(_1194923), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194923), _1194925), _1194925) = _1194925)], (23069 ^ _777864) ^ [_1178143] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1178143) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1178143)))], (16820 ^ _777864) ^ [_1067601, _1067603] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067601), _1067603))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1067601))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1067603))))], (23145 ^ _777864) ^ [_1179726, _1179728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179726)), hAPP(c_Nat_OSuc, _1179728))), -(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(_1179726))), 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)), _1179728)))))], (13567 ^ _777864) ^ [_1006428, _1006430, _1006432, _1006434] : [class_Divides_Osemiring__div(_1006428), -(c_Divides_Odiv__class_Omod(_1006428, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006428), _1006430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006428), _1006432), _1006434)), _1006434) = c_Divides_Odiv__class_Omod(_1006428, _1006430, _1006434))], (48840 ^ _777864) ^ [_1759600] : [-(c_List_Orotate(_1759600, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1759600)))], (8238 ^ _777864) ^ [_914462, _914464, _914466, _914468] : [class_Orderings_Oorder(_914462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914462), _914464), _914466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914462), _914468), _914464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914462), _914468), _914466)))], (6623 ^ _777864) ^ [_887191, _887193] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887191), _887193) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _887193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18888 ^ _777864) ^ [_1102563, _1102565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102563)), c_Int_OBit0(_1102565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102563), _1102565)))], (26431 ^ _777864) ^ [_1243480, _1243482] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243480)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243482))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243480), _1243482)))], (19116 ^ _777864) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (22705 ^ _777864) ^ [_1170735, _1170737, _1170739] : [_1170735 = _1170737, 22708 ^ _777864 : [(22711 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170739, tc_HOL_Obool)), _1170737), _1170735)))], (22709 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170739, tc_HOL_Obool)), _1170735), _1170737)))]]], (51467 ^ _777864) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (25451 ^ _777864) ^ [_1224169, _1224171] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224169), _1224171)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224171), _1224169))))], (33685 ^ _777864) ^ [_1398544, _1398546, _1398548, _1398550] : [33687 ^ _777864 : [(33690 ^ _777864) ^ [] : [hAPP(_1398550, 33686 ^ [_1398544, _1398546, _1398548, _1398550]) = c_Orderings_Obot__class_Obot(tc_fun(_1398546, tc_HOL_Obool))], (33688 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398544), 33686 ^ [_1398544, _1398546, _1398548, _1398550]), _1398548)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398544, tc_fun(_1398546, tc_HOL_Obool)), _1398548), _1398550) = c_Orderings_Obot__class_Obot(tc_fun(_1398546, tc_HOL_Obool)))], (6032 ^ _777864) ^ [_877151, _877153, _877155] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_877151, _877153)), _877155), hAPP(hAPP(hAPP(c_Natural_Oupdate, _877155), _877151), hAPP(_877153, _877155)))))], (41742 ^ _777864) ^ [_1586711, _1586713, _1586715, _1586717, _1586719, _1586721, _1586723, _1586725, _1586727, _1586729, _1586731] : [hAPP(_1586711, hAPP(_1586713, _1586715)) = hAPP(_1586717, hAPP(_1586719, _1586721)), -(hAPP(hAPP(c_Fun_Ocomp(_1586723, _1586725, _1586727, _1586711), _1586713), _1586715) = hAPP(hAPP(c_Fun_Ocomp(_1586729, _1586725, _1586731, _1586717), _1586719), _1586721))], (48055 ^ _777864) ^ [_1740281, _1740283, _1740285, _1740287, _1740289, _1740291] : [hAPP(hAPP(c_List_Oappend(_1740281), _1740283), _1740285) = _1740287, _1740289 = hAPP(hAPP(c_List_Oappend(_1740281), _1740285), _1740291), -(hAPP(hAPP(c_List_Oappend(_1740281), _1740283), _1740289) = hAPP(hAPP(c_List_Oappend(_1740281), _1740287), _1740291))], (26293 ^ _777864) ^ [_1240432, _1240434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240432, tc_HOL_Obool)), _1240434), c_Orderings_Obot__class_Obot(tc_fun(_1240432, tc_HOL_Obool)))), -(_1240434 = c_Orderings_Obot__class_Obot(tc_fun(_1240432, tc_HOL_Obool)))], (45601 ^ _777864) ^ [_1678537, _1678539, _1678541, _1678543] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1678537), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1678539), _1678541)))), -(hBOOL(hAPP(hAPP(hAPP(_1678543, _1678537), _1678539), _1678541))), 45609 ^ _777864 : [(45612 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 45607 ^ [_1678537, _1678539, _1678541, _1678543]), 45608 ^ [_1678537, _1678539, _1678541, _1678543]))), hAPP(45606 ^ [_1678537, _1678539, _1678541, _1678543], 45608 ^ [_1678537, _1678539, _1678541, _1678543]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1678543, 45606 ^ [_1678537, _1678539, _1678541, _1678543]), 45607 ^ [_1678537, _1678539, _1678541, _1678543]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45608 ^ [_1678537, _1678539, _1678541, _1678543]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45622 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1678543, 45606 ^ [_1678537, _1678539, _1678541, _1678543]), 45607 ^ [_1678537, _1678539, _1678541, _1678543]), 45608 ^ [_1678537, _1678539, _1678541, _1678543]))], (45610 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 45606 ^ [_1678537, _1678539, _1678541, _1678543]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 45607 ^ [_1678537, _1678539, _1678541, _1678543]), 45608 ^ [_1678537, _1678539, _1678541, _1678543])))))]]], (11088 ^ _777864) ^ [] : [-(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))))], (10130 ^ _777864) ^ [_947061, _947063, _947065] : [class_Orderings_Olinorder(_947061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947061), _947063), _947065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947061), _947065), _947063)))], (32279 ^ _777864) ^ [_1368084, _1368086, _1368088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368084), _1368086)), 32282 ^ _777864 : [(32289 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1368084), _1368088), _1368086))), -(hAPP(c_Finite__Set_Ocard(_1368084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368084, tc_HOL_Obool)), _1368086), hAPP(hAPP(c_Set_Oinsert(_1368084), _1368088), c_Orderings_Obot__class_Obot(tc_fun(_1368084, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1368084), _1368086))], (32283 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1368084), _1368088), _1368086)), -(hAPP(c_Finite__Set_Ocard(_1368084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368084, tc_HOL_Obool)), _1368086), hAPP(hAPP(c_Set_Oinsert(_1368084), _1368088), c_Orderings_Obot__class_Obot(tc_fun(_1368084, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1368084), _1368086)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (410 ^ _777864) ^ [_784095, _784097, _784099, _784101, _784103, _784105, _784107, _784109, _784111, _784113, _784115, _784117] : [-(c_Finite__Set_Ofolding__image__simple(_784115, _784111, _784107, _784103, _784099, _784095)), c_Finite__Set_Ofolding__image__simple(_784117, _784113, _784109, _784105, _784101, _784097), _784117 = _784115, _784113 = _784111, _784109 = _784107, _784105 = _784103, _784101 = _784099, _784097 = _784095], (19028 ^ _777864) ^ [_1104955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1104955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104955)))], (46238 ^ _777864) ^ [_1694090, _1694092, _1694094, _1694096, _1694098] : [class_Orderings_Olinorder(_1694090), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694092)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694092, _1694090, _1694094), _1694096), _1694098)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694092)), _1694098)))], (18494 ^ _777864) ^ [_1095920] : [c_Int_OMin = _1095920, -(c_Int_OMin = c_Int_OBit1(_1095920))], (39738 ^ _777864) ^ [_1530486, _1530488, _1530490, _1530492] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530486), _1530488)), 39744 ^ _777864 : [(39747 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530490), hAPP(_1530492, 39743 ^ [_1530486, _1530488, _1530490, _1530492])))], (39745 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530486), 39743 ^ [_1530486, _1530488, _1530490, _1530492]), _1530488)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1530486, _1530490)), hAPP(hAPP(c_Product__Type_OSigma(_1530486, _1530490), _1530488), _1530492)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530486, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1530490, tc_HOL_Obool), tc_Nat_Onat, _1530486), c_Finite__Set_Ocard(_1530490)), _1530492)), _1530488))], (19138 ^ _777864) ^ [_1106802] : [-(c_Int_Osucc(c_Int_OBit1(_1106802)) = c_Int_OBit0(c_Int_Osucc(_1106802)))], (5466 ^ _777864) ^ [_861479, _861481] : [_861481 = _861479, -(c_member(_861481) = c_member(_861479))], (9166 ^ _777864) ^ [_930498, _930500] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _930498), _930500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _930498)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _930500)))], (34427 ^ _777864) ^ [_1416527, _1416529, _1416531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416527), _1416529)), hBOOL(hAPP(_1416531, _1416529)), 34438 ^ _777864 : [(34441 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416527), 34436 ^ [_1416527, _1416529, _1416531]), 34437 ^ [_1416527, _1416529, _1416531])))], (34443 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1416531, 34437 ^ [_1416527, _1416529, _1416531])))], (34445 ^ _777864) ^ [] : [hBOOL(hAPP(_1416531, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1416527, tc_HOL_Obool)), 34437 ^ [_1416527, _1416529, _1416531]), hAPP(hAPP(c_Set_Oinsert(_1416527), 34436 ^ [_1416527, _1416529, _1416531]), c_Orderings_Obot__class_Obot(tc_fun(_1416527, tc_HOL_Obool))))))], (34439 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1416527), 34437 ^ [_1416527, _1416529, _1416531])))]], -(hBOOL(hAPP(_1416531, c_Orderings_Obot__class_Obot(tc_fun(_1416527, tc_HOL_Obool)))))], (40100 ^ _777864) ^ [_1538702, _1538704, _1538706] : [hBOOL(hAPP(_1538702, _1538704)), -(hBOOL(hAPP(hAPP(c_member(_1538706), _1538704), hAPP(c_Set_OCollect(_1538706), _1538702))))], (40652 ^ _777864) ^ [_1558344, _1558346, _1558348, _1558350, _1558352, _1558354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558344), _1558346)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558348), _1558350)), 40662 ^ _777864 : [(40665 ^ _777864) ^ [] : [hAPP(c_Finite__Set_Ocard(_1558344), hAPP(c_Set_OCollect(_1558344), hAPP(hAPP(c_COMBS(_1558344, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558344), c_fconj), hAPP(hAPP(c_COMBC(_1558344, tc_fun(_1558344, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558344)), _1558346))), hAPP(hAPP(c_COMBC(_1558344, _1558348, tc_HOL_Obool), _1558352), 40661 ^ [_1558344, _1558346, _1558348, _1558350, _1558352, _1558354])))) = hAPP(_1558354, 40661 ^ [_1558344, _1558346, _1558348, _1558350, _1558352, _1558354])], (40663 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558348), 40661 ^ [_1558344, _1558346, _1558348, _1558350, _1558352, _1558354]), _1558350)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558344, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1558348, tc_HOL_Obool), tc_Nat_Onat, _1558344), c_Finite__Set_Ocard(_1558348)), hAPP(hAPP(c_COMBB(tc_fun(_1558348, tc_HOL_Obool), tc_fun(_1558348, tc_HOL_Obool), _1558344), c_Set_OCollect(_1558348)), hAPP(hAPP(c_COMBB(tc_fun(_1558348, tc_HOL_Obool), tc_fun(_1558348, tc_HOL_Obool), _1558344), hAPP(c_COMBS(_1558348, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558348), c_fconj), hAPP(hAPP(c_COMBC(_1558348, tc_fun(_1558348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558348)), _1558350)))), _1558352)))), _1558346) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558348, tc_Nat_Onat), _1558354), _1558350))], (28735 ^ _777864) ^ [_1296590] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296590) = 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), _1296590), 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))))))], (41169 ^ _777864) ^ [_1571979, _1571981] : [-(hAPP(c_Relation_ORange(_1571979, _1571981), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1571979, _1571981), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1571981, tc_HOL_Obool)))], (24617 ^ _777864) ^ [_1209700, _1209702, _1209704, _1209706] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1209700, _1209702, _1209704, _1209706) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1209700, _1209702), _1209704), _1209706)))], (32003 ^ _777864) ^ [_1362772, _1362774, _1362776] : [class_Orderings_Olinorder(_1362772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362772), _1362774)), hBOOL(hAPP(hAPP(c_member(_1362772), _1362776), _1362774)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362772), _1362776), c_Big__Operators_Olattice_OInf__fin(_1362772, c_Orderings_Oord__class_Omin(_1362772), _1362774)) = _1362776)], (17490 ^ _777864) ^ [_1079917] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1079917))), -(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), _1079917)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51593 ^ _777864) ^ [_1813110, _1813112] : [hBOOL(hAPP(hAPP(c_fdisj, _1813110), _1813112)), -(hBOOL(_1813110)), -(hBOOL(_1813112))], (11795 ^ _777864) ^ [_975057, _975059, _975061, _975063, _975065] : [class_Groups_Oordered__cancel__ab__semigroup__add(_975057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975057), _975059), _975061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975057), _975063), _975065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975057), _975059), _975063)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975057), _975061), _975065))))], (9931 ^ _777864) ^ [_943747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943747)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _943747)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _943747)))], (26945 ^ _777864) ^ [_1253637, _1253639, _1253641, _1253643] : [hBOOL(hAPP(hAPP(c_member(_1253637), _1253639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253637, tc_HOL_Obool)), _1253641), _1253643))), 26948 ^ _777864 : [(26951 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1253637), _1253639), _1253643))], (26949 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1253637), _1253639), _1253641)))]]], (8212 ^ _777864) ^ [_914130, _914132] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914130), _914132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914132), _914130))], (12304 ^ _777864) ^ [_983847, _983849, _983851, _983853] : [class_Groups_Oordered__comm__monoid__add(_983847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983847), c_Groups_Ozero__class_Ozero(_983847)), _983849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983847), _983851), _983853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983847), _983851), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983847), _983849), _983853))))], (38152 ^ _777864) ^ [_1493834, _1493836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1493834, _1493836)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1493834, _1493836), tc_HOL_Obool)))), 38155 ^ _777864 : [(38158 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493836), c_Orderings_Otop__class_Otop(tc_fun(_1493836, tc_HOL_Obool)))))], (38156 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493834), c_Orderings_Otop__class_Otop(tc_fun(_1493834, tc_HOL_Obool)))))]]], (38979 ^ _777864) ^ [_1512709, _1512711, _1512713, _1512715] : [-(c_Wellfounded_Omax__extp(_1512709, _1512711, _1512713, _1512715)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512709), _1512713)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512709), _1512715)), -(_1512715 = c_Orderings_Obot__class_Obot(tc_fun(_1512709, tc_HOL_Obool))), 38993 ^ _777864 : [(38996 ^ _777864) ^ [_1513054] : [hBOOL(hAPP(hAPP(c_member(_1512709), _1513054), _1512715)), hBOOL(hAPP(hAPP(_1512711, 38992 ^ [_1512709, _1512711, _1512713, _1512715]), _1513054))], (38994 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512709), 38992 ^ [_1512709, _1512711, _1512713, _1512715]), _1512713)))]]], (25895 ^ _777864) ^ [_1232539, _1232541] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232539), _1232541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1232539), _1232541)))], (27029 ^ _777864) ^ [_1255196, _1255198, _1255200] : [hAPP(hAPP(c_COMBC(_1255196, tc_fun(_1255196, tc_HOL_Obool), tc_HOL_Obool), c_member(_1255196)), _1255198) = hAPP(hAPP(c_COMBC(_1255196, tc_fun(_1255196, tc_HOL_Obool), tc_HOL_Obool), c_member(_1255196)), _1255200), -(_1255198 = _1255200)], (18038 ^ _777864) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (25435 ^ _777864) ^ [_1223874, _1223876, _1223878] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223874), _1223876)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223874), _1223878)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1223874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223876), _1223878))))], (46843 ^ _777864) ^ [_1711555, _1711557, _1711559, _1711561] : [class_Groups_Oab__group__add(_1711555), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1711555), hAPP(c_List_Omonoid__add__class_Olistsum(_1711555), hAPP(hAPP(c_List_Omap(_1711557, _1711555), _1711559), _1711561))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1711555), hAPP(hAPP(c_List_Omap(_1711557, _1711555), hAPP(c_Fun_Ocomp(_1711555, _1711555, _1711557, c_Groups_Ouminus__class_Ouminus(_1711555)), _1711559)), _1711561)))], (36074 ^ _777864) ^ [_1449449] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1449449))))], (24555 ^ _777864) ^ [_1208736, _1208738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1208736), _1208738))), -(c_Quickcheck_Obeyond(_1208736, _1208738) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (6018 ^ _777864) ^ [_876901, _876903, _876905] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876903))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_876901, _876903, _876905))))], (38146 ^ _777864) ^ [_1493694, _1493696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1493694, _1493696)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1493694, _1493696), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493696), c_Orderings_Otop__class_Otop(tc_fun(_1493696, tc_HOL_Obool)))))], (13030 ^ _777864) ^ [_996500, _996502, _996504] : [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), _996500), _996502)), _996504))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996504), _996500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996502)))], (40833 ^ _777864) ^ [_1564997, _1564999, _1565001, _1565003, _1565005, _1565007, _1565009, _1565011] : [hBOOL(hAPP(hAPP(_1564997, _1564999), _1565001)), hBOOL(hAPP(hAPP(_1565003, _1565001), _1565005)), -(c_Predicate_Opred__comp(_1565007, _1565009, _1565011, _1564997, _1565003, _1564999, _1565005))], (15610 ^ _777864) ^ [_1043795, _1043797] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1043795), _1043797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1043795), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1043797)))], (27668 ^ _777864) ^ [_1270762] : [-(_1270762 = 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)), _1270762), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (51327 ^ _777864) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (11203 ^ _777864) ^ [_964422, _964424, _964426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964422), _964424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964426), _964424))))], (49249 ^ _777864) ^ [_1768670, _1768672, _1768674] : [_1768670 = c_List_Olist_ONil(_1768672), -(c_List_Olast(_1768672, hAPP(hAPP(c_List_Oappend(_1768672), _1768674), _1768670)) = c_List_Olast(_1768672, _1768674))], (16406 ^ _777864) ^ [_1059386, _1059388, _1059390] : [class_Groups_Oordered__ab__group__add__abs(_1059386), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059386), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059386), hAPP(c_Groups_Oabs__class_Oabs(_1059386), _1059388)), hAPP(c_Groups_Oabs__class_Oabs(_1059386), _1059390))), hAPP(c_Groups_Oabs__class_Oabs(_1059386), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059386), _1059388), _1059390)))))], (42990 ^ _777864) ^ [_1613763, _1613765] : [-(hAPP(c_Relation_ORange(_1613763, _1613763), c_Transitive__Closure_Otrancl(_1613763, _1613765)) = hAPP(c_Relation_ORange(_1613763, _1613763), _1613765))], (27610 ^ _777864) ^ [_1269510, _1269512] : [class_Int_Oring__char__0(_1269510), hBOOL(hAPP(hAPP(c_member(_1269510), _1269512), c_Int_Oring__1__class_OInts(_1269510))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269510), c_Groups_Oone__class_Oone(_1269510)), _1269512)), _1269512) = c_Groups_Ozero__class_Ozero(_1269510)], (23033 ^ _777864) ^ [_1177297, _1177299, _1177301, _1177303, _1177305, _1177307] : [-(c_Product__Type_Oprod_Oprod__rec(_1177297, _1177299, _1177301, _1177303, hAPP(hAPP(c_Product__Type_OPair(_1177297, _1177299), _1177305), _1177307)) = hAPP(hAPP(_1177303, _1177305), _1177307))], (8182 ^ _777864) ^ [_913710, _913712] : [_913710 = _913712, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913710) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913712))], (48197 ^ _777864) ^ [_1743101, _1743103, _1743105, _1743107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743103)), _1743105))), -(hAPP(hAPP(c_List_Onth(_1743103), hAPP(hAPP(c_List_Oappend(_1743103), _1743105), _1743107)), _1743101) = hAPP(hAPP(c_List_Onth(_1743103), _1743105), _1743101))], (50785 ^ _777864) ^ [_1802419, _1802421, _1802423] : [class_Orderings_Olinorder(_1802419), c_List_Olinorder__class_Osorted(_1802419, _1802421), -(c_List_Olinorder__class_Osorted(_1802419, c_List_OtakeWhile(_1802419, _1802423, _1802421)))], (43407 ^ _777864) ^ [_1623613, _1623615, _1623617, _1623619] : [hBOOL(hAPP(hAPP(c_member(_1623613), _1623615), c_Wellfounded_Oacc(_1623613, _1623617))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1623613, _1623613)), hAPP(hAPP(c_Product__Type_OPair(_1623613, _1623613), _1623619), _1623615)), c_Transitive__Closure_Ortrancl(_1623613, _1623617))), -(hBOOL(hAPP(hAPP(c_member(_1623613), _1623619), c_Wellfounded_Oacc(_1623613, _1623617))))], (47810 ^ _777864) ^ [_1734231, _1734233, _1734235, _1734237, _1734239, _1734241] : [-(c_Map_Omap__add(_1734231, _1734233, _1734235, c_Map_Omap__upds(_1734231, _1734233, _1734237, _1734239, _1734241)) = c_Map_Omap__upds(_1734231, _1734233, c_Map_Omap__add(_1734231, _1734233, _1734235, _1734237), _1734239, _1734241))], (33723 ^ _777864) ^ [_1399767, _1399769, _1399771, _1399773, _1399775] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399767, tc_fun(_1399769, tc_HOL_Obool)), _1399771), hAPP(hAPP(c_COMBB(tc_fun(_1399769, tc_HOL_Obool), tc_fun(_1399769, tc_HOL_Obool), _1399767), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399769, tc_HOL_Obool)), _1399773)), _1399775)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399769, tc_HOL_Obool)), _1399773), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399767, tc_fun(_1399769, tc_HOL_Obool)), _1399771), _1399775)))], (23025 ^ _777864) ^ [_1177136, _1177138, _1177140, _1177142] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1177136, _1177138), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1177140), _1177142))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1177136), _1177138) = _1177140)], (26891 ^ _777864) ^ [_1252615, _1252617, _1252619, _1252621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1252615, tc_HOL_Obool)), _1252617), _1252619)), hBOOL(hAPP(hAPP(c_member(_1252615), _1252621), _1252617)), -(hBOOL(hAPP(hAPP(c_member(_1252615), _1252621), _1252619)))], (26391 ^ _777864) ^ [_1242653, _1242655, _1242657] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242653), _1242657)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242653), _1242655)))], (26623 ^ _777864) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41736 ^ _777864) ^ [_1586499, _1586501, _1586503, _1586505, _1586507, _1586509, _1586511] : [-(hAPP(c_Fun_Ocomp(_1586499, _1586501, _1586503, _1586505), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1586503, _1586499), _1586507), _1586509), _1586511)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1586503, _1586501), hAPP(c_Fun_Ocomp(_1586499, _1586501, _1586503, _1586505), _1586507)), _1586509), hAPP(_1586505, _1586511)))], (28669 ^ _777864) ^ [_1295328, _1295330, _1295332, _1295334, _1295336, _1295338, _1295340] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1295328, _1295330)), hAPP(hAPP(c_Product__Type_OPair(_1295328, _1295330), _1295332), _1295334)), _1295336)), -(hBOOL(hAPP(hAPP(c_member(_1295338), hAPP(hAPP(_1295340, _1295332), _1295334)), hAPP(c_Set_Oimage(tc_prod(_1295328, _1295330), _1295338, hAPP(c_Product__Type_Oprod_Oprod__case(_1295328, _1295330, _1295338), _1295340)), _1295336))))], (13595 ^ _777864) ^ [_1006894, _1006896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006896, _1006894)), _1006894)))], (10402 ^ _777864) ^ [_951526, _951528] : [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), _951526), _951528))), 10405 ^ _777864 : [(10408 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _951528)))], (10406 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _951526)))]]], (45173 ^ _777864) ^ [_1668806, _1668808, _1668810, _1668812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1668806, _1668806)), hAPP(hAPP(c_Product__Type_OPair(_1668806, _1668806), _1668808), _1668810)), c_Transitive__Closure_Otrancl(_1668806, _1668812))), 45177 ^ _777864 : [(45180 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668806, _1668806)), hAPP(hAPP(c_Product__Type_OPair(_1668806, _1668806), 45176 ^ [_1668806, _1668808, _1668810, _1668812]), _1668810)), _1668812)))], (45178 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668806, _1668806)), hAPP(hAPP(c_Product__Type_OPair(_1668806, _1668806), _1668808), 45176 ^ [_1668806, _1668808, _1668810, _1668812])), c_Transitive__Closure_Ortrancl(_1668806, _1668812))))]]], (50851 ^ _777864) ^ [_1803755, _1803757] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803755)), c_List_Oremdups(_1803755, _1803757))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803755)), _1803757))))], (20 ^ _777864) ^ [_778124, _778126, _778128, _778130] : [-(c_Option_Ois__none(_778128, _778124)), c_Option_Ois__none(_778130, _778126), _778130 = _778128, _778126 = _778124], (3800 ^ _777864) ^ [_835692, _835694] : [_835694 = _835692, -(c_HOL_OAll(_835694) = c_HOL_OAll(_835692))], (15284 ^ _777864) ^ [_1037481, _1037483, _1037485] : [hBOOL(hAPP(_1037481, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037483), _1037485)))), 15287 ^ _777864 : [(15294 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037483), _1037485)), -(hBOOL(hAPP(_1037481, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15288 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037485), _1037483)), -(hBOOL(hAPP(_1037481, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037483)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037485)))))]]], (23083 ^ _777864) ^ [_1178480, _1178482, _1178484, _1178486, _1178488] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1178480, _1178482, _1178480, _1178484), hAPP(c_Product__Type_OPair(_1178482, _1178480), _1178486)), _1178488) = hAPP(_1178488, _1178486))], (44419 ^ _777864) ^ [_1650758, _1650760] : [-(c_Relation_Ototal__on(_1650758, c_Orderings_Obot__class_Obot(tc_fun(_1650758, tc_HOL_Obool)), _1650760))], (47484 ^ _777864) ^ [_1727299, _1727301, _1727303] : [-(hAPP(hAPP(c_List_Ozip(_1727299, _1727301), _1727303), c_List_Olist_ONil(_1727301)) = c_List_Olist_ONil(tc_prod(_1727299, _1727301)))], (30194 ^ _777864) ^ [_1327519, _1327521, _1327523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327519, tc_HOL_Obool)), _1327521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327519, tc_HOL_Obool)), _1327523), _1327521)) = c_Orderings_Obot__class_Obot(tc_fun(_1327519, tc_HOL_Obool)))], (24589 ^ _777864) ^ [_1209219, _1209221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209219), _1209221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1209219)), hAPP(c_Code__Numeral_Oof__nat, _1209221))))], (15136 ^ _777864) ^ [_1034706] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1034706) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5994 ^ _777864) ^ [_876359, _876361, _876363] : [hBOOL(hAPP(c_Com_OWT, _876359)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_876361, _876363, _876359))))], (46326 ^ _777864) ^ [_1696011, _1696013, _1696015, _1696017] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696011)), _1696013) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696015)), _1696017), -(hAPP(hAPP(c_List_Omap(tc_prod(_1696011, _1696015), _1696015), c_Product__Type_Osnd(_1696011, _1696015)), hAPP(hAPP(c_List_Ozip(_1696011, _1696015), _1696013), _1696017)) = _1696017)], (23175 ^ _777864) ^ [_1180439, _1180441] : [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(_1180439))), 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)), _1180441)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180439)), hAPP(c_Nat_OSuc, _1180441))))], (51321 ^ _777864) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (29600 ^ _777864) ^ [_1314994, _1314996, _1314998, _1315000] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314994, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1314994, tc_fun(_1314994, tc_HOL_Obool), tc_HOL_Obool), c_member(_1314994)), _1314996)), hAPP(hAPP(c_COMBC(_1314994, tc_fun(_1314994, tc_HOL_Obool), tc_HOL_Obool), c_member(_1314994)), _1314998)), _1315000)), -(hBOOL(hAPP(hAPP(c_member(_1314994), _1315000), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314994, tc_HOL_Obool)), _1314996), _1314998))))], (48414 ^ _777864) ^ [_1749553, _1749555, _1749557, _1749559, _1749561, _1749563, _1749565, _1749567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749553, _1749553)), hAPP(hAPP(c_Product__Type_OPair(_1749553, _1749553), _1749555), _1749557)), _1749559)), _1749561 = hAPP(hAPP(c_List_Oappend(_1749553), _1749563), hAPP(hAPP(c_List_Olist_OCons(_1749553), _1749555), _1749565)), _1749567 = hAPP(hAPP(c_List_Oappend(_1749553), _1749563), hAPP(hAPP(c_List_Olist_OCons(_1749553), _1749557), _1749565)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749553), tc_List_Olist(_1749553))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1749553), tc_List_Olist(_1749553)), _1749561), _1749567)), c_List_Olistrel1(_1749553, _1749559))))], (36044 ^ _777864) ^ [_1448773] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1448773) = 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), _1448773))))], (2006 ^ _777864) ^ [_807145, _807147] : [_807147 = _807145, -(c_Com_Ocom_Ocom__size(_807147) = c_Com_Ocom_Ocom__size(_807145))], (33297 ^ _777864) ^ [_1389648, _1389650, _1389652] : [33299 ^ _777864 : [(33302 ^ _777864) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1389652, 33298 ^ [_1389648, _1389650, _1389652]))], (33300 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389648), 33298 ^ [_1389648, _1389650, _1389652]), _1389650)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389648, tc_Int_Oint), _1389652), _1389650) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389648, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1389648), c_Int_Onat), _1389652)), _1389650)))], (28554 ^ _777864) ^ [_1291717, _1291719, _1291721, _1291723] : [hAPP(c_Set_Oimage(_1291717, _1291719, _1291721), _1291723) = c_Orderings_Obot__class_Obot(tc_fun(_1291719, tc_HOL_Obool)), -(_1291723 = c_Orderings_Obot__class_Obot(tc_fun(_1291717, tc_HOL_Obool)))], (50979 ^ _777864) ^ [_1806307, _1806309, _1806311] : [-(hAPP(hAPP(c_List_Oappend(_1806307), c_List_OtakeWhile(_1806307, _1806309, _1806311)), c_List_OdropWhile(_1806307, _1806309, _1806311)) = _1806311)], (41120 ^ _777864) ^ [_1570995, _1570997] : [c_Wellfounded_Owf(_1570995, _1570997), -(c_Wellfounded_Owf(tc_List_Olist(_1570995), c_List_Olex(_1570995, _1570997)))], (17234 ^ _777864) ^ [_1075057, _1075059, _1075061, _1075063] : [class_Rings_Olinordered__semidom(_1075057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075057), c_Groups_Oone__class_Oone(_1075057)), _1075059)), 17241 ^ _777864 : [(17248 ^ _777864) ^ [] : [_1075061 = _1075063, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075057), _1075059), _1075061) = hAPP(hAPP(c_Power_Opower__class_Opower(_1075057), _1075059), _1075063))], (17242 ^ _777864) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1075057), _1075059), _1075061) = hAPP(hAPP(c_Power_Opower__class_Opower(_1075057), _1075059), _1075063), -(_1075061 = _1075063)]]], (15314 ^ _777864) ^ [_1038045, _1038047, _1038049] : [class_Groups_Oordered__ab__group__add(_1038045), 15317 ^ _777864 : [(15324 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038045), _1038047), _1038049)), c_Groups_Ozero__class_Ozero(_1038045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038045), _1038047), _1038049)))], (15318 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038045), _1038047), _1038049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038045), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038045), _1038047), _1038049)), c_Groups_Ozero__class_Ozero(_1038045))))]]], (26653 ^ _777864) ^ [_1248097, _1248099, _1248101, _1248103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248097, tc_HOL_Obool)), _1248099), hAPP(hAPP(c_Set_Oinsert(_1248097), _1248101), _1248103))), 26656 ^ _777864 : [(26663 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248097), _1248101), _1248103))), 26666 ^ _777864 : [(26673 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248097), _1248101), _1248099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248097, tc_HOL_Obool)), _1248099), _1248103)))], (26667 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1248097), _1248101), _1248099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248097, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248097, tc_HOL_Obool)), _1248099), hAPP(hAPP(c_Set_Oinsert(_1248097), _1248101), c_Orderings_Obot__class_Obot(tc_fun(_1248097, tc_HOL_Obool))))), _1248103)))]]], (26657 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1248097), _1248101), _1248103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248097, tc_HOL_Obool)), _1248099), _1248103)))]]], (29069 ^ _777864) ^ [_1303682, _1303684, _1303686, _1303688, _1303690] : [c_Equiv__Relations_Oequiv(_1303682, _1303684, _1303686), hBOOL(hAPP(hAPP(c_member(_1303682), _1303688), _1303684)), hBOOL(hAPP(hAPP(c_member(_1303682), _1303690), _1303684)), 29080 ^ _777864 : [(29087 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1303682, _1303682)), hAPP(hAPP(c_Product__Type_OPair(_1303682, _1303682), _1303688), _1303690)), _1303686)), -(hAPP(c_Relation_OImage(_1303682, _1303682, _1303686), hAPP(hAPP(c_Set_Oinsert(_1303682), _1303688), c_Orderings_Obot__class_Obot(tc_fun(_1303682, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1303682, _1303682, _1303686), hAPP(hAPP(c_Set_Oinsert(_1303682), _1303690), c_Orderings_Obot__class_Obot(tc_fun(_1303682, tc_HOL_Obool)))))], (29081 ^ _777864) ^ [] : [hAPP(c_Relation_OImage(_1303682, _1303682, _1303686), hAPP(hAPP(c_Set_Oinsert(_1303682), _1303688), c_Orderings_Obot__class_Obot(tc_fun(_1303682, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1303682, _1303682, _1303686), hAPP(hAPP(c_Set_Oinsert(_1303682), _1303690), c_Orderings_Obot__class_Obot(tc_fun(_1303682, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303682, _1303682)), hAPP(hAPP(c_Product__Type_OPair(_1303682, _1303682), _1303688), _1303690)), _1303686)))]]], (42318 ^ _777864) ^ [_1599828, _1599830] : [42319 ^ _777864 : [(42320 ^ _777864) ^ [_1599874] : [hBOOL(hAPP(_1599828, _1599874))]], -(hBOOL(hAPP(_1599828, c_Hilbert__Choice_OEps(_1599830, _1599828))))], (43044 ^ _777864) ^ [_1615106, _1615108, _1615110, _1615112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615106, _1615106)), _1615108), c_Transitive__Closure_Otrancl(_1615106, _1615110))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615106, _1615106), tc_HOL_Obool)), _1615110), _1615112)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615106, _1615106)), _1615108), c_Transitive__Closure_Otrancl(_1615106, _1615112))))], (27147 ^ _777864) ^ [_1258729, _1258731, _1258733, _1258735] : [-(hBOOL(hAPP(hAPP(c_member(_1258729), _1258731), _1258733))), 27150 ^ _777864 : [(27157 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258729, tc_HOL_Obool)), _1258733), _1258735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258729, tc_HOL_Obool)), _1258733), hAPP(hAPP(c_Set_Oinsert(_1258729), _1258731), _1258735))))], (27151 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258729, tc_HOL_Obool)), _1258733), hAPP(hAPP(c_Set_Oinsert(_1258729), _1258731), _1258735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258729, tc_HOL_Obool)), _1258733), _1258735)))]]], (44752 ^ _777864) ^ [_1658351, _1658353] : [class_Complete__Lattice_Ocomplete__lattice(_1658351), -(c_Complete__Lattice_OSup__class_OSup(_1658351, _1658353) = c_Complete__Lattice_OInf__class_OInf(_1658351, hAPP(c_Set_OCollect(_1658351), hAPP(hAPP(c_COMBB(tc_fun(_1658351, tc_HOL_Obool), tc_HOL_Obool, _1658351), c_HOL_OAll(_1658351)), hAPP(hAPP(c_COMBB(tc_fun(_1658351, tc_HOL_Obool), tc_fun(_1658351, tc_HOL_Obool), _1658351), hAPP(c_COMBS(_1658351, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1658351), c_fimplies), hAPP(hAPP(c_COMBC(_1658351, tc_fun(_1658351, tc_HOL_Obool), tc_HOL_Obool), c_member(_1658351)), _1658353)))), hAPP(c_COMBC(_1658351, _1658351, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1658351)))))))], (44676 ^ _777864) ^ [_1656807, _1656809, _1656811] : [class_Complete__Lattice_Ocomplete__lattice(_1656807), hBOOL(hAPP(hAPP(c_member(_1656807), _1656809), _1656811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1656807), c_Complete__Lattice_OInf__class_OInf(_1656807, _1656811)), _1656809)))], (2634 ^ _777864) ^ [_817015, _817017] : [_817017 = _817015, -(c_DSequence_Ounion(_817017) = c_DSequence_Ounion(_817015))], (5072 ^ _777864) ^ [_855490, _855492, _855494, _855496, _855498, _855500, _855502, _855504] : [-(c_Map_Omap__add(_855504, _855500, _855496, _855492) = c_Map_Omap__add(_855502, _855498, _855494, _855490)), _855504 = _855502, _855500 = _855498, _855496 = _855494, _855492 = _855490], (22566 ^ _777864) ^ [_1168010, _1168012, _1168014, _1168016] : [-(_1168010 = _1168012), hAPP(c_Product__Type_Ofst(_1168014, _1168016), _1168010) = hAPP(c_Product__Type_Ofst(_1168014, _1168016), _1168012), hAPP(c_Product__Type_Osnd(_1168014, _1168016), _1168010) = hAPP(c_Product__Type_Osnd(_1168014, _1168016), _1168012)], (35590 ^ _777864) ^ [_1439849, _1439851, _1439853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439849), _1439851)), -(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)), _1439849)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1439853), _1439851)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1439853), _1439849)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1439851), _1439849)))], (16590 ^ _777864) ^ [_1063016, _1063018] : [class_Rings_Ocomm__semiring__1(_1063016), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1063016), _1063018), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1063016))], (7512 ^ _777864) ^ [_902196, _902198, _902200] : [class_Rings_Ocomm__semiring__1(_902196), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902196), _902198), _902200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902196), _902200), _902198))], (34319 ^ _777864) ^ [_1414289, _1414291, _1414293] : [class_Orderings_Olinorder(_1414289), hAPP(_1414291, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1414289), 34324 ^ [_1414289, _1414291, _1414293]), 34325 ^ [_1414289, _1414291, _1414293])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1414289), hAPP(_1414291, 34324 ^ [_1414289, _1414291, _1414293])), hAPP(_1414291, 34325 ^ [_1414289, _1414291, _1414293])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414289), _1414293)), -(_1414293 = c_Orderings_Obot__class_Obot(tc_fun(_1414289, tc_HOL_Obool))), -(hAPP(_1414291, c_Big__Operators_Olinorder__class_OMin(_1414289, _1414293)) = c_Big__Operators_Olinorder__class_OMin(_1414289, hAPP(c_Set_Oimage(_1414289, _1414289, _1414291), _1414293)))], (32537 ^ _777864) ^ [_1373348, _1373350, _1373352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373348), _1373350)), hBOOL(hAPP(hAPP(c_member(_1373348), _1373352), _1373350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1373348), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373348, tc_HOL_Obool)), _1373350), hAPP(hAPP(c_Set_Oinsert(_1373348), _1373352), c_Orderings_Obot__class_Obot(tc_fun(_1373348, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1373348), _1373350))))], (46100 ^ _777864) ^ [_1690172, _1690174, _1690176] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1690172, tc_HOL_Obool)), hAPP(c_List_Oset(_1690172), c_List_Oremove1(_1690172, _1690174, _1690176))), hAPP(c_List_Oset(_1690172), _1690176))))], (25863 ^ _777864) ^ [_1231946, _1231948, _1231950, _1231952, _1231954] : [class_Divides_Osemiring__div(_1231946), -(_1231948 = c_Groups_Ozero__class_Ozero(_1231946)), -(_1231950 = c_Groups_Ozero__class_Ozero(_1231946)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231946), _1231948), _1231952)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231946), _1231950), _1231954)), 25882 ^ _777864 : [(25889 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231946), _1231952), _1231950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231946), _1231948), _1231954), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231946), _1231952), _1231948) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231946), _1231954), _1231950))], (25883 ^ _777864) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231946), _1231952), _1231948) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231946), _1231954), _1231950), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231946), _1231952), _1231950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231946), _1231948), _1231954))]]], (19850 ^ _777864) ^ [_1120040, _1120042] : [c_Nat__Transfer_Ois__nat(_1120040), c_Nat__Transfer_Ois__nat(_1120042), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120040), _1120042)))], (49053 ^ _777864) ^ [_1764383, _1764385, _1764387] : [-(c_List_Olist_Olist__size(_1764383, _1764385, _1764387) = 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(_1764383, tc_Nat_Onat), _1764385), _1764387))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764383)), _1764387)))], (33322 ^ _777864) ^ [_1390305, _1390307, _1390309, _1390311, _1390313, _1390315] : [hBOOL(hAPP(hAPP(c_member(_1390305), _1390307), _1390309)), hBOOL(hAPP(hAPP(_1390311, _1390307), _1390313)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390305, tc_fun(_1390315, tc_HOL_Obool)), _1390309), _1390311), _1390313)))], (38066 ^ _777864) ^ [_1492355, _1492357] : [-(hBOOL(hAPP(hAPP(c_member(_1492355), _1492357), c_Orderings_Otop__class_Otop(tc_fun(_1492355, tc_HOL_Obool)))))], (18650 ^ _777864) ^ [_1098466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098466), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1098466)), c_Int_OPls)))], (31097 ^ _777864) ^ [_1345968, _1345970, _1345972] : [class_Orderings_Olinorder(_1345968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345968), _1345970)), -(_1345972 = c_Orderings_Obot__class_Obot(tc_fun(_1345968, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345968, tc_HOL_Obool)), _1345972), _1345970)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1345968), c_Big__Operators_Olinorder__class_OMax(_1345968, _1345972)), c_Big__Operators_Olinorder__class_OMax(_1345968, _1345970)) = c_Big__Operators_Olinorder__class_OMax(_1345968, _1345970))], (23297 ^ _777864) ^ [_1183807, _1183809, _1183811, _1183813] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1183807, _1183809, _1183811), hAPP(hAPP(c_COMBB(tc_fun(_1183809, tc_prod(_1183807, _1183809)), tc_fun(_1183809, _1183811), _1183807), hAPP(c_COMBB(tc_prod(_1183807, _1183809), _1183811, _1183809), _1183813)), c_Product__Type_OPair(_1183807, _1183809))) = _1183813)], (19328 ^ _777864) ^ [] : [-(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)))))], (34907 ^ _777864) ^ [_1426005, _1426007] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426005), _1426007))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1426007, _1426005) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1426007), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426007), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1426005)))], (40743 ^ _777864) ^ [_1560959, _1560961, _1560963, _1560965] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1560959, _1560961, _1560963), _1560965), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1560961, _1560963), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1560959, _1560963), tc_HOL_Obool)))], (36656 ^ _777864) ^ [_1461902, _1461904, _1461906, _1461908, _1461910] : [-(hBOOL(hAPP(hAPP(c_member(_1461902), _1461904), _1461906))), -(hAPP(c_Map_Orestrict__map(_1461902, _1461908, _1461910, _1461906), _1461904) = c_Option_Ooption_ONone(_1461908))], (29612 ^ _777864) ^ [_1315398, _1315400, _1315402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315398, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315398, tc_HOL_Obool)), _1315400), _1315402)), _1315400)))], (41001 ^ _777864) ^ [_1568012, _1568014, _1568016] : [c_Wellfounded_Owf(_1568012, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568012, _1568012), tc_HOL_Obool)), _1568014), _1568016)), -(c_Wellfounded_Owf(_1568012, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568012, _1568012), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568012, _1568012), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1568012, _1568012, _1568012), _1568014), _1568014)), hAPP(hAPP(c_Relation_Orel__comp(_1568012, _1568012, _1568012), _1568016), _1568014))), _1568016)))], (40582 ^ _777864) ^ [_1554892, _1554894, _1554896] : [class_Orderings_Olinorder(_1554892), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554892), _1554894)), -(_1554894 = c_Orderings_Obot__class_Obot(tc_fun(_1554892, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1554892), _1554896), c_Big__Operators_Olattice_OSup__fin(_1554892, c_Orderings_Oord__class_Omax(_1554892), _1554894)) = c_Big__Operators_Olattice_OSup__fin(_1554892, c_Orderings_Oord__class_Omax(_1554892), hAPP(c_Set_OCollect(_1554892), hAPP(hAPP(c_COMBB(tc_fun(_1554892, tc_HOL_Obool), tc_HOL_Obool, _1554892), c_HOL_OEx(_1554892)), hAPP(hAPP(c_COMBC(_1554892, tc_fun(_1554892, tc_HOL_Obool), tc_fun(_1554892, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554892, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1554892, tc_HOL_Obool), tc_fun(_1554892, tc_HOL_Obool)), _1554892), c_COMBS(_1554892, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554892, tc_HOL_Obool), tc_fun(_1554892, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1554892), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554892), c_fconj)), hAPP(hAPP(c_COMBC(_1554892, tc_fun(_1554892, _1554892), tc_fun(_1554892, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554892, tc_HOL_Obool), tc_fun(tc_fun(_1554892, _1554892), tc_fun(_1554892, tc_HOL_Obool)), _1554892), c_COMBB(_1554892, tc_HOL_Obool, _1554892)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1554892), _1554896))))), hAPP(hAPP(c_COMBC(_1554892, tc_fun(_1554892, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554892)), _1554894))))))], (27243 ^ _777864) ^ [_1261744, _1261746, _1261748, _1261750] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261744, tc_HOL_Obool)), _1261746), hAPP(hAPP(c_Set_Oinsert(_1261744), _1261748), _1261750)))), 27246 ^ _777864 : [(27249 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261744, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261744, tc_HOL_Obool)), _1261746), hAPP(hAPP(c_Set_Oinsert(_1261744), _1261748), c_Orderings_Obot__class_Obot(tc_fun(_1261744, tc_HOL_Obool))))), _1261750))], (27247 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261744), _1261748), _1261746)))]], 27250 ^ _777864 : [(27253 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261744, tc_HOL_Obool)), _1261746), _1261750))], (27251 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1261744), _1261748), _1261746))]]], (33376 ^ _777864) ^ [_1391497, _1391499, _1391501] : [class_Orderings_Oorder(_1391497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391497), _1391499), _1391501)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1391497, _1391501, _1391499) = c_Orderings_Obot__class_Obot(tc_fun(_1391497, tc_HOL_Obool)))], (24723 ^ _777864) ^ [_1211680, _1211682, _1211684, _1211686, _1211688] : [hBOOL(hAPP(_1211680, hAPP(hAPP(c_Product__Type_OPair(_1211682, _1211684), _1211686), _1211688))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1211682, _1211684, tc_HOL_Obool, _1211680), _1211686), _1211688)))], (28731 ^ _777864) ^ [_1296508, _1296510] : [-(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), _1296508), _1296510)), 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), _1296510), _1296508)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29131 ^ _777864) ^ [_1305111, _1305113, _1305115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305111), _1305113)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1305111, tc_HOL_Obool)), _1305113), _1305115))))], (23609 ^ _777864) ^ [_1190080, _1190082, _1190084] : [class_Orderings_Olinorder(_1190080), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190080), _1190082), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190080), _1190082), _1190084)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190080), _1190082), _1190084))], (22200 ^ _777864) ^ [_1161655, _1161657, _1161659, _1161661, _1161663, _1161665] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1161655, _1161657), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1161659), _1161661))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1161655, _1161657), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1161663), _1161665))), -(_1161657 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1161659 = _1161663)], (38800 ^ _777864) ^ [_1508828, _1508830, _1508832, _1508834, _1508836] : [hAPP(c_Set_Oimage(_1508828, _1508830, _1508832), c_Orderings_Otop__class_Otop(tc_fun(_1508828, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1508830, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508828, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1508828, _1508830, _1508832), _1508834)), _1508836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508830, tc_HOL_Obool)), _1508834), hAPP(c_Set_Oimage(_1508828, _1508830, _1508832), _1508836))))], (46484 ^ _777864) ^ [_1700419, _1700421] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1700419), _1700421))), -(c_Nitpick_Ocard_H(_1700419, _1700421) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10244 ^ _777864) ^ [_948793, _948795, _948797, _948799] : [class_Orderings_Oorder(_948793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948793), _948795), _948797)), _948795 = _948799, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948793), _948799), _948797)))], (12318 ^ _777864) ^ [_984100, _984102, _984104, _984106] : [class_Groups_Oordered__comm__monoid__add(_984100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984100), c_Groups_Ozero__class_Ozero(_984100)), _984102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984100), _984104), _984106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984100), _984104), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984100), _984102), _984106))))], (29093 ^ _777864) ^ [_1304230, _1304232, _1304234, _1304236, _1304238] : [c_Equiv__Relations_Oequiv(_1304230, _1304232, _1304234), 29096 ^ _777864 : [(29107 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1304230, _1304230)), hAPP(hAPP(c_Product__Type_OPair(_1304230, _1304230), _1304236), _1304238)), _1304234))), hAPP(c_Relation_OImage(_1304230, _1304230, _1304234), hAPP(hAPP(c_Set_Oinsert(_1304230), _1304236), c_Orderings_Obot__class_Obot(tc_fun(_1304230, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1304230, _1304230, _1304234), hAPP(hAPP(c_Set_Oinsert(_1304230), _1304238), c_Orderings_Obot__class_Obot(tc_fun(_1304230, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1304230), _1304236), _1304232)), hBOOL(hAPP(hAPP(c_member(_1304230), _1304238), _1304232))], (29097 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1304230, _1304230)), hAPP(hAPP(c_Product__Type_OPair(_1304230, _1304230), _1304236), _1304238)), _1304234)), 29100 ^ _777864 : [(29105 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304230), _1304238), _1304232)))], (29103 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304230), _1304236), _1304232)))], (29101 ^ _777864) ^ [] : [-(hAPP(c_Relation_OImage(_1304230, _1304230, _1304234), hAPP(hAPP(c_Set_Oinsert(_1304230), _1304236), c_Orderings_Obot__class_Obot(tc_fun(_1304230, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1304230, _1304230, _1304234), hAPP(hAPP(c_Set_Oinsert(_1304230), _1304238), c_Orderings_Obot__class_Obot(tc_fun(_1304230, tc_HOL_Obool)))))]]]]], (40970 ^ _777864) ^ [_1567461] : [-(c_Wellfounded_Owf(tc_fun(_1567461, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1567461)))], (51245 ^ _777864) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (41128 ^ _777864) ^ [_1571100, _1571102] : [-(c_List_Olex(_1571100, _1571102) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1571100), tc_List_Olist(_1571100)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1571100, _1571102)))], (38256 ^ _777864) ^ [_1495723, _1495725] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495723, tc_HOL_Obool)), _1495725), c_Orderings_Otop__class_Otop(tc_fun(_1495723, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1495723, tc_HOL_Obool)))], (6342 ^ _777864) ^ [_882457, _882459, _882461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882457), _882459)), _882461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882457), _882461)))], (7060 ^ _777864) ^ [_893828] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _893828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_893828)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20872 ^ _777864) ^ [_1137861, _1137863, _1137865, _1137867, _1137869] : [class_Fields_Ofield(_1137861), -(_1137863 = c_Groups_Ozero__class_Ozero(_1137861)), -(_1137865 = c_Groups_Ozero__class_Ozero(_1137861)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137861), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137861), _1137867), _1137863)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137861), _1137869), _1137865)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137861), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137861), _1137867), _1137865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137861), _1137869), _1137863))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137861), _1137863), _1137865)))], (15954 ^ _777864) ^ [_1051384, _1051386] : [_1051384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051384), _1051386) = _1051386)], (36188 ^ _777864) ^ [_1451393, _1451395, _1451397, _1451399] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451393, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1451395)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1451393, tc_HOL_Obool), tc_Nat_Onat), _1451397), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1451399))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451393, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1451399, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1451395), _1451399))), _1451397))], (44441 ^ _777864) ^ [_1651196, _1651198, _1651200, _1651202, _1651204, _1651206] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651196, _1651196)), hAPP(hAPP(c_Product__Type_OPair(_1651196, _1651196), _1651198), _1651200)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1651196, _1651196), tc_HOL_Obool), _1651202), _1651204))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1651196, _1651196)), hAPP(hAPP(c_Product__Type_OPair(_1651196, _1651196), _1651200), _1651206)), _1651204)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651196, _1651196)), hAPP(hAPP(c_Product__Type_OPair(_1651196, _1651196), _1651198), _1651206)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1651196, _1651196), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1651202)), _1651204))))], (41285 ^ _777864) ^ [_1574988, _1574990, _1574992] : [c_Wellfounded_OwfP(_1574988, _1574990), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1574988, _1574990), _1574992)))], (49994 ^ _777864) ^ [_1784535, _1784537, _1784539] : [class_Orderings_Olinorder(_1784535), c_List_Olinorder__class_Osorted(_1784535, _1784537), 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tc_fun(tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), tc_List_Olist(_1776651)), c_COMBS(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), tc_fun(tc_List_Olist(_1776651), tc_fun(tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), tc_List_Olist(_1776651)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_fun(tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), tc_List_Olist(_1776651)), hAPP(c_If(tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), hAPP(_1776653, _1776655)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1776651), tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), tc_List_Olist(_1776651)), c_Product__Type_OPair(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), hAPP(c_List_Olist_OCons(_1776651), _1776655))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1776651), tc_fun(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651))), tc_fun(tc_fun(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_fun(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), tc_List_Olist(_1776651)), c_COMBB(tc_List_Olist(_1776651), tc_prod(tc_List_Olist(_1776651), tc_List_Olist(_1776651)), tc_List_Olist(_1776651))), c_Product__Type_OPair(tc_List_Olist(_1776651), tc_List_Olist(_1776651)))), hAPP(c_List_Olist_OCons(_1776651), _1776655)))), c_List_Opartition(_1776651, _1776653, _1776657)))], (27374 ^ _777864) ^ [_1264682, _1264684, _1264686] : [class_Rings_Osemiring__1(_1264682), hBOOL(hAPP(hAPP(c_member(_1264682), _1264684), c_Nat_Osemiring__1__class_ONats(_1264682))), hBOOL(hAPP(hAPP(c_member(_1264682), _1264686), c_Nat_Osemiring__1__class_ONats(_1264682))), -(hBOOL(hAPP(hAPP(c_member(_1264682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264682), _1264684), _1264686)), c_Nat_Osemiring__1__class_ONats(_1264682))))], (26331 ^ _777864) ^ [_1241419, _1241421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241421)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241419), _1241421)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241421), _1241419)), -(_1241419 = _1241421)], (37947 ^ _777864) ^ [_1489961, _1489963, _1489965, _1489967] : [-(hAPP(_1489967, _1489963) = c_Option_Ooption_ONone(_1489965)), -(hBOOL(hAPP(hAPP(c_member(_1489961), _1489963), c_Map_Odom(_1489961, _1489965, _1489967))))], (15922 ^ _777864) ^ [_1050593, _1050595, _1050597, _1050599, _1050601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050593), _1050595)), 15925 ^ _777864 : [(15932 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050599), 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), _1050595), _1050593)), _1050597)), _1050601))), -(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), _1050593), _1050597)), _1050599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050595), _1050597)), _1050601))))], (15926 ^ _777864) ^ [] : [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), _1050593), _1050597)), _1050599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050595), _1050597)), _1050601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050599), 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), _1050595), _1050593)), _1050597)), _1050601))))]]], (24663 ^ _777864) ^ [_1210466] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1210466)) = _1210466)], (37837 ^ _777864) ^ [_1487696, _1487698, _1487700] : [class_Orderings_Olinorder(_1487696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487696), _1487698), _1487700)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487696, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1487696, _1487698, _1487700)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487696), _1487700)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487696), _1487698))], (51469 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (23317 ^ _777864) ^ [_1184313, _1184315, _1184317, _1184319, _1184321, _1184323] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1184313, _1184315), _1184315, _1184317), hAPP(hAPP(c_COMBB(_1184319, tc_fun(_1184315, _1184317), tc_prod(_1184313, _1184315)), _1184321), hAPP(hAPP(c_COMBB(_1184313, _1184319, tc_prod(_1184313, _1184315)), _1184323), c_Product__Type_Ofst(_1184313, _1184315)))), c_Product__Type_Osnd(_1184313, _1184315)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1184313, _1184315, _1184317), hAPP(hAPP(c_COMBB(_1184319, tc_fun(_1184315, _1184317), _1184313), _1184321), _1184323)))], (37743 ^ _777864) ^ [_1485981, _1485983, _1485985] : [class_Orderings_Olinorder(_1485981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1485981), _1485983), _1485985)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485981, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1485981, _1485983, _1485985)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485981), _1485985)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1485981), _1485983))], (6558 ^ _777864) ^ [_886156, _886158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886156), _886158)), -(_886158 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886156), 6561 ^ [_886156, _886158])))], (13549 ^ _777864) ^ [_1006091, _1006093, _1006095] : [class_Divides_Osemiring__div(_1006091), -(c_Divides_Odiv__class_Omod(_1006091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006091), _1006093), _1006095), _1006095) = c_Groups_Ozero__class_Ozero(_1006091))], (22514 ^ _777864) ^ [_1166999, _1167001, _1167003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166999, tc_HOL_Obool)), _1167001), _1167003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166999, tc_HOL_Obool)), _1167003), _1167001)), -(_1167001 = _1167003)], (12290 ^ _777864) ^ [_983592, _983594, _983596] : [class_Groups_Oordered__comm__monoid__add(_983592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983592), c_Groups_Ozero__class_Ozero(_983592)), _983594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983592), c_Groups_Ozero__class_Ozero(_983592)), _983596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983592), c_Groups_Ozero__class_Ozero(_983592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983592), _983594), _983596))))], (6695 ^ _777864) ^ [_888196, _888198, _888200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888196), _888198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888198), _888200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _888196)), _888200)))], (23881 ^ _777864) ^ [_1195232, _1195234, _1195236] : [class_Orderings_Olinorder(_1195232), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195232), _1195234), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195232), _1195234), _1195236)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195232), _1195234), _1195236))], (45268 ^ _777864) ^ [_1670998, _1671000] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1670998, _1670998)), _1671000), c_Relation_OId(_1670998))), -(_1671000 = hAPP(hAPP(c_Product__Type_OPair(_1670998, _1670998), 45271 ^ [_1670998, _1671000]), 45271 ^ [_1670998, _1671000]))], (34147 ^ _777864) ^ [_1410584, _1410586, _1410588, _1410590] : [class_Groups_Ocomm__monoid__mult(_1410584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410586), _1410588)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410586, _1410584), _1410590), _1410588) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1410584, _1410586, c_Groups_Otimes__class_Otimes(_1410584)), _1410590), c_Groups_Oone__class_Oone(_1410584)), _1410588))], (2962 ^ _777864) ^ [_822487, _822489, _822491, _822493, _822495, _822497] : [-(c_Com_Ocom_OCall(_822497, _822493, _822489) = c_Com_Ocom_OCall(_822495, _822491, _822487)), _822497 = _822495, _822493 = _822491, _822489 = _822487], (32963 ^ _777864) ^ [_1382217, _1382219, _1382221, _1382223, _1382225] : [class_Rings_Ocomm__semiring__1(_1382217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382219), _1382221)), hBOOL(hAPP(hAPP(c_member(_1382219), _1382223), _1382221)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1382217), hAPP(_1382225, _1382223)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382219, _1382217), _1382225), _1382221))))], (49667 ^ _777864) ^ [_1778156] : [-(c_List_Otranspose(_1778156, c_List_Olist_ONil(tc_List_Olist(_1778156))) = 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[-(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, _1005964, _1005966)), _1005966) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1005964), _1005966))], (11651 ^ _777864) ^ [_972493, _972495, _972497] : [class_Rings_Oordered__ring(_972493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972493), _972495), c_Groups_Ozero__class_Ozero(_972493))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972493), _972497), c_Groups_Ozero__class_Ozero(_972493))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972493), c_Groups_Ozero__class_Ozero(_972493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972493), _972495), _972497))))], (47512 ^ _777864) ^ [_1727830, _1727832, _1727834] : [-(hAPP(hAPP(c_List_Olist__update(_1727830, c_List_Olist_ONil(_1727830)), _1727832), _1727834) = c_List_Olist_ONil(_1727830))], (51451 ^ _777864) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (47442 ^ _777864) ^ [_1726299, _1726301, _1726303, _1726305] : [hAPP(hAPP(c_List_Omap(_1726299, _1726301), _1726303), _1726305) = c_List_Olist_ONil(_1726301), -(_1726305 = c_List_Olist_ONil(_1726299))], (24193 ^ _777864) ^ [_1201553, _1201555] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1201553), _1201555)), _1201555) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1201553), _1201555))], (47336 ^ _777864) ^ [_1724108, _1724110, _1724112, _1724114] : [-(hAPP(hAPP(c_List_Otake(_1724108), _1724110), hAPP(hAPP(c_List_Otake(_1724108), _1724112), _1724114)) = hAPP(hAPP(c_List_Otake(_1724108), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1724110), _1724112)), _1724114))], (8752 ^ _777864) ^ [_923172, _923174, _923176, _923178, _923180] : [class_Rings_Ocomm__semiring__1(_923172), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), _923174), _923176)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), _923178), _923180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), _923174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), _923176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923172), _923178), _923180))))], (48091 ^ _777864) ^ [_1741021, _1741023, _1741025] : [hAPP(hAPP(c_List_Oappend(_1741021), _1741023), _1741025) = _1741023, -(_1741025 = c_List_Olist_ONil(_1741021))], (4816 ^ _777864) ^ [_851536, _851538, _851540, _851542] : [-(c_List_Olinorder__class_Osorted__list__of__set(_851542, _851538) = c_List_Olinorder__class_Osorted__list__of__set(_851540, _851536)), _851542 = _851540, _851538 = _851536], (44287 ^ _777864) ^ [_1647476, _1647478] : [-(c_Relation_Osingle__valued(_1647476, _1647476, c_Relation_OId__on(_1647476, _1647478)))], (27306 ^ _777864) ^ [_1263257, _1263259, _1263261] : [_1263257 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1263259, _1263259), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1263259, _1263259), tc_HOL_Obool)), _1263257), _1263261)))], (5970 ^ _777864) ^ [_875952] : [hAPP(c_Nat_OSuc, _875952) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26207 ^ _777864) ^ [_1238727, _1238729, _1238731, _1238733] : [-(hAPP(hAPP(c_Set_Oinsert(_1238727), _1238729), hAPP(hAPP(c_Set_Oinsert(_1238727), _1238731), _1238733)) = hAPP(hAPP(c_Set_Oinsert(_1238727), _1238731), hAPP(hAPP(c_Set_Oinsert(_1238727), _1238729), _1238733)))], (4394 ^ _777864) ^ [_845075, _845077, _845079, _845081] : [-(c_Big__Operators_Olattice__class_OSup__fin(_845081, _845077) = c_Big__Operators_Olattice__class_OSup__fin(_845079, _845075)), _845081 = _845079, _845077 = _845075], (38534 ^ _777864) ^ [_1501620] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501620), c_Orderings_Otop__class_Otop(tc_fun(_1501620, 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(_1501620), c_Orderings_Otop__class_Otop(tc_fun(_1501620, tc_HOL_Obool))))))], (1542 ^ _777864) ^ [_799907, _799909] : [-(class_Rings_Ono__zero__divisors(_799907)), _799909 = _799907, class_Rings_Ono__zero__divisors(_799909)], (23615 ^ _777864) ^ [_1190205, _1190207, _1190209] : [class_Orderings_Olinorder(_1190205), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190205), _1190207), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190205), _1190207), _1190209)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190205), _1190207), _1190209))], (25289 ^ _777864) ^ [_1221392, _1221394, _1221396, _1221398] : [class_Divides_Osemiring__div(_1221392), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221392), _1221394), _1221396)), 25296 ^ _777864 : [(25303 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221392), _1221394), _1221398)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221392), _1221394), c_Divides_Odiv__class_Omod(_1221392, _1221398, _1221396))))], (25297 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221392), _1221394), c_Divides_Odiv__class_Omod(_1221392, _1221398, _1221396))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221392), _1221394), _1221398)))]]], (49753 ^ _777864) ^ [_1780322, _1780324, _1780326, _1780328] : [-(c_List_Oupt(_1780322, _1780324) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1780326), _1780328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1780322), _1780324)), _1780322 = _1780326, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1780322), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1780324) = _1780328], (49675 ^ _777864) ^ [_1778479, _1778481] : [-(c_Random_Opick(_1778479, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1778479), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1778479, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1778479, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1778479)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1778481)) = c_Random_Opick(_1778479, _1778481))], (40903 ^ _777864) ^ [_1566271, _1566273, _1566275] : [c_Wellfounded_Owf(_1566271, _1566273), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566271, _1566271)), hAPP(hAPP(c_Product__Type_OPair(_1566271, _1566271), _1566275), _1566275)), _1566273))], (9488 ^ _777864) ^ [_936265, _936267, _936269, _936271] : [class_Rings_Olinordered__ring__strict(_936265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936265), c_Groups_Ozero__class_Ozero(_936265)), _936267)), 9495 ^ _777864 : [(9502 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936265), _936269), _936271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936265), _936267), _936269)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936265), _936267), _936271))))], (9496 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936265), _936267), _936269)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936265), _936267), _936271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936265), _936269), _936271)))]]], (36126 ^ _777864) ^ [_1450312, _1450314, _1450316, _1450318, _1450320] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450312, _1450314), _1450316), _1450318), _1450320) = _1450316, -(hAPP(_1450316, _1450318) = _1450320)], (48844 ^ _777864) ^ [_1759686, _1759688, _1759690] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1759686, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759688)), _1759690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1759688, _1759686), _1759690) = _1759690)], (33893 ^ _777864) ^ [_1404395, _1404397, _1404399, _1404401, _1404403, _1404405, _1404407, _1404409] : [hBOOL(hAPP(hAPP(c_member(_1404395), _1404397), _1404399)), hBOOL(hAPP(hAPP(hAPP(_1404401, _1404397), _1404403), _1404405)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404395, tc_fun(_1404407, tc_fun(_1404409, tc_HOL_Obool))), _1404399), _1404401), _1404403), _1404405)))], (36830 ^ _777864) ^ [_1465787, _1465789, _1465791, _1465793] : [class_Groups_Ocomm__monoid__add(_1465787), 36833 ^ _777864 : [(36840 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1465789), _1465791))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465789, _1465787), _1465793), _1465791) = c_Groups_Ozero__class_Ozero(_1465787))], (36834 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465789), _1465791)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465789, _1465787), _1465793), _1465791) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465787, _1465789, c_Groups_Oplus__class_Oplus(_1465787)), _1465793), c_Groups_Ozero__class_Ozero(_1465787)), _1465791))]]], (1042 ^ _777864) ^ [_793657, _793659] : [-(class_Rings_Olinordered__semiring__1(_793657)), _793659 = _793657, class_Rings_Olinordered__semiring__1(_793659)], (30436 ^ _777864) ^ [_1332957, _1332959] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332957), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332959))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332957), _1332959)))], (5930 ^ _777864) ^ [_875311, _875313] : [hAPP(c_Nat_OSuc, _875311) = hAPP(c_Nat_OSuc, _875313), -(_875311 = _875313)], (16208 ^ _777864) ^ [_1055844, _1055846, _1055848] : [class_Groups_Oordered__ab__group__add__abs(_1055844), -(hAPP(c_Groups_Oabs__class_Oabs(_1055844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055844), _1055846), _1055848)) = hAPP(c_Groups_Oabs__class_Oabs(_1055844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055844), _1055848), _1055846)))], (33442 ^ _777864) ^ [_1392619, _1392621, _1392623, _1392625, _1392627] : [class_Orderings_Olinorder(_1392619), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392619, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392619, _1392621, _1392623)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392619, _1392625, _1392627)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1392619, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1392619), _1392621), _1392625), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1392619), _1392623), _1392627)))], (49019 ^ _777864) ^ [_1763398, _1763400, _1763402, _1763404] : [class_Complete__Lattice_Ocomplete__lattice(_1763398), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1763400, _1763398), hAPP(c_List_Oset(_1763400), _1763402)), _1763404) = hAPP(c_List_Ofoldl(_1763398, _1763400, hAPP(c_COMBC(_1763400, _1763398, _1763398), hAPP(hAPP(c_COMBB(_1763398, tc_fun(_1763398, _1763398), _1763400), c_Lattices_Osemilattice__inf__class_Oinf(_1763398)), _1763404)), c_Orderings_Otop__class_Otop(_1763398)), _1763402))], (11883 ^ _777864) ^ [_976606, _976608] : [class_Groups_Olinordered__ab__group__add(_976606), 11886 ^ _777864 : [(11893 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976606), c_Groups_Ozero__class_Ozero(_976606)), _976608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976606), hAPP(c_Groups_Ouminus__class_Ouminus(_976606), _976608)), _976608)))], (11887 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976606), hAPP(c_Groups_Ouminus__class_Ouminus(_976606), _976608)), _976608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976606), c_Groups_Ozero__class_Ozero(_976606)), _976608)))]]], (40845 ^ _777864) ^ [_1565211, _1565213, _1565215, _1565217] : [c_Wellfounded_Owf(_1565211, _1565213), -(c_Wellfounded_Owf(_1565215, hAPP(hAPP(c_Relation_Oinv__image(_1565211, _1565215), _1565213), _1565217)))], (18028 ^ _777864) ^ [_1088343, _1088345] : [class_Int_Onumber__ring(_1088343), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088343), hAPP(c_Int_Onumber__class_Onumber__of(_1088343), c_Int_OPls)), _1088345) = _1088345)], (37102 ^ _777864) ^ [_1472312, _1472314, _1472316, _1472318] : [-(c_Map_Orestrict__map(_1472312, _1472314, _1472316, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1472312, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1472312), _1472318), c_Orderings_Obot__class_Obot(tc_fun(_1472312, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472312, tc_Option_Ooption(_1472314)), _1472316), _1472318), c_Option_Ooption_ONone(_1472314)))], (50174 ^ _777864) ^ [_1787647, _1787649] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1787647, _1787649) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1787647), hAPP(c_Nat_OSuc, _1787649))))], (36950 ^ _777864) ^ [_1468503, _1468505, _1468507, _1468509] : [class_Groups_Ocomm__monoid__add(_1468503), 36953 ^ _777864 : [(36960 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1468505)), _1468507))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468503), _1468509), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1468507, hAPP(c_Nat_OSuc, _1468505))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468503), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468503), _1468509), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1468507, _1468505))), hAPP(_1468509, hAPP(c_Nat_OSuc, _1468505))))], (36954 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1468505)), _1468507)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468503), _1468509), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1468507, hAPP(c_Nat_OSuc, _1468505))) = c_Groups_Ozero__class_Ozero(_1468503))]]], (28952 ^ _777864) ^ [_1300645, _1300647, _1300649, _1300651, _1300653] : [c_Equiv__Relations_Oequiv(_1300645, _1300647, _1300649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300645, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1300645, _1300645, _1300649), hAPP(hAPP(c_Set_Oinsert(_1300645), _1300651), c_Orderings_Obot__class_Obot(tc_fun(_1300645, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1300645, _1300645, _1300649), hAPP(hAPP(c_Set_Oinsert(_1300645), _1300653), c_Orderings_Obot__class_Obot(tc_fun(_1300645, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1300645), _1300651), _1300647)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1300645, _1300645)), hAPP(hAPP(c_Product__Type_OPair(_1300645, _1300645), _1300653), _1300651)), _1300649)))], (29199 ^ _777864) ^ [_1306213, _1306215, _1306217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1306213), _1306217)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306213), hAPP(hAPP(c_Set_Oinsert(_1306213), _1306215), _1306217))))], (5438 ^ _777864) ^ [_861037, _861039, _861041, _861043, _861045, _861047] : [-(c_COMBC(_861047, _861043, _861039) = c_COMBC(_861045, _861041, _861037)), _861047 = _861045, _861043 = _861041, _861039 = _861037], (13978 ^ _777864) ^ [_1013967, _1013969, _1013971] : [-(hBOOL(hAPP(_1013967, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013969), _1013971)))), 13981 ^ _777864 : [(13984 ^ _777864) ^ [] : [hBOOL(hAPP(_1013967, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13982 ^ _777864) ^ [] : [-(_1013971 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13987 ^ _777864 : [(13988 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013971)))], (13994 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13990 ^ [_1013967, _1013969, _1013971]), _1013971)))], (13998 ^ _777864) ^ [] : [hBOOL(hAPP(_1013967, 13989 ^ [_1013967, _1013969, _1013971]))], (13996 ^ _777864) ^ [] : [-(_1013969 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013971), 13989 ^ [_1013967, _1013969, _1013971])), 13990 ^ [_1013967, _1013969, _1013971]))], (13992 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13990 ^ [_1013967, _1013969, _1013971])))]], 13999 ^ _777864 : [(14000 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013971), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14006 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14002 ^ [_1013967, _1013969, _1013971]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14010 ^ _777864) ^ [] : [hBOOL(hAPP(_1013967, 14001 ^ [_1013967, _1013969, _1013971]))], (14008 ^ _777864) ^ [] : [-(_1013969 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013971), 14001 ^ [_1013967, _1013969, _1013971])), 14002 ^ [_1013967, _1013969, _1013971]))], (14004 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013971), 14002 ^ [_1013967, _1013969, _1013971])))]]], (15414 ^ _777864) ^ [_1040106, _1040108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040106), _1040108)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040106), _1040108)))], (50368 ^ _777864) ^ [_1792179, _1792181, _1792183, _1792185] : [hAPP(c_List_Orev(_1792179), _1792181) = hAPP(hAPP(c_List_Olist_OCons(_1792179), _1792183), _1792185), -(_1792181 = hAPP(hAPP(c_List_Oappend(_1792179), hAPP(c_List_Orev(_1792179), _1792185)), hAPP(hAPP(c_List_Olist_OCons(_1792179), _1792183), c_List_Olist_ONil(_1792179))))], (45963 ^ _777864) ^ [_1687335, _1687337, _1687339, _1687341] : [-(hBOOL(hAPP(c_List_Odistinct(_1687335), hAPP(hAPP(c_List_Omap(_1687337, _1687335), _1687339), _1687341)))), hBOOL(hAPP(c_List_Odistinct(_1687337), _1687341)), c_Fun_Oinj__on(_1687337, _1687335, _1687339, hAPP(c_List_Oset(_1687337), _1687341))], (16652 ^ _777864) ^ [_1064302, _1064304, _1064306] : [class_Int_Onumber__ring(_1064302), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064302), hAPP(c_Int_Onumber__class_Onumber__of(_1064302), _1064304)), hAPP(c_Int_Onumber__class_Onumber__of(_1064302), _1064306)) = hAPP(c_Int_Onumber__class_Onumber__of(_1064302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064304), _1064306)))], (50570 ^ _777864) ^ [_1796423, _1796425, _1796427] : [-(hAPP(c_List_Orotate(_1796423, _1796425), hAPP(c_List_Orev(_1796423), _1796427)) = hAPP(c_List_Orev(_1796423), hAPP(c_List_Orotate(_1796423, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796423)), _1796427)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1796425, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796423)), _1796427)))), _1796427)))], (5733 ^ _777864) ^ [_870886, _870888, _870890, _870892, _870894] : [5736 ^ _777864 : [(5742 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_870894, 5734 ^ [_870886, _870888, _870890, _870892, _870894]), 5738 ^ [_870886, _870888, _870890, _870892, _870894]))], (5740 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_870892, 5735 ^ [_870886, _870888, _870890, _870892, _870894], _870888, 5738 ^ [_870886, _870888, _870890, _870892, _870894]))], (5737 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_870890, 5734 ^ [_870886, _870888, _870890, _870892, _870894]), 5735 ^ [_870886, _870888, _870890, _870892, _870894])))]], -(c_Hoare__Mirabelle_Otriple__valid(_870886, _870888, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_870886), _870890), _870892), _870894)))], (47672 ^ _777864) ^ [_1730879, _1730881, _1730883, _1730885] : [_1730879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1730881), _1730879), hAPP(hAPP(c_List_Olist_OCons(_1730881), _1730883), _1730885)) = c_List_Olist_ONil(_1730881))], (30132 ^ _777864) ^ [_1326157, _1326159, _1326161] : [class_Lattices_Oboolean__algebra(_1326157), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1326157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1326157), _1326159), _1326161)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1326157), hAPP(c_Groups_Ouminus__class_Ouminus(_1326157), _1326159)), hAPP(c_Groups_Ouminus__class_Ouminus(_1326157), _1326161)))], (168 ^ _777864) ^ [_780254, _780256, _780258, _780260, _780262, _780264, _780266, _780268] : [-(c_Orderings_Oorder_Omono(_780266, _780262, _780258, _780254)), c_Orderings_Oorder_Omono(_780268, _780264, _780260, _780256), _780268 = _780266, _780264 = _780262, _780260 = _780258, _780256 = _780254], (40985 ^ _777864) ^ [_1567739, _1567741, _1567743] : [c_Wellfounded_Owf(_1567739, _1567741), -(hBOOL(hAPP(hAPP(c_member(_1567739), _1567743), c_Wellfounded_Oacc(_1567739, _1567741))))], (22753 ^ _777864) ^ [_1171613, _1171615, _1171617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171613, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171613, tc_HOL_Obool)), _1171615)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171613, tc_HOL_Obool)), _1171617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171613, tc_HOL_Obool)), _1171617), _1171615)))], (49007 ^ _777864) ^ [_1763092, _1763094, _1763096] : [class_Orderings_Olinorder(_1763092), -(c_Big__Operators_Olattice_OSup__fin(_1763092, c_Orderings_Oord__class_Omax(_1763092), hAPP(c_List_Oset(_1763092), hAPP(hAPP(c_List_Olist_OCons(_1763092), _1763094), _1763096))) = hAPP(c_List_Ofoldl(_1763092, _1763092, c_Orderings_Oord__class_Omax(_1763092), _1763094), _1763096))], (19098 ^ _777864) ^ [_1106170, _1106172] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106170))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106172))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106172)))], (6911 ^ _777864) ^ [_891486, _891488] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891486), hAPP(c_Nat_OSuc, _891488)))), 6912 ^ _777864 : [(6915 ^ _777864) ^ [_891574] : [_891486 = hAPP(c_Nat_OSuc, _891574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891574), _891488))], (6913 ^ _777864) ^ [] : [_891486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (38176 ^ _777864) ^ [_1494323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1494323), c_Orderings_Otop__class_Otop(tc_fun(_1494323, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1494323)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1494323), tc_HOL_Obool)))))], (13475 ^ _777864) ^ [_1004518, _1004520, _1004522, _1004524] : [class_Divides_Osemiring__div(_1004518), -(c_Divides_Odiv__class_Omod(_1004518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004518), _1004520), _1004522), _1004524) = c_Divides_Odiv__class_Omod(_1004518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004518), c_Divides_Odiv__class_Omod(_1004518, _1004520, _1004524)), _1004522), _1004524))], (28374 ^ _777864) ^ [_1286498, _1286500, _1286502, _1286504, _1286506, _1286508] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool)), _1286500), _1286502)), c_Wellfounded_Omax__ext(_1286498, _1286504))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool)), _1286506), _1286508)), c_Wellfounded_Omax__ext(_1286498, _1286504))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286498, tc_HOL_Obool), tc_fun(_1286498, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286498, tc_HOL_Obool)), _1286500), _1286506)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286498, tc_HOL_Obool)), _1286502), _1286508))), c_Wellfounded_Omax__ext(_1286498, _1286504))))], (46539 ^ _777864) ^ [_1702692, _1702694, _1702696, _1702698] : [c_List_Olistrelp(_1702692, hAPP(hAPP(c_COMBC(_1702692, tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_fun(_1702692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1702692, tc_fun(tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_fun(_1702692, tc_HOL_Obool)), _1702692), c_COMBC(_1702692, tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1702692, tc_prod(_1702692, _1702692)), tc_fun(_1702692, tc_fun(tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_HOL_Obool)), _1702692), hAPP(c_COMBB(tc_prod(_1702692, _1702692), tc_fun(tc_fun(tc_prod(_1702692, _1702692), tc_HOL_Obool), tc_HOL_Obool), _1702692), c_member(tc_prod(_1702692, _1702692)))), c_Product__Type_OPair(_1702692, _1702692)))), _1702694), _1702696, _1702698), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702692), tc_List_Olist(_1702692))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702692), tc_List_Olist(_1702692)), _1702696), _1702698)), c_List_Olistrel(_1702692, _1702694))))], (24729 ^ _777864) ^ [_1211805, _1211807, _1211809, _1211811, _1211813] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1211805, _1211807, tc_HOL_Obool, _1211809), _1211811), _1211813)), -(hBOOL(hAPP(_1211809, hAPP(hAPP(c_Product__Type_OPair(_1211805, _1211807), _1211811), _1211813))))], (13726 ^ _777864) ^ [_1009062, _1009064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1009062), _1009064)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1009062, _1009064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1009062), _1009064))], (48880 ^ _777864) ^ [_1760395, _1760397, _1760399, _1760401, _1760403, _1760405] : [-(hAPP(c_List_Ofoldl(_1760395, _1760397, _1760399, _1760401), hAPP(hAPP(c_List_Oappend(_1760397), _1760403), _1760405)) = hAPP(c_List_Ofoldl(_1760395, _1760397, _1760399, hAPP(c_List_Ofoldl(_1760395, _1760397, _1760399, _1760401), _1760403)), _1760405))], (37753 ^ _777864) ^ [_1486176, _1486178, _1486180] : [class_Orderings_Olinorder(_1486176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486176), _1486178), _1486180)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486176, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1486176, _1486178, _1486180)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486176), _1486180)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1486176), _1486178))], (19118 ^ _777864) ^ [_1106509, _1106511] : [class_Int_Onumber__ring(_1106509), class_Int_Oring__char__0(_1106509), 19125 ^ _777864 : [(19132 ^ _777864) ^ [] : [c_Int_Oiszero(_1106509, hAPP(c_Int_Onumber__class_Onumber__of(_1106509), _1106511)), -(c_Int_Oiszero(_1106509, hAPP(c_Int_Onumber__class_Onumber__of(_1106509), c_Int_OBit0(_1106511))))], (19126 ^ _777864) ^ [] : [c_Int_Oiszero(_1106509, hAPP(c_Int_Onumber__class_Onumber__of(_1106509), c_Int_OBit0(_1106511))), -(c_Int_Oiszero(_1106509, hAPP(c_Int_Onumber__class_Onumber__of(_1106509), _1106511)))]]], (23645 ^ _777864) ^ [_1190798, _1190800, _1190802, _1190804] : [class_Orderings_Olinorder(_1190798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190798), _1190800), _1190802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190798), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190798), _1190800), _1190804)), _1190802)))], (26757 ^ _777864) ^ [_1250249, _1250251, _1250253, _1250255] : [26758 ^ _777864 : [(26761 ^ _777864) ^ [] : [_1250251 = _1250255], (26759 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1250249), _1250251), _1250253))]], -(hBOOL(hAPP(hAPP(c_member(_1250249), _1250251), hAPP(hAPP(c_Set_Oinsert(_1250249), _1250255), _1250253))))], (19004 ^ _777864) ^ [_1104527, _1104529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104527)), c_Int_OBit1(_1104529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104527), _1104529)))], (22380 ^ _777864) ^ [_1164817] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1164817)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1164817)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7208 ^ _777864) ^ [_896423, _896425, _896427, _896429, _896431, _896433] : [c_Com_Ocom_OCond(_896423, _896425, _896427) = c_Com_Ocom_OCond(_896429, _896431, _896433), 7211 ^ _777864 : [(7216 ^ _777864) ^ [] : [-(_896427 = _896433)], (7214 ^ _777864) ^ [] : [-(_896425 = _896431)], (7212 ^ _777864) ^ [] : [-(_896423 = _896429)]]], (36886 ^ _777864) ^ [_1467027, _1467029, _1467031, _1467033, _1467035] : [hAPP(_1467027, _1467029) = hAPP(c_Option_Ooption_OSome(_1467031), _1467033), -(hBOOL(hAPP(hAPP(c_member(_1467031), _1467033), c_Map_Oran(_1467035, _1467031, _1467027))))], (51183 ^ _777864) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (26127 ^ _777864) ^ [_1237116, _1237118, _1237120] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1237116, _1237118, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1237116)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1237116), _1237120), c_Com_Ocom_OSKIP), _1237120)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237116), tc_HOL_Obool)))))], (50967 ^ _777864) ^ [_1805945, _1805947, _1805949] : [hBOOL(hAPP(c_List_Odistinct(_1805945), _1805947)), hBOOL(hAPP(hAPP(c_member(_1805945), _1805949), hAPP(c_List_Oset(_1805945), _1805947))), -(c_List_OdropWhile(_1805945, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1805945), c_fNot), hAPP(hAPP(c_COMBC(_1805945, _1805945, tc_HOL_Obool), c_fequal), _1805949)), hAPP(c_List_Orev(_1805945), _1805947)) = hAPP(hAPP(c_List_Olist_OCons(_1805945), _1805949), hAPP(c_List_Orev(_1805945), c_List_OtakeWhile(_1805945, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1805945), c_fNot), hAPP(hAPP(c_COMBC(_1805945, _1805945, tc_HOL_Obool), c_fequal), _1805949)), _1805947))))], (30208 ^ _777864) ^ [_1327970, _1327972, _1327974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327970, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327970, tc_HOL_Obool)), _1327972), _1327974)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327970, tc_HOL_Obool)), _1327972), _1327974)) = _1327972)], (51353 ^ _777864) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (7218 ^ _777864) ^ [_896570, _896572, _896574, _896576, _896578, _896580] : [-(c_Com_Ocom_OCond(_896570, _896572, _896574) = c_Com_Ocom_OCond(_896576, _896578, _896580)), _896570 = _896576, _896572 = _896578, _896574 = _896580], (40195 ^ _777864) ^ [_1540902, _1540904] : [hAPP(c_Set_OCollect(_1540902), _1540904) = c_Orderings_Obot__class_Obot(tc_fun(_1540902, tc_HOL_Obool)), 40198 ^ _777864 : [(40199 ^ _777864) ^ [_1540987] : [hBOOL(hAPP(_1540904, _1540987))]]], (47766 ^ _777864) ^ [_1733055, _1733057, _1733059, _1733061, _1733063] : [-(hAPP(hAPP(c_List_Ozip(_1733055, _1733057), hAPP(hAPP(c_List_Olist_OCons(_1733055), _1733059), _1733061)), _1733063) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1733055, _1733057)), _1733057, c_List_Olist_ONil(tc_prod(_1733055, _1733057)), hAPP(hAPP(c_COMBC(_1733057, tc_fun(tc_List_Olist(_1733057), tc_List_Olist(tc_prod(_1733055, _1733057))), tc_fun(tc_List_Olist(_1733057), tc_List_Olist(tc_prod(_1733055, _1733057)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1733055, _1733057)), tc_List_Olist(tc_prod(_1733055, _1733057))), tc_fun(tc_fun(tc_List_Olist(_1733057), tc_List_Olist(tc_prod(_1733055, _1733057))), tc_fun(tc_List_Olist(_1733057), tc_List_Olist(tc_prod(_1733055, _1733057)))), _1733057), c_COMBB(tc_List_Olist(tc_prod(_1733055, _1733057)), tc_List_Olist(tc_prod(_1733055, _1733057)), tc_List_Olist(_1733057))), hAPP(hAPP(c_COMBB(tc_prod(_1733055, _1733057), tc_fun(tc_List_Olist(tc_prod(_1733055, _1733057)), tc_List_Olist(tc_prod(_1733055, _1733057))), _1733057), c_List_Olist_OCons(tc_prod(_1733055, _1733057))), hAPP(c_Product__Type_OPair(_1733055, _1733057), _1733059)))), hAPP(c_List_Ozip(_1733055, _1733057), _1733061))), _1733063))], (23621 ^ _777864) ^ [_1190330, _1190332, _1190334] : [class_Orderings_Olinorder(_1190330), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190330), _1190332), _1190334) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190330), _1190334), _1190332))], (27894 ^ _777864) ^ [_1274918, _1274920, _1274922] : [class_Lattices_Osemilattice__sup(_1274918), 27897 ^ _777864 : [(27904 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274918), _1274920), _1274922) = _1274922, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274918), _1274920), _1274922)))], (27898 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274918), _1274920), _1274922)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274918), _1274920), _1274922) = _1274922)]]], (7570 ^ _777864) ^ [_903436, _903438] : [c_Option_Ois__none(_903436, _903438), -(_903438 = c_Option_Ooption_ONone(_903436))], (12852 ^ _777864) ^ [_993712, _993714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _993712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _993714)), 12859 ^ _777864 : [(12866 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _993712), _993714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _993712)), hAPP(c_Int_Onat, _993714))))], (12860 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _993712)), hAPP(c_Int_Onat, _993714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _993712), _993714)))]]], (5918 ^ _777864) ^ [_875135, _875137] : [hAPP(c_Nat_OSuc, _875135) = hAPP(c_Nat_OSuc, _875137), -(_875135 = _875137)], (3550 ^ _777864) ^ [_831793, _831795, _831797, _831799, _831801, _831803, _831805, _831807] : [-(c_Random__Sequence_Omap(_831807, _831803, _831799, _831795) = c_Random__Sequence_Omap(_831805, _831801, _831797, _831793)), _831807 = _831805, _831803 = _831801, _831799 = _831797, _831795 = _831793], (17608 ^ _777864) ^ [_1081635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1081635), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081635)))], (50504 ^ _777864) ^ [_1795155, _1795157] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795155)), hAPP(c_List_Orev(_1795155), _1795157)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795155)), _1795157))], (20340 ^ _777864) ^ [_1128195, _1128197, _1128199] : [class_Rings_Odivision__ring(_1128195), -(_1128197 = c_Groups_Ozero__class_Ozero(_1128195)), 20347 ^ _777864 : [(20354 ^ _777864) ^ [] : [_1128199 = _1128197, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128195), _1128199), _1128197) = c_Groups_Oone__class_Oone(_1128195))], (20348 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128195), _1128199), _1128197) = c_Groups_Oone__class_Oone(_1128195), -(_1128199 = _1128197)]]], (49482 ^ _777864) ^ [_1773409, _1773411, _1773413, _1773415] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773409)), _1773411))), c_List_Ofoldr(tc_List_Olist(_1773413), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1773413)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1773413))), _1773415, 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(_1773409)), _1773411)), c_List_Ofoldr(tc_List_Olist(_1773413), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1773413)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1773413), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1773413)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1773413)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1773413), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1773413)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1773413), tc_List_Olist(_1773413), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1773413)))), _1773415), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (25265 ^ _777864) ^ [_1220992, _1220994] : [-(_1220992 = _1220994), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220992), _1220994)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220994), _1220992))], (45130 ^ _777864) ^ [_1667315, _1667317, _1667319, _1667321, _1667323] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1667315, _1667315)), hAPP(hAPP(c_Product__Type_OPair(_1667315, _1667315), _1667317), _1667319)), c_Transitive__Closure_Ortrancl(_1667315, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1667315, _1667315), tc_HOL_Obool)), _1667321), _1667323)))), 45136 ^ _777864 : [(45142 ^ _777864) ^ [] : [45138 ^ [_1667315, _1667317, _1667319, _1667321, _1667323] = 45135 ^ [_1667315, _1667317, _1667319, _1667321, _1667323]], (45140 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667315, _1667315)), hAPP(hAPP(c_Product__Type_OPair(_1667315, _1667315), 45138 ^ [_1667315, _1667317, _1667319, _1667321, _1667323]), 45135 ^ [_1667315, _1667317, _1667319, _1667321, _1667323])), _1667323)))], (45137 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667315, _1667315)), hAPP(hAPP(c_Product__Type_OPair(_1667315, _1667315), 45135 ^ [_1667315, _1667317, _1667319, _1667321, _1667323]), _1667319)), c_Transitive__Closure_Ortrancl(_1667315, _1667321))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667315, _1667315)), hAPP(hAPP(c_Product__Type_OPair(_1667315, _1667315), _1667317), _1667319)), c_Transitive__Closure_Ortrancl(_1667315, _1667321))))], (43721 ^ _777864) ^ [_1630861, _1630863, _1630865, _1630867, _1630869] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630861, tc_fun(_1630863, tc_HOL_Obool)), _1630865), hAPP(hAPP(c_COMBC(_1630861, tc_fun(_1630863, tc_HOL_Obool), tc_fun(_1630863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1630863, tc_HOL_Obool), tc_fun(tc_fun(_1630863, tc_HOL_Obool), tc_fun(_1630863, tc_HOL_Obool)), _1630861), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630863, tc_HOL_Obool))), _1630867)), _1630869)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630863, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630861, tc_fun(_1630863, tc_HOL_Obool)), _1630865), _1630867)), _1630869))], (28875 ^ _777864) ^ [_1299534, _1299536] : [c_Nat__Transfer_Onat__set(_1299534), c_Nat__Transfer_Onat__set(_1299536), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1299534), _1299536)))], (8962 ^ _777864) ^ [_926743, _926745, _926747] : [class_Groups_Oordered__ab__group__add(_926743), 8965 ^ _777864 : [(8972 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926743), _926747), _926745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926743), hAPP(c_Groups_Ouminus__class_Ouminus(_926743), _926745)), hAPP(c_Groups_Ouminus__class_Ouminus(_926743), _926747))))], (8966 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926743), hAPP(c_Groups_Ouminus__class_Ouminus(_926743), _926745)), hAPP(c_Groups_Ouminus__class_Ouminus(_926743), _926747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926743), _926747), _926745)))]]], (2150 ^ _777864) ^ [_809335, _809337, _809339, _809341, _809343, _809345, _809347, _809349, _809351, _809353] : [-(c_Product__Type_Oprod_Oprod__size(_809353, _809349, _809345, _809341, _809337) = c_Product__Type_Oprod_Oprod__size(_809351, _809347, _809343, _809339, _809335)), _809353 = _809351, _809349 = _809347, _809345 = _809343, _809341 = _809339, _809337 = _809335], (10904 ^ _777864) ^ [_959430, _959432, _959434] : [10905 ^ _777864 : [(10908 ^ _777864) ^ [] : [_959430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10906 ^ _777864) ^ [] : [_959432 = _959434]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959430), _959432) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959430), _959434))], (10053 ^ _777864) ^ [_945895, _945897] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945895), _945897)), _945895 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _945897 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (16634 ^ _777864) ^ [_1063867, _1063869, _1063871, _1063873] : [class_Int_Onumber__ring(_1063867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063867), hAPP(c_Int_Onumber__class_Onumber__of(_1063867), _1063869)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063867), hAPP(c_Int_Onumber__class_Onumber__of(_1063867), _1063871)), _1063873)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063867), hAPP(c_Int_Onumber__class_Onumber__of(_1063867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1063869), _1063871))), _1063873))], (25587 ^ _777864) ^ [_1226593, _1226595, _1226597, _1226599] : [class_Divides_Osemiring__div(_1226593), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226593), _1226595), _1226597)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226593), _1226599), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226593), _1226597), _1226595)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226593), _1226599), _1226597)), _1226595))], (46288 ^ _777864) ^ [_1695196, _1695198] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1695196), hAPP(c_List_Oset(_1695196), _1695198))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695196)), _1695198))))], (15854 ^ _777864) ^ [_1049468, _1049470, _1049472, _1049474, _1049476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049468), _1049470)), 15857 ^ _777864 : [(15864 ^ _777864) ^ [] : [_1049474 = 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), _1049470), _1049468)), _1049472)), _1049476), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049468), _1049472)), _1049474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049470), _1049472)), _1049476))], (15858 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049468), _1049472)), _1049474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049470), _1049472)), _1049476), -(_1049474 = 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), _1049470), _1049468)), _1049472)), _1049476))]]], (8046 ^ _777864) ^ [_911981, _911983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911981), _911983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911981)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911983))))], (36030 ^ _777864) ^ [_1448505, _1448507] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1448505), _1448507))))], (27512 ^ _777864) ^ [_1267792, _1267794, _1267796] : [class_Rings_Oring__1(_1267792), hBOOL(hAPP(hAPP(c_member(_1267792), _1267794), c_Int_Oring__1__class_OInts(_1267792))), hBOOL(hAPP(hAPP(c_member(_1267792), _1267796), c_Int_Oring__1__class_OInts(_1267792))), -(hBOOL(hAPP(hAPP(c_member(_1267792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267792), _1267794), _1267796)), c_Int_Oring__1__class_OInts(_1267792))))], (12824 ^ _777864) ^ [_993149] : [-(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), _993149))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (48971 ^ _777864) ^ [_1762326, _1762328] : [class_Complete__Lattice_Ocomplete__lattice(_1762326), -(c_Complete__Lattice_OInf__class_OInf(_1762326, hAPP(c_List_Oset(_1762326), _1762328)) = hAPP(c_List_Ofoldl(_1762326, _1762326, c_Lattices_Osemilattice__inf__class_Oinf(_1762326), c_Orderings_Otop__class_Otop(_1762326)), _1762328))], (36150 ^ _777864) ^ [_1450730] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1450730) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1450730))], (35034 ^ _777864) ^ [_1429000, _1429002, _1429004, _1429006] : [c_Fun_Oinj__on(_1429000, _1429002, _1429004, _1429006), 35037 ^ _777864 : [(35038 ^ _777864) ^ [_1429108] : [hBOOL(hAPP(hAPP(c_member(_1429000), _1429108), _1429006)), 35041 ^ _777864 : [(35042 ^ _777864) ^ [_1429210] : [hBOOL(hAPP(hAPP(c_member(_1429000), _1429210), _1429006)), hAPP(_1429004, _1429108) = hAPP(_1429004, _1429210), -(_1429108 = _1429210)]]]]], (43489 ^ _777864) ^ [_1625444, _1625446, _1625448] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1625444, _1625444), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1625444, _1625444), _1625446)), c_Transitive__Closure_Ortrancl(_1625444, _1625446)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1625444, _1625444), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625444, _1625444)), hAPP(hAPP(c_Product__Type_OPair(_1625444, _1625444), _1625448), _1625448)), c_Transitive__Closure_Otrancl(_1625444, _1625446)))], (38254 ^ _777864) ^ [] : [-(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)) = 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_1400062), hAPP(hAPP(c_COMBB(tc_fun(_1400056, tc_HOL_Obool), tc_fun(_1400056, tc_HOL_Obool), _1400060), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400056, tc_HOL_Obool)), _1400058)), _1400064)))], (51147 ^ _777864) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (26085 ^ _777864) ^ [_1236076, _1236078] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236076), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236078))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236076), _1236078)))], (23407 ^ _777864) ^ [_1186377] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1186377), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6374 ^ _777864) ^ [_883063, _883065, _883067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883063), _883065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544347, _1544345), hAPP(hAPP(c_COMBC(_1544347, _1544345, _1544345), hAPP(hAPP(c_COMBS(_1544347, _1544345, tc_fun(_1544345, _1544345)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1544345, tc_fun(_1544345, _1544345)), _1544347), c_If(_1544345)), hAPP(hAPP(c_COMBC(_1544347, tc_fun(_1544347, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544347)), _1544353))), _1544351)), c_Groups_Ozero__class_Ozero(_1544345))), _1544349))], (6532 ^ _777864) ^ [_885724, _885726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885724), _885726)), _885724))], (43086 ^ _777864) ^ [_1616185, _1616187, _1616189, _1616191, _1616193, _1616195] : [c_Finite__Set_Ofun__left__comm(_1616185, _1616187, _1616189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616185), _1616191)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1616185, _1616187, _1616189), _1616193), hAPP(hAPP(c_Set_Oinsert(_1616185), _1616195), _1616191)) = hAPP(hAPP(_1616189, _1616195), hAPP(hAPP(c_Finite__Set_Ofold(_1616185, _1616187, _1616189), _1616193), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616185, tc_HOL_Obool)), _1616191), hAPP(hAPP(c_Set_Oinsert(_1616185), _1616195), c_Orderings_Obot__class_Obot(tc_fun(_1616185, tc_HOL_Obool)))))))], (9132 ^ _777864) ^ [_929734, _929736, _929738, _929740, _929742] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_929734), 9135 ^ _777864 : [(9136 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929736), _929738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929740), _929742)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929736), _929742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929740), _929738)), -(_929736 = _929740), -(_929738 = _929742)], (9146 ^ _777864) ^ [] : [9147 ^ _777864 : [(9150 ^ _777864) ^ [] : [_929738 = _929742], (9148 ^ _777864) ^ [] : [_929736 = _929740]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929736), _929738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929740), _929742)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929736), _929742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929734), _929740), _929738)))]]], (44035 ^ _777864) ^ [_1640665, _1640667, _1640669, _1640671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640665, _1640665)), hAPP(hAPP(c_Product__Type_OPair(_1640665, _1640665), _1640667), _1640669)), hAPP(c_Relation_Oconverse(_1640665, _1640665), c_Transitive__Closure_Otrancl(_1640665, _1640671)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640665, _1640665)), hAPP(hAPP(c_Product__Type_OPair(_1640665, _1640665), _1640667), _1640669)), c_Transitive__Closure_Otrancl(_1640665, hAPP(c_Relation_Oconverse(_1640665, _1640665), _1640671)))))], (46571 ^ _777864) ^ [_1704124, _1704126, _1704128] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1704124, tc_HOL_Obool)), hAPP(c_List_Oset(_1704124), _1704126)), hAPP(c_List_Oset(_1704124), hAPP(hAPP(c_List_Olist_OCons(_1704124), _1704128), _1704126)))))], (33306 ^ _777864) ^ [_1389878, _1389880, _1389882] : [class_Orderings_Olinorder(_1389878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389878), _1389880), _1389882)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389878, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1389878, _1389880, _1389882)), hAPP(hAPP(c_Set_Oinsert(_1389878), _1389882), c_Orderings_Obot__class_Obot(tc_fun(_1389878, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1389878, _1389880, _1389882))], (17954 ^ _777864) ^ [_1087356] : [-(c_Int_Osucc(c_Int_Opred(_1087356)) = _1087356)], (40630 ^ _777864) ^ [_1556857, _1556859] : [c_Relation_Orefl__on(_1556857, c_Orderings_Otop__class_Otop(tc_fun(_1556857, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1556857, _1556857)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556857, _1556857, tc_HOL_Obool), _1556859))), -(c_Predicate_Oreflp(_1556857, _1556859))], (4128 ^ _777864) ^ [_840920, _840922, _840924, _840926, _840928, _840930, _840932, _840934] : [-(c_Nitpick_Osetsum_H(_840934, _840930, _840926, _840922) = c_Nitpick_Osetsum_H(_840932, _840928, _840924, _840920)), _840934 = _840932, _840930 = _840928, _840926 = _840924, _840922 = _840920], (51171 ^ _777864) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (7530 ^ _777864) ^ [_902591, _902593, _902595, _902597] : [class_Rings_Ocomm__semiring__1(_902591), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902591), _902593), _902595)), _902597) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902591), _902593), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902591), _902595), _902597)))], (48706 ^ _777864) ^ [_1757199, _1757201, _1757203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757201)), _1757203))), -(hAPP(hAPP(c_List_Oappend(_1757201), hAPP(hAPP(c_List_Otake(_1757201), _1757199), _1757203)), hAPP(hAPP(c_List_Olist_OCons(_1757201), hAPP(c_List_Ohd(_1757201), hAPP(hAPP(c_List_Odrop(_1757201), _1757199), _1757203))), c_List_Olist_ONil(_1757201))) = hAPP(hAPP(c_List_Otake(_1757201), hAPP(c_Nat_OSuc, _1757199)), _1757203))], (21850 ^ _777864) ^ [_1155902, _1155904] : [21851 ^ _777864 : [(21854 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1155904), _1155902))], (21852 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1155902), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1155902, _1155904) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (33663 ^ _777864) ^ [_1398089, _1398091, _1398093, _1398095] : [_1398089 = c_Orderings_Obot__class_Obot(tc_fun(_1398091, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398091, tc_fun(_1398093, tc_HOL_Obool)), _1398089), hAPP(c_COMBK(tc_fun(_1398093, tc_HOL_Obool), _1398091), _1398095)) = c_Orderings_Obot__class_Obot(tc_fun(_1398093, tc_HOL_Obool)))], (17080 ^ _777864) ^ [_1072278, _1072280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072278)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1072278), _1072280)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1072278)), _1072280))], (28162 ^ _777864) ^ [_1279972, _1279974, _1279976] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279972, tc_HOL_Obool)), _1279974), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279972, tc_HOL_Obool)), _1279974), _1279976)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279972, tc_HOL_Obool)), _1279974), _1279976))], (24575 ^ _777864) ^ [_1208991, _1208993] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1208991)), hAPP(c_Code__Numeral_Oof__nat, _1208993)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1208991), _1208993)))], (44909 ^ _777864) ^ [_1662335, _1662337, _1662339] : [class_Complete__Lattice_Ocomplete__lattice(_1662335), hBOOL(hAPP(hAPP(c_member(_1662335), _1662337), _1662339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1662335), _1662337), c_Complete__Lattice_OSup__class_OSup(_1662335, _1662339))))], (6577 ^ _777864) ^ [_886484, _886486] : [class_Groups_Ocomm__monoid__add(_886484), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886484), c_Groups_Ozero__class_Ozero(_886484)), _886486) = _886486)], (39347 ^ _777864) ^ [_1522203, _1522205] : [class_Orderings_Olinorder(_1522203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522203), _1522205)), -(c_Big__Operators_Olinorder__class_OMin(_1522203, _1522205) = hAPP(c_Finite__Set_Ofold1(_1522203, c_Orderings_Oord__class_Omin(_1522203)), _1522205))], (24169 ^ _777864) ^ [_1200929, _1200931, _1200933, _1200935] : [class_Orderings_Olinorder(_1200929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200929), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200929), _1200931), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200929), _1200933), _1200935))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200929), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200929), _1200931), _1200933)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200929), _1200931), _1200935)))))], (23307 ^ _777864) ^ [_1184071, _1184073, _1184075, _1184077] : [-(hAPP(c_Nat_Onat_Onat__rec(_1184071, _1184073, _1184075), hAPP(c_Nat_OSuc, _1184077)) = hAPP(hAPP(_1184075, _1184077), hAPP(c_Nat_Onat_Onat__rec(_1184071, _1184073, _1184075), _1184077)))], (38072 ^ _777864) ^ [] : [-(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)))], (33652 ^ _777864) ^ [_1397786, _1397788, _1397790, _1397792] : [33654 ^ _777864 : [(33657 ^ _777864) ^ [] : [hAPP(_1397792, 33653 ^ [_1397786, _1397788, _1397790, _1397792]) = c_Orderings_Obot__class_Obot(tc_fun(_1397786, tc_HOL_Obool))], (33655 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397788), 33653 ^ [_1397786, _1397788, _1397790, _1397792]), _1397790)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1397786, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397788, tc_fun(_1397786, tc_HOL_Obool)), _1397790), _1397792))], (50558 ^ _777864) ^ [_1796194, _1796196] : [-(_1796194 = c_List_Olist_ONil(_1796196)), -(hAPP(c_List_Ohd(_1796196), hAPP(c_List_Orev(_1796196), _1796194)) = c_List_Olast(_1796196, _1796194))], (48932 ^ _777864) ^ [_1761598, _1761600] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761598), _1761600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48935 ^ _777864 : [(48938 ^ _777864) ^ [_1761712] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1761712), hAPP(c_List_Oset(tc_Nat_Onat), _1761600))), -(_1761712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48936 ^ _777864) ^ [] : [-(_1761598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (992 ^ _777864) ^ [_793032, _793034] : [-(class_Groups_Oordered__ab__group__add__abs(_793032)), _793034 = _793032, class_Groups_Oordered__ab__group__add__abs(_793034)], (17102 ^ _777864) ^ [_1072671, _1072673, _1072675] : [class_Groups_Omonoid__mult(_1072671), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072671), hAPP(hAPP(c_Power_Opower__class_Opower(_1072671), _1072673), _1072675)), _1072673) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072671), _1072673), hAPP(hAPP(c_Power_Opower__class_Opower(_1072671), _1072673), _1072675)))], (30368 ^ _777864) ^ [_1331644, _1331646, _1331648, _1331650, _1331652, _1331654, _1331656] : [c_Equiv__Relations_Oequiv(_1331644, _1331646, _1331648), hBOOL(hAPP(hAPP(c_member(tc_fun(_1331644, tc_HOL_Obool)), _1331650), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1331644), _1331646), _1331648))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1331644, tc_HOL_Obool)), _1331652), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1331644), _1331646), _1331648))), hBOOL(hAPP(hAPP(c_member(_1331644), _1331654), _1331650)), hBOOL(hAPP(hAPP(c_member(_1331644), _1331656), _1331652)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1331644, _1331644)), hAPP(hAPP(c_Product__Type_OPair(_1331644, _1331644), _1331654), _1331656)), _1331648)), -(_1331650 = _1331652)], (25959 ^ _777864) ^ [_1233607, _1233609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1233607)), 25962 ^ _777864 : [(25969 ^ _777864) ^ [] : [_1233609 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233607), _1233609)), _1233607)))], (25963 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233607), _1233609)), _1233607)), -(_1233609 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (13469 ^ _777864) ^ [_1004383, _1004385, _1004387, _1004389] : [class_Divides_Osemiring__div(_1004383), -(c_Divides_Odiv__class_Omod(_1004383, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004383), _1004385), _1004387), _1004389) = c_Divides_Odiv__class_Omod(_1004383, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004383), _1004385), c_Divides_Odiv__class_Omod(_1004383, _1004387, _1004389)), _1004389))], (22038 ^ _777864) ^ [_1158843, _1158845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158845)), -(c_Divides_OposDivAlg(_1158843, _1158845) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1158843), _1158845)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1158843, _1158845)))], (25771 ^ _777864) ^ [_1229958, _1229960, _1229962, _1229964] : [class_Rings_Ocomm__ring(_1229958), class_Rings_Odvd(_1229958), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229958), _1229960), _1229962)), 25782 ^ _777864 : [(25789 ^ _777864) ^ [_1230384, _1230386] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229958), _1229960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1229958), _1230386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229958), _1230384), _1229962))), _1229964))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229958), _1229960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229958), _1230386), _1229964))))], (25783 ^ _777864) ^ [_1230211, _1230213] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229958), _1229960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229958), _1230213), _1229964))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229958), _1229960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1229958), _1230213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229958), _1230211), _1229962))), _1229964))))]]], (28448 ^ _777864) ^ [_1289250, _1289252, _1289254, _1289256, _1289258, _1289260] : [_1289250 = hAPP(_1289252, _1289254), hBOOL(hAPP(hAPP(c_member(_1289256), _1289254), _1289258)), -(hBOOL(hAPP(hAPP(c_member(_1289260), _1289250), hAPP(c_Set_Oimage(_1289256, _1289260, _1289252), _1289258))))], (41179 ^ _777864) ^ [_1572208, _1572210, _1572212] : [-(hAPP(c_Set_Oimage(tc_prod(_1572208, _1572210), _1572210, c_Product__Type_Osnd(_1572208, _1572210)), _1572212) = hAPP(c_Relation_ORange(_1572208, _1572210), _1572212))], (18688 ^ _777864) ^ [_1098976, _1098978] : [class_Groups_Omonoid__mult(_1098976), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1098976), _1098978), 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(_1098976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098976), _1098978), _1098978)), _1098978))], (23551 ^ _777864) ^ [_1188945, _1188947, _1188949] : [class_Orderings_Olinorder(_1188945), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188945), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188945), _1188947), _1188949)), _1188949)))], (1342 ^ _777864) ^ [_797407, _797409] : [-(class_Groups_Ouminus(_797407)), _797409 = _797407, class_Groups_Ouminus(_797409)], (19034 ^ _777864) ^ [_1105038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1105038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1105038))))], (28546 ^ _777864) ^ [_1291535, _1291537, _1291539, _1291541] : [_1291541 = c_Orderings_Obot__class_Obot(tc_fun(_1291537, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1291535, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1291537, _1291535, _1291539), _1291541))], (2724 ^ _777864) ^ [_818412, _818414, _818416, _818418] : [-(c_Code__Numeral_Onat__of__aux(_818418, _818414) = c_Code__Numeral_Onat__of__aux(_818416, _818412)), _818418 = _818416, _818414 = _818412], (43735 ^ _777864) ^ [_1631638, _1631640] : [-(hAPP(c_Relation_Oconverse(_1631638, _1631638), c_Relation_OId__on(_1631638, _1631640)) = c_Relation_OId__on(_1631638, _1631640))], (29996 ^ _777864) ^ [_1323375, _1323377, _1323379, _1323381] : [class_Lattices_Osemilattice__inf(_1323375), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323375), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323375), _1323377), _1323379)), _1323381) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323375), _1323377), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323375), _1323379), _1323381)))], (30492 ^ _777864) ^ [_1335156, _1335158, _1335160, _1335162] : [hBOOL(hAPP(hAPP(c_member(_1335156), _1335158), c_SetInterval_Oord_OlessThan(_1335156, _1335160, _1335162))), -(hBOOL(hAPP(hAPP(_1335160, _1335158), _1335162)))], (50496 ^ _777864) ^ [_1794994, _1794996] : [hBOOL(hAPP(c_List_Odistinct(_1794994), _1794996)), -(hBOOL(hAPP(c_List_Odistinct(_1794994), hAPP(c_List_Orev(_1794994), _1794996))))], (17962 ^ _777864) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50213 ^ _777864) ^ [_1788415, _1788417] : [class_Orderings_Olinorder(_1788415), hBOOL(hAPP(c_Finite__Set_Ofinite(_1788415), _1788417)), 50220 ^ _777864 : [(50225 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1788415), c_List_Olinorder__class_Osorted__list__of__set(_1788415, _1788417))))], (50223 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1788415, c_List_Olinorder__class_Osorted__list__of__set(_1788415, _1788417)))], (50221 ^ _777864) ^ [] : [-(hAPP(c_List_Oset(_1788415), c_List_Olinorder__class_Osorted__list__of__set(_1788415, _1788417)) = _1788417)]]], (8834 ^ _777864) ^ [_924819] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924819))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15592 ^ _777864) ^ [_1043414, _1043416, _1043418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043414), _1043416)), _1043418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043414), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043418), _1043416))))], (34009 ^ _777864) ^ [_1407298, _1407300, _1407302, _1407304, _1407306, _1407308, _1407310] : [c_Equiv__Relations_Oequiv(_1407298, _1407300, _1407302), c_Equiv__Relations_Ocongruent(_1407298, tc_fun(_1407304, tc_HOL_Obool), _1407302, _1407306), hBOOL(hAPP(hAPP(c_member(tc_fun(_1407298, tc_HOL_Obool)), _1407308), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1407298), _1407300), _1407302))), 34023 ^ _777864 : [(34026 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1407304, tc_HOL_Obool)), hAPP(_1407306, 34022 ^ [_1407298, _1407300, _1407302, _1407304, _1407306, _1407308, _1407310])), _1407310))], (34024 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407298), 34022 ^ [_1407298, _1407300, _1407302, _1407304, _1407306, _1407308, _1407310]), _1407300)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1407304, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407298, tc_fun(_1407304, tc_HOL_Obool)), _1407308), _1407306)), _1407310)))], (45801 ^ _777864) ^ [_1683540, _1683542, _1683544, _1683546, _1683548, _1683550] : [-(hAPP(hAPP(c_Option_Omap(_1683540, _1683542), _1683544), hAPP(hAPP(c_Option_Omap(_1683546, _1683540), _1683548), _1683550)) = hAPP(hAPP(c_Option_Omap(_1683546, _1683542), hAPP(c_Fun_Ocomp(_1683540, _1683542, _1683546, _1683544), _1683548)), _1683550))], (38011 ^ _777864) ^ [_1491240, _1491242, _1491244, _1491246, _1491248, _1491250, _1491252] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1491240, _1491242, _1491244, _1491246, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491240, tc_HOL_Obool)), _1491248), hAPP(hAPP(c_Set_Oinsert(_1491240), _1491250), c_Orderings_Obot__class_Obot(tc_fun(_1491240, tc_HOL_Obool))))), _1491252)), hBOOL(hAPP(hAPP(c_member(_1491240), _1491250), _1491248)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1491240, _1491242, _1491244, _1491246, _1491248), hAPP(hAPP(_1491244, _1491250), _1491252))))], (6611 ^ _777864) ^ [_887010] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887010) = _887010)], (44854 ^ _777864) ^ [_1661207, _1661209, _1661211] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1661207, tc_HOL_Obool)), _1661209), _1661211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661207, tc_HOL_Obool)), _1661209), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661207, tc_HOL_Obool), _1661211))))], (13646 ^ _777864) ^ [_1007740, _1007742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007740), _1007742)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007740, _1007742) = _1007740)], (33028 ^ _777864) ^ [_1383406, _1383408, _1383410] : [class_Groups_Oordered__ab__group__add(_1383406), -(hAPP(c_Set_Oimage(_1383406, _1383406, c_Groups_Ouminus__class_Ouminus(_1383406)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1383406, _1383408, _1383410)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1383406, hAPP(c_Groups_Ouminus__class_Ouminus(_1383406), _1383410), hAPP(c_Groups_Ouminus__class_Ouminus(_1383406), _1383408)))], (3420 ^ _777864) ^ [_829738, _829740, _829742, _829744, _829746, _829748] : [-(c_Predicate_ORangeP(_829748, _829744, _829740) = c_Predicate_ORangeP(_829746, _829742, _829738)), _829748 = _829746, _829744 = _829742, _829740 = _829738], (25001 ^ _777864) ^ [_1216768, _1216770] : [_1216770 = _1216768, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216768), _1216770)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216770), _1216768)))], (6078 ^ _777864) ^ [_877931, _877933, _877935] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_877931, _877933, _877935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _877935)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39259 ^ _777864) ^ [_1520418, _1520420, _1520422, _1520424, _1520426, _1520428] : [hBOOL(hAPP(hAPP(c_member(_1520418), _1520420), _1520422)), 39262 ^ _777864 : [(39269 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520424, tc_HOL_Obool)), _1520426), _1520428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520424, _1520418), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520424, _1520418), _1520426), hAPP(c_COMBK(tc_fun(_1520418, tc_HOL_Obool), _1520424), _1520422))), hAPP(hAPP(c_Product__Type_OSigma(_1520424, _1520418), _1520428), hAPP(c_COMBK(tc_fun(_1520418, tc_HOL_Obool), _1520424), _1520422)))))], (39263 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520424, _1520418), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520424, _1520418), _1520426), hAPP(c_COMBK(tc_fun(_1520418, tc_HOL_Obool), _1520424), _1520422))), hAPP(hAPP(c_Product__Type_OSigma(_1520424, _1520418), _1520428), hAPP(c_COMBK(tc_fun(_1520418, tc_HOL_Obool), _1520424), _1520422)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520424, tc_HOL_Obool)), _1520426), _1520428)))]]], (13662 ^ _777864) ^ [_1007996, _1007998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007996), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13665 ^ _777864 : [(13668 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007996), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007998, _1007996))))], (13666 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007998, _1007996)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (28853 ^ _777864) ^ [_1299213, _1299215] : [c_Nat__Transfer_Ois__nat(_1299213), c_Nat__Transfer_Onat__set(_1299215), 28860 ^ _777864 : [(28867 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1299213)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1299215))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1299213), _1299215)))], (28861 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1299213), _1299215)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1299213)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1299215))))]]], (36038 ^ _777864) ^ [_1448657] : [-(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)), _1448657)) = hAPP(c_Int_Onat, _1448657))], (23431 ^ _777864) ^ [_1186860, _1186862, _1186864, _1186866, _1186868] : [class_Orderings_Olinorder(_1186860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186860), _1186862), _1186864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186860), _1186866), _1186868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186860), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186860), _1186862), _1186866)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186860), _1186864), _1186868))))], (47284 ^ _777864) ^ [_1722715, _1722717, _1722719, _1722721] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1722715), tc_List_Olist(_1722715))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722715), tc_List_Olist(_1722715)), _1722717), _1722719)), c_List_Olexord(_1722715, _1722721)))), 47285 ^ _777864 : [(47292 ^ _777864) ^ [_1723022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723022), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722715)), _1722717)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722715)), _1722719)))), hAPP(hAPP(c_List_Otake(_1722715), _1723022), _1722717) = hAPP(hAPP(c_List_Otake(_1722715), _1723022), _1722719), hBOOL(hAPP(hAPP(c_member(tc_prod(_1722715, _1722715)), hAPP(hAPP(c_Product__Type_OPair(_1722715, _1722715), hAPP(hAPP(c_List_Onth(_1722715), _1722717), _1723022)), hAPP(hAPP(c_List_Onth(_1722715), _1722719), _1723022))), _1722721))], (47286 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722715)), _1722717)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722715)), _1722719))), hAPP(hAPP(c_List_Otake(_1722715), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722715)), _1722717)), _1722719) = _1722717]]], (14608 ^ _777864) ^ [_1024727, _1024729, _1024731] : [-(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), _1024727), _1024729)), _1024729)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024727, _1024729))), _1024731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024727), _1024731))], (50120 ^ _777864) ^ [_1786524, _1786526, _1786528, _1786530, _1786532] : [class_Orderings_Olinorder(_1786524), c_List_Olinorder__class_Osorted(_1786524, hAPP(hAPP(c_List_Omap(_1786526, _1786524), _1786528), _1786530)), -(c_List_Olinorder__class_Osorted(_1786524, hAPP(hAPP(c_List_Omap(_1786526, _1786524), _1786528), c_List_Olinorder__class_Oinsort__insert__key(_1786526, _1786524, _1786528, _1786532, _1786530))))], (47704 ^ _777864) ^ [_1731433, _1731435] : [-(c_List_Oset__Cons(_1731433, _1731435, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1731433)), c_List_Olist_ONil(_1731433)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1731433), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1731433, tc_List_Olist(_1731433), hAPP(hAPP(c_COMBC(_1731433, tc_List_Olist(_1731433), tc_List_Olist(_1731433)), c_List_Olist_OCons(_1731433)), c_List_Olist_ONil(_1731433))), _1731435))], (11263 ^ _777864) ^ [_965516, _965518, _965520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965516), _965518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _965520), _965516)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _965520), _965518))))], (32527 ^ _777864) ^ [_1373119, _1373121, _1373123] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373119), _1373121)), hBOOL(hAPP(hAPP(c_member(_1373119), _1373123), _1373121)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1373119), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373119, tc_HOL_Obool)), _1373121), hAPP(hAPP(c_Set_Oinsert(_1373119), _1373123), c_Orderings_Obot__class_Obot(tc_fun(_1373119, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1373119), _1373121))], (7486 ^ _777864) ^ [_901558, _901560, _901562, _901564, _901566, _901568] : [c_Com_Ocom_OCond(_901558, _901560, _901562) = c_Com_Ocom_OLocal(_901564, _901566, _901568)], (40114 ^ _777864) ^ [_1539020] : [-(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)), _1539020)))))], (8548 ^ _777864) ^ [_919648, _919650, _919652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _919648), _919650)), _919652) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _919648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _919650), _919652)))], (45721 ^ _777864) ^ [_1681388, _1681390] : [-(hAPP(hAPP(c_List_Omap(_1681388, _1681388), c_COMBI(_1681388)), _1681390) = _1681390)], (43860 ^ _777864) ^ [_1635828, _1635830, _1635832, _1635834, _1635836] : [class_Complete__Lattice_Ocomplete__lattice(_1635828), class_Orderings_Olinorder(_1635828), 43867 ^ _777864 : [(43877 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1635828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635830, _1635828), _1635832), _1635834)), _1635836))), 43878 ^ _777864 : [(43879 ^ _777864) ^ [_1636176] : [hBOOL(hAPP(hAPP(c_member(_1635830), _1636176), _1635832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1635828), hAPP(_1635834, _1636176)), _1635836))]]], (43868 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1635828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635830, _1635828), _1635832), _1635834)), _1635836)), 43872 ^ _777864 : [(43875 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1635828), hAPP(_1635834, 43871 ^ [_1635828, _1635830, _1635832, _1635834, _1635836])), _1635836)))], (43873 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1635830), 43871 ^ [_1635828, _1635830, _1635832, _1635834, _1635836]), _1635832)))]]]]], (19010 ^ _777864) ^ [_1104628, _1104630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104628), _1104630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104628)), c_Int_OBit1(_1104630))))], (42998 ^ _777864) ^ [_1613925, _1613927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1613925, _1613925)), _1613927)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1613925, _1613925)), c_Transitive__Closure_Otrancl(_1613925, _1613927))))], (22472 ^ _777864) ^ [_1166312, _1166314, _1166316] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166312), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166314)), _1166316)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1166312, _1166314), hAPP(c_Divides_OnegateSnd, _1166316))))], (19672 ^ _777864) ^ [_1116621] : [_1116621 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1116621) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51155 ^ _777864) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (13218 ^ _777864) ^ [_999842, _999844, _999846] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999842), _999844) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999842), _999846), -(_999842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_999844 = _999846)], (46196 ^ _777864) ^ [_1693011, _1693013, _1693015] : [class_Orderings_Olinorder(_1693011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1693011), _1693013)), -(c_List_Olinorder__class_Osorted__list__of__set(_1693011, hAPP(hAPP(c_Set_Oinsert(_1693011), _1693015), _1693013)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693011, _1693011, c_COMBI(_1693011)), _1693015), c_List_Olinorder__class_Osorted__list__of__set(_1693011, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1693011, tc_HOL_Obool)), _1693013), hAPP(hAPP(c_Set_Oinsert(_1693011), _1693015), c_Orderings_Obot__class_Obot(tc_fun(_1693011, tc_HOL_Obool)))))))], (17370 ^ _777864) ^ [_1077608, _1077610, _1077612] : [class_Rings_Olinordered__semidom(_1077608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077608), c_Groups_Oone__class_Oone(_1077608)), _1077610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077608), c_Groups_Oone__class_Oone(_1077608)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077608), _1077610), hAPP(c_Nat_OSuc, _1077612)))))], (43495 ^ _777864) ^ [_1625630, _1625632, _1625634, _1625636] : [class_Complete__Lattice_Ocomplete__lattice(_1625630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1625632), _1625634)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625632, _1625630), _1625634), _1625636) = hAPP(hAPP(c_Finite__Set_Ofold(_1625632, _1625630, hAPP(hAPP(c_COMBB(_1625630, tc_fun(_1625630, _1625630), _1625632), c_Lattices_Osemilattice__inf__class_Oinf(_1625630)), _1625636)), c_Orderings_Otop__class_Otop(_1625630)), _1625634))], (21858 ^ _777864) ^ [_1156037, _1156039] : [-(c_Random_Olog(_1156037, _1156039) = 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(_1156037, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1156039), _1156037)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1156037), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1156039), _1156037)))], (23597 ^ _777864) ^ [_1189794, _1189796, _1189798, _1189800] : [class_Orderings_Olinorder(_1189794), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189794), _1189796), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189794), _1189798), _1189800)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189794), _1189798), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189794), _1189796), _1189800)))], (29960 ^ _777864) ^ [_1322524, _1322526, _1322528, _1322530] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322524, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322524, tc_HOL_Obool)), _1322526), _1322528)), _1322530) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322524, tc_HOL_Obool)), _1322526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322524, tc_HOL_Obool)), _1322528), _1322530)))], (4858 ^ _777864) ^ [_852161, _852163, _852165, _852167] : [-(c_List_Oupt(_852167, _852163) = c_List_Oupt(_852165, _852161)), _852167 = _852165, _852163 = _852161], (48374 ^ _777864) ^ [_1748538, _1748540, _1748542, _1748544, _1748546, _1748548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748538), tc_List_Olist(_1748538))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748538), tc_List_Olist(_1748538)), hAPP(hAPP(c_List_Olist_OCons(_1748538), _1748540), _1748542)), hAPP(hAPP(c_List_Olist_OCons(_1748538), _1748544), _1748546))), c_List_Olistrel1(_1748538, _1748548))), 48379 ^ _777864 : [(48382 ^ _777864) ^ [] : [-(_1748542 = _1748546)], (48380 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748538, _1748538)), hAPP(hAPP(c_Product__Type_OPair(_1748538, _1748538), _1748540), _1748544)), _1748548)))]], 48383 ^ _777864 : [(48386 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748538), tc_List_Olist(_1748538))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748538), tc_List_Olist(_1748538)), _1748542), _1748546)), c_List_Olistrel1(_1748538, _1748548))))], (48384 ^ _777864) ^ [] : [-(_1748540 = _1748544)]]], (39247 ^ _777864) ^ [_1520180, _1520182, _1520184, _1520186] : [c_Finite__Set_Ofolding__one(_1520180, _1520182, _1520184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520180), _1520186)), -(hAPP(_1520184, _1520186) = hAPP(c_Finite__Set_Ofold1(_1520180, _1520182), _1520186))], (43805 ^ _777864) ^ [_1633555, _1633557, _1633559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1633557, _1633555)), _1633559)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1633555, _1633557)), hAPP(c_Relation_Oconverse(_1633557, _1633555), _1633559))))], (30563 ^ _777864) ^ [_1336629, _1336631, _1336633, _1336635, _1336637, _1336639] : [-(hBOOL(hAPP(hAPP(c_member(_1336629), _1336631), c_SetInterval_Oord_OatLeastLessThan(_1336629, _1336633, _1336635, _1336637, _1336639)))), hBOOL(hAPP(hAPP(_1336633, _1336637), _1336631)), hBOOL(hAPP(hAPP(_1336635, _1336631), _1336639))], (23503 ^ _777864) ^ [_1188130, _1188132, _1188134, _1188136] : [class_Orderings_Olinorder(_1188130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), _1188132), _1188134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188130), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188130), _1188132), _1188136)), _1188134)))], (23103 ^ _777864) ^ [_1178900, _1178902] : [class_Rings_Osemiring__1(_1178900), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1178900), _1178902) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1178900, hAPP(hAPP(c_COMBC(_1178900, _1178900, _1178900), c_Groups_Oplus__class_Oplus(_1178900)), c_Groups_Oone__class_Oone(_1178900)), _1178902, c_Groups_Ozero__class_Ozero(_1178900)))], (7004 ^ _777864) ^ [_892985, _892987, _892989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _892985), _892987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _892985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _892987), _892989))))], (17380 ^ _777864) ^ [_1077797, _1077799, _1077801, _1077803] : [class_Rings_Olinordered__semidom(_1077797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077799), _1077801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077797), c_Groups_Oone__class_Oone(_1077797)), _1077803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077797), hAPP(hAPP(c_Power_Opower__class_Opower(_1077797), _1077803), _1077799)), hAPP(hAPP(c_Power_Opower__class_Opower(_1077797), _1077803), _1077801))))], (16702 ^ _777864) ^ [_1065301, _1065303, _1065305] : [class_Rings_Olinordered__idom(_1065301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065301), c_Groups_Ozero__class_Ozero(_1065301)), _1065303)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065301), hAPP(c_Groups_Oabs__class_Oabs(_1065301), _1065305)), _1065303) = hAPP(c_Groups_Oabs__class_Oabs(_1065301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065301), _1065305), _1065303)))], (39257 ^ _777864) ^ [_1520345, _1520347, _1520349, _1520351] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1520345, _1520347)), hAPP(hAPP(c_Product__Type_OSigma(_1520345, _1520347), hAPP(hAPP(c_Set_Oinsert(_1520345), _1520349), c_Orderings_Obot__class_Obot(tc_fun(_1520345, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1520347, tc_HOL_Obool), _1520345), _1520351))) = hAPP(c_Finite__Set_Ocard(_1520347), _1520351))], (18476 ^ _777864) ^ [_1095677] : [c_Int_OBit1(_1095677) = c_Int_OMin, -(_1095677 = c_Int_OMin)], (15580 ^ _777864) ^ [_1043162, _1043164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043162), _1043164)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043164), _1043162)) = _1043164)], (39704 ^ _777864) ^ [_1529532, _1529534, _1529536, _1529538, _1529540, _1529542] : [class_Groups_Ocomm__monoid__mult(_1529532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529534), _1529536)), 39714 ^ _777864 : [(39717 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529538), hAPP(_1529540, 39713 ^ [_1529532, _1529534, _1529536, _1529538, _1529540, _1529542])))], (39715 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1529534), 39713 ^ [_1529532, _1529534, _1529536, _1529538, _1529540, _1529542]), _1529536)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529534, _1529532), hAPP(hAPP(c_COMBS(_1529534, tc_fun(_1529538, tc_HOL_Obool), _1529532), hAPP(hAPP(c_COMBB(tc_fun(_1529538, _1529532), tc_fun(tc_fun(_1529538, tc_HOL_Obool), _1529532), _1529534), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529538, _1529532)), _1529542)), _1529540)), _1529536) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1529534, _1529538), _1529532), hAPP(c_Product__Type_Oprod_Oprod__case(_1529534, _1529538, _1529532), _1529542)), hAPP(hAPP(c_Product__Type_OSigma(_1529534, _1529538), _1529536), _1529540)))], (8776 ^ _777864) ^ [_923778, _923780, _923782, _923784] : [class_Rings_Ocomm__semiring__1(_923778), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923778), _923780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923778), _923782), _923784)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923778), _923782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923778), _923780), _923784)))], (43273 ^ _777864) ^ [_1620406, _1620408] : [-(c_Transitive__Closure_Ortrancl(_1620406, c_Transitive__Closure_Ortrancl(_1620406, _1620408)) = c_Transitive__Closure_Ortrancl(_1620406, _1620408))], (8433 ^ _777864) ^ [_917574] : [-(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, _917574)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39205 ^ _777864) ^ [_1519078, _1519080] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519078, _1519078), tc_HOL_Obool)), c_Relation_OId__on(_1519078, _1519080)), hAPP(hAPP(c_Product__Type_OSigma(_1519078, _1519078), _1519080), hAPP(c_COMBK(tc_fun(_1519078, tc_HOL_Obool), _1519078), _1519080)))))], (24019 ^ _777864) ^ [_1197772, _1197774, _1197776] : [class_Orderings_Olinorder(_1197772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197772), _1197774), _1197776)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197772), _1197776), _1197774) = _1197776)], (22070 ^ _777864) ^ [_1159374, _1159376] : [_1159374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1159376, _1159374) = 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), _1159376)))], (15755 ^ _777864) ^ [_1047109, _1047111, _1047113] : [-(hBOOL(hAPP(_1047109, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047111), _1047113)))), 15758 ^ _777864 : [(15761 ^ _777864) ^ [] : [hBOOL(hAPP(_1047109, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15759 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1047111), _1047113)))]], 15763 ^ _777864 : [(15766 ^ _777864) ^ [] : [hBOOL(hAPP(_1047109, 15762 ^ [_1047109, _1047111, _1047113]))], (15764 ^ _777864) ^ [] : [-(_1047111 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047113), 15762 ^ [_1047109, _1047111, _1047113]))]]], (37803 ^ _777864) ^ [_1487055, _1487057, _1487059] : [class_Orderings_Olinorder(_1487055), 37806 ^ _777864 : [(37813 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487055), _1487059), _1487057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487055, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487055), _1487057)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487055), _1487059))))], (37807 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487055, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487055), _1487057)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487055), _1487059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487055), _1487059), _1487057)))]]], (4868 ^ _777864) ^ [_852310, _852312] : [_852312 = _852310, -(c_List_Omonoid__add__class_Olistsum(_852312) = c_List_Omonoid__add__class_Olistsum(_852310))], (38810 ^ _777864) ^ [_1509071, _1509073, _1509075, _1509077] : [-(hAPP(c_Set_Oimage(_1509071, _1509073, _1509075), hAPP(c_Set_Ovimage(_1509071, _1509073, _1509075), _1509077)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509073, tc_HOL_Obool)), _1509077), hAPP(c_Set_Oimage(_1509071, _1509073, _1509075), c_Orderings_Otop__class_Otop(tc_fun(_1509071, tc_HOL_Obool)))))], (45182 ^ _777864) ^ [_1669066, _1669068, _1669070, _1669072] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1669066, _1669066)), hAPP(hAPP(c_Product__Type_OPair(_1669066, _1669066), _1669068), _1669070)), c_Transitive__Closure_Otrancl(_1669066, _1669072))), 45186 ^ _777864 : [(45189 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669066, _1669066)), hAPP(hAPP(c_Product__Type_OPair(_1669066, _1669066), 45185 ^ [_1669066, _1669068, _1669070, _1669072]), _1669070)), c_Transitive__Closure_Ortrancl(_1669066, _1669072))))], (45187 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669066, _1669066)), hAPP(hAPP(c_Product__Type_OPair(_1669066, _1669066), _1669068), 45185 ^ [_1669066, _1669068, _1669070, _1669072])), _1669072)))]]], (5657 ^ _777864) ^ [_869079, _869081, _869083, _869085, _869087, _869089, _869091] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869079), _869081), _869083), _869085) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_869079), _869087), _869089), _869091)), _869081 = _869087, _869083 = _869089, _869085 = _869091], (36596 ^ _777864) ^ [_1460210, _1460212, _1460214] : [class_Groups_Ocomm__monoid__add(_1460210), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460212, _1460210), hAPP(c_COMBK(_1460210, _1460212), c_Groups_Ozero__class_Ozero(_1460210))), _1460214) = c_Groups_Ozero__class_Ozero(_1460210))], (29832 ^ _777864) ^ [_1319468, _1319470] : [class_Lattices_Obounded__lattice__bot(_1319468), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319468), _1319470), c_Orderings_Obot__class_Obot(_1319468)) = c_Orderings_Obot__class_Obot(_1319468))], (10574 ^ _777864) ^ [_954285, _954287, _954289] : [class_Orderings_Olinorder(_954285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954285), _954287), _954289)), 10581 ^ _777864 : [(10588 ^ _777864) ^ [] : [_954287 = _954289, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954285), _954287), _954289))], (10582 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954285), _954287), _954289))), -(_954287 = _954289)]]], (7796 ^ _777864) ^ [_907403, _907405, _907407, _907409] : [c_Com_Ocom_OAss(_907403, _907405) = c_Com_Ocom_OWhile(_907407, _907409)], (8372 ^ _777864) ^ [_916576, _916578, _916580] : [class_Orderings_Opreorder(_916576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916576), _916578), _916580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916576), _916580), _916578))], (48167 ^ _777864) ^ [_1742335, _1742337, _1742339, _1742341, _1742343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742335), tc_List_Olist(_1742335))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742335), tc_List_Olist(_1742335)), _1742337), _1742339)), c_List_Olexord(_1742335, _1742341))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1742335), tc_List_Olist(_1742335))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1742335), tc_List_Olist(_1742335)), hAPP(hAPP(c_List_Oappend(_1742335), _1742343), _1742337)), hAPP(hAPP(c_List_Oappend(_1742335), _1742343), _1742339))), c_List_Olexord(_1742335, _1742341))))], (40954 ^ _777864) ^ [_1567164, _1567166, _1567168, _1567170, _1567172, _1567174, _1567176] : [-(c_Predicate_Opred__comp(_1567164, _1567166, _1567168, _1567170, _1567172, _1567174, _1567176)), 40955 ^ _777864 : [(40956 ^ _777864) ^ [_1567229] : [hBOOL(hAPP(hAPP(_1567170, _1567174), _1567229)), hBOOL(hAPP(hAPP(_1567172, _1567229), _1567176))]]], (20280 ^ _777864) ^ [_1127365, _1127367, _1127369, _1127371] : [class_Fields_Ofield__inverse__zero(_1127365), 20283 ^ _777864 : [(20284 ^ _777864) ^ [] : [_1127367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127365), _1127369), _1127371), 20287 ^ _777864 : [(20294 ^ _777864) ^ [] : [_1127371 = c_Groups_Ozero__class_Ozero(_1127365), -(_1127367 = c_Groups_Ozero__class_Ozero(_1127365))], (20288 ^ _777864) ^ [] : [-(_1127371 = c_Groups_Ozero__class_Ozero(_1127365)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127365), _1127367), _1127371) = _1127369)]]], (20300 ^ _777864) ^ [] : [-(_1127367 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127365), _1127369), _1127371)), 20303 ^ _777864 : [(20306 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127365), _1127367), _1127371) = _1127369], (20304 ^ _777864) ^ [] : [_1127371 = c_Groups_Ozero__class_Ozero(_1127365)]], 20307 ^ _777864 : [(20310 ^ _777864) ^ [] : [_1127367 = c_Groups_Ozero__class_Ozero(_1127365)], (20308 ^ _777864) ^ [] : [-(_1127371 = c_Groups_Ozero__class_Ozero(_1127365))]]]]], (14175 ^ _777864) ^ [_1017689] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017689, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5160 ^ _777864) ^ [_856842, _856844] : [_856844 = _856842, -(c_Nat_Osemiring__1__class_Oof__nat(_856844) = c_Nat_Osemiring__1__class_Oof__nat(_856842))], (50168 ^ _777864) ^ [_1787516, _1787518, _1787520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787516), _1787518)), _1787520)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1787516, _1787520)), _1787518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1787516), _1787518))], (1402 ^ _777864) ^ [_798157, _798159] : [-(class_Groups_Olinordered__ab__semigroup__add(_798157)), _798159 = _798157, class_Groups_Olinordered__ab__semigroup__add(_798159)], (2042 ^ _777864) ^ [_807677, _807679, _807681, _807683, _807685, _807687] : [-(c_Power_Opower_Opower(_807687, _807683, _807679) = c_Power_Opower_Opower(_807685, _807681, _807677)), _807687 = _807685, _807683 = _807681, _807679 = _807677], (9290 ^ _777864) ^ [_932613, _932615] : [class_Groups_Ogroup__add(_932613), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932613), _932615), hAPP(c_Groups_Ouminus__class_Ouminus(_932613), _932615)) = c_Groups_Ozero__class_Ozero(_932613))], (14923 ^ _777864) ^ [_1030767, _1030769, _1030771] : [class_Fields_Olinordered__field__inverse__zero(_1030767), 14929 ^ _777864 : [(14934 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030767), 14928 ^ [_1030767, _1030769, _1030771]), _1030769)), _1030771))], (14932 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030767), 14928 ^ [_1030767, _1030769, _1030771]), c_Groups_Oone__class_Oone(_1030767))))], (14930 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030767), c_Groups_Ozero__class_Ozero(_1030767)), 14928 ^ [_1030767, _1030769, _1030771])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1030767), _1030769), _1030771)))], (3972 ^ _777864) ^ [_838364, _838366, _838368, _838370, _838372, _838374, _838376, _838378, _838380, _838382, _838384, _838386] : [-(c_Map_Omap__comp(_838386, _838382, _838378, _838374, _838370, _838366) = c_Map_Omap__comp(_838384, _838380, _838376, _838372, _838368, _838364)), _838386 = _838384, _838382 = _838380, _838378 = _838376, _838374 = _838372, _838370 = _838368, _838366 = _838364], (5210 ^ _777864) ^ [_857603, _857605, _857607, _857609, _857611, _857613, _857615, _857617] : [-(c_List_Ofoldl(_857617, _857613, _857609, _857605) = c_List_Ofoldl(_857615, _857611, _857607, _857603)), _857617 = _857615, _857613 = _857611, _857609 = _857607, _857605 = _857603], (22004 ^ _777864) ^ [_1158259, _1158261] : [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), _1158259))), 22007 ^ _777864 : [(22014 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158261)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158259)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158261), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158259)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158259)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158261), 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), _1158259)))))], (22008 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158261)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158259))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158261), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1158259)) = 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), _1158261)))]]], (18804 ^ _777864) ^ [_1100887, _1100889] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1100887))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100889)) = 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)))), _1100887), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100889)))], (2022 ^ _777864) ^ [_807379, _807381, _807383, _807385] : [-(c_SMT_Oz3mod(_807385, _807381) = c_SMT_Oz3mod(_807383, _807379)), _807385 = _807383, _807381 = _807379], (46589 ^ _777864) ^ [_1704552, _1704554, _1704556, _1704558, _1704560] : [-(hAPP(hAPP(c_List_Olist_OCons(_1704552), _1704554), _1704556) = hAPP(hAPP(c_List_Olist_OCons(_1704552), _1704558), _1704560)), _1704554 = _1704558, _1704556 = _1704560], (31865 ^ _777864) ^ [_1360264, _1360266, _1360268, _1360270] : [c_Finite__Set_Ofolding__one(_1360264, _1360266, _1360268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360264), _1360270)), -(_1360270 = c_Orderings_Obot__class_Obot(tc_fun(_1360264, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1360264), hAPP(hAPP(_1360266, 31878 ^ [_1360264, _1360266, _1360268, _1360270]), 31879 ^ [_1360264, _1360266, _1360268, _1360270])), hAPP(hAPP(c_Set_Oinsert(_1360264), 31878 ^ [_1360264, _1360266, _1360268, _1360270]), hAPP(hAPP(c_Set_Oinsert(_1360264), 31879 ^ [_1360264, _1360266, _1360268, _1360270]), c_Orderings_Obot__class_Obot(tc_fun(_1360264, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1360264), hAPP(_1360268, _1360270)), _1360270)))], (51449 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (24623 ^ _777864) ^ [_1209851, _1209853, _1209855, _1209857, _1209859] : [_1209851 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1209853, _1209855, _1209857, _1209859), _1209851) = c_Lazy__Sequence_Oempty(_1209855))], (38220 ^ _777864) ^ [] : [-(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))], (6880 ^ _777864) ^ [_891011] : [6881 ^ _777864 : [(6882 ^ _777864) ^ [_891053] : [_891011 = hAPP(c_Nat_OSuc, _891053)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _891011)))], (45513 ^ _777864) ^ [_1676325, _1676327, _1676329, _1676331, _1676333, _1676335] : [-(c_Map_Omap__add(_1676325, _1676327, _1676329, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1676325, tc_Option_Ooption(_1676327)), _1676331), _1676333), hAPP(c_Option_Ooption_OSome(_1676327), _1676335))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1676325, tc_Option_Ooption(_1676327)), c_Map_Omap__add(_1676325, _1676327, _1676329, _1676331)), _1676333), hAPP(c_Option_Ooption_OSome(_1676327), _1676335)))], (3500 ^ _777864) ^ [_831032, _831034] : [_831034 = _831032, -(c_Nitpick_ORep__Frac(_831034) = c_Nitpick_ORep__Frac(_831032))], (40094 ^ _777864) ^ [_1538525, _1538527] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1538525)), -(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)), _1538525))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1538527))))) = 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)), _1538525))), 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, _1538527))))))], (7836 ^ _777864) ^ [_908202, _908204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908202), _908204)), -(_908204 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908202), 7839 ^ [_908202, _908204])))], (7725 ^ _777864) ^ [_905994, _905996, _905998, _906000] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905994, _905996)), _905998), _906000))), 7726 ^ _777864 : [(7733 ^ _777864) ^ [] : [hBOOL(hAPP(_905994, _905998)), 7736 ^ _777864 : [(7737 ^ _777864) ^ [_906213] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_905996), _905998), _906213)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_905994, _905996)), _906213), _906000))]]], (7727 ^ _777864) ^ [] : [_906000 = _905998, -(hBOOL(hAPP(_905994, _905998)))]]], (36584 ^ _777864) ^ [_1459846, _1459848, _1459850, _1459852, _1459854] : [class_Rings_Osemiring__0(_1459846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459846), _1459848), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459850, _1459846), _1459852), _1459854)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459850, _1459846), hAPP(hAPP(c_COMBB(_1459846, _1459846, _1459850), hAPP(c_Groups_Otimes__class_Otimes(_1459846), _1459848)), _1459852)), _1459854))], (22883 ^ _777864) ^ [_1174390, _1174392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174390), _1174392)), -(c_Divides_Odivmod__nat(_1174390, _1174392) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174390))], (38530 ^ _777864) ^ [_1501468, _1501470] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1501468, 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(_1501468, tc_HOL_Obool)), tc_fun(_1501468, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1501468, tc_HOL_Obool)), tc_fun(_1501468, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1501468, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1501470)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1501468, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1501470))], (47788 ^ _777864) ^ [_1733771, _1733773, _1733775, _1733777, _1733779, _1733781, _1733783] : [hBOOL(hAPP(hAPP(c_member(_1733771), _1733773), hAPP(c_List_Oset(_1733771), hAPP(hAPP(c_List_Otake(_1733771), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733775)), _1733777)), _1733779)))), -(c_Map_Omap__upds(_1733771, _1733775, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1733771, tc_Option_Ooption(_1733775)), _1733781), _1733773), hAPP(c_Option_Ooption_OSome(_1733775), _1733783)), _1733779, _1733777) = c_Map_Omap__upds(_1733771, _1733775, _1733781, _1733779, _1733777))], (26223 ^ _777864) ^ [_1239074, _1239076, _1239078, _1239080, _1239082] : [-(hAPP(hAPP(c_Set_Oinsert(_1239074), _1239076), hAPP(hAPP(c_Set_Oinsert(_1239074), _1239078), c_Orderings_Obot__class_Obot(tc_fun(_1239074, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1239074), _1239080), hAPP(hAPP(c_Set_Oinsert(_1239074), _1239082), c_Orderings_Obot__class_Obot(tc_fun(_1239074, tc_HOL_Obool))))), 26224 ^ _777864 : [(26231 ^ _777864) ^ [] : [_1239076 = _1239082, _1239078 = _1239080], (26225 ^ _777864) ^ [] : [_1239076 = _1239080, _1239078 = _1239082]]], (50036 ^ _777864) ^ [_1785165, _1785167] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1785165, _1785167))))], (28653 ^ _777864) ^ [_1294505, _1294507, _1294509, _1294511, _1294513] : [c_Hoare__Mirabelle_Ohoare__valids(_1294505, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1294505), tc_HOL_Obool)), _1294507), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1294505), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), hAPP(hAPP(c_COMBB(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1294505)), _1294509)), c_Com_Ocom_OBODY)), _1294511)), _1294513)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1294505), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), hAPP(hAPP(c_COMBB(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1294505)), _1294509)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1294511)), _1294513)), -(c_Hoare__Mirabelle_Ohoare__valids(_1294505, _1294507, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1294505), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), hAPP(hAPP(c_COMBB(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1294505, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1294505))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1294505)), _1294509)), c_Com_Ocom_OBODY)), _1294511)), _1294513)))], (4978 ^ _777864) ^ [_854013, _854015] : [_854015 = _854013, -(c_List_Otranspose__rel(_854015) = c_List_Otranspose__rel(_854013))], (28833 ^ _777864) ^ [_1298910, _1298912] : [c_Nat__Transfer_Onat__set(_1298910), c_Nat__Transfer_Onat__set(_1298912), 28840 ^ _777864 : [(28847 ^ _777864) ^ [] : [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), _1298910)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1298912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298910), _1298912)))], (28841 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298910), _1298912)), -(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), _1298910)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1298912))))]]], (1272 ^ _777864) ^ [_796532, _796534] : [-(class_Lattices_Osemilattice__sup(_796532)), _796534 = _796532, class_Lattices_Osemilattice__sup(_796534)], (36976 ^ _777864) ^ [_1469058, _1469060, _1469062, _1469064, _1469066] : [class_Groups_Ocomm__monoid__add(_1469058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1469060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469062), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469058), _1469064), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1469060, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469062), _1469066))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469058), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469058), _1469064), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1469060, _1469062))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469058), _1469064), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469062), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1469062), _1469066)))))], (41360 ^ _777864) ^ [_1576672, _1576674] : [c_Wellfounded_OwfP(_1576672, hAPP(hAPP(c_COMBC(_1576672, tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_fun(_1576672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576672, tc_fun(tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_fun(_1576672, tc_HOL_Obool)), _1576672), c_COMBC(_1576672, tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576672, tc_prod(_1576672, _1576672)), tc_fun(_1576672, tc_fun(tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_HOL_Obool)), _1576672), hAPP(c_COMBB(tc_prod(_1576672, _1576672), tc_fun(tc_fun(tc_prod(_1576672, _1576672), tc_HOL_Obool), tc_HOL_Obool), _1576672), c_member(tc_prod(_1576672, _1576672)))), c_Product__Type_OPair(_1576672, _1576672)))), _1576674)), -(c_Wellfounded_Owf(_1576672, _1576674))], (36092 ^ _777864) ^ [_1449718, _1449720, _1449722, _1449724, _1449726] : [hAPP(_1449718, _1449720) = _1449722, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449724, _1449726), _1449718), _1449720), _1449722) = _1449718)], (22524 ^ _777864) ^ [_1167172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1167172)), 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), _1167172)) = 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), _1167172))))))], (41037 ^ _777864) ^ [_1568912, _1568914, _1568916] : [c_Wellfounded_Owf(_1568912, _1568914), c_Wellfounded_Owf(_1568912, _1568916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568912, _1568912), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1568912, _1568912, _1568912), _1568914), _1568916)), _1568914)), -(c_Wellfounded_Owf(_1568912, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568912, _1568912), tc_HOL_Obool)), _1568914), _1568916)))], (13818 ^ _777864) ^ [_1010844, _1010846, _1010848, _1010850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010846), _1010848)), -(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), _1010848), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010850, _1010844))), _1010846))))], (12558 ^ _777864) ^ [_988662, _988664, _988666, _988668] : [class_Rings_Olinordered__semiring__strict(_988662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988662), _988664), _988666)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988662), _988664), _988668))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988662), c_Groups_Ozero__class_Ozero(_988662)), _988664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988662), _988666), _988668)))], (51473 ^ _777864) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (15876 ^ _777864) ^ [_1049931, _1049933] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049931, _1049933) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049931, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1049933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049931, _1049933)), _1049933))], (21958 ^ _777864) ^ [_1157656, _1157658] : [_1157656 = _1157658, -(c_Random_Oinc__shift(_1157656, _1157658) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38700 ^ _777864) ^ [_1506418, _1506420, _1506422, _1506424, _1506426, _1506428] : [hAPP(_1506418, _1506420) = _1506422, hBOOL(hAPP(hAPP(c_member(_1506424), _1506422), _1506426)), -(hBOOL(hAPP(hAPP(c_member(_1506428), _1506420), hAPP(c_Set_Ovimage(_1506428, _1506424, _1506418), _1506426))))], (45090 ^ _777864) ^ [_1666362, _1666364, _1666366, _1666368, _1666370, _1666372, _1666374] : [c_Finite__Set_Ofun__left__comm(_1666362, _1666364, _1666366), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1666362, _1666364, _1666366, _1666368, hAPP(hAPP(c_Set_Oinsert(_1666362), _1666370), _1666372)), _1666374)), -(hBOOL(hAPP(hAPP(c_member(_1666362), _1666370), _1666372))), 45102 ^ _777864 : [(45105 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1666362, _1666364, _1666366, _1666368, _1666372), 45101 ^ [_1666362, _1666364, _1666366, _1666368, _1666370, _1666372, _1666374])))], (45103 ^ _777864) ^ [] : [-(_1666374 = hAPP(hAPP(_1666366, _1666370), 45101 ^ [_1666362, _1666364, _1666366, _1666368, _1666370, _1666372, _1666374]))]]], (22891 ^ _777864) ^ [_1174533, _1174535, _1174537, _1174539, _1174541] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1174533, _1174535), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1174537), _1174539))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174541)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1174533, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174535), _1174541)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1174537), _1174541)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174535), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1174537, _1174541))), _1174539)))))], (23215 ^ _777864) ^ [_1181407, _1181409] : [-(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), _1181407)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1181409), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1181407))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24215 ^ _777864) ^ [_1201974, _1201976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201974), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1201976, _1201974) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201974)))], (12764 ^ _777864) ^ [_992148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992148)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _992148)) = _992148)], (25085 ^ _777864) ^ [_1218123, _1218125, _1218127] : [_1218123 = _1218125, 25096 ^ _777864 : [(25099 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218127), _1218123))], (25097 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218123), _1218127)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218125), _1218127)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218127), _1218125)))], (21994 ^ _777864) ^ [_1158190, _1158192] : [-(c_Divides_OposDivAlg(_1158190, _1158192) = hAPP(c_Divides_Oadjust(_1158192), c_Divides_OposDivAlg(_1158190, 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)))), _1158192)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158190), _1158192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158192), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28675 ^ _777864) ^ [_1295513, _1295515] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1295513), _1295515) = 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)), _1295513)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1295515))))], (11923 ^ _777864) ^ [_977246, _977248] : [class_Rings_Olinordered__semidom(_977246), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977246), c_Groups_Ozero__class_Ozero(_977246)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_977246), _977248))))], (38214 ^ _777864) ^ [_1494989, _1494991] : [class_Lattices_Obounded__lattice__top(_1494989), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1494989), c_Orderings_Otop__class_Otop(_1494989)), _1494991) = c_Orderings_Otop__class_Otop(_1494989))], (43313 ^ _777864) ^ [_1621390, _1621392] : [-(c_Transitive__Closure_Otrancl(_1621390, _1621392) = hAPP(hAPP(c_Relation_Orel__comp(_1621390, _1621390, _1621390), c_Transitive__Closure_Ortrancl(_1621390, _1621392)), _1621392))], (24317 ^ _777864) ^ [_1203721] : [-(c_Nitpick_Ozero__frac(_1203721) = c_Nitpick_OAbs__Frac(_1203721, 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))))], (18104 ^ _777864) ^ [_1089454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089454), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089454)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12255 ^ _777864) ^ [_982989, _982991] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982989)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982991)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982989), _982991)))], (7024 ^ _777864) ^ [_893231, _893233] : [-(c_Option_Ooption_Ooption__size(_893231, _893233, c_Option_Ooption_ONone(_893231)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43345 ^ _777864) ^ [_1622244, _1622246, _1622248, _1622250] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622244, _1622244)), hAPP(hAPP(c_Product__Type_OPair(_1622244, _1622244), _1622246), _1622248)), c_Transitive__Closure_Ortrancl(_1622244, _1622250))), -(_1622246 = _1622248), 43352 ^ _777864 : [(43355 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622244, _1622244)), hAPP(hAPP(c_Product__Type_OPair(_1622244, _1622244), _1622246), _1622248)), c_Transitive__Closure_Otrancl(_1622244, _1622250))))], (43353 ^ _777864) ^ [] : [_1622246 = _1622248]]], (38350 ^ _777864) ^ [_1497704, _1497706, _1497708, _1497710] : [c_Fun_Oinj__on(_1497704, _1497706, _1497708, c_Orderings_Otop__class_Otop(tc_fun(_1497704, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1497704, _1497706, c_Orderings_Otop__class_Otop(tc_fun(_1497704, tc_HOL_Obool)), _1497708), hAPP(_1497708, _1497710)) = _1497710)], (21526 ^ _777864) ^ [_1149723, _1149725, _1149727, _1149729] : [class_Fields_Olinordered__field__inverse__zero(_1149723), class_Int_Onumber(_1149723), 21533 ^ _777864 : [(21534 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149723), _1149725), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))), _1149729)), 21537 ^ _777864 : [(21544 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)))), 21547 ^ _777864 : [(21554 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)), c_Groups_Ozero__class_Ozero(_1149723)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), _1149729)))], (21548 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)), c_Groups_Ozero__class_Ozero(_1149723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149723), _1149729), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))), _1149725)))]]], (21538 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), _1149725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149723), _1149729), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)))))]]], (21560 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149723), _1149725), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))), _1149729))), 21563 ^ _777864 : [(21566 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), _1149725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149723), _1149729), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))))], (21564 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))))]], 21567 ^ _777864 : [(21570 ^ _777864) ^ [] : [21571 ^ _777864 : [(21574 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149723), _1149729), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727))), _1149725))], (21572 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)), c_Groups_Ozero__class_Ozero(_1149723))))]], 21575 ^ _777864 : [(21578 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), _1149729))], (21576 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)), c_Groups_Ozero__class_Ozero(_1149723)))]]], (21568 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149723), c_Groups_Ozero__class_Ozero(_1149723)), hAPP(c_Int_Onumber__class_Onumber__of(_1149723), _1149727)))]]]]], (36602 ^ _777864) ^ [_1460325, _1460327, _1460329, _1460331] : [class_Groups_Oordered__ab__group__add__abs(_1460325), -(hAPP(c_Groups_Oabs__class_Oabs(_1460325), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460327, _1460325), hAPP(hAPP(c_COMBB(_1460325, _1460325, _1460327), c_Groups_Oabs__class_Oabs(_1460325)), _1460329)), _1460331)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460327, _1460325), hAPP(hAPP(c_COMBB(_1460325, _1460325, _1460327), c_Groups_Oabs__class_Oabs(_1460325)), _1460329)), _1460331))], (13698 ^ _777864) ^ [_1008609, _1008611, _1008613] : [class_Lattices_Oboolean__algebra(_1008609), 13701 ^ _777864 : [(13708 ^ _777864) ^ [] : [_1008611 = _1008613, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1008609), _1008611) = hAPP(c_Groups_Ouminus__class_Ouminus(_1008609), _1008613))], (13702 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1008609), _1008611) = hAPP(c_Groups_Ouminus__class_Ouminus(_1008609), _1008613), -(_1008611 = _1008613)]]], (30969 ^ _777864) ^ [_1343904, _1343906, _1343908] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343904, _1343906) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1343908), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1343904 = _1343906, _1343906 = _1343908], (36214 ^ _777864) ^ [_1451901, _1451903, _1451905, _1451907] : [c_Fun_Oinj__on(_1451901, _1451903, _1451905, _1451907), -(c_Fun_Oinj__on(_1451903, _1451901, c_Fun_Othe__inv__into(_1451901, _1451903, _1451907, _1451905), hAPP(c_Set_Oimage(_1451901, _1451903, _1451905), _1451907)))], (12085 ^ _777864) ^ [_980202, _980204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _980202)), _980204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980202), _980204)))], (18474 ^ _777864) ^ [_1095640] : [c_Int_OPls = c_Int_OBit1(_1095640)], (23999 ^ _777864) ^ [_1197432, _1197434, _1197436, _1197438] : [class_Orderings_Olinorder(_1197432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197432), _1197434), _1197436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197432), _1197434), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197432), _1197438), _1197436))))], (19226 ^ _777864) ^ [_1108404, _1108406] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1108404)), c_Int_OBit1(_1108406)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1108404)), _1108406)))], (8604 ^ _777864) ^ [_920585] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _920585), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _920585)], (23049 ^ _777864) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (6034 ^ _777864) ^ [_877200, _877202, _877204, _877206, _877208] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_877200, _877202, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_877200), _877204), _877206), _877208)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19154 ^ _777864) ^ [_1107123, _1107125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107123), _1107125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1107123)), c_Int_OBit1(_1107125))))], (36572 ^ _777864) ^ [_1459324, _1459326, _1459328, _1459330, _1459332, _1459334, _1459336] : [class_Rings_Osemiring__0(_1459324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459324), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459326, _1459324), _1459328), _1459330)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459332, _1459324), _1459334), _1459336)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459326, _1459324), hAPP(hAPP(c_COMBC(_1459326, tc_fun(_1459332, tc_HOL_Obool), _1459324), hAPP(hAPP(c_COMBB(tc_fun(_1459332, _1459324), tc_fun(tc_fun(_1459332, tc_HOL_Obool), _1459324), _1459326), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459332, _1459324)), hAPP(hAPP(c_COMBC(_1459326, tc_fun(_1459332, _1459324), tc_fun(_1459332, _1459324)), hAPP(hAPP(c_COMBB(tc_fun(_1459324, _1459324), tc_fun(tc_fun(_1459332, _1459324), tc_fun(_1459332, _1459324)), _1459326), c_COMBB(_1459324, _1459324, _1459332)), hAPP(hAPP(c_COMBB(_1459324, tc_fun(_1459324, _1459324), _1459326), c_Groups_Otimes__class_Otimes(_1459324)), _1459328))), _1459334))), _1459336)), _1459330))], (8578 ^ _777864) ^ [_920135, _920137, _920139] : [class_Int_Oring__char__0(_920135), 8581 ^ _777864 : [(8588 ^ _777864) ^ [] : [_920137 = _920139, -(hAPP(c_Int_Oring__1__class_Oof__int(_920135), _920137) = hAPP(c_Int_Oring__1__class_Oof__int(_920135), _920139))], (8582 ^ _777864) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_920135), _920137) = hAPP(c_Int_Oring__1__class_Oof__int(_920135), _920139), -(_920137 = _920139)]]], (11020 ^ _777864) ^ [_961406, _961408, _961410] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961406), _961408)), _961410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961406), _961410)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961408), _961410)))], (47460 ^ _777864) ^ [_1726729, _1726731] : [-(c_List_Osublist(_1726729, _1726731, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1726729))], (48516 ^ _777864) ^ [_1752498, _1752500] : [hBOOL(hAPP(c_List_Odistinct(_1752498), hAPP(c_List_Orotate1(_1752498), _1752500))), -(hBOOL(hAPP(c_List_Odistinct(_1752498), _1752500)))], (6789 ^ _777864) ^ [_889633, _889635] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _889633, _889635, _889633))], (14988 ^ _777864) ^ [_1032080, _1032082, _1032084, _1032086, _1032088] : [class_Groups_Oordered__ab__group__add(_1032080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032080), _1032082), _1032084) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032080), _1032086), _1032088), 14995 ^ _777864 : [(15002 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032080), _1032086), _1032088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032080), _1032082), _1032084)))], (14996 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032080), _1032082), _1032084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032080), _1032086), _1032088)))]]], (4730 ^ _777864) ^ [_850165, _850167, _850169, _850171, _850173, _850175, _850177, _850179, _850181, _850183] : [-(c_List_Olinorder__class_Oinsort__insert__key(_850183, _850179, _850175, _850171, _850167) = c_List_Olinorder__class_Oinsort__insert__key(_850181, _850177, _850173, _850169, _850165)), _850183 = _850181, _850179 = _850177, _850175 = _850173, _850171 = _850169, _850167 = _850165], (15186 ^ _777864) ^ [_1035563, _1035565, _1035567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035563), _1035565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035563), _1035567)), 15193 ^ _777864 : [(15200 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035565), _1035567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035565), _1035563)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035567), _1035563))))], (15194 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035565), _1035563)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035567), _1035563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035565), _1035567)))]]], (50484 ^ _777864) ^ [_1794716, _1794718, _1794720] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1794716), tc_List_Olist(_1794716), c_List_Oappend(_1794716), _1794718), _1794720) = hAPP(hAPP(c_List_Oappend(_1794716), _1794718), c_List_Oconcat(_1794716, _1794720)))], (24819 ^ _777864) ^ [_1213645, _1213647, _1213649, _1213651] : [class_Rings_Ocomm__semiring__1(_1213645), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213645), _1213647), _1213649)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213645), _1213647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213645), _1213651), _1213649))))], (11985 ^ _777864) ^ [_978426, _978428] : [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), _978426), _978428))), 11988 ^ _777864 : [(11991 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978428)))], (11989 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978426)))]]], (23333 ^ _777864) ^ [_1184700, _1184702] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184700), hAPP(c_Nat_OSuc, _1184702)) = 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), _1184700), _1184702)))], (16852 ^ _777864) ^ [_1068301, _1068303, _1068305] : [class_Rings_Olinordered__semidom(_1068301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068301), c_Groups_Oone__class_Oone(_1068301)), _1068303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068301), c_Groups_Oone__class_Oone(_1068301)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068301), _1068303), _1068305))))], (43893 ^ _777864) ^ [_1636537, _1636539, _1636541, _1636543, _1636545] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636539, _1636537)), hAPP(hAPP(c_Product__Type_OPair(_1636539, _1636537), _1636543), _1636541)), _1636545)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636537, _1636539)), hAPP(hAPP(c_Product__Type_OPair(_1636537, _1636539), _1636541), _1636543)), hAPP(c_Relation_Oconverse(_1636539, _1636537), _1636545))))], (4826 ^ _777864) ^ [_851685, _851687] : [_851687 = _851685, -(c_SetInterval_Oord__class_OatMost(_851687) = c_SetInterval_Oord__class_OatMost(_851685))], (17520 ^ _777864) ^ [_1080354, _1080356] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080354))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080356)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1860 ^ _777864) ^ [_804770, _804772, _804774, _804776, _804778, _804780, _804782, _804784] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_804784, _804780, _804776, _804772) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_804782, _804778, _804774, _804770)), _804784 = _804782, _804780 = _804778, _804776 = _804774, _804772 = _804770], (8200 ^ _777864) ^ [_914030, _914032, _914034] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914030), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914032), _914034)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _914030), _914034)))], (2032 ^ _777864) ^ [_807528, _807530, _807532, _807534] : [-(c_SMT_Oz3div(_807534, _807530) = c_SMT_Oz3div(_807532, _807528)), _807534 = _807532, _807530 = _807528], (5812 ^ _777864) ^ [_873217, _873219, _873221, _873223] : [hAPP(c_Com_Ocom_OBODY, _873217) = c_Com_Ocom_OLocal(_873219, _873221, _873223)], (9937 ^ _777864) ^ [_943850, _943852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943850)), 9940 ^ _777864 : [(9947 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _943850), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _943850)), _943852)))], (9941 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _943850)), _943852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _943850), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943852))))]]], (14320 ^ _777864) ^ [_1019965, _1019967, _1019969, _1019971] : [class_Divides_Osemiring__div(_1019965), 14323 ^ _777864 : [(14330 ^ _777864) ^ [] : [-(_1019967 = c_Groups_Ozero__class_Ozero(_1019965)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019965), _1019967), _1019969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019965), _1019967), _1019971)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019965), _1019969), _1019971))], (14324 ^ _777864) ^ [] : [_1019967 = c_Groups_Ozero__class_Ozero(_1019965), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019965), _1019967), _1019969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019965), _1019967), _1019971)) = c_Groups_Ozero__class_Ozero(_1019965))]]], (51437 ^ _777864) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (18010 ^ _777864) ^ [_1088068] : [class_Int_Onumber__ring(_1088068), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088068), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1088068))], (41886 ^ _777864) ^ [_1589869, _1589871, _1589873, _1589875, _1589877] : [class_Groups_Ocomm__monoid__mult(_1589869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589871), _1589873)), c_Fun_Oinj__on(_1589871, _1589871, _1589875, _1589873), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589871, _1589869), _1589877), hAPP(c_Set_Oimage(_1589871, _1589871, _1589875), _1589873)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589871, _1589869), hAPP(c_Fun_Ocomp(_1589871, _1589869, _1589871, _1589877), _1589875)), _1589873))], (36578 ^ _777864) ^ [_1459663, _1459665, _1459667, _1459669, _1459671] : [class_Rings_Osemiring__0(_1459663), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459663), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459665, _1459663), _1459667), _1459669)), _1459671) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459665, _1459663), hAPP(hAPP(c_COMBC(_1459665, _1459663, _1459663), hAPP(hAPP(c_COMBB(_1459663, tc_fun(_1459663, _1459663), _1459665), c_Groups_Otimes__class_Otimes(_1459663)), _1459667)), _1459671)), _1459669))], (29804 ^ _777864) ^ [_1318936, _1318938, _1318940, _1318942] : [class_Lattices_Osemilattice__inf(_1318936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318936), _1318938), _1318940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318936), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318936), _1318938), _1318942)), _1318940)))], (11329 ^ _777864) ^ [_966654, _966656] : [class_Rings_Olinordered__idom(_966654), 11332 ^ _777864 : [(11339 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _966656), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966654), hAPP(c_Int_Oring__1__class_Oof__int(_966654), _966656)), c_Groups_Ozero__class_Ozero(_966654))))], (11333 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966654), hAPP(c_Int_Oring__1__class_Oof__int(_966654), _966656)), c_Groups_Ozero__class_Ozero(_966654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _966656), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5140 ^ _777864) ^ [_856544, _856546, _856548, _856550] : [-(c_List_Oconcat(_856550, _856546) = c_List_Oconcat(_856548, _856544)), _856550 = _856548, _856546 = _856544], (15982 ^ _777864) ^ [_1051780, _1051782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1051780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051782), _1051780))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1051782), _1051780) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051782), _1051780)), _1051780)))], (19446 ^ _777864) ^ [_1112229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112229), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1112229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1112229 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30613 ^ _777864) ^ [_1337640, _1337642] : [30614 ^ _777864 : [(30617 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337642), _1337640))], (30615 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337640), _1337642)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1337640, _1337642))], (32213 ^ _777864) ^ [_1366689, _1366691, _1366693] : [class_Orderings_Olinorder(_1366689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366689), _1366691)), -(_1366691 = c_Orderings_Obot__class_Obot(tc_fun(_1366689, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366689), _1366693)), -(_1366693 = c_Orderings_Obot__class_Obot(tc_fun(_1366689, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366689, tc_HOL_Obool)), _1366691), _1366693) = c_Orderings_Obot__class_Obot(tc_fun(_1366689, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1366689, c_Orderings_Oord__class_Omax(_1366689), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366689, tc_HOL_Obool)), _1366691), _1366693)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366689), c_Big__Operators_Olattice_OSup__fin(_1366689, c_Orderings_Oord__class_Omax(_1366689), _1366691)), c_Big__Operators_Olattice_OSup__fin(_1366689, c_Orderings_Oord__class_Omax(_1366689), _1366693)))], (30687 ^ _777864) ^ [_1338979, _1338981, _1338983, _1338985] : [hBOOL(hAPP(hAPP(c_member(_1338979), _1338981), c_SetInterval_Oord_OatLeast(_1338979, _1338983, _1338985))), -(hBOOL(hAPP(hAPP(_1338983, _1338985), _1338981)))], (29588 ^ _777864) ^ [_1314733, _1314735, _1314737] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314733), _1314735), _1314737) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314733, tc_HOL_Obool), tc_HOL_Obool)), -(_1314735 = c_Orderings_Obot__class_Obot(tc_fun(_1314733, tc_HOL_Obool)))], (3316 ^ _777864) ^ [_828136, _828138] : [_828138 = _828136, -(c_Wellfounded_Omeasure(_828138) = c_Wellfounded_Omeasure(_828136))], (10346 ^ _777864) ^ [_950495, _950497, _950499] : [class_Rings_Olinordered__semidom(_950495), 10349 ^ _777864 : [(10356 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950497), _950499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950495), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_950495), _950497)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_950495), _950499))))], (10350 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950495), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_950495), _950497)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_950495), _950499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950497), _950499)))]]], (47163 ^ _777864) ^ [_1719225, _1719227, _1719229] : [hBOOL(hAPP(hAPP(c_member(_1719225), _1719227), hAPP(c_List_Oset(_1719225), _1719229))), 47167 ^ _777864 : [(47170 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1719225), _1719229), 47166 ^ [_1719225, _1719227, _1719229]) = _1719227)], (47168 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47166 ^ [_1719225, _1719227, _1719229]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719225)), _1719229))))]]], (40118 ^ _777864) ^ [_1539082, _1539084, _1539086, _1539088] : [-(hAPP(c_Set_OCollect(tc_prod(_1539082, _1539084)), hAPP(c_Product__Type_Oprod_Oprod__case(_1539082, _1539084, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1539082, tc_fun(_1539084, tc_HOL_Obool), tc_fun(_1539084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539084, tc_HOL_Obool), tc_fun(_1539084, tc_HOL_Obool)), _1539082), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539084)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539082), c_fconj), _1539086))), _1539088))) = hAPP(hAPP(c_Product__Type_OSigma(_1539082, _1539084), hAPP(c_Set_OCollect(_1539082), _1539086)), hAPP(c_COMBK(tc_fun(_1539084, tc_HOL_Obool), _1539082), hAPP(c_Set_OCollect(_1539084), _1539088))))], (3806 ^ _777864) ^ [_835777, _835779, _835781, _835783] : [-(c_Relation_ORange(_835783, _835779) = c_Relation_ORange(_835781, _835777)), _835783 = _835781, _835779 = _835777], (26191 ^ _777864) ^ [_1238403, _1238405] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1238403, _1238405, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1238403), tc_HOL_Obool))))], (50672 ^ _777864) ^ [_1799737, _1799739] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1799737), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1799737))), _1799739))), 50675 ^ _777864 : [(50682 ^ _777864) ^ [] : [-(_1799739 = c_List_Olist_ONil(tc_List_Olist(_1799737))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1799737))), c_List_Otranspose(_1799737, _1799739)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799737)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1799737)), _1799739), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50676 ^ _777864) ^ [] : [_1799739 = c_List_Olist_ONil(tc_List_Olist(_1799737)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1799737))), c_List_Otranspose(_1799737, _1799739)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40446 ^ _777864) ^ [_1549493, _1549495, _1549497, _1549499, _1549501, _1549503] : [hBOOL(hAPP(hAPP(c_member(_1549493), _1549495), _1549497)), -(hAPP(c_Fun_Ooverride__on(_1549493, _1549499, _1549501, _1549503, _1549497), _1549495) = hAPP(_1549503, _1549495))], (33332 ^ _777864) ^ [_1390526, _1390528, _1390530, _1390532, _1390534] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390526, tc_fun(_1390528, tc_HOL_Obool)), _1390530), _1390532), _1390534)), 33336 ^ _777864 : [(33339 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1390532, 33335 ^ [_1390526, _1390528, _1390530, _1390532, _1390534]), _1390534)))], (33337 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390526), 33335 ^ [_1390526, _1390528, _1390530, _1390532, _1390534]), _1390530)))]]], (14276 ^ _777864) ^ [_1019301, _1019303] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019301), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019303)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019301, _1019303)))], (16190 ^ _777864) ^ [_1055419, _1055421, _1055423] : [class_Groups_Oordered__ab__group__add__abs(_1055419), -(hAPP(c_Groups_Oabs__class_Oabs(_1055419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055419), hAPP(c_Groups_Oabs__class_Oabs(_1055419), _1055421)), hAPP(c_Groups_Oabs__class_Oabs(_1055419), _1055423))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055419), hAPP(c_Groups_Oabs__class_Oabs(_1055419), _1055421)), hAPP(c_Groups_Oabs__class_Oabs(_1055419), _1055423)))], (7038 ^ _777864) ^ [_893476, _893478] : [class_Groups_Olinordered__ab__group__add(_893476), 7041 ^ _777864 : [(7048 ^ _777864) ^ [] : [_893478 = c_Groups_Ozero__class_Ozero(_893476), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893476), _893478), _893478) = c_Groups_Ozero__class_Ozero(_893476))], (7042 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_893476), _893478), _893478) = c_Groups_Ozero__class_Ozero(_893476), -(_893478 = c_Groups_Ozero__class_Ozero(_893476))]]], (42285 ^ _777864) ^ [_1599275, _1599277, _1599279] : [42286 ^ _777864 : [(42287 ^ _777864) ^ [_1599329] : [hBOOL(hAPP(_1599275, _1599329))]], _1599277 = c_Hilbert__Choice_OEps(_1599279, _1599275), -(hBOOL(hAPP(_1599275, _1599277)))], (27227 ^ _777864) ^ [_1261412, _1261414, _1261416, _1261418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261412, tc_HOL_Obool)), _1261414), hAPP(hAPP(c_Set_Oinsert(_1261412), _1261416), _1261418))), 27230 ^ _777864 : [(27237 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261412), _1261416), _1261414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261412, tc_HOL_Obool)), _1261414), _1261418)))], (27231 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1261412), _1261416), _1261414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261412, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261412, tc_HOL_Obool)), _1261414), hAPP(hAPP(c_Set_Oinsert(_1261412), _1261416), c_Orderings_Obot__class_Obot(tc_fun(_1261412, tc_HOL_Obool))))), _1261418)))]]], (40843 ^ _777864) ^ [_1565180] : [-(c_Wellfounded_Owf(_1565180, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1565180, _1565180), tc_HOL_Obool))))], (29958 ^ _777864) ^ [_1322440, _1322442, _1322444, _1322446] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322440, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322440, tc_HOL_Obool)), _1322442), _1322444)), _1322446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322440, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322440, tc_HOL_Obool)), _1322442), _1322446)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322440, tc_HOL_Obool)), _1322444), _1322446)))], (4720 ^ _777864) ^ [_850016, _850018, _850020, _850022] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_850022, _850018) = c_SetInterval_Oord__class_OatLeastLessThan(_850020, _850016)), _850022 = _850020, _850018 = _850016], (39181 ^ _777864) ^ [_1518378, _1518380, _1518382] : [-(hAPP(c_Finite__Set_Ofold1(_1518378, _1518380), hAPP(hAPP(c_Set_Oinsert(_1518378), _1518382), c_Orderings_Obot__class_Obot(tc_fun(_1518378, tc_HOL_Obool)))) = _1518382)], (28402 ^ _777864) ^ [_1287902, _1287904, _1287906, _1287908, _1287910, _1287912] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1287908, _1287908)), hAPP(hAPP(c_Product__Type_OPair(_1287908, _1287908), hAPP(_1287912, _1287904)), hAPP(_1287912, _1287906))), _1287910)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1287902, _1287902)), hAPP(hAPP(c_Product__Type_OPair(_1287902, _1287902), _1287904), _1287906)), hAPP(hAPP(c_Relation_Oinv__image(_1287908, _1287902), _1287910), _1287912))))], (43799 ^ _777864) ^ [_1633440, _1633442, _1633444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1633440, _1633442)), hAPP(c_Relation_Oconverse(_1633442, _1633440), _1633444))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1633442, _1633440)), _1633444)))], (23735 ^ _777864) ^ [_1192591, _1192593, _1192595] : [class_Int_Onumber(_1192591), class_Orderings_Oord(_1192591), 23742 ^ _777864 : [(23749 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192591), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192593)), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192595)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192591), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192593)), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192595)) = hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192595))], (23743 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192591), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192593)), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192595))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1192591), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192593)), hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192595)) = hAPP(c_Int_Onumber__class_Onumber__of(_1192591), _1192593))]]], (39884 ^ _777864) ^ [_1534344, _1534346, _1534348] : [-(c_Relation_Orefl__on(_1534344, _1534346, _1534348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534344, _1534344), tc_HOL_Obool)), _1534348), hAPP(hAPP(c_Product__Type_OSigma(_1534344, _1534344), _1534346), hAPP(c_COMBK(tc_fun(_1534344, tc_HOL_Obool), _1534344), _1534346)))), 39890 ^ _777864 : [(39893 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534344, _1534344)), hAPP(hAPP(c_Product__Type_OPair(_1534344, _1534344), 39889 ^ [_1534344, _1534346, _1534348]), 39889 ^ [_1534344, _1534346, _1534348])), _1534348))], (39891 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534344), 39889 ^ [_1534344, _1534346, _1534348]), _1534346)))]]], (5988 ^ _777864) ^ [_876262, _876264, _876266] : [hBOOL(hAPP(c_Com_OWT, _876266)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_876262, _876264, _876266))))], (18894 ^ _777864) ^ [_1102664, _1102666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102664), _1102666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102664)), c_Int_OBit0(_1102666))))], (23151 ^ _777864) ^ [_1179853, _1179855] : [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(_1179853))), 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)), _1179855)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179853)), hAPP(c_Nat_OSuc, _1179855))))], (34677 ^ _777864) ^ [_1421754, _1421756, _1421758, _1421760] : [class_Orderings_Oorder(_1421754), 34680 ^ _777864 : [(34689 ^ _777864) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1421754, _1421756, _1421758) = hAPP(hAPP(c_Set_Oinsert(_1421754), _1421760), c_Orderings_Obot__class_Obot(tc_fun(_1421754, tc_HOL_Obool)))), _1421756 = _1421758, _1421758 = _1421760], (34681 ^ _777864) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1421754, _1421756, _1421758) = hAPP(hAPP(c_Set_Oinsert(_1421754), _1421760), c_Orderings_Obot__class_Obot(tc_fun(_1421754, tc_HOL_Obool))), 34684 ^ _777864 : [(34687 ^ _777864) ^ [] : [-(_1421758 = _1421760)], (34685 ^ _777864) ^ [] : [-(_1421756 = _1421758)]]]]], (42659 ^ _777864) ^ [_1607402, _1607404, _1607406, _1607408] : [class_Orderings_Olinorder(_1607402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607402), _1607404)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1607402, _1607402, c_Orderings_Oord__class_Omin(_1607402)), _1607406), hAPP(hAPP(c_Set_Oinsert(_1607402), _1607408), _1607404)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1607402), _1607408), hAPP(hAPP(c_Finite__Set_Ofold(_1607402, _1607402, c_Orderings_Oord__class_Omin(_1607402)), _1607406), _1607404)))], (17254 ^ _777864) ^ [_1075396, _1075398, _1075400] : [class_Groups_Omonoid__mult(_1075396), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075396), _1075398), hAPP(c_Nat_OSuc, _1075400)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075396), hAPP(hAPP(c_Power_Opower__class_Opower(_1075396), _1075398), _1075400)), _1075398))], (18514 ^ _777864) ^ [_1096239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1096239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1096239)))], (28639 ^ _777864) ^ [_1293776, _1293778, _1293780, _1293782, _1293784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293780, _1293776)), hAPP(hAPP(c_Product__Type_OPair(_1293780, _1293776), _1293784), _1293778)), _1293782)), -(hBOOL(hAPP(hAPP(c_member(_1293776), _1293778), hAPP(c_Relation_OImage(_1293780, _1293776, _1293782), hAPP(hAPP(c_Set_Oinsert(_1293780), _1293784), c_Orderings_Obot__class_Obot(tc_fun(_1293780, tc_HOL_Obool)))))))], (598 ^ _777864) ^ [_787081, _787083, _787085, _787087, _787089, _787091, _787093, _787095, _787097, _787099] : [-(c_Finite__Set_Ofolding__image(_787097, _787093, _787089, _787085, _787081)), c_Finite__Set_Ofolding__image(_787099, _787095, _787091, _787087, _787083), _787099 = _787097, _787095 = _787093, _787091 = _787089, _787087 = _787085, _787083 = _787081], (47366 ^ _777864) ^ [_1724835, _1724837, _1724839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724835), tc_List_Olist(_1724835))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724835), tc_List_Olist(_1724835)), c_List_Olist_ONil(_1724835)), _1724837)), c_List_Olistrel(_1724835, _1724839))), -(_1724837 = c_List_Olist_ONil(_1724835))], (7859 ^ _777864) ^ [_908562, _908564, _908566, _908568] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_908562, _908564)), _908566), _908568)), 7863 ^ _777864 : [(7866 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_908564), 7862 ^ [_908562, _908564, _908566, _908568]), _908568)))], (7864 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_908562), _908566), 7862 ^ [_908562, _908564, _908566, _908568])))]]], (47944 ^ _777864) ^ [_1737533, _1737535, _1737537, _1737539] : [-(hAPP(hAPP(c_List_Onth(_1737533), hAPP(hAPP(c_List_Oappend(_1737533), _1737535), hAPP(hAPP(c_List_Olist_OCons(_1737533), _1737537), _1737539))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737533)), _1737535)) = _1737537)], (7346 ^ _777864) ^ [_898879, _898881, _898883, _898885, _898887] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_898879, _898881, _898883)), _898885), _898887)), 7351 ^ _777864 : [(7354 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898881), _898885), _898887)))], (7352 ^ _777864) ^ [] : [-(hBOOL(hAPP(_898879, _898885)))]], 7355 ^ _777864 : [(7358 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898883), _898885), _898887)))], (7356 ^ _777864) ^ [] : [hBOOL(hAPP(_898879, _898885))]]], (20390 ^ _777864) ^ [_1128971, _1128973, _1128975] : [class_Fields_Olinordered__field(_1128971), -(_1128973 = c_Groups_Ozero__class_Ozero(_1128971)), -(hAPP(c_Groups_Oabs__class_Oabs(_1128971), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128971), _1128975), _1128973)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128971), hAPP(c_Groups_Oabs__class_Oabs(_1128971), _1128975)), hAPP(c_Groups_Oabs__class_Oabs(_1128971), _1128973)))], (32699 ^ _777864) ^ [_1376852, _1376854, _1376856, _1376858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376852), _1376854)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376856), _1376858)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1376852, _1376856)), c_Sum__Type_OPlus(_1376852, _1376856, _1376854, _1376858))))], (38760 ^ _777864) ^ [_1507763, _1507765, _1507767, _1507769, _1507771] : [-(hAPP(c_Set_Ovimage(_1507763, _1507765, _1507767), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507765, tc_HOL_Obool)), _1507769), _1507771)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507763, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1507763, _1507765, _1507767), _1507769)), hAPP(c_Set_Ovimage(_1507763, _1507765, _1507767), _1507771)))], (39654 ^ _777864) ^ [_1528346, _1528348, _1528350] : [class_Orderings_Olinorder(_1528346), -(_1528348 = c_Orderings_Obot__class_Obot(tc_fun(_1528346, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1528346, tc_HOL_Obool)), _1528348), _1528350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528346), _1528350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1528346), hAPP(c_Finite__Set_Ofold1(_1528346, c_Orderings_Oord__class_Omin(_1528346)), _1528350)), hAPP(c_Finite__Set_Ofold1(_1528346, c_Orderings_Oord__class_Omin(_1528346)), _1528348))))], (23761 ^ _777864) ^ [_1193100, _1193102] : [23762 ^ _777864 : [(23765 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1193102), _1193100))], (23763 ^ _777864) ^ [] : [_1193100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1193102, _1193100) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193102))], (47996 ^ _777864) ^ [_1738930, _1738932, _1738934, _1738936] : [-(c_Map_Omap__of(_1738930, _1738932, hAPP(hAPP(c_List_Oappend(tc_prod(_1738930, _1738932)), _1738934), _1738936)) = c_Map_Omap__add(_1738930, _1738932, c_Map_Omap__of(_1738930, _1738932, _1738936), c_Map_Omap__of(_1738930, _1738932, _1738934)))], (43823 ^ _777864) ^ [_1634699, _1634701, _1634703, _1634705, _1634707] : [hBOOL(hAPP(hAPP(c_member(_1634699), _1634701), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634703, tc_fun(_1634699, tc_HOL_Obool)), _1634705), _1634707))), 43826 ^ _777864 : [(43827 ^ _777864) ^ [_1634823] : [hBOOL(hAPP(hAPP(c_member(_1634703), _1634823), _1634705)), -(hBOOL(hAPP(hAPP(c_member(_1634699), _1634701), hAPP(_1634707, _1634823))))]]], (34469 ^ _777864) ^ [_1417517, _1417519, _1417521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1417517, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1417517, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417517), _1417519)), hAPP(c_Set_OPow(_1417517), _1417521))), hAPP(c_Set_OPow(_1417517), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417517, tc_HOL_Obool)), _1417519), _1417521)))))], (29778 ^ _777864) ^ [_1318442, _1318444, _1318446, _1318448, _1318450] : [class_Lattices_Osemilattice__inf(_1318442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318442), _1318444), _1318446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318442), _1318448), _1318450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318442), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318442), _1318444), _1318448)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318442), _1318446), _1318450))))], (51465 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (50323 ^ _777864) ^ [_1790751, _1790753, _1790755] : [50324 ^ _777864 : [(50327 ^ _777864) ^ [] : [_1790755 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50325 ^ _777864) ^ [] : [-(_1790751 = c_List_Olist_ONil(tc_List_Olist(_1790753)))]], 50331 ^ _777864 : [(50334 ^ _777864) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790753)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1790753)), _1790751), 50330 ^ [_1790751, _1790753, _1790755])) = _1790755], (50332 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50330 ^ [_1790751, _1790753, _1790755]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1790753))), _1790751))))]], -(c_List_Otranspose(_1790753, _1790751) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1790753)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1790753)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1790753), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1790753)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1790753)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1790753), hAPP(hAPP(c_COMBB(tc_List_Olist(_1790753), tc_fun(tc_Nat_Onat, _1790753), tc_Nat_Onat), c_List_Onth(_1790753)), hAPP(c_List_Onth(tc_List_Olist(_1790753)), _1790751))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1790753))), _1790751)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1790755)))], (28278 ^ _777864) ^ [_1282576, _1282578, _1282580, _1282582] : [28279 ^ _777864 : [(28282 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1282576), _1282578), _1282582))], (28280 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1282576), _1282578), _1282580))]], -(hBOOL(hAPP(hAPP(c_member(_1282576), _1282578), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282576, tc_HOL_Obool)), _1282580), _1282582))))], (26501 ^ _777864) ^ [_1244772, _1244774] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244772), _1244774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244772), _1244774)))], (3238 ^ _777864) ^ [_826885, _826887] : [_826887 = _826885, -(c_SetInterval_Oord__class_OatLeast(_826887) = c_SetInterval_Oord__class_OatLeast(_826885))], (38394 ^ _777864) ^ [_1498469, _1498471] : [class_Lattices_Oboolean__algebra(_1498469), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1498469), hAPP(c_Groups_Ouminus__class_Ouminus(_1498469), _1498471)), _1498471) = c_Orderings_Otop__class_Otop(_1498469))], (9674 ^ _777864) ^ [_939553] : [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)), _939553)), _939553) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (26131 ^ _777864) ^ [_1237228, _1237230, _1237232, _1237234] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237228, tc_HOL_Obool)), _1237230), hAPP(hAPP(c_Set_Oinsert(_1237228), _1237232), _1237234)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237228, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237228, tc_HOL_Obool)), _1237230), _1237234)), hAPP(hAPP(c_Set_Oinsert(_1237228), _1237232), c_Orderings_Obot__class_Obot(tc_fun(_1237228, tc_HOL_Obool)))))], (27680 ^ _777864) ^ [_1270944, _1270946, _1270948, _1270950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270944), _1270946)), 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)), _1270944), _1270948)), 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)), _1270946), _1270950)), 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)), _1270946), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270948), _1270950))), c_FunDef_Omin__weak)))], (6633 ^ _777864) ^ [_887334, _887336] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887334), _887336) = _887334, -(_887336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10334 ^ _777864) ^ [_950227, _950229, _950231] : [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, _950227)), _950229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950227)), _950231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950229), _950231)))], (34475 ^ _777864) ^ [_1417761, _1417763] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1417761, tc_HOL_Obool)), hAPP(c_Set_OPow(_1417761), _1417763))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417761), _1417763)))], (32874 ^ _777864) ^ [_1380552, _1380554, _1380556] : [class_Groups_Ocomm__monoid__mult(_1380552), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380554, _1380552), _1380556), c_Orderings_Obot__class_Obot(tc_fun(_1380554, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1380552))], (11483 ^ _777864) ^ [_969295, _969297, _969299] : [class_Groups_Oordered__comm__monoid__add(_969295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969295), _969297), c_Groups_Ozero__class_Ozero(_969295))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969295), _969299), c_Groups_Ozero__class_Ozero(_969295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969295), _969297), _969299)), c_Groups_Ozero__class_Ozero(_969295))))], (23291 ^ _777864) ^ [_1183629, _1183631, _1183633, _1183635, _1183637, _1183639] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183629, _1183631, _1183633), _1183635), hAPP(hAPP(c_Product__Type_OPair(_1183629, _1183631), _1183637), _1183639)) = hAPP(hAPP(_1183635, _1183637), _1183639))], (17126 ^ _777864) ^ [_1073195, _1073197, _1073199, _1073201] : [class_Groups_Omonoid__mult(_1073195), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1073195), _1073197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073199), _1073201)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1073195), hAPP(hAPP(c_Power_Opower__class_Opower(_1073195), _1073197), _1073199)), _1073201))], (26397 ^ _777864) ^ [_1242772, _1242774, _1242776] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242772), _1242774)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242772), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242772), _1242776)))))], (48139 ^ _777864) ^ [_1741854, _1741856, _1741858] : [_1741858 = c_List_Olist_ONil(_1741856), -(_1741854 = hAPP(hAPP(c_List_Oappend(_1741856), _1741854), _1741858))], (37953 ^ _777864) ^ [_1490019, _1490021, _1490023, _1490025, _1490027] : [hAPP(_1490019, _1490021) = hAPP(c_Option_Ooption_OSome(_1490023), _1490025), -(hBOOL(hAPP(hAPP(c_member(_1490027), _1490021), c_Map_Odom(_1490027, _1490023, _1490019))))], (39944 ^ _777864) ^ [_1535609, _1535611, _1535613, _1535615, _1535617] : [c_Relation_Orefl__on(_1535609, _1535611, _1535613), hBOOL(hAPP(hAPP(c_member(tc_prod(_1535609, _1535609)), hAPP(hAPP(c_Product__Type_OPair(_1535609, _1535609), _1535615), _1535617)), _1535613)), -(hBOOL(hAPP(hAPP(c_member(_1535609), _1535615), _1535611)))], (43427 ^ _777864) ^ [_1624076, _1624078, _1624080, _1624082] : [c_Wellfounded_Owf(_1624076, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624076, _1624076)), hAPP(hAPP(c_Product__Type_OPair(_1624076, _1624076), _1624078), _1624080)), _1624082)), 43430 ^ _777864 : [(43433 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624076, _1624076)), hAPP(hAPP(c_Product__Type_OPair(_1624076, _1624076), _1624080), _1624078)), c_Transitive__Closure_Ortrancl(_1624076, _1624082)))], (43431 ^ _777864) ^ [] : [-(c_Wellfounded_Owf(_1624076, _1624082))]]], (15724 ^ _777864) ^ [_1046514, _1046516, _1046518] : [-(hBOOL(hAPP(_1046514, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046516), _1046518)))), 15727 ^ _777864 : [(15730 ^ _777864) ^ [] : [hBOOL(hAPP(_1046514, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15728 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046516), _1046518)))]], 15732 ^ _777864 : [(15735 ^ _777864) ^ [] : [hBOOL(hAPP(_1046514, 15731 ^ [_1046514, _1046516, _1046518]))], (15733 ^ _777864) ^ [] : [-(_1046516 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046518), 15731 ^ [_1046514, _1046516, _1046518]))]]], (17298 ^ _777864) ^ [_1076316, _1076318, _1076320, _1076322] : [class_Rings_Olinordered__semidom(_1076316), hAPP(hAPP(c_Power_Opower__class_Opower(_1076316), _1076318), hAPP(c_Nat_OSuc, _1076320)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1076316), _1076322), hAPP(c_Nat_OSuc, _1076320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076316), c_Groups_Ozero__class_Ozero(_1076316)), _1076318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076316), c_Groups_Ozero__class_Ozero(_1076316)), _1076322)), -(_1076318 = _1076322)], (3270 ^ _777864) ^ [_827361, _827363, _827365, _827367, _827369, _827371, _827373, _827375, _827377, _827379] : [-(c_Fun_Ooverride__on(_827379, _827375, _827371, _827367, _827363) = c_Fun_Ooverride__on(_827377, _827373, _827369, _827365, _827361)), _827379 = _827377, _827375 = _827373, _827371 = _827369, _827367 = _827365, _827363 = _827361], (33622 ^ _777864) ^ [_1397153, _1397155, _1397157, _1397159, _1397161] : [-(hBOOL(hAPP(hAPP(c_member(_1397153), _1397155), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397157, tc_fun(_1397153, tc_HOL_Obool)), _1397159), _1397161)))), 33623 ^ _777864 : [(33624 ^ _777864) ^ [_1397235] : [hBOOL(hAPP(hAPP(c_member(_1397157), _1397235), _1397159)), hBOOL(hAPP(hAPP(c_member(_1397153), _1397155), hAPP(_1397161, _1397235)))]]], (37150 ^ _777864) ^ [_1473684, _1473686, _1473688, _1473690, _1473692] : [class_Groups_Ocomm__monoid__add(_1473684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473686), _1473688)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473686), _1473690)), 37164 ^ _777864 : [(37167 ^ _777864) ^ [] : [hAPP(_1473692, 37163 ^ [_1473684, _1473686, _1473688, _1473690, _1473692]) = c_Groups_Ozero__class_Ozero(_1473684)], (37165 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473686), 37163 ^ [_1473684, _1473686, _1473688, _1473690, _1473692]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473686, tc_HOL_Obool)), _1473688), _1473690))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473686, _1473684), _1473692), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473686, tc_HOL_Obool)), _1473688), _1473690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1473684), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473686, _1473684), _1473692), _1473688)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473686, _1473684), _1473692), _1473690)))], (39281 ^ _777864) ^ [_1521021, _1521023, _1521025, _1521027] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521021, _1521023)), hAPP(hAPP(c_Product__Type_OSigma(_1521021, _1521023), _1521025), hAPP(c_COMBK(tc_fun(_1521023, tc_HOL_Obool), _1521021), _1521027)))), -(_1521027 = c_Orderings_Obot__class_Obot(tc_fun(_1521023, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521021), _1521025)))], (42535 ^ _777864) ^ [_1604808, _1604810, _1604812, _1604814, _1604816, _1604818, _1604820, _1604822] : [class_Groups_Ocomm__monoid__add(_1604808), c_Fun_Oinj__on(_1604810, _1604812, _1604814, _1604816), _1604818 = hAPP(c_Set_Oimage(_1604810, _1604812, _1604814), _1604816), 42549 ^ _777864 : [(42552 ^ _777864) ^ [] : [hAPP(_1604820, 42548 ^ [_1604808, _1604810, _1604812, _1604814, _1604816, _1604818, _1604820, _1604822]) = hAPP(_1604822, hAPP(_1604814, 42548 ^ [_1604808, _1604810, _1604812, _1604814, _1604816, _1604818, _1604820, _1604822]))], (42550 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604810), 42548 ^ [_1604808, _1604810, _1604812, _1604814, _1604816, _1604818, _1604820, _1604822]), _1604816)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1604812, _1604808), _1604822), _1604818) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1604810, _1604808), _1604820), _1604816))], (51425 ^ _777864) ^ [_1811162, _1811164] : [-(class_Smallcheck_Osmall(tc_prod(_1811162, _1811164))), class_Smallcheck_Osmall(_1811162), class_Smallcheck_Osmall(_1811164)], (38372 ^ _777864) ^ [_1498072, _1498074, _1498076] : [-(c_Map_Odom(_1498072, _1498074, hAPP(hAPP(c_COMBB(_1498074, tc_Option_Ooption(_1498074), _1498072), c_Option_Ooption_OSome(_1498074)), _1498076)) = c_Orderings_Otop__class_Otop(tc_fun(_1498072, tc_HOL_Obool)))], (4256 ^ _777864) ^ [_842954, _842956, _842958, _842960] : [-(c_List_Olistset(_842960, _842956) = c_List_Olistset(_842958, _842954)), _842960 = _842958, _842956 = _842954], (5758 ^ _777864) ^ [_871560, _871562, _871564, _871566, _871568, _871570] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_871560, _871562, _871564), _871566, _871568, hAPP(hAPP(hAPP(c_Natural_Oupdate, _871570), c_Com_Ovname_OLoc(_871560)), hAPP(hAPP(c_Natural_Ogetlocs, _871566), _871560))), 5762 ^ _777864 : [(5765 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_871564, hAPP(hAPP(hAPP(c_Natural_Oupdate, _871566), c_Com_Ovname_OLoc(_871560)), hAPP(_871562, _871566)), _871568, 5761 ^ [_871560, _871562, _871564, _871566, _871568, _871570]))], (5763 ^ _777864) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _871570), c_Com_Ovname_OLoc(_871560)), hAPP(hAPP(c_Natural_Ogetlocs, _871566), _871560)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 5761 ^ [_871560, _871562, _871564, _871566, _871568, _871570]), c_Com_Ovname_OLoc(_871560)), hAPP(hAPP(c_Natural_Ogetlocs, _871566), _871560)))]]], (48582 ^ _777864) ^ [_1753995, _1753997, _1753999, _1754001] : [hAPP(hAPP(c_List_Oappend(_1753995), _1753997), _1753999) = _1754001, 48585 ^ _777864 : [(48588 ^ _777864) ^ [] : [-(_1753999 = hAPP(hAPP(c_List_Odrop(_1753995), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753995)), _1753997)), _1754001))], (48586 ^ _777864) ^ [] : [-(_1753997 = hAPP(hAPP(c_List_Otake(_1753995), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753995)), _1753997)), _1754001))]]], (31797 ^ _777864) ^ [_1358772, _1358774] : [class_Orderings_Olinorder(_1358772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358772), _1358774)), -(_1358774 = c_Orderings_Obot__class_Obot(tc_fun(_1358772, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1358772), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1358772), 31810 ^ [_1358772, _1358774]), 31811 ^ [_1358772, _1358774])), hAPP(hAPP(c_Set_Oinsert(_1358772), 31810 ^ [_1358772, _1358774]), hAPP(hAPP(c_Set_Oinsert(_1358772), 31811 ^ [_1358772, _1358774]), c_Orderings_Obot__class_Obot(tc_fun(_1358772, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1358772), c_Big__Operators_Olinorder__class_OMin(_1358772, _1358774)), _1358774)))], (6530 ^ _777864) ^ [_885676, _885678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885676), _885678)), _885678))], (5589 ^ _777864) ^ [_867046, _867048, _867050, _867052] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _867046), _867048, _867050, _867052), 5593 ^ _777864 : [(5596 ^ _777864) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _867046)), _867048, 5592 ^ [_867046, _867048, _867050, _867052], _867052))], (5594 ^ _777864) ^ [] : [-(_867050 = hAPP(c_Nat_OSuc, 5592 ^ [_867046, _867048, _867050, _867052]))]]], (8391 ^ _777864) ^ [_916866, _916868] : [class_Rings_Olinordered__idom(_916866), 8394 ^ _777864 : [(8401 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _916868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916866), c_Groups_Ozero__class_Ozero(_916866)), hAPP(c_Int_Oring__1__class_Oof__int(_916866), _916868))))], (8395 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916866), c_Groups_Ozero__class_Ozero(_916866)), hAPP(c_Int_Oring__1__class_Oof__int(_916866), _916868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _916868)))]]], (40308 ^ _777864) ^ [_1544075, _1544077, _1544079, _1544081, _1544083] : [-(c_Map_Odom(_1544075, _1544077, hAPP(hAPP(c_COMBS(_1544075, tc_Option_Ooption(_1544077), tc_Option_Ooption(_1544077)), hAPP(hAPP(c_COMBS(_1544075, tc_Option_Ooption(_1544077), tc_fun(tc_Option_Ooption(_1544077), tc_Option_Ooption(_1544077))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1544077), tc_fun(tc_Option_Ooption(_1544077), tc_Option_Ooption(_1544077))), _1544075), c_If(tc_Option_Ooption(_1544077))), _1544079)), _1544081)), _1544083)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544075, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544075, tc_HOL_Obool)), c_Map_Odom(_1544075, _1544077, _1544081)), hAPP(c_Set_OCollect(_1544075), _1544079))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544075, tc_HOL_Obool)), c_Map_Odom(_1544075, _1544077, _1544083)), hAPP(c_Set_OCollect(_1544075), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544075), c_fNot), _1544079)))))], (5746 ^ _777864) ^ [_871285, _871287, _871289] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _871285)), _871287), _871289)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _871285))), _871287), _871289)))], (6989 ^ _777864) ^ [_892787, _892789] : [-(_892787 = c_Option_Ooption_ONone(_892789)), -(_892787 = hAPP(c_Option_Ooption_OSome(_892789), 6992 ^ [_892787, _892789]))], (15274 ^ _777864) ^ [_1037278, _1037280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1037278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037278), _1037280)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037280), _1037278)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1037280)), hAPP(c_Int_Onat, _1037278)))], (43335 ^ _777864) ^ [_1621977, _1621979, _1621981, _1621983, _1621985] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621977, _1621977)), hAPP(hAPP(c_Product__Type_OPair(_1621977, _1621977), _1621979), _1621981)), c_Transitive__Closure_Ortrancl(_1621977, _1621983))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621977, _1621977)), hAPP(hAPP(c_Product__Type_OPair(_1621977, _1621977), _1621981), _1621985)), _1621983)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621977, _1621977)), hAPP(hAPP(c_Product__Type_OPair(_1621977, _1621977), _1621979), _1621985)), c_Transitive__Closure_Otrancl(_1621977, _1621983))))], (47756 ^ _777864) ^ [_1732636] : [-(c_List_Olistset(_1732636, c_List_Olist_ONil(tc_fun(_1732636, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1732636)), c_List_Olist_ONil(_1732636)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1732636), tc_HOL_Obool))))], (13561 ^ _777864) ^ [_1006301, _1006303, _1006305, _1006307] : [class_Divides_Osemiring__div(_1006301), -(c_Divides_Odiv__class_Omod(_1006301, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006301), _1006303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006301), _1006305), _1006307)), _1006305) = c_Divides_Odiv__class_Omod(_1006301, _1006303, _1006305))], (1632 ^ _777864) ^ [_801032, _801034] : [-(class_Orderings_Olinorder(_801032)), _801034 = _801032, class_Orderings_Olinorder(_801034)], (19730 ^ _777864) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (6983 ^ _777864) ^ [_892672, _892674] : [_892672 = c_Option_Ooption_ONone(_892674), 6986 ^ _777864 : [(6987 ^ _777864) ^ [_892744] : [_892672 = hAPP(c_Option_Ooption_OSome(_892674), _892744)]]], (51385 ^ _777864) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (24495 ^ _777864) ^ [_1207268, _1207270] : [-(c_Divides_Odivmod__nat(_1207268, _1207270) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1207268, _1207270)))], (6645 ^ _777864) ^ [_887561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887561), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49600 ^ _777864) ^ [_1776066, _1776068, _1776070, _1776072, _1776074] : [c_List_Opartition(_1776066, _1776068, _1776070) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776066), tc_List_Olist(_1776066)), _1776072), _1776074), 49603 ^ _777864 : [(49610 ^ _777864) ^ [_1776328] : [hBOOL(hAPP(hAPP(c_member(_1776066), _1776328), hAPP(c_List_Oset(_1776066), _1776074))), hBOOL(hAPP(_1776068, _1776328))], (49604 ^ _777864) ^ [_1776219] : [hBOOL(hAPP(hAPP(c_member(_1776066), _1776219), hAPP(c_List_Oset(_1776066), _1776072))), -(hBOOL(hAPP(_1776068, _1776219)))]]], (29814 ^ _777864) ^ [_1319115, _1319117, _1319119, _1319121] : [class_Lattices_Osemilattice__inf(_1319115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319115), _1319117), _1319119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319115), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319115), _1319121), _1319117)), _1319119)))], (6064 ^ _777864) ^ [_877707, _877709] : [_877707 = _877709, -(c_Com_Ovname_OGlb(_877707) = c_Com_Ovname_OGlb(_877709))], (38500 ^ _777864) ^ [_1500718, _1500720, _1500722, _1500724] : [hAPP(c_Set_Oimage(_1500718, _1500720, _1500722), c_Orderings_Otop__class_Otop(tc_fun(_1500718, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1500720, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500720, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500720, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1500718, _1500720, _1500722), _1500724))), hAPP(c_Set_Oimage(_1500718, _1500720, _1500722), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1500718, tc_HOL_Obool)), _1500724)))))], (18304 ^ _777864) ^ [_1092601] : [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), _1092601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1092601)))], (30068 ^ _777864) ^ [_1324935, _1324937] : [class_Lattices_Osemilattice__inf(_1324935), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324935), _1324937), _1324937) = _1324937)], (7502 ^ _777864) ^ [_902001, _902003, _902005, _902007, _902009] : [c_Com_Ocom_OCall(_902001, _902003, _902005) = c_Com_Ocom_OSemi(_902007, _902009)], (4170 ^ _777864) ^ [_841607, _841609] : [_841609 = _841607, -(c_Random_Orange(_841609) = c_Random_Orange(_841607))], (41027 ^ _777864) ^ [_1568735, _1568737, _1568739] : [c_Wellfounded_Owf(_1568735, _1568737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1568735, tc_HOL_Obool)), _1568739), hAPP(c_Relation_OImage(_1568735, _1568735, _1568737), _1568739))), -(_1568739 = c_Orderings_Obot__class_Obot(tc_fun(_1568735, tc_HOL_Obool)))], (30214 ^ _777864) ^ [_1328198, _1328200] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1328198), _1328200) = 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)), _1328198)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1328200))))], (20188 ^ _777864) ^ [_1125868, _1125870, _1125872, _1125874] : [class_Rings_Odivision__ring(_1125868), -(_1125870 = c_Groups_Ozero__class_Ozero(_1125868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125868), _1125872), _1125870) = _1125874, -(_1125872 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125868), _1125874), _1125870))], (48 ^ _777864) ^ [_778510, _778512] : [-(class_Rings_Odivision__ring__inverse__zero(_778510)), _778512 = _778510, class_Rings_Odivision__ring__inverse__zero(_778512)], (5328 ^ _777864) ^ [_859404, _859406] : [_859406 = _859404, -(tc_List_Olist(_859406) = tc_List_Olist(_859404))], (34487 ^ _777864) ^ [_1417989, _1417991] : [hAPP(c_Set_OPow(_1417989), _1417991) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1417989, tc_HOL_Obool), tc_HOL_Obool))], (44069 ^ _777864) ^ [_1641654, _1641656, _1641658] : [c_Relation_Orefl__on(_1641654, _1641656, _1641658), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1641654, _1641654), tc_HOL_Obool)), _1641658), hAPP(hAPP(c_Relation_Orel__comp(_1641654, _1641654, _1641654), hAPP(c_Relation_Oconverse(_1641654, _1641654), _1641658)), _1641658))))], (45846 ^ _777864) ^ [_1684539, _1684541, _1684543, _1684545, _1684547] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1684539), tc_Option_Ooption(_1684541), _1684543, hAPP(c_Option_Omap(_1684539, _1684541), _1684545)), hAPP(c_COMBK(tc_Option_Ooption(_1684539), _1684543), c_Option_Ooption_ONone(_1684539))), _1684547) = c_Option_Ooption_ONone(_1684541))], (1142 ^ _777864) ^ [_794907, _794909] : [-(class_Rings_Ocomm__ring(_794907)), _794909 = _794907, class_Rings_Ocomm__ring(_794909)], (47422 ^ _777864) ^ [_1725792, _1725794, _1725796, _1725798] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725792)), hAPP(hAPP(c_List_Olist__update(_1725792, _1725794), _1725796), _1725798)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725792)), _1725794))], (2684 ^ _777864) ^ [_817792, _817794] : [_817794 = _817792, -(c_Lazy__Sequence_Ohb__not__seq(_817794) = c_Lazy__Sequence_Ohb__not__seq(_817792))], (5044 ^ _777864) ^ [_855016, _855018] : [_855018 = _855016, -(c_List_Onth(_855018) = c_List_Onth(_855016))], (19780 ^ _777864) ^ [_1118585, _1118587, _1118589, _1118591] : [class_Rings_Odivision__ring(_1118585), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118585), _1118587), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118585), _1118589), _1118591)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118585), _1118587), _1118589)), _1118591))], (44194 ^ _777864) ^ [_1645337, _1645339, _1645341] : [_1645339 = _1645341, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645337, _1645337)), hAPP(hAPP(c_Product__Type_OPair(_1645337, _1645337), _1645339), _1645341)), c_Relation_OId(_1645337))))], (40080 ^ _777864) ^ [_1538287] : [-(c_Finite__Set_Ofun__left__comm__idem(_1538287, tc_fun(_1538287, tc_HOL_Obool), c_Set_Oinsert(_1538287)))], (28418 ^ _777864) ^ [_1288641, _1288643] : [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)), _1288641), 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)), _1288643), 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)), _1288641), _1288643)), c_Int_Ointrel)))], (45517 ^ _777864) ^ [_1676484, _1676486, _1676488, _1676490] : [c_Fun_Oinj__on(_1676484, tc_Option_Ooption(_1676486), c_Map_Omap__add(_1676484, _1676486, _1676488, _1676490), c_Map_Odom(_1676484, _1676486, _1676490)), -(c_Fun_Oinj__on(_1676484, tc_Option_Ooption(_1676486), _1676490, c_Map_Odom(_1676484, _1676486, _1676490)))], (50362 ^ _777864) ^ [_1792017, _1792019] : [-(c_Fun_Oinj__on(tc_List_Olist(_1792017), tc_List_Olist(_1792017), c_List_Orev(_1792017), _1792019))], (23243 ^ _777864) ^ [_1181979, _1181981] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181979), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181981)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181979)) = 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), _1181981), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1181979)))), 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)))], (3670 ^ _777864) ^ [_833769, _833771] : [_833771 = _833769, -(tc_Lazy__Sequence_Olazy__sequence(_833771) = tc_Lazy__Sequence_Olazy__sequence(_833769))], (1896 ^ _777864) ^ [_805372, _805374, _805376, _805378, _805380, _805382] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_805382, _805378, _805374) = c_Hoare__Mirabelle_Otriple_Otriple__size(_805380, _805376, _805372)), _805382 = _805380, _805378 = _805376, _805374 = _805372], (40546 ^ _777864) ^ [_1553295, _1553297, _1553299] : [class_Lattices_Odistrib__lattice(_1553295), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553295), _1553297)), -(_1553297 = c_Orderings_Obot__class_Obot(tc_fun(_1553295, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553295), _1553299)), -(_1553299 = c_Orderings_Obot__class_Obot(tc_fun(_1553295, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1553295), c_Big__Operators_Olattice__class_OSup__fin(_1553295, _1553297)), c_Big__Operators_Olattice__class_OSup__fin(_1553295, _1553299)) = c_Big__Operators_Olattice__class_OSup__fin(_1553295, hAPP(c_Set_OCollect(_1553295), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_HOL_Obool), tc_HOL_Obool, _1553295), c_HOL_OEx(_1553295)), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool)), tc_fun(_1553295, tc_HOL_Obool), _1553295), hAPP(c_COMBB(tc_fun(_1553295, tc_HOL_Obool), tc_HOL_Obool, _1553295), c_HOL_OEx(_1553295))), hAPP(hAPP(c_COMBC(_1553295, tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool)), tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_fun(tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool))), tc_fun(tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool)), tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool))), _1553295), c_COMBS(_1553295, tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_fun(_1553295, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1553295, tc_fun(tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool))), _1553295), hAPP(c_COMBB(tc_fun(_1553295, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool)), _1553295), c_COMBS(_1553295, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool)), tc_fun(_1553295, tc_fun(_1553295, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1553295), hAPP(c_COMBB(tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1553295), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553295), c_fconj))), hAPP(hAPP(c_COMBC(_1553295, tc_fun(_1553295, tc_fun(_1553295, _1553295)), tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1553295, _1553295), tc_fun(_1553295, tc_HOL_Obool)), tc_fun(tc_fun(_1553295, tc_fun(_1553295, _1553295)), tc_fun(_1553295, tc_fun(_1553295, tc_HOL_Obool))), _1553295), c_COMBB(tc_fun(_1553295, _1553295), tc_fun(_1553295, tc_HOL_Obool), _1553295)), hAPP(hAPP(c_COMBB(tc_fun(_1553295, tc_HOL_Obool), tc_fun(tc_fun(_1553295, _1553295), tc_fun(_1553295, tc_HOL_Obool)), _1553295), c_COMBB(_1553295, tc_HOL_Obool, _1553295)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1553295)))))), hAPP(hAPP(c_COMBC(_1553295, tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1553295, tc_HOL_Obool), tc_fun(_1553295, tc_HOL_Obool)), _1553295), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1553295)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1553295), c_fconj), hAPP(hAPP(c_COMBC(_1553295, tc_fun(_1553295, tc_HOL_Obool), tc_HOL_Obool), c_member(_1553295)), _1553297)))), hAPP(hAPP(c_COMBC(_1553295, tc_fun(_1553295, tc_HOL_Obool), tc_HOL_Obool), c_member(_1553295)), _1553299))))))))], (13437 ^ _777864) ^ [_1003687, _1003689, _1003691, _1003693] : [class_Divides_Osemiring__div(_1003687), -(c_Divides_Odiv__class_Omod(_1003687, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003687), _1003689), _1003691), _1003693) = c_Divides_Odiv__class_Omod(_1003687, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003687), c_Divides_Odiv__class_Omod(_1003687, _1003689, _1003693)), c_Divides_Odiv__class_Omod(_1003687, _1003691, _1003693)), _1003693))], (19320 ^ _777864) ^ [_1110032] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1110032), 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), _1110032), _1110032))], (3166 ^ _777864) ^ [_825743, _825745, _825747, _825749, _825751, _825753] : [-(c_SetInterval_Oord_OatLeast(_825753, _825749, _825745) = c_SetInterval_Oord_OatLeast(_825751, _825747, _825743)), _825753 = _825751, _825749 = _825747, _825745 = _825743], (43917 ^ _777864) ^ [_1637161, _1637163, _1637165] : [c_Relation_Orefl__on(_1637161, _1637163, _1637165), -(c_Relation_Orefl__on(_1637161, _1637163, hAPP(c_Relation_Oconverse(_1637161, _1637161), _1637165)))], (6753 ^ _777864) ^ [_889092, _889094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889092), _889094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889092)), hAPP(c_Nat_OSuc, _889094))))], (19278 ^ _777864) ^ [_1109354] : [class_Rings_Osemiring__1(_1109354), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109354), c_Groups_Ozero__class_Ozero(_1109354)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1109354))], (46384 ^ _777864) ^ [_1697695, _1697697] : [-(c_List_Olenlex(_1697695, _1697697) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1697695)), tc_List_Olist(_1697695)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1697695), c_Wellfounded_Oless__than, c_List_Olex(_1697695, _1697697))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1697695), tc_List_Olist(_1697695), tc_prod(tc_Nat_Onat, tc_List_Olist(_1697695))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1697695), tc_prod(tc_Nat_Onat, tc_List_Olist(_1697695))), tc_List_Olist(_1697695)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1697695))), c_Nat_Osize__class_Osize(tc_List_Olist(_1697695)))), c_COMBI(tc_List_Olist(_1697695)))))], (45146 ^ _777864) ^ [_1667874, _1667876, _1667878, _1667880, _1667882] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1667874, _1667874)), hAPP(hAPP(c_Product__Type_OPair(_1667874, _1667874), _1667876), _1667878)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1667874, _1667874), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1667880)), _1667882))), 45150 ^ _777864 : [(45153 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667874, _1667874)), hAPP(hAPP(c_Product__Type_OPair(_1667874, _1667874), 45149 ^ [_1667874, _1667876, _1667878, _1667880, _1667882]), _1667878)), _1667882)))], (45151 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667874, _1667874)), hAPP(hAPP(c_Product__Type_OPair(_1667874, _1667874), _1667876), 45149 ^ [_1667874, _1667876, _1667878, _1667880, _1667882])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1667874, _1667874), tc_HOL_Obool), _1667880), _1667882))))]]], (49731 ^ _777864) ^ [_1779904, _1779906, _1779908, _1779910, _1779912] : [class_Orderings_Olinorder(_1779904), c_List_Olinorder__class_Osorted(_1779904, hAPP(hAPP(c_List_Omap(_1779906, _1779904), _1779908), _1779910)), -(c_List_Olinorder__class_Osorted(_1779904, hAPP(hAPP(c_List_Omap(_1779906, _1779904), _1779908), hAPP(c_List_Ofilter(_1779906, _1779912), _1779910))))], (22458 ^ _777864) ^ [_1166043, _1166045, _1166047, _1166049] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1166043, _1166045, _1166047, c_Code__Numeral_OSuc__code__numeral(_1166049)) = hAPP(_1166047, _1166049))], (28586 ^ _777864) ^ [_1292516, _1292518, _1292520, _1292522, _1292524] : [hBOOL(hAPP(hAPP(c_member(_1292516), _1292518), hAPP(c_Relation_OImage(_1292520, _1292516, _1292522), _1292524))), 28590 ^ _777864 : [(28593 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1292520, _1292516)), hAPP(hAPP(c_Product__Type_OPair(_1292520, _1292516), 28589 ^ [_1292516, _1292518, _1292520, _1292522, _1292524]), _1292518)), _1292522)))], (28591 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292520), 28589 ^ [_1292516, _1292518, _1292520, _1292522, _1292524]), _1292524)))]]], (49598 ^ _777864) ^ [_1775979, _1775981, _1775983] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1775979, tc_HOL_Obool)), hAPP(c_List_Oset(_1775979), _1775981)), hAPP(hAPP(c_Set_Oinsert(_1775979), _1775983), c_Orderings_Obot__class_Obot(tc_fun(_1775979, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1775979), hAPP(c_List_Ofilter(_1775979, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1775979), c_fNot), hAPP(hAPP(c_COMBC(_1775979, _1775979, tc_HOL_Obool), c_fequal), _1775983))), _1775981)))], (11581 ^ _777864) ^ [_971148, _971150, _971152, _971154] : [class_Rings_Oordered__ring(_971148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971148), _971150), _971152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971148), _971154), c_Groups_Ozero__class_Ozero(_971148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971148), _971154), _971152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971148), _971154), _971150))))], (47998 ^ _777864) ^ [_1738987, _1738989, _1738991, _1738993] : [-(hAPP(hAPP(c_List_Oappend(_1738987), hAPP(hAPP(c_List_Oappend(_1738987), _1738989), _1738991)), _1738993) = hAPP(hAPP(c_List_Oappend(_1738987), _1738989), hAPP(hAPP(c_List_Oappend(_1738987), _1738991), _1738993)))], (49067 ^ _777864) ^ [_1764827, _1764829] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1764827)), c_List_Olist_ONil(_1764827)), c_List_Olists(_1764827, _1764829))))], (51173 ^ _777864) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (32321 ^ _777864) ^ [_1368895, _1368897] : [hAPP(c_Finite__Set_Ocard(_1368895), _1368897) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1368897 = c_Orderings_Obot__class_Obot(tc_fun(_1368895, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368895), _1368897))], (344 ^ _777864) ^ [_783028, _783030, _783032, _783034, _783036, _783038, _783040, _783042, _783044, _783046] : [-(c_Typedef_Otype__definition(_783044, _783040, _783036, _783032, _783028)), c_Typedef_Otype__definition(_783046, _783042, _783038, _783034, _783030), _783046 = _783044, _783042 = _783040, _783038 = _783036, _783034 = _783032, _783030 = _783028], (51415 ^ _777864) ^ [_1811033, _1811035] : [-(class_Finite__Set_Ofinite(tc_prod(_1811033, _1811035))), class_Finite__Set_Ofinite(_1811033), class_Finite__Set_Ofinite(_1811035)], (51455 ^ _777864) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (39850 ^ _777864) ^ [_1533252, _1533254, _1533256, _1533258, _1533260, _1533262] : [-(c_Product__Type_Omap__pair(_1533252, _1533254, _1533256, _1533258, _1533260, _1533262) = hAPP(c_Product__Type_Oprod_Oprod__case(_1533252, _1533256, tc_prod(_1533254, _1533258)), hAPP(hAPP(c_COMBC(_1533252, tc_fun(_1533256, _1533258), tc_fun(_1533256, tc_prod(_1533254, _1533258))), hAPP(hAPP(c_COMBB(tc_fun(_1533258, tc_prod(_1533254, _1533258)), tc_fun(tc_fun(_1533256, _1533258), tc_fun(_1533256, tc_prod(_1533254, _1533258))), _1533252), c_COMBB(_1533258, tc_prod(_1533254, _1533258), _1533256)), hAPP(hAPP(c_COMBB(_1533254, tc_fun(_1533258, tc_prod(_1533254, _1533258)), _1533252), c_Product__Type_OPair(_1533254, _1533258)), _1533260))), _1533262)))], (26805 ^ _777864) ^ [_1251165, _1251167, _1251169] : [-(hBOOL(hAPP(hAPP(c_member(_1251165), _1251167), hAPP(hAPP(c_Set_Oinsert(_1251165), _1251167), _1251169))))], (27822 ^ _777864) ^ [_1273430, _1273432, _1273434] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273430, tc_HOL_Obool)), _1273432), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273430, tc_HOL_Obool)), _1273432), _1273434))))], (46931 ^ _777864) ^ [_1713643] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1713643) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46934 ^ _777864 : [(46935 ^ _777864) ^ [_1713718] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713718), hAPP(c_List_Oset(tc_Nat_Onat), _1713643))), -(_1713718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18040 ^ _777864) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (4934 ^ _777864) ^ [_853305, _853307] : [_853307 = _853305, -(c_Groups_Oone__class_Oone(_853307) = c_Groups_Oone__class_Oone(_853305))], (40214 ^ _777864) ^ [_1541351, _1541353, _1541355, _1541357] : [hBOOL(hAPP(hAPP(c_member(_1541351), _1541353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541351, tc_HOL_Obool)), _1541355), hAPP(c_Set_OCollect(_1541351), _1541357)))), 40217 ^ _777864 : [(40220 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1541357, _1541353)))], (40218 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541351), _1541353), _1541355)))]]], (10748 ^ _777864) ^ [_956826, _956828, _956830] : [class_Orderings_Olinorder(_956826), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956826), _956828), _956830))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956826), _956830), _956828)))], (41252 ^ _777864) ^ [_1574366, _1574368] : [c_Wellfounded_OwfP(_1574366, _1574368), -(c_Wellfounded_Owf(_1574366, hAPP(c_Set_OCollect(tc_prod(_1574366, _1574366)), hAPP(c_Product__Type_Oprod_Oprod__case(_1574366, _1574366, tc_HOL_Obool), _1574368))))], (25681 ^ _777864) ^ [_1228424] : [_1228424 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228424), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (49940 ^ _777864) ^ [_1783694, _1783696] : [49941 ^ _777864 : [(49944 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1783696), _1783694))], (49942 ^ _777864) ^ [] : [_1783696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1783694, _1783696) = c_List_Olist_ONil(tc_Nat_Onat))], (12722 ^ _777864) ^ [_991507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991507), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _991507) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15090 ^ _777864) ^ [_1033799, _1033801, _1033803, _1033805] : [class_Divides_Oring__div(_1033799), -(c_Divides_Odiv__class_Omod(_1033799, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033799), _1033801), _1033803), _1033805) = c_Divides_Odiv__class_Omod(_1033799, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033799), _1033801), c_Divides_Odiv__class_Omod(_1033799, _1033803, _1033805)), _1033805))], (14972 ^ _777864) ^ [_1031752, _1031754, _1031756] : [class_Rings_Oring__1(_1031752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031754), _1031756)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031756), _1031754)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031752), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031752), _1031756)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031752), _1031754)))], (6643 ^ _777864) ^ [_887509, _887511] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887509), hAPP(c_Nat_OSuc, _887511)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887509), _887511)))], (12274 ^ _777864) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35088 ^ _777864) ^ [_1430149, _1430151, _1430153, _1430155, _1430157, _1430159] : [c_Fun_Oinj__on(_1430149, _1430151, _1430153, _1430155), hBOOL(hAPP(hAPP(c_member(_1430149), _1430157), _1430155)), hBOOL(hAPP(hAPP(c_member(_1430149), _1430159), _1430155)), 35099 ^ _777864 : [(35106 ^ _777864) ^ [] : [_1430157 = _1430159, -(hAPP(_1430153, _1430157) = hAPP(_1430153, _1430159))], (35100 ^ _777864) ^ [] : [hAPP(_1430153, _1430157) = hAPP(_1430153, _1430159), -(_1430157 = _1430159)]]], (38663 ^ _777864) ^ [_1505650] : [-(c_Equiv__Relations_Oequivp(_1505650, c_fequal))], (47576 ^ _777864) ^ [_1728939, _1728941] : [-(_1728941 = c_List_Olist_ONil(_1728939)), -(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(_1728939)), _1728941))))], (46689 ^ _777864) ^ [_1706611, _1706613, _1706615, _1706617, _1706619, _1706621] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1706611, _1706611)), hAPP(hAPP(c_Product__Type_OPair(_1706611, _1706611), _1706613), _1706615)), _1706617)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706611), tc_List_Olist(_1706611))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706611), tc_List_Olist(_1706611)), _1706619), _1706621)), c_List_Olistrel(_1706611, _1706617))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1706611), tc_List_Olist(_1706611))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1706611), tc_List_Olist(_1706611)), hAPP(hAPP(c_List_Olist_OCons(_1706611), _1706613), _1706619)), hAPP(hAPP(c_List_Olist_OCons(_1706611), _1706615), _1706621))), c_List_Olistrel(_1706611, _1706617))))], (46733 ^ _777864) ^ [_1708029, _1708031, _1708033] : [-(c_List_Oset__Cons(_1708029, _1708031, _1708033) = hAPP(c_Set_OCollect(tc_List_Olist(_1708029)), hAPP(hAPP(c_COMBB(tc_fun(_1708029, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1708029)), c_HOL_OEx(_1708029)), hAPP(hAPP(c_COMBB(tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_fun(_1708029, tc_HOL_Obool), tc_List_Olist(_1708029)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_HOL_Obool, _1708029), c_HOL_OEx(tc_List_Olist(_1708029)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708029), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1708029, tc_fun(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), tc_fun(tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), tc_List_Olist(_1708029)), c_COMBS(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1708029, tc_fun(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), tc_List_Olist(_1708029)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708029), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), _1708029), c_COMBS(tc_List_Olist(_1708029), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1708029)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1708029), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708029)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708029), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_List_Olist(_1708029))), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1708029), tc_List_Olist(_1708029)), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_fun(tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_List_Olist(_1708029))), tc_fun(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool))), tc_List_Olist(_1708029)), c_COMBB(tc_fun(tc_List_Olist(_1708029), tc_List_Olist(_1708029)), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), _1708029)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1708029), tc_List_Olist(_1708029)), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), tc_List_Olist(_1708029)), c_COMBB(tc_List_Olist(_1708029), tc_HOL_Obool, tc_List_Olist(_1708029))), c_fequal))), c_List_Olist_OCons(_1708029)))))), hAPP(hAPP(c_COMBC(_1708029, tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool)), _1708029), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1708029))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1708029), c_fconj), hAPP(hAPP(c_COMBC(_1708029, tc_fun(_1708029, tc_HOL_Obool), tc_HOL_Obool), c_member(_1708029)), _1708031)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708029), tc_fun(tc_List_Olist(_1708029), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1708029))), _1708033)))))))], (1072 ^ _777864) ^ [_794032, _794034] : [-(class_Rings_Olinordered__ring(_794032)), _794034 = _794032, class_Rings_Olinordered__ring(_794034)], (27714 ^ _777864) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omax__strict), c_FunDef_Omax__weak)))], (25463 ^ _777864) ^ [_1224373] : [_1224373 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224373), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24125 ^ _777864) ^ [_1199880, _1199882, _1199884, _1199886] : [class_Orderings_Olinorder(_1199880), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199880), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199880), _1199882), _1199884)), _1199886) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199880), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199880), _1199882), _1199886)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199880), _1199884), _1199886)))], (48486 ^ _777864) ^ [_1751787, _1751789, _1751791, _1751793] : [-(hAPP(hAPP(c_List_Odrop(_1751787), _1751789), hAPP(hAPP(c_List_Oappend(_1751787), _1751791), _1751793)) = hAPP(hAPP(c_List_Oappend(_1751787), hAPP(hAPP(c_List_Odrop(_1751787), _1751789), _1751791)), hAPP(hAPP(c_List_Odrop(_1751787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1751789), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751787)), _1751791))), _1751793)))], (21720 ^ _777864) ^ [_1153503, _1153505, _1153507, _1153509] : [class_Fields_Olinordered__field__inverse__zero(_1153503), class_Int_Onumber(_1153503), 21727 ^ _777864 : [(21728 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153503), _1153505), _1153507)), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509))), 21731 ^ _777864 : [(21738 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), _1153507))), 21741 ^ _777864 : [(21748 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), _1153507), c_Groups_Ozero__class_Ozero(_1153503)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509))))], (21742 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), _1153507), c_Groups_Ozero__class_Ozero(_1153503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153503), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)), _1153507)), _1153505)))]]], (21732 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), _1153507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), _1153505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153503), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)), _1153507))))]]], (21754 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153503), _1153505), _1153507)), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)))), 21757 ^ _777864 : [(21760 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), _1153505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153503), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)), _1153507)))], (21758 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), _1153507)))]], 21761 ^ _777864 : [(21764 ^ _777864) ^ [] : [21765 ^ _777864 : [(21768 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153503), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)), _1153507)), _1153505))], (21766 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), _1153507), c_Groups_Ozero__class_Ozero(_1153503))))]], 21769 ^ _777864 : [(21772 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), hAPP(c_Int_Onumber__class_Onumber__of(_1153503), _1153509)))], (21770 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), _1153507), c_Groups_Ozero__class_Ozero(_1153503)))]]], (21762 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153503), c_Groups_Ozero__class_Ozero(_1153503)), _1153507))]]]]], (46575 ^ _777864) ^ [_1704232, _1704234, _1704236, _1704238, _1704240, _1704242] : [-(c_List_Ofoldr(_1704232, _1704234, _1704236, hAPP(hAPP(c_List_Olist_OCons(_1704232), _1704238), _1704240), _1704242) = hAPP(hAPP(_1704236, _1704238), c_List_Ofoldr(_1704232, _1704234, _1704236, _1704240, _1704242)))], (42240 ^ _777864) ^ [_1598183, _1598185, _1598187, _1598189, _1598191, _1598193] : [c_Finite__Set_Ofolding__idem(_1598183, _1598185, _1598187, _1598189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598183), _1598191)), -(hAPP(_1598189, hAPP(hAPP(c_Set_Oinsert(_1598183), _1598193), _1598191)) = hAPP(c_Fun_Ocomp(_1598185, _1598185, _1598185, hAPP(_1598189, _1598191)), hAPP(_1598187, _1598193)))], (30044 ^ _777864) ^ [_1324483, _1324485, _1324487] : [class_Lattices_Osemilattice__inf(_1324483), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324483), _1324485), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324483), _1324485), _1324487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324483), _1324485), _1324487))], (28526 ^ _777864) ^ [_1291102, _1291104, _1291106, _1291108, _1291110, _1291112] : [hBOOL(hAPP(hAPP(c_member(_1291102), _1291104), _1291106)), _1291108 = hAPP(_1291110, _1291104), -(hBOOL(hAPP(hAPP(c_member(_1291112), _1291108), hAPP(c_Set_Oimage(_1291102, _1291112, _1291110), _1291106))))], (6012 ^ _777864) ^ [_876804, _876806, _876808] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_876804, _876806, _876808))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _876806))))], (23419 ^ _777864) ^ [_1186637, _1186639, _1186641, _1186643] : [class_Orderings_Olinorder(_1186637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186637), _1186639), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186637), _1186641), _1186643))), 23426 ^ _777864 : [(23429 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186637), _1186639), _1186643)))], (23427 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186637), _1186639), _1186641)))]]], (47514 ^ _777864) ^ [_1727870, _1727872, _1727874] : [-(hAPP(hAPP(c_List_Olist__update(_1727870, c_List_Olist_ONil(_1727870)), _1727872), _1727874) = c_List_Olist_ONil(_1727870))], (41412 ^ _777864) ^ [_1578617, _1578619] : [c_Wellfounded_OwfP(_1578617, _1578619), -(c_Wellfounded_Oacyclic(_1578617, hAPP(c_Set_OCollect(tc_prod(_1578617, _1578617)), hAPP(c_Product__Type_Oprod_Oprod__case(_1578617, _1578617, tc_HOL_Obool), _1578619))))], (45723 ^ _777864) ^ [_1681424] : [-(hAPP(c_List_Omap(_1681424, _1681424), c_COMBI(_1681424)) = c_Fun_Oid(tc_List_Olist(_1681424)))], (50384 ^ _777864) ^ [_1792578] : [-(c_List_Oconcat(_1792578, c_List_Olist_ONil(tc_List_Olist(_1792578))) = c_List_Olist_ONil(_1792578))], (11367 ^ _777864) ^ [_967229, _967231, _967233] : [class_Rings_Olinordered__idom(_967229), -(c_Groups_Osgn__class_Osgn(_967229, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967229), _967231), _967233)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967229), c_Groups_Osgn__class_Osgn(_967229, _967231)), c_Groups_Osgn__class_Osgn(_967229, _967233)))], (27654 ^ _777864) ^ [_1270485, _1270487, _1270489, _1270491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270485), _1270487)), 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)), _1270485), _1270489)), 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)), _1270487), _1270491)), 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)), _1270487), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270489), _1270491))), c_FunDef_Omin__strict)))], (38196 ^ _777864) ^ [_1494665, _1494667] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494665, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1494665, tc_HOL_Obool))), _1494667) = c_Orderings_Otop__class_Otop(tc_fun(_1494665, tc_HOL_Obool)))], (12934 ^ _777864) ^ [_994924, _994926] : [-(_994924 = hAPP(c_Int_Onat, _994926)), 12937 ^ _777864 : [(12940 ^ _777864) ^ [] : [_994926 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994924)], (12938 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994926)))]], 12941 ^ _777864 : [(12944 ^ _777864) ^ [] : [_994924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12942 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994926))]]], (9812 ^ _777864) ^ [_941870, _941872, _941874] : [class_Rings_Olinordered__ring__strict(_941870), 9815 ^ _777864 : [(9816 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941870), c_Groups_Ozero__class_Ozero(_941870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941870), _941872), _941872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941870), _941874), _941874)))), _941872 = c_Groups_Ozero__class_Ozero(_941870), _941874 = c_Groups_Ozero__class_Ozero(_941870)], (9826 ^ _777864) ^ [] : [9827 ^ _777864 : [(9830 ^ _777864) ^ [] : [-(_941874 = c_Groups_Ozero__class_Ozero(_941870))], (9828 ^ _777864) ^ [] : [-(_941872 = c_Groups_Ozero__class_Ozero(_941870))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941870), c_Groups_Ozero__class_Ozero(_941870)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941870), _941872), _941872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941870), _941874), _941874)))))]]], (42297 ^ _777864) ^ [_1599466, _1599468] : [-(c_Hilbert__Choice_OEps(_1599466, hAPP(hAPP(c_COMBC(_1599466, _1599466, tc_HOL_Obool), c_fequal), _1599468)) = _1599468)], (9893 ^ _777864) ^ [_943211, _943213] : [class_Rings_Olinordered__idom(_943211), 9896 ^ _777864 : [(9903 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943211), _943213), c_Groups_Ozero__class_Ozero(_943211))), -(c_Groups_Osgn__class_Osgn(_943211, _943213) = hAPP(c_Groups_Ouminus__class_Ouminus(_943211), c_Groups_Oone__class_Oone(_943211)))], (9897 ^ _777864) ^ [] : [c_Groups_Osgn__class_Osgn(_943211, _943213) = hAPP(c_Groups_Ouminus__class_Ouminus(_943211), c_Groups_Oone__class_Oone(_943211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943211), _943213), c_Groups_Ozero__class_Ozero(_943211))))]]], (38236 ^ _777864) ^ [] : [-(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)))], (40815 ^ _777864) ^ [_1564129, _1564131, _1564133, _1564135, _1564137, _1564139, _1564141] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564129, _1564133)), hAPP(hAPP(c_Product__Type_OPair(_1564129, _1564133), _1564139), _1564141)), hAPP(hAPP(c_Relation_Orel__comp(_1564129, _1564131, _1564133), _1564135), _1564137))), -(c_Predicate_Opred__comp(_1564129, _1564131, _1564133, hAPP(hAPP(c_COMBC(_1564129, tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_fun(_1564131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564131, tc_fun(tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_fun(_1564131, tc_HOL_Obool)), _1564129), c_COMBC(_1564131, tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564131, tc_prod(_1564129, _1564131)), tc_fun(_1564131, tc_fun(tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_HOL_Obool)), _1564129), hAPP(c_COMBB(tc_prod(_1564129, _1564131), tc_fun(tc_fun(tc_prod(_1564129, _1564131), tc_HOL_Obool), tc_HOL_Obool), _1564131), c_member(tc_prod(_1564129, _1564131)))), c_Product__Type_OPair(_1564129, _1564131)))), _1564135), hAPP(hAPP(c_COMBC(_1564131, tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_fun(_1564133, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564133, tc_fun(tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_fun(_1564133, tc_HOL_Obool)), _1564131), c_COMBC(_1564133, tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564133, tc_prod(_1564131, _1564133)), tc_fun(_1564133, tc_fun(tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_HOL_Obool)), _1564131), hAPP(c_COMBB(tc_prod(_1564131, _1564133), tc_fun(tc_fun(tc_prod(_1564131, _1564133), tc_HOL_Obool), tc_HOL_Obool), _1564133), c_member(tc_prod(_1564131, _1564133)))), c_Product__Type_OPair(_1564131, _1564133)))), _1564137), _1564139, _1564141))], (7816 ^ _777864) ^ [_907913, _907915] : [class_Rings_Olinordered__semidom(_907913), 7819 ^ _777864 : [(7826 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _907915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907913), c_Groups_Ozero__class_Ozero(_907913)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_907913), _907915))))], (7820 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907913), c_Groups_Ozero__class_Ozero(_907913)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_907913), _907915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _907915)))]]], (18564 ^ _777864) ^ [_1097057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1097057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1097057)))], (17132 ^ _777864) ^ [_1073334] : [-(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), _1073334)) = 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), _1073334))))], (10642 ^ _777864) ^ [_955292, _955294, _955296] : [class_Orderings_Olinorder(_955292), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955292), _955294), _955296))), 10649 ^ _777864 : [(10656 ^ _777864) ^ [] : [_955294 = _955296, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955292), _955294), _955296)))], (10650 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955292), _955294), _955296)), -(_955294 = _955296)]]], (13425 ^ _777864) ^ [_1003417, _1003419, _1003421, _1003423] : [class_Divides_Osemiring__div(_1003417), -(c_Divides_Odiv__class_Omod(_1003417, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003417), _1003419), _1003421), _1003423) = c_Divides_Odiv__class_Omod(_1003417, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003417), _1003419), c_Divides_Odiv__class_Omod(_1003417, _1003421, _1003423)), _1003423))], (1122 ^ _777864) ^ [_794657, _794659] : [-(class_Groups_Ogroup__add(_794657)), _794659 = _794657, class_Groups_Ogroup__add(_794659)], (51369 ^ _777864) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (22889 ^ _777864) ^ [_1174489, _1174491] : [-(c_Divides_Odivmod__nat(_1174489, _1174491) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1174489), _1174491)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1174489, _1174491)))], (45741 ^ _777864) ^ [_1681966, _1681968, _1681970, _1681972, _1681974, _1681976] : [c_Map_Omap__comp(_1681966, _1681968, _1681970, _1681972, _1681974, _1681976) = c_Option_Ooption_ONone(_1681968), -(hAPP(_1681974, _1681976) = c_Option_Ooption_ONone(_1681966)), 45749 ^ _777864 : [(45752 ^ _777864) ^ [] : [-(hAPP(_1681972, 45748 ^ [_1681966, _1681968, _1681970, _1681972, _1681974, _1681976]) = c_Option_Ooption_ONone(_1681968))], (45750 ^ _777864) ^ [] : [-(hAPP(_1681974, _1681976) = hAPP(c_Option_Ooption_OSome(_1681966), 45748 ^ [_1681966, _1681968, _1681970, _1681972, _1681974, _1681976]))]]], (46599 ^ _777864) ^ [_1704754, _1704756, _1704758, _1704760, _1704762, _1704764] : [c_List_Olistrelp(_1704754, _1704756, hAPP(hAPP(c_List_Olist_OCons(_1704754), _1704758), _1704760), hAPP(hAPP(c_List_Olist_OCons(_1704754), _1704762), _1704764)), 46602 ^ _777864 : [(46605 ^ _777864) ^ [] : [-(c_List_Olistrelp(_1704754, _1704756, _1704760, _1704764))], (46603 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1704756, _1704758), _1704762)))]]], (21078 ^ _777864) ^ [_1141304, _1141306] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141304), _1141306), hAPP(c_Int_Onumber__class_Onumber__of(_1141304), c_Int_OBit1(c_Int_OPls))) = _1141306), class_Fields_Ofield(_1141304), class_Int_Onumber__ring(_1141304)], (78 ^ _777864) ^ [_778885, _778887, _778889, _778891, _778893, _778895, _778897, _778899] : [-(c_Nat__Transfer_Otransfer__morphism(_778897, _778893, _778889, _778885)), c_Nat__Transfer_Otransfer__morphism(_778899, _778895, _778891, _778887), _778899 = _778897, _778895 = _778893, _778891 = _778889, _778887 = _778885], (51511 ^ _777864) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (42589 ^ _777864) ^ [_1606049, _1606051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606049), _1606051)), -(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), _1606049), _1606051)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (31567 ^ _777864) ^ [_1354914, _1354916] : [class_Orderings_Olinorder(_1354914), -(c_Big__Operators_Olinorder__class_OMin(_1354914, hAPP(hAPP(c_Set_Oinsert(_1354914), _1354916), c_Orderings_Obot__class_Obot(tc_fun(_1354914, tc_HOL_Obool)))) = _1354916)], (10934 ^ _777864) ^ [_959888, _959890, _959892] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959888)), _959890) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _959888)), _959892), -(_959890 = _959892)], (37524 ^ _777864) ^ [_1481698, _1481700, _1481702, _1481704] : [c_Finite__Set_Ofolding__one__idem(_1481698, _1481700, _1481702), -(hAPP(hAPP(_1481700, _1481704), _1481704) = _1481704)], (41346 ^ _777864) ^ [_1576284, _1576286, _1576288, _1576290, _1576292] : [-(hAPP(c_Relation_ODomain(_1576284, _1576286), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1576284, _1576286)), hAPP(hAPP(c_Product__Type_OPair(_1576284, _1576286), _1576288), _1576290)), _1576292)) = hAPP(hAPP(c_Set_Oinsert(_1576284), _1576288), hAPP(c_Relation_ODomain(_1576284, _1576286), _1576292)))], (20734 ^ _777864) ^ [_1135429, _1135431, _1135433, _1135435] : [class_Fields_Olinordered__field__inverse__zero(_1135429), 20737 ^ _777864 : [(20738 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135431), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135429), _1135433), _1135435))), 20741 ^ _777864 : [(20748 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), c_Groups_Ozero__class_Ozero(_1135429)), _1135435))), 20751 ^ _777864 : [(20758 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135435), c_Groups_Ozero__class_Ozero(_1135429)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135431), c_Groups_Ozero__class_Ozero(_1135429))))], (20752 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135435), c_Groups_Ozero__class_Ozero(_1135429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135429), _1135431), _1135435))))]]], (20742 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), c_Groups_Ozero__class_Ozero(_1135429)), _1135435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135429), _1135431), _1135435)), _1135433)))]]], (20764 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135431), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135429), _1135433), _1135435)))), 20767 ^ _777864 : [(20770 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135429), _1135431), _1135435)), _1135433))], (20768 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), c_Groups_Ozero__class_Ozero(_1135429)), _1135435)))]], 20771 ^ _777864 : [(20774 ^ _777864) ^ [] : [20775 ^ _777864 : [(20778 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135429), _1135431), _1135435)))], (20776 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135435), c_Groups_Ozero__class_Ozero(_1135429))))]], 20779 ^ _777864 : [(20782 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135431), c_Groups_Ozero__class_Ozero(_1135429)))], (20780 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), _1135435), c_Groups_Ozero__class_Ozero(_1135429)))]]], (20772 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135429), c_Groups_Ozero__class_Ozero(_1135429)), _1135435))]]]]], (6162 ^ _777864) ^ [_879185, _879187] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _879185), _879187)), -(_879187 = _879185)], (7200 ^ _777864) ^ [_896271, _896273] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_896271, _896273))), 7203 ^ _777864 : [(7206 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _896273)))], (7204 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _896271)))]]], (7254 ^ _777864) ^ [_897198] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _897198) = _897198)], (37723 ^ _777864) ^ [_1485564, _1485566, _1485568] : [class_Orderings_Oorder(_1485564), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485564, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1485564, _1485566, _1485568)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485564), _1485568)) = c_Orderings_Obot__class_Obot(tc_fun(_1485564, tc_HOL_Obool)))], (37196 ^ _777864) ^ [_1474644, _1474646, _1474648] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474644, tc_Nat_Onat), _1474646), _1474648)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474644, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1474644), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1474646)), _1474648))], (51267 ^ _777864) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (51161 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (37558 ^ _777864) ^ [_1482256, _1482258, _1482260, _1482262, _1482264] : [c_Finite__Set_Ofolding__one__idem(_1482256, _1482258, _1482260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482256), _1482262)), -(_1482264 = c_Orderings_Obot__class_Obot(tc_fun(_1482256, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482256, tc_HOL_Obool)), _1482264), _1482262)), -(hAPP(hAPP(_1482258, hAPP(_1482260, _1482264)), hAPP(_1482260, _1482262)) = hAPP(_1482260, _1482262))], (29225 ^ _777864) ^ [_1306682, _1306684, _1306686] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1306682), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306682, tc_HOL_Obool)), _1306684), _1306686))), 29228 ^ _777864 : [(29231 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306682), _1306686)))], (29229 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306682), _1306684)))]]], (38532 ^ _777864) ^ [_1501564] : [-(c_Fun_Oinj__on(_1501564, tc_fun(_1501564, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1501564, tc_fun(_1501564, tc_HOL_Obool), tc_fun(_1501564, tc_HOL_Obool)), c_Set_Oinsert(_1501564)), c_Orderings_Obot__class_Obot(tc_fun(_1501564, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1501564, tc_HOL_Obool))))], (38376 ^ _777864) ^ [_1498140, _1498142, _1498144, _1498146] : [c_Fun_Oinj__on(_1498140, _1498142, _1498144, c_Orderings_Otop__class_Otop(tc_fun(_1498140, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1498140, tc_fun(_1498146, _1498142), hAPP(hAPP(c_COMBB(_1498142, tc_fun(_1498146, _1498142), _1498140), c_COMBK(_1498142, _1498146)), _1498144), c_Orderings_Otop__class_Otop(tc_fun(_1498140, tc_HOL_Obool))))], (45920 ^ _777864) ^ [_1686303, _1686305, _1686307] : [-(hAPP(c_Option_Omap(_1686303, _1686305), _1686307) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1686305), _1686303, c_Option_Ooption_ONone(_1686305), hAPP(hAPP(c_COMBB(_1686305, tc_Option_Ooption(_1686305), _1686303), c_Option_Ooption_OSome(_1686305)), _1686307)))], (36110 ^ _777864) ^ [_1450000, _1450002, _1450004, _1450006, _1450008, _1450010] : [_1450000 = _1450002, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450004, _1450006), _1450008), _1450002), _1450010), _1450000) = _1450010)], (24423 ^ _777864) ^ [_1205653, _1205655, _1205657, _1205659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205653, tc_HOL_Obool)), _1205655), _1205657)), hBOOL(hAPP(_1205655, _1205659)), -(hBOOL(hAPP(_1205657, _1205659)))], (6923 ^ _777864) ^ [_891708, _891710] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _891708) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _891710), -(hBOOL(hAPP(c_Com_OWT, _891710)))], (9172 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (48546 ^ _777864) ^ [_1753145, _1753147, _1753149, _1753151] : [-(hAPP(hAPP(c_List_Odrop(_1753145), hAPP(c_Nat_OSuc, _1753147)), hAPP(hAPP(c_List_Olist_OCons(_1753145), _1753149), _1753151)) = hAPP(hAPP(c_List_Odrop(_1753145), _1753147), _1753151))], (38258 ^ _777864) ^ [_1495769, _1495771] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495769), c_Orderings_Otop__class_Otop(tc_fun(_1495769, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1495769), _1495771) = hAPP(c_Finite__Set_Ocard(_1495769), c_Orderings_Otop__class_Otop(tc_fun(_1495769, tc_HOL_Obool))), -(_1495771 = c_Orderings_Otop__class_Otop(tc_fun(_1495769, tc_HOL_Obool)))], (31025 ^ _777864) ^ [_1344783, _1344785, _1344787] : [class_Orderings_Olinorder(_1344783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344783), _1344785)), -(_1344785 = c_Orderings_Obot__class_Obot(tc_fun(_1344783, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1344783, hAPP(hAPP(c_Set_Oinsert(_1344783), _1344787), _1344785)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1344783), _1344787), c_Big__Operators_Olinorder__class_OMax(_1344783, _1344785)))], (19142 ^ _777864) ^ [_1106862, _1106864] : [class_Int_Onumber__ring(_1106862), -(hAPP(c_Int_Onumber__class_Onumber__of(_1106862), c_Int_OBit0(_1106864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106862), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106862), c_Groups_Ozero__class_Ozero(_1106862)), hAPP(c_Int_Onumber__class_Onumber__of(_1106862), _1106864))), hAPP(c_Int_Onumber__class_Onumber__of(_1106862), _1106864)))], (14886 ^ _777864) ^ [_1030049, _1030051, _1030053] : [class_Divides_Osemiring__div(_1030049), -(_1030051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030049), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1030049), _1030051), _1030053)), _1030053)), c_Divides_Odiv__class_Omod(_1030049, _1030051, _1030053)))], (4684 ^ _777864) ^ [_849476, _849478] : [_849478 = _849476, -(c_Option_Ooption_ONone(_849478) = c_Option_Ooption_ONone(_849476))], (36490 ^ _777864) ^ [_1457583, _1457585, _1457587, _1457589, _1457591] : [-(hBOOL(hAPP(hAPP(c_member(_1457583), _1457585), _1457587))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1457583, tc_Option_Ooption(_1457589)), c_Map_Orestrict__map(_1457583, _1457589, _1457591, _1457587)), _1457585), c_Option_Ooption_ONone(_1457589)) = c_Map_Orestrict__map(_1457583, _1457589, _1457591, _1457587))], (26171 ^ _777864) ^ [_1238063, _1238065, _1238067, _1238069] : [c_Hoare__Mirabelle_Ohoare__derivs(_1238063, _1238065, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1238063)), _1238067), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1238063), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1238063, _1238065, _1238069), -(c_Hoare__Mirabelle_Ohoare__derivs(_1238063, _1238065, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1238063)), _1238067), _1238069)))], (46515 ^ _777864) ^ [_1701952, _1701954, _1701956] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701952), tc_List_Olist(_1701952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701952), tc_List_Olist(_1701952)), _1701954), _1701954)), c_List_Olistrel(_1701952, c_Transitive__Closure_Ortrancl(_1701952, _1701956)))))], (28292 ^ _777864) ^ [_1282892, _1282894, _1282896, _1282898] : [hBOOL(hAPP(hAPP(c_member(_1282892), _1282894), _1282896)), -(hBOOL(hAPP(hAPP(c_member(_1282892), _1282894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282892, tc_HOL_Obool)), _1282898), _1282896))))], (8550 ^ _777864) ^ [_919699, _919701] : [class_Rings_Oring__1__no__zero__divisors(_919699), 8553 ^ _777864 : [(8554 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919699), _919701), _919701) = c_Groups_Oone__class_Oone(_919699), -(_919701 = c_Groups_Oone__class_Oone(_919699)), -(_919701 = hAPP(c_Groups_Ouminus__class_Ouminus(_919699), c_Groups_Oone__class_Oone(_919699)))], (8564 ^ _777864) ^ [] : [8565 ^ _777864 : [(8568 ^ _777864) ^ [] : [_919701 = hAPP(c_Groups_Ouminus__class_Ouminus(_919699), c_Groups_Oone__class_Oone(_919699))], (8566 ^ _777864) ^ [] : [_919701 = c_Groups_Oone__class_Oone(_919699)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919699), _919701), _919701) = c_Groups_Oone__class_Oone(_919699))]]], (47528 ^ _777864) ^ [_1728106, _1728108, _1728110, _1728112, _1728114] : [class_Orderings_Olinorder(_1728106), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1728108, _1728106, _1728110), _1728112), _1728114) = c_List_Olist_ONil(_1728108)], (33803 ^ _777864) ^ [_1402266, _1402268, _1402270, _1402272, _1402274] : [-(_1402266 = c_Orderings_Obot__class_Obot(tc_fun(_1402268, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402268, tc_fun(_1402270, tc_HOL_Obool)), _1402266), hAPP(hAPP(c_COMBB(tc_fun(_1402270, tc_HOL_Obool), tc_fun(_1402270, tc_HOL_Obool), _1402268), hAPP(c_Set_Oinsert(_1402270), _1402272)), _1402274)) = hAPP(hAPP(c_Set_Oinsert(_1402270), _1402272), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402268, tc_fun(_1402270, tc_HOL_Obool)), _1402266), _1402274)))], (30448 ^ _777864) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (33482 ^ _777864) ^ [_1393518, _1393520, _1393522, _1393524, _1393526, _1393528, _1393530, _1393532, _1393534, _1393536] : [c_Equiv__Relations_Oequiv(_1393518, _1393520, _1393522), c_Equiv__Relations_Oequiv(_1393524, _1393526, _1393528), c_Equiv__Relations_Ocongruent2(_1393518, _1393524, tc_fun(_1393530, tc_HOL_Obool), _1393522, _1393528, _1393532), hBOOL(hAPP(hAPP(c_member(_1393518), _1393534), _1393520)), hBOOL(hAPP(hAPP(c_member(_1393524), _1393536), _1393526)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393518, tc_fun(_1393530, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1393518, _1393518, _1393522), hAPP(hAPP(c_Set_Oinsert(_1393518), _1393534), c_Orderings_Obot__class_Obot(tc_fun(_1393518, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1393524, tc_fun(_1393530, tc_HOL_Obool)), tc_fun(_1393530, tc_HOL_Obool), _1393518), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393524, tc_fun(_1393530, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1393524, _1393524, _1393528), hAPP(hAPP(c_Set_Oinsert(_1393524), _1393536), c_Orderings_Obot__class_Obot(tc_fun(_1393524, tc_HOL_Obool)))))), _1393532)) = hAPP(hAPP(_1393532, _1393534), _1393536))], (17140 ^ _777864) ^ [_1073501, _1073503] : [class_Groups_Omonoid__mult(_1073501), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1073501), _1073503), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1073503)], (48957 ^ _777864) ^ [_1762035, _1762037] : [-(c_List_Olist_Olist__size(_1762035, _1762037, c_List_Olist_ONil(_1762035)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51199 ^ _777864) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (10476 ^ _777864) ^ [_952833, _952835, _952837, _952839] : [class_Orderings_Oorder(_952833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952833), _952835), _952837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952833), _952839), _952835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952833), _952839), _952837)))], (16004 ^ _777864) ^ [_1052082, _1052084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052084)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1052084), _1052082)), _1052084) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1052084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052082), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (13720 ^ _777864) ^ [_1008967, _1008969] : [class_Lattices_Oboolean__algebra(_1008967), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1008967), hAPP(c_Groups_Ouminus__class_Ouminus(_1008967), _1008969)) = _1008969)], (7616 ^ _777864) ^ [_904125, _904127, _904129] : [-(hBOOL(hAPP(_904125, _904127))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_904125, _904129)), _904127), _904127)))], (43110 ^ _777864) ^ [_1616701, _1616703, _1616705, _1616707, _1616709] : [c_Finite__Set_Ofun__left__comm(_1616701, _1616703, _1616705), -(c_Finite__Set_Ofun__left__comm(_1616707, _1616703, hAPP(hAPP(c_COMBB(_1616701, tc_fun(_1616703, _1616703), _1616707), _1616705), _1616709)))], (25977 ^ _777864) ^ [_1233974, _1233976, _1233978, _1233980] : [class_Orderings_Oorder(_1233974), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1233974, 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)))), _1233976), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233974), hAPP(_1233976, _1233978)), hAPP(_1233976, _1233980)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233978), _1233980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233980), _1233978)))], (34699 ^ _777864) ^ [_1422098, _1422100] : [class_Orderings_Oorder(_1422098), -(c_SetInterval_Oord__class_OatLeastAtMost(_1422098, _1422100, _1422100) = hAPP(hAPP(c_Set_Oinsert(_1422098), _1422100), c_Orderings_Obot__class_Obot(tc_fun(_1422098, tc_HOL_Obool))))], (1312 ^ _777864) ^ [_797032, _797034] : [-(class_Lattices_Olattice(_797032)), _797034 = _797032, class_Lattices_Olattice(_797034)], (9694 ^ _777864) ^ [_939867] : [class_Rings_Oring__1(_939867), -(hAPP(c_Int_Oring__1__class_Oof__int(_939867), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_939867))], (36508 ^ _777864) ^ [_1457962, _1457964, _1457966, _1457968, _1457970] : [hBOOL(hAPP(hAPP(c_member(_1457962), _1457964), _1457966)), -(hAPP(c_Map_Orestrict__map(_1457962, _1457968, _1457970, _1457966), _1457964) = hAPP(_1457970, _1457964))], (1732 ^ _777864) ^ [_802282, _802284] : [-(class_Power_Opower(_802282)), _802284 = _802282, class_Power_Opower(_802284)], (22512 ^ _777864) ^ [_1166955, _1166957] : [-(c_Divides_Odivmod__int(_1166955, _1166957) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1166955), _1166957)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166955, _1166957)))], (22462 ^ _777864) ^ [_1166125, _1166127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166125), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166127), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166125, _1166127) = 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), _1166125), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166127)))))], (44330 ^ _777864) ^ [_1648550, _1648552, _1648554, _1648556, _1648558] : [c_Relation_Osingle__valued(_1648550, _1648550, _1648552), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648550, _1648550)), hAPP(hAPP(c_Product__Type_OPair(_1648550, _1648550), _1648554), _1648556)), c_Transitive__Closure_Ortrancl(_1648550, _1648552))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648550, _1648550)), hAPP(hAPP(c_Product__Type_OPair(_1648550, _1648550), _1648554), _1648558)), c_Transitive__Closure_Ortrancl(_1648550, _1648552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1648550, _1648550)), hAPP(hAPP(c_Product__Type_OPair(_1648550, _1648550), _1648556), _1648558)), c_Transitive__Closure_Ortrancl(_1648550, _1648552)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1648550, _1648550)), hAPP(hAPP(c_Product__Type_OPair(_1648550, _1648550), _1648558), _1648556)), c_Transitive__Closure_Ortrancl(_1648550, _1648552))))], (50925 ^ _777864) ^ [_1805006, _1805008] : [c_List_Oremdups(_1805006, _1805008) = _1805008, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805006)), c_List_Oremdups(_1805006, _1805008)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805006)), _1805008))], (43647 ^ _777864) ^ [_1628794, _1628796, _1628798, _1628800, _1628802] : [-(_1628794 = c_Orderings_Obot__class_Obot(tc_fun(_1628796, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628798, tc_HOL_Obool)), _1628800), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628796, tc_fun(_1628798, tc_HOL_Obool)), _1628794), _1628802)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628796, tc_fun(_1628798, tc_HOL_Obool)), _1628794), hAPP(hAPP(c_COMBB(tc_fun(_1628798, tc_HOL_Obool), tc_fun(_1628798, tc_HOL_Obool), _1628796), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628798, tc_HOL_Obool)), _1628800)), _1628802)))], (24755 ^ _777864) ^ [_1212524, _1212526, _1212528] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1212524), _1212526)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1212524), _1212528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1212524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212526), _1212528)))], (50382 ^ _777864) ^ [_1792546] : [-(hAPP(c_List_Orev(_1792546), c_List_Olist_ONil(_1792546)) = c_List_Olist_ONil(_1792546))], (12270 ^ _777864) ^ [] : [-(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))], (30979 ^ _777864) ^ [_1344061, _1344063, _1344065] : [class_Orderings_Olinorder(_1344061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344061, tc_HOL_Obool)), _1344063), _1344065)), -(_1344063 = c_Orderings_Obot__class_Obot(tc_fun(_1344061, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344061), _1344065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344061), c_Big__Operators_Olinorder__class_OMax(_1344061, _1344063)), c_Big__Operators_Olinorder__class_OMax(_1344061, _1344065))))], (36450 ^ _777864) ^ [_1456591, _1456593] : [class_Orderings_Olinorder(_1456591), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456591, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1456591), _1456593)), hAPP(hAPP(c_Set_Oinsert(_1456591), _1456593), c_Orderings_Obot__class_Obot(tc_fun(_1456591, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1456591), _1456593))], (28906 ^ _777864) ^ [_1300011, _1300013] : [c_Nat__Transfer_Onat__set(_1300011), c_Nat__Transfer_Onat__set(_1300013), 28913 ^ _777864 : [(28920 ^ _777864) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1300011) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1300013), -(_1300011 = _1300013)], (28914 ^ _777864) ^ [] : [_1300011 = _1300013, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1300011) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1300013))]]], (13196 ^ _777864) ^ [_999432, _999434, _999436, _999438] : [class_Orderings_Oord(_999432), 13199 ^ _777864 : [(13208 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999434, _999432)), _999436), _999438))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999434, _999432)), _999436), _999438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999434, _999432)), _999438), _999436)))], (13200 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999434, _999432)), _999436), _999438)), 13203 ^ _777864 : [(13206 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999434, _999432)), _999438), _999436))], (13204 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999434, _999432)), _999436), _999438)))]]]]], (6972 ^ _777864) ^ [_892541, _892543] : [c_Option_Ooption_ONone(_892541) = hAPP(c_Option_Ooption_OSome(_892541), _892543)], (8038 ^ _777864) ^ [_911815, _911817] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911815)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911817)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911815), _911817)))], (30162 ^ _777864) ^ [_1326799, _1326801, _1326803, _1326805] : [hBOOL(hAPP(hAPP(c_member(_1326799), _1326801), _1326803)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326799, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1326799), _1326801), _1326805)), _1326803) = hAPP(hAPP(c_Set_Oinsert(_1326799), _1326801), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326799, tc_HOL_Obool)), _1326805), _1326803)))], (15206 ^ _777864) ^ [_1035916, _1035918, _1035920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035916), _1035918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035916), _1035920)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035918), _1035916)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035920), _1035916)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035918), _1035920))], (26679 ^ _777864) ^ [_1248624, _1248626, _1248628, _1248630] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248624, tc_HOL_Obool)), _1248626), hAPP(hAPP(c_Set_Oinsert(_1248624), _1248628), _1248630)))), 26682 ^ _777864 : [(26685 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248624, tc_HOL_Obool)), _1248626), _1248630))], (26683 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248624), _1248628), _1248630)))]], 26686 ^ _777864 : [(26689 ^ _777864) ^ [] : [26690 ^ _777864 : [(26693 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1248624, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248624, tc_HOL_Obool)), _1248626), hAPP(hAPP(c_Set_Oinsert(_1248624), _1248628), c_Orderings_Obot__class_Obot(tc_fun(_1248624, tc_HOL_Obool))))), _1248630))], (26691 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248624), _1248628), _1248626)))]], 26694 ^ _777864 : [(26697 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248624, tc_HOL_Obool)), _1248626), _1248630))], (26695 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1248624), _1248628), _1248626))]]], (26687 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1248624), _1248628), _1248630))]]], (40939 ^ _777864) ^ [_1566867, _1566869] : [c_Wellfounded_Owf(_1566867, _1566869), -(c_Wellfounded_Owf(tc_fun(_1566867, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1566867, _1566869)))], (40909 ^ _777864) ^ [_1566389, _1566391, _1566393] : [c_Wellfounded_Owf(_1566389, _1566391), -(c_Wellfounded_Owf(_1566389, c_Wellfounded_Omlex__prod(_1566389, _1566393, _1566391)))], (5580 ^ _777864) ^ [_866775, _866777, _866779, _866781, _866783, _866785] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_866775, _866777, _866779), _866781, _866783, _866785), 5584 ^ _777864 : [(5587 ^ _777864) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _866777), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _866781), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_866779, _866781)), _866783, 5583 ^ [_866775, _866777, _866779, _866781, _866783, _866785]))], (5585 ^ _777864) ^ [] : [-(_866785 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 5583 ^ [_866775, _866777, _866779, _866781, _866783, _866785]), hAPP(c_Natural_Ogetlocs, _866781))), _866775), hAPP(hAPP(c_Natural_Ogetlocs, 5583 ^ [_866775, _866777, _866779, _866781, _866783, _866785]), c_Com_ORes)))]]], (33977 ^ _777864) ^ [_1406296, _1406298, _1406300, _1406302, _1406304, _1406306, _1406308, _1406310, _1406312, _1406314, _1406316] : [c_Equiv__Relations_Oequiv(_1406296, _1406298, _1406300), c_Equiv__Relations_Oequiv(_1406302, _1406304, _1406306), c_Equiv__Relations_Ocongruent2(_1406296, _1406302, tc_fun(_1406308, tc_HOL_Obool), _1406300, _1406306, _1406310), hBOOL(hAPP(hAPP(c_member(tc_fun(_1406296, tc_HOL_Obool)), _1406312), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1406296), _1406298), _1406300))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1406302, tc_HOL_Obool)), _1406314), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1406302), _1406304), _1406306))), 33999 ^ _777864 : [(34005 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1406308, tc_HOL_Obool)), hAPP(hAPP(_1406310, 33998 ^ [_1406296, _1406298, _1406300, _1406302, _1406304, _1406306, _1406308, _1406310, _1406312, _1406314, _1406316]), 34001 ^ [_1406296, _1406298, _1406300, _1406302, _1406304, _1406306, _1406308, _1406310, _1406312, _1406314, _1406316])), _1406316))], (34003 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406302), 34001 ^ [_1406296, _1406298, _1406300, _1406302, _1406304, _1406306, _1406308, _1406310, _1406312, _1406314, _1406316]), _1406304)))], (34000 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406296), 33998 ^ [_1406296, _1406298, _1406300, _1406302, _1406304, _1406306, _1406308, _1406310, _1406312, _1406314, _1406316]), _1406298)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1406308, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406296, tc_fun(_1406308, tc_HOL_Obool)), _1406312), hAPP(hAPP(c_COMBB(tc_fun(_1406302, tc_fun(_1406308, tc_HOL_Obool)), tc_fun(_1406308, tc_HOL_Obool), _1406296), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406302, tc_fun(_1406308, tc_HOL_Obool)), _1406314)), _1406310))), _1406316)))], (30849 ^ _777864) ^ [_1341995, _1341997, _1341999] : [class_Lattices_Olattice(_1341995), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341995), _1341997)), hBOOL(hAPP(hAPP(c_member(_1341995), _1341999), _1341997)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1341995), _1341999), c_Big__Operators_Olattice__class_OInf__fin(_1341995, _1341997)) = _1341999)], (48235 ^ _777864) ^ [_1744177, _1744179, _1744181, _1744183, _1744185, _1744187] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744177), tc_List_Olist(_1744177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744177), tc_List_Olist(_1744177)), hAPP(hAPP(c_List_Oappend(_1744177), _1744179), hAPP(hAPP(c_List_Olist_OCons(_1744177), _1744181), c_List_Olist_ONil(_1744177)))), hAPP(hAPP(c_List_Oappend(_1744177), _1744183), hAPP(hAPP(c_List_Olist_OCons(_1744177), _1744185), c_List_Olist_ONil(_1744177))))), c_List_Olistrel1(_1744177, _1744187))), 48240 ^ _777864 : [(48243 ^ _777864) ^ [] : [-(_1744181 = _1744185)], (48241 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744177), tc_List_Olist(_1744177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744177), tc_List_Olist(_1744177)), _1744179), _1744183)), c_List_Olistrel1(_1744177, _1744187))))]], 48244 ^ _777864 : [(48247 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1744177, _1744177)), hAPP(hAPP(c_Product__Type_OPair(_1744177, _1744177), _1744181), _1744185)), _1744187)))], (48245 ^ _777864) ^ [] : [-(_1744179 = _1744183)]]], (33295 ^ _777864) ^ [_1389607, _1389609] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1389607, _1389609)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1389609), hAPP(c_Nat_OSuc, _1389607)))], (43229 ^ _777864) ^ [_1619314, _1619316] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1619314, _1619314, _1619314), c_Transitive__Closure_Ortrancl(_1619314, _1619316)), c_Transitive__Closure_Ortrancl(_1619314, _1619316)) = c_Transitive__Closure_Ortrancl(_1619314, _1619316))], (6380 ^ _777864) ^ [_883174, _883176, _883178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883174), _883176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _883176), _883178))))], (49069 ^ _777864) ^ [_1764866, _1764868, _1764870] : [c_Relation_Orefl__on(_1764866, _1764868, _1764870), -(c_Relation_Orefl__on(tc_List_Olist(_1764866), c_List_Olists(_1764866, _1764868), c_List_Olistrel(_1764866, _1764870)))], (21986 ^ _777864) ^ [_1158049, _1158051] : [21987 ^ _777864 : [(21990 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158051), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21988 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158049), _1158051))]], -(c_Divides_OposDivAlg(_1158049, _1158051) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158049))], (41093 ^ _777864) ^ [_1570306, _1570308, _1570310, _1570312] : [c_Wellfounded_Owf(_1570306, _1570308), c_Fun_Oinj__on(_1570306, _1570310, _1570312, c_Orderings_Otop__class_Otop(tc_fun(_1570306, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1570310, hAPP(c_Set_Oimage(tc_prod(_1570306, _1570306), tc_prod(_1570310, _1570310), c_Product__Type_Omap__pair(_1570306, _1570310, _1570306, _1570310, _1570312, _1570312)), _1570308)))], (38306 ^ _777864) ^ [_1496646, _1496648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496646, tc_HOL_Obool)), _1496648), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496646, tc_HOL_Obool)), _1496648)) = c_Orderings_Otop__class_Otop(tc_fun(_1496646, tc_HOL_Obool)))], (30426 ^ _777864) ^ [_1332770, _1332772] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332770), 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)))), _1332772)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332772), _1332770)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332770), _1332772)))], (41219 ^ _777864) ^ [_1573721, _1573723, _1573725, _1573727, _1573729] : [hBOOL(hAPP(hAPP(_1573721, _1573723), _1573725)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1573727, _1573729, _1573721), _1573725)))], (10532 ^ _777864) ^ [_953765, _953767, _953769] : [class_Orderings_Oorder(_953765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953765), _953767), _953769)), -(_953769 = _953767), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953765), _953767), _953769)))], (11279 ^ _777864) ^ [_965798, _965800] : [11280 ^ _777864 : [(11283 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _965800))], (11281 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _965798))]], 11284 ^ _777864 : [(11291 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965798), _965800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _965798)), hAPP(c_Int_Onat, _965800))))], (11285 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _965798)), hAPP(c_Int_Onat, _965800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965798), _965800)))]]], (17030 ^ _777864) ^ [_1071443] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071443) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1071443))], (46490 ^ _777864) ^ [_1700485, _1700487, _1700489, _1700491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700485), tc_List_Olist(_1700485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700485), tc_List_Olist(_1700485)), _1700487), _1700489)), c_List_Olistrel(_1700485, _1700491))), 46493 ^ _777864 : [(46496 ^ _777864) ^ [_1700821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1700485, _1700485)), _1700821), hAPP(c_List_Oset(tc_prod(_1700485, _1700485)), hAPP(hAPP(c_List_Ozip(_1700485, _1700485), _1700487), _1700489)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1700485, _1700485, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1700485, tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_fun(_1700485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700485, tc_fun(tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_fun(_1700485, tc_HOL_Obool)), _1700485), c_COMBC(_1700485, tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1700485, tc_prod(_1700485, _1700485)), tc_fun(_1700485, tc_fun(tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_HOL_Obool)), _1700485), hAPP(c_COMBB(tc_prod(_1700485, _1700485), tc_fun(tc_fun(tc_prod(_1700485, _1700485), tc_HOL_Obool), tc_HOL_Obool), _1700485), c_member(tc_prod(_1700485, _1700485)))), c_Product__Type_OPair(_1700485, _1700485)))), _1700491)), _1700821)))], (46494 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700485)), _1700487) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700485)), _1700489))]]], (40747 ^ _777864) ^ [_1561069, _1561071, _1561073, _1561075, _1561077, _1561079, _1561081] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561069, _1561071, _1561073), hAPP(hAPP(c_Relation_Orel__comp(_1561069, _1561075, _1561071), _1561077), _1561079)), _1561081) = hAPP(hAPP(c_Relation_Orel__comp(_1561069, _1561075, _1561073), _1561077), hAPP(hAPP(c_Relation_Orel__comp(_1561075, _1561071, _1561073), _1561079), _1561081)))], (43657 ^ _777864) ^ [_1629060, _1629062, _1629064, _1629066, _1629068] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629060, tc_fun(_1629062, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1629060), _1629064), _1629066)), _1629068) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1629062, tc_HOL_Obool)), hAPP(_1629068, _1629064)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629060, tc_fun(_1629062, tc_HOL_Obool)), _1629066), _1629068)))], (7956 ^ _777864) ^ [_910352, _910354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910352)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910352), _910354)))], (5531 ^ _777864) ^ [_865219, _865221, _865223, _865225] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _865219)), _865221, _865223, _865225), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _865219), _865221, hAPP(c_Nat_OSuc, _865223), _865225))], (47202 ^ _777864) ^ [_1720103, _1720105, _1720107, _1720109] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720103) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1720105), hAPP(hAPP(c_List_Olist_OCons(_1720105), _1720107), _1720109)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720103)) = hAPP(hAPP(c_List_Onth(_1720105), _1720109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720103)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32339 ^ _777864) ^ [_1369194, _1369196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1369194), _1369196))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369194), _1369196)))], (26443 ^ _777864) ^ [_1243696, _1243698] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243696), _1243698)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1243696), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243698), _1243696)) = _1243698)], (42828 ^ _777864) ^ [_1610753, _1610755, _1610757] : [class_Orderings_Olinorder(_1610753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610753), _1610755)), -(c_Big__Operators_Olinorder__class_OMax(_1610753, hAPP(hAPP(c_Set_Oinsert(_1610753), _1610757), _1610755)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610753, _1610753, c_Orderings_Oord__class_Omax(_1610753)), _1610757), _1610755))], (28286 ^ _777864) ^ [_1282761, _1282763, _1282765, _1282767] : [hBOOL(hAPP(hAPP(c_member(_1282761), _1282763), _1282765)), -(hBOOL(hAPP(hAPP(c_member(_1282761), _1282763), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282761, tc_HOL_Obool)), _1282765), _1282767))))], (51191 ^ _777864) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (6348 ^ _777864) ^ [_882568, _882570, _882572, _882574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882568), _882570)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882572), _882570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882568), _882574), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882572), _882574)))], (49671 ^ _777864) ^ [_1778273, _1778275, _1778277, _1778279] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1778273, tc_Nat_Onat), _1778273), c_Product__Type_Ofst(_1778273, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1778273, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1778273, tc_Nat_Onat)), _1778275), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1778273, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1778273, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1778273, tc_Nat_Onat), _1778277), _1778279))) = hAPP(hAPP(c_List_Omap(tc_prod(_1778273, tc_Nat_Onat), _1778273), c_Product__Type_Ofst(_1778273, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1778273, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1778273, tc_Nat_Onat)), _1778275), c_Product__Type_Osnd(_1778273, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1778273, tc_Nat_Onat), _1778277), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1778279)))))], (9650 ^ _777864) ^ [_939145, _939147] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939145)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939147)), _939145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _939147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17738 ^ _777864) ^ [_1083578, _1083580] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083578) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083580), 17741 ^ _777864 : [(17748 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083578)))), 17751 ^ _777864 : [(17758 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083580)))), -(_1083578 = _1083580)], (17752 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083580))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083578) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (17742 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083580)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (46360 ^ _777864) ^ [_1696691, _1696693, _1696695, _1696697, _1696699] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696691)), _1696693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696695)), _1696697), 46363 ^ _777864 : [(46372 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1696691, _1696695), _1696693), _1696697) = _1696699), hAPP(hAPP(c_List_Omap(tc_prod(_1696691, _1696695), _1696691), c_Product__Type_Ofst(_1696691, _1696695)), _1696699) = _1696693, hAPP(hAPP(c_List_Omap(tc_prod(_1696691, _1696695), _1696695), c_Product__Type_Osnd(_1696691, _1696695)), _1696699) = _1696697], (46364 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Ozip(_1696691, _1696695), _1696693), _1696697) = _1696699, 46367 ^ _777864 : [(46370 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1696691, _1696695), _1696695), c_Product__Type_Osnd(_1696691, _1696695)), _1696699) = _1696697)], (46368 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1696691, _1696695), _1696691), c_Product__Type_Ofst(_1696691, _1696695)), _1696699) = _1696693)]]]]], (46559 ^ _777864) ^ [_1703879, _1703881, _1703883, _1703885] : [hBOOL(hAPP(hAPP(c_member(_1703879), _1703881), hAPP(c_List_Oset(_1703879), hAPP(hAPP(c_List_Olist_OCons(_1703879), _1703883), _1703885)))), -(_1703881 = _1703883), -(hBOOL(hAPP(hAPP(c_member(_1703879), _1703881), hAPP(c_List_Oset(_1703879), _1703885))))], (35512 ^ _777864) ^ [_1438327, _1438329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1438327)), 35521 ^ _777864 : [(35524 ^ _777864) ^ [] : [hBOOL(hAPP(_1438329, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35517 ^ [_1438327, _1438329]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 35518 ^ [_1438327, _1438329]), _1438327))))], (35522 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1438329, 35517 ^ [_1438327, _1438329])))]], 35525 ^ _777864 : [(35528 ^ _777864) ^ [] : [hBOOL(hAPP(_1438329, 35517 ^ [_1438327, _1438329]))], (35526 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1438329, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35517 ^ [_1438327, _1438329]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 35518 ^ [_1438327, _1438329]), _1438327)))))]], 35529 ^ _777864 : [(35539 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1438329, 35546 ^ [_1438327, _1438329]))), 35540 ^ _777864 : [(35541 ^ _777864) ^ [_1438874] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1438874), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1438327))), hBOOL(hAPP(_1438329, _1438874))]]], (35530 ^ _777864) ^ [] : [35531 ^ _777864 : [(35532 ^ _777864) ^ [_1438759] : [hBOOL(hAPP(_1438329, _1438759))]], 35534 ^ _777864 : [(35537 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1438329, 35533 ^ [_1438327, _1438329])))], (35535 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35533 ^ [_1438327, _1438329]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1438327))))]]]]], (6468 ^ _777864) ^ [_884658, _884660, _884662] : [_884660 = _884662, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884658), _884660) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884658), _884662))], (28873 ^ _777864) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (46807 ^ _777864) ^ [_1710441, _1710443, _1710445, _1710447, _1710449] : [class_Groups_Oab__group__add(_1710441), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1710441), hAPP(hAPP(c_List_Omap(_1710443, _1710441), hAPP(hAPP(c_COMBS(_1710443, _1710441, _1710441), hAPP(hAPP(c_COMBB(_1710441, tc_fun(_1710441, _1710441), _1710443), c_Groups_Ominus__class_Ominus(_1710441)), _1710445)), _1710447)), _1710449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1710441), hAPP(c_List_Omonoid__add__class_Olistsum(_1710441), hAPP(hAPP(c_List_Omap(_1710443, _1710441), _1710445), _1710449))), hAPP(c_List_Omonoid__add__class_Olistsum(_1710441), hAPP(hAPP(c_List_Omap(_1710443, _1710441), _1710447), _1710449))))], (30809 ^ _777864) ^ [_1341374, _1341376] : [class_Lattices_Olattice(_1341374), -(c_Big__Operators_Olattice__class_OInf__fin(_1341374, hAPP(hAPP(c_Set_Oinsert(_1341374), _1341376), c_Orderings_Obot__class_Obot(tc_fun(_1341374, tc_HOL_Obool)))) = _1341376)], (26437 ^ _777864) ^ [_1243585, _1243587] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243585), _1243587)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243585)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243587))))], (50867 ^ _777864) ^ [_1804056, _1804058] : [_1804058 = c_List_Olist_ONil(_1804056), -(c_List_Olist_ONil(_1804056) = c_List_Oremdups(_1804056, _1804058))], (47666 ^ _777864) ^ [_1730806, _1730808, _1730810] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1730806))), -(c_List_Osublist(_1730808, hAPP(hAPP(c_List_Olist_OCons(_1730808), _1730810), c_List_Olist_ONil(_1730808)), _1730806) = c_List_Olist_ONil(_1730808))], (1112 ^ _777864) ^ [_794532, _794534] : [-(class_Rings_Ocomm__ring__1(_794532)), _794534 = _794532, class_Rings_Ocomm__ring__1(_794534)], (50092 ^ _777864) ^ [_1785994, _1785996, _1785998, _1786000, _1786002] : [class_Orderings_Olinorder(_1785994), 50095 ^ _777864 : [(50102 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1785994, hAPP(hAPP(c_List_Omap(_1785996, _1785994), _1785998), _1786002)), -(c_List_Olinorder__class_Osorted(_1785994, hAPP(hAPP(c_List_Omap(_1785996, _1785994), _1785998), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1785996, _1785994, _1785998), _1786000), _1786002))))], (50096 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1785994, hAPP(hAPP(c_List_Omap(_1785996, _1785994), _1785998), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1785996, _1785994, _1785998), _1786000), _1786002))), -(c_List_Olinorder__class_Osorted(_1785994, hAPP(hAPP(c_List_Omap(_1785996, _1785994), _1785998), _1786002)))]]], (51439 ^ _777864) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (17086 ^ _777864) ^ [_1072395, _1072397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072395)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1072395)), _1072397) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1072395), _1072397)))], (19106 ^ _777864) ^ [_1106330] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106330))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106330)))))], (3488 ^ _777864) ^ [_830862, _830864] : [_830864 = _830862, -(c_Nitpick_Odenom(_830864) = c_Nitpick_Odenom(_830862))], (28168 ^ _777864) ^ [_1280199, _1280201, _1280203, _1280205] : [28169 ^ _777864 : [(28170 ^ _777864) ^ [_1280309] : [hBOOL(hAPP(hAPP(c_member(_1280199), _1280309), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280199, tc_HOL_Obool)), _1280201), _1280203))), hBOOL(hAPP(_1280205, _1280309))]], 28178 ^ _777864 : [(28181 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1280205, 28177 ^ [_1280199, _1280201, _1280203, _1280205])))], (28179 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280199), 28177 ^ [_1280199, _1280201, _1280203, _1280205]), _1280201)))]], 28183 ^ _777864 : [(28186 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1280205, 28182 ^ [_1280199, _1280201, _1280203, _1280205])))], (28184 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280199), 28182 ^ [_1280199, _1280201, _1280203, _1280205]), _1280203)))]]], (48794 ^ _777864) ^ [_1758629, _1758631, _1758633] : [-(hAPP(c_List_Oset(_1758629), hAPP(c_List_Orotate(_1758629, _1758631), _1758633)) = hAPP(c_List_Oset(_1758629), _1758633))], (25121 ^ _777864) ^ [_1218699, _1218701] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218699), _1218701)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218701), _1218699)), -(_1218699 = _1218701)], (35052 ^ _777864) ^ [_1429385, _1429387, _1429389, _1429391] : [35054 ^ _777864 : [(35058 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429385), 35056 ^ [_1429385, _1429387, _1429389, _1429391]), _1429391)))], (35060 ^ _777864) ^ [] : [-(hAPP(_1429389, 35053 ^ [_1429385, _1429387, _1429389, _1429391]) = hAPP(_1429389, 35056 ^ [_1429385, _1429387, _1429389, _1429391]))], (35062 ^ _777864) ^ [] : [35053 ^ [_1429385, _1429387, _1429389, _1429391] = 35056 ^ [_1429385, _1429387, _1429389, _1429391]], (35055 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1429385), 35053 ^ [_1429385, _1429387, _1429389, _1429391]), _1429391)))]], -(c_Fun_Oinj__on(_1429385, _1429387, _1429389, _1429391))], (21268 ^ _777864) ^ [_1144722, _1144724, _1144726, _1144728] : [class_Fields_Olinordered__field(_1144722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144722), c_Groups_Ozero__class_Ozero(_1144722)), _1144724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144722), _1144726), _1144724)), _1144728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144722), _1144726), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144722), _1144728), _1144724))))], (32896 ^ _777864) ^ [_1380894, _1380896, _1380898, _1380900] : [class_Groups_Ocomm__monoid__mult(_1380894), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380896), _1380898))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380896, _1380894), _1380900), _1380898) = c_Groups_Oone__class_Oone(_1380894))], (49793 ^ _777864) ^ [_1780975, _1780977, _1780979] : [class_Orderings_Olinorder(_1780975), 49796 ^ _777864 : [(49815 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1780975, hAPP(hAPP(c_List_Oappend(_1780975), _1780977), _1780979))), c_List_Olinorder__class_Osorted(_1780975, _1780977), c_List_Olinorder__class_Osorted(_1780975, _1780979), 49825 ^ _777864 : [(49831 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1780975), 49824 ^ [_1780975, _1780977, _1780979]), 49827 ^ [_1780975, _1780977, _1780979]))], (49829 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780975), 49827 ^ [_1780975, _1780977, _1780979]), hAPP(c_List_Oset(_1780975), _1780979))))], (49826 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780975), 49824 ^ [_1780975, _1780977, _1780979]), hAPP(c_List_Oset(_1780975), _1780977))))]]], (49797 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1780975, hAPP(hAPP(c_List_Oappend(_1780975), _1780977), _1780979)), 49800 ^ _777864 : [(49805 ^ _777864) ^ [_1781211] : [hBOOL(hAPP(hAPP(c_member(_1780975), _1781211), hAPP(c_List_Oset(_1780975), _1780977))), 49808 ^ _777864 : [(49809 ^ _777864) ^ [_1781321] : [hBOOL(hAPP(hAPP(c_member(_1780975), _1781321), hAPP(c_List_Oset(_1780975), _1780979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1780975), _1781211), _1781321)))]]], (49803 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1780975, _1780979))], (49801 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1780975, _1780977))]]]]], (22298 ^ _777864) ^ [_1163110, _1163112, _1163114, _1163116] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1163110, _1163112), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1163114), _1163116))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163110), _1163112), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1163116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163114)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163114)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1163116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1163112), _1163116))))))], (28727 ^ _777864) ^ [] : [-(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))))], (5806 ^ _777864) ^ [_873050, _873052, _873054, _873056, _873058, _873060] : [c_Com_Ocom_OLocal(_873050, _873052, _873054) = c_Com_Ocom_OCall(_873056, _873058, _873060)], (17434 ^ _777864) ^ [_1078823, _1078825, _1078827, _1078829] : [class_Rings_Olinordered__semidom(_1078823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078825), _1078827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078823), c_Groups_Oone__class_Oone(_1078823)), _1078829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078823), hAPP(hAPP(c_Power_Opower__class_Opower(_1078823), _1078829), _1078825)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078823), _1078829), _1078827))))], (33547 ^ _777864) ^ [_1395453, _1395455, _1395457, _1395459, _1395461, _1395463] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395453, tc_fun(_1395455, tc_HOL_Obool)), _1395457), hAPP(hAPP(c_COMBC(_1395453, tc_fun(_1395459, tc_fun(_1395455, tc_HOL_Obool)), tc_fun(_1395455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395459, tc_HOL_Obool), tc_fun(tc_fun(_1395459, tc_fun(_1395455, tc_HOL_Obool)), tc_fun(_1395455, tc_HOL_Obool)), _1395453), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395459, tc_fun(_1395455, tc_HOL_Obool))), _1395461)), _1395463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395459, tc_fun(_1395455, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395453, tc_fun(_1395459, tc_HOL_Obool)), _1395457), _1395461)), _1395463))], (34049 ^ _777864) ^ [_1408310, _1408312] : [-(c_Relation_OId__on(_1408310, _1408312) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408310, tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool)), _1408312), hAPP(hAPP(c_COMBC(_1408310, tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool), tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1408310, _1408310), tc_fun(tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool), tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool)), _1408310), c_Set_Oinsert(tc_prod(_1408310, _1408310))), hAPP(hAPP(c_COMBS(_1408310, _1408310, tc_prod(_1408310, _1408310)), c_Product__Type_OPair(_1408310, _1408310)), c_COMBI(_1408310)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1408310, _1408310), tc_HOL_Obool)))))], (44788 ^ _777864) ^ [_1659548, _1659550, _1659552] : [-(hAPP(c_Relation_ORange(_1659548, _1659550), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1659548, _1659550), tc_HOL_Obool), _1659552)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1659548, _1659550), tc_HOL_Obool), tc_fun(_1659550, tc_HOL_Obool)), _1659552), c_Relation_ORange(_1659548, _1659550)))], (34559 ^ _777864) ^ [_1419814, _1419816] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1419814, _1419816)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1419814), hAPP(c_Nat_OSuc, _1419816)))], (43887 ^ _777864) ^ [_1636370, _1636372, _1636374, _1636376, _1636378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636370, _1636372)), hAPP(hAPP(c_Product__Type_OPair(_1636370, _1636372), _1636374), _1636376)), hAPP(c_Relation_Oconverse(_1636372, _1636370), _1636378))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636372, _1636370)), hAPP(hAPP(c_Product__Type_OPair(_1636372, _1636370), _1636376), _1636374)), _1636378)))], (48324 ^ _777864) ^ [_1746814, _1746816, _1746818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746814), tc_List_Olist(_1746814))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746814), tc_List_Olist(_1746814)), c_List_Olist_ONil(_1746814)), _1746816)), c_List_Olistrel1(_1746814, _1746818)))], (16658 ^ _777864) ^ [_1064437, _1064439, _1064441] : [class_Int_Onumber__ring(_1064437), -(hAPP(c_Int_Onumber__class_Onumber__of(_1064437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064439), _1064441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064437), hAPP(c_Int_Onumber__class_Onumber__of(_1064437), _1064439)), hAPP(c_Int_Onumber__class_Onumber__of(_1064437), _1064441)))], (46276 ^ _777864) ^ [_1694936, _1694938, _1694940, _1694942, _1694944, _1694946, _1694948] : [hAPP(hAPP(c_List_Omap(_1694936, _1694938), _1694940), _1694942) = hAPP(hAPP(c_List_Omap(_1694944, _1694938), _1694946), _1694948), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694936)), _1694942) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694944)), _1694948))], (15530 ^ _777864) ^ [_1042229, _1042231, _1042233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042229), _1042231)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042233), _1042231)), _1042229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042231), _1042229)))], (51255 ^ _777864) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (44945 ^ _777864) ^ [_1662988, _1662990, _1662992, _1662994, _1662996] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1662988, tc_fun(_1662990, tc_HOL_Obool)), _1662992), hAPP(hAPP(c_COMBS(_1662988, tc_fun(_1662990, tc_HOL_Obool), tc_fun(_1662990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662990, tc_HOL_Obool), tc_fun(tc_fun(_1662990, tc_HOL_Obool), tc_fun(_1662990, tc_HOL_Obool)), _1662988), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662990, tc_HOL_Obool))), _1662994)), _1662996)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662990, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662990, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662988, tc_fun(_1662990, tc_HOL_Obool), _1662994), _1662992))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662990, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662988, tc_fun(_1662990, tc_HOL_Obool), _1662996), _1662992))))], (33563 ^ _777864) ^ [_1395909, _1395911, _1395913, _1395915, _1395917] : [class_Complete__Lattice_Ocomplete__lattice(_1395909), 33566 ^ _777864 : [(33567 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395911, _1395909), _1395913), _1395915)), _1395917)), 33570 ^ _777864 : [(33571 ^ _777864) ^ [_1396090] : [hBOOL(hAPP(hAPP(c_member(_1395911), _1396090), _1395913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395909), hAPP(_1395915, _1396090)), _1395917)))]]], (33577 ^ _777864) ^ [] : [33579 ^ _777864 : [(33582 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395909), hAPP(_1395915, 33578 ^ [_1395909, _1395911, _1395913, _1395915, _1395917])), _1395917))], (33580 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395911), 33578 ^ [_1395909, _1395911, _1395913, _1395915, _1395917]), _1395913)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395911, _1395909), _1395913), _1395915)), _1395917)))]]], (8352 ^ _777864) ^ [_916270, _916272, _916274] : [class_Orderings_Oorder(_916270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916270), _916272), _916274)), _916272 = _916274], (2182 ^ _777864) ^ [_809873, _809875, _809877, _809879, _809881, _809883, _809885, _809887, _809889, _809891] : [-(c_Product__Type_Oprod_Oprod__rec(_809891, _809887, _809883, _809879, _809875) = c_Product__Type_Oprod_Oprod__rec(_809889, _809885, _809881, _809877, _809873)), _809891 = _809889, _809887 = _809885, _809883 = _809881, _809879 = _809877, _809875 = _809873], (37544 ^ _777864) ^ [_1482040, _1482042, _1482044, _1482046, _1482048] : [c_Finite__Set_Ofolding__one__idem(_1482040, _1482042, _1482044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482040), _1482046)), -(_1482046 = c_Orderings_Obot__class_Obot(tc_fun(_1482040, tc_HOL_Obool))), -(hAPP(_1482044, hAPP(hAPP(c_Set_Oinsert(_1482040), _1482048), _1482046)) = hAPP(hAPP(_1482042, _1482048), hAPP(_1482044, _1482046)))], (36238 ^ _777864) ^ [] : [-(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))))], (41734 ^ _777864) ^ [_1586437, _1586439, _1586441, _1586443, _1586445, _1586447] : [-(hAPP(c_Set_Ovimage(_1586437, _1586439, hAPP(c_Fun_Ocomp(_1586441, _1586439, _1586437, _1586443), _1586445)), _1586447) = hAPP(c_Set_Ovimage(_1586437, _1586441, _1586445), hAPP(c_Set_Ovimage(_1586441, _1586439, _1586443), _1586447)))], (46404 ^ _777864) ^ [_1698435, _1698437, _1698439] : [-(_1698435 = _1698437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698439)), _1698435) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698439)), _1698437), 46410 ^ _777864 : [(46413 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1698439, _1698439, tc_HOL_Obool), c_fequal), 46409 ^ [_1698435, _1698437, _1698439]))], (46411 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1698439, _1698439)), 46409 ^ [_1698435, _1698437, _1698439]), hAPP(c_List_Oset(tc_prod(_1698439, _1698439)), hAPP(hAPP(c_List_Ozip(_1698439, _1698439), _1698435), _1698437)))))]]], (16814 ^ _777864) ^ [_1067456, _1067458, _1067460] : [class_Int_Onumber__ring(_1067456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067456), hAPP(c_Groups_Ouminus__class_Ouminus(_1067456), hAPP(c_Int_Onumber__class_Onumber__of(_1067456), _1067458))), _1067460) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067456), hAPP(c_Int_Onumber__class_Onumber__of(_1067456), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1067458))), _1067460))], (15776 ^ _777864) ^ [_1047514, _1047516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047514), _1047516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047514), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1047516), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14157 ^ _777864) ^ [_1017405, _1017407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017405), _1017407)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017405), _1017407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31039 ^ _777864) ^ [_1344991, _1344993, _1344995] : [class_Lattices_Olattice(_1344991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344991), _1344993)), -(_1344995 = c_Orderings_Obot__class_Obot(tc_fun(_1344991, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1344991, tc_HOL_Obool)), _1344995), _1344993)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1344991), c_Big__Operators_Olattice__class_OSup__fin(_1344991, _1344995)), c_Big__Operators_Olattice__class_OSup__fin(_1344991, _1344993)) = c_Big__Operators_Olattice__class_OSup__fin(_1344991, _1344993))], (28092 ^ _777864) ^ [_1278408, _1278410, _1278412] : [class_Lattices_Osemilattice__sup(_1278408), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278408), _1278410), _1278412) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278408), _1278412), _1278410))], (47978 ^ _777864) ^ [_1738360, _1738362, _1738364] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738360)), hAPP(hAPP(c_List_Oappend(_1738360), _1738362), _1738364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738360)), _1738362)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738360)), _1738364)))], (7814 ^ _777864) ^ [_907885, _907887] : [c_Com_Ocom_OWhile(_907885, _907887) = c_Com_Ocom_OSKIP], (50819 ^ _777864) ^ [_1803070, _1803072, _1803074, _1803076, _1803078] : [-(c_Map_Omap__upds(_1803070, _1803072, _1803074, _1803076, _1803078) = c_Map_Omap__add(_1803070, _1803072, _1803074, c_Map_Omap__of(_1803070, _1803072, hAPP(c_List_Orev(tc_prod(_1803070, _1803072)), hAPP(hAPP(c_List_Ozip(_1803070, _1803072), _1803076), _1803078)))))], (2 ^ _777864) ^ [_777891] : [-(_777891 = _777891)], (45739 ^ _777864) ^ [_1681889, _1681891, _1681893, _1681895, _1681897] : [-(c_Map_Omap__comp(_1681889, _1681891, _1681893, hAPP(c_COMBK(tc_Option_Ooption(_1681891), _1681889), c_Option_Ooption_ONone(_1681891)), _1681895, _1681897) = c_Option_Ooption_ONone(_1681891))], (39201 ^ _777864) ^ [_1518853, _1518855, _1518857, _1518859, _1518861] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518853, _1518855), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518853, tc_HOL_Obool)), _1518857), _1518859)), hAPP(c_COMBK(tc_fun(_1518855, tc_HOL_Obool), _1518853), _1518861)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518853, _1518855), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518853, _1518855), _1518857), hAPP(c_COMBK(tc_fun(_1518855, tc_HOL_Obool), _1518853), _1518861))), hAPP(hAPP(c_Product__Type_OSigma(_1518853, _1518855), _1518859), hAPP(c_COMBK(tc_fun(_1518855, tc_HOL_Obool), _1518853), _1518861))))], (8382 ^ _777864) ^ [_916736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _916736)), 8386 ^ _777864 : [(8389 ^ _777864) ^ [] : [-(_916736 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8385 ^ [_916736]))], (8387 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8385 ^ [_916736])))]]], (1242 ^ _777864) ^ [_796157, _796159] : [-(class_Complete__Lattice_Ocomplete__lattice(_796157)), _796159 = _796157, class_Complete__Lattice_Ocomplete__lattice(_796159)], (51195 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (23277 ^ _777864) ^ [_1183083] : [-(c_Divides_Oadjust(_1183083) = 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)), _1183083))))), 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)), _1183083))))), 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))))))))], (45017 ^ _777864) ^ [_1664437, _1664439] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1664437, tc_HOL_Obool)), _1664439)), 45023 ^ _777864 : [(45026 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1664437), 45022 ^ [_1664437, _1664439]))], (45024 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1664437, tc_HOL_Obool)), 45022 ^ [_1664437, _1664439]), _1664439)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1664437), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1664437, tc_HOL_Obool), _1664439))))], (50038 ^ _777864) ^ [_1785195, _1785197, _1785199] : [class_Orderings_Olinorder(_1785195), c_List_Olinorder__class_Osorted(_1785195, _1785197), -(c_List_Olinorder__class_Osorted(_1785195, c_List_Oremove1(_1785195, _1785199, _1785197)))], (50176 ^ _777864) ^ [_1787688, _1787690, _1787692] : [class_Orderings_Olinorder(_1787688), 50179 ^ _777864 : [(50192 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1787688, hAPP(hAPP(c_List_Olist_OCons(_1787688), _1787690), _1787692))), 50196 ^ _777864 : [(50199 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1787688), _1787690), 50195 ^ [_1787688, _1787690, _1787692]))], (50197 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1787688), 50195 ^ [_1787688, _1787690, _1787692]), hAPP(c_List_Oset(_1787688), _1787692))))]], c_List_Olinorder__class_Osorted(_1787688, _1787692)], (50180 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1787688, hAPP(hAPP(c_List_Olist_OCons(_1787688), _1787690), _1787692)), 50183 ^ _777864 : [(50184 ^ _777864) ^ [_1787856] : [hBOOL(hAPP(hAPP(c_member(_1787688), _1787856), hAPP(c_List_Oset(_1787688), _1787692))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1787688), _1787690), _1787856)))], (50190 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1787688, _1787692))]]]]], (24603 ^ _777864) ^ [_1209496, _1209498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209496), _1209498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1209496)), hAPP(c_Code__Numeral_Oof__nat, _1209498))))], (44955 ^ _777864) ^ [_1663338, _1663340, _1663342] : [class_Complete__Lattice_Ocomplete__lattice(_1663338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1663338), _1663340)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1663338), _1663342), c_Complete__Lattice_OSup__class_OSup(_1663338, _1663340)) = hAPP(hAPP(c_Finite__Set_Ofold(_1663338, _1663338, c_Lattices_Osemilattice__sup__class_Osup(_1663338)), _1663342), _1663340))], (24583 ^ _777864) ^ [_1209114, _1209116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1209114)), hAPP(c_Code__Numeral_Oof__nat, _1209116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209114), _1209116)))], (37282 ^ _777864) ^ [_1476370, _1476372] : [hAPP(_1476370, 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), _1476370), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476372)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1476370), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1476372)))], (6042 ^ _777864) ^ [_877348, _877350, _877352, _877354] : [-(c_Com_Ovname_Ovname__case(_877348, _877350, _877352, c_Com_Ovname_OGlb(_877354)) = hAPP(_877350, _877354))], (3040 ^ _777864) ^ [_823682, _823684] : [_823684 = _823682, -(c_Nat_Osemiring__1__class_ONats(_823684) = c_Nat_Osemiring__1__class_ONats(_823682))], (9174 ^ _777864) ^ [_930682] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930682)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930682))], (36496 ^ _777864) ^ [_1457660, _1457662, _1457664, _1457666] : [class_Groups_Oordered__ab__group__add__abs(_1457660), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457660), hAPP(c_Groups_Oabs__class_Oabs(_1457660), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457662, _1457660), _1457664), _1457666))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457662, _1457660), hAPP(hAPP(c_COMBB(_1457660, _1457660, _1457662), c_Groups_Oabs__class_Oabs(_1457660)), _1457664)), _1457666))))], (8632 ^ _777864) ^ [_921144] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _921144)) = _921144)], (43927 ^ _777864) ^ [_1637412, _1637414, _1637416, _1637418] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1637412, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637414, tc_fun(_1637412, tc_HOL_Obool)), _1637416), _1637418)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637414, tc_fun(_1637412, tc_HOL_Obool)), _1637416), hAPP(hAPP(c_COMBB(tc_fun(_1637412, tc_HOL_Obool), tc_fun(_1637412, tc_HOL_Obool), _1637414), c_Groups_Ouminus__class_Ouminus(tc_fun(_1637412, tc_HOL_Obool))), _1637418)))], (33112 ^ _777864) ^ [_1385284, _1385286, _1385288, _1385290, _1385292] : [class_Groups_Ocomm__monoid__mult(_1385284), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385286), _1385288)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385286), _1385290)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, _1385284), _1385292), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385286, tc_HOL_Obool)), _1385288), _1385290))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, _1385284), _1385292), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385286, tc_HOL_Obool)), _1385288), _1385290))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, _1385284), _1385292), _1385288)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385286, _1385284), _1385292), _1385290)))], (36324 ^ _777864) ^ [_1454030] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1454030)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1454030), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1454030)))], (34629 ^ _777864) ^ [_1420923, _1420925, _1420927] : [class_Orderings_Oorder(_1420923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420923), _1420925), _1420927)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1420923, _1420927, _1420925) = c_Orderings_Obot__class_Obot(tc_fun(_1420923, tc_HOL_Obool)))], (36820 ^ _777864) ^ [_1465592, _1465594, _1465596, _1465598] : [class_Groups_Ocomm__monoid__add(_1465592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465594), _1465596)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465594, _1465592), _1465598), _1465596) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1465592, _1465594, c_Groups_Oplus__class_Oplus(_1465592)), _1465598), c_Groups_Ozero__class_Ozero(_1465592)), _1465596))], (4374 ^ _777864) ^ [_844777, _844779, _844781, _844783] : [-(c_Complete__Lattice_OSup__class_OSup(_844783, _844779) = c_Complete__Lattice_OSup__class_OSup(_844781, _844777)), _844783 = _844781, _844779 = _844777], (27708 ^ _777864) ^ [_1271506] : 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class_Rings_Olinordered__semiring__1__strict(_792909)], (1612 ^ _777864) ^ [_800782, _800784] : [-(class_Rings_Ozero__neq__one(_800782)), _800784 = _800782, class_Rings_Ozero__neq__one(_800784)], (24413 ^ _777864) ^ [_1205488, _1205490, _1205492, _1205494] : [hBOOL(hAPP(_1205488, _1205490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205492, tc_HOL_Obool)), _1205488), _1205494)), -(hBOOL(hAPP(_1205494, _1205490)))], (11209 ^ _777864) ^ [_964533, _964535, _964537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964533), _964535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964533), _964537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964535), _964537))))], (43733 ^ _777864) ^ [_1631556, _1631558, _1631560, _1631562] : [-(hAPP(c_Set_OPow(_1631556), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631558, tc_fun(_1631556, tc_HOL_Obool)), _1631560), 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hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1707906)), hAPP(hAPP(c_List_Olist_OCons(_1707906), _1707910), _1707912)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1707906), tc_HOL_Obool)))) = c_List_Oset__Cons(_1707906, hAPP(c_Relation_OImage(_1707906, _1707906, _1707908), hAPP(hAPP(c_Set_Oinsert(_1707906), _1707910), c_Orderings_Obot__class_Obot(tc_fun(_1707906, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1707906), tc_List_Olist(_1707906), c_List_Olistrel(_1707906, _1707908)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1707906)), _1707912), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1707906), tc_HOL_Obool))))))], (14272 ^ _777864) ^ [_1019171, _1019173, _1019175] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019171), _1019173)), _1019175), _1019173) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019175, _1019173))], (22576 ^ _777864) ^ [_1168197, _1168199, _1168201, _1168203] : [hAPP(c_Product__Type_Ofst(_1168197, _1168199), _1168201) = hAPP(c_Product__Type_Ofst(_1168197, _1168199), _1168203), hAPP(c_Product__Type_Osnd(_1168197, _1168199), _1168201) = hAPP(c_Product__Type_Osnd(_1168197, _1168199), _1168203), -(_1168201 = _1168203)], (38170 ^ _777864) ^ [_1494208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1494208)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1494208), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494208), c_Orderings_Otop__class_Otop(tc_fun(_1494208, tc_HOL_Obool)))))], (51157 ^ _777864) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (34103 ^ _777864) ^ [_1409632] : [-(c_Relation_OId__on(_1409632, c_Orderings_Obot__class_Obot(tc_fun(_1409632, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1409632, _1409632), tc_HOL_Obool)))], (16424 ^ _777864) ^ [_1059811, _1059813, _1059815] : [class_Groups_Oordered__ab__group__add__abs(_1059811), 16427 ^ _777864 : [(16436 ^ 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hAPP(c_Int_Onumber__class_Onumber__of(_1083063), c_Int_OMin))], (28160 ^ _777864) ^ [_1279923, _1279925, _1279927] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279923, tc_HOL_Obool)), _1279925), _1279927) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279923, tc_HOL_Obool)), _1279927), _1279925))], (22120 ^ _777864) ^ [_1160198, _1160200, _1160202, _1160204, _1160206] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1160198, _1160200), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1160202), _1160204))), -(_1160200 = 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), _1160206), _1160198), _1160200), 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), _1160206), _1160202)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1160206), _1160204)), _1160200))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1160206), _1160204), _1160200)))))], (8294 ^ _777864) ^ [_915366, _915368, _915370, _915372] : [class_Orderings_Oorder(_915366), _915368 = _915370, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915366), _915372), _915370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915366), _915372), _915368)))], (15362 ^ _777864) ^ [_1039008, _1039010, _1039012, _1039014, _1039016, _1039018] : [class_Rings_Oring(_1039008), 15365 ^ _777864 : [(15372 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039008), _1039010), _1039016)), _1039012)), _1039014) = _1039018, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), _1039010), _1039012)), _1039014) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), _1039016), _1039012)), _1039018))], (15366 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), _1039010), _1039012)), _1039014) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), _1039016), _1039012)), _1039018), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039008), _1039010), _1039016)), _1039012)), _1039014) = _1039018)]]], (32391 ^ _777864) ^ [_1370186, _1370188, _1370190] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370186), _1370188)), -(hBOOL(hAPP(hAPP(c_member(_1370186), _1370190), _1370188))), -(hAPP(c_Finite__Set_Ocard(_1370186), hAPP(hAPP(c_Set_Oinsert(_1370186), _1370190), _1370188)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1370186), _1370188)))], (51057 ^ _777864) ^ [_1807462, _1807464] : [class_Lattices_Odistrib__lattice(_1807462), -(class_Lattices_Odistrib__lattice(tc_fun(_1807464, _1807462)))], (3010 ^ _777864) ^ [_823227, _823229] : [_823229 = _823227, -(c_Divides_Odiv__class_Odiv(_823229) = c_Divides_Odiv__class_Odiv(_823227))], (47063 ^ _777864) ^ [_1716783, _1716785, _1716787] : [47065 ^ _777864 : [(47068 ^ _777864) ^ [] : [hBOOL(hAPP(_1716787, hAPP(hAPP(c_List_Onth(_1716783), _1716785), 47064 ^ [_1716783, _1716785, _1716787])))], (47066 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47064 ^ [_1716783, _1716785, _1716787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716783)), _1716785))))]], 47069 ^ _777864 : [(47070 ^ _777864) ^ [_1716985] : [hBOOL(hAPP(hAPP(c_member(_1716783), _1716985), hAPP(c_List_Oset(_1716783), _1716785))), -(hBOOL(hAPP(_1716787, _1716985)))]]], (29902 ^ _777864) ^ [_1321028, _1321030, _1321032, _1321034] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321028, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321028, tc_HOL_Obool)), _1321030), _1321032)), _1321034) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321028, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321028, tc_HOL_Obool)), _1321030), _1321034)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321028, tc_HOL_Obool)), _1321032), _1321034)))], (23367 ^ _777864) ^ [_1185525, _1185527] : [-(_1185525 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23370 ^ _777864 : [(23377 ^ _777864) ^ [] : [-(_1185527 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1185525, _1185527) = 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, _1185527))), 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, _1185525)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1185527))), c_Divides_Opdivmod(_1185525, _1185527)), 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), _1185527))))), c_Divides_Opdivmod(_1185525, _1185527)))))], (23371 ^ _777864) ^ [] : [_1185527 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185525, _1185527) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185525))]]], (48265 ^ _777864) ^ [_1745055, _1745057, _1745059, _1745061, _1745063] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745055), tc_List_Olist(_1745055))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745055), tc_List_Olist(_1745055)), hAPP(hAPP(c_List_Oappend(_1745055), _1745057), _1745059)), hAPP(hAPP(c_List_Oappend(_1745055), _1745057), _1745061))), c_List_Olexord(_1745055, _1745063))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1745055, _1745055)), hAPP(hAPP(c_Product__Type_OPair(_1745055, _1745055), 48270 ^ [_1745055, _1745057, _1745059, _1745061, _1745063]), 48270 ^ [_1745055, _1745057, _1745059, _1745061, _1745063])), _1745063))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745055), tc_List_Olist(_1745055))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745055), tc_List_Olist(_1745055)), _1745059), _1745061)), c_List_Olexord(_1745055, _1745063))))], (11721 ^ _777864) ^ [_973768, _973770, _973772] : [class_Rings_Olinordered__ring__strict(_973768), 11724 ^ _777864 : [(11739 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973768), _973770), _973772)), c_Groups_Ozero__class_Ozero(_973768)))), 11740 ^ _777864 : [(11747 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), _973770), c_Groups_Ozero__class_Ozero(_973768))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), c_Groups_Ozero__class_Ozero(_973768)), _973772))], (11741 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), c_Groups_Ozero__class_Ozero(_973768)), _973770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), _973772), c_Groups_Ozero__class_Ozero(_973768)))]]], (11725 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973768), _973770), _973772)), c_Groups_Ozero__class_Ozero(_973768))), 11730 ^ _777864 : [(11733 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), _973772), c_Groups_Ozero__class_Ozero(_973768))))], (11731 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), c_Groups_Ozero__class_Ozero(_973768)), _973770)))]], 11734 ^ _777864 : [(11737 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), c_Groups_Ozero__class_Ozero(_973768)), _973772)))], (11735 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973768), _973770), c_Groups_Ozero__class_Ozero(_973768))))]]]]], (18582 ^ _777864) ^ [_1097336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097336), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1097336)), c_Int_OMin)))], (41928 ^ _777864) ^ [_1590818] : [-(c_Nitpick_Odenom(_1590818) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1590818, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1590818)))], (47570 ^ _777864) ^ [_1728845, _1728847] : [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(_1728845)), _1728847))), _1728847 = c_List_Olist_ONil(_1728845)], (18284 ^ _777864) ^ [_1092275, _1092277] : [class_Int_Onumber__ring(_1092275), class_Rings_Olinordered__idom(_1092275), 18291 ^ _777864 : [(18298 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092277), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092275), hAPP(c_Int_Onumber__class_Onumber__of(_1092275), _1092277)), c_Groups_Ozero__class_Ozero(_1092275))))], (18292 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1092275), hAPP(c_Int_Onumber__class_Onumber__of(_1092275), _1092277)), c_Groups_Ozero__class_Ozero(_1092275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092277), c_Int_OPls)))]]], (41463 ^ _777864) ^ [_1579645, _1579647] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579645, _1579645)), _1579647)), c_Wellfounded_Oacyclic(_1579645, 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hAPP(hAPP(c_Power_Opower__class_Opower(_1056169), _1056173), _1056175)))], (34597 ^ _777864) ^ [_1420485, _1420487, _1420489] : [class_Orderings_Oorder(_1420485), 34600 ^ _777864 : [(34607 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420485), _1420487), _1420489))), -(c_Orderings_Obot__class_Obot(tc_fun(_1420485, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1420485, _1420487, _1420489))], (34601 ^ _777864) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1420485, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1420485, _1420487, _1420489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420485), _1420487), _1420489))]]], (45955 ^ _777864) ^ [_1687184, _1687186, _1687188, _1687190] : [hBOOL(hAPP(c_List_Odistinct(_1687184), hAPP(hAPP(c_List_Omap(_1687186, _1687184), _1687188), _1687190))), 45958 ^ _777864 : [(45961 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1687186, _1687184, _1687188, hAPP(c_List_Oset(_1687186), _1687190)))], (45959 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1687186), _1687190)))]]], (23785 ^ _777864) ^ [_1193383, _1193385] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1193383)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1193385)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1193385))), 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, _1193383))), 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), _1193383)), c_Int_Onat)))))], (12754 ^ _777864) ^ [_991995, _991997] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _991995) = _991997), _991995 = hAPP(c_Int_Onat, _991997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991997))], (16386 ^ _777864) ^ [_1058922, _1058924, _1058926, _1058928, _1058930] : [class_Rings_Olinordered__idom(_1058922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058922), hAPP(c_Groups_Oabs__class_Oabs(_1058922), _1058924)), _1058926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058922), hAPP(c_Groups_Oabs__class_Oabs(_1058922), _1058928)), _1058930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058922), hAPP(c_Groups_Oabs__class_Oabs(_1058922), _1058924)), hAPP(c_Groups_Oabs__class_Oabs(_1058922), _1058928))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058922), _1058926), _1058930))))], (48914 ^ _777864) ^ [_1761236] : [class_Groups_Omonoid__add(_1761236), 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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), _1185080))))), c_Divides_Opdivmod(_1185078, _1185080)))))], (23349 ^ _777864) ^ [] : [_1185080 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185078, _1185080) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185078))]]], (13164 ^ _777864) ^ [_998987, _998989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998987), _998989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998989), _998987)))], (41716 ^ _777864) ^ [_1585975, _1585977, _1585979, _1585981, _1585983, _1585985, _1585987] : [hAPP(c_Fun_Ocomp(_1585975, _1585977, _1585979, _1585981), _1585983) = hAPP(c_Fun_Ocomp(_1585977, _1585977, _1585979, c_Fun_Oid(_1585977)), _1585985), -(hAPP(_1585981, hAPP(_1585983, _1585987)) = hAPP(_1585985, _1585987))], (28134 ^ _777864) ^ [_1279321, _1279323, _1279325, _1279327] : [class_Lattices_Osemilattice__sup(_1279321), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279321), _1279323), _1279325)), _1279327) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279321), _1279323), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279321), _1279325), _1279327)))], (1846 ^ _777864) ^ [_803843, _803845, _803847, _803849] : [-(v_Q(_803847, _803843)), v_Q(_803849, _803845), _803849 = _803847, _803845 = _803843], (2596 ^ _777864) ^ [_816416, _816418, _816420, _816422] : [-(c_Divides_Odivmod__nat(_816422, _816418) = c_Divides_Odivmod__nat(_816420, _816416)), _816422 = _816420, _816418 = _816416], (7518 ^ _777864) ^ [_902305, _902307, _902309, _902311] : [class_Rings_Ocomm__semiring__1(_902305), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902305), _902307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902305), _902309), _902311)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902305), _902309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902305), _902307), _902311)))], (43209 ^ _777864) ^ [_1618646, _1618648, _1618650, _1618652] : [-(c_Transitive__Closure_Otrancl(_1618646, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1618646, _1618646)), hAPP(hAPP(c_Product__Type_OPair(_1618646, _1618646), _1618648), _1618650)), _1618652)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1618646, _1618646), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1618646, _1618652)), hAPP(c_Set_OCollect(tc_prod(_1618646, _1618646)), hAPP(c_Product__Type_Oprod_Oprod__case(_1618646, _1618646, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1618646, tc_fun(_1618646, tc_HOL_Obool), tc_fun(_1618646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1618646, tc_HOL_Obool), tc_fun(_1618646, tc_HOL_Obool)), _1618646), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1618646)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1618646), c_fconj), hAPP(hAPP(c_COMBC(_1618646, tc_fun(tc_prod(_1618646, _1618646), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1618646, _1618646), tc_fun(tc_fun(tc_prod(_1618646, _1618646), tc_HOL_Obool), tc_HOL_Obool), _1618646), c_member(tc_prod(_1618646, _1618646))), hAPP(hAPP(c_COMBC(_1618646, _1618646, tc_prod(_1618646, _1618646)), c_Product__Type_OPair(_1618646, _1618646)), _1618648))), c_Transitive__Closure_Ortrancl(_1618646, _1618652))))), hAPP(hAPP(c_COMBC(_1618646, tc_fun(tc_prod(_1618646, _1618646), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1618646, _1618646), tc_fun(tc_fun(tc_prod(_1618646, _1618646), tc_HOL_Obool), tc_HOL_Obool), _1618646), c_member(tc_prod(_1618646, _1618646))), hAPP(c_Product__Type_OPair(_1618646, _1618646), _1618650))), c_Transitive__Closure_Ortrancl(_1618646, _1618652)))))))], (7498 ^ _777864) ^ [_901883, _901885, _901887, _901889, _901891] : [c_Com_Ocom_OSemi(_901883, _901885) = c_Com_Ocom_OCall(_901887, _901889, _901891)], (17278 ^ _777864) ^ [_1075908, _1075910, _1075912] : [class_Rings_Olinordered__idom(_1075908), -(hAPP(c_Groups_Oabs__class_Oabs(_1075908), hAPP(hAPP(c_Power_Opower__class_Opower(_1075908), hAPP(c_Groups_Ouminus__class_Ouminus(_1075908), _1075910)), _1075912)) = hAPP(c_Groups_Oabs__class_Oabs(_1075908), hAPP(hAPP(c_Power_Opower__class_Opower(_1075908), _1075910), _1075912)))], (5228 ^ _777864) ^ [_857904, _857906, _857908, _857910] : [-(c_List_Oremdups(_857910, _857906) = c_List_Oremdups(_857908, _857904)), _857910 = _857908, _857906 = _857904], (51519 ^ _777864) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (37997 ^ _777864) ^ [_1491000, _1491002, _1491004, _1491006, _1491008] : [class_Groups_Oab__semigroup__mult(_1491000), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1491000, _1491000, c_Groups_Otimes__class_Otimes(_1491000), _1491002, _1491004), _1491006)), -(hBOOL(hAPP(hAPP(c_member(_1491000), _1491002), _1491004))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1491000, _1491000, c_Groups_Otimes__class_Otimes(_1491000), _1491008, hAPP(hAPP(c_Set_Oinsert(_1491000), _1491002), _1491004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1491000), _1491008), _1491006))))], (14081 ^ _777864) ^ [_1015870, _1015872, _1015874] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1015870), _1015872)), _1015874) = 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), _1015870), _1015874)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015872), _1015874))), 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, _1015870, _1015874)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1015872, _1015874))), _1015874)))], (9268 ^ _777864) ^ [_932252, _932254] : [class_Groups_Ogroup__add(_932252), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932252), hAPP(c_Groups_Ouminus__class_Ouminus(_932252), _932254)), _932254) = c_Groups_Ozero__class_Ozero(_932252))], (51247 ^ _777864) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (22905 ^ _777864) ^ [_1174840, _1174842, _1174844, _1174846, _1174848] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1174840, _1174842), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1174844), _1174846))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174842)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174848), _1174840), _1174842), 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), _1174848), _1174844)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174848), _1174846)), _1174842))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174848), _1174846), _1174842)))))], (9778 ^ _777864) ^ [_941236, _941238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _941236)), 9781 ^ _777864 : [(9788 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _941238), _941236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _941238)), hAPP(c_Int_Onat, _941236))))], (9782 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _941238)), hAPP(c_Int_Onat, _941236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _941238), _941236)))]]], (13922 ^ _777864) ^ [_1012842, _1012844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1012842, _1012844))))], (47594 ^ _777864) ^ [_1729274, _1729276, _1729278, _1729280] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729274, tc_HOL_Obool)), hAPP(c_List_Oset(_1729274), hAPP(hAPP(c_List_Olist__update(_1729274, _1729276), _1729278), _1729280))), hAPP(hAPP(c_Set_Oinsert(_1729274), _1729280), hAPP(c_List_Oset(_1729274), _1729276)))))], (51387 ^ _777864) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (26349 ^ _777864) ^ [_1241680, _1241682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241680), _1241682)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1241682), _1241680))], (5196 ^ _777864) ^ [_857382, _857384, _857386, _857388, _857390, _857392] : [-(c_Finite__Set_Ofold(_857392, _857388, _857384) = c_Finite__Set_Ofold(_857390, _857386, _857382)), _857392 = _857390, _857388 = _857386, _857384 = _857382], (12444 ^ _777864) ^ [_986471, _986473, _986475, _986477, _986479] : [class_Rings_Olinordered__semiring__strict(_986471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986471), _986473), _986475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986471), _986477), _986479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986471), c_Groups_Ozero__class_Ozero(_986471)), _986473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986471), c_Groups_Ozero__class_Ozero(_986471)), _986477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986471), _986473), _986477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986471), _986475), _986479))))], (37847 ^ _777864) ^ [_1487891, _1487893] : [class_Groups_Oordered__ab__group__add(_1487891), -(hAPP(c_Set_Oimage(_1487891, _1487891, c_Groups_Ouminus__class_Ouminus(_1487891)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487891), _1487893)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1487891), hAPP(c_Groups_Ouminus__class_Ouminus(_1487891), _1487893)))], (46274 ^ _777864) ^ [_1694884, _1694886, _1694888, _1694890] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694884)), hAPP(hAPP(c_List_Omap(_1694886, _1694884), _1694888), _1694890)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694886)), _1694890))], (18968 ^ _777864) ^ [_1103909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1103909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103909)))], (40082 ^ _777864) ^ [_1538312, _1538314] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1538312))), -(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)), _1538312))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1538314)))) = 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)), _1538312))), 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, _1538314))))))], (5496 ^ _777864) ^ [_861900, _861902, _861904, _861906] : [-(hAPP(_861906, _861902) = hAPP(_861904, _861900)), _861906 = _861904, _861902 = _861900], (39490 ^ _777864) ^ [_1525412, _1525414, _1525416] : [class_Orderings_Olinorder(_1525412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525412), _1525414)), -(_1525414 = c_Orderings_Obot__class_Obot(tc_fun(_1525412, tc_HOL_Obool))), 39501 ^ _777864 : [(39511 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525412), hAPP(c_Finite__Set_Ofold1(_1525412, c_Orderings_Oord__class_Omin(_1525412)), _1525414)), _1525416))), 39512 ^ _777864 : [(39513 ^ _777864) ^ [_1525801] : [hBOOL(hAPP(hAPP(c_member(_1525412), _1525801), _1525414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525412), _1525801), _1525416))]]], (39502 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525412), hAPP(c_Finite__Set_Ofold1(_1525412, c_Orderings_Oord__class_Omin(_1525412)), _1525414)), _1525416)), 39506 ^ _777864 : [(39509 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525412), 39505 ^ [_1525412, _1525414, _1525416]), _1525416)))], (39507 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525412), 39505 ^ [_1525412, _1525414, _1525416]), _1525414)))]]]]], (24721 ^ _777864) ^ [_1211624, _1211626, _1211628, _1211630, _1211632, _1211634] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1211624, _1211626, _1211628, _1211630), _1211632), _1211634) = hAPP(_1211630, hAPP(hAPP(c_Product__Type_OPair(_1211624, _1211626), _1211632), _1211634)))], (7802 ^ _777864) ^ [_907571, _907573, _907575, _907577, _907579] : [c_Com_Ocom_OCall(_907571, _907573, _907575) = c_Com_Ocom_OWhile(_907577, _907579)], (38768 ^ _777864) ^ [_1508039, _1508041, _1508043, _1508045] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508039, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508041, _1508039, _1508043), hAPP(c_Set_Ovimage(_1508041, _1508039, _1508043), _1508045))), _1508045)))], (28584 ^ _777864) ^ [_1292408, _1292410, _1292412, _1292414, _1292416] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1292408, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292408, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1292410, _1292408, _1292412), _1292414)), hAPP(c_Set_Oimage(_1292410, _1292408, _1292412), _1292416))), hAPP(c_Set_Oimage(_1292410, _1292408, _1292412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292410, tc_HOL_Obool)), _1292414), _1292416)))))], (27105 ^ _777864) ^ [_1257773, _1257775, _1257777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257773, tc_HOL_Obool)), _1257775), _1257777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257773, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1257773, tc_fun(_1257773, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257773)), _1257775)), hAPP(hAPP(c_COMBC(_1257773, tc_fun(_1257773, tc_HOL_Obool), tc_HOL_Obool), c_member(_1257773)), _1257777))))], (4654 ^ _777864) ^ [_849005, _849007, _849009, _849011, _849013, _849015, _849017, _849019] : [-(c_List_Omap__filter(_849019, _849015, _849011, _849007) = c_List_Omap__filter(_849017, _849013, _849009, _849005)), _849019 = _849017, _849015 = _849013, _849011 = _849009, _849007 = _849005], (49705 ^ _777864) ^ [_1779351, _1779353, _1779355] : [-(c_List_Osublist(_1779351, _1779353, _1779355) = hAPP(hAPP(c_List_Omap(tc_prod(_1779351, tc_Nat_Onat), _1779351), c_Product__Type_Ofst(_1779351, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1779351, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1779351, 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(_1779351, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1779351, tc_Nat_Onat))), _1779355)), hAPP(hAPP(c_List_Ozip(_1779351, tc_Nat_Onat), _1779353), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779351)), _1779353))))))], (37428 ^ _777864) ^ [_1479678, _1479680, _1479682, _1479684, _1479686, _1479688] : [class_Groups_Oordered__ab__group__add(_1479678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479680), _1479682)), 37438 ^ _777864 : [(37441 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479678), c_Groups_Ozero__class_Ozero(_1479678)), hAPP(_1479684, 37437 ^ [_1479678, _1479680, _1479682, _1479684, _1479686, _1479688])))], (37439 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479680), 37437 ^ [_1479678, _1479680, _1479682, _1479684, _1479686, _1479688]), _1479682)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479680, _1479678), _1479684), _1479682) = _1479686, hBOOL(hAPP(hAPP(c_member(_1479680), _1479688), _1479682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479678), hAPP(_1479684, _1479688)), _1479686)))], (17620 ^ _777864) ^ [_1081807] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081807))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1081807)) = _1081807)], (44386 ^ _777864) ^ [_1649895, _1649897, _1649899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649895, _1649895)), _1649897), c_Transitive__Closure_Ortrancl(_1649895, _1649899))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649895, _1649895)), _1649897), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1649895, _1649895), tc_HOL_Obool), 44389 ^ [_1649895, _1649897, _1649899]), _1649899))))], (3026 ^ _777864) ^ [_823461, _823463, _823465, _823467, _823469, _823471] : [-(c_Partial__Function_Oflat__lub(_823471, _823467, _823463) = c_Partial__Function_Oflat__lub(_823469, _823465, _823461)), _823471 = _823469, _823467 = _823465, _823463 = _823461], (19236 ^ _777864) ^ [_1108633] : [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), _1108633))), 19239 ^ _777864 : [(19242 ^ _777864) ^ [] : [-(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(_1108633)))))], (19240 ^ _777864) ^ [] : [-(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(_1108633)))))]]], (49578 ^ _777864) ^ [_1775460, _1775462, _1775464] : [-(c_List_Opartition(_1775460, _1775462, _1775464) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1775460), tc_List_Olist(_1775460)), hAPP(c_List_Ofilter(_1775460, _1775462), _1775464)), hAPP(c_List_Ofilter(_1775460, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1775460, c_fNot), _1775462)), _1775464)))], (7172 ^ _777864) ^ [_895790, _895792, _895794, _895796, _895798, _895800] : [c_Natural_Oevaln(_895790, _895792, _895794, _895796), c_Natural_Oevaln(_895798, _895796, _895794, _895800), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_895790, _895798), _895792, _895794, _895800))], (49954 ^ _777864) ^ [_1783920, _1783922, _1783924] : [class_Orderings_Olinorder(_1783920), c_List_Olinorder__class_Osorted(_1783920, _1783922), -(c_List_Olinorder__class_Osorted(_1783920, hAPP(hAPP(c_List_Odrop(_1783920), _1783924), _1783922)))], (34966 ^ _777864) ^ [_1427384, _1427386, _1427388] : [class_Orderings_Olinorder(_1427384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427384), _1427386), _1427388)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427384, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1427384), _1427386), c_Orderings_Obot__class_Obot(tc_fun(_1427384, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1427384, _1427386, _1427388)) = c_SetInterval_Oord__class_OatLeastAtMost(_1427384, _1427386, _1427388))], (28540 ^ _777864) ^ [_1291424, _1291426, _1291428, _1291430] : [c_Orderings_Obot__class_Obot(tc_fun(_1291424, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1291426, _1291424, _1291428), _1291430), -(_1291430 = c_Orderings_Obot__class_Obot(tc_fun(_1291426, tc_HOL_Obool)))], (39605 ^ _777864) ^ [_1527469, _1527471, _1527473] : [class_Orderings_Olinorder(_1527469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527469), _1527471)), -(_1527471 = c_Orderings_Obot__class_Obot(tc_fun(_1527469, tc_HOL_Obool))), 39616 ^ _777864 : [(39617 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1527469), _1527473), hAPP(c_Finite__Set_Ofold1(_1527469, c_Orderings_Oord__class_Omin(_1527469)), _1527471))), 39620 ^ _777864 : [(39621 ^ _777864) ^ [_1527762] : [hBOOL(hAPP(hAPP(c_member(_1527469), _1527762), _1527471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1527469), _1527473), _1527762)))]]], (39627 ^ _777864) ^ [] : [39629 ^ _777864 : [(39632 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1527469), _1527473), 39628 ^ [_1527469, _1527471, _1527473]))], (39630 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527469), 39628 ^ [_1527469, _1527471, _1527473]), _1527471)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1527469), _1527473), hAPP(c_Finite__Set_Ofold1(_1527469, c_Orderings_Oord__class_Omin(_1527469)), _1527471))))]]], (18698 ^ _777864) ^ [] : [-(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)))))], (36036 ^ _777864) ^ [_1448607, _1448609] : [-(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)), _1448607)), 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), _1448609), _1448607))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1448607), _1448609))], (27552 ^ _777864) ^ [_1268500, _1268502] : [class_Rings_Oring__1(_1268500), hBOOL(hAPP(hAPP(c_member(_1268500), _1268502), c_Int_Oring__1__class_OInts(_1268500))), -(hBOOL(hAPP(hAPP(c_member(_1268500), hAPP(c_Groups_Ouminus__class_Ouminus(_1268500), _1268502)), c_Int_Oring__1__class_OInts(_1268500))))], (47476 ^ _777864) ^ [_1727169, _1727171, _1727173] : [c_List_Olist_ONil(_1727169) = hAPP(hAPP(c_List_Olist_OCons(_1727169), _1727171), _1727173)], (47758 ^ _777864) ^ [_1732686, _1732688, _1732690, _1732692, _1732694] : [-(hAPP(hAPP(c_List_Ozip(_1732686, _1732688), _1732690), hAPP(hAPP(c_List_Olist_OCons(_1732688), _1732692), _1732694)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1732686, _1732688)), _1732686, c_List_Olist_ONil(tc_prod(_1732686, _1732688)), hAPP(hAPP(c_COMBC(_1732686, tc_fun(tc_List_Olist(_1732686), tc_List_Olist(tc_prod(_1732686, _1732688))), tc_fun(tc_List_Olist(_1732686), tc_List_Olist(tc_prod(_1732686, _1732688)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1732686, _1732688)), tc_List_Olist(tc_prod(_1732686, _1732688))), tc_fun(tc_fun(tc_List_Olist(_1732686), tc_List_Olist(tc_prod(_1732686, _1732688))), tc_fun(tc_List_Olist(_1732686), tc_List_Olist(tc_prod(_1732686, _1732688)))), _1732686), c_COMBB(tc_List_Olist(tc_prod(_1732686, _1732688)), tc_List_Olist(tc_prod(_1732686, _1732688)), tc_List_Olist(_1732686))), hAPP(hAPP(c_COMBB(tc_prod(_1732686, _1732688), tc_fun(tc_List_Olist(tc_prod(_1732686, _1732688)), tc_List_Olist(tc_prod(_1732686, _1732688))), _1732686), c_List_Olist_OCons(tc_prod(_1732686, _1732688))), hAPP(hAPP(c_COMBC(_1732686, _1732688, tc_prod(_1732686, _1732688)), c_Product__Type_OPair(_1732686, _1732688)), _1732692)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732686), tc_List_Olist(_1732688), tc_List_Olist(tc_prod(_1732686, _1732688))), c_List_Ozip(_1732686, _1732688)), _1732694))), _1732690))], (19486 ^ _777864) ^ [_1112799, _1112801, _1112803] : [class_Rings_Oring__1(_1112799), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1112799), hAPP(c_Groups_Ouminus__class_Ouminus(_1112799), _1112801)), 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)))), _1112803)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1112799), _1112801), 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)))), _1112803)))], (7482 ^ _777864) ^ [_901428, _901430, _901432, _901434, _901436, _901438] : [c_Com_Ocom_OCall(_901428, _901430, _901432) = c_Com_Ocom_OCond(_901434, _901436, _901438)], (7576 ^ _777864) ^ [_903513, _903515] : [_903515 = c_Option_Ooption_ONone(_903513), -(c_Option_Ois__none(_903513, _903515))], (42118 ^ _777864) ^ [_1595327, _1595329, _1595331, _1595333, _1595335, _1595337] : [c_Finite__Set_Ofolding(_1595327, _1595329, _1595331, _1595333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595327), _1595335)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595327), _1595337)), -(hAPP(c_Fun_Ocomp(_1595329, _1595329, _1595329, hAPP(_1595333, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1595327, tc_HOL_Obool)), _1595335), _1595337))), hAPP(_1595333, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595327, tc_HOL_Obool)), _1595335), _1595337))) = hAPP(c_Fun_Ocomp(_1595329, _1595329, _1595329, hAPP(_1595333, _1595335)), hAPP(_1595333, _1595337)))], (34964 ^ _777864) ^ [_1427337, _1427339] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1427337, _1427339)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1427339), _1427337)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (29906 ^ _777864) ^ [_1321196, _1321198, _1321200, _1321202] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321196, tc_HOL_Obool)), _1321198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321196, tc_HOL_Obool)), _1321200), _1321202)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321196, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321196, tc_HOL_Obool)), _1321198), _1321200)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321196, tc_HOL_Obool)), _1321198), _1321202)))], (36478 ^ _777864) ^ [_1457211, _1457213, _1457215, _1457217, _1457219] : [hAPP(_1457211, _1457213) = c_Option_Ooption_ONone(_1457215), -(c_Map_Oran(_1457217, _1457215, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1457217, tc_Option_Ooption(_1457215)), _1457211), _1457213), hAPP(c_Option_Ooption_OSome(_1457215), _1457219))) = hAPP(hAPP(c_Set_Oinsert(_1457215), _1457219), c_Map_Oran(_1457217, _1457215, _1457211)))], (16470 ^ _777864) ^ [_1060615, _1060617, _1060619] : [class_Rings_Olinordered__idom(_1060615), 16473 ^ _777864 : [(16482 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), hAPP(c_Groups_Oabs__class_Oabs(_1060615), _1060617)), _1060619))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), _1060617), _1060619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), hAPP(c_Groups_Ouminus__class_Ouminus(_1060615), _1060617)), _1060619))], (16474 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), hAPP(c_Groups_Oabs__class_Oabs(_1060615), _1060617)), _1060619)), 16477 ^ _777864 : [(16480 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), hAPP(c_Groups_Ouminus__class_Ouminus(_1060615), _1060617)), _1060619)))], (16478 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060615), _1060617), _1060619)))]]]]], (17502 ^ _777864) ^ [_1080068] : [class_Power_Opower(_1080068), -(c_Power_Opower__class_Opower(_1080068) = c_Power_Opower_Opower(_1080068, c_Groups_Oone__class_Oone(_1080068), c_Groups_Otimes__class_Otimes(_1080068)))], (43565 ^ _777864) ^ [_1627131, _1627133, _1627135, _1627137] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627135), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627131, tc_fun(_1627135, tc_HOL_Obool)), _1627133), _1627137)))), 43566 ^ _777864 : [(43567 ^ _777864) ^ [_1627205] : [hBOOL(hAPP(hAPP(c_member(_1627131), _1627205), _1627133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627135), hAPP(_1627137, _1627205)))]]], (38086 ^ _777864) ^ [_1492725, _1492727, _1492729, _1492731, _1492733] : [c_Fun_Oinj__on(_1492725, _1492727, _1492729, c_Orderings_Otop__class_Otop(tc_fun(_1492725, tc_HOL_Obool))), 38089 ^ _777864 : [(38096 ^ _777864) ^ [] : [_1492731 = _1492733, -(hAPP(_1492729, _1492731) = hAPP(_1492729, _1492733))], (38090 ^ _777864) ^ [] : [hAPP(_1492729, _1492731) = hAPP(_1492729, _1492733), -(_1492731 = _1492733)]]], (2854 ^ _777864) ^ [_820609, _820611] : [_820611 = _820609, -(c_New__DSequence_Opos__empty(_820611) = c_New__DSequence_Opos__empty(_820609))], (36418 ^ _777864) ^ [_1455877, _1455879] : [class_Orderings_Oorder(_1455877), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1455877, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1455877), _1455879), c_Orderings_Obot__class_Obot(tc_fun(_1455877, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1455877), _1455879)) = hAPP(hAPP(c_Set_Oinsert(_1455877), _1455879), c_Orderings_Obot__class_Obot(tc_fun(_1455877, tc_HOL_Obool))))], (26853 ^ _777864) ^ [_1251932, _1251934, _1251936, _1251938] : [-(hBOOL(hAPP(hAPP(c_member(_1251932), _1251934), _1251936))), -(hBOOL(hAPP(hAPP(c_member(_1251932), _1251934), _1251938))), 26860 ^ _777864 : [(26867 ^ _777864) ^ [] : [_1251936 = _1251938, -(hAPP(hAPP(c_Set_Oinsert(_1251932), _1251934), _1251936) = hAPP(hAPP(c_Set_Oinsert(_1251932), _1251934), _1251938))], (26861 ^ _777864) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1251932), _1251934), _1251936) = hAPP(hAPP(c_Set_Oinsert(_1251932), _1251934), _1251938), -(_1251936 = _1251938)]]], (35236 ^ _777864) ^ [_1433026, _1433028] : [35238 ^ _777864 : [(35241 ^ _777864) ^ [] : [hBOOL(hAPP(_1433028, 35237 ^ [_1433026, _1433028]))], (35239 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35237 ^ [_1433026, _1433028]), _1433026)))]], 35242 ^ _777864 : [(35243 ^ _777864) ^ [_1433177] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1433177), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1433026))), -(hBOOL(hAPP(_1433028, _1433177)))]]], (24561 ^ _777864) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (43605 ^ _777864) ^ [_1627977, _1627979, _1627981, _1627983] : [_1627977 = c_Orderings_Obot__class_Obot(tc_fun(_1627979, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627979, tc_fun(_1627981, tc_HOL_Obool)), _1627977), hAPP(c_COMBK(tc_fun(_1627981, tc_HOL_Obool), _1627979), _1627983)) = c_Orderings_Otop__class_Otop(tc_fun(_1627981, tc_HOL_Obool)))], (6705 ^ _777864) ^ [_888365, _888367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888365), _888367)), -(hAPP(c_Nat_OSuc, _888365) = _888367), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _888365)), _888367)))], (32813 ^ _777864) ^ [_1379425, _1379427, _1379429] : [class_Groups_Ocomm__monoid__mult(_1379425), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379427, _1379425), hAPP(c_COMBK(_1379425, _1379427), c_Groups_Oone__class_Oone(_1379425))), _1379429) = c_Groups_Oone__class_Oone(_1379425))], (27844 ^ _777864) ^ [_1273905, _1273907, _1273909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273905, tc_HOL_Obool)), _1273907), _1273909)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273905, tc_HOL_Obool)), _1273909), _1273907) = _1273909)], (47426 ^ _777864) ^ [_1725954, _1725956, _1725958, _1725960] : [c_List_Olist_ONil(_1725954) = hAPP(hAPP(c_List_Omap(_1725956, _1725954), _1725958), _1725960), -(_1725960 = c_List_Olist_ONil(_1725956))], (41278 ^ _777864) ^ [_1574870, _1574872] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1574870, _1574872), 41279 ^ [_1574870, _1574872])), -(c_Wellfounded_OwfP(_1574870, _1574872))], (11148 ^ _777864) ^ [_963384, _963386] : [11149 ^ _777864 : [(11152 ^ _777864) ^ [] : [_963384 = _963386], (11150 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963384), _963386))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963384), _963386)))], (33084 ^ _777864) ^ [_1384784, _1384786, _1384788, _1384790, _1384792] : [class_Groups_Ocomm__monoid__mult(_1384784), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384786), _1384788)), -(hBOOL(hAPP(hAPP(c_member(_1384786), _1384790), _1384788))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384786, _1384784), _1384792), hAPP(hAPP(c_Set_Oinsert(_1384786), _1384790), _1384788)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384784), hAPP(_1384792, _1384790)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384786, _1384784), _1384792), _1384788)))], (27870 ^ _777864) ^ [_1274490, _1274492, _1274494] : [class_Lattices_Olattice(_1274490), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274490), _1274492), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274490), _1274492), _1274494))))], (39910 ^ _777864) ^ [_1534954, _1534956] : [-(c_Relation_Orefl__on(_1534954, _1534956, c_Relation_OId__on(_1534954, _1534956)))], (8740 ^ _777864) ^ [_922818, _922820, _922822, _922824, _922826] : [class_Rings_Ocomm__semiring__1(_922818), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), _922820), _922822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), _922824), _922826)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), _922820), _922824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922818), _922822), _922826)))], (23709 ^ _777864) ^ [_1191885, _1191887, _1191889] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1191885), _1191887)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1191889), _1191887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1191885), _1191889)), _1191887))], (47640 ^ _777864) ^ [_1730291, _1730293, _1730295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730291), tc_List_Olist(_1730291))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730291), tc_List_Olist(_1730291)), _1730293), c_List_Olist_ONil(_1730291))), c_List_Olex(_1730291, _1730295)))], (14083 ^ _777864) ^ [_1015953, _1015955] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1015953)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1015955)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015953), _1015955)))], (13431 ^ _777864) ^ [_1003552, _1003554, _1003556, _1003558] : [class_Divides_Osemiring__div(_1003552), -(c_Divides_Odiv__class_Omod(_1003552, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003552), _1003554), _1003556), _1003558) = c_Divides_Odiv__class_Omod(_1003552, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003552), c_Divides_Odiv__class_Omod(_1003552, _1003554, _1003558)), _1003556), _1003558))], (47636 ^ _777864) ^ [_1730143, _1730145, _1730147] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730143), tc_List_Olist(_1730143))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730143), tc_List_Olist(_1730143)), _1730145), c_List_Olist_ONil(_1730143))), c_List_Olexord(_1730143, _1730147)))], (33783 ^ _777864) ^ [_1401770, _1401772, _1401774, _1401776, _1401778] : [_1401770 = c_Orderings_Obot__class_Obot(tc_fun(_1401772, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1401774), _1401776), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401772, tc_fun(_1401774, tc_HOL_Obool)), _1401770), _1401778)) = hAPP(hAPP(c_Set_Oinsert(_1401774), _1401776), c_Orderings_Obot__class_Obot(tc_fun(_1401774, tc_HOL_Obool))))], (2222 ^ _777864) ^ [_810563, _810565, _810567, _810569, _810571, _810573, _810575, _810577] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810577, _810573, _810569, _810565) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810575, _810571, _810567, _810563)), _810577 = _810575, _810573 = _810571, _810569 = _810567, _810565 = _810563], (6133 ^ _777864) ^ [_878731, _878733, _878735] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_878731), _878733), _878735)), -(c_Natural_Oevaln(_878731, _878733, 6136 ^ [_878731, _878733, _878735], _878735))], (34705 ^ _777864) ^ [_1422207, _1422209, _1422211] : [class_Groups_Oordered__ab__group__add(_1422207), -(hAPP(c_Set_Oimage(_1422207, _1422207, c_Groups_Ouminus__class_Ouminus(_1422207)), c_SetInterval_Oord__class_OatLeastAtMost(_1422207, _1422209, _1422211)) = c_SetInterval_Oord__class_OatLeastAtMost(_1422207, hAPP(c_Groups_Ouminus__class_Ouminus(_1422207), _1422211), hAPP(c_Groups_Ouminus__class_Ouminus(_1422207), _1422209)))], (50795 ^ _777864) ^ [_1802558, _1802560] : [-(c_List_OtakeWhile(_1802558, _1802560, c_List_Olist_ONil(_1802558)) = c_List_Olist_ONil(_1802558))], (51333 ^ _777864) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (46478 ^ _777864) ^ [_1700182, _1700184] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1700182), _1700184)), -(c_Nitpick_Ocard_H(_1700182, _1700184) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700182)), c_Hilbert__Choice_OEps(tc_List_Olist(_1700182), hAPP(hAPP(c_COMBS(tc_List_Olist(_1700182), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1700182)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700182), tc_fun(_1700182, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1700182, tc_HOL_Obool), tc_fun(tc_fun(_1700182, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1700182)), c_fequal), c_List_Oset(_1700182))), _1700184))), c_List_Odistinct(_1700182)))))], (16308 ^ _777864) ^ [_1057648, _1057650] : [16309 ^ _777864 : [(16312 ^ _777864) ^ [] : [_1057650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16310 ^ _777864) ^ [] : [-(_1057648 = 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), _1057648)), _1057650))))], (38052 ^ _777864) ^ [_1492120, _1492122, _1492124] : [class_Lattices_Oboolean__algebra(_1492120), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492120), _1492122), _1492124) = c_Orderings_Obot__class_Obot(_1492120), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1492120), _1492122), _1492124) = c_Orderings_Otop__class_Otop(_1492120), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1492120), _1492122) = _1492124)], (50366 ^ _777864) ^ [_1792105, _1792107] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792105)), c_List_Oconcat(_1792105, _1792107)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1792105), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1792105))), _1792107)))], (44433 ^ _777864) ^ [_1650995, _1650997, _1650999, _1651001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650995, _1650995)), hAPP(hAPP(c_Product__Type_OPair(_1650995, _1650995), _1650997), _1650999)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650995, _1650995), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1651001))), -(_1650997 = _1650999)], (41057 ^ _777864) ^ [_1569295, _1569297] : [c_FunDef_Oreduction__pair(_1569295, _1569297), 41060 ^ _777864 : [(41063 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1569295, _1569295, _1569295), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool), tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool)), _1569297)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool), tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool)), _1569297))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool), tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool)), _1569297))))], (41061 ^ _777864) ^ [] : [-(c_Wellfounded_Owf(_1569295, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool), tc_fun(tc_prod(_1569295, _1569295), tc_HOL_Obool)), _1569297)))]]], (40863 ^ _777864) ^ [_1565508, _1565510] : [c_Wellfounded_Owf(_1565508, _1565510), -(c_Wellfounded_Owf(_1565508, hAPP(hAPP(c_Relation_Orel__comp(_1565508, _1565508, _1565508), _1565510), _1565510)))], (51137 ^ _777864) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (38742 ^ _777864) ^ [_1507352, _1507354, _1507356, _1507358, _1507360] : [hBOOL(hAPP(hAPP(c_member(_1507352), _1507354), hAPP(c_Set_Ovimage(_1507352, _1507356, _1507358), _1507360))), -(hBOOL(hAPP(hAPP(c_member(_1507356), hAPP(_1507358, _1507354)), _1507360)))], (34541 ^ _777864) ^ [_1419487, _1419489, _1419491, _1419493] : [class_Orderings_Olinorder(_1419487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419487), _1419489), _1419491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419487), _1419491), _1419493)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419487, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1419487, _1419489, _1419491)), c_SetInterval_Oord__class_OatLeastAtMost(_1419487, _1419491, _1419493)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1419487, _1419489, _1419493))], (41497 ^ _777864) ^ [_1580118, _1580120, _1580122] : [c_Relation_Orefl__on(_1580118, _1580120, _1580122), 41500 ^ _777864 : [(41507 ^ _777864) ^ [_1580602] : [hBOOL(hAPP(hAPP(c_member(_1580118), _1580602), _1580120)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580118, _1580118)), hAPP(hAPP(c_Product__Type_OPair(_1580118, _1580118), _1580602), _1580602)), _1580122)))], (41501 ^ _777864) ^ [_1580329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580118, _1580118)), _1580329), _1580122)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1580118, _1580118, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1580118, tc_fun(_1580118, tc_HOL_Obool), tc_fun(_1580118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1580118, tc_HOL_Obool), tc_fun(_1580118, tc_HOL_Obool)), _1580118), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1580118)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580118), c_fconj), hAPP(hAPP(c_COMBC(_1580118, tc_fun(_1580118, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580118)), _1580120)))), hAPP(hAPP(c_COMBC(_1580118, tc_fun(_1580118, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580118)), _1580120))), _1580329)))]]], (26101 ^ _777864) ^ [_1236356, _1236358, _1236360] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236356, tc_HOL_Obool)), _1236358), hAPP(hAPP(c_Set_Oinsert(_1236356), _1236360), _1236358))))], (24057 ^ _777864) ^ [_1198431, _1198433, _1198435, _1198437, _1198439] : [class_Orderings_Olinorder(_1198431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198431), _1198433), _1198435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198431), _1198437), _1198439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198431), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198431), _1198433), _1198437)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198431), _1198435), _1198439))))], (28350 ^ _777864) ^ [_1284503, _1284505, _1284507, _1284509] : [c_FunDef_Oreduction__pair(_1284503, _1284505), -(c_FunDef_Oreduction__pair(_1284507, hAPP(hAPP(c_FunDef_Orp__inv__image(_1284503, _1284507), _1284505), _1284509)))], (48748 ^ _777864) ^ [_1757935, _1757937] : [-(_1757935 = c_List_Olist_ONil(_1757937)), -(hBOOL(hAPP(hAPP(c_member(_1757937), hAPP(c_List_Ohd(_1757937), _1757935)), hAPP(c_List_Oset(_1757937), _1757935))))], (51045 ^ _777864) ^ [_1807304, _1807306] : [class_Lattices_Olattice(_1807304), -(class_Lattices_Osemilattice__sup(tc_fun(_1807306, _1807304)))], (19286 ^ _777864) ^ [] : [-(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))))], (28499 ^ _777864) ^ [_1290481, _1290483, _1290485, _1290487, _1290489, _1290491] : [-(hAPP(c_Set_Oimage(_1290481, _1290483, _1290485), hAPP(c_Set_Oimage(_1290487, _1290481, _1290489), _1290491)) = hAPP(c_Set_Oimage(_1290487, _1290483, hAPP(hAPP(c_COMBB(_1290481, _1290483, _1290487), _1290485), _1290489)), _1290491))], (36516 ^ _777864) ^ [_1458138, _1458140, _1458142] : [class_Groups_Ocomm__monoid__add(_1458138), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458140, _1458138), _1458142), c_Orderings_Obot__class_Obot(tc_fun(_1458140, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1458138))], (23813 ^ _777864) ^ [_1194035, _1194037, _1194039, _1194041] : [class_Orderings_Olinorder(_1194035), 23816 ^ _777864 : [(23825 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194035), _1194037), _1194039)), _1194041))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), _1194037), _1194041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), _1194039), _1194041))], (23817 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194035), _1194037), _1194039)), _1194041)), 23820 ^ _777864 : [(23823 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), _1194039), _1194041)))], (23821 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194035), _1194037), _1194041)))]]]]], (45561 ^ _777864) ^ [_1677761, _1677763, _1677765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1677761), _1677763)), -(c_Smallcheck_Osmall_H(_1677765, _1677761, _1677763) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (4112 ^ _777864) ^ [_840686, _840688] : [_840688 = _840686, -(c_Groups_Ouminus__class_Ouminus(_840688) = c_Groups_Ouminus__class_Ouminus(_840686))], (39301 ^ _777864) ^ [_1521364, _1521366, _1521368, _1521370] : [_1521364 = c_Orderings_Obot__class_Obot(tc_fun(_1521366, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1521368, _1521366), _1521368, c_Product__Type_Ofst(_1521368, _1521366)), hAPP(hAPP(c_Product__Type_OSigma(_1521368, _1521366), _1521370), hAPP(c_COMBK(tc_fun(_1521366, tc_HOL_Obool), _1521368), _1521364))) = c_Orderings_Obot__class_Obot(tc_fun(_1521368, tc_HOL_Obool)))], (392 ^ _777864) ^ [_783826, _783828, _783830, _783832, _783834, _783836] : [-(c_Big__Operators_Osemilattice__big(_783834, _783830, _783826)), c_Big__Operators_Osemilattice__big(_783836, _783832, _783828), _783836 = _783834, _783832 = _783830, _783828 = _783826], (24745 ^ _777864) ^ [_1212152, _1212154, _1212156, _1212158] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1212152, _1212154, _1212156), c_Product__Type_Ocurry(_1212152, _1212154, _1212156, _1212158)) = _1212158)], (51011 ^ _777864) ^ [_1806832, _1806834] : [-(c_List_OdropWhile(_1806832, _1806834, c_List_Olist_ONil(_1806832)) = c_List_Olist_ONil(_1806832))], (11537 ^ _777864) ^ [_970302, _970304, _970306, _970308, _970310] : [class_Rings_Oordered__semiring(_970302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970302), _970304), _970306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970302), _970308), _970310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970302), c_Groups_Ozero__class_Ozero(_970302)), _970306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970302), c_Groups_Ozero__class_Ozero(_970302)), _970308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970302), _970304), _970308)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970302), _970306), _970310))))], (39209 ^ _777864) ^ [_1519225, _1519227, _1519229, _1519231, _1519233, _1519235] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519225, _1519227)), hAPP(hAPP(c_Product__Type_OPair(_1519225, _1519227), _1519229), _1519231)), hAPP(hAPP(c_Product__Type_OSigma(_1519225, _1519227), _1519233), _1519235))), 39212 ^ _777864 : [(39215 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519227), _1519231), hAPP(_1519235, _1519229))))], (39213 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519225), _1519229), _1519233)))]]], (9997 ^ _777864) ^ [_944907, _944909] : [-(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), _944907))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944909))))], (23281 ^ _777864) ^ [_1183246, _1183248, _1183250, _1183252, _1183254] : [-(hAPP(c_Nat_Onat_Onat__rec(_1183246, _1183248, _1183250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1183252)), _1183254)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1183246), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1183252))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183246, _1183246), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1183246, tc_fun(_1183246, _1183246)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1183246, tc_fun(_1183246, _1183246)), tc_Int_Oint), c_If(_1183246)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1183246, _1183248, _1183250), _1183254))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183246, _1183246), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1183246, _1183246), tc_Int_Oint), _1183250), 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)), _1183254))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1183246, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1183246, _1183248, _1183250)), 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)), _1183254))))))], (15696 ^ _777864) ^ [_1045998, _1046000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1045998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045998), hAPP(c_Nat_OSuc, _1046000))), _1045998)))], (48173 ^ _777864) ^ [_1742588, _1742590, _1742592] : [hBOOL(hAPP(c_List_Odistinct(_1742588), hAPP(hAPP(c_List_Oappend(_1742588), _1742590), _1742592))), 48176 ^ _777864 : [(48181 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1742588, tc_HOL_Obool)), hAPP(c_List_Oset(_1742588), _1742590)), hAPP(c_List_Oset(_1742588), _1742592)) = c_Orderings_Obot__class_Obot(tc_fun(_1742588, tc_HOL_Obool)))], (48179 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1742588), _1742592)))], (48177 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1742588), _1742590)))]]], (12151 ^ _777864) ^ [_981286, _981288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981288)), 12158 ^ _777864 : [(12165 ^ _777864) ^ [] : [_981286 = _981288, -(hAPP(c_Int_Onat, _981286) = hAPP(c_Int_Onat, _981288))], (12159 ^ _777864) ^ [] : [hAPP(c_Int_Onat, _981286) = hAPP(c_Int_Onat, _981288), -(_981286 = _981288)]]], (624 ^ _777864) ^ [_787526, _787528, _787530, _787532, _787534, _787536, _787538, _787540] : [-(c_Finite__Set_Ofolding__idem(_787538, _787534, _787530, _787526)), c_Finite__Set_Ofolding__idem(_787540, _787536, _787532, _787528), _787540 = _787538, _787536 = _787534, _787532 = _787530, _787528 = _787526], (7688 ^ _777864) ^ [_905317, _905319, _905321, _905323, _905325] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_905317, _905319), _905321, _905323, _905325)), 7689 ^ _777864 : [(7696 ^ _777864) ^ [] : [hBOOL(hAPP(_905317, _905321)), 7699 ^ _777864 : [(7700 ^ _777864) ^ [_905527] : [c_Natural_Oevaln(_905319, _905321, _905323, _905527), c_Natural_Oevaln(c_Com_Ocom_OWhile(_905317, _905319), _905527, _905323, _905325)]]], (7690 ^ _777864) ^ [] : [_905325 = _905321, -(hBOOL(hAPP(_905317, _905321)))]]], (44202 ^ _777864) ^ [_1645496] : [-(c_Transitive__Closure_Ortrancl(_1645496, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1645496, _1645496), tc_HOL_Obool))) = c_Relation_OId(_1645496))], (39129 ^ _777864) ^ [_1516671, _1516673, _1516675, _1516677] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1516671, _1516673)), hAPP(hAPP(c_Product__Type_OSigma(_1516671, _1516673), _1516675), hAPP(c_COMBK(tc_fun(_1516673, tc_HOL_Obool), _1516671), _1516677))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1516671), _1516675)), hAPP(c_Finite__Set_Ocard(_1516673), _1516677)))], (47690 ^ _777864) ^ [_1731238, _1731240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731238)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731240)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731238), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731240)) = c_List_Olist_ONil(tc_Int_Oint))], (16918 ^ _777864) ^ [_1069521, _1069523, _1069525, _1069527] : [class_Rings_Olinordered__semidom(_1069521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069523), _1069525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069521), c_Groups_Ozero__class_Ozero(_1069521)), _1069527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069521), _1069527), c_Groups_Oone__class_Oone(_1069521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069521), hAPP(hAPP(c_Power_Opower__class_Opower(_1069521), _1069527), _1069525)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069521), _1069527), _1069523))))], (23313 ^ _777864) ^ [_1184195, _1184197, _1184199, _1184201, _1184203] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184195, _1184197, _1184199), _1184201), _1184203) = hAPP(hAPP(_1184201, hAPP(c_Product__Type_Ofst(_1184195, _1184197), _1184203)), hAPP(c_Product__Type_Osnd(_1184195, _1184197), _1184203)))], (33098 ^ _777864) ^ [_1385034, _1385036, _1385038, _1385040, _1385042] : [class_Groups_Ocomm__monoid__mult(_1385034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385036), _1385038)), -(hBOOL(hAPP(hAPP(c_member(_1385036), _1385040), _1385038))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385036, _1385034), _1385042), hAPP(hAPP(c_Set_Oinsert(_1385036), _1385040), _1385038)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385034), hAPP(_1385042, _1385040)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385036, _1385034), _1385042), _1385038)))], (11060 ^ _777864) ^ [_962065, _962067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962065), _962067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962065)), hAPP(c_Nat_OSuc, _962067))))], (24749 ^ _777864) ^ [_1212229, _1212231, _1212233, _1212235, _1212237, _1212239, _1212241] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1212229, _1212231, _1212233, _1212235, _1212237, _1212239, _1212241) = c_New__DSequence_Oneg__decr__bind(_1212229, _1212231, hAPP(hAPP(hAPP(_1212233, _1212237), _1212239), _1212241), hAPP(hAPP(c_COMBC(_1212229, 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(_1212231)))), hAPP(hAPP(c_COMBC(_1212229, 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(_1212231))))), hAPP(hAPP(c_COMBC(_1212229, 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(_1212231)))))), _1212235), _1212237)), _1212239)), _1212241)))], (12986 ^ _777864) ^ [_995795, _995797] : [class_Rings_Olinordered__idom(_995795), 12989 ^ _777864 : [(12996 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995795), c_Groups_Ozero__class_Ozero(_995795)), _995797)), -(c_Groups_Osgn__class_Osgn(_995795, _995797) = c_Groups_Oone__class_Oone(_995795))], (12990 ^ _777864) ^ [] : [c_Groups_Osgn__class_Osgn(_995795, _995797) = c_Groups_Oone__class_Oone(_995795), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995795), c_Groups_Ozero__class_Ozero(_995795)), _995797)))]]], (36548 ^ _777864) ^ [_1458604, _1458606, _1458608, _1458610] : [class_Groups_Oab__group__add(_1458604), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458606, _1458604), hAPP(hAPP(c_COMBB(_1458604, _1458604, _1458606), c_Groups_Ouminus__class_Ouminus(_1458604)), _1458608)), _1458610) = hAPP(c_Groups_Ouminus__class_Ouminus(_1458604), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458606, _1458604), _1458608), _1458610)))], (51459 ^ _777864) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (28030 ^ _777864) ^ [_1277346, _1277348, _1277350, _1277352] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277346, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277346, tc_HOL_Obool)), _1277348), _1277350)), _1277352) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277346, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277346, tc_HOL_Obool)), _1277348), _1277352)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277346, tc_HOL_Obool)), _1277350), _1277352)))], (39387 ^ _777864) ^ [_1522843, _1522845, _1522847, _1522849, _1522851, _1522853] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522843, _1522845), hAPP(hAPP(c_Set_Oinsert(_1522843), _1522847), _1522849)), hAPP(c_COMBK(tc_fun(_1522845, tc_HOL_Obool), _1522843), hAPP(hAPP(c_Set_Oinsert(_1522845), _1522851), _1522853))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1522843, _1522845)), hAPP(hAPP(c_Product__Type_OPair(_1522843, _1522845), _1522847), _1522851)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1522843, _1522845), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522843, _1522845), _1522849), hAPP(c_COMBK(tc_fun(_1522845, tc_HOL_Obool), _1522843), hAPP(hAPP(c_Set_Oinsert(_1522845), _1522851), _1522853)))), hAPP(hAPP(c_Product__Type_OSigma(_1522843, _1522845), hAPP(hAPP(c_Set_Oinsert(_1522843), _1522847), _1522849)), hAPP(c_COMBK(tc_fun(_1522845, tc_HOL_Obool), _1522843), _1522853)))))], (21970 ^ _777864) ^ [_1157780] : [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), _1157780))), 21973 ^ _777864 : [(21980 ^ _777864) ^ [] : [-(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), _1157780)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157780)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157780)), 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), _1157780)))))], (21974 ^ _777864) ^ [] : [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), _1157780))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1157780)) = 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)))]]], (39155 ^ _777864) ^ [_1517363, _1517365, _1517367] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517363, _1517365), _1517367), hAPP(c_COMBK(tc_fun(_1517365, tc_HOL_Obool), _1517363), c_Orderings_Obot__class_Obot(tc_fun(_1517365, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517363, _1517365), tc_HOL_Obool)))], (14902 ^ _777864) ^ [_1030355, _1030357, _1030359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030355)), 14908 ^ _777864 : [(14911 ^ _777864) ^ [] : [hBOOL(hAPP(_1030357, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 14907 ^ [_1030355, _1030357, _1030359]), _1030355)))], (14909 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1030357, 14907 ^ [_1030355, _1030357, _1030359])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030359)), 14916 ^ _777864 : [(14917 ^ _777864) ^ [_1030644] : [hBOOL(hAPP(_1030357, _1030644)), -(hBOOL(hAPP(_1030357, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030359), _1030355)))))]]], (41762 ^ _777864) ^ [_1587225, _1587227, _1587229, _1587231, _1587233, _1587235, _1587237] : [-(hAPP(c_Fun_Ocomp(_1587225, _1587227, _1587229, _1587231), hAPP(c_Fun_Ocomp(_1587233, _1587225, _1587229, _1587235), _1587237)) = hAPP(c_Fun_Ocomp(_1587233, _1587227, _1587229, hAPP(c_Fun_Ocomp(_1587225, _1587227, _1587233, _1587231), _1587235)), _1587237))], (44111 ^ _777864) ^ [_1642616, _1642618, _1642620, _1642622, _1642624] : [class_Complete__Lattice_Ocomplete__lattice(_1642616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1642618), _1642620)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1642616), _1642622), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642618, _1642616), _1642620), _1642624)) = hAPP(hAPP(c_Finite__Set_Ofold(_1642618, _1642616, hAPP(hAPP(c_COMBB(_1642616, tc_fun(_1642616, _1642616), _1642618), c_Lattices_Osemilattice__inf__class_Oinf(_1642616)), _1642624)), _1642622), _1642620))], (28895 ^ _777864) ^ [_1299838] : [28897 ^ _777864 : [(28900 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28896 ^ [_1299838]))], (28898 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28896 ^ [_1299838]), _1299838)))]], -(c_Nat__Transfer_Onat__set(_1299838))], (41932 ^ _777864) ^ [_1590888, _1590890, _1590892, _1590894, _1590896, _1590898] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1590888, tc_fun(_1590890, tc_HOL_Obool)), _1590892), hAPP(c_Fun_Ocomp(_1590894, tc_fun(_1590890, tc_HOL_Obool), _1590888, _1590896), _1590898)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1590894, tc_fun(_1590890, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1590888, _1590894, _1590898), _1590892)), _1590896))], (10594 ^ _777864) ^ [_954541, _954543, _954545] : [class_Orderings_Opreorder(_954541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954541), _954543), _954545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954541), _954543), _954545)))], (6036 ^ _777864) ^ [_877246] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(_877246)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24955 ^ _777864) ^ [_1215996, _1215998] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215996), _1215998)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215998), _1215996))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215998), _1215996)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215996), _1215998)))], (16758 ^ _777864) ^ [_1066549, _1066551] : [class_Groups_Oordered__ab__group__add__abs(_1066549), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066549), _1066551), c_Groups_Ozero__class_Ozero(_1066549))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066549), _1066551) = hAPP(c_Groups_Ouminus__class_Ouminus(_1066549), _1066551))], (47638 ^ _777864) ^ [_1730217, _1730219, _1730221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730217), tc_List_Olist(_1730217))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730217), tc_List_Olist(_1730217)), c_List_Olist_ONil(_1730217)), _1730219)), c_List_Olex(_1730217, _1730221)))], (50474 ^ _777864) ^ [_1794439, _1794441] : [-(hAPP(c_List_Orev(_1794439), c_List_Oconcat(_1794439, _1794441)) = c_List_Oconcat(_1794439, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1794439), tc_List_Olist(_1794439)), c_List_Orev(_1794439)), hAPP(c_List_Orev(tc_List_Olist(_1794439)), _1794441))))], (1022 ^ _777864) ^ [_793407, _793409] : [-(class_Rings_Olinordered__ring__strict(_793407)), _793409 = _793407, class_Rings_Olinordered__ring__strict(_793409)], (34895 ^ _777864) ^ [_1425780, _1425782, _1425784, _1425786] : [class_Orderings_Oorder(_1425780), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425780, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1425780, _1425782, _1425784)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425780, _1425784, _1425786)) = c_Orderings_Obot__class_Obot(tc_fun(_1425780, tc_HOL_Obool)))], (37629 ^ _777864) ^ [_1483782, _1483784] : [class_Orderings_Oorder(_1483782), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483782, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1483782), _1483784)), hAPP(c_SetInterval_Oord__class_OatLeast(_1483782), _1483784)) = hAPP(hAPP(c_Set_Oinsert(_1483782), _1483784), c_Orderings_Obot__class_Obot(tc_fun(_1483782, tc_HOL_Obool))))], (35892 ^ _777864) ^ [_1445548, _1445550, _1445552, _1445554] : [class_Orderings_Oorder(_1445548), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445548, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1445548, _1445550, _1445552)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445548, _1445552), _1445554)) = c_Orderings_Obot__class_Obot(tc_fun(_1445548, tc_HOL_Obool)))], (45467 ^ _777864) ^ [_1675506, _1675508, _1675510] : [-(c_Map_Omap__add(_1675506, _1675508, hAPP(c_COMBK(tc_Option_Ooption(_1675508), _1675506), c_Option_Ooption_ONone(_1675508)), _1675510) = _1675510)], (17704 ^ _777864) ^ [_1083003, _1083005, _1083007, _1083009, _1083011] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1083003, _1083005, _1083007), _1083009), hAPP(c_Nat_OSuc, _1083011)) = hAPP(hAPP(_1083007, _1083009), hAPP(hAPP(c_Power_Opower_Opower(_1083003, _1083005, _1083007), _1083009), _1083011)))], (11197 ^ _777864) ^ [_964311, _964313, _964315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964311), _964313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964313), _964315))))], (14274 ^ _777864) ^ [_1019218, _1019220, _1019222] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019218), _1019220)), _1019222) = 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), _1019218), _1019222)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019220), _1019222))), 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, _1019218, _1019222)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019220, _1019222))), _1019222)))], (12241 ^ _777864) ^ [_982744, _982746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982746)), -(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), _982744), _982746))))], (25931 ^ _777864) ^ [_1233156, _1233158, _1233160] : [class_Rings_Ocomm__semiring__1(_1233156), 25936 ^ _777864 : [(25939 ^ _777864) ^ [] : [_1233160 = c_Groups_Oone__class_Oone(_1233156)], (25937 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1233158))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1233156), _1233160), hAPP(hAPP(c_Power_Opower__class_Opower(_1233156), _1233160), _1233158))))], (48959 ^ _777864) ^ [_1762066, _1762068, _1762070, _1762072, _1762074] : [c_Finite__Set_Ofun__left__comm__idem(_1762066, _1762068, _1762070), -(hAPP(hAPP(c_Finite__Set_Ofold(_1762066, _1762068, _1762070), _1762072), hAPP(c_List_Oset(_1762066), _1762074)) = hAPP(c_List_Ofoldl(_1762068, _1762066, hAPP(c_COMBC(_1762066, _1762068, _1762068), _1762070), _1762072), _1762074))], (11030 ^ _777864) ^ [_961557, _961559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961559)), _961557)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961557), _961559))], (47706 ^ _777864) ^ [_1731523, _1731525, _1731527, _1731529] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731523) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1731525), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731523)), hAPP(hAPP(c_List_Olist_OCons(_1731525), _1731527), _1731529)) = c_List_Olist_ONil(_1731525))], (36320 ^ _777864) ^ [_1453983] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1453983) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453983))], (7556 ^ _777864) ^ [_903201, _903203, _903205, _903207] : [-(hAPP(c_Option_Ooption_Ooption__case(_903201, _903203, _903205, _903207), c_Option_Ooption_ONone(_903203)) = _903205)], (24083 ^ _777864) ^ [_1198925, _1198927, _1198929, _1198931] : [class_Groups_Oordered__ab__group__add(_1198925), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1198925), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198925), _1198927), _1198929)), _1198931) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198925), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1198925), _1198927), _1198931)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1198925), _1198929), _1198931)))], (19344 ^ _777864) ^ [] : [-(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))))], (31523 ^ _777864) ^ [_1353964, _1353966] : [class_Lattices_Olattice(_1353964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353964), _1353966)), -(_1353966 = c_Orderings_Obot__class_Obot(tc_fun(_1353964, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1353964), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1353964), 31536 ^ [_1353964, _1353966]), 31537 ^ [_1353964, _1353966])), hAPP(hAPP(c_Set_Oinsert(_1353964), 31536 ^ [_1353964, _1353966]), hAPP(hAPP(c_Set_Oinsert(_1353964), 31537 ^ [_1353964, _1353966]), c_Orderings_Obot__class_Obot(tc_fun(_1353964, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1353964), c_Big__Operators_Olattice__class_OSup__fin(_1353964, _1353966)), _1353966)))], (24221 ^ _777864) ^ [_1202080, _1202082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202080), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24224 ^ _777864 : [(24233 ^ _777864) ^ [] : [-(c_Nitpick_Onorm__frac(_1202082, _1202080) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1202082), _1202080)), 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), _1202082))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202080)))), -(_1202082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1202080 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24225 ^ _777864) ^ [] : [24226 ^ _777864 : [(24229 ^ _777864) ^ [] : [_1202080 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24227 ^ _777864) ^ [] : [_1202082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1202082, _1202080) = 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)))]]], (36360 ^ _777864) ^ [_1454660, _1454662, _1454664] : [class_Orderings_Olinorder(_1454660), 36363 ^ _777864 : [(36370 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454660), _1454662), _1454664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1454660, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454660), _1454662)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454660), _1454664))))], (36364 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1454660, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454660), _1454662)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454660), _1454664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454660), _1454662), _1454664)))]]], (46232 ^ _777864) ^ [_1693998, _1694000, _1694002] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693998)), _1694000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693998)), _1694002)), _1694000 = _1694002], (19834 ^ _777864) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46687 ^ _777864) ^ [_1706556, _1706558, _1706560] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706556)), hAPP(hAPP(c_List_Olist_OCons(_1706556), _1706558), _1706560)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706556)), _1706560)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33000 ^ _777864) ^ [_1382910, _1382912, _1382914, _1382916, _1382918] : [class_Groups_Ocomm__monoid__mult(_1382910), class_Rings_Odvd(_1382910), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382912), _1382914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382912, tc_HOL_Obool)), _1382916), _1382914)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1382910), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382912, _1382910), _1382918), _1382916)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382912, _1382910), _1382918), _1382914))))], (2204 ^ _777864) ^ [_810262, _810264, _810266, _810268, _810270, _810272, _810274, _810276] : [-(c_Random_Oiterate(_810276, _810272, _810268, _810264) = c_Random_Oiterate(_810274, _810270, _810266, _810262)), _810276 = _810274, _810272 = _810270, _810268 = _810266, _810264 = _810262], (37651 ^ _777864) ^ [_1484166, _1484168, _1484170] : [class_Orderings_Oord(_1484166), 37654 ^ _777864 : [(37661 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484166), _1484170), _1484168)), -(hBOOL(hAPP(hAPP(c_member(_1484166), _1484168), hAPP(c_SetInterval_Oord__class_OatLeast(_1484166), _1484170))))], (37655 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484166), _1484168), hAPP(c_SetInterval_Oord__class_OatLeast(_1484166), _1484170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484166), _1484170), _1484168)))]]], (1212 ^ _777864) ^ [_795782, _795784] : [-(class_Rings_Oidom(_795782)), _795784 = _795782, class_Rings_Oidom(_795784)], (25275 ^ _777864) ^ [_1221143, _1221145, _1221147, _1221149] : [class_Rings_Ocomm__semiring__1(_1221143), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221143), _1221145), _1221147)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221143), _1221145), _1221149)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221143), _1221145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221143), _1221147), _1221149))))], (33146 ^ _777864) ^ [_1386165, _1386167, _1386169, _1386171, _1386173] : [class_Groups_Ocomm__monoid__mult(_1386165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386167), _1386169)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386167, _1386165), _1386171), hAPP(hAPP(c_Set_Oinsert(_1386167), _1386173), _1386169)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386165), hAPP(_1386171, _1386173)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386167, _1386165), _1386171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386167, tc_HOL_Obool)), _1386169), hAPP(hAPP(c_Set_Oinsert(_1386167), _1386173), c_Orderings_Obot__class_Obot(tc_fun(_1386167, tc_HOL_Obool)))))))], (44714 ^ _777864) ^ [_1657513, _1657515, _1657517, _1657519] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657513, tc_fun(_1657515, tc_HOL_Obool)), _1657517), _1657519) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657515, tc_HOL_Obool), hAPP(c_Set_Oimage(_1657513, tc_fun(_1657515, tc_HOL_Obool), _1657519), _1657517)))], (14352 ^ _777864) ^ [_1020490, _1020492, _1020494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1020490), _1020492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020494), _1020492)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020494), _1020490))))], (3852 ^ _777864) ^ [_836466, _836468] : [_836468 = _836466, -(c_Equiv__Relations_Oquotient(_836468) = c_Equiv__Relations_Oquotient(_836466))], (35158 ^ _777864) ^ [_1431378, _1431380, _1431382, _1431384, _1431386] : [c_Fun_Oinj__on(_1431378, _1431380, _1431382, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431378, tc_HOL_Obool)), _1431384), _1431386)), 35161 ^ _777864 : [(35168 ^ _777864) ^ [] : [_1431384 = _1431386, -(hAPP(c_Set_Oimage(_1431378, _1431380, _1431382), _1431384) = hAPP(c_Set_Oimage(_1431378, _1431380, _1431382), _1431386))], (35162 ^ _777864) ^ [] : [hAPP(c_Set_Oimage(_1431378, _1431380, _1431382), _1431384) = hAPP(c_Set_Oimage(_1431378, _1431380, _1431382), _1431386), -(_1431384 = _1431386)]]], (34223 ^ _777864) ^ [_1412333, _1412335, _1412337, _1412339, _1412341, _1412343, _1412345] : [c_Big__Operators_Ocomm__monoid__big(_1412333, _1412335, _1412337, _1412339, _1412341), 34226 ^ _777864 : [(34233 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1412335), _1412343))), -(hAPP(hAPP(_1412341, _1412345), _1412343) = _1412339)], (34227 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1412335), _1412343)), -(hAPP(hAPP(_1412341, _1412345), _1412343) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1412333, _1412335, _1412337), _1412345), _1412339), _1412343))]]], (14686 ^ _777864) ^ [_1026404, _1026406, _1026408] : [hBOOL(hAPP(_1026404, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026406), _1026408))), 14689 ^ _777864 : [(14696 ^ _777864) ^ [] : [-(_1026408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14699 ^ _777864 : [(14700 ^ _777864) ^ [_1026656, _1026658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026656), _1026408)), _1026406 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026408), _1026658)), _1026656), -(hBOOL(hAPP(_1026404, _1026658)))]]], (14690 ^ _777864) ^ [] : [_1026408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1026404, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (44467 ^ _777864) ^ [_1652002, _1652004, _1652006] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652002, _1652002)), _1652004), c_Transitive__Closure_Otrancl(_1652002, _1652006))), 44471 ^ _777864 : [(44474 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652002, _1652002)), _1652004), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1652002, _1652002), tc_HOL_Obool), 44470 ^ [_1652002, _1652004, _1652006]), _1652006))))], (44472 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 44470 ^ [_1652002, _1652004, _1652006])))]]], (9220 ^ _777864) ^ [_931444, _931446] : [class_Groups_Oordered__ab__group__add(_931444), 9223 ^ _777864 : [(9230 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931444), _931446), c_Groups_Ozero__class_Ozero(_931444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931444), c_Groups_Ozero__class_Ozero(_931444)), hAPP(c_Groups_Ouminus__class_Ouminus(_931444), _931446))))], (9224 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931444), c_Groups_Ozero__class_Ozero(_931444)), hAPP(c_Groups_Ouminus__class_Ouminus(_931444), _931446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931444), _931446), c_Groups_Ozero__class_Ozero(_931444))))]]], (10810 ^ _777864) ^ [_957752, _957754, _957756, _957758, _957760] : [class_Groups_Oordered__ab__semigroup__add(_957752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957752), _957754), _957756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957752), _957758), _957760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957752), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957752), _957754), _957758)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957752), _957756), _957760))))], (7671 ^ _777864) ^ [_905032, _905034, _905036, _905038, _905040] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_905032, _905034), _905036, _905038, _905040), 7676 ^ _777864 : [(7679 ^ _777864) ^ [] : [hBOOL(hAPP(_905032, _905036))], (7677 ^ _777864) ^ [] : [-(_905040 = _905036)]], 7680 ^ _777864 : [(7686 ^ _777864) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_905032, _905034), 7682 ^ [_905032, _905034, _905036, _905038, _905040], _905038, _905040))], (7684 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_905034, _905036, _905038, 7682 ^ [_905032, _905034, _905036, _905038, _905040]))], (7681 ^ _777864) ^ [] : [-(hBOOL(hAPP(_905032, _905036)))]]], (48428 ^ _777864) ^ [_1749932, _1749934, _1749936, _1749938, _1749940, _1749942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749932, _1749932)), hAPP(hAPP(c_Product__Type_OPair(_1749932, _1749932), _1749934), _1749936)), c_Transitive__Closure_Ortrancl(_1749932, _1749938))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749932), tc_List_Olist(_1749932))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1749932), tc_List_Olist(_1749932)), _1749940), _1749942)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1749932), c_List_Olistrel1(_1749932, _1749938)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1749932), tc_List_Olist(_1749932))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1749932), tc_List_Olist(_1749932)), hAPP(hAPP(c_List_Olist_OCons(_1749932), _1749934), _1749940)), hAPP(hAPP(c_List_Olist_OCons(_1749932), _1749936), _1749942))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1749932), c_List_Olistrel1(_1749932, _1749938)))))], (10682 ^ _777864) ^ [_955835, _955837, _955839] : [class_Orderings_Oorder(_955835), 10685 ^ _777864 : [(10686 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955835), _955837), _955839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955835), _955837), _955839))), -(_955837 = _955839)], (10696 ^ _777864) ^ [] : [10697 ^ _777864 : [(10700 ^ _777864) ^ [] : [_955837 = _955839], (10698 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955835), _955837), _955839))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955835), _955837), _955839)))]]], (25795 ^ _777864) ^ [_1230571, _1230573, _1230575, _1230577] : [class_Rings_Ocomm__ring(_1230571), class_Rings_Odvd(_1230571), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230571), _1230573), _1230575)), 25806 ^ _777864 : [(25813 ^ _777864) ^ [_1230997, _1230999] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230571), _1230573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1230571), _1230999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230571), _1230997), _1230575))), _1230577))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230571), _1230573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230571), _1230999), _1230577))))], (25807 ^ _777864) ^ [_1230824, _1230826] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230571), _1230573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230571), _1230826), _1230577))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1230571), _1230573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1230571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1230571), _1230826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230571), _1230824), _1230575))), _1230577))))]]], (27314 ^ _777864) ^ [_1263416, _1263418, _1263420, _1263422] : [-(c_Nitpick_Ofold__graph_H(_1263416, _1263418, _1263420, _1263422, c_Orderings_Obot__class_Obot(tc_fun(_1263416, tc_HOL_Obool)), _1263422))], (3676 ^ _777864) ^ [_833854, _833856, _833858, _833860] : [-(c_New__DSequence_Oneg__single(_833860, _833856) = c_New__DSequence_Oneg__single(_833858, _833854)), _833860 = _833858, _833856 = _833854], (15622 ^ _777864) ^ [_1044047, _1044049] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044047, _1044049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044047), _1044049)), _1044049)))], (46523 ^ _777864) ^ [_1702181, _1702183, _1702185, _1702187, _1702189] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702181), tc_List_Olist(_1702181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702181), tc_List_Olist(_1702181)), _1702183), _1702185)), c_List_Olistrel(_1702181, c_Transitive__Closure_Ortrancl(_1702181, _1702187)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702181), tc_List_Olist(_1702181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702181), tc_List_Olist(_1702181)), _1702185), _1702189)), c_List_Olistrel(_1702181, c_Transitive__Closure_Ortrancl(_1702181, _1702187)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702181), tc_List_Olist(_1702181))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702181), tc_List_Olist(_1702181)), _1702183), _1702189)), c_List_Olistrel(_1702181, c_Transitive__Closure_Ortrancl(_1702181, _1702187)))))], (38710 ^ _777864) ^ [_1506611, _1506613, _1506615, _1506617, _1506619] : [-(hAPP(c_Set_Ovimage(_1506611, _1506613, _1506615), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506613, tc_HOL_Obool)), _1506617), _1506619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1506611, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1506611, _1506613, _1506615), _1506617)), hAPP(c_Set_Ovimage(_1506611, _1506613, _1506615), _1506619)))], (50813 ^ _777864) ^ [_1802917, _1802919, _1802921, _1802923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802917), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802919)), c_List_OtakeWhile(_1802919, _1802921, _1802923)))), -(hAPP(hAPP(c_List_Onth(_1802919), c_List_OtakeWhile(_1802919, _1802921, _1802923)), _1802917) = hAPP(hAPP(c_List_Onth(_1802919), _1802923), _1802917))], (21946 ^ _777864) ^ [_1157477, _1157479, _1157481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1157477), _1157479)), -(c_Random_Ominus__shift(_1157481, _1157477, _1157479) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1157481), _1157477)), _1157479))], (35066 ^ _777864) ^ [_1429777, _1429779] : [-(hAPP(c_Set_Oimage(_1429777, _1429777, c_COMBI(_1429777)), _1429779) = _1429779)], (29964 ^ _777864) ^ [_1322681] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1322681) = c_Orderings_Oord__class_Omin(_1322681)), class_Lattices_Osemilattice__inf(_1322681), class_Orderings_Olinorder(_1322681)], (7158 ^ _777864) ^ [_895522, _895524, _895526, _895528, _895530] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_895522, _895524, _895526)), _895528), _895530)), 7163 ^ _777864 : [(7166 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895524), _895528), _895530)))], (7164 ^ _777864) ^ [] : [-(hBOOL(hAPP(_895522, _895528)))]], 7167 ^ _777864 : [(7170 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895526), _895528), _895530)))], (7168 ^ _777864) ^ [] : [hBOOL(hAPP(_895522, _895528))]]], (14169 ^ _777864) ^ [_1017625, _1017627, _1017629] : [-(_1017625 = 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), _1017625), _1017627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017625), _1017629)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017627), _1017629))], (48814 ^ _777864) ^ [_1759005, _1759007, _1759009, _1759011] : [-(hAPP(c_List_Orotate(_1759005, _1759007), hAPP(c_List_Orotate(_1759005, _1759009), _1759011)) = hAPP(c_List_Orotate(_1759005, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1759007), _1759009)), _1759011))], (19222 ^ _777864) ^ [_1108338] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1108338)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1108338)))], (7564 ^ _777864) ^ [_903314, _903316] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_903314, _903316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _903316)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41960 ^ _777864) ^ [_1591822, _1591824, _1591826, _1591828, _1591830] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1591822, _1591824, _1591826), _1591828), _1591830)), 41963 ^ _777864 : [(41966 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1591826, _1591830)))], (41964 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1591824, _1591828), _1591830)))]]], (13525 ^ _777864) ^ [_1005621, _1005623, _1005625, _1005627] : [class_Divides_Oring__div(_1005621), c_Divides_Odiv__class_Omod(_1005621, _1005623, _1005625) = c_Divides_Odiv__class_Omod(_1005621, _1005627, _1005625), -(c_Divides_Odiv__class_Omod(_1005621, hAPP(c_Groups_Ouminus__class_Ouminus(_1005621), _1005623), _1005625) = c_Divides_Odiv__class_Omod(_1005621, hAPP(c_Groups_Ouminus__class_Ouminus(_1005621), _1005627), _1005625))], (51181 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (4962 ^ _777864) ^ [_853779, _853781] : [_853781 = _853779, -(c_Orderings_Oord__class_Omax(_853781) = c_Orderings_Oord__class_Omax(_853779))], (41399 ^ _777864) ^ [_1578384, _1578386, _1578388, _1578390] : [hBOOL(hAPP(c_Predicate_ODomainP(_1578384, _1578386, _1578388), _1578390)), -(hBOOL(hAPP(hAPP(_1578388, _1578390), 41402 ^ [_1578384, _1578386, _1578388, _1578390])))], (10021 ^ _777864) ^ [_945383, _945385, _945387] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945383), _945385)), _945387) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945385), _945387)))], (48043 ^ _777864) ^ [_1740057, _1740059, _1740061, _1740063] : [hAPP(hAPP(c_List_Oappend(_1740057), _1740059), _1740061) = hAPP(hAPP(c_List_Oappend(_1740057), _1740063), _1740061), -(_1740059 = _1740063)], (50738 ^ _777864) ^ [_1801568, _1801570, _1801572] : [c_List_OtakeWhile(_1801568, _1801570, _1801572) = _1801572, 50741 ^ _777864 : [(50742 ^ _777864) ^ [_1801655] : [hBOOL(hAPP(hAPP(c_member(_1801568), _1801655), hAPP(c_List_Oset(_1801568), _1801572))), -(hBOOL(hAPP(_1801570, _1801655)))]]], (26879 ^ _777864) ^ [_1252381, _1252383, _1252385, _1252387] : [hBOOL(hAPP(hAPP(c_member(_1252381), _1252383), _1252385)), -(hBOOL(hAPP(hAPP(c_member(_1252381), _1252383), hAPP(hAPP(c_Set_Oinsert(_1252381), _1252387), _1252385))))], (50524 ^ _777864) ^ [_1795536, _1795538, _1795540] : [hAPP(c_List_Orev(_1795536), _1795538) = _1795540, -(_1795538 = hAPP(c_List_Orev(_1795536), _1795540))], (25445 ^ _777864) ^ [_1224064, _1224066] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1224066), _1224064))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224064), _1224066)))], (45309 ^ _777864) ^ [_1672150, _1672152, _1672154, _1672156, _1672158, _1672160, _1672162, _1672164] : [c_Finite__Set_Ofolding__image__simple__idem(_1672150, _1672152, _1672154, _1672156, _1672158, _1672160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672152), _1672162)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672152), _1672164)), -(hAPP(_1672160, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1672152, tc_HOL_Obool)), _1672162), _1672164)) = hAPP(hAPP(_1672154, hAPP(_1672160, _1672162)), hAPP(_1672160, _1672164)))], (36632 ^ _777864) ^ [_1461198, _1461200, _1461202, _1461204] : [class_Groups_Ocomm__monoid__add(_1461198), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461198), _1461200), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1461202)), hAPP(c_Nat_OSuc, _1461204))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461198), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1461198, tc_Nat_Onat), _1461200), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1461202), _1461204)))], (49588 ^ _777864) ^ [_1775805, _1775807, _1775809, _1775811] : [hBOOL(hAPP(hAPP(c_member(_1775805), _1775807), hAPP(c_List_Oset(_1775805), _1775809))), -(hBOOL(hAPP(_1775811, _1775807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775805)), hAPP(c_List_Ofilter(_1775805, _1775811), _1775809))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775805)), _1775809))))], (2130 ^ _777864) ^ [_809037, _809039, _809041, _809043] : [-(c_Divides_OnegDivAlg(_809043, _809039) = c_Divides_OnegDivAlg(_809041, _809037)), _809043 = _809041, _809039 = _809037], (46046 ^ _777864) ^ [_1689223, _1689225] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1689223, _1689225)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1689223, _1689225))], (19348 ^ _777864) ^ [_1110523] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1110523))), 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), _1110523), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (6605 ^ _777864) ^ [_886915, _886917] : [class_Groups_Ocomm__monoid__add(_886915), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886915), _886917), c_Groups_Ozero__class_Ozero(_886915)) = _886917)], (25101 ^ _777864) ^ [_1218387, _1218389, _1218391] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218387), _1218389)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218389), _1218391)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218387), _1218391)))], (49061 ^ _777864) ^ [_1764684, _1764686, _1764688] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1764684)), _1764686), c_Wellfounded_Oacc(tc_List_Olist(_1764684), c_List_Olistrel1(_1764684, _1764688)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1764684)), _1764686), c_List_Olists(_1764684, c_Wellfounded_Oacc(_1764684, _1764688)))))], (31207 ^ _777864) ^ [_1347937, _1347939, _1347941, _1347943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347937, _1347939)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347941, _1347943)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347941), _1347943)), 31210 ^ _777864 : [(31213 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347941), _1347937)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347939), _1347943)), 31220 ^ _777864 : [(31227 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347939), _1347943)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347943), _1347939)))], (31221 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347941), _1347937)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347937), _1347941)))]]], (31211 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347937), _1347939)))]]], (31311 ^ _777864) ^ [_1349661, _1349663, _1349665] : [class_Lattices_Olattice(_1349661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349661), _1349663)), 31318 ^ _777864 : [(31325 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349661, tc_HOL_Obool)), _1349663), hAPP(hAPP(c_Set_Oinsert(_1349661), _1349665), c_Orderings_Obot__class_Obot(tc_fun(_1349661, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349661, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1349661, hAPP(hAPP(c_Set_Oinsert(_1349661), _1349665), _1349663)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1349661), _1349665), c_Big__Operators_Olattice__class_OInf__fin(_1349661, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349661, tc_HOL_Obool)), _1349663), hAPP(hAPP(c_Set_Oinsert(_1349661), _1349665), c_Orderings_Obot__class_Obot(tc_fun(_1349661, tc_HOL_Obool)))))))], (31319 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349661, tc_HOL_Obool)), _1349663), hAPP(hAPP(c_Set_Oinsert(_1349661), _1349665), c_Orderings_Obot__class_Obot(tc_fun(_1349661, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349661, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1349661, hAPP(hAPP(c_Set_Oinsert(_1349661), _1349665), _1349663)) = _1349665)]]], (18532 ^ _777864) ^ [_1096518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096518), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1096518)), c_Int_OPls)))], (38524 ^ _777864) ^ [_1501267, _1501269, _1501271, _1501273, _1501275] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1501267)), hAPP(c_Set_Oimage(_1501269, tc_Option_Ooption(_1501267), _1501271), c_Orderings_Otop__class_Otop(tc_fun(_1501269, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1501267)), hAPP(c_Set_Oimage(_1501269, tc_Option_Ooption(_1501267), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1501269, tc_Option_Ooption(_1501267)), _1501271), _1501273), hAPP(c_Option_Ooption_OSome(_1501267), _1501275))), c_Orderings_Otop__class_Otop(tc_fun(_1501269, tc_HOL_Obool))))))], (33727 ^ _777864) ^ [_1399966, _1399968, _1399970, _1399972, _1399974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399966, tc_HOL_Obool)), _1399968), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399970, tc_fun(_1399966, tc_HOL_Obool)), _1399972), _1399974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399970, tc_fun(_1399966, tc_HOL_Obool)), _1399972), hAPP(hAPP(c_COMBB(tc_fun(_1399966, tc_HOL_Obool), tc_fun(_1399966, tc_HOL_Obool), _1399970), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399966, tc_HOL_Obool)), _1399968)), _1399974)))], (14764 ^ _777864) ^ [_1027919, _1027921, _1027923] : [-(hBOOL(hAPP(_1027919, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027921, _1027923)))), 14767 ^ _777864 : [(14770 ^ _777864) ^ [] : [hBOOL(hAPP(_1027919, _1027921))], (14768 ^ _777864) ^ [] : [-(_1027923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14771 ^ _777864 : [(14776 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14774 ^ [_1027919, _1027921, _1027923]), _1027923)))], (14778 ^ _777864) ^ [] : [-(_1027921 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027923), 14773 ^ [_1027919, _1027921, _1027923])), 14774 ^ [_1027919, _1027921, _1027923]))], (14780 ^ _777864) ^ [] : [hBOOL(hAPP(_1027919, 14774 ^ [_1027919, _1027921, _1027923]))], (14772 ^ _777864) ^ [] : [_1027923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (34421 ^ _777864) ^ [_1416400, _1416402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1416400), _1416402)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1416400, tc_HOL_Obool)), hAPP(c_Set_OPow(_1416400), _1416402)) = 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(_1416400), _1416402)))], (3702 ^ _777864) ^ [_834237, _834239, _834241, _834243] : [-(c_New__DSequence_Opos__single(_834243, _834239) = c_New__DSequence_Opos__single(_834241, _834237)), _834243 = _834241, _834239 = _834237], (48223 ^ _777864) ^ [_1743708, _1743710, _1743712, _1743714, _1743716, _1743718, _1743720] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1743708, _1743708)), hAPP(hAPP(c_Product__Type_OPair(_1743708, _1743708), _1743710), _1743712)), _1743714)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1743708), tc_List_Olist(_1743708))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743708), tc_List_Olist(_1743708)), hAPP(hAPP(c_List_Oappend(_1743708), _1743716), hAPP(hAPP(c_List_Olist_OCons(_1743708), _1743710), _1743718))), hAPP(hAPP(c_List_Oappend(_1743708), _1743716), hAPP(hAPP(c_List_Olist_OCons(_1743708), _1743712), _1743720)))), c_List_Olexord(_1743708, _1743714))))], (42746 ^ _777864) ^ [_1609202, _1609204, _1609206, _1609208] : [class_Lattices_Osemilattice__inf(_1609202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609202), _1609204)), hBOOL(hAPP(hAPP(c_member(_1609202), _1609206), _1609204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609202), hAPP(hAPP(c_Finite__Set_Ofold(_1609202, _1609202, c_Lattices_Osemilattice__inf__class_Oinf(_1609202)), _1609208), _1609204)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1609202), _1609206), _1609208))))], (47216 ^ _777864) ^ [_1720482, _1720484, _1720486, _1720488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1720482), tc_List_Olist(_1720482))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720482), tc_List_Olist(_1720482)), _1720484), _1720486)), c_List_Olex(_1720482, _1720488))), 47219 ^ _777864 : [(47222 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720482)), _1720484) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720482)), _1720486))], (47220 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1720482), tc_List_Olist(_1720482))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720482), tc_List_Olist(_1720482)), _1720484), _1720486)), c_List_Olexord(_1720482, _1720488))))]]], (44017 ^ _777864) ^ [_1640195, _1640197, _1640199, _1640201, _1640203] : [-(_1640195 = c_Orderings_Obot__class_Obot(tc_fun(_1640197, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640199, tc_HOL_Obool)), _1640201), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640197, tc_fun(_1640199, tc_HOL_Obool)), _1640195), _1640203)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640197, tc_fun(_1640199, tc_HOL_Obool)), _1640195), hAPP(hAPP(c_COMBB(tc_fun(_1640199, tc_HOL_Obool), tc_fun(_1640199, tc_HOL_Obool), _1640197), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640199, tc_HOL_Obool)), _1640201)), _1640203)))], (31899 ^ _777864) ^ [_1360948, _1360950, _1360952] : [class_Orderings_Olinorder(_1360948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360948), _1360950)), hBOOL(hAPP(hAPP(c_member(_1360948), _1360952), _1360950)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1360948), _1360952), c_Big__Operators_Olattice_OInf__fin(_1360948, c_Orderings_Oord__class_Omin(_1360948), _1360950)) = c_Big__Operators_Olattice_OInf__fin(_1360948, c_Orderings_Oord__class_Omin(_1360948), _1360950))], (526 ^ _777864) ^ [_785997, _785999, _786001, _786003, _786005, _786007, _786009, _786011] : [-(c_Equiv__Relations_Ocongruent(_786009, _786005, _786001, _785997)), c_Equiv__Relations_Ocongruent(_786011, _786007, _786003, _785999), _786011 = _786009, _786007 = _786005, _786003 = _786001, _785999 = _785997], (14270 ^ _777864) ^ [_1019136, _1019138] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019136, _1019138)), _1019138) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40440 ^ _777864) ^ [_1549284, _1549286, _1549288, _1549290] : [-(c_Fun_Ooverride__on(_1549284, _1549286, _1549288, _1549290, c_Orderings_Obot__class_Obot(tc_fun(_1549284, tc_HOL_Obool))) = _1549288)], (9062 ^ _777864) ^ [_928456, _928458, _928460] : [class_Rings_Ono__zero__divisors(_928456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928456), _928458), _928460) = c_Groups_Ozero__class_Ozero(_928456), -(_928458 = c_Groups_Ozero__class_Ozero(_928456)), -(_928460 = c_Groups_Ozero__class_Ozero(_928456))], (23221 ^ _777864) ^ [_1181461, _1181463, _1181465] : [class_Int_Onumber__ring(_1181461), 23224 ^ _777864 : [(23231 ^ _777864) ^ [] : [-(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), _1181463)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181461), hAPP(c_Int_Onumber__class_Onumber__of(_1181461), _1181465)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1181463))) = c_Groups_Oone__class_Oone(_1181461))], (23225 ^ _777864) ^ [] : [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), _1181463))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181461), hAPP(c_Int_Onumber__class_Onumber__of(_1181461), _1181465)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1181463))) = hAPP(hAPP(c_HOL_OLet(_1181461, _1181461), hAPP(hAPP(c_Power_Opower__class_Opower(_1181461), hAPP(c_Int_Onumber__class_Onumber__of(_1181461), _1181465)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181463))), hAPP(hAPP(c_COMBS(_1181461, _1181461, _1181461), hAPP(hAPP(c_COMBB(_1181461, tc_fun(_1181461, _1181461), _1181461), c_Groups_Otimes__class_Otimes(_1181461)), hAPP(c_Groups_Otimes__class_Otimes(_1181461), hAPP(c_Int_Onumber__class_Onumber__of(_1181461), _1181465)))), c_COMBI(_1181461))))]]], (32715 ^ _777864) ^ [_1377142, _1377144, _1377146, _1377148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1377142, _1377144)), c_Sum__Type_OPlus(_1377142, _1377144, _1377146, _1377148))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1377144), _1377148)))], (40733 ^ _777864) ^ [_1560672, _1560674, _1560676, _1560678, _1560680, _1560682, _1560684, _1560686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560672, _1560674)), hAPP(hAPP(c_Product__Type_OPair(_1560672, _1560674), _1560676), _1560678)), _1560680)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560674, _1560682)), hAPP(hAPP(c_Product__Type_OPair(_1560674, _1560682), _1560678), _1560684)), _1560686)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560672, _1560682)), hAPP(hAPP(c_Product__Type_OPair(_1560672, _1560682), _1560676), _1560684)), hAPP(hAPP(c_Relation_Orel__comp(_1560672, _1560674, _1560682), _1560680), _1560686))))], (41714 ^ _777864) ^ [_1585938, _1585940, _1585942] : [-(hAPP(c_Fun_Ocomp(_1585938, _1585938, _1585940, c_Fun_Oid(_1585938)), _1585942) = _1585942)], (46801 ^ _777864) ^ [_1710312, _1710314, _1710316] : [class_Groups_Omonoid__add(_1710312), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1710312), hAPP(hAPP(c_List_Olist_OCons(_1710312), _1710314), _1710316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1710312), _1710314), hAPP(c_List_Omonoid__add__class_Olistsum(_1710312), _1710316)))], (33456 ^ _777864) ^ [_1392946, _1392948, _1392950, _1392952] : [class_Orderings_Olinorder(_1392946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392946), _1392948), _1392950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392946), _1392950), _1392952)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392946, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392946, _1392948, _1392950)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1392946, _1392950, _1392952)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1392946, _1392948, _1392952))], (17260 ^ _777864) ^ [_1075527, _1075529, _1075531] : [class_Power_Opower(_1075527), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075527), _1075529), hAPP(c_Nat_OSuc, _1075531)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075527), _1075529), hAPP(hAPP(c_Power_Opower__class_Opower(_1075527), _1075529), _1075531)))], (14368 ^ _777864) ^ [_1020802, _1020804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020802)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020802), _1020804)), _1020802) = _1020804)], (7904 ^ _777864) ^ [_909484, _909486, _909488, _909490, _909492] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_909484, _909486), _909488, _909490, _909492), 7908 ^ _777864 : [(7911 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_909486, 7907 ^ [_909484, _909486, _909488, _909490, _909492], _909490, _909492))], (7909 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_909484, _909488, _909490, 7907 ^ [_909484, _909486, _909488, _909490, _909492]))]]], (6892 ^ _777864) ^ [_891204] : [_891204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891204), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (502 ^ _777864) ^ [_785679, _785681, _785683, _785685] : [-(c_Nitpick_Owf_H(_785683, _785679)), c_Nitpick_Owf_H(_785685, _785681), _785685 = _785683, _785681 = _785679], (19408 ^ _777864) ^ [_1111557, _1111559] : [class_Rings_Olinordered__idom(_1111557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111557), hAPP(hAPP(c_Power_Opower__class_Opower(_1111557), _1111559), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1111557)))], (19598 ^ _777864) ^ [_1115166, _1115168] : [-(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), _1115166)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1115168))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115166))) = 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), _1115168)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115166)))], (5966 ^ _777864) ^ [_875883, _875885] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_875883, _875885))))], (27344 ^ _777864) ^ [_1264173, _1264175] : [class_Int_Onumber__ring(_1264173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1264175)), -(hBOOL(hAPP(hAPP(c_member(_1264173), hAPP(c_Int_Onumber__class_Onumber__of(_1264173), _1264175)), c_Nat_Osemiring__1__class_ONats(_1264173))))], (12211 ^ _777864) ^ [_982268, _982270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982270)), 12218 ^ _777864 : [(12225 ^ _777864) ^ [] : [_982268 = _982270, -(hAPP(c_Int_Onat, _982268) = hAPP(c_Int_Onat, _982270))], (12219 ^ _777864) ^ [] : [hAPP(c_Int_Onat, _982268) = hAPP(c_Int_Onat, _982270), -(_982268 = _982270)]]], (1352 ^ _777864) ^ [_797532, _797534] : [-(class_Finite__Set_Ofinite(_797532)), _797534 = _797532, class_Finite__Set_Ofinite(_797534)], (18316 ^ _777864) ^ [_1092786, _1092788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092786), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092786)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092788)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092788))], (44508 ^ _777864) ^ [_1652957, _1652959, _1652961] : [44510 ^ _777864 : [(44511 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652957), 44509 ^ [_1652957, _1652959, _1652961]), _1652959)))], (44516 ^ _777864) ^ [] : [44509 ^ [_1652957, _1652959, _1652961] = 44512 ^ [_1652957, _1652959, _1652961]], (44520 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652957, _1652957)), hAPP(hAPP(c_Product__Type_OPair(_1652957, _1652957), 44512 ^ [_1652957, _1652959, _1652961]), 44509 ^ [_1652957, _1652959, _1652961])), _1652961))], (44518 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652957, _1652957)), hAPP(hAPP(c_Product__Type_OPair(_1652957, _1652957), 44509 ^ [_1652957, _1652959, _1652961]), 44512 ^ [_1652957, _1652959, _1652961])), _1652961))], (44514 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652957), 44512 ^ [_1652957, _1652959, _1652961]), _1652959)))]], -(c_Relation_Ototal__on(_1652957, _1652959, _1652961))], (47032 ^ _777864) ^ [_1716016, _1716018, _1716020, _1716022, _1716024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1716016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716018)), _1716020))), -(hAPP(hAPP(c_List_Onth(_1716022), hAPP(hAPP(c_List_Omap(_1716018, _1716022), _1716024), _1716020)), _1716016) = hAPP(_1716024, hAPP(hAPP(c_List_Onth(_1716018), _1716020), _1716016)))], (34531 ^ _777864) ^ [_1419138, _1419140, _1419142] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1419138), _1419140)), c_Fun_Oinj__on(_1419138, tc_fun(tc_fun(_1419138, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1419138, tc_fun(tc_prod(_1419138, _1419138), tc_HOL_Obool), tc_fun(tc_fun(_1419138, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419138, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1419138, _1419138), tc_HOL_Obool), tc_fun(tc_fun(_1419138, tc_HOL_Obool), tc_HOL_Obool)), _1419138), c_Equiv__Relations_Oquotient(_1419138)), hAPP(hAPP(c_COMBC(_1419138, tc_fun(_1419138, tc_HOL_Obool), tc_fun(_1419138, tc_HOL_Obool)), c_Set_Oinsert(_1419138)), c_Orderings_Obot__class_Obot(tc_fun(_1419138, tc_HOL_Obool))))), _1419142), _1419140), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1419138, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1419138), _1419140), _1419142)) = hAPP(c_Finite__Set_Ocard(_1419138), _1419140))], (42030 ^ _777864) ^ [_1593452, _1593454, _1593456, _1593458, _1593460, _1593462, _1593464, _1593466] : [c_Finite__Set_Ofolding__image(_1593452, _1593454, _1593456, _1593458, _1593460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593454), _1593462)), -(hAPP(hAPP(_1593460, hAPP(hAPP(c_COMBS(_1593454, _1593452, _1593452), hAPP(hAPP(c_COMBB(_1593452, tc_fun(_1593452, _1593452), _1593454), _1593456), _1593464)), _1593466)), _1593462) = hAPP(hAPP(_1593456, hAPP(hAPP(_1593460, _1593464), _1593462)), hAPP(hAPP(_1593460, _1593466), _1593462)))], (23285 ^ _777864) ^ [_1183504, _1183506, _1183508, _1183510, _1183512, _1183514] : [_1183504 = _1183506, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183508, _1183510, _1183512), _1183514), _1183504) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183508, _1183510, _1183512), _1183514), _1183506))], (6799 ^ _777864) ^ [_889768] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _889768)], (42334 ^ _777864) ^ [_1600209, _1600211] : [42336 ^ _777864 : [(42339 ^ _777864) ^ [] : [42335 ^ [_1600209, _1600211] = c_Orderings_Obot__class_Obot(tc_fun(_1600209, tc_HOL_Obool))], (42337 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600209, tc_HOL_Obool)), 42335 ^ [_1600209, _1600211]), hAPP(c_Relation_OImage(_1600209, _1600209, _1600211), 42335 ^ [_1600209, _1600211]))))]], -(c_Wellfounded_Owf(_1600209, _1600211))], (5278 ^ _777864) ^ [_858627, _858629, _858631, _858633, _858635, _858637, _858639, _858641] : [-(c_Fun_Ocomp(_858641, _858637, _858633, _858629) = c_Fun_Ocomp(_858639, _858635, _858631, _858627)), _858641 = _858639, _858637 = _858635, _858633 = _858631, _858629 = _858627], (48542 ^ _777864) ^ [_1753046, _1753048] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753046)), hAPP(c_List_Orotate1(_1753046), _1753048)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753046)), _1753048))], (36764 ^ _777864) ^ [_1464414, _1464416, _1464418, _1464420, _1464422] : [class_Groups_Ocomm__monoid__add(_1464414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464416), _1464418)), -(hBOOL(hAPP(hAPP(c_member(_1464416), _1464420), _1464418))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464416, _1464414), _1464422), hAPP(hAPP(c_Set_Oinsert(_1464416), _1464420), _1464418)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464414), hAPP(_1464422, _1464420)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464416, _1464414), _1464422), _1464418)))], (14844 ^ _777864) ^ [_1029317, _1029319] : [-(_1029317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14847 ^ _777864 : [(14854 ^ _777864) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029319, _1029317) = 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), _1029319)), _1029317) = 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), _1029319), _1029317))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14848 ^ _777864) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1029319, _1029317) = 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), _1029319)), _1029317) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029319), _1029317)))]]], (27810 ^ _777864) ^ [_1273240, _1273242] : [class_Lattices_Obounded__lattice__bot(_1273240), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273240), _1273242), c_Orderings_Obot__class_Obot(_1273240)) = _1273242)], (14982 ^ _777864) ^ [_1031951, _1031953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031951), _1031953)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031953)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031951)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031953), _1031951)))], (27388 ^ _777864) ^ [_1264937] : [class_Rings_Osemiring__1(_1264937), -(hBOOL(hAPP(hAPP(c_member(_1264937), c_Groups_Oone__class_Oone(_1264937)), c_Nat_Osemiring__1__class_ONats(_1264937))))], (24357 ^ _777864) ^ [_1204285, _1204287, _1204289, _1204291, _1204293, _1204295] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1204285, _1204287, _1204289), _1204291), hAPP(hAPP(c_Product__Type_OPair(_1204285, _1204287), _1204293), _1204295)) = hAPP(hAPP(_1204291, _1204293), _1204295))], (10202 ^ _777864) ^ [_948136, _948138, _948140, _948142] : [class_Orderings_Oord(_948136), _948138 = _948140, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948136), _948140), _948142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948136), _948138), _948142)))], (33815 ^ _777864) ^ [_1402519, _1402521, _1402523, _1402525, _1402527] : [-(_1402519 = c_Orderings_Obot__class_Obot(tc_fun(_1402521, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402523, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402521, tc_fun(_1402523, tc_HOL_Obool)), _1402519), _1402525)), _1402527) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402521, tc_fun(_1402523, tc_HOL_Obool)), _1402519), hAPP(hAPP(c_COMBC(_1402521, tc_fun(_1402523, tc_HOL_Obool), tc_fun(_1402523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402523, tc_HOL_Obool), tc_fun(tc_fun(_1402523, tc_HOL_Obool), tc_fun(_1402523, tc_HOL_Obool)), _1402521), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402523, tc_HOL_Obool))), _1402525)), _1402527)))], (51453 ^ _777864) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (40050 ^ _777864) ^ [_1537816] : [class_Lattices_Osemilattice__inf(_1537816), -(c_Finite__Set_Ofun__left__comm__idem(_1537816, _1537816, c_Lattices_Osemilattice__inf__class_Oinf(_1537816)))], (46078 ^ _777864) ^ [_1689748, _1689750, _1689752, _1689754] : [-(hBOOL(hAPP(hAPP(c_member(_1689748), _1689750), hAPP(c_List_Oset(_1689748), _1689752)))), hBOOL(hAPP(hAPP(c_member(_1689748), _1689750), hAPP(c_List_Oset(_1689748), c_List_Oremove1(_1689748, _1689754, _1689752))))], (45661 ^ _777864) ^ [_1680132, _1680134, _1680136, _1680138, _1680140, _1680142, _1680144] : [-(c_Map_Omap__comp(_1680132, _1680134, _1680136, _1680138, _1680140, _1680142) = hAPP(c_Option_Ooption_OSome(_1680134), _1680144)), 45662 ^ _777864 : [(45663 ^ _777864) ^ [_1680210] : [hAPP(_1680140, _1680142) = hAPP(c_Option_Ooption_OSome(_1680132), _1680210), hAPP(_1680138, _1680210) = hAPP(c_Option_Ooption_OSome(_1680134), _1680144)]]], (19914 ^ _777864) ^ [_1121064, _1121066, _1121068] : [class_Fields_Olinordered__field__inverse__zero(_1121064), 19917 ^ _777864 : [(19932 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121064), _1121066), _1121068)), c_Groups_Ozero__class_Ozero(_1121064)))), 19933 ^ _777864 : [(19940 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), _1121066), c_Groups_Ozero__class_Ozero(_1121064))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), c_Groups_Ozero__class_Ozero(_1121064)), _1121068))], (19934 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), c_Groups_Ozero__class_Ozero(_1121064)), _1121066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), _1121068), c_Groups_Ozero__class_Ozero(_1121064)))]]], (19918 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121064), _1121066), _1121068)), c_Groups_Ozero__class_Ozero(_1121064))), 19923 ^ _777864 : [(19926 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), _1121068), c_Groups_Ozero__class_Ozero(_1121064))))], (19924 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), c_Groups_Ozero__class_Ozero(_1121064)), _1121066)))]], 19927 ^ _777864 : [(19930 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), c_Groups_Ozero__class_Ozero(_1121064)), _1121068)))], (19928 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1121064), _1121066), c_Groups_Ozero__class_Ozero(_1121064))))]]]]], (5968 ^ _777864) ^ [_875913, _875915] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_875913, _875915))))], (454 ^ _777864) ^ [_784833, _784835, _784837, _784839, _784841, _784843, _784845, _784847, _784849, _784851, _784853, _784855, _784857, _784859] : [-(c_Predicate_Opred__comp(_784857, _784853, _784849, _784845, _784841, _784837, _784833)), c_Predicate_Opred__comp(_784859, _784855, _784851, _784847, _784843, _784839, _784835), _784859 = _784857, _784855 = _784853, _784851 = _784849, _784847 = _784845, _784843 = _784841, _784839 = _784837, _784835 = _784833], (19822 ^ _777864) ^ [_1119546, _1119548, _1119550, _1119552] : [class_Fields_Ofield__inverse__zero(_1119546), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1119546), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119546), _1119548), _1119550)), _1119552) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119546), hAPP(hAPP(c_Power_Opower__class_Opower(_1119546), _1119548), _1119552)), hAPP(hAPP(c_Power_Opower__class_Opower(_1119546), _1119550), _1119552)))], (38068 ^ _777864) ^ [_1492392] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1492392), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1492392)), c_Option_Ooption_ONone(_1492392)), hAPP(c_Set_Oimage(_1492392, tc_Option_Ooption(_1492392), c_Option_Ooption_OSome(_1492392)), c_Orderings_Otop__class_Otop(tc_fun(_1492392, tc_HOL_Obool)))))], (1622 ^ _777864) ^ [_800907, _800909] : [-(class_Orderings_Opreorder(_800907)), _800909 = _800907, class_Orderings_Opreorder(_800909)], (40201 ^ _777864) ^ [_1541010, _1541012] : [-(hBOOL(hAPP(_1541012, 40202 ^ [_1541010, _1541012]))), -(hAPP(c_Set_OCollect(_1541010), _1541012) = c_Orderings_Obot__class_Obot(tc_fun(_1541010, tc_HOL_Obool)))], (51383 ^ _777864) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (2000 ^ _777864) ^ [_807060, _807062] : [_807062 = _807060, -(c_HOL_Obool_Obool__size(_807062) = c_HOL_Obool_Obool__size(_807060))], (48067 ^ _777864) ^ [_1740551, _1740553, _1740555] : [class_Groups_Omonoid__add(_1740551), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1740551), hAPP(hAPP(c_List_Oappend(_1740551), _1740553), _1740555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1740551), hAPP(c_List_Omonoid__add__class_Olistsum(_1740551), _1740553)), hAPP(c_List_Omonoid__add__class_Olistsum(_1740551), _1740555)))], (38828 ^ _777864) ^ [_1509456, _1509458, _1509460, _1509462] : [hBOOL(hAPP(hAPP(c_member(_1509456), _1509458), _1509460)), -(hAPP(c_Set_Ovimage(_1509462, _1509456, hAPP(c_COMBK(_1509456, _1509462), _1509458)), _1509460) = c_Orderings_Otop__class_Otop(tc_fun(_1509462, tc_HOL_Obool)))], (45114 ^ _777864) ^ [_1666756, _1666758, _1666760, _1666762, _1666764] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1666756, _1666756)), hAPP(hAPP(c_Product__Type_OPair(_1666756, _1666756), _1666758), _1666760)), c_Transitive__Closure_Ortrancl(_1666756, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1666756, _1666756), tc_HOL_Obool)), _1666762), _1666764)))), 45120 ^ _777864 : [(45126 ^ _777864) ^ [] : [45119 ^ [_1666756, _1666758, _1666760, _1666762, _1666764] = 45122 ^ [_1666756, _1666758, _1666760, _1666762, _1666764]], (45124 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666756, _1666756)), hAPP(hAPP(c_Product__Type_OPair(_1666756, _1666756), 45119 ^ [_1666756, _1666758, _1666760, _1666762, _1666764]), 45122 ^ [_1666756, _1666758, _1666760, _1666762, _1666764])), _1666764)))], (45121 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666756, _1666756)), hAPP(hAPP(c_Product__Type_OPair(_1666756, _1666756), _1666758), 45119 ^ [_1666756, _1666758, _1666760, _1666762, _1666764])), c_Transitive__Closure_Ortrancl(_1666756, _1666762))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666756, _1666756)), hAPP(hAPP(c_Product__Type_OPair(_1666756, _1666756), _1666758), _1666760)), c_Transitive__Closure_Ortrancl(_1666756, _1666762))))], (30120 ^ _777864) ^ [_1325899, _1325901, _1325903] : [class_Lattices_Oboolean__algebra(_1325899), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1325899), _1325901), _1325903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325899), _1325901), hAPP(c_Groups_Ouminus__class_Ouminus(_1325899), _1325903)))], (51355 ^ _777864) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (51275 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (34986 ^ _777864) ^ [_1427884, _1427886, _1427888, _1427890, _1427892] : [-(c_Fun_Oinj__on(_1427884, _1427886, _1427888, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427884, tc_HOL_Obool)), _1427890), _1427892))), c_Fun_Oinj__on(_1427884, _1427886, _1427888, _1427890), c_Fun_Oinj__on(_1427884, _1427886, _1427888, _1427892), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427886, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427884, _1427886, _1427888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427884, tc_HOL_Obool)), _1427890), _1427892))), hAPP(c_Set_Oimage(_1427884, _1427886, _1427888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427884, tc_HOL_Obool)), _1427892), _1427890))) = c_Orderings_Obot__class_Obot(tc_fun(_1427886, tc_HOL_Obool))], (51487 ^ _777864) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (32331 ^ _777864) ^ [_1369050, _1369052] : [32332 ^ _777864 : [(32335 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369050), _1369052)))], (32333 ^ _777864) ^ [] : [_1369052 = c_Orderings_Obot__class_Obot(tc_fun(_1369050, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1369050), _1369052) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40284 ^ _777864) ^ [_1542962, _1542964, _1542966, _1542968] : [-(hAPP(c_Set_Ovimage(_1542962, _1542964, _1542966), _1542968) = hAPP(c_Set_OCollect(_1542962), hAPP(hAPP(c_COMBC(_1542962, tc_fun(_1542964, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1542964, tc_fun(tc_fun(_1542964, tc_HOL_Obool), tc_HOL_Obool), _1542962), c_member(_1542964)), _1542966)), _1542968)))], (47044 ^ _777864) ^ [_1716300, _1716302, _1716304, _1716306] : [-(hAPP(hAPP(c_List_Onth(_1716300), hAPP(hAPP(c_List_Olist_OCons(_1716300), _1716302), _1716304)), _1716306) = c_Nat_Onat_Onat__case(_1716300, _1716302, hAPP(c_List_Onth(_1716300), _1716304), _1716306))], (36528 ^ _777864) ^ [_1458356, _1458358, _1458360, _1458362] : [class_Groups_Ocomm__monoid__add(_1458356), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1458358), _1458360))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458358, _1458356), _1458362), _1458360) = c_Groups_Ozero__class_Ozero(_1458356))], (48672 ^ _777864) ^ [_1756260, _1756262, _1756264, _1756266] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1756260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1756262), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1756260)), hAPP(hAPP(c_List_Olist_OCons(_1756262), _1756264), _1756266)) = hAPP(hAPP(c_List_Olist_OCons(_1756262), _1756264), _1756266))], (46699 ^ _777864) ^ [_1706946, _1706948, _1706950, _1706952] : [-(c_Map_Omap__of(_1706946, _1706948, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1706946, _1706948)), _1706950), _1706952)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1706946, tc_Option_Ooption(_1706948)), c_Map_Omap__of(_1706946, _1706948, _1706952)), hAPP(c_Product__Type_Ofst(_1706946, _1706948), _1706950)), hAPP(c_Option_Ooption_OSome(_1706948), hAPP(c_Product__Type_Osnd(_1706946, _1706948), _1706950))))], (28460 ^ _777864) ^ [_1289517, _1289519, _1289521, _1289523, _1289525] : [-(hAPP(c_Set_Oimage(_1289517, _1289519, _1289521), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289517, tc_HOL_Obool)), _1289523), _1289525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289519, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1289517, _1289519, _1289521), _1289523)), hAPP(c_Set_Oimage(_1289517, _1289519, _1289521), _1289525)))], (15096 ^ _777864) ^ [_1033934, _1033936, _1033938, _1033940] : [class_Divides_Oring__div(_1033934), -(c_Divides_Odiv__class_Omod(_1033934, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033934), _1033936), _1033938), _1033940) = c_Divides_Odiv__class_Omod(_1033934, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033934), c_Divides_Odiv__class_Omod(_1033934, _1033936, _1033940)), _1033938), _1033940))], (3938 ^ _777864) ^ [_837837, _837839, _837841, _837843, _837845, _837847] : [-(c_Smallcheck_Ofull__small_H(_837847, _837843, _837839) = c_Smallcheck_Ofull__small_H(_837845, _837841, _837837)), _837847 = _837845, _837843 = _837841, _837839 = _837837], (10380 ^ _777864) ^ [_951123, _951125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951123), _951125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _951123)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _951125))))], (18344 ^ _777864) ^ [_1093290, _1093292] : [class_Int_Onumber__ring(_1093290), -(hAPP(c_Int_Onumber__class_Onumber__of(_1093290), c_Int_Opred(_1093292)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093290), hAPP(c_Groups_Ouminus__class_Ouminus(_1093290), c_Groups_Oone__class_Oone(_1093290))), hAPP(c_Int_Onumber__class_Onumber__of(_1093290), _1093292)))], (21108 ^ _777864) ^ [] : [-(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))], (40134 ^ _777864) ^ [_1539603, _1539605, _1539607] : [hBOOL(hAPP(_1539607, _1539605)), -(hBOOL(hAPP(hAPP(c_member(_1539603), _1539605), hAPP(c_Set_OCollect(_1539603), _1539607))))], (39897 ^ _777864) ^ [_1534693, _1534695, _1534697] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534693), _1534695)), 39903 ^ _777864 : [(39906 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1534697, 39902 ^ [_1534693, _1534695, _1534697])))], (39904 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534693), 39902 ^ [_1534693, _1534695, _1534697]), _1534695)))]], -(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(_1534693, tc_Nat_Onat), _1534697), _1534695))))], (9542 ^ _777864) ^ [_937252, _937254, _937256, _937258] : [class_Rings_Olinordered__ring__strict(_937252), 9545 ^ _777864 : [(9560 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937252), _937254), _937256)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937252), _937258), _937256)))), 9561 ^ _777864 : [(9568 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937256), c_Groups_Ozero__class_Ozero(_937252))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937258), _937254))], (9562 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), c_Groups_Ozero__class_Ozero(_937252)), _937256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937254), _937258))]]], (9546 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937252), _937254), _937256)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937252), _937258), _937256))), 9551 ^ _777864 : [(9554 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937254), _937258)))], (9552 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), c_Groups_Ozero__class_Ozero(_937252)), _937256)))]], 9555 ^ _777864 : [(9558 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937258), _937254)))], (9556 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937252), _937256), c_Groups_Ozero__class_Ozero(_937252))))]]]]], (2446 ^ _777864) ^ [_813993, _813995, _813997, _813999, _814001, _814003] : [-(c_Nitpick_Otimes__frac(_814003, _813999, _813995) = c_Nitpick_Otimes__frac(_814001, _813997, _813993)), _814003 = _814001, _813999 = _813997, _813995 = _813993], (47194 ^ _777864) ^ [_1719843, _1719845] : [-(hAPP(c_List_Oset(_1719843), _1719845) = hAPP(c_Set_OCollect(_1719843), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1719843), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1719843, 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)), _1719843), 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)), _1719843), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1719843, tc_fun(tc_Nat_Onat, _1719843), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719843, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1719843), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1719843), c_COMBB(_1719843, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1719843), _1719845))))), 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(_1719843)), _1719845))))))], (47440 ^ _777864) ^ [_1726206, _1726208, _1726210, _1726212, _1726214, _1726216] : [-(hAPP(hAPP(c_List_Omap(_1726206, _1726208), _1726210), hAPP(hAPP(c_List_Olist__update(_1726206, _1726212), _1726214), _1726216)) = hAPP(hAPP(c_List_Olist__update(_1726208, hAPP(hAPP(c_List_Omap(_1726206, _1726208), _1726210), _1726212)), _1726214), hAPP(_1726210, _1726216)))], (49876 ^ _777864) ^ [_1782529, _1782531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1782529), _1782531)), -(c_List_Oupt(_1782529, hAPP(c_Nat_OSuc, _1782531)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1782529, _1782531)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1782531), c_List_Olist_ONil(tc_Nat_Onat))))], (254 ^ _777864) ^ [_781595, _781597, _781599, _781601, _781603, _781605, _781607, _781609, _781611, _781613, _781615, _781617] : [-(c_Equiv__Relations_Ocongruent2(_781615, _781611, _781607, _781603, _781599, _781595)), c_Equiv__Relations_Ocongruent2(_781617, _781613, _781609, _781605, _781601, _781597), _781617 = _781615, _781613 = _781611, _781609 = _781607, _781605 = _781603, _781601 = _781599, _781597 = _781595], (46905 ^ _777864) ^ [_1713071, _1713073, _1713075, _1713077] : [class_Groups_Ocomm__monoid__add(_1713071), 46908 ^ _777864 : [(46915 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1713073), _1713075))), -(c_Nitpick_Osetsum_H(_1713073, _1713071, _1713077, _1713075) = c_Groups_Ozero__class_Ozero(_1713071))], (46909 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1713073), _1713075)), -(c_Nitpick_Osetsum_H(_1713073, _1713071, _1713077, _1713075) = hAPP(c_List_Omonoid__add__class_Olistsum(_1713071), hAPP(hAPP(c_List_Omap(_1713073, _1713071), _1713077), c_Hilbert__Choice_OEps(tc_List_Olist(_1713073), hAPP(hAPP(c_COMBS(tc_List_Olist(_1713073), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1713073)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713073), tc_fun(_1713073, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1713073, tc_HOL_Obool), tc_fun(tc_fun(_1713073, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1713073)), c_fequal), c_List_Oset(_1713073))), _1713075))), c_List_Odistinct(_1713073))))))]]], (18454 ^ _777864) ^ [_1095267, _1095269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095267), _1095269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1095267)), c_Int_OBit1(_1095269))))], (19262 ^ _777864) ^ [_1109113, _1109115] : [class_Rings_Oring__1__no__zero__divisors(_1109113), 19265 ^ _777864 : [(19272 ^ _777864) ^ [] : [_1109115 = c_Groups_Ozero__class_Ozero(_1109113), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109113), _1109115), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1109113))], (19266 ^ _777864) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1109113), _1109115), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1109113), -(_1109115 = c_Groups_Ozero__class_Ozero(_1109113))]]], (1532 ^ _777864) ^ [_799782, _799784] : [-(class_Rings_Oordered__semiring(_799782)), _799784 = _799782, class_Rings_Oordered__semiring(_799784)], (37171 ^ _777864) ^ [_1474179, _1474181, _1474183] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474179), _1474181)), 37174 ^ _777864 : [(37175 ^ _777864) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474179, tc_Nat_Onat), _1474183), _1474181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 37178 ^ _777864 : [(37179 ^ _777864) ^ [_1474341] : [hBOOL(hAPP(hAPP(c_member(_1474179), _1474341), _1474181)), -(hAPP(_1474183, _1474341) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37185 ^ _777864) ^ [] : [37187 ^ _777864 : [(37190 ^ _777864) ^ [] : [hAPP(_1474183, 37186 ^ [_1474179, _1474181, _1474183]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37188 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474179), 37186 ^ [_1474179, _1474181, _1474183]), _1474181)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474179, tc_Nat_Onat), _1474183), _1474181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49115 ^ _777864) ^ [_1765878, _1765880, _1765882, _1765884] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765878)), hAPP(hAPP(c_List_Olist_OCons(_1765878), _1765880), _1765882)), c_List_Olists(_1765878, _1765884)))), hBOOL(hAPP(hAPP(c_member(_1765878), _1765880), _1765884)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765878)), _1765882), c_List_Olists(_1765878, _1765884)))], (1422 ^ _777864) ^ [_798407, _798409] : [-(class_Groups_Oordered__ab__semigroup__add(_798407)), _798409 = _798407, class_Groups_Oordered__ab__semigroup__add(_798409)], (38518 ^ _777864) ^ [_1501146, _1501148, _1501150, _1501152] : [_1501150 = _1501152, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1501146, _1501148, hAPP(hAPP(c_Set_Oinsert(_1501146), _1501150), c_Orderings_Obot__class_Obot(tc_fun(_1501146, tc_HOL_Obool)))), _1501152)))], (23081 ^ _777864) ^ [_1178429, _1178431] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178429), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1178431))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1178429), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1178431))), 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))))], (43034 ^ _777864) ^ [_1614833, _1614835, _1614837, _1614839, _1614841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614833, _1614833)), hAPP(hAPP(c_Product__Type_OPair(_1614833, _1614833), _1614835), _1614837)), c_Transitive__Closure_Otrancl(_1614833, _1614839))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614833, _1614833)), hAPP(hAPP(c_Product__Type_OPair(_1614833, _1614833), _1614837), _1614841)), c_Transitive__Closure_Otrancl(_1614833, _1614839))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614833, _1614833)), hAPP(hAPP(c_Product__Type_OPair(_1614833, _1614833), _1614835), _1614841)), c_Transitive__Closure_Otrancl(_1614833, _1614839))))], (3748 ^ _777864) ^ [_834918, _834920, _834922, _834924, _834926, _834928] : [-(c_Finite__Set_Ofold__image(_834928, _834924, _834920) = c_Finite__Set_Ofold__image(_834926, _834922, _834918)), _834928 = _834926, _834924 = _834922, _834920 = _834918], (35956 ^ _777864) ^ [_1446828, _1446830, _1446832, _1446834] : [class_Orderings_Olinorder(_1446828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446828), _1446830), _1446832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446828), _1446832), _1446834)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446828, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1446828, _1446830, _1446832)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446828, _1446832, _1446834)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446828, _1446830), _1446834))], (43761 ^ _777864) ^ [_1632483, _1632485, _1632487, _1632489] : [c_Orderings_Otop__class_Otop(tc_fun(_1632483, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632485, tc_fun(_1632483, tc_HOL_Obool)), _1632487), _1632489), 43764 ^ _777864 : [(43765 ^ _777864) ^ [_1632599] : [hBOOL(hAPP(hAPP(c_member(_1632485), _1632599), _1632487)), -(hAPP(_1632489, _1632599) = c_Orderings_Otop__class_Otop(tc_fun(_1632483, tc_HOL_Obool)))]]], (24445 ^ _777864) ^ [_1206080, _1206082, _1206084] : [-(c_Nitpick_Oof__frac(_1206082, _1206080, _1206084) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206080), hAPP(c_Int_Oring__1__class_Oof__int(_1206080), hAPP(c_Nitpick_Onum(_1206082), _1206084))), hAPP(c_Int_Oring__1__class_Oof__int(_1206080), hAPP(c_Nitpick_Odenom(_1206082), _1206084)))), class_Rings_Oinverse(_1206080), class_Rings_Oring__1(_1206080)], (42343 ^ _777864) ^ [_1600406, _1600408, _1600410, _1600412, _1600414, _1600416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600406, tc_HOL_Obool)), _1600408), _1600410)), 42349 ^ _777864 : [(42352 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600412, tc_HOL_Obool)), hAPP(_1600414, 42348 ^ [_1600406, _1600408, _1600410, _1600412, _1600414, _1600416])), hAPP(_1600416, 42348 ^ [_1600406, _1600408, _1600410, _1600412, _1600414, _1600416])))], (42350 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600406), 42348 ^ [_1600406, _1600408, _1600410, _1600412, _1600414, _1600416]), _1600408)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1600406, _1600412), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1600406, _1600412), _1600408), _1600414)), hAPP(hAPP(c_Product__Type_OSigma(_1600406, _1600412), _1600410), _1600416))))], (51177 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (43698 ^ _777864) ^ [_1630151, _1630153, _1630155, _1630157] : [-(hAPP(c_Relation_Oconverse(_1630151, _1630153), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630151, _1630153), tc_HOL_Obool)), _1630155), _1630157)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630153, _1630151), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1630151, _1630153), _1630155)), hAPP(c_Relation_Oconverse(_1630151, _1630153), _1630157)))], (3062 ^ _777864) ^ [_824001, _824003, _824005, _824007, _824009, _824011, _824013, _824015] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_824015, _824011, _824007, _824003) = c_SetInterval_Oord_OgreaterThanLessThan(_824013, _824009, _824005, _824001)), _824015 = _824013, _824011 = _824009, _824007 = _824005, _824003 = _824001], (27674 ^ _777864) ^ [_1270807, _1270809, _1270811, _1270813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270807), _1270809)), -(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), _1270807), _1270811)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1270809), _1270813))), c_FunDef_Opair__leq)))], (40116 ^ _777864) ^ [_1539051] : [-(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)), _1539051)))))], (49580 ^ _777864) ^ [_1775524, _1775526, _1775528, _1775530, _1775532] : [-(hAPP(c_List_Ofilter(_1775524, _1775526), hAPP(hAPP(c_List_Omap(_1775528, _1775524), _1775530), _1775532)) = hAPP(hAPP(c_List_Omap(_1775528, _1775524), _1775530), hAPP(c_List_Ofilter(_1775528, hAPP(c_Fun_Ocomp(_1775524, tc_HOL_Obool, _1775528, _1775526), _1775530)), _1775532)))], (43545 ^ _777864) ^ [_1626733, _1626735, _1626737, _1626739, _1626741, _1626743] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626733, tc_fun(_1626735, tc_HOL_Obool)), _1626737), _1626739), _1626741)), hBOOL(hAPP(hAPP(c_member(_1626733), _1626743), _1626737)), -(hBOOL(hAPP(hAPP(_1626739, _1626743), _1626741)))], (27360 ^ _777864) ^ [_1264427, _1264429, _1264431] : [class_Rings_Osemiring__1(_1264427), hBOOL(hAPP(hAPP(c_member(_1264427), _1264429), c_Nat_Osemiring__1__class_ONats(_1264427))), hBOOL(hAPP(hAPP(c_member(_1264427), _1264431), c_Nat_Osemiring__1__class_ONats(_1264427))), -(hBOOL(hAPP(hAPP(c_member(_1264427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264427), _1264429), _1264431)), c_Nat_Osemiring__1__class_ONats(_1264427))))], (34051 ^ _777864) ^ [_1408434, _1408436, _1408438, _1408440, _1408442] : [class_Groups_Ocomm__monoid__mult(_1408434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408436), _1408438)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408436), _1408440)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408436, tc_HOL_Obool)), _1408438), _1408440) = c_Orderings_Obot__class_Obot(tc_fun(_1408436, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1408434, _1408436, c_Groups_Otimes__class_Otimes(_1408434)), _1408442), c_Groups_Oone__class_Oone(_1408434)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408436, tc_HOL_Obool)), _1408438), _1408440)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408434), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1408434, _1408436, c_Groups_Otimes__class_Otimes(_1408434)), _1408442), c_Groups_Oone__class_Oone(_1408434)), _1408438)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1408434, _1408436, c_Groups_Otimes__class_Otimes(_1408434)), _1408442), c_Groups_Oone__class_Oone(_1408434)), _1408440)))], (35312 ^ _777864) ^ [_1434505, _1434507, _1434509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434505)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1434507), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1434509)), 35319 ^ _777864 : [(35320 ^ _777864) ^ [_1434713] : [35322 ^ _777864 : [(35328 ^ _777864) ^ [] : [-(_1434713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35324 ^ [_1434505, _1434507, _1434509, _1434713]), 35321 ^ [_1434505, _1434507, _1434509, _1434713]))], (35326 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35324 ^ [_1434505, _1434507, _1434509, _1434713]), _1434509)))], (35323 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35321 ^ [_1434505, _1434507, _1434509, _1434713]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1434505))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434507), _1434713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434507), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1434713), _1434505))))]]], (41942 ^ _777864) ^ [] : [-(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))], (50530 ^ _777864) ^ [_1795631, _1795633, _1795635] : [_1795633 = hAPP(c_List_Orev(_1795631), _1795635), -(hAPP(c_List_Orev(_1795631), _1795633) = _1795635)], (12276 ^ _777864) ^ [_983337, _983339, _983341] : [class_Groups_Oordered__comm__monoid__add(_983337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983337), c_Groups_Ozero__class_Ozero(_983337)), _983339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983337), c_Groups_Ozero__class_Ozero(_983337)), _983341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983337), c_Groups_Ozero__class_Ozero(_983337)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983337), _983339), _983341))))], (38406 ^ _777864) ^ [_1498679, _1498681, _1498683, _1498685, _1498687] : [c_Fun_Oinj__on(_1498679, _1498681, _1498683, c_Orderings_Otop__class_Otop(tc_fun(_1498679, tc_HOL_Obool))), 38409 ^ _777864 : [(38416 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1498679), _1498685), _1498687)), -(hBOOL(hAPP(hAPP(c_member(_1498681), hAPP(_1498683, _1498685)), hAPP(c_Set_Oimage(_1498679, _1498681, _1498683), _1498687))))], (38410 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1498681), hAPP(_1498683, _1498685)), hAPP(c_Set_Oimage(_1498679, _1498681, _1498683), _1498687))), -(hBOOL(hAPP(hAPP(c_member(_1498679), _1498685), _1498687)))]]], (42281 ^ _777864) ^ [_1599158, _1599160, _1599162] : [-(hAPP(c_New__DSequence_Opos__single(_1599158, _1599160), _1599162) = c_Lazy__Sequence_Osingle(_1599158, _1599160))], (36902 ^ _777864) ^ [_1467417, _1467419, _1467421, _1467423, _1467425] : [class_Groups_Ocomm__monoid__add(_1467417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467419), _1467421)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467419), _1467423)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467419, tc_HOL_Obool)), _1467421), _1467423) = c_Orderings_Obot__class_Obot(tc_fun(_1467419, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467419, _1467417), _1467425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467419, tc_HOL_Obool)), _1467421), _1467423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467417), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467419, _1467417), _1467425), _1467421)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467419, _1467417), _1467425), _1467423)))], (49372 ^ _777864) ^ [_1771331, _1771333, _1771335, _1771337] : [-(hAPP(hAPP(c_List_Omap(_1771331, _1771333), _1771335), c_List_Obutlast(_1771331, _1771337)) = c_List_Obutlast(_1771333, hAPP(hAPP(c_List_Omap(_1771331, _1771333), _1771335), _1771337)))], (40468 ^ _777864) ^ [_1550252, _1550254, _1550256] : [class_Groups_Olinordered__ab__semigroup__add(_1550252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550252), _1550254)), -(_1550254 = c_Orderings_Obot__class_Obot(tc_fun(_1550252, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1550252), _1550256), c_Big__Operators_Olinorder__class_OMax(_1550252, _1550254)) = c_Big__Operators_Olinorder__class_OMax(_1550252, hAPP(c_Set_OCollect(_1550252), hAPP(hAPP(c_COMBB(tc_fun(_1550252, tc_HOL_Obool), tc_HOL_Obool, _1550252), c_HOL_OEx(_1550252)), hAPP(hAPP(c_COMBC(_1550252, tc_fun(_1550252, tc_HOL_Obool), tc_fun(_1550252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550252, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1550252, tc_HOL_Obool), tc_fun(_1550252, tc_HOL_Obool)), _1550252), c_COMBS(_1550252, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550252, tc_HOL_Obool), tc_fun(_1550252, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1550252), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550252), c_fconj)), hAPP(hAPP(c_COMBC(_1550252, tc_fun(_1550252, _1550252), tc_fun(_1550252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550252, tc_HOL_Obool), tc_fun(tc_fun(_1550252, _1550252), tc_fun(_1550252, tc_HOL_Obool)), _1550252), c_COMBB(_1550252, tc_HOL_Obool, _1550252)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1550252), _1550256))))), hAPP(hAPP(c_COMBC(_1550252, tc_fun(_1550252, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550252)), _1550254))))))], (41940 ^ _777864) ^ [] : [-(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))], (39421 ^ _777864) ^ [_1524094, _1524096, _1524098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524094), _1524096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524094, _1524094), tc_HOL_Obool)), _1524098), hAPP(hAPP(c_Product__Type_OSigma(_1524094, _1524094), _1524096), hAPP(c_COMBK(tc_fun(_1524094, tc_HOL_Obool), _1524094), _1524096)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1524094, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1524094), _1524096), _1524098))))], (44831 ^ _777864) ^ [_1660773, _1660775, _1660777] : [class_Complete__Lattice_Ocomplete__lattice(_1660773), 44834 ^ _777864 : [(44835 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660773), c_Complete__Lattice_OSup__class_OSup(_1660773, _1660775)), _1660777)), 44838 ^ _777864 : [(44839 ^ _777864) ^ [_1660931] : [hBOOL(hAPP(hAPP(c_member(_1660773), _1660931), _1660775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660773), _1660931), _1660777)))]]], (44845 ^ _777864) ^ [] : [44847 ^ _777864 : [(44850 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660773), 44846 ^ [_1660773, _1660775, _1660777]), _1660777))], (44848 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660773), 44846 ^ [_1660773, _1660775, _1660777]), _1660775)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660773), c_Complete__Lattice_OSup__class_OSup(_1660773, _1660775)), _1660777)))]]], (18870 ^ _777864) ^ [_1102218, _1102220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102218), _1102220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1102218)), c_Int_OBit0(_1102220))))], (5050 ^ _777864) ^ [_855101, _855103, _855105, _855107, _855109, _855111, _855113, _855115, _855117, _855119] : [-(c_Map_Omap__upds(_855119, _855115, _855111, _855107, _855103) = c_Map_Omap__upds(_855117, _855113, _855109, _855105, _855101)), _855119 = _855117, _855115 = _855113, _855111 = _855109, _855107 = _855105, _855103 = _855101], (23459 ^ _777864) ^ [_1187380, _1187382, _1187384, _1187386] : [class_Orderings_Olinorder(_1187380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187380), _1187382), _1187384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187380), _1187382), _1187386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187380), _1187382), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187380), _1187384), _1187386))))], (16602 ^ _777864) ^ [_1063266, _1063268, _1063270] : [class_Int_Onumber__ring(_1063266), class_Rings_Olinordered__idom(_1063266), 16609 ^ _777864 : [(16616 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1063268), _1063270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063266), hAPP(c_Int_Onumber__class_Onumber__of(_1063266), _1063268)), hAPP(c_Int_Onumber__class_Onumber__of(_1063266), _1063270))))], (16610 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1063266), hAPP(c_Int_Onumber__class_Onumber__of(_1063266), _1063268)), hAPP(c_Int_Onumber__class_Onumber__of(_1063266), _1063270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1063268), _1063270)))]]], (30528 ^ _777864) ^ [_1335848, _1335850, _1335852, _1335854] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1335848, tc_HOL_Obool)), _1335850), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1335848), _1335852), _1335854))), 30532 ^ _777864 : [(30535 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1335848), 30531 ^ [_1335848, _1335850, _1335852, _1335854]), _1335852)))], (30533 ^ _777864) ^ [] : [-(_1335850 = hAPP(c_Relation_OImage(_1335848, _1335848, _1335854), hAPP(hAPP(c_Set_Oinsert(_1335848), 30531 ^ [_1335848, _1335850, _1335852, _1335854]), c_Orderings_Obot__class_Obot(tc_fun(_1335848, tc_HOL_Obool)))))]]], (27211 ^ _777864) ^ [_1260979, _1260981, _1260983] : [hBOOL(hAPP(hAPP(c_member(_1260979), _1260981), _1260983)), -(hAPP(hAPP(c_Set_Oinsert(_1260979), _1260981), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260979, tc_HOL_Obool)), _1260983), hAPP(hAPP(c_Set_Oinsert(_1260979), _1260981), c_Orderings_Obot__class_Obot(tc_fun(_1260979, tc_HOL_Obool))))) = _1260983)], (46170 ^ _777864) ^ [_1691997, _1691999, _1692001, _1692003, _1692005, _1692007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1691997, _1691999)), hAPP(hAPP(c_Product__Type_OPair(_1691997, _1691999), _1692001), _1692003)), hAPP(c_List_Oset(tc_prod(_1691997, _1691999)), hAPP(hAPP(c_List_Ozip(_1691997, _1691999), _1692005), _1692007)))), -(hBOOL(hAPP(hAPP(c_member(_1691997), _1692001), hAPP(c_List_Oset(_1691997), _1692005))))], (26939 ^ _777864) ^ [_1253492, _1253494, _1253496] : [hBOOL(hAPP(hAPP(c_member(_1253492), _1253494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1253492, tc_HOL_Obool)), _1253496))), hBOOL(hAPP(hAPP(c_member(_1253492), _1253494), _1253496))], (51575 ^ _777864) ^ [_1812849, _1812851] : [hBOOL(hAPP(hAPP(c_fconj, _1812849), _1812851)), -(hBOOL(_1812851))], (28330 ^ _777864) ^ [_1283999, _1284001, _1284003] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283999, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283999, tc_HOL_Obool)), _1284001), _1284003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283999, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283999, tc_HOL_Obool)), _1284001)), _1284003))], (27492 ^ _777864) ^ [_1267442] : [class_Rings_Oring__1(_1267442), -(hBOOL(hAPP(hAPP(c_member(_1267442), c_Groups_Ozero__class_Ozero(_1267442)), c_Int_Oring__1__class_OInts(_1267442))))], (11929 ^ _777864) ^ [_977349, _977351, _977353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977349), _977351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977353), _977349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977353), _977351))))], (9432 ^ _777864) ^ [_935245, _935247, _935249] : [class_Rings_Olinordered__semiring__strict(_935245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935245), c_Groups_Ozero__class_Ozero(_935245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935245), _935247), _935249))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935245), c_Groups_Ozero__class_Ozero(_935245)), _935247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935245), c_Groups_Ozero__class_Ozero(_935245)), _935249)))], (47380 ^ _777864) ^ [_1725089, _1725091, _1725093, _1725095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725089)), _1725091)), _1725093)), -(hAPP(hAPP(c_List_Olist__update(_1725089, _1725091), _1725093), _1725095) = _1725091)], (5552 ^ _777864) ^ [_865911, _865913, _865915, _865917, _865919, _865921] : [-(c_Natural_Oevaln(c_Com_Ocom_OCall(_865911, _865913, _865915), _865917, _865919, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865921), hAPP(c_Natural_Ogetlocs, _865917))), _865911), hAPP(hAPP(c_Natural_Ogetlocs, _865921), c_Com_ORes)))), 5553 ^ _777864 : [(5554 ^ _777864) ^ [_866060] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865921), hAPP(c_Natural_Ogetlocs, _865917))), _865911), hAPP(hAPP(c_Natural_Ogetlocs, _865921), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _866060), hAPP(c_Natural_Ogetlocs, _865917))), _865911), hAPP(hAPP(c_Natural_Ogetlocs, _866060), c_Com_ORes)), c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _865913), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865917), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_865915, _865917)), _865919, _866060)]]], (14280 ^ _777864) ^ [_1019385, _1019387, _1019389, _1019391] : [class_Divides_Osemiring__div(_1019385), -(_1019387 = c_Groups_Ozero__class_Ozero(_1019385)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019385), _1019387), _1019389)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019385), _1019387), _1019391)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019385), _1019389), _1019391))], (24457 ^ _777864) ^ [_1206319, _1206321] : [-(c_Nitpick_Ouminus__frac(_1206319, _1206321) = c_Nitpick_OAbs__Frac(_1206319, 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(_1206319), _1206321))), hAPP(c_Nitpick_Odenom(_1206319), _1206321))))], (39846 ^ _777864) ^ [_1533140, _1533142, _1533144, _1533146, _1533148, _1533150, _1533152, _1533154] : [-(hAPP(c_Product__Type_Omap__pair(_1533140, _1533142, _1533144, _1533146, _1533148, _1533150), hAPP(hAPP(c_Product__Type_OPair(_1533140, _1533144), _1533152), _1533154)) = hAPP(hAPP(c_Product__Type_OPair(_1533142, _1533146), hAPP(_1533148, _1533152)), hAPP(_1533150, _1533154)))], (5414 ^ _777864) ^ [_860667, _860669, _860671, _860673] : [-(c_COMBK(_860673, _860669) = c_COMBK(_860671, _860667)), _860673 = _860671, _860669 = _860667], (44152 ^ _777864) ^ [_1644297, _1644299, _1644301, _1644303, _1644305] : [44154 ^ _777864 : [(44157 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1644303, 44153 ^ [_1644297, _1644299, _1644301, _1644303, _1644305]), _1644305))], (44155 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644297), 44153 ^ [_1644297, _1644299, _1644301, _1644303, _1644305]), _1644301)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644297, tc_fun(_1644299, tc_HOL_Obool)), _1644301), _1644303), _1644305)))], (40152 ^ _777864) ^ [_1539944, _1539946, _1539948] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539944), hAPP(c_Set_OCollect(_1539944), hAPP(hAPP(c_COMBS(_1539944, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539944), c_fdisj), _1539946)), _1539948)))), 40155 ^ _777864 : [(40158 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539944), hAPP(c_Set_OCollect(_1539944), _1539948))))], (40156 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539944), hAPP(c_Set_OCollect(_1539944), _1539946))))]]], (15430 ^ _777864) ^ [_1040391, _1040393] : [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), _1040391), _1040393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040393), _1040391)))], (43935 ^ _777864) ^ [_1637787, _1637789, _1637791, _1637793, _1637795, _1637797] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637787, tc_fun(_1637789, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637791, tc_fun(_1637787, tc_HOL_Obool)), _1637793), _1637795)), _1637797) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637791, tc_fun(_1637789, tc_HOL_Obool)), _1637793), hAPP(hAPP(c_COMBC(_1637791, tc_fun(_1637787, tc_fun(_1637789, tc_HOL_Obool)), tc_fun(_1637789, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637787, tc_HOL_Obool), tc_fun(tc_fun(_1637787, tc_fun(_1637789, tc_HOL_Obool)), tc_fun(_1637789, tc_HOL_Obool)), _1637791), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637787, tc_fun(_1637789, tc_HOL_Obool))), _1637795)), _1637797)))], (15052 ^ _777864) ^ [_1033107, _1033109, _1033111, _1033113, _1033115] : [class_Groups_Oordered__ab__group__add(_1033107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033107), _1033109), _1033111) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033107), _1033113), _1033115), 15059 ^ _777864 : [(15066 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033107), _1033113), _1033115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033107), _1033109), _1033111)))], (15060 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033107), _1033109), _1033111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033107), _1033113), _1033115)))]]], (38284 ^ _777864) ^ [_1496237] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496237, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1496237, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1496237, tc_HOL_Obool)))], (39914 ^ _777864) ^ [_1535020, _1535022, _1535024, _1535026, _1535028] : [c_Relation_Orefl__on(_1535020, _1535022, _1535024), c_Relation_Orefl__on(_1535020, _1535026, _1535028), -(c_Relation_Orefl__on(_1535020, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535020, tc_HOL_Obool)), _1535022), _1535026), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1535020, _1535020), tc_HOL_Obool)), _1535024), _1535028)))], (18526 ^ _777864) ^ [_1096423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1096423)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096423), c_Int_OPls)))], (30545 ^ _777864) ^ [_1336256, _1336258, _1336260, _1336262, _1336264, _1336266] : [-(hBOOL(hAPP(hAPP(c_member(_1336256), _1336258), c_SetInterval_Oord_OgreaterThanAtMost(_1336256, _1336260, _1336262, _1336264, _1336266)))), hBOOL(hAPP(hAPP(_1336262, _1336264), _1336258)), hBOOL(hAPP(hAPP(_1336260, _1336258), _1336266))], (25035 ^ _777864) ^ [_1217304, _1217306] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217304), _1217306))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217304), _1217306)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217306), _1217304)))], (28344 ^ _777864) ^ [_1284350, _1284352, _1284354, _1284356] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1284350), _1284356) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1284354), _1284352), -(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), _1284350), _1284352)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1284354), _1284356))), c_Int_Ointrel)))], (24381 ^ _777864) ^ [] : [-(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)))], (13692 ^ _777864) ^ [_1008518, _1008520] : [class_Lattices_Oab__semigroup__idem__mult(_1008518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008518), _1008520), _1008520) = _1008520)], (45589 ^ _777864) ^ [_1678208, _1678210] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1678208), _1678210) = c_Smallcheck_Osmall_H(_1678208, hAPP(c_Code__Numeral_Oint__of, _1678210), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1678210))))], (13146 ^ _777864) ^ [_998680, _998682, _998684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _998680)), 13149 ^ _777864 : [(13156 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998682), _998684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998680), _998682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998680), _998684))))], (13150 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998680), _998682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _998680), _998684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998682), _998684)))]]], (48906 ^ _777864) ^ [_1761082, _1761084, _1761086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1761082), _1761084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1761082), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761084), _1761086))))], (45906 ^ _777864) ^ [_1685997, _1685999, _1686001] : [-(c_Map_Odom(_1685997, _1685999, c_Map_Omap__of(_1685997, _1685999, _1686001)) = hAPP(c_Set_Oimage(tc_prod(_1685997, _1685999), _1685997, c_Product__Type_Ofst(_1685997, _1685999)), hAPP(c_List_Oset(tc_prod(_1685997, _1685999)), _1686001)))], (29055 ^ _777864) ^ [_1303349, _1303351, _1303353, _1303355, _1303357] : [hAPP(c_Relation_OImage(_1303349, _1303349, _1303351), hAPP(hAPP(c_Set_Oinsert(_1303349), _1303353), c_Orderings_Obot__class_Obot(tc_fun(_1303349, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1303349, _1303349, _1303351), hAPP(hAPP(c_Set_Oinsert(_1303349), _1303355), c_Orderings_Obot__class_Obot(tc_fun(_1303349, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1303349, _1303357, _1303351), hBOOL(hAPP(hAPP(c_member(_1303349), _1303355), _1303357)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1303349, _1303349)), hAPP(hAPP(c_Product__Type_OPair(_1303349, _1303349), _1303353), _1303355)), _1303351)))], (25319 ^ _777864) ^ [_1221906, _1221908, _1221910, _1221912] : [class_Divides_Osemiring__div(_1221906), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221906), _1221908), _1221910)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221906), _1221908), _1221912)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1221906), _1221908), c_Divides_Odiv__class_Omod(_1221906, _1221910, _1221912))))], (47678 ^ _777864) ^ [_1730990, _1730992, _1730994, _1730996] : [-(_1730990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1730992), _1730990), hAPP(hAPP(c_List_Olist_OCons(_1730992), _1730994), _1730996)) = hAPP(hAPP(c_List_Olist_OCons(_1730992), _1730994), hAPP(hAPP(c_List_Otake(_1730992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1730990), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1730996)))], (50420 ^ _777864) ^ [_1793237, _1793239] : [50422 ^ _777864 : [(50425 ^ _777864) ^ [] : [50421 ^ [_1793237, _1793239] = c_List_Olist_ONil(_1793237)], (50423 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1793237)), 50421 ^ [_1793237, _1793239]), hAPP(c_List_Oset(tc_List_Olist(_1793237)), _1793239))))]], -(c_List_Olist_ONil(_1793237) = c_List_Oconcat(_1793237, _1793239))], (18022 ^ _777864) ^ [_1088242, _1088244] : [class_Int_Onumber__ring(_1088242), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088242), _1088244), hAPP(c_Int_Onumber__class_Onumber__of(_1088242), c_Int_OPls)) = _1088244)], (13407 ^ _777864) ^ [_1003112, _1003114] : [class_Divides_Osemiring__div(_1003112), -(c_Divides_Odiv__class_Omod(_1003112, _1003114, _1003114) = c_Groups_Ozero__class_Ozero(_1003112))], (1562 ^ _777864) ^ [_800157, _800159] : [-(class_Rings_Ocomm__semiring__1(_800157)), _800159 = _800157, class_Rings_Ocomm__semiring__1(_800159)], (11114 ^ _777864) ^ [_962932, _962934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962932), _962934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962932), _962934))), -(_962932 = _962934)], (30224 ^ _777864) ^ [_1328499, _1328501, _1328503] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328499, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328499, tc_HOL_Obool)), _1328501), _1328503)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328499, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328499, tc_HOL_Obool)), _1328501)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328499, tc_HOL_Obool)), _1328503)))], (22594 ^ _777864) ^ [_1168539, _1168541, _1168543] : [-(_1168539 = hAPP(hAPP(c_Product__Type_OPair(_1168541, _1168543), hAPP(c_Product__Type_Ofst(_1168541, _1168543), _1168539)), hAPP(c_Product__Type_Osnd(_1168541, _1168543), _1168539)))], (3180 ^ _777864) ^ [_825964, _825966, _825968, _825970, _825972, _825974, _825976, _825978] : [-(c_SetInterval_Oord_OatLeastAtMost(_825978, _825974, _825970, _825966) = c_SetInterval_Oord_OatLeastAtMost(_825976, _825972, _825968, _825964)), _825978 = _825976, _825974 = _825972, _825970 = _825968, _825966 = _825964], (34105 ^ _777864) ^ [_1409671, _1409673, _1409675] : [-(hAPP(c_Relation_OImage(_1409671, _1409671, c_Relation_OId__on(_1409671, _1409673)), _1409675) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409671, tc_HOL_Obool)), _1409673), _1409675))], (27850 ^ _777864) ^ [_1274026, _1274028, _1274030, _1274032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274026, tc_HOL_Obool)), _1274028), _1274030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274026, tc_HOL_Obool)), _1274032), _1274030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274026, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274026, tc_HOL_Obool)), _1274028), _1274032)), _1274030)))], (36732 ^ _777864) ^ [_1463739, _1463741, _1463743, _1463745, _1463747] : [hBOOL(hAPP(hAPP(c_member(_1463739), _1463741), _1463743)), -(hAPP(c_Map_Orestrict__map(_1463739, _1463745, _1463747, _1463743), _1463741) = hAPP(_1463747, _1463741))], (19836 ^ _777864) ^ [_1119862, _1119864] : [c_Nat__Transfer_Ois__nat(_1119862), c_Nat__Transfer_Ois__nat(_1119864), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1119862), _1119864)))], (31783 ^ _777864) ^ [_1358572, _1358574] : [class_Groups_Olinordered__ab__group__add(_1358572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358572), _1358574)), -(_1358574 = c_Orderings_Obot__class_Obot(tc_fun(_1358572, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1358572), c_Big__Operators_Olinorder__class_OMin(_1358572, _1358574)) = c_Big__Operators_Olinorder__class_OMax(_1358572, hAPP(c_Set_Oimage(_1358572, _1358572, c_Groups_Ouminus__class_Ouminus(_1358572)), _1358574)))], (43911 ^ _777864) ^ [_1637070, _1637072, _1637074] : [c_Relation_Orefl__on(_1637070, _1637072, hAPP(c_Relation_Oconverse(_1637070, _1637070), _1637074)), -(c_Relation_Orefl__on(_1637070, _1637072, _1637074))], (35854 ^ _777864) ^ [_1444669, _1444671, _1444673, _1444675] : [class_Orderings_Olinorder(_1444669), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444669), _1444671), _1444673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444669), _1444673), _1444675)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444669, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444669, _1444671), _1444673)), c_SetInterval_Oord__class_OatLeastAtMost(_1444669, _1444673, _1444675)) = c_SetInterval_Oord__class_OatLeastAtMost(_1444669, _1444671, _1444675))], (35030 ^ _777864) ^ [_1428891, _1428893] : [-(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)), _1428891), _1428893))], (11395 ^ _777864) ^ [_967780, _967782] : [class_Groups_Olinordered__ab__group__add(_967780), 11398 ^ _777864 : [(11405 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967780), _967782), c_Groups_Ozero__class_Ozero(_967780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967780), _967782), _967782)), c_Groups_Ozero__class_Ozero(_967780))))], (11399 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967780), _967782), _967782)), c_Groups_Ozero__class_Ozero(_967780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967780), _967782), c_Groups_Ozero__class_Ozero(_967780))))]]], (26593 ^ _777864) ^ [_1246381, _1246383] : [-(c_Set_Othe__elem(_1246381, _1246383) = c_HOL_OThe(_1246381, hAPP(hAPP(c_COMBB(tc_fun(_1246381, tc_HOL_Obool), tc_HOL_Obool, _1246381), hAPP(c_fequal, _1246383)), hAPP(hAPP(c_COMBC(_1246381, tc_fun(_1246381, tc_HOL_Obool), tc_fun(_1246381, tc_HOL_Obool)), c_Set_Oinsert(_1246381)), c_Orderings_Obot__class_Obot(tc_fun(_1246381, tc_HOL_Obool))))))], (19100 ^ _777864) ^ [_1106235] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1106235)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1106235))))], (42619 ^ _777864) ^ [_1606560, _1606562, _1606564, _1606566, _1606568, _1606570] : [c_Finite__Set_Ofolding(_1606560, _1606562, _1606564, _1606566), hBOOL(hAPP(c_Finite__Set_Ofinite(_1606560), _1606568)), -(hAPP(hAPP(_1606566, _1606568), _1606570) = hAPP(hAPP(c_Finite__Set_Ofold(_1606560, _1606562, _1606564), _1606570), _1606568))], (24577 ^ _777864) ^ [_1209037] : [-(c_Quickcheck_Obeyond(_1209037, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (7832 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7548 ^ _777864) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9048 ^ _777864) ^ [_928236, _928238, _928240] : [class_Rings_Ono__zero__divisors(_928236), -(_928238 = c_Groups_Ozero__class_Ozero(_928236)), -(_928240 = c_Groups_Ozero__class_Ozero(_928236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928236), _928238), _928240) = c_Groups_Ozero__class_Ozero(_928236)], (13782 ^ _777864) ^ [_1010132, _1010134, _1010136] : [-(hBOOL(hAPP(_1010132, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1010134, _1010136)))), 13785 ^ _777864 : [(13788 ^ _777864) ^ [] : [hBOOL(hAPP(_1010132, _1010134))], (13786 ^ _777864) ^ [] : [-(_1010136 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 13791 ^ _777864 : [(13792 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1010136)))], (13798 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13794 ^ [_1010132, _1010134, _1010136]), _1010136)))], (13802 ^ _777864) ^ [] : [hBOOL(hAPP(_1010132, 13794 ^ [_1010132, _1010134, _1010136]))], (13800 ^ _777864) ^ [] : [-(_1010134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010136), 13793 ^ [_1010132, _1010134, _1010136])), 13794 ^ [_1010132, _1010134, _1010136]))], (13796 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13794 ^ [_1010132, _1010134, _1010136])))]], 13803 ^ _777864 : [(13804 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010136), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13810 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 13806 ^ [_1010132, _1010134, _1010136]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13814 ^ _777864) ^ [] : [hBOOL(hAPP(_1010132, 13806 ^ [_1010132, _1010134, _1010136]))], (13812 ^ _777864) ^ [] : [-(_1010134 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1010136), 13805 ^ [_1010132, _1010134, _1010136])), 13806 ^ [_1010132, _1010134, _1010136]))], (13808 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1010136), 13806 ^ [_1010132, _1010134, _1010136])))]]], (36692 ^ _777864) ^ [_1462673, _1462675, _1462677, _1462679, _1462681] : [class_Groups_Ocomm__monoid__add(_1462673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462675), _1462677)), 36699 ^ _777864 : [(36706 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1462675), _1462679), _1462677))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462675, _1462673), hAPP(hAPP(c_COMBC(_1462675, _1462673, _1462673), hAPP(hAPP(c_COMBS(_1462675, _1462673, tc_fun(_1462673, _1462673)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1462673, tc_fun(_1462673, _1462673)), _1462675), c_If(_1462673)), hAPP(hAPP(c_COMBC(_1462675, _1462675, tc_HOL_Obool), c_fequal), _1462679))), _1462681)), c_Groups_Ozero__class_Ozero(_1462673))), _1462677) = c_Groups_Ozero__class_Ozero(_1462673))], (36700 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1462675), _1462679), _1462677)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462675, _1462673), hAPP(hAPP(c_COMBC(_1462675, _1462673, _1462673), hAPP(hAPP(c_COMBS(_1462675, _1462673, tc_fun(_1462673, _1462673)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1462673, tc_fun(_1462673, _1462673)), _1462675), c_If(_1462673)), hAPP(hAPP(c_COMBC(_1462675, _1462675, tc_HOL_Obool), c_fequal), _1462679))), _1462681)), c_Groups_Ozero__class_Ozero(_1462673))), _1462677) = hAPP(_1462681, _1462679))]]], (48734 ^ _777864) ^ [_1757779, _1757781, _1757783] : [-(_1757779 = c_List_Olist_ONil(_1757781)), -(hAPP(c_List_Ohd(_1757781), hAPP(hAPP(c_List_Oappend(_1757781), _1757779), _1757783)) = hAPP(c_List_Ohd(_1757781), _1757779))], (12202 ^ _777864) ^ [_982102] : [12204 ^ _777864 : [(12207 ^ _777864) ^ [] : [hBOOL(hAPP(_982102, hAPP(c_Int_Onat, 12203 ^ [_982102])))], (12205 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12203 ^ [_982102])))]], 12208 ^ _777864 : [(12209 ^ _777864) ^ [_982235] : [-(hBOOL(hAPP(_982102, _982235)))]]], (34503 ^ _777864) ^ [_1418416, _1418418, _1418420] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418416, tc_HOL_Obool)), _1418418), hAPP(c_Set_OPow(_1418416), _1418420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1418416, tc_HOL_Obool)), _1418418), _1418420)))], (38374 ^ _777864) ^ [] : [-(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)))], (11303 ^ _777864) ^ [_966222, _966224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _966222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _966224)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _966222)), hAPP(c_Int_Onat, _966224)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _966222), _966224)))], (15630 ^ _777864) ^ [_1044199, _1044201] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044199), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1044201)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044199), _1044201)))], (16342 ^ _777864) ^ [_1058192, _1058194] : [class_Groups_Oordered__ab__group__add__abs(_1058192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058192), c_Groups_Ozero__class_Ozero(_1058192)), hAPP(c_Groups_Oabs__class_Oabs(_1058192), _1058194))))], (29980 ^ _777864) ^ [_1322947, _1322949, _1322951, _1322953] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322947, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322947, tc_HOL_Obool)), _1322949), _1322951)), _1322953) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322947, tc_HOL_Obool)), _1322949), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322947, tc_HOL_Obool)), _1322951), _1322953)))], (42306 ^ _777864) ^ [_1599618, _1599620] : [42307 ^ _777864 : [(42308 ^ _777864) ^ [_1599664] : [hBOOL(hAPP(_1599618, _1599664))]], -(hBOOL(hAPP(_1599618, c_Hilbert__Choice_OEps(_1599620, _1599618))))], (22436 ^ _777864) ^ [_1165672, _1165674] : [_1165672 = _1165674, -(c_Code__Numeral_OSuc__code__numeral(_1165672) = c_Code__Numeral_OSuc__code__numeral(_1165674))], (4752 ^ _777864) ^ [_850554, _850556, _850558, _850560, _850562, _850564] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_850564, _850560, _850556) = c_SetInterval_Oord__class_OatLeastAtMost(_850562, _850558, _850554)), _850564 = _850562, _850560 = _850558, _850556 = _850554], (33454 ^ _777864) ^ [_1392905, _1392907] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1392905, _1392907)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1392907), _1392905)))], (34359 ^ _777864) ^ [_1415095, _1415097, _1415099] : [class_Lattices_Olattice(_1415095), hAPP(_1415097, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1415095), 34364 ^ [_1415095, _1415097, _1415099]), 34365 ^ [_1415095, _1415097, _1415099])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1415095), hAPP(_1415097, 34364 ^ [_1415095, _1415097, _1415099])), hAPP(_1415097, 34365 ^ [_1415095, _1415097, _1415099])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415095), _1415099)), -(_1415099 = c_Orderings_Obot__class_Obot(tc_fun(_1415095, tc_HOL_Obool))), -(hAPP(_1415097, c_Big__Operators_Olattice__class_OSup__fin(_1415095, _1415099)) = c_Big__Operators_Olattice__class_OSup__fin(_1415095, hAPP(c_Set_Oimage(_1415095, _1415095, _1415097), _1415099)))], (22929 ^ _777864) ^ [_1175470, _1175472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1175470)), -(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(_1175470), _1175472))), _1175470)))], (10672 ^ _777864) ^ [_955715, _955717, _955719] : [class_Orderings_Olinorder(_955715), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955715), _955717), _955719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955715), _955719), _955717)))], (15180 ^ _777864) ^ [_1035410, _1035412, _1035414] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035410), _1035412)), _1035414) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035412), _1035414)))], (18054 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (30186 ^ _777864) ^ [_1327302, _1327304, _1327306, _1327308, _1327310] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327302, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1327304, _1327302, _1327306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327304, tc_HOL_Obool)), _1327308), _1327310))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327302, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1327304, _1327302, _1327306), _1327308)), hAPP(c_Set_Oimage(_1327304, _1327302, _1327306), _1327310)))))], (51253 ^ _777864) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51265 ^ _777864) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (49713 ^ _777864) ^ [_1779531, _1779533] : [class_Orderings_Olinorder(_1779531), -(c_List_Olinorder__class_Osorted(_1779531, hAPP(hAPP(c_List_Olist_OCons(_1779531), _1779533), c_List_Olist_ONil(_1779531))))], (44216 ^ _777864) ^ [_1645758, _1645760] : [-(c_Transitive__Closure_Otrancl(_1645758, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645758, _1645758), tc_HOL_Obool)), _1645760), c_Relation_OId(_1645758))) = c_Transitive__Closure_Ortrancl(_1645758, _1645760))], (37769 ^ _777864) ^ [_1486514] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1486514)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1486514))], (40367 ^ _777864) ^ [_1546480, _1546482, _1546484] : [class_Orderings_Olinorder(_1546480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546480), _1546482)), -(_1546482 = c_Orderings_Obot__class_Obot(tc_fun(_1546480, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1546480), _1546484)), -(_1546484 = c_Orderings_Obot__class_Obot(tc_fun(_1546480, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1546480), c_Big__Operators_Olattice_OSup__fin(_1546480, c_Orderings_Oord__class_Omax(_1546480), _1546482)), c_Big__Operators_Olattice_OSup__fin(_1546480, c_Orderings_Oord__class_Omax(_1546480), _1546484)) = c_Big__Operators_Olattice_OSup__fin(_1546480, c_Orderings_Oord__class_Omax(_1546480), hAPP(c_Set_OCollect(_1546480), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_HOL_Obool), tc_HOL_Obool, _1546480), c_HOL_OEx(_1546480)), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool)), tc_fun(_1546480, tc_HOL_Obool), _1546480), hAPP(c_COMBB(tc_fun(_1546480, tc_HOL_Obool), tc_HOL_Obool, _1546480), c_HOL_OEx(_1546480))), hAPP(hAPP(c_COMBC(_1546480, tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool)), tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_fun(tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool))), tc_fun(tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool)), tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool))), _1546480), c_COMBS(_1546480, tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_fun(_1546480, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1546480, tc_fun(tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool))), _1546480), hAPP(c_COMBB(tc_fun(_1546480, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool)), _1546480), c_COMBS(_1546480, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool)), tc_fun(_1546480, tc_fun(_1546480, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1546480), hAPP(c_COMBB(tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1546480), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546480), c_fconj))), hAPP(hAPP(c_COMBC(_1546480, tc_fun(_1546480, tc_fun(_1546480, _1546480)), tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1546480, _1546480), tc_fun(_1546480, tc_HOL_Obool)), tc_fun(tc_fun(_1546480, tc_fun(_1546480, _1546480)), tc_fun(_1546480, tc_fun(_1546480, tc_HOL_Obool))), _1546480), c_COMBB(tc_fun(_1546480, _1546480), tc_fun(_1546480, tc_HOL_Obool), _1546480)), hAPP(hAPP(c_COMBB(tc_fun(_1546480, tc_HOL_Obool), tc_fun(tc_fun(_1546480, _1546480), tc_fun(_1546480, tc_HOL_Obool)), _1546480), c_COMBB(_1546480, tc_HOL_Obool, _1546480)), c_fequal))), c_Orderings_Oord__class_Omin(_1546480)))))), hAPP(hAPP(c_COMBC(_1546480, tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546480, tc_HOL_Obool), tc_fun(_1546480, tc_HOL_Obool)), _1546480), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546480)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546480), c_fconj), hAPP(hAPP(c_COMBC(_1546480, tc_fun(_1546480, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546480)), _1546482)))), hAPP(hAPP(c_COMBC(_1546480, tc_fun(_1546480, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546480)), _1546484))))))))], (51033 ^ _777864) ^ [_1807146, _1807148] : [class_Lattices_Obounded__lattice(_1807146), -(class_Lattices_Obounded__lattice__top(tc_fun(_1807148, _1807146)))], (44943 ^ _777864) ^ [_1662914, _1662916, _1662918] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662914, tc_HOL_Obool)), _1662916), _1662918) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662914, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1662914, tc_HOL_Obool)), _1662916), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1662914, tc_HOL_Obool)), _1662918), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1662914, tc_HOL_Obool), tc_HOL_Obool))))))], (19716 ^ _777864) ^ [_1117325, _1117327] : [class_Fields_Olinordered__field__inverse__zero(_1117325), class_Int_Onumber__ring(_1117325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117325), c_Groups_Ozero__class_Ozero(_1117325)), _1117327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117325), c_Groups_Ozero__class_Ozero(_1117325)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117325), _1117327), hAPP(c_Int_Onumber__class_Onumber__of(_1117325), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25457 ^ _777864) ^ [_1224292] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1224292), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1224292 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (38234 ^ _777864) ^ [] : [-(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))], (48740 ^ _777864) ^ [_1757839, _1757841, _1757843] : [-(hAPP(c_List_Ohd(_1757839), hAPP(hAPP(c_List_Olist_OCons(_1757839), _1757841), _1757843)) = _1757841)], (43739 ^ _777864) ^ [_1631716, _1631718, _1631720, _1631722, _1631724] : [-(hAPP(c_Relation_Oconverse(_1631716, _1631718), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631720, tc_fun(tc_prod(_1631716, _1631718), tc_HOL_Obool)), _1631722), _1631724)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631720, tc_fun(tc_prod(_1631718, _1631716), tc_HOL_Obool)), _1631722), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1631716, _1631718), tc_HOL_Obool), tc_fun(tc_prod(_1631718, _1631716), tc_HOL_Obool), _1631720), c_Relation_Oconverse(_1631716, _1631718)), _1631724)))], (23001 ^ _777864) ^ [_1176740, _1176742, _1176744, _1176746] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176740, _1176742), _1176744)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176740, _1176742), _1176746)), -(_1176744 = _1176746)], (27952 ^ _777864) ^ [_1275912, _1275914, _1275916] : [class_Lattices_Osemilattice__sup(_1275912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275912), _1275914), _1275916)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275912), _1275914), _1275916) = _1275916)], (49160 ^ _777864) ^ [_1767045, _1767047, _1767049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767045), tc_List_Olist(_1767045))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767045), tc_List_Olist(_1767045)), c_List_Olist_ONil(_1767045)), _1767047)), c_List_Olexord(_1767045, _1767049))), -(_1767047 = hAPP(hAPP(c_List_Olist_OCons(_1767045), 49163 ^ [_1767045, _1767047, _1767049]), 49164 ^ [_1767045, _1767047, _1767049]))], (1442 ^ _777864) ^ [_798657, _798659] : [-(class_Groups_Ocancel__ab__semigroup__add(_798657)), _798659 = _798657, class_Groups_Ocancel__ab__semigroup__add(_798659)], (35634 ^ _777864) ^ [_1440767, _1440769, _1440771, _1440773, _1440775] : [class_Orderings_Olinorder(_1440767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440767), _1440769), _1440771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440767), _1440773), _1440775)), 35645 ^ _777864 : [(35654 ^ _777864) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440767, _1440769), _1440771) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440767, _1440773), _1440775)), _1440769 = _1440773, _1440771 = _1440775], (35646 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440767, _1440769), _1440771) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440767, _1440773), _1440775), 35649 ^ _777864 : [(35652 ^ _777864) ^ [] : [-(_1440771 = _1440775)], (35650 ^ _777864) ^ [] : [-(_1440769 = _1440773)]]]]], (47596 ^ _777864) ^ [_1729340, _1729342, _1729344, _1729346, _1729348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729340), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729342)), _1729344))), 47599 ^ _777864 : [(47606 ^ _777864) ^ [] : [-(_1729340 = _1729346), -(hAPP(hAPP(c_List_Onth(_1729342), hAPP(hAPP(c_List_Olist__update(_1729342, _1729344), _1729340), _1729348)), _1729346) = hAPP(hAPP(c_List_Onth(_1729342), _1729344), _1729346))], (47600 ^ _777864) ^ [] : [_1729340 = _1729346, -(hAPP(hAPP(c_List_Onth(_1729342), hAPP(hAPP(c_List_Olist__update(_1729342, _1729344), _1729340), _1729348)), _1729346) = _1729348)]]], (37717 ^ _777864) ^ [_1485421, _1485423, _1485425, _1485427] : [class_Orderings_Olinorder(_1485421), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485421, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1485421, _1485423, _1485425)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485421), _1485427)) = c_SetInterval_Oord__class_OatLeastAtMost(_1485421, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1485421), _1485423), _1485427), _1485425))], (45671 ^ _777864) ^ [_1680372, _1680374, _1680376, _1680378, _1680380, _1680382, _1680384] : [hAPP(_1680372, _1680374) = hAPP(c_Option_Ooption_OSome(_1680376), _1680378), -(c_Map_Omap__comp(_1680376, _1680380, _1680382, _1680384, _1680372, _1680374) = hAPP(_1680384, _1680378))], (22626 ^ _777864) ^ [_1169194, _1169196, _1169198] : [hBOOL(hAPP(_1169194, 22627 ^ [_1169194, _1169196, _1169198])), 22630 ^ _777864 : [(22631 ^ _777864) ^ [_1169305, _1169307] : [-(hBOOL(hAPP(_1169194, hAPP(hAPP(c_Product__Type_OPair(_1169196, _1169198), _1169307), _1169305))))]]], (2718 ^ _777864) ^ [_818327, _818329] : [_818329 = _818327, -(c_New__DSequence_Opos__not__seq(_818329) = c_New__DSequence_Opos__not__seq(_818327))], (39325 ^ _777864) ^ [_1521849, _1521851, _1521853] : [-(hAPP(c_Finite__Set_Ofold1(_1521849, _1521851), _1521853) = c_HOL_OThe(_1521849, c_Finite__Set_Ofold1Set(_1521849, _1521851, _1521853)))], (33879 ^ _777864) ^ [_1404094, _1404096, _1404098, _1404100, _1404102, _1404104] : [c_Equiv__Relations_Oequiv(_1404094, _1404096, _1404098), c_Equiv__Relations_Ocongruent(_1404094, tc_fun(_1404100, tc_HOL_Obool), _1404098, _1404102), hBOOL(hAPP(hAPP(c_member(_1404094), _1404104), _1404096)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404094, tc_fun(_1404100, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404094, _1404094, _1404098), hAPP(hAPP(c_Set_Oinsert(_1404094), _1404104), c_Orderings_Obot__class_Obot(tc_fun(_1404094, tc_HOL_Obool))))), _1404102) = hAPP(_1404102, _1404104))], (26793 ^ _777864) ^ [_1250934, _1250936, _1250938] : [-(hBOOL(hAPP(hAPP(c_member(_1250934), _1250936), _1250938))), -(hBOOL(hAPP(hAPP(c_member(_1250934), _1250936), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1250934, tc_HOL_Obool)), _1250938))))], (39171 ^ _777864) ^ [_1518043, _1518045, _1518047, _1518049, _1518051] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518043, _1518045), _1518047), hAPP(hAPP(c_COMBS(_1518043, tc_fun(_1518045, tc_HOL_Obool), tc_fun(_1518045, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518045, tc_HOL_Obool), tc_fun(tc_fun(_1518045, tc_HOL_Obool), tc_fun(_1518045, tc_HOL_Obool)), _1518043), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1518045, tc_HOL_Obool))), _1518049)), _1518051)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518043, _1518045), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518043, _1518045), _1518047), _1518049)), hAPP(hAPP(c_Product__Type_OSigma(_1518043, _1518045), _1518047), _1518051)))], (14610 ^ _777864) ^ [_1024788, _1024790, _1024792] : [-(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), _1024788), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024790), _1024788))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024790, _1024788))), _1024792) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024790), _1024792))], (24071 ^ _777864) ^ [_1198702, _1198704, _1198706, _1198708] : [class_Orderings_Olinorder(_1198702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198702), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198702), _1198704), _1198706)), _1198708)), 24078 ^ _777864 : [(24081 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198702), _1198706), _1198708)))], (24079 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198702), _1198704), _1198708)))]]], (25577 ^ _777864) ^ [_1226416, _1226418, _1226420] : [class_Divides_Osemiring__div(_1226416), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226416), _1226418), _1226420)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226416), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226416), _1226420), _1226418)), _1226418) = _1226420)], (5709 ^ _777864) ^ [_870163, _870165, _870167, _870169, _870171] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_870163, _870165, _870167)), _870169), hAPP(hAPP(hAPP(c_Natural_Oupdate, _870171), c_Com_Ovname_OLoc(_870163)), hAPP(hAPP(c_Natural_Ogetlocs, _870169), _870163))))), 5710 ^ _777864 : [(5711 ^ _777864) ^ [_870292] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _870171), c_Com_Ovname_OLoc(_870163)), hAPP(hAPP(c_Natural_Ogetlocs, _870169), _870163)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _870292), c_Com_Ovname_OLoc(_870163)), hAPP(hAPP(c_Natural_Ogetlocs, _870169), _870163)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870167), hAPP(hAPP(hAPP(c_Natural_Oupdate, _870169), c_Com_Ovname_OLoc(_870163)), hAPP(_870165, _870169))), _870292))]]], (48670 ^ _777864) ^ [_1756183, _1756185, _1756187, _1756189] : [-(hAPP(c_List_Orotate1(_1756185), hAPP(hAPP(c_List_Olist_OCons(_1756185), _1756187), _1756189)) = hAPP(hAPP(c_List_Oappend(_1756185), _1756189), hAPP(hAPP(c_List_Olist_OCons(_1756185), _1756187), c_List_Olist_ONil(_1756185))))], (14199 ^ _777864) ^ [_1018036, _1018038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1018036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018038, _1018036)), _1018036)))], (38950 ^ _777864) ^ [_1512111, _1512113, _1512115, _1512117, _1512119, _1512121] : [c_Typedef_Otype__definition(_1512111, _1512113, _1512115, _1512117, _1512119), hBOOL(hAPP(hAPP(c_member(_1512113), _1512121), _1512119)), -(hAPP(_1512115, hAPP(_1512117, _1512121)) = _1512121)], (14584 ^ _777864) ^ [_1024285, _1024287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1024285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1024287, _1024285)), _1024285)))], (43305 ^ _777864) ^ [_1621247, _1621249] : [-(c_Relation_Orefl__on(_1621247, c_Orderings_Otop__class_Otop(tc_fun(_1621247, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1621247, _1621249)))], (22140 ^ _777864) ^ [_1160624, _1160626, _1160628] : [22142 ^ _777864 : [(22145 ^ _777864) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1160624, _1160626), 22141 ^ [_1160624, _1160626, _1160628]))], (22143 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1160626, 22141 ^ [_1160624, _1160626, _1160628]), _1160628)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1160624, _1160626), _1160628)))], (44134 ^ _777864) ^ [_1643582, _1643584, _1643586, _1643588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643582, _1643582)), hAPP(hAPP(c_Product__Type_OPair(_1643582, _1643582), _1643586), _1643588)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool)), _1643584), c_Relation_OId(_1643582)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1643582, tc_fun(_1643582, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1643582, tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_fun(_1643582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643582, tc_fun(tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_fun(_1643582, tc_HOL_Obool)), _1643582), c_COMBC(_1643582, tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643582, tc_prod(_1643582, _1643582)), tc_fun(_1643582, tc_fun(tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_HOL_Obool)), _1643582), hAPP(c_COMBB(tc_prod(_1643582, _1643582), tc_fun(tc_fun(tc_prod(_1643582, _1643582), tc_HOL_Obool), tc_HOL_Obool), _1643582), c_member(tc_prod(_1643582, _1643582)))), c_Product__Type_OPair(_1643582, _1643582)))), _1643584)), c_fequal), _1643586), _1643588)))], (23759 ^ _777864) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (51435 ^ _777864) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (9356 ^ _777864) ^ [_933830, _933832, _933834, _933836] : [class_Rings_Olinordered__semiring__strict(_933830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933830), _933832), _933834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933830), c_Groups_Ozero__class_Ozero(_933830)), _933836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933830), _933832), _933836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933830), _933834), _933836))))], (48894 ^ _777864) ^ [_1760794, _1760796, _1760798, _1760800] : [class_Groups_Osemigroup__add(_1760794), -(hAPP(c_List_Ofoldl(_1760794, _1760794, c_Groups_Oplus__class_Oplus(_1760794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1760794), _1760796), _1760798)), _1760800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1760794), _1760796), hAPP(c_List_Ofoldl(_1760794, _1760794, c_Groups_Oplus__class_Oplus(_1760794), _1760798), _1760800)))], (17858 ^ _777864) ^ [_1085585] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085585))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085585)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (26833 ^ _777864) ^ [_1251576, _1251578] : [hBOOL(hAPP(hAPP(c_member(_1251576), _1251578), c_Orderings_Obot__class_Obot(tc_fun(_1251576, tc_HOL_Obool))))], (30863 ^ _777864) ^ [_1342224, _1342226, _1342228] : [class_Lattices_Olattice(_1342224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342224), _1342226)), hBOOL(hAPP(hAPP(c_member(_1342224), _1342228), _1342226)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1342224), _1342228), c_Big__Operators_Olattice__class_OSup__fin(_1342224, _1342226)) = c_Big__Operators_Olattice__class_OSup__fin(_1342224, _1342226))], (28310 ^ _777864) ^ [_1283448, _1283450, _1283452] : [-(hAPP(hAPP(c_Set_Oinsert(_1283448), _1283450), _1283452) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283448, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1283448), _1283450), c_Orderings_Obot__class_Obot(tc_fun(_1283448, tc_HOL_Obool)))), _1283452))], (22819 ^ _777864) ^ [_1173021, _1173023, _1173025, _1173027, _1173029] : [-(c_Product__Type_Oprod_Oprod__size(_1173021, _1173023, _1173025, _1173027, _1173029) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1173025, hAPP(c_Product__Type_Ofst(_1173021, _1173023), _1173029))), hAPP(_1173027, hAPP(c_Product__Type_Osnd(_1173021, _1173023), _1173029)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24201 ^ _777864) ^ [_1201759] : [class_Orderings_Olinorder(_1201759), -(c_Orderings_Oord_Omin(_1201759, hAPP(c_COMBC(_1201759, _1201759, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1201759))) = c_Orderings_Oord__class_Omax(_1201759))], (22480 ^ _777864) ^ [_1166460, _1166462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166460), 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)), _1166462)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166460, _1166462) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1166460, _1166462)))], (23875 ^ _777864) ^ [_1195123, _1195125, _1195127] : [class_Orderings_Olinorder(_1195123), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195123), _1195125), _1195127) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195123), _1195127), _1195125))], (46320 ^ _777864) ^ [_1695854, _1695856, _1695858, _1695860] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695854)), _1695856) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695858)), _1695860), -(hAPP(hAPP(c_List_Omap(tc_prod(_1695854, _1695858), _1695854), c_Product__Type_Ofst(_1695854, _1695858)), hAPP(hAPP(c_List_Ozip(_1695854, _1695858), _1695856), _1695860)) = _1695856)], (45737 ^ _777864) ^ [_1681839, _1681841, _1681843, _1681845, _1681847] : [-(c_Map_Omap__comp(_1681839, _1681841, _1681843, _1681845, hAPP(c_COMBK(tc_Option_Ooption(_1681839), _1681843), c_Option_Ooption_ONone(_1681839)), _1681847) = c_Option_Ooption_ONone(_1681841))], (8423 ^ _777864) ^ [_917381, _917383, _917385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917381), _917383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917385)), -(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), _917385)), _917381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917385)), _917383))))], (50847 ^ _777864) ^ [_1803657, _1803659] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803657)), c_List_Oremdups(_1803657, c_List_Oconcat(_1803657, _1803659))) = hAPP(c_Finite__Set_Ocard(_1803657), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1803657), tc_fun(_1803657, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1803657)), _1803659)), c_List_Oset(_1803657))))], (51311 ^ _777864) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (44979 ^ _777864) ^ [_1663695, _1663697] : [class_Complete__Lattice_Ocomplete__lattice(_1663695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1663695), _1663697)), -(c_Complete__Lattice_OSup__class_OSup(_1663695, _1663697) = hAPP(hAPP(c_Finite__Set_Ofold(_1663695, _1663695, c_Lattices_Osemilattice__sup__class_Osup(_1663695)), c_Orderings_Obot__class_Obot(_1663695)), _1663697))], (50512 ^ _777864) ^ [_1795322, _1795324, _1795326] : [hAPP(c_List_Orev(_1795322), _1795324) = hAPP(c_List_Orev(_1795322), _1795326), -(_1795324 = _1795326)], (14680 ^ _777864) ^ [_1026253, _1026255, _1026257] : [class_Divides_Osemiring__div(_1026253), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026253), c_Divides_Odiv__class_Omod(_1026253, _1026255, _1026257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026253), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1026253), _1026255), _1026257)), _1026257)) = _1026255)], (15132 ^ _777864) ^ [_1034648] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034648), _1034648) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16316 ^ _777864) ^ [_1057784, _1057786] : [class_Groups_Oordered__ab__group__add__abs(_1057784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057784), c_Groups_Ozero__class_Ozero(_1057784)), _1057786)), -(hAPP(c_Groups_Oabs__class_Oabs(_1057784), _1057786) = _1057786)], (31841 ^ _777864) ^ [_1359740, _1359742, _1359744] : [class_Orderings_Olinorder(_1359740), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359740), _1359742)), hBOOL(hAPP(hAPP(c_member(_1359740), _1359744), _1359742)), 31852 ^ _777864 : [(31859 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359740, tc_HOL_Obool)), _1359742), hAPP(hAPP(c_Set_Oinsert(_1359740), _1359744), c_Orderings_Obot__class_Obot(tc_fun(_1359740, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359740, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1359740, c_Orderings_Oord__class_Omin(_1359740), _1359742) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1359740), _1359744), c_Big__Operators_Olattice_OInf__fin(_1359740, c_Orderings_Oord__class_Omin(_1359740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359740, tc_HOL_Obool)), _1359742), hAPP(hAPP(c_Set_Oinsert(_1359740), _1359744), c_Orderings_Obot__class_Obot(tc_fun(_1359740, tc_HOL_Obool)))))))], (31853 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1359740, tc_HOL_Obool)), _1359742), hAPP(hAPP(c_Set_Oinsert(_1359740), _1359744), c_Orderings_Obot__class_Obot(tc_fun(_1359740, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1359740, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1359740, c_Orderings_Oord__class_Omin(_1359740), _1359742) = _1359744)]]], (6801 ^ _777864) ^ [_889806, _889808] : [c_Com_Ocom_OAss(_889806, _889808) = c_Com_Ocom_OSKIP], (48312 ^ _777864) ^ [_1746451, _1746453, _1746455, _1746457] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746451), tc_List_Olist(_1746451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746451), tc_List_Olist(_1746451)), _1746453), _1746455)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1746451), c_List_Olistrel1(_1746451, _1746457)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746451)), _1746453) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746451)), _1746455))], (39784 ^ _777864) ^ [_1531564, _1531566, _1531568] : [class_Lattices_Oab__semigroup__idem__mult(_1531564), hAPP(_1531566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1531564), 39789 ^ [_1531564, _1531566, _1531568]), 39790 ^ [_1531564, _1531566, _1531568])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1531564), hAPP(_1531566, 39789 ^ [_1531564, _1531566, _1531568])), hAPP(_1531566, 39790 ^ [_1531564, _1531566, _1531568])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531564), _1531568)), -(_1531568 = c_Orderings_Obot__class_Obot(tc_fun(_1531564, tc_HOL_Obool))), -(hAPP(_1531566, hAPP(c_Finite__Set_Ofold1(_1531564, c_Groups_Otimes__class_Otimes(_1531564)), _1531568)) = hAPP(c_Finite__Set_Ofold1(_1531564, c_Groups_Otimes__class_Otimes(_1531564)), hAPP(c_Set_Oimage(_1531564, _1531564, _1531566), _1531568)))], (11054 ^ _777864) ^ [_961960, _961962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961960)), hAPP(c_Nat_OSuc, _961962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961960), _961962)))], (48820 ^ _777864) ^ [_1759176, _1759178, _1759180] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759176)), hAPP(c_List_Orotate(_1759176, _1759178), _1759180)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759176)), _1759180))], (49562 ^ _777864) ^ [_1775107, _1775109, _1775111] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775107)), hAPP(c_List_Ofilter(_1775107, _1775109), _1775111))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775107)), hAPP(c_List_Ofilter(_1775107, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1775107), c_fNot), _1775109)), _1775111))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775107)), _1775111))], (44716 ^ _777864) ^ [_1657570, _1657572, _1657574] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657570, tc_HOL_Obool)), _1657572), _1657574) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657570, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1657570, tc_HOL_Obool)), _1657572), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1657570, tc_HOL_Obool)), _1657574), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1657570, tc_HOL_Obool), tc_HOL_Obool))))))], (5543 ^ _777864) ^ [_865552, _865554, _865556, _865558, _865560, _865562] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_865552, _865554, _865556), _865558, _865560, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865562), hAPP(c_Natural_Ogetlocs, _865558))), _865552), hAPP(hAPP(c_Natural_Ogetlocs, _865562), c_Com_ORes))), 5547 ^ _777864 : [(5550 ^ _777864) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _865554), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865558), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_865556, _865558)), _865560, 5546 ^ [_865552, _865554, _865556, _865558, _865560, _865562]))], (5548 ^ _777864) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865562), hAPP(c_Natural_Ogetlocs, _865558))), _865552), hAPP(hAPP(c_Natural_Ogetlocs, _865562), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 5546 ^ [_865552, _865554, _865556, _865558, _865560, _865562]), hAPP(c_Natural_Ogetlocs, _865558))), _865552), hAPP(hAPP(c_Natural_Ogetlocs, 5546 ^ [_865552, _865554, _865556, _865558, _865560, _865562]), c_Com_ORes)))]]], (29299 ^ _777864) ^ [_1308204, _1308206, _1308208] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1308204, tc_HOL_Obool), tc_fun(_1308204, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1308204, tc_HOL_Obool), tc_fun(_1308204, tc_HOL_Obool)), _1308206), _1308208)), c_Wellfounded_Ofinite__psubset(_1308204)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1308204, tc_HOL_Obool)), _1308206), _1308208)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308204), _1308208))], (49964 ^ _777864) ^ [_1784067, _1784069, _1784071] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1784067), c_List_Oupt(_1784069, _1784071)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1784069), _1784067), _1784071))], (41772 ^ _777864) ^ [_1587463, _1587465, _1587467, _1587469, _1587471, _1587473] : [-(hAPP(hAPP(c_Fun_Ocomp(_1587463, _1587465, _1587467, hAPP(c_COMBK(_1587465, _1587463), _1587469)), _1587471), _1587473) = _1587469)], (33943 ^ _777864) ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338] : [c_Equiv__Relations_Oequiv(_1405326, _1405328, _1405330), c_Equiv__Relations_Ocongruent(_1405326, tc_fun(_1405332, tc_HOL_Obool), _1405330, _1405334), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405326, tc_fun(_1405332, tc_HOL_Obool)), _1405336), _1405334) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405326, tc_fun(_1405332, tc_HOL_Obool)), _1405338), _1405334), hBOOL(hAPP(hAPP(c_member(tc_fun(_1405326, tc_HOL_Obool)), _1405336), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1405326), _1405328), _1405330))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1405326, tc_HOL_Obool)), _1405338), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1405326), _1405328), _1405330))), 33965 ^ _777864 : [(33969 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405326), 33967 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338]), _1405328)))], (33971 ^ _777864) ^ [] : [-(hAPP(_1405334, 33964 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338]) = hAPP(_1405334, 33967 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338]))], (33973 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1405326, _1405326)), hAPP(hAPP(c_Product__Type_OPair(_1405326, _1405326), 33964 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338]), 33967 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338])), _1405330))], (33966 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405326), 33964 ^ [_1405326, _1405328, _1405330, _1405332, _1405334, _1405336, _1405338]), _1405328)))]], -(_1405336 = _1405338)], (7558 ^ _777864) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28538 ^ _777864) ^ [_1291359, _1291361, _1291363] : [-(hAPP(c_Relation_OImage(_1291359, _1291361, _1291363), c_Orderings_Obot__class_Obot(tc_fun(_1291359, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1291361, tc_HOL_Obool)))], (44265 ^ _777864) ^ [_1647116] : [-(c_Relation_Osingle__valued(_1647116, _1647116, c_Relation_OId(_1647116)))], (24359 ^ _777864) ^ [_1204343, _1204345, _1204347] : [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), _1204343), _1204345))), -(hBOOL(hAPP(hAPP(_1204347, _1204343), _1204345))), 24366 ^ _777864 : [(24369 ^ _777864) ^ [] : [-(24365 ^ [_1204343, _1204345, _1204347] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1204347, 24365 ^ [_1204343, _1204345, _1204347]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 24364 ^ [_1204343, _1204345, _1204347], 24365 ^ [_1204343, _1204345, _1204347]))))], (24375 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1204347, 24364 ^ [_1204343, _1204345, _1204347]), 24365 ^ [_1204343, _1204345, _1204347]))], (24367 ^ _777864) ^ [] : [-(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), 24364 ^ [_1204343, _1204345, _1204347]), 24365 ^ [_1204343, _1204345, _1204347]))))]]], (24549 ^ _777864) ^ [_1208649, _1208651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1208649), _1208651)), -(c_Quickcheck_Obeyond(_1208649, _1208651) = _1208651)], (5820 ^ _777864) ^ [_873450, _873452, _873454, _873456, _873458, _873460] : [c_Com_Ocom_OCall(_873450, _873452, _873454) = c_Com_Ocom_OCall(_873456, _873458, _873460), 5823 ^ _777864 : [(5828 ^ _777864) ^ [] : [-(_873454 = _873460)], (5826 ^ _777864) ^ [] : [-(_873452 = _873458)], (5824 ^ _777864) ^ [] : [-(_873450 = _873456)]]], (23413 ^ _777864) ^ [_1186478, _1186480, _1186482, _1186484] : [class_Groups_Oordered__ab__group__add(_1186478), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186478), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186478), _1186480), _1186482)), _1186484) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1186478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186478), _1186480), _1186484)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1186478), _1186482), _1186484)))], (50154 ^ _777864) ^ [_1787198] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1787198) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1787198)))], (16834 ^ _777864) ^ [_1067972, _1067974, _1067976, _1067978] : [class_Rings_Olinordered__semidom(_1067972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067972), _1067974), _1067976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067972), c_Groups_Ozero__class_Ozero(_1067972)), _1067974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1067978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067972), hAPP(hAPP(c_Power_Opower__class_Opower(_1067972), _1067974), _1067978)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067972), _1067976), _1067978))))], (50797 ^ _777864) ^ [_1802591, _1802593, _1802595, _1802597, _1802599] : [hBOOL(hAPP(hAPP(c_member(_1802591), _1802593), hAPP(c_List_Oset(_1802591), _1802595))), -(hBOOL(hAPP(_1802597, _1802593))), -(c_List_OtakeWhile(_1802591, _1802597, hAPP(hAPP(c_List_Oappend(_1802591), _1802595), _1802599)) = c_List_OtakeWhile(_1802591, _1802597, _1802595))], (26461 ^ _777864) ^ [_1244069] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244069), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244069) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35970 ^ _777864) ^ [_1447097, _1447099, _1447101, _1447103] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447097), _1447099)), 35973 ^ _777864 : [(35974 ^ _777864) ^ [_1447255] : [35976 ^ _777864 : [(35982 ^ _777864) ^ [] : [-(_1447255 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35978 ^ [_1447097, _1447099, _1447101, _1447103, _1447255]), 35975 ^ [_1447097, _1447099, _1447101, _1447103, _1447255]))], (35980 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35978 ^ [_1447097, _1447099, _1447101, _1447103, _1447255]), _1447101)))], (35977 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35975 ^ [_1447097, _1447099, _1447101, _1447103, _1447255]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1447099))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447255), _1447103)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447255), _1447099)), _1447103)))]]], (15620 ^ _777864) ^ [_1044000, _1044002] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044000), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1044002), _1044000)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044002), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1044002, _1044000)))], (5322 ^ _777864) ^ [_859319, _859321] : [_859321 = _859319, -(c_Nat_Osize__class_Osize(_859321) = c_Nat_Osize__class_Osize(_859319))], (46110 ^ _777864) ^ [_1690371, _1690373, _1690375] : [class_Orderings_Olinorder(_1690371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1690371), _1690373)), -(c_List_Olinorder__class_Osorted__list__of__set(_1690371, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1690371, tc_HOL_Obool)), _1690373), hAPP(hAPP(c_Set_Oinsert(_1690371), _1690375), c_Orderings_Obot__class_Obot(tc_fun(_1690371, tc_HOL_Obool))))) = c_List_Oremove1(_1690371, _1690375, c_List_Olinorder__class_Osorted__list__of__set(_1690371, _1690373)))], (21254 ^ _777864) ^ [_1144453, _1144455, _1144457, _1144459] : [class_Fields_Olinordered__field(_1144453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144453), c_Groups_Ozero__class_Ozero(_1144453)), _1144455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144453), _1144457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144453), _1144459), _1144455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144453), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144453), _1144457), _1144455)), _1144459)))], (48121 ^ _777864) ^ [_1741545, _1741547, _1741549] : [_1741545 = hAPP(hAPP(c_List_Oappend(_1741547), _1741549), _1741545), -(_1741549 = c_List_Olist_ONil(_1741547))], (12251 ^ _777864) ^ [_982897, _982899] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982897)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982899)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982897), _982899)))], (27526 ^ _777864) ^ [_1268047, _1268049, _1268051] : [class_Rings_Oring__1(_1268047), hBOOL(hAPP(hAPP(c_member(_1268047), _1268049), c_Int_Oring__1__class_OInts(_1268047))), hBOOL(hAPP(hAPP(c_member(_1268047), _1268051), c_Int_Oring__1__class_OInts(_1268047))), -(hBOOL(hAPP(hAPP(c_member(_1268047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268047), _1268049), _1268051)), c_Int_Oring__1__class_OInts(_1268047))))], (15616 ^ _777864) ^ [_1043907, _1043909] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043907), hAPP(c_Nat_OSuc, _1043909)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043907), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1043909))], (26511 ^ _777864) ^ [_1244940, _1244942] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244940)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244942))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244942), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244940)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8052 ^ _777864) ^ [] : [-(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)))], (43463 ^ _777864) ^ [_1624954, _1624956] : [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), _1624954), _1624956)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1624954), _1624956)))], (43899 ^ _777864) ^ [_1636710, _1636712, _1636714, _1636716, _1636718] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636710, _1636712)), hAPP(hAPP(c_Product__Type_OPair(_1636710, _1636712), _1636714), _1636716)), _1636718)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636712, _1636710)), hAPP(hAPP(c_Product__Type_OPair(_1636712, _1636710), _1636716), _1636714)), hAPP(c_Relation_Oconverse(_1636710, _1636712), _1636718))))], (3858 ^ _777864) ^ [_836551, _836553, _836555, _836557, _836559, _836561, _836563, _836565, _836567, _836569] : [-(c_Finite__Set_Ofold__graph(_836569, _836565, _836561, _836557, _836553) = c_Finite__Set_Ofold__graph(_836567, _836563, _836559, _836555, _836551)), _836569 = _836567, _836565 = _836563, _836561 = _836559, _836557 = _836555, _836553 = _836551], (17044 ^ _777864) ^ [_1071676, _1071678] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071676), _1071678)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1071676)), _1071678))], (51133 ^ _777864) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (48850 ^ _777864) ^ [_1759799, _1759801, _1759803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759799)), _1759801)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1759799, _1759803), _1759801) = _1759801)], (51399 ^ _777864) ^ [_1810829, _1810831] : [-(class_Finite__Set_Ofinite(tc_sum(_1810829, _1810831))), class_Finite__Set_Ofinite(_1810829), class_Finite__Set_Ofinite(_1810831)], (41212 ^ _777864) ^ [_1573556, _1573558, _1573560, _1573562] : [hBOOL(hAPP(hAPP(c_member(_1573556), _1573558), hAPP(c_Relation_ORange(_1573560, _1573556), _1573562))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573560, _1573556)), hAPP(hAPP(c_Product__Type_OPair(_1573560, _1573556), 41215 ^ [_1573556, _1573558, _1573560, _1573562]), _1573558)), _1573562)))], (18488 ^ _777864) ^ [_1095845] : [c_Int_OMin = c_Int_OBit1(_1095845), -(c_Int_OMin = _1095845)], (35249 ^ _777864) ^ [_1433280, _1433282] : [35251 ^ _777864 : [(35254 ^ _777864) ^ [] : [hBOOL(hAPP(_1433282, 35250 ^ [_1433280, _1433282]))], (35252 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35250 ^ [_1433280, _1433282]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1433280))))]], 35255 ^ _777864 : [(35256 ^ _777864) ^ [_1433435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1433435), _1433280)), -(hBOOL(hAPP(_1433282, _1433435)))]]], (18944 ^ _777864) ^ [_1103473] : [-(c_Int_OBit0(_1103473) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1103473), _1103473))], (24685 ^ _777864) ^ [_1210878, _1210880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210878)), hAPP(c_Code__Numeral_Onat__of, _1210880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1210878), _1210880)))], (15270 ^ _777864) ^ [_1037176, _1037178, _1037180] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037176), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1037178, _1037180)), _1037180) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037176), _1037178), _1037180))], (24455 ^ _777864) ^ [_1206273, _1206275] : [-(c_Nitpick_Oinverse__frac(_1206273, _1206275) = hAPP(hAPP(c_Nitpick_Ofrac(_1206273), hAPP(c_Nitpick_Odenom(_1206273), _1206275)), hAPP(c_Nitpick_Onum(_1206273), _1206275)))], (24921 ^ _777864) ^ [_1215423, _1215425] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215423), _1215425)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215425), _1215423))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215425), _1215423)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215423), _1215425)))], (8488 ^ _777864) ^ [_918538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918538), 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)), _918538)), _918538)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19016 ^ _777864) ^ [_1104747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1104747)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104747), c_Int_OPls)))], (1672 ^ _777864) ^ [_801532, _801534] : [-(class_Rings_Osemiring__0(_801532)), _801534 = _801532, class_Rings_Osemiring__0(_801534)], (38382 ^ _777864) ^ [_1498287] : [class_Lattices_Oboolean__algebra(_1498287), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1498287), c_Orderings_Obot__class_Obot(_1498287)) = c_Orderings_Otop__class_Otop(_1498287))], (36240 ^ _777864) ^ [_1452415, _1452417, _1452419, _1452421] : [class_Orderings_Olinorder(_1452415), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452415, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1452415, _1452417, _1452419)), hAPP(c_SetInterval_Oord__class_OatMost(_1452415), _1452421)) = c_SetInterval_Oord__class_OatLeastAtMost(_1452415, _1452417, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1452415), _1452419), _1452421)))], (3826 ^ _777864) ^ [_836075, _836077, _836079, _836081, _836083, _836085] : [-(c_Set_Ovimage(_836085, _836081, _836077) = c_Set_Ovimage(_836083, _836079, _836075)), _836085 = _836083, _836081 = _836079, _836077 = _836075], (34561 ^ _777864) ^ [_1419856, _1419858] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1419856, _1419858) = 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), _1419856), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1419858))))], (34481 ^ _777864) ^ [_1417866, _1417868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417866), _1417868)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1417866, tc_HOL_Obool)), hAPP(c_Set_OPow(_1417866), _1417868))))], (40252 ^ _777864) ^ [_1542252, _1542254, _1542256] : [-(hBOOL(hAPP(_1542252, _1542254))), -(hAPP(c_Set_OCollect(_1542256), hAPP(hAPP(c_COMBS(_1542256, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542256), c_fconj), hAPP(c_fequal, _1542254))), _1542252)) = c_Orderings_Obot__class_Obot(tc_fun(_1542256, tc_HOL_Obool)))], (41126 ^ _777864) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (26885 ^ _777864) ^ [_1252506, _1252508, _1252510] : [hBOOL(hAPP(hAPP(c_member(_1252506), _1252508), _1252510)), -(hAPP(hAPP(c_Set_Oinsert(_1252506), _1252508), _1252510) = _1252510)], (6759 ^ _777864) ^ [_889218, _889220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889218), hAPP(c_Nat_OSuc, _889220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889218), _889220))), -(_889218 = _889220)], (29279 ^ _777864) ^ [_1307679, _1307681, _1307683, _1307685] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307679, tc_HOL_Obool)), _1307681), hAPP(hAPP(c_Set_Oinsert(_1307679), _1307683), _1307685)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307679, tc_HOL_Obool)), _1307681), _1307685))))], (31647 ^ _777864) ^ [_1356177, _1356179, _1356181] : [class_Orderings_Olinorder(_1356177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356177), _1356179)), -(_1356181 = c_Orderings_Obot__class_Obot(tc_fun(_1356177, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356177, tc_HOL_Obool)), _1356181), _1356179)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1356177), c_Big__Operators_Olinorder__class_OMin(_1356177, _1356181)), c_Big__Operators_Olinorder__class_OMin(_1356177, _1356179)) = c_Big__Operators_Olinorder__class_OMin(_1356177, _1356179))], (28366 ^ _777864) ^ [_1285817, _1285819, _1285821, _1285823, _1285825, _1285827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1285817, _1285819)), hAPP(hAPP(c_Product__Type_OPair(_1285817, _1285819), _1285825), _1285827)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool)), _1285821), _1285823))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285817, tc_fun(_1285819, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1285817, tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_fun(_1285819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285819, tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_fun(_1285819, tc_HOL_Obool)), _1285817), c_COMBC(_1285819, tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285819, tc_prod(_1285817, _1285819)), tc_fun(_1285819, tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), _1285817), hAPP(c_COMBB(tc_prod(_1285817, _1285819), tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool), _1285819), c_member(tc_prod(_1285817, _1285819)))), c_Product__Type_OPair(_1285817, _1285819)))), _1285821)), hAPP(hAPP(c_COMBC(_1285817, tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_fun(_1285819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285819, tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_fun(_1285819, tc_HOL_Obool)), _1285817), c_COMBC(_1285819, tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285819, tc_prod(_1285817, _1285819)), tc_fun(_1285819, tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool)), _1285817), hAPP(c_COMBB(tc_prod(_1285817, _1285819), tc_fun(tc_fun(tc_prod(_1285817, _1285819), tc_HOL_Obool), tc_HOL_Obool), _1285819), c_member(tc_prod(_1285817, _1285819)))), c_Product__Type_OPair(_1285817, _1285819)))), _1285823)), _1285825), _1285827)))], (7550 ^ _777864) ^ [_903072, _903074, _903076, _903078, _903080] : [-(c_Option_Ooption_Ooption__rec(_903072, _903074, _903076, _903078, hAPP(c_Option_Ooption_OSome(_903074), _903080)) = hAPP(_903078, _903080))], (50566 ^ _777864) ^ [_1796291, _1796293, _1796295] : [-(hAPP(c_List_Orev(_1796291), hAPP(hAPP(c_List_Odrop(_1796291), _1796293), _1796295)) = hAPP(hAPP(c_List_Otake(_1796291), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796291)), _1796295)), _1796293)), hAPP(c_List_Orev(_1796291), _1796295)))], (2860 ^ _777864) ^ [_820694, _820696, _820698, _820700, _820702, _820704, _820706, _820708, _820710, _820712, _820714, _820716, _820718, _820720] : [-(c_New__Random__Sequence_Oneg__decr__bind(_820720, _820716, _820712, _820708, _820704, _820700, _820696) = c_New__Random__Sequence_Oneg__decr__bind(_820718, _820714, _820710, _820706, _820702, _820698, _820694)), _820720 = _820718, _820716 = _820714, _820712 = _820710, _820708 = _820706, _820704 = _820702, _820700 = _820698, _820696 = _820694], (23793 ^ _777864) ^ [_1193677, _1193679, _1193681, _1193683] : [class_Orderings_Olinorder(_1193677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193677), _1193679), _1193681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193677), _1193679), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193677), _1193681), _1193683))))], (2280 ^ _777864) ^ [_811468, _811470, _811472, _811474] : [-(c_Groups_Osgn__class_Osgn(_811474, _811470) = c_Groups_Osgn__class_Osgn(_811472, _811468)), _811474 = _811472, _811470 = _811468], (2944 ^ _777864) ^ [_822186, _822188, _822190, _822192, _822194, _822196, _822198, _822200] : [-(c_New__DSequence_Oneg__bind(_822200, _822196, _822192, _822188) = c_New__DSequence_Oneg__bind(_822198, _822194, _822190, _822186)), _822200 = _822198, _822196 = _822194, _822192 = _822190, _822188 = _822186], (44931 ^ _777864) ^ [_1662700, _1662702, _1662704] : [class_Complete__Lattice_Ocomplete__lattice(_1662700), -(c_Complete__Lattice_OSup__class_OSup(_1662700, hAPP(hAPP(c_Set_Oinsert(_1662700), _1662702), _1662704)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1662700), _1662702), c_Complete__Lattice_OSup__class_OSup(_1662700, _1662704)))], (45725 ^ _777864) ^ [_1681459] : [-(hAPP(c_List_Omap(_1681459, _1681459), c_Fun_Oid(_1681459)) = c_Fun_Oid(tc_List_Olist(_1681459)))], (50439 ^ _777864) ^ [_1793649, _1793651] : [50441 ^ _777864 : [(50444 ^ _777864) ^ [] : [50440 ^ [_1793649, _1793651] = c_List_Olist_ONil(_1793649)], (50442 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1793649)), 50440 ^ [_1793649, _1793651]), hAPP(c_List_Oset(tc_List_Olist(_1793649)), _1793651))))]], -(c_List_Oconcat(_1793649, _1793651) = c_List_Olist_ONil(_1793649))], (24641 ^ _777864) ^ [_1210126, _1210128] : [_1210126 = _1210128, -(hAPP(c_Code__Numeral_Onat__of, _1210126) = hAPP(c_Code__Numeral_Onat__of, _1210128))], (39552 ^ _777864) ^ [_1526540, _1526542, _1526544] : [class_Lattices_Oab__semigroup__idem__mult(_1526540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526540), _1526542)), -(_1526542 = c_Orderings_Obot__class_Obot(tc_fun(_1526540, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526540), _1526544)), -(_1526544 = c_Orderings_Obot__class_Obot(tc_fun(_1526540, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1526540, c_Groups_Otimes__class_Otimes(_1526540)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526540, tc_HOL_Obool)), _1526542), _1526544)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1526540), hAPP(c_Finite__Set_Ofold1(_1526540, c_Groups_Otimes__class_Otimes(_1526540)), _1526542)), hAPP(c_Finite__Set_Ofold1(_1526540, c_Groups_Otimes__class_Otimes(_1526540)), _1526544)))], (4610 ^ _777864) ^ [_848321, _848323] : [_848323 = _848321, -(c_Set_OCollect(_848323) = c_Set_OCollect(_848321))], (8188 ^ _777864) ^ [_913801] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _913801) = _913801)], (28615 ^ _777864) ^ [_1293238, _1293240, _1293242, _1293244] : [_1293238 = c_Orderings_Obot__class_Obot(tc_fun(_1293240, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1293240, _1293242, hAPP(c_COMBK(_1293242, _1293240), _1293244)), _1293238) = c_Orderings_Obot__class_Obot(tc_fun(_1293242, tc_HOL_Obool)))], (48912 ^ _777864) ^ [_1761197, _1761199, _1761201, _1761203] : [-(hAPP(c_List_Ofoldl(_1761197, _1761199, _1761201, _1761203), c_List_Olist_ONil(_1761199)) = _1761203)], (49468 ^ _777864) ^ [_1773159, _1773161, _1773163, _1773165] : [-(hAPP(hAPP(c_List_Oappend(_1773159), _1773161), hAPP(hAPP(c_List_Olist_OCons(_1773159), _1773163), c_List_Olist_ONil(_1773159))) = _1773165), -(_1773165 = c_List_Olist_ONil(_1773159)), c_List_Obutlast(_1773159, _1773165) = _1773161, c_List_Olast(_1773159, _1773165) = _1773163], (40797 ^ _777864) ^ [_1562734, _1562736, _1562738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562734, _1562734), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1562734, _1562734, _1562734), _1562736), _1562738)), _1562736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1562734, _1562736)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1562734, _1562738)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1562734, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1562734, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1562734, tc_HOL_Obool), tc_fun(_1562734, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1562734, _1562736))))], (42184 ^ _777864) ^ [_1597017, _1597019, _1597021, _1597023] : [-(c_Random__Sequence_Omap(_1597017, _1597019, _1597021, _1597023) = c_Random__Sequence_Obind(_1597017, _1597019, _1597023, hAPP(c_Fun_Ocomp(_1597019, 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(_1597019)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1597017, c_Random__Sequence_Osingle(_1597019)), _1597021)))], (38452 ^ _777864) ^ [_1499621, _1499623] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499621), c_Orderings_Otop__class_Otop(tc_fun(_1499621, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1499621, _1499621, _1499623), c_Orderings_Otop__class_Otop(tc_fun(_1499621, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1499621, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1499621, _1499621, _1499623, c_Orderings_Otop__class_Otop(tc_fun(_1499621, tc_HOL_Obool))))], (41564 ^ _777864) ^ [_1582263, _1582265, _1582267, _1582269] : [41566 ^ _777864 : [(41569 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582263, _1582263, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1582263, tc_fun(_1582263, _1582265), tc_fun(_1582263, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582265, tc_HOL_Obool), tc_fun(tc_fun(_1582263, _1582265), tc_fun(_1582263, tc_HOL_Obool)), _1582263), c_COMBB(_1582265, tc_HOL_Obool, _1582263)), hAPP(hAPP(c_COMBB(_1582265, tc_fun(_1582265, tc_HOL_Obool), _1582263), c_fequal), _1582269))), _1582269)), 41565 ^ [_1582263, _1582265, _1582267, _1582269]))], (41567 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582263, _1582263)), 41565 ^ [_1582263, _1582265, _1582267, _1582269]), _1582267)))]], -(c_Equiv__Relations_Ocongruent(_1582263, _1582265, _1582267, _1582269))], (43743 ^ _777864) ^ [_1631847, _1631849, _1631851, _1631853] : [-(hAPP(c_Relation_Oconverse(_1631847, _1631847), hAPP(hAPP(c_Relation_Oinv__image(_1631849, _1631847), _1631851), _1631853)) = hAPP(hAPP(c_Relation_Oinv__image(_1631849, _1631847), hAPP(c_Relation_Oconverse(_1631849, _1631849), _1631851)), _1631853))], (24741 ^ _777864) ^ [_1212055, _1212057, _1212059, _1212061, _1212063, _1212065] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1212055, _1212057, _1212059, _1212061), _1212063), _1212065) = hAPP(_1212061, hAPP(hAPP(c_Product__Type_OPair(_1212055, _1212057), _1212063), _1212065)))], (3778 ^ _777864) ^ [_835373, _835375] : [_835375 = _835373, -(c_SetInterval_Oord__class_OgreaterThan(_835375) = c_SetInterval_Oord__class_OgreaterThan(_835373))], (19860 ^ _777864) ^ [_1120175, _1120177] : [c_Nat__Transfer_Ois__nat(_1120175), c_Nat__Transfer_Ois__nat(_1120177), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120175, _1120177)))], (6615 ^ _777864) ^ [_887080, _887082] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887080), _887082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6618 ^ _777864 : [(6621 ^ _777864) ^ [] : [-(_887082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6619 ^ _777864) ^ [] : [-(_887080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16796 ^ _777864) ^ [_1067146, _1067148, _1067150, _1067152] : [class_Int_Onumber__ring(_1067146), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067146), hAPP(c_Int_Onumber__class_Onumber__of(_1067146), _1067148)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067146), hAPP(c_Int_Onumber__class_Onumber__of(_1067146), _1067150)), _1067152)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067146), hAPP(c_Int_Onumber__class_Onumber__of(_1067146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067148), _1067150))), _1067152))], (38585 ^ _777864) ^ [] : [-(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))], (4468 ^ _777864) ^ [_846198, _846200, _846202, _846204] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_846204, _846200) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_846202, _846198)), _846204 = _846202, _846200 = _846198], (46037 ^ _777864) ^ [_1689009, _1689011, _1689013, _1689015, _1689017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1689009, _1689011)), hAPP(hAPP(c_Product__Type_OPair(_1689009, _1689011), _1689013), _1689015)), hAPP(c_List_Oset(tc_prod(_1689009, _1689011)), _1689017))), -(hAPP(c_Map_Omap__of(_1689009, _1689011, _1689017), _1689013) = hAPP(c_Option_Ooption_OSome(_1689011), 46040 ^ [_1689009, _1689011, _1689013, _1689015, _1689017]))], (13238 ^ _777864) ^ [_1000168, _1000170, _1000172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000168)), 13241 ^ _777864 : [(13248 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000170), _1000172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000168), _1000170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000168), _1000172))))], (13242 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000168), _1000170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000168), _1000172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000170), _1000172)))]]], (23401 ^ _777864) ^ [_1186248, _1186250, _1186252, _1186254, _1186256] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186248, _1186250, tc_HOL_Obool), _1186252), hAPP(hAPP(c_Product__Type_OPair(_1186248, _1186250), _1186254), _1186256))), -(hBOOL(hAPP(hAPP(_1186252, _1186254), _1186256)))], (17932 ^ _777864) ^ [_1087014] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087014) = 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(_1087014)))))], (37403 ^ _777864) ^ [_1479180, _1479182, _1479184, _1479186, _1479188] : [class_Groups_Oordered__ab__group__add(_1479180), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479182), _1479184)), 37413 ^ _777864 : [(37416 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479180), c_Groups_Ozero__class_Ozero(_1479180)), hAPP(_1479186, 37412 ^ [_1479180, _1479182, _1479184, _1479186, _1479188])))], (37414 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479182), 37412 ^ [_1479180, _1479182, _1479184, _1479186, _1479188]), _1479184)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479182, _1479180), _1479186), _1479184) = c_Groups_Ozero__class_Ozero(_1479180), hBOOL(hAPP(hAPP(c_member(_1479182), _1479188), _1479184)), -(hAPP(_1479186, _1479188) = c_Groups_Ozero__class_Ozero(_1479180))], (31375 ^ _777864) ^ [_1350956, _1350958, _1350960] : [class_Orderings_Olinorder(_1350956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350956), _1350958)), 31382 ^ _777864 : [(31389 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350956, tc_HOL_Obool)), _1350958), hAPP(hAPP(c_Set_Oinsert(_1350956), _1350960), c_Orderings_Obot__class_Obot(tc_fun(_1350956, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350956, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1350956, hAPP(hAPP(c_Set_Oinsert(_1350956), _1350960), _1350958)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1350956), _1350960), c_Big__Operators_Olinorder__class_OMax(_1350956, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350956, tc_HOL_Obool)), _1350958), hAPP(hAPP(c_Set_Oinsert(_1350956), _1350960), c_Orderings_Obot__class_Obot(tc_fun(_1350956, tc_HOL_Obool)))))))], (31383 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350956, tc_HOL_Obool)), _1350958), hAPP(hAPP(c_Set_Oinsert(_1350956), _1350960), c_Orderings_Obot__class_Obot(tc_fun(_1350956, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1350956, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1350956, hAPP(hAPP(c_Set_Oinsert(_1350956), _1350960), _1350958)) = _1350960)]]], (26775 ^ _777864) ^ [_1250599, _1250601, _1250603, _1250605] : [hBOOL(hAPP(hAPP(c_member(_1250599), _1250601), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250599, tc_HOL_Obool)), _1250603), _1250605))), 26778 ^ _777864 : [(26781 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1250599), _1250601), _1250605))], (26779 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1250599), _1250601), _1250603)))]]], (24383 ^ _777864) ^ [_1204914, _1204916, _1204918, _1204920, _1204922, _1204924] : [-(c_Nitpick_Opair__box_Opair__box__size(_1204914, _1204916, _1204918, _1204920, c_Nitpick_Opair__box_OPairBox(_1204914, _1204916, _1204922, _1204924)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1204918, _1204922)), hAPP(_1204920, _1204924))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7745 ^ _777864) ^ [_906393, _906395, _906397] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_906393, _906395)), _906397), _906397)), hBOOL(hAPP(_906393, _906397)), 7753 ^ _777864 : [(7756 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_906393, _906395)), 7752 ^ [_906393, _906395, _906397]), _906397)))], (7754 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_906395), _906397), 7752 ^ [_906393, _906395, _906397])))]]], (22855 ^ _777864) ^ [_1173849, _1173851, _1173853] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173849, tc_HOL_Obool)), _1173851) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173849, tc_HOL_Obool)), _1173853), -(_1173851 = _1173853)], (47558 ^ _777864) ^ [_1728636, _1728638] : [_1728638 = c_List_Olist_ONil(_1728636), -(hAPP(c_List_Oset(_1728636), _1728638) = c_Orderings_Obot__class_Obot(tc_fun(_1728636, tc_HOL_Obool)))], (5868 ^ _777864) ^ [_874221, _874223, _874225, _874227, _874229, _874231] : [c_Com_Ocom_OLocal(_874221, _874223, _874225) = c_Com_Ocom_OLocal(_874227, _874229, _874231), 5871 ^ _777864 : [(5876 ^ _777864) ^ [] : [-(_874225 = _874231)], (5874 ^ _777864) ^ [] : [-(_874223 = _874229)], (5872 ^ _777864) ^ [] : [-(_874221 = _874227)]]], (49374 ^ _777864) ^ [_1771396, _1771398, _1771400] : [_1771396 = c_List_Olist_ONil(_1771398), -(c_List_Obutlast(_1771398, hAPP(hAPP(c_List_Oappend(_1771398), _1771400), _1771396)) = c_List_Obutlast(_1771398, _1771400))], (50338 ^ _777864) ^ [_1791261, _1791263] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1791261)), c_List_Otranspose__rel(_1791261)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1791261)), c_List_Olist_ONil(_1791261)), _1791263))), -(c_List_Otranspose(_1791261, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1791261)), c_List_Olist_ONil(_1791261)), _1791263)) = c_List_Otranspose(_1791261, _1791263))], (7232 ^ _777864) ^ [_896814, _896816, _896818, _896820] : [c_Com_Ocom_OSemi(_896814, _896816) = c_Com_Ocom_OSemi(_896818, _896820), 7235 ^ _777864 : [(7238 ^ _777864) ^ [] : [-(_896816 = _896820)], (7236 ^ _777864) ^ [] : [-(_896814 = _896818)]]], (38834 ^ _777864) ^ [_1509581, _1509583, _1509585, _1509587] : [-(hBOOL(hAPP(hAPP(c_member(_1509581), _1509583), _1509585))), -(hAPP(c_Set_Ovimage(_1509587, _1509581, hAPP(c_COMBK(_1509581, _1509587), _1509583)), _1509585) = c_Orderings_Obot__class_Obot(tc_fun(_1509587, tc_HOL_Obool)))], (42722 ^ _777864) ^ [_1608742, _1608744, _1608746, _1608748, _1608750] : [c_Finite__Set_Ofolding__one__idem(_1608742, _1608744, _1608746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608742), _1608748)), -(hAPP(_1608746, hAPP(hAPP(c_Set_Oinsert(_1608742), _1608750), _1608748)) = hAPP(hAPP(c_Finite__Set_Ofold(_1608742, _1608742, _1608744), _1608750), _1608748))], (17560 ^ _777864) ^ [_1081033, _1081035] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081033)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081033)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081035)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081033)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1081035))))], (26637 ^ _777864) ^ [_1247614] : [-(c_Option_Oset(_1247614, c_Option_Ooption_ONone(_1247614)) = c_Orderings_Obot__class_Obot(tc_fun(_1247614, tc_HOL_Obool)))], (5519 ^ _777864) ^ [_864976, _864978, _864980, _864982] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _864976)), _864978, _864980, _864982), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _864976), _864978, hAPP(c_Nat_OSuc, _864980), _864982))], (48822 ^ _777864) ^ [_1759223, _1759225, _1759227] : [-(hAPP(c_List_Orotate(_1759223, _1759225), _1759227) = hAPP(c_List_Orotate(_1759223, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1759225, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759223)), _1759227))), _1759227))], (30717 ^ _777864) ^ [_1339563, _1339565, _1339567] : [class_Lattices_Olattice(_1339563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339563), _1339565)), hBOOL(hAPP(hAPP(c_member(_1339563), _1339567), _1339565)), 30728 ^ _777864 : [(30735 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339563, tc_HOL_Obool)), _1339565), hAPP(hAPP(c_Set_Oinsert(_1339563), _1339567), c_Orderings_Obot__class_Obot(tc_fun(_1339563, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1339563, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1339563, _1339565) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1339563), _1339567), c_Big__Operators_Olattice__class_OInf__fin(_1339563, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339563, tc_HOL_Obool)), _1339565), hAPP(hAPP(c_Set_Oinsert(_1339563), _1339567), c_Orderings_Obot__class_Obot(tc_fun(_1339563, tc_HOL_Obool)))))))], (30729 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339563, tc_HOL_Obool)), _1339565), hAPP(hAPP(c_Set_Oinsert(_1339563), _1339567), c_Orderings_Obot__class_Obot(tc_fun(_1339563, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1339563, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1339563, _1339565) = _1339567)]]], (11066 ^ _777864) ^ [_962176, _962178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962176), _962178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962176), hAPP(c_Nat_OSuc, _962178))))], (8170 ^ _777864) ^ [_913519, _913521] : [_913519 = _913521, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913519) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913521))], (29880 ^ _777864) ^ [_1320435, _1320437, _1320439, _1320441] : [hBOOL(hAPP(hAPP(c_member(_1320435), _1320437), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320435, tc_HOL_Obool)), _1320439), _1320441))), 29883 ^ _777864 : [(29886 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320435), _1320437), _1320441)))], (29884 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1320435), _1320437), _1320439)))]]], (49506 ^ _777864) ^ [_1774110, _1774112, _1774114] : [49508 ^ _777864 : [(49511 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1774112, 49507 ^ [_1774110, _1774112, _1774114])))], (49509 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774110), 49507 ^ [_1774110, _1774112, _1774114]), hAPP(c_List_Oset(_1774110), _1774114))))]], -(hAPP(c_List_Ofilter(_1774110, _1774112), _1774114) = c_List_Olist_ONil(_1774110))], (2926 ^ _777864) ^ [_821885, _821887, _821889, _821891, _821893, _821895, _821897, _821899] : [-(c_Lazy__Sequence_Ohb__bind(_821899, _821895, _821891, _821887) = c_Lazy__Sequence_Ohb__bind(_821897, _821893, _821889, _821885)), _821899 = _821897, _821895 = _821893, _821891 = _821889, _821887 = _821885], (14876 ^ _777864) ^ [_1029864, _1029866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029864), _1029866)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029866), _1029864) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1029866), _1029864)), _1029864)))], (42374 ^ _777864) ^ [_1601261, _1601263, _1601265, _1601267] : [class_Groups_Ocomm__monoid__mult(_1601261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1601263), _1601265)), 42384 ^ _777864 : [(42387 ^ _777864) ^ [] : [hAPP(_1601267, 42383 ^ [_1601261, _1601263, _1601265, _1601267]) = c_Groups_Oone__class_Oone(_1601261)], (42385 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601263), 42383 ^ [_1601261, _1601263, _1601265, _1601267]), _1601265)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1601261, _1601263, c_Groups_Otimes__class_Otimes(_1601261)), _1601267), c_Groups_Oone__class_Oone(_1601261)), _1601265) = c_Groups_Oone__class_Oone(_1601261))], (51337 ^ _777864) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (38722 ^ _777864) ^ [_1506894, _1506896, _1506898, _1506900, _1506902] : [hBOOL(hAPP(_1506900, hAPP(_1506898, _1506902))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1506894, _1506896, _1506898), _1506900), _1506902)))], (22600 ^ _777864) ^ [_1168672, _1168674, _1168676, _1168678, _1168680, _1168682] : [hAPP(hAPP(c_Product__Type_OPair(_1168672, _1168674), _1168676), _1168678) = hAPP(hAPP(c_Product__Type_OPair(_1168672, _1168674), _1168680), _1168682), 22603 ^ _777864 : [(22606 ^ _777864) ^ [] : [-(_1168678 = _1168682)], (22604 ^ _777864) ^ [] : [-(_1168676 = _1168680)]]], (7659 ^ _777864) ^ [_904788, _904790, _904792, _904794] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_904788, _904790), _904792, _904794, _904792)), 7660 ^ _777864 : [(7663 ^ _777864) ^ [_904875] : [c_Natural_Oevaln(_904790, _904792, _904794, _904875), c_Natural_Oevaln(c_Com_Ocom_OWhile(_904788, _904790), _904875, _904794, _904792)], (7661 ^ _777864) ^ [] : [-(hBOOL(hAPP(_904788, _904792)))]]], (41944 ^ _777864) ^ [_1591218, _1591220, _1591222, _1591224, _1591226] : [c_Hoare__Mirabelle_Ohoare__valids(_1591218, _1591220, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1591218)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1591218), c_Hoare__Mirabelle_Opeek__and(_1591218, _1591222, _1591224)), _1591226), _1591222)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1591218), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1591218, _1591220, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1591218)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1591218), _1591222), c_Com_Ocom_OWhile(_1591224, _1591226)), c_Hoare__Mirabelle_Opeek__and(_1591218, _1591222, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1591224)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1591218), tc_HOL_Obool)))))], (29792 ^ _777864) ^ [_1318713, _1318715, _1318717, _1318719] : [class_Lattices_Osemilattice__inf(_1318713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318713), _1318715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318713), _1318717), _1318719))), 29799 ^ _777864 : [(29802 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318713), _1318715), _1318719)))], (29800 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318713), _1318715), _1318717)))]]], (10504 ^ _777864) ^ [_953299, _953301, _953303, _953305] : [class_Orderings_Oorder(_953299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953299), _953301), _953303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953299), _953305), _953301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953299), _953305), _953303)))], (43729 ^ _777864) ^ [_1631259, _1631261, _1631263, _1631265, _1631267, _1631269, _1631271] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631259, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631261, tc_fun(_1631259, tc_HOL_Obool)), _1631263), _1631265)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631267, tc_fun(_1631259, tc_HOL_Obool)), _1631269), _1631271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631261, tc_fun(_1631259, tc_HOL_Obool)), _1631263), hAPP(hAPP(c_COMBB(tc_fun(_1631267, tc_fun(_1631259, tc_HOL_Obool)), tc_fun(_1631259, tc_HOL_Obool), _1631261), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631267, tc_fun(_1631259, tc_HOL_Obool)), _1631269)), hAPP(hAPP(c_COMBC(_1631261, tc_fun(_1631267, tc_fun(_1631259, tc_HOL_Obool)), tc_fun(_1631267, tc_fun(_1631259, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1631259, tc_HOL_Obool), tc_fun(_1631259, tc_HOL_Obool)), tc_fun(tc_fun(_1631267, tc_fun(_1631259, tc_HOL_Obool)), tc_fun(_1631267, tc_fun(_1631259, tc_HOL_Obool))), _1631261), c_COMBB(tc_fun(_1631259, tc_HOL_Obool), tc_fun(_1631259, tc_HOL_Obool), _1631267)), hAPP(hAPP(c_COMBB(tc_fun(_1631259, tc_HOL_Obool), tc_fun(tc_fun(_1631259, tc_HOL_Obool), tc_fun(_1631259, tc_HOL_Obool)), _1631261), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631259, tc_HOL_Obool))), _1631265))), _1631271))))], (29638 ^ _777864) ^ [_1315955, _1315957, _1315959, _1315961, _1315963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315955, tc_HOL_Obool)), _1315957), _1315959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315955, tc_HOL_Obool)), _1315961), _1315963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315955, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315955, tc_HOL_Obool)), _1315957), _1315961)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315955, tc_HOL_Obool)), _1315959), _1315963))))], (44186 ^ _777864) ^ [_1645163, _1645165, _1645167] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1645163, _1645163, _1645165), c_Relation_OId(_1645163)), _1645167) = _1645167)], (1222 ^ _777864) ^ [_795907, _795909] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_795907)), _795909 = _795907, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_795909)], (50947 ^ _777864) ^ [_1805415, _1805417] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805415)), c_List_Oremdups(_1805415, _1805417)) = hAPP(c_Finite__Set_Ocard(_1805415), hAPP(c_List_Oset(_1805415), _1805417)))], (22598 ^ _777864) ^ [_1168635, _1168637] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1168635), _1168637) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1168635, _1168637)))], (5916 ^ _777864) ^ [_875094] : [hAPP(c_Nat_OSuc, _875094) = _875094], (47494 ^ _777864) ^ [_1727478, _1727480, _1727482, _1727484] : [-(c_List_Ofoldr(_1727478, _1727480, _1727482, c_List_Olist_ONil(_1727478), _1727484) = _1727484)], (37929 ^ _777864) ^ [_1489621, _1489623, _1489625, _1489627] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489621, _1489623, _1489625, _1489627, c_Orderings_Obot__class_Obot(tc_fun(_1489621, tc_HOL_Obool))), _1489627)))], (18782 ^ _777864) ^ [_1100426, _1100428] : [class_Int_Onumber__ring(_1100426), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100426), hAPP(c_Int_Onumber__class_Onumber__of(_1100426), _1100428)), c_Groups_Oone__class_Oone(_1100426)) = hAPP(c_Int_Onumber__class_Onumber__of(_1100426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100428), c_Int_OBit1(c_Int_OPls))))], (26717 ^ _777864) ^ [_1249526, _1249528] : [class_Orderings_Oorder(_1249526), 26724 ^ _777864 : [(26727 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249526), hAPP(_1249528, 26722 ^ [_1249526, _1249528])), hAPP(_1249528, 26723 ^ [_1249526, _1249528])))], (26725 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26722 ^ [_1249526, _1249528]), 26723 ^ [_1249526, _1249528])))]], -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1249526, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1249528))], (32351 ^ _777864) ^ [_1369426, _1369428, _1369430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369426), _1369428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369426, tc_HOL_Obool)), _1369430), _1369428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369426), _1369428)), hAPP(c_Finite__Set_Ocard(_1369426), _1369430))), -(_1369430 = _1369428)], (19870 ^ _777864) ^ [_1120306, _1120308] : [c_Nat__Transfer_Ois__nat(_1120306), c_Nat__Transfer_Ois__nat(_1120308), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1120306), _1120308)))], (26273 ^ _777864) ^ [_1239975, _1239977, _1239979] : [class_Orderings_Obot(_1239975), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1239977, _1239975)), _1239979) = c_Orderings_Obot__class_Obot(_1239975))], (1412 ^ _777864) ^ [_798282, _798284] : [-(class_Rings_Olinordered__semiring__strict(_798282)), _798284 = _798282, class_Rings_Olinordered__semiring__strict(_798284)], (23303 ^ _777864) ^ [_1183975, _1183977, _1183979, _1183981, _1183983, _1183985, _1183987] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1183975, _1183977, _1183979, _1183981), _1183983), _1183985), _1183987) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183977, _1183979, _1183981), _1183985), hAPP(_1183983, _1183987)))], (21110 ^ _777864) ^ [_1141785, _1141787, _1141789, _1141791] : [class_Fields_Olinordered__field__inverse__zero(_1141785), 21113 ^ _777864 : [(21114 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141787), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141785), _1141789), _1141791))), 21117 ^ _777864 : [(21124 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), c_Groups_Ozero__class_Ozero(_1141785)), _1141791))), 21127 ^ _777864 : [(21134 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), _1141791), c_Groups_Ozero__class_Ozero(_1141785)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141787), c_Groups_Ozero__class_Ozero(_1141785))))], (21128 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), _1141791), c_Groups_Ozero__class_Ozero(_1141785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141785), _1141787), _1141791))))]]], (21118 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), c_Groups_Ozero__class_Ozero(_1141785)), _1141791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141785), _1141787), _1141791)), _1141789)))]]], (21140 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141787), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141785), _1141789), _1141791)))), 21143 ^ _777864 : [(21146 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141785), _1141787), _1141791)), _1141789))], (21144 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), c_Groups_Ozero__class_Ozero(_1141785)), _1141791)))]], 21147 ^ _777864 : [(21150 ^ _777864) ^ [] : [21151 ^ _777864 : [(21154 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141785), _1141787), _1141791)))], (21152 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), _1141791), c_Groups_Ozero__class_Ozero(_1141785))))]], 21155 ^ _777864 : [(21158 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141785), _1141787), c_Groups_Ozero__class_Ozero(_1141785)))], (21156 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), _1141791), c_Groups_Ozero__class_Ozero(_1141785)))]]], (21148 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141785), c_Groups_Ozero__class_Ozero(_1141785)), _1141791))]]]]], (16326 ^ _777864) ^ [_1057939, _1057941] : [class_Groups_Oordered__ab__group__add__abs(_1057939), 16329 ^ _777864 : [(16336 ^ _777864) ^ [] : [_1057941 = c_Groups_Ozero__class_Ozero(_1057939), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057939), hAPP(c_Groups_Oabs__class_Oabs(_1057939), _1057941)), c_Groups_Ozero__class_Ozero(_1057939))))], (16330 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057939), hAPP(c_Groups_Oabs__class_Oabs(_1057939), _1057941)), c_Groups_Ozero__class_Ozero(_1057939))), -(_1057941 = c_Groups_Ozero__class_Ozero(_1057939))]]], (47410 ^ _777864) ^ [_1725604, _1725606] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725604)), _1725606) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1725606 = c_List_Olist_ONil(_1725604))], (2306 ^ _777864) ^ [_811851, _811853] : [_811853 = _811851, -(c_Natural_Oevalc(_811853) = c_Natural_Oevalc(_811851))], (41380 ^ _777864) ^ [_1577736, _1577738, _1577740, _1577742] : [hBOOL(hAPP(hAPP(c_member(_1577736), _1577742), hAPP(c_Relation_ODomain(_1577736, _1577738), _1577740))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1577736, _1577738, hAPP(hAPP(c_COMBC(_1577736, tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_fun(_1577738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577738, tc_fun(tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_fun(_1577738, tc_HOL_Obool)), _1577736), c_COMBC(_1577738, tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577738, tc_prod(_1577736, _1577738)), tc_fun(_1577738, tc_fun(tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_HOL_Obool)), _1577736), hAPP(c_COMBB(tc_prod(_1577736, _1577738), tc_fun(tc_fun(tc_prod(_1577736, _1577738), tc_HOL_Obool), tc_HOL_Obool), _1577738), c_member(tc_prod(_1577736, _1577738)))), c_Product__Type_OPair(_1577736, _1577738)))), _1577740)), _1577742)))], (32111 ^ _777864) ^ [_1364474, _1364476, _1364478] : [class_Orderings_Olinorder(_1364474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364474), _1364476)), 32118 ^ _777864 : [(32125 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364474, tc_HOL_Obool)), _1364476), hAPP(hAPP(c_Set_Oinsert(_1364474), _1364478), c_Orderings_Obot__class_Obot(tc_fun(_1364474, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364474, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1364474, c_Orderings_Oord__class_Omin(_1364474), hAPP(hAPP(c_Set_Oinsert(_1364474), _1364478), _1364476)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1364474), _1364478), c_Big__Operators_Olattice_OInf__fin(_1364474, c_Orderings_Oord__class_Omin(_1364474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364474, tc_HOL_Obool)), _1364476), hAPP(hAPP(c_Set_Oinsert(_1364474), _1364478), c_Orderings_Obot__class_Obot(tc_fun(_1364474, tc_HOL_Obool)))))))], (32119 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364474, tc_HOL_Obool)), _1364476), hAPP(hAPP(c_Set_Oinsert(_1364474), _1364478), c_Orderings_Obot__class_Obot(tc_fun(_1364474, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364474, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1364474, c_Orderings_Oord__class_Omin(_1364474), hAPP(hAPP(c_Set_Oinsert(_1364474), _1364478), _1364476)) = _1364478)]]], (16083 ^ _777864) ^ [_1053647, _1053649, _1053651] : [class_Fields_Olinordered__field(_1053647), 16089 ^ _777864 : [(16092 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053647), _1053649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053647), _1053651), 16088 ^ [_1053647, _1053649, _1053651])))], (16090 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053647), c_Groups_Ozero__class_Ozero(_1053647)), 16088 ^ [_1053647, _1053649, _1053651])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053647), _1053649), _1053651)))], (47008 ^ _777864) ^ [_1715139, _1715141, _1715143, _1715145, _1715147, _1715149] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715139), tc_List_Olist(_1715139))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715139), tc_List_Olist(_1715139)), hAPP(hAPP(c_List_Olist_OCons(_1715139), _1715141), _1715143)), hAPP(hAPP(c_List_Olist_OCons(_1715139), _1715145), _1715147))), c_List_Olexord(_1715139, _1715149)))), 47009 ^ _777864 : [(47012 ^ _777864) ^ [] : [_1715141 = _1715145, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715139), tc_List_Olist(_1715139))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715139), tc_List_Olist(_1715139)), _1715143), _1715147)), c_List_Olexord(_1715139, _1715149)))], (47010 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1715139, _1715139)), hAPP(hAPP(c_Product__Type_OPair(_1715139, _1715139), _1715141), _1715145)), _1715149))]]], (49685 ^ _777864) ^ [_1778846, _1778848, _1778850, _1778852, _1778854] : [-(hAPP(hAPP(c_List_Omap(_1778846, _1778848), _1778850), hAPP(c_List_Ofilter(_1778846, _1778852), _1778854)) = c_List_Omap__filter(_1778846, _1778848, hAPP(hAPP(c_COMBC(_1778846, tc_Option_Ooption(_1778848), tc_Option_Ooption(_1778848)), hAPP(hAPP(c_COMBS(_1778846, tc_Option_Ooption(_1778848), tc_fun(tc_Option_Ooption(_1778848), tc_Option_Ooption(_1778848))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1778848), tc_fun(tc_Option_Ooption(_1778848), tc_Option_Ooption(_1778848))), _1778846), c_If(tc_Option_Ooption(_1778848))), _1778852)), hAPP(hAPP(c_COMBB(_1778848, tc_Option_Ooption(_1778848), _1778846), c_Option_Ooption_OSome(_1778848)), _1778850))), c_Option_Ooption_ONone(_1778848)), _1778854))], (41181 ^ _777864) ^ [_1572275, _1572277, _1572279, _1572281] : [hBOOL(hAPP(hAPP(c_member(_1572275), _1572277), hAPP(c_Relation_ORange(_1572279, _1572275), _1572281))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572279, _1572275)), hAPP(hAPP(c_Product__Type_OPair(_1572279, _1572275), 41184 ^ [_1572275, _1572277, _1572279, _1572281]), _1572277)), _1572281)))], (23327 ^ _777864) ^ [_1184591, _1184593] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1184591), _1184593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1184591)), _1184593)))], (2240 ^ _777864) ^ [_810864, _810866] : [_810866 = _810864, -(c_Divides_Oadjust(_810866) = c_Divides_Oadjust(_810864))], (15078 ^ _777864) ^ [_1033571, _1033573, _1033575] : [class_Groups_Ogroup__add(_1033571), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033571), _1033573), _1033575)), _1033575) = _1033573)], (47338 ^ _777864) ^ [_1724167, _1724169, _1724171, _1724173, _1724175] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1724167, _1724169)), _1724171), hAPP(hAPP(c_List_Ozip(_1724167, _1724169), _1724173), _1724175)) = hAPP(hAPP(c_List_Ozip(_1724167, _1724169), hAPP(hAPP(c_List_Otake(_1724167), _1724171), _1724173)), hAPP(hAPP(c_List_Otake(_1724169), _1724171), _1724175)))], (13361 ^ _777864) ^ [_1002297, _1002299, _1002301, _1002303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002299), _1002301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002301), 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), _1002299), _1002297)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002299), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002303, _1002297))), _1002301))))], (40306 ^ _777864) ^ [_1543927, _1543929, _1543931, _1543933, _1543935, _1543937] : [-(hAPP(c_Set_Oimage(_1543927, _1543929, hAPP(hAPP(c_COMBS(_1543927, _1543929, _1543929), hAPP(hAPP(c_COMBS(_1543927, _1543929, tc_fun(_1543929, _1543929)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1543929, tc_fun(_1543929, _1543929)), _1543927), c_If(_1543929)), _1543931)), _1543933)), _1543935)), _1543937) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543929, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1543927, _1543929, _1543933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543927, tc_HOL_Obool)), _1543937), hAPP(c_Set_OCollect(_1543927), _1543931)))), hAPP(c_Set_Oimage(_1543927, _1543929, _1543935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543927, tc_HOL_Obool)), _1543937), hAPP(c_Set_OCollect(_1543927), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1543927), c_fNot), _1543931))))))], (46747 ^ _777864) ^ [_1708953, _1708955, _1708957, _1708959, _1708961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708953), tc_List_Olist(_1708953))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708953), tc_List_Olist(_1708953)), hAPP(hAPP(c_List_Olist_OCons(_1708953), _1708955), _1708957)), _1708959)), c_List_Olistrel(_1708953, _1708961))), 46752 ^ _777864 : [(46757 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708953), tc_List_Olist(_1708953))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708953), tc_List_Olist(_1708953)), _1708957), 46751 ^ [_1708953, _1708955, _1708957, _1708959, _1708961])), c_List_Olistrel(_1708953, _1708961))))], (46755 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708953, _1708953)), hAPP(hAPP(c_Product__Type_OPair(_1708953, _1708953), _1708955), 46750 ^ [_1708953, _1708955, _1708957, _1708959, _1708961])), _1708961)))], (46753 ^ _777864) ^ [] : [-(_1708959 = hAPP(hAPP(c_List_Olist_OCons(_1708953), 46750 ^ [_1708953, _1708955, _1708957, _1708959, _1708961]), 46751 ^ [_1708953, _1708955, _1708957, _1708959, _1708961]))]]], (14958 ^ _777864) ^ [_1031429, _1031431, _1031433] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031429), _1031431)), _1031433) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031429), _1031433)), _1031431))], (29285 ^ _777864) ^ [_1307832, _1307834, _1307836, _1307838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307832), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307832, tc_HOL_Obool)), _1307834), _1307838))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307832), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307832, tc_HOL_Obool)), _1307834), hAPP(hAPP(c_Set_Oinsert(_1307832), _1307836), _1307838)))))], (51215 ^ _777864) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11907 ^ _777864) ^ [_977000, _977002] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977000), _977002) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _977000 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977002 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49261 ^ _777864) ^ [_1768833, _1768835] : [-(_1768833 = c_List_Olist_ONil(_1768835)), -(hBOOL(hAPP(hAPP(c_member(_1768835), c_List_Olast(_1768835, _1768833)), hAPP(c_List_Oset(_1768835), _1768833))))], (49430 ^ _777864) ^ [_1772428, _1772430, _1772432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772430)), _1772432))), -(hAPP(hAPP(c_List_Otake(_1772430), _1772428), c_List_Obutlast(_1772430, _1772432)) = hAPP(hAPP(c_List_Otake(_1772430), _1772428), _1772432))], (20924 ^ _777864) ^ [_1138718, _1138720, _1138722, _1138724] : [class_Fields_Ofield__inverse__zero(_1138718), class_Int_Onumber(_1138718), 20931 ^ _777864 : [(20932 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138718), _1138722), _1138724), 20935 ^ _777864 : [(20942 ^ _777864) ^ [] : [_1138724 = c_Groups_Ozero__class_Ozero(_1138718), -(hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720) = c_Groups_Ozero__class_Ozero(_1138718))], (20936 ^ _777864) ^ [] : [-(_1138724 = c_Groups_Ozero__class_Ozero(_1138718)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138718), hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720)), _1138724) = _1138722)]]], (20948 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138718), _1138722), _1138724)), 20951 ^ _777864 : [(20954 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138718), hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720)), _1138724) = _1138722], (20952 ^ _777864) ^ [] : [_1138724 = c_Groups_Ozero__class_Ozero(_1138718)]], 20955 ^ _777864 : [(20958 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1138718), _1138720) = c_Groups_Ozero__class_Ozero(_1138718)], (20956 ^ _777864) ^ [] : [-(_1138724 = c_Groups_Ozero__class_Ozero(_1138718))]]]]], (18722 ^ _777864) ^ [_1099493, _1099495] : [class_Int_Onumber__ring(_1099493), class_Rings_Olinordered__idom(_1099493), 18729 ^ _777864 : [(18736 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099495), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099493), hAPP(c_Int_Onumber__class_Onumber__of(_1099493), _1099495)), c_Groups_Oone__class_Oone(_1099493))))], (18730 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099493), hAPP(c_Int_Onumber__class_Onumber__of(_1099493), _1099495)), c_Groups_Oone__class_Oone(_1099493))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1099495), c_Int_OBit1(c_Int_OPls))))]]], (20812 ^ _777864) ^ [_1136793, _1136795, _1136797, _1136799] : [class_Fields_Ofield(_1136793), -(_1136795 = c_Groups_Ozero__class_Ozero(_1136793)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136793), _1136797), _1136795)), _1136799) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136793), _1136797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136793), _1136795), _1136799))), _1136795))], (51273 ^ _777864) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (14085 ^ _777864) ^ [_1015999, _1016001] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015999), _1016001)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1015999)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016001)))], (10093 ^ _777864) ^ [_946403, _946405, _946407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946403), _946405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946405), _946407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946403), _946407)))], (51485 ^ _777864) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (6476 ^ _777864) ^ [_884814, _884816] : [class_Groups_Olinordered__ab__group__add(_884814), 6479 ^ _777864 : [(6486 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884814), _884816), c_Groups_Ozero__class_Ozero(_884814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884814), _884816), _884816)), c_Groups_Ozero__class_Ozero(_884814))))], (6480 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_884814), _884816), _884816)), c_Groups_Ozero__class_Ozero(_884814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_884814), _884816), c_Groups_Ozero__class_Ozero(_884814))))]]], (49125 ^ _777864) ^ [_1766113, _1766115, _1766117] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1766113)), _1766115), c_List_Olists(_1766113, _1766117))), 49128 ^ _777864 : [(49129 ^ _777864) ^ [_1766221] : [hBOOL(hAPP(hAPP(c_member(_1766113), _1766221), hAPP(c_List_Oset(_1766113), _1766115))), -(hBOOL(hAPP(hAPP(c_member(_1766113), _1766221), _1766117)))]]], (6679 ^ _777864) ^ [_887975, _887977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887975)), _887977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887975), _887977)))], (24829 ^ _777864) ^ [_1213824, _1213826, _1213828, _1213830] : [class_Rings_Ocomm__semiring__1(_1213824), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213824), _1213826), _1213828)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213824), _1213826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213824), _1213828), _1213830))))], (44439 ^ _777864) ^ [_1651138, _1651140, _1651142] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651138, _1651138)), hAPP(hAPP(c_Product__Type_OPair(_1651138, _1651138), _1651140), _1651140)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1651138, _1651138), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1651142))))], (12109 ^ _777864) ^ [_980589] : [-(hBOOL(hAPP(_980589, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12116 ^ [_980589])))), 12110 ^ _777864 : [(12111 ^ _777864) ^ [_980641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980641)), hBOOL(hAPP(_980589, _980641))]]], (37198 ^ _777864) ^ [_1474702, _1474704, _1474706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474702), _1474704)), 37201 ^ _777864 : [(37221 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474702, tc_Nat_Onat), _1474706), _1474704) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 37222 ^ _777864 : [(37223 ^ _777864) ^ [_1475183] : [hBOOL(hAPP(hAPP(c_member(_1474702), _1475183), _1474704)), hAPP(_1474706, _1475183) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37231 ^ _777864 : [(37236 ^ _777864) ^ [] : [hAPP(_1474706, 37230 ^ [_1474702, _1474704, _1474706, _1475183]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37234 ^ _777864) ^ [] : [_1475183 = 37230 ^ [_1474702, _1474704, _1474706, _1475183]], (37232 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474702), 37230 ^ [_1474702, _1474704, _1474706, _1475183]), _1474704)))]]]]], (37202 ^ _777864) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474702, tc_Nat_Onat), _1474706), _1474704) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37206 ^ _777864 : [(37211 ^ _777864) ^ [_1475022] : [hBOOL(hAPP(hAPP(c_member(_1474702), _1475022), _1474704)), -(37205 ^ [_1474702, _1474704, _1474706] = _1475022), -(hAPP(_1474706, _1475022) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37209 ^ _777864) ^ [] : [-(hAPP(_1474706, 37205 ^ [_1474702, _1474704, _1474706]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37207 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474702), 37205 ^ [_1474702, _1474704, _1474706]), _1474704)))]]]]], (50855 ^ _777864) ^ [_1803858] : [-(c_List_Oembed__list(_1803858) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1803858))], (14938 ^ _777864) ^ [_1031116, _1031118, _1031120, _1031122, _1031124] : [class_Groups_Oab__group__add(_1031116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031116), _1031118), _1031120) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031116), _1031122), _1031124), 14945 ^ _777864 : [(14952 ^ _777864) ^ [] : [_1031122 = _1031124, -(_1031118 = _1031120)], (14946 ^ _777864) ^ [] : [_1031118 = _1031120, -(_1031122 = _1031124)]]], (46050 ^ _777864) ^ [_1689288, _1689290] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1689288), _1689290) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1689288, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1689290), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (25141 ^ _777864) ^ [_1219001, _1219003, _1219005] : [_1219001 = _1219003, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219003), _1219005)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219001), _1219005)))], (11168 ^ _777864) ^ [_963741, _963743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963741), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963743), _963741))))], (32721 ^ _777864) ^ [_1377255, _1377257, _1377259, _1377261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1377255), _1377257)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377259), _1377261)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1377255, _1377259)), c_Sum__Type_OPlus(_1377255, _1377259, _1377257, _1377261)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1377255), _1377257)), hAPP(c_Finite__Set_Ocard(_1377259), _1377261)))], (35028 ^ _777864) ^ [_1428860, _1428862] : [-(c_Fun_Oinj__on(_1428860, tc_Option_Ooption(_1428860), c_Option_Ooption_OSome(_1428860), _1428862))], (22082 ^ _777864) ^ [_1159513, _1159515] : [-(c_Divides_Opdivmod(_1159513, _1159515) = 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), _1159513)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1159515))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1159513), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1159515))))], (7510 ^ _777864) ^ [] : [-(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))], (12095 ^ _777864) ^ [_980368, _980370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _980370)), -(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), _980368), _980370))))], (35904 ^ _777864) ^ [_1445814, _1445816, _1445818] : [class_Groups_Oordered__ab__group__add(_1445814), -(hAPP(c_Set_Oimage(_1445814, _1445814, c_Groups_Ouminus__class_Ouminus(_1445814)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445814, _1445816), _1445818)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1445814, hAPP(c_Groups_Ouminus__class_Ouminus(_1445814), _1445818), hAPP(c_Groups_Ouminus__class_Ouminus(_1445814), _1445816)))], (26319 ^ _777864) ^ [_1241061, _1241063, _1241065, _1241067, _1241069] : [c_Hoare__Mirabelle_Ohoare__derivs(_1241061, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241061)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241061), _1241063), hAPP(c_Com_Ocom_OBODY, _1241065)), _1241067)), _1241069), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241061)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241061), _1241063), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1241065))), _1241067)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241061), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1241061, _1241069, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241061)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241061), _1241063), hAPP(c_Com_Ocom_OBODY, _1241065)), _1241067)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241061), tc_HOL_Obool)))))], (6933 ^ _777864) ^ [_891847, _891849, _891851, _891853] : [class_Rings_Olinordered__semidom(_891847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891847), c_Groups_Ozero__class_Ozero(_891847)), _891849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891847), _891851), _891853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_891847), _891851), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_891847), _891849), _891853))))], (49673 ^ _777864) ^ [_1778416, _1778418] : [-(c_Random_Oselect__weight(_1778416, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1778416), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1778416, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1778416, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1778416)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1778418)) = c_Random_Oselect__weight(_1778416, _1778418))], (40915 ^ _777864) ^ [_1566476, _1566478, _1566480] : [c_Wellfounded_Owf(_1566476, _1566478), -(c_Wellfounded_Owf(_1566476, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1566476, _1566476), tc_HOL_Obool)), _1566480), _1566478)))], (19210 ^ _777864) ^ [_1108142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1108142)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108142), c_Int_OMin)))], (49687 ^ _777864) ^ [_1778972, _1778974, _1778976, _1778978, _1778980] : [class_Orderings_Olinorder(_1778972), hBOOL(hAPP(hAPP(c_member(_1778974), _1778976), hAPP(c_List_Oset(_1778974), _1778978))), c_List_Olinorder__class_Osorted(_1778972, hAPP(hAPP(c_List_Omap(_1778974, _1778972), _1778980), _1778978)), hAPP(c_List_Ohd(_1778974), hAPP(c_List_Ofilter(_1778974, hAPP(hAPP(c_COMBB(_1778972, tc_HOL_Obool, _1778974), hAPP(c_fequal, hAPP(_1778980, _1778976))), _1778980)), _1778978)) = _1778976, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1778974, _1778972, _1778980), _1778976), c_List_Oremove1(_1778974, _1778976, _1778978)) = _1778978)], (10912 ^ _777864) ^ [_959588, _959590] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959588), _959590) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_959588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_959590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51643 ^ _777864) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), v_na, v_s1))], (30150 ^ _777864) ^ [_1326634, _1326636, _1326638, _1326640] : [-(hBOOL(hAPP(hAPP(c_member(_1326634), _1326636), _1326638))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326634, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1326634), _1326636), _1326640)), _1326638) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326634, tc_HOL_Obool)), _1326640), _1326638))], (51523 ^ _777864) ^ [_1812095, _1812097, _1812099, _1812101] : [-(hAPP(hAPP(c_COMBK(_1812095, _1812097), _1812099), _1812101) = _1812099)], (32886 ^ _777864) ^ [_1380770, _1380772, _1380774, _1380776] : [class_Groups_Ocomm__monoid__mult(_1380770), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380772), _1380774))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380772, _1380770), _1380776), _1380774) = c_Groups_Oone__class_Oone(_1380770))], (18678 ^ _777864) ^ [_1098856] : [class_Int_Onumber__ring(_1098856), c_Int_Oiszero(_1098856, hAPP(c_Int_Onumber__class_Onumber__of(_1098856), c_Int_OBit1(c_Int_OPls)))], (35008 ^ _777864) ^ [_1428466, _1428468, _1428470, _1428472, _1428474] : [-(c_Fun_Oinj__on(_1428466, _1428468, _1428470, hAPP(hAPP(c_Set_Oinsert(_1428466), _1428472), _1428474))), c_Fun_Oinj__on(_1428466, _1428468, _1428470, _1428474), -(hBOOL(hAPP(hAPP(c_member(_1428468), hAPP(_1428470, _1428472)), hAPP(c_Set_Oimage(_1428466, _1428468, _1428470), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428466, tc_HOL_Obool)), _1428474), hAPP(hAPP(c_Set_Oinsert(_1428466), _1428472), c_Orderings_Obot__class_Obot(tc_fun(_1428466, tc_HOL_Obool))))))))], (44208 ^ _777864) ^ [_1645615, _1645617] : [-(c_Transitive__Closure_Ortrancl(_1645615, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645615, _1645615), tc_HOL_Obool)), _1645617), c_Relation_OId(_1645615))) = c_Transitive__Closure_Ortrancl(_1645615, _1645617))], (3328 ^ _777864) ^ [_828306, _828308, _828310, _828312, _828314, _828316] : [-(c_Wellfounded_Omlex__prod(_828316, _828312, _828308) = c_Wellfounded_Omlex__prod(_828314, _828310, _828306)), _828316 = _828314, _828312 = _828310, _828308 = _828306], (13535 ^ _777864) ^ [_1005808] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005808, _1005808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29215 ^ _777864) ^ [_1306495, _1306497, _1306499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1306495), _1306497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306495, tc_HOL_Obool)), _1306499), _1306497)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306495), _1306499)))], (44222 ^ _777864) ^ [_1645909, _1645911] : [-(c_Relation_Orefl__on(_1645909, c_Orderings_Otop__class_Otop(tc_fun(_1645909, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645909, _1645909), tc_HOL_Obool)), _1645911), c_Relation_OId(_1645909))))], (13656 ^ _777864) ^ [_1007891, _1007893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1007891), 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, _1007893, _1007891)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14730 ^ _777864) ^ [_1027263, _1027265, _1027267, _1027269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1027263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027265), _1027267)), -(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), _1027267), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027269, _1027263))), _1027265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027267), _1027263))))], (5537 ^ _777864) ^ [_865334, _865336, _865338, _865340, _865342, _865344] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _865334), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865336), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_865338, _865336)), _865340, _865342), -(c_Natural_Oevaln(c_Com_Ocom_OCall(_865344, _865334, _865338), _865336, _865340, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _865342), hAPP(c_Natural_Ogetlocs, _865336))), _865344), hAPP(hAPP(c_Natural_Ogetlocs, _865342), c_Com_ORes))))], (4042 ^ _777864) ^ [_839517, _839519, _839521, _839523] : [-(c_Nitpick_Ocard_H(_839523, _839519) = c_Nitpick_Ocard_H(_839521, _839517)), _839523 = _839521, _839519 = _839517], (43751 ^ _777864) ^ [_1632115, _1632117, _1632119, _1632121, _1632123, _1632125] : [class_Complete__Lattice_Ocomplete__lattice(_1632115), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632117, tc_fun(_1632119, _1632115)), _1632121), _1632123), _1632125) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632117, _1632115), _1632121), hAPP(hAPP(c_COMBC(_1632117, _1632119, _1632115), _1632123), _1632125)))], (51243 ^ _777864) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (30226 ^ _777864) ^ [_1328572, _1328574, _1328576] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328572, tc_HOL_Obool)), _1328574), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328572, tc_HOL_Obool)), _1328576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328572, tc_HOL_Obool)), _1328574), _1328576))], (13505 ^ _777864) ^ [_1005217, _1005219, _1005221, _1005223, _1005225, _1005227] : [class_Divides_Osemiring__div(_1005217), c_Divides_Odiv__class_Omod(_1005217, _1005219, _1005221) = c_Divides_Odiv__class_Omod(_1005217, _1005223, _1005221), c_Divides_Odiv__class_Omod(_1005217, _1005225, _1005221) = c_Divides_Odiv__class_Omod(_1005217, _1005227, _1005221), -(c_Divides_Odiv__class_Omod(_1005217, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005217), _1005219), _1005225), _1005221) = c_Divides_Odiv__class_Omod(_1005217, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005217), _1005223), _1005227), _1005221))], (33857 ^ _777864) ^ [_1403552, _1403554, _1403556, _1403558, _1403560] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403552, tc_fun(_1403554, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1403552), _1403556), _1403558)), _1403560) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403554, tc_HOL_Obool)), hAPP(_1403560, _1403556)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403552, tc_fun(_1403554, tc_HOL_Obool)), _1403558), _1403560)))], (43525 ^ _777864) ^ [_1626295, _1626297, _1626299, _1626301, _1626303, _1626305] : [hBOOL(hAPP(hAPP(c_member(_1626295), _1626297), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626299, tc_fun(_1626295, tc_HOL_Obool)), _1626301), _1626303))), hBOOL(hAPP(hAPP(c_member(_1626299), _1626305), _1626301)), -(hBOOL(hAPP(hAPP(c_member(_1626295), _1626297), hAPP(_1626303, _1626305))))], (49392 ^ _777864) ^ [_1771680, _1771682, _1771684] : [-(_1771680 = c_List_Olist_ONil(_1771682)), -(c_List_Obutlast(_1771682, hAPP(hAPP(c_List_Olist_OCons(_1771682), _1771684), _1771680)) = hAPP(hAPP(c_List_Olist_OCons(_1771682), _1771684), c_List_Obutlast(_1771682, _1771680)))], (42214 ^ _777864) ^ [_1597640, _1597642, _1597644, _1597646, _1597648] : [c_Finite__Set_Ofolding__idem(_1597640, _1597642, _1597644, _1597646), -(hAPP(c_Fun_Ocomp(_1597642, _1597642, _1597642, hAPP(_1597644, _1597648)), hAPP(_1597644, _1597648)) = hAPP(_1597644, _1597648))], (36476 ^ _777864) ^ [_1457124, _1457126, _1457128] : [-(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), _1457124)), 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))), _1457126))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1457128))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1457128)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1457124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1457124), 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), _1457128), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1457126)))))], (8198 ^ _777864) ^ [_913979, _913981, _913983] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _913979), _913981)), _913983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _913979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _913981), _913983)))], (40683 ^ _777864) ^ [_1559274, _1559276] : [-(c_Product__Type_Omap__pair(_1559274, _1559274, _1559276, _1559276, c_Fun_Oid(_1559274), c_Fun_Oid(_1559276)) = c_Fun_Oid(tc_prod(_1559274, _1559276)))], (51457 ^ _777864) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (48786 ^ _777864) ^ [_1758472, _1758474, _1758476] : [_1758476 = c_List_Olist_ONil(_1758472), -(hAPP(c_List_Orotate(_1758472, _1758474), _1758476) = c_List_Olist_ONil(_1758472))], (51329 ^ _777864) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (28747 ^ _777864) ^ [_1297001, _1297003, _1297005, _1297007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297001), _1297007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297005), _1297003))), -(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), _1297001), _1297003)), 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), _1297005), _1297007)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (51203 ^ _777864) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (26533 ^ _777864) ^ [_1245334, _1245336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245336)), 26540 ^ _777864 : [(26547 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245334), _1245336)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1245334)), hAPP(c_Int_Onat, _1245336))))], (26541 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1245334)), hAPP(c_Int_Onat, _1245336))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1245334), _1245336)))]]], (18794 ^ _777864) ^ [_1100674, _1100676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1100674)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1100676)), _1100674) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100676), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100674), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (16560 ^ _777864) ^ [_1062442, _1062444, _1062446, _1062448] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062442), hAPP(c_Int_Onumber__class_Onumber__of(_1062442), _1062444)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062442), _1062446), _1062448)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062442), hAPP(c_Int_Onumber__class_Onumber__of(_1062442), _1062444)), _1062446)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062442), hAPP(c_Int_Onumber__class_Onumber__of(_1062442), _1062444)), _1062448))), class_Int_Onumber(_1062442), class_Rings_Oring(_1062442)], (28372 ^ _777864) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (39004 ^ _777864) ^ [_1513222, _1513224, _1513226, _1513228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513222), _1513224)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513222), _1513226)), -(_1513226 = c_Orderings_Obot__class_Obot(tc_fun(_1513222, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1513222, tc_HOL_Obool), tc_fun(_1513222, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1513222, tc_HOL_Obool), tc_fun(_1513222, tc_HOL_Obool)), _1513224), _1513226)), c_Wellfounded_Omax__ext(_1513222, _1513228)))), 39018 ^ _777864 : [(39021 ^ _777864) ^ [_1513627] : [hBOOL(hAPP(hAPP(c_member(_1513222), _1513627), _1513226)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1513222, _1513222)), hAPP(hAPP(c_Product__Type_OPair(_1513222, _1513222), 39017 ^ [_1513222, _1513224, _1513226, _1513228]), _1513627)), _1513228))], (39019 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513222), 39017 ^ [_1513222, _1513224, _1513226, _1513228]), _1513224)))]]], (22759 ^ _777864) ^ [_1171760, _1171762, _1171764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171760, tc_HOL_Obool)), _1171764), _1171762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171760, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171760, tc_HOL_Obool)), _1171762)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171760, tc_HOL_Obool)), _1171764))))], (11046 ^ _777864) ^ [_961796, _961798] : [11047 ^ _777864 : [(11050 ^ _777864) ^ [] : [_961796 = hAPP(c_Nat_OSuc, _961798)], (11048 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961796), _961798))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961796), hAPP(c_Nat_OSuc, _961798))))], (48296 ^ _777864) ^ [_1745852, _1745854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1745852), tc_List_Olist(_1745852)), tc_HOL_Obool)), c_List_Olistrel1(_1745852, c_Transitive__Closure_Ortrancl(_1745852, _1745854))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1745852), c_List_Olistrel1(_1745852, _1745854)))))], (14374 ^ _777864) ^ [_1020907, _1020909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020907)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020909), _1020907)), _1020907) = _1020909)], (16418 ^ _777864) ^ [_1059702, _1059704] : [class_Groups_Oordered__ab__group__add__abs(_1059702), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059702), hAPP(c_Groups_Ouminus__class_Ouminus(_1059702), _1059704)), hAPP(c_Groups_Oabs__class_Oabs(_1059702), _1059704))))], (9090 ^ _777864) ^ [_928810] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _928810)) = _928810)], (1742 ^ _777864) ^ [_802407, _802409] : [-(class_Groups_Ozero(_802407)), _802409 = _802407, class_Groups_Ozero(_802409)], (4186 ^ _777864) ^ [_841841, _841843, _841845, _841847] : [-(c_Random_Oselect(_841847, _841843) = c_Random_Oselect(_841845, _841841)), _841847 = _841845, _841843 = _841841], (5166 ^ _777864) ^ [_856927, _856929, _856931, _856933, _856935, _856937] : [-(c_List_Oremove1(_856937, _856933, _856929) = c_List_Oremove1(_856935, _856931, _856927)), _856937 = _856935, _856933 = _856931, _856929 = _856927], (14626 ^ _777864) ^ [_1025147, _1025149, _1025151, _1025153] : [class_Divides_Osemiring__div(_1025147), -(_1025149 = c_Groups_Ozero__class_Ozero(_1025147)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025147), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025147), _1025151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025147), _1025149), _1025153))), _1025149) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025147), _1025153), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025147), _1025151), _1025149)))], (21896 ^ _777864) ^ [_1156622, _1156624] : [21897 ^ _777864 : [(21900 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156624), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21898 ^ _777864) ^ [] : [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), _1156622), _1156624)))]], -(c_Divides_OnegDivAlg(_1156622, _1156624) = 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), _1156622), _1156624)))], (2578 ^ _777864) ^ [_816115, _816117, _816119, _816121, _816123, _816125, _816127, _816129] : [-(c_Nitpick_Opair__box_OPairBox(_816129, _816125, _816121, _816117) = c_Nitpick_Opair__box_OPairBox(_816127, _816123, _816119, _816115)), _816129 = _816127, _816125 = _816123, _816121 = _816119, _816117 = _816115], (4118 ^ _777864) ^ [_840771, _840773, _840775, _840777] : [-(c_Hilbert__Choice_OEps(_840777, _840773) = c_Hilbert__Choice_OEps(_840775, _840771)), _840777 = _840775, _840773 = _840771], (7798 ^ _777864) ^ [_907456, _907458, _907460, _907462] : [c_Com_Ocom_OWhile(_907456, _907458) = c_Com_Ocom_OAss(_907460, _907462)], (3256 ^ _777864) ^ [_827140, _827142, _827144, _827146, _827148, _827150] : [-(c_Finite__Set_Ofold1Set(_827150, _827146, _827142) = c_Finite__Set_Ofold1Set(_827148, _827144, _827140)), _827150 = _827148, _827146 = _827144, _827142 = _827140], (44664 ^ _777864) ^ [_1656446, _1656448] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656446, tc_HOL_Obool), _1656448) = hAPP(c_Set_OCollect(_1656446), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1656446, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1656446), c_HOL_OAll(tc_fun(_1656446, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1656446, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1656446, tc_HOL_Obool), tc_HOL_Obool), _1656446), hAPP(c_COMBS(tc_fun(_1656446, 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(_1656446, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1656446, tc_HOL_Obool), tc_fun(tc_fun(_1656446, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1656446, tc_HOL_Obool))), _1656448)))), c_member(_1656446)))))], (44712 ^ _777864) ^ [_1657456, _1657458, _1657460, _1657462] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657456, tc_HOL_Obool), hAPP(c_Set_Oimage(_1657458, tc_fun(_1657456, tc_HOL_Obool), _1657460), _1657462)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657458, tc_fun(_1657456, tc_HOL_Obool)), _1657462), _1657460))], (32591 ^ _777864) ^ [_1374622, _1374624, _1374626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1374622), _1374624)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374622), _1374626)), 32601 ^ _777864 : [(32604 ^ _777864) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32602 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1374622), 32600 ^ [_1374622, _1374624, _1374626]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1374622, tc_HOL_Obool)), _1374624), _1374626))))]], -(hAPP(c_Finite__Set_Ocard(_1374622), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1374622, tc_HOL_Obool)), _1374624), _1374626)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1374622), _1374624)), hAPP(c_Finite__Set_Ocard(_1374622), _1374626)))], (44776 ^ _777864) ^ [_1659067, _1659069, _1659071] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659067, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659067, tc_HOL_Obool), _1659069)), _1659071) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659067, tc_HOL_Obool), tc_fun(_1659067, tc_HOL_Obool)), _1659069), hAPP(hAPP(c_COMBC(tc_fun(_1659067, tc_HOL_Obool), tc_fun(_1659067, tc_HOL_Obool), tc_fun(_1659067, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659067, tc_HOL_Obool))), _1659071)))], (15138 ^ _777864) ^ [_1034732, _1034734] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034732)), hAPP(c_Nat_OSuc, _1034734)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034732), _1034734))], (38748 ^ _777864) ^ [_1507479, _1507481, _1507483, _1507485, _1507487] : [hBOOL(hAPP(hAPP(c_member(_1507483), hAPP(_1507485, _1507481)), _1507487)), -(hBOOL(hAPP(hAPP(c_member(_1507479), _1507481), hAPP(c_Set_Ovimage(_1507479, _1507483, _1507485), _1507487))))], (1372 ^ _777864) ^ [_797782, _797784] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_797782)), _797784 = _797782, class_Groups_Oordered__cancel__ab__semigroup__add(_797784)], (29540 ^ _777864) ^ [_1313755, _1313757, _1313759, _1313761] : [hBOOL(hAPP(hAPP(c_member(_1313755), _1313757), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313755, tc_HOL_Obool)), _1313759), _1313761))), 29543 ^ _777864 : [(29546 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313755), _1313757), _1313761)))], (29544 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313755), _1313757), _1313759)))]]], (40264 ^ _777864) ^ [_1542529, _1542531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542529), hAPP(c_Set_OCollect(_1542529), _1542531))), 40267 ^ _777864 : [(40274 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542529), c_Orderings_Otop__class_Otop(tc_fun(_1542529, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542529), hAPP(c_Set_OCollect(_1542529), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542529), c_fNot), _1542531)))))], (40268 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542529), hAPP(c_Set_OCollect(_1542529), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542529), c_fNot), _1542531)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1542529), c_Orderings_Otop__class_Otop(tc_fun(_1542529, tc_HOL_Obool)))))]]], (50597 ^ _777864) ^ [_1797540, _1797542, _1797544] : [50599 ^ _777864 : [(50602 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1797540), tc_List_Olist(_1797540), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1797540), tc_fun(tc_List_Olist(_1797540), tc_Nat_Onat), tc_fun(tc_List_Olist(_1797540), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1797540), tc_Nat_Onat), tc_fun(tc_List_Olist(_1797540), tc_HOL_Obool)), tc_List_Olist(_1797540)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1797540))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1797540)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1797540))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1797540)))), 50598 ^ [_1797540, _1797542, _1797544]))], (50600 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1797540), tc_List_Olist(_1797540))), 50598 ^ [_1797540, _1797542, _1797544]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1797540), tc_List_Olist(_1797540))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1797540), tc_List_Olist(_1797540)), _1797542), _1797544)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1797540))), _1797542) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1797540))), _1797544), 50607 ^ _777864 : [(50614 ^ _777864) ^ [] : [_1797542 = _1797544, -(c_List_Oconcat(_1797540, _1797542) = c_List_Oconcat(_1797540, _1797544))], (50608 ^ _777864) ^ [] : [c_List_Oconcat(_1797540, _1797542) = c_List_Oconcat(_1797540, _1797544), -(_1797542 = _1797544)]]], (27187 ^ _777864) ^ [_1259566, _1259568, _1259570] : [_1259570 = hAPP(c_Option_Ooption_OSome(_1259566), _1259568), -(hBOOL(hAPP(hAPP(c_member(_1259566), _1259568), c_Option_Oset(_1259566, _1259570))))], (12380 ^ _777864) ^ [_985244, _985246, _985248, _985250] : [class_Rings_Olinordered__ring__strict(_985244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985244), _985246), c_Groups_Ozero__class_Ozero(_985244))), 12387 ^ _777864 : [(12394 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985244), _985250), _985248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985244), _985246), _985248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985244), _985246), _985250))))], (12388 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985244), _985246), _985248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985244), _985246), _985250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985244), _985250), _985248)))]]], (47432 ^ _777864) ^ [_1726057, _1726059, _1726061, _1726063] : [_1726063 = c_List_Olist_ONil(_1726059), -(c_List_Olist_ONil(_1726057) = hAPP(hAPP(c_List_Omap(_1726059, _1726057), _1726061), _1726063))], (6536 ^ _777864) ^ [_885812, _885814] : [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), _885812), _885814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885814)))], (28759 ^ _777864) ^ [_1297414, _1297416, _1297418, _1297420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297414), _1297420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297418), _1297416))), -(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), _1297414), _1297416)), 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), _1297418), _1297420)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (38776 ^ _777864) ^ [_1508259, _1508261, _1508263, _1508265, _1508267] : [hBOOL(hAPP(hAPP(c_member(_1508259), _1508261), hAPP(c_Set_Ovimage(_1508259, _1508263, _1508265), hAPP(hAPP(c_Set_Oinsert(_1508263), _1508267), c_Orderings_Obot__class_Obot(tc_fun(_1508263, tc_HOL_Obool)))))), -(hAPP(_1508265, _1508261) = _1508267)], (8032 ^ _777864) ^ [_911680, _911682, _911684] : [class_Rings_Osemiring__1(_911680), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _911682), _911684)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911680), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911680), _911682)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911680), _911684)))], (41473 ^ _777864) ^ [_1579803, _1579805] : [c_Nitpick_Owf_H(_1579803, _1579805), 41476 ^ _777864 : [(41479 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579803, _1579803)), _1579805))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (41477 ^ _777864) ^ [] : [-(c_Wellfounded_Oacyclic(_1579803, _1579805))]]], (49558 ^ _777864) ^ [_1774993, _1774995, _1774997, _1774999] : [-(hAPP(c_List_Ofilter(_1774993, _1774995), hAPP(c_List_Ofilter(_1774993, _1774997), _1774999)) = hAPP(c_List_Ofilter(_1774993, hAPP(hAPP(c_COMBS(_1774993, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1774993), c_fconj), _1774997)), _1774995)), _1774999))], (8608 ^ _777864) ^ [_920640, _920642, _920644] : [class_Rings_Oring__1(_920640), -(hAPP(c_Int_Oring__1__class_Oof__int(_920640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _920642), _920644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920640), hAPP(c_Int_Oring__1__class_Oof__int(_920640), _920642)), hAPP(c_Int_Oring__1__class_Oof__int(_920640), _920644)))], (25233 ^ _777864) ^ [_1220473, _1220475] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220473), _1220475)), 25238 ^ _777864 : [(25241 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220475), _1220473))], (25239 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220473), _1220475)))]], -(_1220473 = _1220475)], (20862 ^ _777864) ^ [_1137683, _1137685, _1137687, _1137689] : [class_Fields_Ofield(_1137683), -(_1137685 = c_Groups_Ozero__class_Ozero(_1137683)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137683), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137683), _1137687), _1137685)), _1137689) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137683), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137683), _1137687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137683), _1137685), _1137689))), _1137685))], (5635 ^ _777864) ^ [_868566, _868568, _868570] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _868566)), _868568), _868570)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _868566))), _868568), _868570)))], (46176 ^ _777864) ^ [_1692178, _1692180, _1692182, _1692184, _1692186, _1692188] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1692178, _1692180)), hAPP(hAPP(c_Product__Type_OPair(_1692178, _1692180), _1692182), _1692184)), hAPP(c_List_Oset(tc_prod(_1692178, _1692180)), hAPP(hAPP(c_List_Ozip(_1692178, _1692180), _1692186), _1692188)))), -(hBOOL(hAPP(hAPP(c_member(_1692180), _1692184), hAPP(c_List_Oset(_1692180), _1692188))))], (33755 ^ _777864) ^ [_1401036, _1401038, _1401040, _1401042, _1401044] : [class_Complete__Lattice_Ocomplete__lattice(_1401036), hBOOL(hAPP(hAPP(c_member(_1401038), _1401040), _1401042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401036), hAPP(_1401044, _1401040)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401038, _1401036), _1401042), _1401044))))], (50054 ^ _777864) ^ [_1785427, _1785429, _1785431] : [class_Orderings_Olinorder(_1785427), c_List_Olinorder__class_Osorted(_1785427, _1785429), -(c_List_Olinorder__class_Osorted(_1785427, c_List_Olinorder__class_Oinsort__insert__key(_1785427, _1785427, c_COMBI(_1785427), _1785431, _1785429)))], (21098 ^ _777864) ^ [_1141606, _1141608] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141606), _1141608), hAPP(c_Int_Onumber__class_Onumber__of(_1141606), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1141606), _1141608)), class_Fields_Ofield__inverse__zero(_1141606), class_Int_Onumber__ring(_1141606)], (48490 ^ _777864) ^ [_1751921, _1751923] : [hAPP(c_List_Orotate1(_1751921), _1751923) = c_List_Olist_ONil(_1751921), -(_1751923 = c_List_Olist_ONil(_1751921))], (42916 ^ _777864) ^ [_1612462, _1612464, _1612466] : [class_Lattices_Olattice(_1612462), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612462), _1612464)), -(hBOOL(hAPP(hAPP(c_member(_1612462), _1612466), _1612464))), -(c_Big__Operators_Olattice__class_OInf__fin(_1612462, hAPP(hAPP(c_Set_Oinsert(_1612462), _1612466), _1612464)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612462, _1612462, c_Lattices_Osemilattice__inf__class_Oinf(_1612462)), _1612466), _1612464))], (48816 ^ _777864) ^ [_1759058, _1759060, _1759062, _1759064, _1759066] : [-(hAPP(c_List_Orotate(_1759058, _1759060), hAPP(hAPP(c_List_Omap(_1759062, _1759058), _1759064), _1759066)) = hAPP(hAPP(c_List_Omap(_1759062, _1759058), _1759064), hAPP(c_List_Orotate(_1759062, _1759060), _1759066)))], (12021 ^ _777864) ^ [_979100, _979102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _979100)), _979102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979100), _979102)))], (36620 ^ _777864) ^ [_1460882, _1460884, _1460886, _1460888] : [-(hAPP(c_Map_Orestrict__map(_1460882, _1460884, hAPP(c_COMBK(tc_Option_Ooption(_1460884), _1460882), c_Option_Ooption_ONone(_1460884)), _1460886), _1460888) = c_Option_Ooption_ONone(_1460884))], (44782 ^ _777864) ^ [_1659307, _1659309, _1659311, _1659313] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659307, tc_HOL_Obool), tc_fun(_1659309, tc_HOL_Obool)), _1659311), hAPP(hAPP(c_COMBC(tc_fun(_1659307, tc_HOL_Obool), tc_fun(_1659307, tc_fun(_1659309, tc_HOL_Obool)), tc_fun(_1659309, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659307, tc_fun(_1659309, tc_HOL_Obool))), _1659313)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659307, tc_fun(_1659309, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659307, tc_HOL_Obool), _1659311)), _1659313))], (43259 ^ _777864) ^ [_1620047, _1620049, _1620051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1620047, _1620047), tc_HOL_Obool)), _1620049), c_Transitive__Closure_Ortrancl(_1620047, _1620051))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1620047, _1620047), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1620047, _1620049)), c_Transitive__Closure_Ortrancl(_1620047, _1620051))))], (40745 ^ _777864) ^ [_1561014, _1561016, _1561018, _1561020] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561014, _1561016, _1561018), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561014, _1561016), tc_HOL_Obool))), _1561020) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561014, _1561018), tc_HOL_Obool)))], (41824 ^ _777864) ^ [_1588620, _1588622, _1588624, _1588626, _1588628] : [c_Fun_Oinj__on(_1588620, _1588622, _1588624, c_Orderings_Otop__class_Otop(tc_fun(_1588620, tc_HOL_Obool))), c_Fun_Oinj__on(_1588626, _1588620, _1588628, c_Orderings_Otop__class_Otop(tc_fun(_1588626, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1588626, _1588622, hAPP(c_Fun_Ocomp(_1588620, _1588622, _1588626, _1588624), _1588628), c_Orderings_Otop__class_Otop(tc_fun(_1588626, tc_HOL_Obool))))], (32773 ^ _777864) ^ [_1378511, _1378513, _1378515] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1378511), _1378513), _1378515) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1378511), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1378511, tc_Int_Oint), _1378513), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378515))), class_Groups_Ocomm__monoid__add(_1378511), class_Groups_Ocomm__monoid__mult(_1378511)], (12734 ^ _777864) ^ [_991689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _991689)))], (5752 ^ _777864) ^ [_871406, _871408, _871410] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _871406))), _871408), _871410)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _871406)), _871408), _871410)))], (47628 ^ _777864) ^ [_1729930, _1729932, _1729934, _1729936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729930), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729932)), _1729934))), -(hAPP(hAPP(c_List_Onth(_1729932), hAPP(hAPP(c_List_Olist__update(_1729932, _1729934), _1729930), _1729936)), _1729930) = _1729936)], (47133 ^ _777864) ^ [_1718629, _1718631, _1718633, _1718635] : [hBOOL(hAPP(c_List_Odistinct(_1718629), _1718631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718633), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718629)), _1718631))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718635), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718629)), _1718631))), 47144 ^ _777864 : [(47151 ^ _777864) ^ [] : [_1718633 = _1718635, -(hAPP(hAPP(c_List_Onth(_1718629), _1718631), _1718633) = hAPP(hAPP(c_List_Onth(_1718629), _1718631), _1718635))], (47145 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Onth(_1718629), _1718631), _1718633) = hAPP(hAPP(c_List_Onth(_1718629), _1718631), _1718635), -(_1718633 = _1718635)]]], (38542 ^ _777864) ^ [_1501755, _1501757, _1501759, _1501761] : [c_Fun_Oinj__on(_1501755, _1501757, _1501759, c_Orderings_Otop__class_Otop(tc_fun(_1501755, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501757, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1501755, _1501757, _1501759), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1501755, tc_HOL_Obool)), _1501761))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1501757, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1501755, _1501757, _1501759), _1501761)))))], (12746 ^ _777864) ^ [_991880, _991882] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _991880) = _991882, 12749 ^ _777864 : [(12752 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991882)))], (12750 ^ _777864) ^ [] : [-(_991880 = hAPP(c_Int_Onat, _991882))]]], (46296 ^ _777864) ^ [_1695362, _1695364] : [hBOOL(hAPP(c_List_Odistinct(_1695362), _1695364)), -(hAPP(c_Finite__Set_Ocard(_1695362), hAPP(c_List_Oset(_1695362), _1695364)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695362)), _1695364))], (51263 ^ _777864) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (4846 ^ _777864) ^ [_851991, _851993] : [_851993 = _851991, -(c_Lattices_Osemilattice__sup__class_Osup(_851993) = c_Lattices_Osemilattice__sup__class_Osup(_851991))], (46819 ^ _777864) ^ [_1710903, _1710905, _1710907, _1710909, _1710911] : [class_Rings_Osemiring__0(_1710903), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1710903), hAPP(hAPP(c_List_Omap(_1710905, _1710903), hAPP(hAPP(c_COMBB(_1710903, _1710903, _1710905), hAPP(c_Groups_Otimes__class_Otimes(_1710903), _1710907)), _1710909)), _1710911)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1710903), _1710907), hAPP(c_List_Omonoid__add__class_Olistsum(_1710903), hAPP(hAPP(c_List_Omap(_1710905, _1710903), _1710909), _1710911))))], (44413 ^ _777864) ^ [_1650569, _1650571, _1650573] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1650569, _1650569, _1650569), _1650571), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650569, _1650569), tc_HOL_Obool), _1650573), _1650571)) = hAPP(hAPP(c_Relation_Orel__comp(_1650569, _1650569, _1650569), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650569, _1650569), tc_HOL_Obool), _1650573), _1650571)), _1650571))], (19392 ^ _777864) ^ [_1111333, _1111335] : [class_Rings_Olinordered__idom(_1111333), 19395 ^ _777864 : [(19402 ^ _777864) ^ [] : [-(_1111335 = c_Groups_Ozero__class_Ozero(_1111333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111333), c_Groups_Ozero__class_Ozero(_1111333)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111333), _1111335), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19396 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111333), c_Groups_Ozero__class_Ozero(_1111333)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111333), _1111335), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1111335 = c_Groups_Ozero__class_Ozero(_1111333)]]], (47612 ^ _777864) ^ [_1729636, _1729638, _1729640, _1729642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729636), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729638)), _1729640))), 47615 ^ _777864 : [(47622 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Onth(_1729638), _1729640), _1729636) = _1729642, -(hAPP(hAPP(c_List_Olist__update(_1729638, _1729640), _1729636), _1729642) = _1729640)], (47616 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1729638, _1729640), _1729636), _1729642) = _1729640, -(hAPP(hAPP(c_List_Onth(_1729638), _1729640), _1729636) = _1729642)]]], (6002 ^ _777864) ^ [_876517, _876519, _876521] : [hAPP(c_Com_Ocom_OBODY, _876517) = c_Com_Ocom_OAss(_876519, _876521)], (46192 ^ _777864) ^ [_1692765, _1692767, _1692769, _1692771, _1692773, _1692775] : [-(hAPP(hAPP(c_List_Ozip(_1692765, _1692767), hAPP(hAPP(c_List_Omap(_1692769, _1692765), _1692771), _1692773)), _1692775) = hAPP(hAPP(c_List_Omap(tc_prod(_1692769, _1692767), tc_prod(_1692765, _1692767)), hAPP(c_Product__Type_Oprod_Oprod__case(_1692769, _1692767, tc_prod(_1692765, _1692767)), hAPP(hAPP(c_COMBB(_1692765, tc_fun(_1692767, tc_prod(_1692765, _1692767)), _1692769), c_Product__Type_OPair(_1692765, _1692767)), _1692771))), hAPP(hAPP(c_List_Ozip(_1692769, _1692767), _1692773), _1692775)))], (24489 ^ _777864) ^ [_1207003, _1207005, _1207007] : [-(c_HOL_OThe(tc_prod(_1207003, _1207005), hAPP(c_Product__Type_Oprod_Oprod__case(_1207003, _1207005, tc_HOL_Obool), _1207007)) = c_HOL_OThe(tc_prod(_1207003, _1207005), hAPP(hAPP(c_COMBS(tc_prod(_1207003, _1207005), _1207005, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1207003, tc_fun(_1207005, tc_HOL_Obool), tc_prod(_1207003, _1207005)), _1207007), c_Product__Type_Ofst(_1207003, _1207005))), c_Product__Type_Osnd(_1207003, _1207005))))], (33929 ^ _777864) ^ [_1405075, _1405077, _1405079, _1405081, _1405083, _1405085, _1405087, _1405089] : [c_Equiv__Relations_Oequiv(_1405075, _1405077, _1405079), c_Equiv__Relations_Ocongruent2(_1405075, _1405081, _1405083, _1405079, _1405085, _1405087), hBOOL(hAPP(hAPP(c_member(_1405075), _1405089), _1405077)), -(c_Equiv__Relations_Ocongruent(_1405081, _1405083, _1405085, hAPP(_1405087, _1405089)))], (27181 ^ _777864) ^ [_1259461, _1259463, _1259465] : [hBOOL(hAPP(hAPP(c_member(_1259461), _1259463), c_Option_Oset(_1259461, _1259465))), -(_1259465 = hAPP(c_Option_Ooption_OSome(_1259461), _1259463))], (36268 ^ _777864) ^ [_1453023, _1453025, _1453027] : [class_Orderings_Oorder(_1453023), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1453023, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1453023), _1453025)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1453023, _1453025, _1453027)) = c_Orderings_Obot__class_Obot(tc_fun(_1453023, tc_HOL_Obool)))], (29938 ^ _777864) ^ [_1322025, _1322027, _1322029] : [class_Lattices_Olattice(_1322025), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322025), _1322027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1322025), _1322027), _1322029)) = _1322027)], (36122 ^ _777864) ^ [_1450173, _1450175, _1450177, _1450179, _1450181] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450173, _1450175), _1450177), _1450179), _1450181), _1450179) = _1450181)], (43445 ^ _777864) ^ [_1624518, _1624520, _1624522, _1624524] : [c_Wellfounded_Oacyclic(_1624518, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624518, _1624518)), hAPP(hAPP(c_Product__Type_OPair(_1624518, _1624518), _1624520), _1624522)), _1624524)), 43448 ^ _777864 : [(43451 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624518, _1624518)), hAPP(hAPP(c_Product__Type_OPair(_1624518, _1624518), _1624522), _1624520)), c_Transitive__Closure_Ortrancl(_1624518, _1624524)))], (43449 ^ _777864) ^ [] : [-(c_Wellfounded_Oacyclic(_1624518, _1624524))]]], (47208 ^ _777864) ^ [_1720184, _1720186] : [class_Groups_Ocomm__monoid__add(_1720184), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1720184), _1720186) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1720184), hAPP(c_List_Onth(_1720184), _1720186)), 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(_1720184)), _1720186))))], (51021 ^ _777864) ^ [_1806988, _1806990] : [class_Lattices_Obounded__lattice(_1806988), -(class_Lattices_Obounded__lattice(tc_fun(_1806990, _1806988)))], (1362 ^ _777864) ^ [_797657, _797659] : [-(class_Smallcheck_Osmall(_797657)), _797659 = _797657, class_Smallcheck_Osmall(_797659)], (33765 ^ _777864) ^ [_1401227, _1401229, _1401231, _1401233, _1401235, _1401237] : [hBOOL(hAPP(hAPP(c_member(_1401227), _1401229), _1401231)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401227, tc_fun(_1401233, tc_HOL_Obool)), _1401231), hAPP(hAPP(c_COMBB(tc_fun(_1401233, tc_HOL_Obool), tc_fun(_1401233, tc_HOL_Obool), _1401227), hAPP(c_Set_Oinsert(_1401233), _1401235)), _1401237)) = hAPP(hAPP(c_Set_Oinsert(_1401233), _1401235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401227, tc_fun(_1401233, tc_HOL_Obool)), _1401231), _1401237)))], (41315 ^ _777864) ^ [_1575520, _1575522] : [-(hAPP(c_Relation_ODomain(_1575520, _1575522), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575520, _1575522), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1575520, tc_HOL_Obool)))], (43515 ^ _777864) ^ [_1626072, _1626074, _1626076, _1626078, _1626080, _1626082, _1626084, _1626086] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626072, tc_fun(_1626074, tc_fun(_1626076, tc_HOL_Obool))), _1626078), _1626080), _1626082), _1626084)), hBOOL(hAPP(hAPP(c_member(_1626072), _1626086), _1626078)), -(hBOOL(hAPP(hAPP(hAPP(_1626080, _1626086), _1626082), _1626084)))], (10960 ^ _777864) ^ [_960321, _960323, _960325] : [class_Groups_Oordered__ab__group__add(_960321), 10963 ^ _777864 : [(10970 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960321), _960325), hAPP(c_Groups_Ouminus__class_Ouminus(_960321), _960323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960321), _960323), hAPP(c_Groups_Ouminus__class_Ouminus(_960321), _960325))))], (10964 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960321), _960323), hAPP(c_Groups_Ouminus__class_Ouminus(_960321), _960325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960321), _960325), hAPP(c_Groups_Ouminus__class_Ouminus(_960321), _960323))))]]], (47500 ^ _777864) ^ [_1727618, _1727620, _1727622, _1727624] : [hAPP(hAPP(c_List_Olist__update(_1727618, _1727620), _1727622), _1727624) = c_List_Olist_ONil(_1727618), -(_1727620 = c_List_Olist_ONil(_1727618))], (8040 ^ _777864) ^ [_911876, _911878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911876)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _911878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911876), _911878)))], (51225 ^ _777864) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (46146 ^ _777864) ^ [_1691152, _1691154, _1691156] : [-(hAPP(hAPP(c_List_Ozip(_1691152, _1691154), hAPP(hAPP(c_List_Omap(tc_prod(_1691152, _1691154), _1691152), c_Product__Type_Ofst(_1691152, _1691154)), _1691156)), hAPP(hAPP(c_List_Omap(tc_prod(_1691152, _1691154), _1691154), c_Product__Type_Osnd(_1691152, _1691154)), _1691156)) = _1691156)], (16238 ^ _777864) ^ [_1056433] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056433)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056433))], (34463 ^ _777864) ^ [_1417372, _1417374, _1417376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417372, tc_HOL_Obool)), _1417374), _1417376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1417372, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417372), _1417374)), hAPP(c_Set_OPow(_1417372), _1417376))))], (13499 ^ _777864) ^ [_1005082, _1005084, _1005086, _1005088] : [class_Divides_Osemiring__div(_1005082), -(c_Divides_Odiv__class_Omod(_1005082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005082), c_Divides_Odiv__class_Omod(_1005082, _1005084, _1005086)), _1005088), _1005086) = c_Divides_Odiv__class_Omod(_1005082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1005082), _1005084), _1005088), _1005086))], (18852 ^ _777864) ^ [_1101934, _1101936] : [c_Int_OBit0(_1101934) = c_Int_OBit0(_1101936), -(_1101934 = _1101936)], (35550 ^ _777864) ^ [_1439021, _1439023, _1439025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439021)), 35553 ^ _777864 : [(35554 ^ _777864) ^ [_1439155] : [35556 ^ _777864 : [(35562 ^ _777864) ^ [] : [-(_1439155 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35558 ^ [_1439021, _1439023, _1439025, _1439155]), 35555 ^ [_1439021, _1439023, _1439025, _1439155]))], (35560 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35558 ^ [_1439021, _1439023, _1439025, _1439155]), _1439023)))], (35557 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35555 ^ [_1439021, _1439023, _1439025, _1439155]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1439021))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439155), _1439025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1439155), _1439021)), _1439025)))]]], (25651 ^ _777864) ^ [_1227835, _1227837, _1227839, _1227841, _1227843] : [class_Rings_Ocomm__semiring__1(_1227835), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227835), hAPP(hAPP(c_Power_Opower__class_Opower(_1227835), _1227837), _1227839)), _1227841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227843), _1227839)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227835), hAPP(hAPP(c_Power_Opower__class_Opower(_1227835), _1227837), _1227843)), _1227841)))], (27312 ^ _777864) ^ [_1263378, _1263380, _1263382, _1263384] : [-(c_Nitpick_Ofold__graph_H(_1263378, _1263380, _1263382, _1263384, c_Orderings_Obot__class_Obot(tc_fun(_1263378, tc_HOL_Obool)), _1263384))], (14606 ^ _777864) ^ [_1024674, _1024676, _1024678] : [-(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), _1024674), _1024676)), _1024678)), _1024676) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1024678), _1024676))], (23945 ^ _777864) ^ [_1196510, _1196512, _1196514] : [class_Orderings_Olinorder(_1196510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196510), _1196512), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196510), _1196514), _1196512))))], (5878 ^ _777864) ^ [_874368, _874370, _874372, _874374, _874376, _874378] : [-(c_Com_Ocom_OLocal(_874368, _874370, _874372) = c_Com_Ocom_OLocal(_874374, _874376, _874378)), _874368 = _874374, _874370 = _874376, _874372 = _874378], (2338 ^ _777864) ^ [_812319, _812321] : [_812321 = _812319, -(c_Nitpick_Ozero__frac(_812321) = c_Nitpick_Ozero__frac(_812319))], (40176 ^ _777864) ^ [_1540565, _1540567, _1540569] : [-(hAPP(c_Set_OCollect(_1540565), hAPP(hAPP(c_COMBS(_1540565, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540565), c_fdisj), _1540567)), _1540569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540565, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1540565), _1540567)), hAPP(c_Set_OCollect(_1540565), _1540569)))], (1252 ^ _777864) ^ [_796282, _796284] : [-(class_Lattices_Obounded__lattice__top(_796282)), _796284 = _796282, class_Lattices_Obounded__lattice__top(_796284)], (39069 ^ _777864) ^ [_1515219, _1515221, _1515223] : [class_Groups_Oab__semigroup__mult(_1515219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515219), _1515221)), -(_1515221 = c_Orderings_Obot__class_Obot(tc_fun(_1515219, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515219), _1515223)), -(_1515223 = c_Orderings_Obot__class_Obot(tc_fun(_1515219, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515219, tc_HOL_Obool)), _1515221), _1515223) = c_Orderings_Obot__class_Obot(tc_fun(_1515219, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1515219, c_Groups_Otimes__class_Otimes(_1515219)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515219, tc_HOL_Obool)), _1515221), _1515223)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1515219), hAPP(c_Finite__Set_Ofold1(_1515219, c_Groups_Otimes__class_Otimes(_1515219)), _1515221)), hAPP(c_Finite__Set_Ofold1(_1515219, c_Groups_Otimes__class_Otimes(_1515219)), _1515223)))], (6803 ^ _777864) ^ [_889846, _889848] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_889846, _889848)], (44277 ^ _777864) ^ [_1647309, _1647311, _1647313, _1647315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1647309, _1647311), tc_HOL_Obool)), _1647313), _1647315)), c_Relation_Osingle__valued(_1647309, _1647311, _1647315), -(c_Relation_Osingle__valued(_1647309, _1647311, _1647313))], (50879 ^ _777864) ^ [_1804251, _1804253] : [_1804253 = c_List_Olist_ONil(_1804251), -(c_List_Oremdups(_1804251, _1804253) = c_List_Olist_ONil(_1804251))], (5408 ^ _777864) ^ [_860582, _860584] : [_860584 = _860582, -(c_COMBI(_860584) = c_COMBI(_860582))], (7300 ^ _777864) ^ [_898011, _898013, _898015, _898017, _898019, _898021] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_898011, _898013, _898015), _898017, _898019, _898021)), 7301 ^ _777864 : [(7308 ^ _777864) ^ [] : [-(hBOOL(hAPP(_898011, _898017))), c_Natural_Oevaln(_898015, _898017, _898019, _898021)], (7302 ^ _777864) ^ [] : [hBOOL(hAPP(_898011, _898017)), c_Natural_Oevaln(_898013, _898017, _898019, _898021)]]], (16278 ^ _777864) ^ [_1057132, _1057134] : [class_Int_Onumber__ring(_1057132), class_Rings_Olinordered__idom(_1057132), 16285 ^ _777864 : [(16292 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057132), hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134)), c_Groups_Ozero__class_Ozero(_1057132)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1057132), hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134)) = hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134))], (16286 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057132), hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134)), c_Groups_Ozero__class_Ozero(_1057132))), -(hAPP(c_Groups_Oabs__class_Oabs(_1057132), hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1057132), hAPP(c_Int_Onumber__class_Onumber__of(_1057132), _1057134)))]]], (7494 ^ _777864) ^ [_901774, _901776, _901778, _901780] : [c_Com_Ocom_OSemi(_901774, _901776) = c_Com_Ocom_OAss(_901778, _901780)], (26745 ^ _777864) ^ [_1250072, _1250074] : [hBOOL(hAPP(hAPP(c_member(_1250072), _1250074), c_Orderings_Obot__class_Obot(tc_fun(_1250072, tc_HOL_Obool))))], (1082 ^ _777864) ^ [_794157, _794159] : [-(class_Rings_Olinordered__idom(_794157)), _794159 = _794157, class_Rings_Olinordered__idom(_794159)], (6813 ^ _777864) ^ [_890073, _890075] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890073), _890075), 6818 ^ _777864 : [(6821 ^ _777864) ^ [] : [-(_890075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6819 ^ _777864) ^ [] : [-(_890073 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6822 ^ _777864 : [(6825 ^ _777864) ^ [] : [-(_890075 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6823 ^ _777864) ^ [] : [-(_890073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6659 ^ _777864) ^ [_887718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887718), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3520 ^ _777864) ^ [_831338, _831340] : [_831340 = _831338, -(c_Hoare__Mirabelle_Otriple_Otriple(_831340) = c_Hoare__Mirabelle_Otriple_Otriple(_831338))], (18016 ^ _777864) ^ [_1088155] : [class_Int_Onumber__ring(_1088155), -(c_Groups_Ozero__class_Ozero(_1088155) = hAPP(c_Int_Onumber__class_Onumber__of(_1088155), c_Int_OPls))], (29163 ^ _777864) ^ [_1305670] : [c_Nat__Transfer_Onat__set(_1305670), 29166 ^ _777864 : [(29173 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1305670))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1305670)))], (29167 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1305670)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1305670))))]]], (30462 ^ _777864) ^ [_1334554, _1334556, _1334558, _1334560, _1334562] : [hBOOL(hAPP(hAPP(c_member(_1334554), _1334556), c_SetInterval_Oord_OgreaterThanLessThan(_1334554, _1334558, _1334560, _1334562))), 30465 ^ _777864 : [(30468 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1334558, _1334556), _1334562)))], (30466 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1334558, _1334560), _1334556)))]]], (3592 ^ _777864) ^ [_832480, _832482, _832484, _832486, _832488, _832490, _832492, _832494] : [-(c_New__Random__Sequence_Oneg__map(_832494, _832490, _832486, _832482) = c_New__Random__Sequence_Oneg__map(_832492, _832488, _832484, _832480)), _832494 = _832492, _832490 = _832488, _832486 = _832484, _832482 = _832480], (13736 ^ _777864) ^ [_1009255, _1009257, _1009259] : [hBOOL(hAPP(_1009255, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1009257, _1009259))), 13739 ^ _777864 : [(13764 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009259), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13767 ^ _777864 : [(13768 ^ _777864) ^ [_1009877, _1009879] : [-(hBOOL(hAPP(_1009255, _1009877))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009259), _1009877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1009877), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1009257 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009259), _1009879)), _1009877)]]], (13746 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009259)), 13749 ^ _777864 : [(13750 ^ _777864) ^ [_1009585, _1009587] : [-(hBOOL(hAPP(_1009255, _1009585))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1009585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1009585), _1009259)), _1009257 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1009259), _1009587)), _1009585)]]], (13740 ^ _777864) ^ [] : [_1009259 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1009255, _1009257)))]]], (34279 ^ _777864) ^ [_1413471, _1413473, _1413475] : [class_Orderings_Olinorder(_1413471), hAPP(_1413473, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413471), 34284 ^ [_1413471, _1413473, _1413475]), 34285 ^ [_1413471, _1413473, _1413475])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1413471), hAPP(_1413473, 34284 ^ [_1413471, _1413473, _1413475])), hAPP(_1413473, 34285 ^ [_1413471, _1413473, _1413475])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413471), _1413475)), -(_1413475 = c_Orderings_Obot__class_Obot(tc_fun(_1413471, tc_HOL_Obool))), -(hAPP(_1413473, c_Big__Operators_Olattice_OInf__fin(_1413471, c_Orderings_Oord__class_Omin(_1413471), _1413475)) = c_Big__Operators_Olattice_OInf__fin(_1413471, c_Orderings_Oord__class_Omin(_1413471), hAPP(c_Set_Oimage(_1413471, _1413471, _1413473), _1413475)))], (1810 ^ _777864) ^ [_803301, _803303, _803305, _803307] : [-(v_P(_803305, _803301)), v_P(_803307, _803303), _803307 = _803305, _803303 = _803301], (43587 ^ _777864) ^ [_1627597, _1627599, _1627601] : [-(hAPP(c_Relation_ODomain(_1627597, _1627599), hAPP(c_Relation_Oconverse(_1627599, _1627597), _1627601)) = hAPP(c_Relation_ORange(_1627599, _1627597), _1627601))], (28793 ^ _777864) ^ [_1298187] : [-(hAPP(c_Relation_OField(_1298187), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1298187, _1298187), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1298187, tc_HOL_Obool)))], (50568 ^ _777864) ^ [_1796357, _1796359, _1796361] : [-(hAPP(c_List_Orev(_1796357), hAPP(hAPP(c_List_Otake(_1796357), _1796359), _1796361)) = hAPP(hAPP(c_List_Odrop(_1796357), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796357)), _1796361)), _1796359)), hAPP(c_List_Orev(_1796357), _1796361)))], (40462 ^ _777864) ^ [_1549929, _1549931, _1549933, _1549935] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1549929, _1549931), _1549933), _1549935) = hAPP(c_Set_OCollect(tc_prod(_1549931, _1549931)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549931, _1549931, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549931, tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_fun(_1549931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549931, tc_fun(tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_fun(_1549931, tc_HOL_Obool)), _1549931), c_COMBC(_1549931, tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549931, tc_prod(_1549929, _1549929)), tc_fun(_1549931, tc_fun(tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_HOL_Obool)), _1549931), hAPP(c_COMBB(tc_prod(_1549929, _1549929), tc_fun(tc_fun(tc_prod(_1549929, _1549929), tc_HOL_Obool), tc_HOL_Obool), _1549931), c_member(tc_prod(_1549929, _1549929)))), hAPP(hAPP(c_COMBC(_1549931, tc_fun(_1549931, _1549929), tc_fun(_1549931, tc_prod(_1549929, _1549929))), hAPP(hAPP(c_COMBB(tc_fun(_1549929, tc_prod(_1549929, _1549929)), tc_fun(tc_fun(_1549931, _1549929), tc_fun(_1549931, tc_prod(_1549929, _1549929))), _1549931), c_COMBB(_1549929, tc_prod(_1549929, _1549929), _1549931)), hAPP(hAPP(c_COMBB(_1549929, tc_fun(_1549929, tc_prod(_1549929, _1549929)), _1549931), c_Product__Type_OPair(_1549929, _1549929)), _1549935))), _1549935)))), _1549933))))], (37825 ^ _777864) ^ [_1487458, _1487460] : [class_Orderings_Olinorder(_1487458), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487458, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1487458), _1487460)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487458), _1487460))], (46793 ^ _777864) ^ [_1710068, _1710070, _1710072] : [-(c_Random_Oselect__weight(_1710068, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710068)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1710068), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1710070)), _1710072)) = c_Random_Oselect__weight(_1710068, _1710072))], (940 ^ _777864) ^ [_792320, _792322, _792324, _792326, _792328, _792330] : [-(c_Finite__Set_Ofun__left__comm(_792328, _792324, _792320)), c_Finite__Set_Ofun__left__comm(_792330, _792326, _792322), _792330 = _792328, _792326 = _792324, _792322 = _792320], (25529 ^ _777864) ^ [_1225426, _1225428, _1225430] : [class_Divides_Osemiring__div(_1225426), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225426), _1225428), _1225430)), -(c_Divides_Odiv__class_Omod(_1225426, _1225430, _1225428) = c_Groups_Ozero__class_Ozero(_1225426))], (7790 ^ _777864) ^ [_907234, _907236, _907238] : [c_Com_Ocom_OWhile(_907234, _907236) = hAPP(c_Com_Ocom_OBODY, _907238)], (27824 ^ _777864) ^ [_1273478, _1273480, _1273482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273478, tc_HOL_Obool)), _1273480), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273478, tc_HOL_Obool)), _1273482), _1273480))))], (45731 ^ _777864) ^ [_1681630, _1681632, _1681634, _1681636, _1681638] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1681630), tc_List_Olist(_1681632), tc_List_Olist(_1681634), hAPP(c_List_Omap(_1681630, _1681632), _1681636)), hAPP(c_List_Omap(_1681634, _1681630), _1681638)) = hAPP(c_List_Omap(_1681634, _1681632), hAPP(c_Fun_Ocomp(_1681630, _1681632, _1681634, _1681636), _1681638)))], (9008 ^ _777864) ^ [_927641, _927643] : [class_Rings_Ocomm__semiring__1(_927641), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927641), _927643), c_Groups_Ozero__class_Ozero(_927641)) = c_Groups_Ozero__class_Ozero(_927641))], (38027 ^ _777864) ^ [_1491686, _1491688, _1491690, _1491692, _1491694] : [-(_1491686 = c_Option_Ooption_ONone(_1491688)), -(c_Map_Odom(_1491690, _1491688, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1491690, tc_Option_Ooption(_1491688)), _1491692), _1491694), _1491686)) = hAPP(hAPP(c_Set_Oinsert(_1491690), _1491694), c_Map_Odom(_1491690, _1491688, _1491692)))], (24659 ^ _777864) ^ [_1210408] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1210408)) = _1210408)], (50321 ^ _777864) ^ [_1790546, _1790548, _1790550, _1790552] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1790546, tc_Nat_Onat), _1790546), c_Product__Type_Ofst(_1790546, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1790546, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1790546, 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(_1790546, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1790546, tc_Nat_Onat))), _1790548)), hAPP(hAPP(c_List_Ozip(_1790546, tc_Nat_Onat), _1790550), c_List_Oupt(_1790552, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790552), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790546)), _1790550)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1790546, tc_Nat_Onat), _1790546), c_Product__Type_Ofst(_1790546, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1790546, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1790546, 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(_1790546, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1790546, tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_prod(_1790546, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1790546, tc_Nat_Onat))), _1790552))), _1790548)), hAPP(hAPP(c_List_Ozip(_1790546, tc_Nat_Onat), _1790550), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790546)), _1790550))))))], (40787 ^ _777864) ^ [_1562375, _1562377, _1562379, _1562381, _1562383, _1562385, _1562387, _1562389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562375, _1562377), tc_HOL_Obool)), _1562379), hAPP(hAPP(c_Product__Type_OSigma(_1562375, _1562377), _1562381), hAPP(c_COMBK(tc_fun(_1562377, tc_HOL_Obool), _1562375), _1562383)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562377, _1562385), tc_HOL_Obool)), _1562387), hAPP(hAPP(c_Product__Type_OSigma(_1562377, _1562385), _1562383), hAPP(c_COMBK(tc_fun(_1562385, tc_HOL_Obool), _1562377), _1562389)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562375, _1562385), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1562375, _1562377, _1562385), _1562379), _1562387)), hAPP(hAPP(c_Product__Type_OSigma(_1562375, _1562385), _1562381), hAPP(c_COMBK(tc_fun(_1562385, tc_HOL_Obool), _1562375), _1562389)))))], (8602 ^ _777864) ^ [_920548, _920550] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _920548), _920550) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _920550), _920548))], (17722 ^ _777864) ^ [_1083313, _1083315] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1083313), hAPP(hAPP(c_Power_Opower__class_Opower(_1083313), hAPP(c_Int_Onumber__class_Onumber__of(_1083313), c_Int_OMin)), _1083315)) = c_Groups_Oone__class_Oone(_1083313)), class_Int_Onumber__ring(_1083313), class_Rings_Olinordered__idom(_1083313)], (45813 ^ _777864) ^ [_1683874, _1683876, _1683878, _1683880, _1683882] : [hAPP(hAPP(c_Option_Omap(_1683874, _1683876), _1683878), _1683880) = hAPP(c_Option_Ooption_OSome(_1683876), _1683882), 45817 ^ _777864 : [(45820 ^ _777864) ^ [] : [-(hAPP(_1683878, 45816 ^ [_1683874, _1683876, _1683878, _1683880, _1683882]) = _1683882)], (45818 ^ _777864) ^ [] : [-(_1683880 = hAPP(c_Option_Ooption_OSome(_1683874), 45816 ^ [_1683874, _1683876, _1683878, _1683880, _1683882]))]]], (14516 ^ _777864) ^ [_1023253, _1023255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023253)), 14519 ^ _777864 : [(14526 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023253), _1023255)), -(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), _1023255), _1023253))))], (14520 ^ _777864) ^ [] : [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), _1023255), _1023253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023253), _1023255)))]]], (3966 ^ _777864) ^ [_838279, _838281] : [_838281 = _838279, -(c_Smallcheck_Osmall__class_Osmall(_838281) = c_Smallcheck_Osmall__class_Osmall(_838279))], (42324 ^ _777864) ^ [_1599932, _1599934, _1599936] : [hBOOL(hAPP(_1599932, _1599934)), -(hBOOL(hAPP(_1599932, c_Hilbert__Choice_OEps(_1599936, _1599932))))], (51537 ^ _777864) ^ [_1812381, _1812383] : [_1812381 = _1812383, -(hBOOL(hAPP(hAPP(c_fequal, _1812381), _1812383)))], (41633 ^ _777864) ^ [_1583957, _1583959, _1583961, _1583963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583957), _1583959)), 41639 ^ _777864 : [(41642 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583961), hAPP(_1583963, 41638 ^ [_1583957, _1583959, _1583961, _1583963])))], (41640 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583957), 41638 ^ [_1583957, _1583959, _1583961, _1583963]), _1583959)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1583961), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1583957, tc_fun(_1583961, tc_HOL_Obool)), _1583959), _1583963))))], (29243 ^ _777864) ^ [_1307010, _1307012, _1307014] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307010), _1307012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307010), _1307014)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307010), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307010, tc_HOL_Obool)), _1307012), _1307014))))], (30699 ^ _777864) ^ [_1339227, _1339229, _1339231, _1339233, _1339235] : [hBOOL(hAPP(hAPP(c_member(_1339227), _1339229), c_SetInterval_Oord_OatLeastAtMost(_1339227, _1339231, _1339233, _1339235))), 30702 ^ _777864 : [(30705 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1339231, _1339229), _1339235)))], (30703 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1339231, _1339233), _1339229)))]]], (30096 ^ _777864) ^ [_1325343, _1325345, _1325347, _1325349] : [class_Lattices_Olattice(_1325343), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325343), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325343), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325343), _1325345), _1325347)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325343), _1325345), _1325349))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325343), _1325345), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325343), _1325347), _1325349)))))], (44784 ^ _777864) ^ [_1659397, _1659399, _1659401, _1659403] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1659397, _1659399), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659397, tc_HOL_Obool), _1659401)), _1659403) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659397, tc_HOL_Obool), tc_fun(tc_prod(_1659397, _1659399), tc_HOL_Obool)), _1659401), hAPP(hAPP(c_COMBC(tc_fun(_1659397, tc_HOL_Obool), tc_fun(_1659397, tc_fun(_1659399, tc_HOL_Obool)), tc_fun(tc_prod(_1659397, _1659399), tc_HOL_Obool)), c_Product__Type_OSigma(_1659397, _1659399)), _1659403)))], (44907 ^ _777864) ^ [_1662278, _1662280, _1662282, _1662284] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1662278, tc_fun(_1662280, tc_HOL_Obool)), _1662282), _1662284) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662280, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662278, tc_fun(_1662280, tc_HOL_Obool), _1662284), _1662282)))], (21234 ^ _777864) ^ [_1144072, _1144074, _1144076, _1144078] : [class_Fields_Olinordered__field(_1144072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144072), c_Groups_Ozero__class_Ozero(_1144072)), _1144074)), 21241 ^ _777864 : [(21248 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144072), _1144076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144072), _1144078), _1144074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144072), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144072), _1144076), _1144074)), _1144078)))], (21242 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144072), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144072), _1144076), _1144074)), _1144078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144072), _1144076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144072), _1144078), _1144074))))]]], (23013 ^ _777864) ^ [_1176930, _1176932, _1176934] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176930, _1176932), _1176934)), -(c_Divides_Odivmod__nat(_1176930, _1176932) = _1176934)], (10894 ^ _777864) ^ [_959318, _959320, _959322] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959318), _959320) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959318), _959322), -(_959320 = _959322), -(_959318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28566 ^ _777864) ^ [_1291945, _1291947, _1291949, _1291951, _1291953, _1291955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1291945, _1291947), tc_HOL_Obool)), _1291949), _1291951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291945, tc_HOL_Obool)), _1291953), _1291955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291947, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1291945, _1291947, _1291949), _1291953)), hAPP(c_Relation_OImage(_1291945, _1291947, _1291951), _1291955))))], (42332 ^ _777864) ^ [_1600103, _1600105, _1600107, _1600109] : [-(c_Hilbert__Choice_OEps(tc_prod(_1600103, _1600105), hAPP(c_Product__Type_Oprod_Oprod__case(_1600103, _1600105, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1600103, tc_fun(_1600105, tc_HOL_Obool), tc_fun(_1600105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1600105, tc_HOL_Obool), tc_fun(_1600105, tc_HOL_Obool)), _1600103), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1600105)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1600103), c_fconj), hAPP(c_fequal, _1600107)))), hAPP(c_fequal, _1600109)))) = hAPP(hAPP(c_Product__Type_OPair(_1600103, _1600105), _1600107), _1600109))], (10065 ^ _777864) ^ [_946064] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946064), _946064)))))], (4510 ^ _777864) ^ [_846815, _846817, _846819, _846821] : [-(c_List_Olistrel(_846821, _846817) = c_List_Olistrel(_846819, _846815)), _846821 = _846819, _846817 = _846815], (14044 ^ _777864) ^ [_1015168, _1015170, _1015172] : [hBOOL(hAPP(_1015168, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015170), _1015172))), 14049 ^ _777864 : [(14052 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1015168, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14050 ^ _777864) ^ [] : [-(_1015172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14054 ^ _777864 : [(14059 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1015168, 14053 ^ [_1015168, _1015170, _1015172])))], (14057 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015172), hAPP(c_Nat_OSuc, 14053 ^ [_1015168, _1015170, _1015172])))))], (14055 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015172), 14053 ^ [_1015168, _1015170, _1015172])), _1015170)))]]], (34449 ^ _777864) ^ [_1417052, _1417054, _1417056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417052, tc_HOL_Obool)), _1417054), _1417056)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417052, tc_HOL_Obool)), _1417054), hAPP(c_Set_OPow(_1417052), _1417056))))], (48696 ^ _777864) ^ [_1756796, _1756798, _1756800, _1756802, _1756804] : [-(hAPP(hAPP(c_List_Ozip(_1756796, _1756798), hAPP(hAPP(c_List_Oappend(_1756796), _1756800), _1756802)), _1756804) = hAPP(hAPP(c_List_Oappend(tc_prod(_1756796, _1756798)), hAPP(hAPP(c_List_Ozip(_1756796, _1756798), _1756800), hAPP(hAPP(c_List_Otake(_1756798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756796)), _1756800)), _1756804))), hAPP(hAPP(c_List_Ozip(_1756796, _1756798), _1756802), hAPP(hAPP(c_List_Odrop(_1756798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756796)), _1756800)), _1756804))))], (49416 ^ _777864) ^ [_1772057, _1772059, _1772061] : [-(c_List_Obutlast(_1772057, hAPP(hAPP(c_List_Odrop(_1772057), _1772059), _1772061)) = hAPP(hAPP(c_List_Odrop(_1772057), _1772059), c_List_Obutlast(_1772057, _1772061)))], (40518 ^ _777864) ^ [_1552323, _1552325, _1552327] : [class_Lattices_Odistrib__lattice(_1552323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552323), _1552325)), -(_1552325 = c_Orderings_Obot__class_Obot(tc_fun(_1552323, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1552323), _1552327), c_Big__Operators_Olattice__class_OInf__fin(_1552323, _1552325)) = c_Big__Operators_Olattice__class_OInf__fin(_1552323, hAPP(c_Set_OCollect(_1552323), hAPP(hAPP(c_COMBB(tc_fun(_1552323, tc_HOL_Obool), tc_HOL_Obool, _1552323), c_HOL_OEx(_1552323)), hAPP(hAPP(c_COMBC(_1552323, tc_fun(_1552323, tc_HOL_Obool), tc_fun(_1552323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552323, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1552323, tc_HOL_Obool), tc_fun(_1552323, tc_HOL_Obool)), _1552323), c_COMBS(_1552323, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552323, tc_HOL_Obool), tc_fun(_1552323, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1552323), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1552323), c_fconj)), hAPP(hAPP(c_COMBC(_1552323, tc_fun(_1552323, _1552323), tc_fun(_1552323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552323, tc_HOL_Obool), tc_fun(tc_fun(_1552323, _1552323), tc_fun(_1552323, tc_HOL_Obool)), _1552323), c_COMBB(_1552323, tc_HOL_Obool, _1552323)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1552323), _1552327))))), hAPP(hAPP(c_COMBC(_1552323, tc_fun(_1552323, tc_HOL_Obool), tc_HOL_Obool), c_member(_1552323)), _1552325))))))], (42556 ^ _777864) ^ [_1605300, _1605302, _1605304, _1605306, _1605308, _1605310, _1605312, _1605314] : [class_Groups_Ocomm__monoid__add(_1605300), class_Orderings_Oord(_1605302), _1605304 = _1605306, _1605308 = _1605310, 42574 ^ _777864 : [(42579 ^ _777864) ^ [] : [hAPP(_1605312, 42573 ^ [_1605300, _1605302, _1605304, _1605306, _1605308, _1605310, _1605312, _1605314]) = hAPP(_1605314, 42573 ^ [_1605300, _1605302, _1605304, _1605306, _1605308, _1605310, _1605312, _1605314])], (42577 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1605302), 42573 ^ [_1605300, _1605302, _1605304, _1605306, _1605308, _1605310, _1605312, _1605314]), _1605310)))], (42575 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605302), _1605306), 42573 ^ [_1605300, _1605302, _1605304, _1605306, _1605308, _1605310, _1605312, _1605314])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1605302, _1605300), _1605312), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1605302, _1605304), _1605308)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1605302, _1605300), _1605314), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1605302, _1605306), _1605310)))], (26581 ^ _777864) ^ [_1246153, _1246155] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1246153), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246155))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1246153))), _1246155)))], (24839 ^ _777864) ^ [_1214003, _1214005, _1214007] : [class_Rings_Ocomm__semiring__1(_1214003), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214003), _1214005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214003), _1214007), _1214005))))], (51445 ^ _777864) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (5906 ^ _777864) ^ [_874887, _874889, _874891, _874893] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_874887, _874889), _874891, _874893, hAPP(hAPP(hAPP(c_Natural_Oupdate, _874891), _874887), hAPP(_874889, _874891))))], (19622 ^ _777864) ^ [_1115538, _1115540, _1115542] : [class_Int_Onumber__ring(_1115538), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1115538), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115538), _1115540), _1115542)), 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(_1115538), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1115538), hAPP(hAPP(c_Power_Opower__class_Opower(_1115538), _1115540), 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(_1115538), _1115542), 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(_1115538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115538), hAPP(c_Int_Onumber__class_Onumber__of(_1115538), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1115540)), _1115542)))], (34791 ^ _777864) ^ [_1423834, _1423836, _1423838, _1423840, _1423842, _1423844] : [c_Fun_Oinj__on(_1423834, _1423836, _1423838, _1423840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423836, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1423834, _1423836, _1423838), _1423840)), _1423842)), c_Fun_Oinj__on(_1423836, _1423834, _1423844, _1423842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423834, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1423836, _1423834, _1423844), _1423842)), _1423840)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423834), _1423840)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423836), _1423842)), -(hAPP(c_Finite__Set_Ocard(_1423834), _1423840) = hAPP(c_Finite__Set_Ocard(_1423836), _1423842))], (40620 ^ _777864) ^ [_1556635] : [-(c_Int_Oint__ge__less__than2(_1556635) = 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), _1556635)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (46433 ^ _777864) ^ [_1699048, _1699050, _1699052, _1699054, _1699056] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699048)), _1699050) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699052)), _1699054), 46436 ^ _777864 : [(46444 ^ _777864) ^ [] : [46445 ^ _777864 : [(46446 ^ _777864) ^ [_1699336] : [hAPP(c_Map_Omap__of(_1699048, _1699052, hAPP(hAPP(c_List_Ozip(_1699048, _1699052), _1699050), _1699054)), _1699056) = hAPP(c_Option_Ooption_OSome(_1699052), _1699336)]], -(hBOOL(hAPP(hAPP(c_member(_1699048), _1699056), hAPP(c_List_Oset(_1699048), _1699050))))], (46437 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1699048), _1699056), hAPP(c_List_Oset(_1699048), _1699050))), -(hAPP(c_Map_Omap__of(_1699048, _1699052, hAPP(hAPP(c_List_Ozip(_1699048, _1699052), _1699050), _1699054)), _1699056) = hAPP(c_Option_Ooption_OSome(_1699052), 46440 ^ [_1699048, _1699050, _1699052, _1699054, _1699056]))]]], (45208 ^ _777864) ^ [_1669690, _1669692, _1669694, _1669696] : [class_Orderings_Olinorder(_1669690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1669690), _1669692)), 45218 ^ _777864 : [(45221 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669690), _1669694), 45217 ^ [_1669690, _1669692, _1669694, _1669696]))], (45219 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1669690), 45217 ^ [_1669690, _1669692, _1669694, _1669696]), _1669692)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669690), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1669690), _1669694), _1669696)), hAPP(hAPP(c_Finite__Set_Ofold(_1669690, _1669690, c_Orderings_Oord__class_Omin(_1669690)), _1669696), _1669692))))], (41529 ^ _777864) ^ [_1581378, _1581380, _1581382] : [hBOOL(hAPP(hAPP(c_member(_1581380), _1581378), c_Orderings_Obot__class_Obot(tc_fun(_1581380, tc_HOL_Obool)))), -(hBOOL(hAPP(_1581382, _1581378)))], (27838 ^ _777864) ^ [_1273784, _1273786, _1273788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273784, tc_HOL_Obool)), _1273786), _1273788)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273784, tc_HOL_Obool)), _1273786), _1273788) = _1273788)], (39167 ^ _777864) ^ [_1517850, _1517852, _1517854, _1517856, _1517858] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1517850, _1517852), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517850, tc_HOL_Obool)), _1517854), _1517856)), _1517858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517850, _1517852), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517850, _1517852), _1517854), _1517858)), hAPP(hAPP(c_Product__Type_OSigma(_1517850, _1517852), _1517856), _1517858)))], (18824 ^ _777864) ^ [_1101327, _1101329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101327), 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)))), _1101329))), 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)))), _1101327)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101329), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1101327))], (18218 ^ _777864) ^ [_1091267] : [class_Int_Onumber__ring(_1091267), c_Int_Oiszero(_1091267, hAPP(c_Int_Onumber__class_Onumber__of(_1091267), c_Int_OMin))], (42702 ^ _777864) ^ [_1608288, _1608290, _1608292, _1608294, _1608296, _1608298] : [c_Finite__Set_Ofun__left__comm__idem(_1608288, _1608290, _1608292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608288), _1608294)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1608288, _1608290, _1608292), _1608296), hAPP(hAPP(c_Set_Oinsert(_1608288), _1608298), _1608294)) = hAPP(hAPP(c_Finite__Set_Ofold(_1608288, _1608290, _1608292), hAPP(hAPP(_1608292, _1608298), _1608296)), _1608294))], (13413 ^ _777864) ^ [_1003199, _1003201, _1003203] : [class_Divides_Osemiring__div(_1003199), -(c_Divides_Odiv__class_Omod(_1003199, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003199), _1003201), _1003203), _1003203) = c_Divides_Odiv__class_Omod(_1003199, _1003201, _1003203))], (10490 ^ _777864) ^ [_953066, _953068, _953070, _953072] : [class_Orderings_Opreorder(_953066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953066), _953068), _953070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953066), _953070), _953072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953066), _953068), _953072)))], (8006 ^ _777864) ^ [_911228, _911230, _911232] : [class_Rings_Olinordered__semidom(_911228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911230), _911232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911228), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911228), _911230)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911228), _911232))))], (14121 ^ _777864) ^ [_1016781, _1016783] : [class_Divides_Osemiring__div(_1016781), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1016781), c_Groups_Ozero__class_Ozero(_1016781)), _1016783) = c_Groups_Ozero__class_Ozero(_1016781))], (37683 ^ _777864) ^ [_1484726, _1484728] : [class_Orderings_Olinorder(_1484726), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484726, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484726), _1484728)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1484726), _1484728))], (20330 ^ _777864) ^ [_1128081, _1128083] : [class_Rings_Odivision__ring(_1128081), -(_1128083 = c_Groups_Ozero__class_Ozero(_1128081)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128081), _1128083), _1128083) = c_Groups_Oone__class_Oone(_1128081))], (50853 ^ _777864) ^ [_1803802, _1803804, _1803806, _1803808] : [-(c_List_Oremdups(_1803802, hAPP(hAPP(c_List_Omap(_1803804, _1803802), _1803806), c_List_Oremdups(_1803804, _1803808))) = c_List_Oremdups(_1803802, hAPP(hAPP(c_List_Omap(_1803804, _1803802), _1803806), _1803808)))], (49618 ^ _777864) ^ [_1776496, _1776498, _1776500] : [hBOOL(hAPP(c_List_Odistinct(_1776496), _1776498)), -(hAPP(c_List_Ofilter(_1776496, hAPP(hAPP(c_COMBC(_1776496, tc_fun(_1776496, tc_HOL_Obool), tc_HOL_Obool), c_member(_1776496)), hAPP(c_List_Oset(_1776496), c_List_Osublist(_1776496, _1776498, _1776500)))), _1776498) = c_List_Osublist(_1776496, _1776498, _1776500))], (12055 ^ _777864) ^ [_979665, _979667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _979665)), _979667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979665), _979667)))], (18378 ^ _777864) ^ [_1093856, _1093858] : [class_Int_Onumber__ring(_1093856), 18381 ^ _777864 : [(18388 ^ _777864) ^ [] : [c_Int_Oiszero(_1093856, hAPP(c_Int_Onumber__class_Onumber__of(_1093856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093858), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1093856), _1093858) = c_Groups_Oone__class_Oone(_1093856))], (18382 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1093856), _1093858) = c_Groups_Oone__class_Oone(_1093856), -(c_Int_Oiszero(_1093856, hAPP(c_Int_Onumber__class_Onumber__of(_1093856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093858), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (4454 ^ _777864) ^ [_845977, _845979, _845981, _845983, _845985, _845987] : [-(c_Big__Operators_Olattice_OSup__fin(_845987, _845983, _845979) = c_Big__Operators_Olattice_OSup__fin(_845985, _845981, _845977)), _845987 = _845985, _845983 = _845981, _845979 = _845977], (30442 ^ _777864) ^ [_1333058, _1333060] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1333058), _1333060)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1333058), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1333060))))], (29205 ^ _777864) ^ [_1306326, _1306328, _1306330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306326, tc_HOL_Obool)), _1306328), _1306330)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306326), _1306330)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306326), _1306328)))], (110 ^ _777864) ^ [_779363, _779365, _779367, _779369, _779371, _779373] : [-(c_Nitpick_Oless__frac(_779371, _779367, _779363)), c_Nitpick_Oless__frac(_779373, _779369, _779365), _779373 = _779371, _779369 = _779367, _779365 = _779363], (30631 ^ _777864) ^ [_1337964, _1337966] : [30632 ^ _777864 : [(30635 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337966), _1337964))], (30633 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337964), _1337966)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1337964, _1337966))], (49225 ^ _777864) ^ [_1768342, _1768344, _1768346] : [_1768342 = c_List_Olist_ONil(_1768344), -(c_List_Olast(_1768344, hAPP(hAPP(c_List_Olist_OCons(_1768344), _1768346), _1768342)) = _1768346)], (7474 ^ _777864) ^ [_901205, _901207, _901209] : [c_Com_Ocom_OSemi(_901205, _901207) = hAPP(c_Com_Ocom_OBODY, _901209)], (18400 ^ _777864) ^ [_1094242, _1094244] : [class_Int_Onumber__ring(_1094242), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1094242), hAPP(c_Int_Onumber__class_Onumber__of(_1094242), _1094244)), c_Groups_Oone__class_Oone(_1094242)) = hAPP(c_Int_Onumber__class_Onumber__of(_1094242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094244), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (8996 ^ _777864) ^ [_927423, _927425, _927427] : [class_Groups_Ogroup__add(_927423), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927423), hAPP(c_Groups_Ouminus__class_Ouminus(_927423), _927425)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927423), _927425), _927427)) = _927427)], (49616 ^ _777864) ^ [_1776448, _1776450] : [-(c_List_Opartition(_1776448, _1776450, c_List_Olist_ONil(_1776448)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776448), tc_List_Olist(_1776448)), c_List_Olist_ONil(_1776448)), c_List_Olist_ONil(_1776448)))], (2794 ^ _777864) ^ [_819621, _819623, _819625, _819627, _819629, _819631, _819633, _819635] : [-(c_Lazy__Sequence_Obind(_819635, _819631, _819627, _819623) = c_Lazy__Sequence_Obind(_819633, _819629, _819625, _819621)), _819635 = _819633, _819631 = _819629, _819627 = _819625, _819623 = _819621], (51291 ^ _777864) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (5681 ^ _777864) ^ [_869501, _869503, _869505, _869507] : [c_Natural_Oevaln(_869501, _869503, _869505, _869507), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869501), _869503), _869507)))], (19354 ^ _777864) ^ [_1110654, _1110656, _1110658] : [class_Rings_Olinordered__semidom(_1110654), hAPP(hAPP(c_Power_Opower__class_Opower(_1110654), _1110656), 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(_1110654), _1110658), 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(_1110654), c_Groups_Ozero__class_Ozero(_1110654)), _1110656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110654), c_Groups_Ozero__class_Ozero(_1110654)), _1110658)), -(_1110656 = _1110658)], (25409 ^ _777864) ^ [_1223441, _1223443, _1223445] : [class_Rings_Olinordered__idom(_1223441), 25412 ^ _777864 : [(25419 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223441), _1223443), _1223445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223441), hAPP(c_Groups_Oabs__class_Oabs(_1223441), _1223443)), _1223445)))], (25413 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223441), hAPP(c_Groups_Oabs__class_Oabs(_1223441), _1223443)), _1223445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223441), _1223443), _1223445)))]]], (7436 ^ _777864) ^ [_900544, _900546, _900548, _900550] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_900544, _900546)), _900548), _900550))), 7437 ^ _777864 : [(7438 ^ _777864) ^ [_900612] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_900544), _900548), _900612)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_900546), _900612), _900550))]]], (32547 ^ _777864) ^ [_1373581, _1373583, _1373585, _1373587] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373581), _1373583)), hBOOL(hAPP(hAPP(c_member(_1373581), _1373585), _1373583)), hBOOL(hAPP(hAPP(c_member(_1373581), _1373587), _1373583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1373581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373581, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373581, tc_HOL_Obool)), _1373583), hAPP(hAPP(c_Set_Oinsert(_1373581), _1373585), c_Orderings_Obot__class_Obot(tc_fun(_1373581, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1373581), _1373587), c_Orderings_Obot__class_Obot(tc_fun(_1373581, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1373581), _1373583))))], (22048 ^ _777864) ^ [_1159018, _1159020] : [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), _1159018), _1159020))), 22051 ^ _777864 : [(22060 ^ _777864) ^ [] : [-(c_Divides_OnegDivAlg(_1159018, _1159020) = hAPP(c_Divides_Oadjust(_1159020), c_Divides_OnegDivAlg(_1159018, 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)))), _1159020)))), -(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), _1159018), _1159020)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159020), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22052 ^ _777864) ^ [] : [22053 ^ _777864 : [(22056 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159020), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22054 ^ _777864) ^ [] : [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), _1159018), _1159020)))]], -(c_Divides_OnegDivAlg(_1159018, _1159020) = 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), _1159018), _1159020)))]]], (45191 ^ _777864) ^ [_1669326, _1669328, _1669330, _1669332] : [class_Orderings_Olinorder(_1669326), hBOOL(hAPP(c_Finite__Set_Ofinite(_1669326), _1669328)), 45201 ^ _777864 : [(45204 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669326), 45200 ^ [_1669326, _1669328, _1669330, _1669332]), _1669330))], (45202 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1669326), 45200 ^ [_1669326, _1669328, _1669330, _1669332]), _1669328)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669326), hAPP(hAPP(c_Finite__Set_Ofold(_1669326, _1669326, c_Orderings_Oord__class_Omax(_1669326)), _1669332), _1669328)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1669326), _1669330), _1669332))))], (42988 ^ _777864) ^ [_1613723, _1613725] : [-(hAPP(c_Relation_ODomain(_1613723, _1613723), c_Transitive__Closure_Otrancl(_1613723, _1613725)) = hAPP(c_Relation_ODomain(_1613723, _1613723), _1613725))], (30138 ^ _777864) ^ [_1326296, _1326298, _1326300, _1326302] : [hBOOL(hAPP(hAPP(c_member(_1326296), _1326298), _1326300)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326296, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1326296), _1326298), _1326302)), _1326300) = hAPP(hAPP(c_Set_Oinsert(_1326296), _1326298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326296, tc_HOL_Obool)), _1326302), _1326300)))], (41325 ^ _777864) ^ [_1575787, _1575789, _1575791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575787, _1575789)), _1575791)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1575787), hAPP(c_Relation_ODomain(_1575787, _1575789), _1575791))))], (45414 ^ _777864) ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1674337, _1674339)), _1674341), hAPP(hAPP(c_Relation_Orel__comp(_1674337, _1674343, _1674339), _1674345), _1674347))), 45420 ^ _777864 : [(45425 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1674343, _1674339)), hAPP(hAPP(c_Product__Type_OPair(_1674343, _1674339), 45418 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347]), 45419 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347])), _1674347)))], (45423 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1674337, _1674343)), hAPP(hAPP(c_Product__Type_OPair(_1674337, _1674343), 45417 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347]), 45418 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347])), _1674345)))], (45421 ^ _777864) ^ [] : [-(_1674341 = hAPP(hAPP(c_Product__Type_OPair(_1674337, _1674339), 45417 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347]), 45419 ^ [_1674337, _1674339, _1674341, _1674343, _1674345, _1674347]))]]], (16220 ^ _777864) ^ [_1056064, _1056066] : [class_Groups_Oordered__ab__group__add__abs(_1056064), -(hAPP(c_Groups_Oabs__class_Oabs(_1056064), hAPP(c_Groups_Ouminus__class_Ouminus(_1056064), _1056066)) = hAPP(c_Groups_Oabs__class_Oabs(_1056064), _1056066))], (28647 ^ _777864) ^ [_1293984, _1293986, _1293988, _1293990, _1293992] : [c_Hoare__Mirabelle_Ohoare__derivs(_1293984, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1293984), tc_HOL_Obool)), _1293986), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1293984), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), hAPP(hAPP(c_COMBB(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1293984)), _1293988)), c_Com_Ocom_OBODY)), _1293990)), _1293992)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1293984), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), hAPP(hAPP(c_COMBB(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1293984)), _1293988)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1293990)), _1293992)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1293984, _1293986, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1293984), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), hAPP(hAPP(c_COMBB(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1293984, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1293984))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1293984)), _1293988)), c_Com_Ocom_OBODY)), _1293990)), _1293992)))], (3244 ^ _777864) ^ [_826970, _826972] : [_826972 = _826970, -(c_Int_OBit0(_826972) = c_Int_OBit0(_826970))], (35760 ^ _777864) ^ [_1443015, _1443017, _1443019] : [class_Orderings_Oorder(_1443015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443015), _1443017), _1443019)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443015, _1443019), _1443017) = c_Orderings_Obot__class_Obot(tc_fun(_1443015, tc_HOL_Obool)))], (10860 ^ _777864) ^ [_958720, _958722, _958724, _958726] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_958720), 10863 ^ _777864 : [(10870 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958720), _958722), _958726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958720), _958722), _958724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958720), _958726), _958724))))], (10864 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958720), _958722), _958724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958720), _958726), _958724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958720), _958722), _958726)))]]], (5844 ^ _777864) ^ [_873835, _873837] : [hAPP(c_Com_Ocom_OBODY, _873835) = hAPP(c_Com_Ocom_OBODY, _873837), -(_873835 = _873837)], (3732 ^ _777864) ^ [_834684, _834686] : [_834686 = _834684, -(c_Rings_Odvd__class_Odvd(_834686) = c_Rings_Odvd__class_Odvd(_834684))], (14089 ^ _777864) ^ [_1016108, _1016110, _1016112] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016108), _1016110)), _1016112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016108), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016110), _1016112))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016108), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016110, _1016112))), _1016112)))], (2344 ^ _777864) ^ [_812404, _812406, _812408, _812410] : [-(c_Nitpick_Onat__lcm(_812410, _812406) = c_Nitpick_Onat__lcm(_812408, _812404)), _812410 = _812408, _812406 = _812404], (48754 ^ _777864) ^ [_1757986, _1757988] : [-(_1757986 = c_List_Olist_ONil(_1757988)), -(hAPP(c_List_Ohd(_1757988), _1757986) = hAPP(hAPP(c_List_Onth(_1757988), _1757986), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34167 ^ _777864) ^ [_1410995, _1410997, _1410999, _1411001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1410995, _1410995)), hAPP(hAPP(c_Product__Type_OPair(_1410995, _1410995), _1410997), _1410999)), c_Relation_OId__on(_1410995, _1411001))), 34170 ^ _777864 : [(34173 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410995), _1410997), _1411001)))], (34171 ^ _777864) ^ [] : [-(_1410997 = _1410999)]]], (15390 ^ _777864) ^ [_1039629, _1039631, _1039633] : [class_Groups_Oab__group__add(_1039629), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039629), _1039631), _1039633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039629), _1039631), hAPP(c_Groups_Ouminus__class_Ouminus(_1039629), _1039633)))], (26129 ^ _777864) ^ [_1237172, _1237174, _1237176] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1237172, _1237174, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1237172)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1237172), _1237176), c_Com_Ocom_OSKIP), _1237176)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237172), tc_HOL_Obool)))))], (47936 ^ _777864) ^ [_1737301, _1737303, _1737305, _1737307, _1737309, _1737311] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737301)), _1737303) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737305)), _1737307), -(c_Map_Omap__upds(_1737301, _1737305, _1737309, _1737303, hAPP(hAPP(c_List_Oappend(_1737305), _1737307), _1737311)) = c_Map_Omap__upds(_1737301, _1737305, _1737309, _1737303, _1737307))], (35026 ^ _777864) ^ [_1428835] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1428835))], (36328 ^ _777864) ^ [_1454100, _1454102, _1454104] : [class_Orderings_Oord(_1454100), 36331 ^ _777864 : [(36338 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454100), _1454102), _1454104)), -(hBOOL(hAPP(hAPP(c_member(_1454100), _1454102), hAPP(c_SetInterval_Oord__class_OlessThan(_1454100), _1454104))))], (36332 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1454100), _1454102), hAPP(c_SetInterval_Oord__class_OlessThan(_1454100), _1454104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454100), _1454102), _1454104)))]]], (16936 ^ _777864) ^ [_1069860, _1069862, _1069864] : [class_Rings_Olinordered__semidom(_1069860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069860), c_Groups_Ozero__class_Ozero(_1069860)), _1069862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069860), _1069862), c_Groups_Oone__class_Oone(_1069860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069860), hAPP(hAPP(c_Power_Opower__class_Opower(_1069860), _1069862), hAPP(c_Nat_OSuc, _1069864))), c_Groups_Oone__class_Oone(_1069860))))], (23319 ^ _777864) ^ [_1184414, _1184416, _1184418, _1184420, _1184422] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184414, _1184416, _1184418), _1184420), _1184422) = hAPP(hAPP(_1184420, hAPP(c_Product__Type_Ofst(_1184414, _1184416), _1184422)), hAPP(c_Product__Type_Osnd(_1184414, _1184416), _1184422)))], (42679 ^ _777864) ^ [_1607863, _1607865] : [c_Wellfounded_Oacyclic(_1607863, _1607865), 42682 ^ _777864 : [(42683 ^ _777864) ^ [_1607948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607863, _1607863)), hAPP(hAPP(c_Product__Type_OPair(_1607863, _1607863), _1607948), _1607948)), c_Transitive__Closure_Otrancl(_1607863, _1607865)))]]], (45807 ^ _777864) ^ [_1683687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1683687)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1683687), tc_HOL_Obool))))], (21838 ^ _777864) ^ [_1155772, _1155774] : [-(_1155772 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1155772, _1155774) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1155772), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1155774)))], (13545 ^ _777864) ^ [_1006007, _1006009] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1006007), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1006009)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006007, _1006009)))], (42220 ^ _777864) ^ [_1597761, _1597763, _1597765, _1597767, _1597769, _1597771, _1597773] : [c_Finite__Set_Ofolding__idem(_1597761, _1597763, _1597765, _1597767), -(hAPP(c_Fun_Ocomp(_1597763, _1597763, _1597769, hAPP(_1597765, _1597771)), hAPP(c_Fun_Ocomp(_1597763, _1597763, _1597769, hAPP(_1597765, _1597771)), _1597773)) = hAPP(c_Fun_Ocomp(_1597763, _1597763, _1597769, hAPP(_1597765, _1597771)), _1597773))], (28338 ^ _777864) ^ [_1284203, _1284205, _1284207, _1284209] : [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), _1284203), _1284205)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1284207), _1284209))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1284203), _1284209) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1284207), _1284205))], (51361 ^ _777864) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (3364 ^ _777864) ^ [_828846, _828848, _828850, _828852, _828854, _828856, _828858, _828860] : [-(c_Recdef_Osame__fst(_828860, _828856, _828852, _828848) = c_Recdef_Osame__fst(_828858, _828854, _828850, _828846)), _828860 = _828858, _828856 = _828854, _828852 = _828850, _828848 = _828846], (7100 ^ _777864) ^ [_894497, _894499, _894501] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_894497, _894499, _894501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _894499)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _894501))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6843 ^ _777864) ^ [_890498, _890500] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890498), _890500) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6848 ^ _777864 : [(6851 ^ _777864) ^ [] : [-(_890500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6849 ^ _777864) ^ [] : [-(_890498 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 6852 ^ _777864 : [(6855 ^ _777864) ^ [] : [-(_890500 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6853 ^ _777864) ^ [] : [-(_890498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31601 ^ _777864) ^ [_1355428, _1355430, _1355432] : [class_Orderings_Olinorder(_1355428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355428), _1355430)), hBOOL(hAPP(hAPP(c_member(_1355428), _1355432), _1355430)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355428), _1355432), c_Big__Operators_Olinorder__class_OMin(_1355428, _1355430)) = c_Big__Operators_Olinorder__class_OMin(_1355428, _1355430))], (51367 ^ _777864) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (24487 ^ _777864) ^ [_1206953, _1206955, _1206957, _1206959, _1206961, _1206963] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1206953, _1206955, _1206957, _1206959, c_Nitpick_Opair__box_OPairBox(_1206953, _1206955, _1206961, _1206963)) = hAPP(hAPP(_1206959, _1206961), _1206963))], (5296 ^ _777864) ^ [_858928, _858930] : [_858930 = _858928, -(c_List_Oappend(_858930) = c_List_Oappend(_858928))], (17586 ^ _777864) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15254 ^ _777864) ^ [_1036797, _1036799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036797), _1036799)), _1036797)))], (24935 ^ _777864) ^ [_1215653, _1215655, _1215657] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215653), _1215655)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215655), _1215653))), 24950 ^ _777864 : [(24953 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215657), _1215653))], (24951 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215653), _1215657)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215655), _1215657)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1215657), _1215655)))], (41998 ^ _777864) ^ [_1592674, _1592676, _1592678, _1592680, _1592682, _1592684, _1592686, _1592688] : [c_Finite__Set_Ofolding__image(_1592674, _1592676, _1592678, _1592680, _1592682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592676), _1592684)), c_Fun_Oinj__on(_1592676, _1592676, _1592686, _1592684), -(hAPP(hAPP(_1592682, _1592688), hAPP(c_Set_Oimage(_1592676, _1592676, _1592686), _1592684)) = hAPP(hAPP(_1592682, hAPP(c_Fun_Ocomp(_1592676, _1592674, _1592676, _1592688), _1592686)), _1592684))], (18052 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (49174 ^ _777864) ^ [_1767411, _1767413, _1767415, _1767417] : [-(_1767411 = c_List_Olist_ONil(_1767413)), 49177 ^ _777864 : [(49184 ^ _777864) ^ [] : [-(_1767415 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767413)), _1767411)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1767413, hAPP(hAPP(c_List_Olist__update(_1767413, _1767411), _1767415), _1767417)) = c_List_Olast(_1767413, _1767411))], (49178 ^ _777864) ^ [] : [_1767415 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767413)), _1767411)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1767413, hAPP(hAPP(c_List_Olist__update(_1767413, _1767411), _1767415), _1767417)) = _1767417)]]], (1782 ^ _777864) ^ [_802907, _802909] : [-(hBOOL(_802907)), _802909 = _802907, hBOOL(_802909)], (3452 ^ _777864) ^ [_830260, _830262, _830264, _830266, _830268, _830270, _830272, _830274] : [-(c_Product__Type_Oapsnd(_830274, _830270, _830266, _830262) = c_Product__Type_Oapsnd(_830272, _830268, _830264, _830260)), _830274 = _830272, _830270 = _830268, _830266 = _830264, _830262 = _830260], (19228 ^ _777864) ^ [_1108449, _1108451] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1108449)), c_Int_OBit1(_1108451)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1108449), c_Int_Osucc(_1108451))))], (6174 ^ _777864) ^ [_879415, _879417, _879419, _879421] : [class_Groups_Ocancel__semigroup__add(_879415), 6177 ^ _777864 : [(6184 ^ _777864) ^ [] : [_879419 = _879421, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879415), _879417), _879419) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879415), _879417), _879421))], (6178 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879415), _879417), _879419) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879415), _879417), _879421), -(_879419 = _879421)]]], (48326 ^ _777864) ^ [_1746888, _1746890, _1746892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746888), tc_List_Olist(_1746888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746888), tc_List_Olist(_1746888)), _1746890), c_List_Olist_ONil(_1746888))), c_List_Olistrel1(_1746888, _1746892)))], (41200 ^ _777864) ^ [_1572848, _1572850, _1572852, _1572854] : [hBOOL(hAPP(c_Predicate_ORangeP(_1572848, _1572850, hAPP(hAPP(c_COMBC(_1572848, tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_fun(_1572850, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572850, tc_fun(tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_fun(_1572850, tc_HOL_Obool)), _1572848), c_COMBC(_1572850, tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1572850, tc_prod(_1572848, _1572850)), tc_fun(_1572850, tc_fun(tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_HOL_Obool)), _1572848), hAPP(c_COMBB(tc_prod(_1572848, _1572850), tc_fun(tc_fun(tc_prod(_1572848, _1572850), tc_HOL_Obool), tc_HOL_Obool), _1572850), c_member(tc_prod(_1572848, _1572850)))), c_Product__Type_OPair(_1572848, _1572850)))), _1572852)), _1572854)), -(hBOOL(hAPP(hAPP(c_member(_1572850), _1572854), hAPP(c_Relation_ORange(_1572848, _1572850), _1572852))))], (15896 ^ _777864) ^ [_1050198, _1050200] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1050198), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1050200), _1050198)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050200), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050200, _1050198)))], (6873 ^ _777864) ^ [_890920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _890920)), -(_890920 = hAPP(c_Nat_OSuc, 6876 ^ [_890920]))], (29666 ^ _777864) ^ [_1316521, _1316523, _1316525] : [class_Lattices_Osemilattice__inf(_1316521), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316521), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316521), _1316523), _1316525)), _1316525)))], (13493 ^ _777864) ^ [_1004939, _1004941, _1004943, _1004945] : [class_Divides_Osemiring__div(_1004939), -(c_Divides_Odiv__class_Omod(_1004939, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004939), _1004941), _1004943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004939), _1004945), _1004943)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004939), c_Divides_Odiv__class_Omod(_1004939, _1004941, _1004945)), _1004943))], (27620 ^ _777864) ^ [_1269696, _1269698, _1269700, _1269702, _1269704, _1269706, _1269708] : [hBOOL(hAPP(_1269696, _1269698)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1269700, _1269700)), hAPP(hAPP(c_Product__Type_OPair(_1269700, _1269700), _1269702), _1269704)), hAPP(_1269706, _1269698))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1269708, _1269700), tc_prod(_1269708, _1269700))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1269708, _1269700), tc_prod(_1269708, _1269700)), hAPP(hAPP(c_Product__Type_OPair(_1269708, _1269700), _1269698), _1269702)), hAPP(hAPP(c_Product__Type_OPair(_1269708, _1269700), _1269698), _1269704))), c_Recdef_Osame__fst(_1269708, _1269700, _1269696, _1269706))))], (8266 ^ _777864) ^ [_914928, _914930, _914932, _914934] : [class_Orderings_Oorder(_914928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914928), _914930), _914932)), _914930 = _914934, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914928), _914934), _914932)))], (41366 ^ _777864) ^ [_1576981, _1576983] : [c_Wellfounded_Owf(_1576981, _1576983), -(c_Wellfounded_OwfP(_1576981, hAPP(hAPP(c_COMBC(_1576981, tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_fun(_1576981, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576981, tc_fun(tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_fun(_1576981, tc_HOL_Obool)), _1576981), c_COMBC(_1576981, tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576981, tc_prod(_1576981, _1576981)), tc_fun(_1576981, tc_fun(tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_HOL_Obool)), _1576981), hAPP(c_COMBB(tc_prod(_1576981, _1576981), tc_fun(tc_fun(tc_prod(_1576981, _1576981), tc_HOL_Obool), tc_HOL_Obool), _1576981), c_member(tc_prod(_1576981, _1576981)))), c_Product__Type_OPair(_1576981, _1576981)))), _1576983)))], (37892 ^ _777864) ^ [_1488795, _1488797, _1488799, _1488801] : [c_Map_Odom(_1488795, _1488797, _1488799) = hAPP(hAPP(c_Set_Oinsert(_1488795), _1488801), c_Orderings_Obot__class_Obot(tc_fun(_1488795, tc_HOL_Obool))), -(_1488799 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1488795, tc_Option_Ooption(_1488797)), hAPP(c_COMBK(tc_Option_Ooption(_1488797), _1488795), c_Option_Ooption_ONone(_1488797))), _1488801), hAPP(c_Option_Ooption_OSome(_1488797), 37895 ^ [_1488795, _1488797, _1488799, _1488801])))], (35404 ^ _777864) ^ [_1436228, _1436230, _1436232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436228)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1436230), _1436232)), 35411 ^ _777864 : [(35412 ^ _777864) ^ [_1436424] : [35414 ^ _777864 : [(35420 ^ _777864) ^ [] : [-(_1436424 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35416 ^ [_1436228, _1436230, _1436232, _1436424]), 35413 ^ [_1436228, _1436230, _1436232, _1436424]))], (35418 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35416 ^ [_1436228, _1436230, _1436232, _1436424]), _1436232)))], (35415 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35413 ^ [_1436228, _1436230, _1436232, _1436424]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1436228))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436230), _1436424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436230), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1436424), _1436228))))]]], (46607 ^ _777864) ^ [_1704911, _1704913, _1704915, _1704917, _1704919, _1704921] : [-(c_List_Olistrelp(_1704911, _1704913, hAPP(hAPP(c_List_Olist_OCons(_1704911), _1704915), _1704917), hAPP(hAPP(c_List_Olist_OCons(_1704911), _1704919), _1704921))), hBOOL(hAPP(hAPP(_1704913, _1704915), _1704919)), c_List_Olistrelp(_1704911, _1704913, _1704917, _1704921)], (48538 ^ _777864) ^ [_1752905, _1752907, _1752909, _1752911, _1752913] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1752905, _1752907)), _1752909), hAPP(hAPP(c_List_Ozip(_1752905, _1752907), _1752911), _1752913)) = hAPP(hAPP(c_List_Ozip(_1752905, _1752907), hAPP(hAPP(c_List_Odrop(_1752905), _1752909), _1752911)), hAPP(hAPP(c_List_Odrop(_1752907), _1752909), _1752913)))], (24009 ^ _777864) ^ [_1197611, _1197613, _1197615] : [class_Orderings_Olinorder(_1197611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197611), _1197613), _1197615)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197611), _1197613), _1197615) = _1197615)], (47814 ^ _777864) ^ [_1734368, _1734370, _1734372, _1734374, _1734376, _1734378, _1734380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734368)), _1734370)), _1734372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734372), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734374)), _1734376))), -(c_Map_Omap__upds(_1734368, _1734374, _1734378, _1734370, hAPP(hAPP(c_List_Olist__update(_1734374, _1734376), _1734372), _1734380)) = c_Map_Omap__upds(_1734368, _1734374, _1734378, _1734370, _1734376))], (29616 ^ _777864) ^ [_1315494, _1315496, _1315498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315494, tc_HOL_Obool)), _1315496), _1315498)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315494, tc_HOL_Obool)), _1315496), _1315498) = _1315496)], (20488 ^ _777864) ^ [_1130763, _1130765, _1130767, _1130769, _1130771] : [class_Fields_Olinordered__field(_1130763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130763), c_Groups_Ozero__class_Ozero(_1130763)), _1130765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130763), _1130765), _1130767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130763), c_Groups_Ozero__class_Ozero(_1130763)), _1130769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130763), _1130769), _1130771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130763), _1130765), _1130771)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130763), _1130767), _1130769))))], (46160 ^ _777864) ^ [_1691762, _1691764, _1691766, _1691768] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1691762, _1691762)), hAPP(hAPP(c_Product__Type_OPair(_1691762, _1691762), _1691764), _1691766)), hAPP(c_List_Oset(tc_prod(_1691762, _1691762)), hAPP(hAPP(c_List_Ozip(_1691762, _1691762), _1691768), _1691768))))), hBOOL(hAPP(hAPP(c_member(_1691762), _1691764), hAPP(c_List_Oset(_1691762), _1691768))), _1691764 = _1691766], (15998 ^ _777864) ^ [_1052020, _1052022] : [-(_1052020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052020), _1052022) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052020), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1052022)))], (3634 ^ _777864) ^ [_833167, _833169, _833171, _833173, _833175, _833177, _833179, _833181] : [-(c_New__Random__Sequence_Opos__map(_833181, _833177, _833173, _833169) = c_New__Random__Sequence_Opos__map(_833179, _833175, _833171, _833167)), _833181 = _833179, _833177 = _833175, _833173 = _833171, _833169 = _833167], (44374 ^ _777864) ^ [_1649619, _1649621, _1649623] : [c_Relation_Osingle__valued(_1649619, _1649619, _1649621), -(c_Relation_Osingle__valued(_1649619, _1649619, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1649619, _1649619), tc_HOL_Obool), _1649623), _1649621)))], (46675 ^ _777864) ^ [_1706333, _1706335, _1706337, _1706339, _1706341, _1706343] : [_1706333 = _1706335, -(hAPP(c_Map_Omap__of(_1706337, _1706339, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1706337, _1706339)), hAPP(hAPP(c_Product__Type_OPair(_1706337, _1706339), _1706333), _1706341)), _1706343)), _1706335) = hAPP(c_Option_Ooption_OSome(_1706339), _1706341))], (38308 ^ _777864) ^ [_1496695, _1496697] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496695, tc_HOL_Obool)), _1496697) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1496695, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1496695, tc_HOL_Obool))), _1496697))], (8782 ^ _777864) ^ [_923921, _923923, _923925] : [class_Rings_Ocomm__semiring__1(_923921), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923921), _923923), _923925) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923921), _923925), _923923))], (48728 ^ _777864) ^ [_1757666, _1757668, _1757670] : [_1757666 = c_List_Olist_ONil(_1757668), -(hAPP(c_List_Ohd(_1757668), hAPP(hAPP(c_List_Oappend(_1757668), _1757666), _1757670)) = hAPP(c_List_Ohd(_1757668), _1757670))], (16866 ^ _777864) ^ [_1068542, _1068544, _1068546, _1068548] : [class_Rings_Olinordered__semidom(_1068542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068542), c_Groups_Oone__class_Oone(_1068542)), _1068544)), 16873 ^ _777864 : [(16880 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068546), _1068548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068542), hAPP(hAPP(c_Power_Opower__class_Opower(_1068542), _1068544), _1068546)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068542), _1068544), _1068548))))], (16874 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068542), hAPP(hAPP(c_Power_Opower__class_Opower(_1068542), _1068544), _1068546)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068542), _1068544), _1068548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068546), _1068548)))]]], (28689 ^ _777864) ^ [_1295805, _1295807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1295805), _1295807)), -(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)), _1295805)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1295807))))], (46785 ^ _777864) ^ [_1709893, _1709895, _1709897, _1709899] : [-(hBOOL(hAPP(hAPP(c_member(_1709893), _1709895), hAPP(c_List_Oset(_1709893), _1709897)))), hBOOL(hAPP(hAPP(c_member(_1709893), _1709895), hAPP(c_List_Oset(_1709893), c_List_Osublist(_1709893, _1709897, _1709899))))], (15300 ^ _777864) ^ [_1037770, _1037772, _1037774] : [-(hBOOL(hAPP(_1037770, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037772), _1037774))))), 15303 ^ _777864 : [(15306 ^ _777864) ^ [] : [hBOOL(hAPP(_1037770, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037772)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1037774))))], (15304 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1037774), _1037772)))]], 15307 ^ _777864 : [(15310 ^ _777864) ^ [] : [hBOOL(hAPP(_1037770, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15308 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037772), _1037774)))]]], (46627 ^ _777864) ^ [_1705303, _1705305, _1705307, _1705309, _1705311] : [-(hAPP(hAPP(c_List_Omap(_1705303, _1705305), _1705307), hAPP(hAPP(c_List_Olist_OCons(_1705303), _1705309), _1705311)) = hAPP(hAPP(c_List_Olist_OCons(_1705305), hAPP(_1705307, _1705309)), hAPP(hAPP(c_List_Omap(_1705303, _1705305), _1705307), _1705311)))], (41418 ^ _777864) ^ [_1578723, _1578725, _1578727, _1578729] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1578723), _1578725))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578727), hAPP(c_Set_Oimage(_1578723, _1578727, _1578729), _1578725))), 41426 ^ _777864 : [(41429 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1578723), hAPP(c_Set_OCollect(_1578723), hAPP(hAPP(c_COMBS(_1578723, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578723), c_fconj), hAPP(hAPP(c_COMBC(_1578723, tc_fun(_1578723, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578723)), _1578725))), hAPP(hAPP(c_COMBC(_1578723, _1578727, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1578727, tc_fun(_1578727, tc_HOL_Obool), _1578723), c_fequal), _1578729)), hAPP(_1578729, 41425 ^ [_1578723, _1578725, _1578727, _1578729]))))))], (41427 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578723), 41425 ^ [_1578723, _1578725, _1578727, _1578729]), _1578725)))]]], (51231 ^ _777864) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (15216 ^ _777864) ^ [_1036117, _1036119, _1036121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036117), _1036119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036117), _1036121)), 15223 ^ _777864 : [(15230 ^ _777864) ^ [] : [_1036119 = _1036121, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036119), _1036117) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036121), _1036117))], (15224 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036119), _1036117) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036121), _1036117), -(_1036119 = _1036121)]]], (32477 ^ _777864) ^ [_1372055, _1372057, _1372059] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372055), _1372057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372055, tc_HOL_Obool)), _1372059), _1372057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1372055), _1372059)), hAPP(c_Finite__Set_Ocard(_1372055), _1372057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1372055, tc_HOL_Obool)), _1372059), _1372057)))], (19148 ^ _777864) ^ [_1107022, _1107024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1107022)), c_Int_OBit1(_1107024))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107022), _1107024)))], (22588 ^ _777864) ^ [_1168426, _1168428, _1168430, _1168432, _1168434] : [hAPP(c_Product__Type_Ofst(_1168426, _1168428), hAPP(hAPP(c_Product__Type_OPair(_1168426, _1168428), _1168430), _1168432)) = _1168434, -(_1168430 = _1168434)], (28358 ^ _777864) ^ [_1284620, _1284622] : [-(c_FunDef_Orp__inv__image(_1284620, _1284622) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))))), tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))), tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)), tc_fun(tc_fun(_1284622, _1284620), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool)), c_COMBS(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)), tc_fun(tc_fun(_1284622, _1284620), tc_fun(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), tc_fun(tc_prod(_1284620, _1284620), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool))), tc_fun(_1284622, _1284620)), c_Product__Type_OPair(tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool), tc_fun(tc_prod(_1284622, _1284622), tc_HOL_Obool)))), c_Relation_Oinv__image(_1284620, _1284622))))), c_Relation_Oinv__image(_1284620, _1284622))))], (11253 ^ _777864) ^ [_965362, _965364] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _965362), _965364))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965362), _965364)), -(_965362 = _965364)], (20444 ^ _777864) ^ [_1129917, _1129919, _1129921, _1129923, _1129925] : [class_Fields_Olinordered__field(_1129917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129917), c_Groups_Ozero__class_Ozero(_1129917)), _1129919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129917), _1129919), _1129921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129917), c_Groups_Ozero__class_Ozero(_1129917)), _1129923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129917), _1129923), _1129925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129917), _1129919), _1129925)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129917), _1129921), _1129923))))], (26981 ^ _777864) ^ [_1254392, _1254394, _1254396] : [hBOOL(hAPP(_1254396, _1254394)), -(hBOOL(hAPP(hAPP(c_member(_1254392), _1254394), _1254396)))], (37985 ^ _777864) ^ [_1490712, _1490714, _1490716] : [_1490716 = hAPP(c_COMBK(tc_Option_Ooption(_1490714), _1490712), c_Option_Ooption_ONone(_1490714)), -(c_Map_Odom(_1490712, _1490714, _1490716) = c_Orderings_Obot__class_Obot(tc_fun(_1490712, tc_HOL_Obool)))], (30877 ^ _777864) ^ [_1342459, _1342461, _1342463] : [class_Lattices_Olattice(_1342459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342459), _1342461)), hBOOL(hAPP(hAPP(c_member(_1342459), _1342463), _1342461)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1342459), _1342463), c_Big__Operators_Olattice__class_OInf__fin(_1342459, _1342461)) = c_Big__Operators_Olattice__class_OInf__fin(_1342459, _1342461))], (30056 ^ _777864) ^ [_1324717, _1324719, _1324721] : [class_Lattices_Olattice(_1324717), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324717), _1324719), _1324721) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324717), _1324721), _1324719))], (51301 ^ _777864) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (18184 ^ _777864) ^ [_1090689, _1090691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090689)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090691)))), 18187 ^ _777864 : [(18190 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1090691))], (18188 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090689), _1090691)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090689), _1090691))], (2514 ^ _777864) ^ [_815039, _815041, _815043, _815045] : [-(c_Nitpick_Ouminus__frac(_815045, _815041) = c_Nitpick_Ouminus__frac(_815043, _815039)), _815045 = _815043, _815041 = _815039], (15436 ^ _777864) ^ [_1040490, _1040492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040492), _1040490)), -(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), _1040490), _1040492))))], (18076 ^ _777864) ^ [_1089040, _1089042] : [class_Int_Onumber__ring(_1089040), 18079 ^ _777864 : [(18086 ^ _777864) ^ [] : [c_Int_Oiszero(_1089040, hAPP(c_Int_Onumber__class_Onumber__of(_1089040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1089042)))), -(c_Groups_Ozero__class_Ozero(_1089040) = hAPP(c_Int_Onumber__class_Onumber__of(_1089040), _1089042))], (18080 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(_1089040) = hAPP(c_Int_Onumber__class_Onumber__of(_1089040), _1089042), -(c_Int_Oiszero(_1089040, hAPP(c_Int_Onumber__class_Onumber__of(_1089040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1089042)))))]]], (44023 ^ _777864) ^ [_1640303, _1640305, _1640307, _1640309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640303, _1640303)), hAPP(hAPP(c_Product__Type_OPair(_1640303, _1640303), _1640305), _1640307)), c_Transitive__Closure_Ortrancl(_1640303, _1640309))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640303, _1640303)), hAPP(hAPP(c_Product__Type_OPair(_1640303, _1640303), _1640307), _1640305)), c_Transitive__Closure_Ortrancl(_1640303, hAPP(c_Relation_Oconverse(_1640303, _1640303), _1640309)))))], (26587 ^ _777864) ^ [_1246264, _1246266] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1246264))), _1246266)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1246264), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246266))))], (22284 ^ _777864) ^ [_1162800, _1162802, _1162804, _1162806, _1162808, _1162810, _1162812] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162800, _1162802), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1162804), _1162806))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162808, _1162802), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1162810), _1162812))), -(_1162802 = 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), _1162800), _1162808), _1162802), 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), _1162804), _1162810)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1162806), _1162812)), _1162802))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1162806), _1162812), _1162802)))))], (18410 ^ _777864) ^ [_1094473, _1094475] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1094473), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1094475)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1094473), 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)))), _1094475)))], (3738 ^ _777864) ^ [_834769, _834771, _834773, _834775] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_834775, _834771) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_834773, _834769)), _834775 = _834773, _834771 = _834769], (43241 ^ _777864) ^ [_1619634, _1619636, _1619638] : [-(c_Transitive__Closure_Ortrancl(_1619634, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619634, _1619634), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1619634, _1619636)), c_Transitive__Closure_Ortrancl(_1619634, _1619638))) = c_Transitive__Closure_Ortrancl(_1619634, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619634, _1619634), tc_HOL_Obool)), _1619636), _1619638)))], (14103 ^ _777864) ^ [_1016409, _1016411, _1016413] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016411), _1016413)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016409), _1016411)), _1016413))], (8332 ^ _777864) ^ [_915964, _915966, _915968] : [class_Orderings_Opreorder(_915964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915964), _915966), _915968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915964), _915968), _915966))], (40122 ^ _777864) ^ [_1539328, _1539330] : [-(hAPP(c_Set_OCollect(_1539328), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539328), c_fNot), _1539330)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1539328, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1539328), _1539330)))], (7490 ^ _777864) ^ [_901679, _901681, _901683] : [c_Com_Ocom_OCond(_901679, _901681, _901683) = c_Com_Ocom_OSKIP], (4678 ^ _777864) ^ [_849391, _849393] : [_849393 = _849391, -(c_Option_Ooption_OSome(_849393) = c_Option_Ooption_OSome(_849391))], (22490 ^ _777864) ^ [_1166619, _1166621] : [-(_1166619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1166621, _1166619), c_Divides_Odivmod__int(_1166621, _1166619))))], (29950 ^ _777864) ^ [_1322245, _1322247, _1322249, _1322251] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322245, tc_HOL_Obool)), _1322247), _1322249), _1322251)), -(hBOOL(hAPP(_1322247, _1322251)))], (16712 ^ _777864) ^ [_1065502, _1065504, _1065506] : [class_Rings_Oordered__ring__abs(_1065502), -(hAPP(c_Groups_Oabs__class_Oabs(_1065502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065502), _1065504), _1065506)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065502), hAPP(c_Groups_Oabs__class_Oabs(_1065502), _1065504)), hAPP(c_Groups_Oabs__class_Oabs(_1065502), _1065506))), 16719 ^ _777864 : [(16722 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065502), _1065504), c_Groups_Ozero__class_Ozero(_1065502)))], (16720 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065502), c_Groups_Ozero__class_Ozero(_1065502)), _1065504))]], 16723 ^ _777864 : [(16726 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065502), _1065506), c_Groups_Ozero__class_Ozero(_1065502)))], (16724 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065502), c_Groups_Ozero__class_Ozero(_1065502)), _1065506))]]], (9298 ^ _777864) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28695 ^ _777864) ^ [_1295910, _1295912] : [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)), _1295910)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1295912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1295910), _1295912)))], (47702 ^ _777864) ^ [_1731356, _1731358] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1731356), tc_List_Olist(_1731356), c_List_Olistrel(_1731356, _1731358)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1731356)), c_List_Olist_ONil(_1731356)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1731356), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1731356)), c_List_Olist_ONil(_1731356)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1731356), tc_HOL_Obool))))], (36650 ^ _777864) ^ [_1461723, _1461725, _1461727, _1461729, _1461731] : [class_Groups_Ocomm__monoid__add(_1461723), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461723), _1461725), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1461727), _1461729), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1461731), _1461729))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461723), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1461723, tc_Nat_Onat), _1461725), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1461729))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1461727, _1461731)))], (6095 ^ _777864) ^ [_878168] : [6096 ^ _777864 : [(6097 ^ _777864) ^ [_878216] : [hAPP(c_Com_Obody, _878168) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _878216)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _878168))))], (36344 ^ _777864) ^ [_1454368, _1454370, _1454372] : [class_Orderings_Olinorder(_1454368), 36347 ^ _777864 : [(36354 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454368), _1454370), _1454372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454368, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454368), _1454370)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454368), _1454372))))], (36348 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1454368, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454368), _1454370)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454368), _1454372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454368), _1454370), _1454372)))]]], (12093 ^ _777864) ^ [_980339] : [-(hAPP(c_Nat_OSuc, _980339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _980339))], (48690 ^ _777864) ^ [_1756685, _1756687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756685)), _1756687)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1756685), _1756687) = _1756687)], (33717 ^ _777864) ^ [_1399480, _1399482, _1399484, _1399486, _1399488, _1399490] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399480, tc_fun(_1399482, tc_HOL_Obool)), _1399484), hAPP(hAPP(c_COMBB(_1399486, tc_fun(_1399482, tc_HOL_Obool), _1399480), _1399488), _1399490)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399486, tc_fun(_1399482, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1399480, _1399486, _1399490), _1399484)), _1399488))], (9160 ^ _777864) ^ [_930305, _930307, _930309, _930311, _930313] : [class_Rings_Osemiring(_930305), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930305), _930307), _930309)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930305), _930311), _930309)), _930313)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930305), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930305), _930307), _930311)), _930309)), _930313))], (34497 ^ _777864) ^ [_1418269, _1418271, _1418273] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418269, tc_HOL_Obool)), _1418271), hAPP(c_Set_OPow(_1418269), _1418273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1418269, tc_HOL_Obool)), _1418271), _1418273)))], (22803 ^ _777864) ^ [_1172745, _1172747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172747)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1172745), _1172747) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1172745, _1172747)))], (11949 ^ _777864) ^ [_977729, _977731, _977733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977729), _977731)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977733), _977731))), 11952 ^ _777864 : [(11955 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977729), _977733)))], (11953 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977731)))]]], (33206 ^ _777864) ^ [_1387549, _1387551, _1387553, _1387555, _1387557] : [class_Fields_Ofield(_1387549), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387551), _1387553)), -(hAPP(_1387555, _1387557) = c_Groups_Ozero__class_Ozero(_1387549)), 33217 ^ _777864 : [(33224 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387551), _1387557), _1387553))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387551, _1387549), _1387555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387551, tc_HOL_Obool)), _1387553), hAPP(hAPP(c_Set_Oinsert(_1387551), _1387557), c_Orderings_Obot__class_Obot(tc_fun(_1387551, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387551, _1387549), _1387555), _1387553))], (33218 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1387551), _1387557), _1387553)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387551, _1387549), _1387555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387551, tc_HOL_Obool)), _1387553), hAPP(hAPP(c_Set_Oinsert(_1387551), _1387557), c_Orderings_Obot__class_Obot(tc_fun(_1387551, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387549), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387551, _1387549), _1387555), _1387553)), hAPP(_1387555, _1387557)))]]], (41393 ^ _777864) ^ [_1578258, _1578260, _1578262, _1578264, _1578266] : [hBOOL(hAPP(hAPP(_1578258, _1578260), _1578262)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1578264, _1578266, _1578258), _1578260)))], (6673 ^ _777864) ^ [_887866, _887868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887866)), hAPP(c_Nat_OSuc, _887868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887866), _887868)))], (7192 ^ _777864) ^ [_896142, _896144, _896146] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_896142, _896144, _896146))), 7195 ^ _777864 : [(7198 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _896146)))], (7196 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _896144)))]]], (10420 ^ _777864) ^ [_951822, _951824, _951826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951822), _951824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951822), _951826))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _951822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951824), _951826)))], (19300 ^ _777864) ^ [] : [-(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))))))], (43435 ^ _777864) ^ [_1624271, _1624273, _1624275, _1624277] : [-(c_Wellfounded_Owf(_1624271, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624271, _1624271)), hAPP(hAPP(c_Product__Type_OPair(_1624271, _1624271), _1624273), _1624275)), _1624277))), c_Wellfounded_Owf(_1624271, _1624277), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624271, _1624271)), hAPP(hAPP(c_Product__Type_OPair(_1624271, _1624271), _1624275), _1624273)), c_Transitive__Closure_Ortrancl(_1624271, _1624277))))], (24695 ^ _777864) ^ [_1211055] : [-(c_Code__Numeral_OSuc__code__numeral(_1211055) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1211055))))], (18466 ^ _777864) ^ [_1095490, _1095492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095490), _1095492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1095490)), c_Int_OBit1(_1095492))))], (30266 ^ _777864) ^ [_1329496, _1329498, _1329500] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1329496), hAPP(hAPP(c_Set_Oinsert(_1329496), _1329498), c_Orderings_Obot__class_Obot(tc_fun(_1329496, tc_HOL_Obool)))), _1329500) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1329496, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1329496, _1329496, _1329500), hAPP(hAPP(c_Set_Oinsert(_1329496), _1329498), c_Orderings_Obot__class_Obot(tc_fun(_1329496, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1329496, tc_HOL_Obool), tc_HOL_Obool))))], (11231 ^ _777864) ^ [_964958, _964960, _964962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964958), _964960)), _964962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964958), _964962)))], (43696 ^ _777864) ^ [_1630067, _1630069, _1630071, _1630073, _1630075] : [-(hAPP(hAPP(c_Set_Oinsert(_1630067), _1630069), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630071, tc_fun(_1630067, tc_HOL_Obool)), _1630073), _1630075)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630071, tc_fun(_1630067, tc_HOL_Obool)), _1630073), hAPP(hAPP(c_COMBB(tc_fun(_1630067, tc_HOL_Obool), tc_fun(_1630067, tc_HOL_Obool), _1630071), hAPP(c_Set_Oinsert(_1630067), _1630069)), _1630075)))], (754 ^ _777864) ^ [_789501, _789503, _789505, _789507] : [-(c_Wellfounded_Oacyclic(_789505, _789501)), c_Wellfounded_Oacyclic(_789507, _789503), _789507 = _789505, _789503 = _789501], (20594 ^ _777864) ^ [_1132795, _1132797, _1132799, _1132801] : [class_Fields_Olinordered__field(_1132795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132795), _1132797), c_Groups_Ozero__class_Ozero(_1132795))), 20601 ^ _777864 : [(20608 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132795), _1132801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132795), _1132799), _1132797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132795), _1132799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132795), _1132801), _1132797))))], (20602 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132795), _1132799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132795), _1132801), _1132797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132795), _1132801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132795), _1132799), _1132797))))]]], (49301 ^ _777864) ^ [_1769669, _1769671, _1769673] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769669, _1769669)), hAPP(hAPP(c_Product__Type_OPair(_1769669, _1769669), 49302 ^ [_1769669, _1769671, _1769673]), 49302 ^ [_1769669, _1769671, _1769673])), _1769671))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769669), tc_List_Olist(_1769669))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769669), tc_List_Olist(_1769669)), _1769673), _1769673)), c_List_Olexord(_1769669, _1769671)))], (44121 ^ _777864) ^ [_1642847, _1642849, _1642851, _1642853, _1642855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1642847, _1642847)), hAPP(hAPP(c_Product__Type_OPair(_1642847, _1642847), hAPP(_1642849, hAPP(c_Nat_OSuc, 44122 ^ [_1642847, _1642849, _1642851, _1642853, _1642855]))), hAPP(_1642849, 44122 ^ [_1642847, _1642849, _1642851, _1642853, _1642855]))), c_Transitive__Closure_Ortrancl(_1642847, _1642851))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1642847, _1642847)), hAPP(hAPP(c_Product__Type_OPair(_1642847, _1642847), hAPP(_1642849, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1642853), _1642855))), hAPP(_1642849, _1642853))), c_Transitive__Closure_Ortrancl(_1642847, _1642851))))], (42074 ^ _777864) ^ [_1594460, _1594462, _1594464, _1594466, _1594468, _1594470, _1594472, _1594474] : [c_Finite__Set_Ofolding(_1594460, _1594462, _1594464, _1594466), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594460), _1594468)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594460), _1594470)), -(hAPP(c_Fun_Ocomp(_1594462, _1594462, _1594472, hAPP(_1594466, _1594470)), hAPP(c_Fun_Ocomp(_1594462, _1594462, _1594472, hAPP(_1594466, _1594468)), _1594474)) = hAPP(c_Fun_Ocomp(_1594462, _1594462, _1594472, hAPP(_1594466, _1594468)), hAPP(c_Fun_Ocomp(_1594462, _1594462, _1594472, hAPP(_1594466, _1594470)), _1594474)))], (24181 ^ _777864) ^ [_1201275, _1201277, _1201279] : [class_Groups_Olinordered__ab__group__add(_1201275), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1201275), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201275), _1201277), _1201279)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201275), hAPP(c_Groups_Ouminus__class_Ouminus(_1201275), _1201277)), hAPP(c_Groups_Ouminus__class_Ouminus(_1201275), _1201279)))], (47488 ^ _777864) ^ [_1727385, _1727387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1727385), _1727387)), -(c_List_Oupto(_1727387, _1727385) = c_List_Olist_ONil(tc_Int_Oint))], (43811 ^ _777864) ^ [_1633703, _1633705, _1633707, _1633709, _1633711, _1633713] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633703, tc_fun(_1633705, tc_fun(_1633707, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1633703, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_fun(_1633705, tc_fun(_1633707, tc_HOL_Obool)), _1633703), hAPP(c_COMBC(_1633705, tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_fun(_1633707, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1633707, tc_fun(tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_fun(_1633707, tc_HOL_Obool)), _1633705), c_COMBC(_1633707, tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1633707, tc_prod(_1633705, _1633707)), tc_fun(_1633707, tc_fun(tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_HOL_Obool)), _1633705), hAPP(c_COMBB(tc_prod(_1633705, _1633707), tc_fun(tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool), tc_HOL_Obool), _1633707), c_member(tc_prod(_1633705, _1633707)))), c_Product__Type_OPair(_1633705, _1633707))))), _1633709)), _1633711), _1633713)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633705, _1633707)), hAPP(hAPP(c_Product__Type_OPair(_1633705, _1633707), _1633711), _1633713)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633703, tc_fun(tc_prod(_1633705, _1633707), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1633703, tc_HOL_Obool))), _1633709))))], (40636 ^ _777864) ^ [_1556978, _1556980, _1556982] : [c_Predicate_Oreflp(_1556978, _1556980), -(hBOOL(hAPP(hAPP(_1556980, _1556982), _1556982)))], (51153 ^ _777864) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11104 ^ _777864) ^ [_962763, _962765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962763), _962765))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962763), _962765)), -(_962763 = _962765)], (45323 ^ _777864) ^ [_1672443, _1672445] : [-(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)))), _1672443)) = 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)))), _1672445))), 45325 ^ _777864 : [(45328 ^ _777864) ^ [] : [45329 ^ _777864 : [(45332 ^ _777864) ^ [] : [hBOOL(hAPP(_1672445, 45324 ^ [_1672443, _1672445]))], (45330 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1672443, 45324 ^ [_1672443, _1672445])))]], 45333 ^ _777864 : [(45336 ^ _777864) ^ [] : [hBOOL(hAPP(_1672443, 45324 ^ [_1672443, _1672445]))], (45334 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1672445, 45324 ^ [_1672443, _1672445])))]]], (45326 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 45324 ^ [_1672443, _1672445])))]]], (4052 ^ _777864) ^ [_839666, _839668, _839670, _839672, _839674, _839676, _839678, _839680, _839682, _839684, _839686, _839688] : [-(c_Product__Type_Omap__pair(_839688, _839684, _839680, _839676, _839672, _839668) = c_Product__Type_Omap__pair(_839686, _839682, _839678, _839674, _839670, _839666)), _839688 = _839686, _839684 = _839682, _839680 = _839678, _839676 = _839674, _839672 = _839670, _839668 = _839666], (9328 ^ _777864) ^ [_933292, _933294, _933296, _933298] : [class_Rings_Olinordered__comm__semiring__strict(_933292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933292), _933294), _933296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933292), c_Groups_Ozero__class_Ozero(_933292)), _933298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933292), _933298), _933294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933292), _933298), _933296))))], (24089 ^ _777864) ^ [_1199084, _1199086] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199084)), hAPP(c_Nat_OSuc, _1199086)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1199084), _1199086)))], (24499 ^ _777864) ^ [_1207340, _1207342] : [-(c_HOL_OThe(_1207340, hAPP(c_fequal, _1207342)) = _1207342)], (35916 ^ _777864) ^ [_1446081, _1446083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1446081), _1446083))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1446081), hAPP(c_Nat_OSuc, _1446083)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23051 ^ _777864) ^ [_1177652, _1177654] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1177652), _1177654) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1177652), _1177654))], (13832 ^ _777864) ^ [_1011100, _1011102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011100)), -(c_SMT_Oz3mod(_1011102, _1011100) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011102, _1011100))], (27322 ^ _777864) ^ [_1263622, _1263624, _1263626, _1263628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1263628, _1263624)), hAPP(_1263628, _1263626))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263622, _1263622)), hAPP(hAPP(c_Product__Type_OPair(_1263622, _1263622), _1263624), _1263626)), hAPP(c_Wellfounded_Omeasure(_1263622), _1263628))))], (48085 ^ _777864) ^ [_1740902, _1740904, _1740906] : [_1740904 = c_List_Olist_ONil(_1740902), -(hAPP(hAPP(c_List_Oappend(_1740902), _1740904), _1740906) = _1740906)], (51235 ^ _777864) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (48760 ^ _777864) ^ [_1758033, _1758035] : [-(_1758033 = c_List_Olist_ONil(_1758035)), -(hAPP(c_List_Orotate1(_1758035), _1758033) = hAPP(hAPP(c_List_Oappend(_1758035), hAPP(c_List_Otl(_1758035), _1758033)), hAPP(hAPP(c_List_Olist_OCons(_1758035), hAPP(c_List_Ohd(_1758035), _1758033)), c_List_Olist_ONil(_1758035))))], (45993 ^ _777864) ^ [_1687945, _1687947, _1687949, _1687951, _1687953] : [hBOOL(hAPP(c_List_Odistinct(_1687945), hAPP(hAPP(c_List_Omap(tc_prod(_1687945, _1687947), _1687945), c_Product__Type_Ofst(_1687945, _1687947)), _1687949))), 45996 ^ _777864 : [(46003 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1687945, _1687947)), hAPP(hAPP(c_Product__Type_OPair(_1687945, _1687947), _1687953), _1687951)), hAPP(c_List_Oset(tc_prod(_1687945, _1687947)), _1687949))), -(hAPP(c_Option_Ooption_OSome(_1687947), _1687951) = hAPP(c_Map_Omap__of(_1687945, _1687947, _1687949), _1687953))], (45997 ^ _777864) ^ [] : [hAPP(c_Option_Ooption_OSome(_1687947), _1687951) = hAPP(c_Map_Omap__of(_1687945, _1687947, _1687949), _1687953), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687945, _1687947)), hAPP(hAPP(c_Product__Type_OPair(_1687945, _1687947), _1687953), _1687951)), hAPP(c_List_Oset(tc_prod(_1687945, _1687947)), _1687949))))]]], (14115 ^ _777864) ^ [_1016642, _1016644, _1016646] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016642), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016644, _1016646)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016642), _1016644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016642), _1016646)))], (21282 ^ _777864) ^ [_1144991, _1144993, _1144995, _1144997] : [class_Fields_Olinordered__field(_1144991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144991), _1144993), c_Groups_Ozero__class_Ozero(_1144991))), 21289 ^ _777864 : [(21296 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144991), _1144997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144991), _1144995), _1144993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144991), _1144995), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144991), _1144997), _1144993))))], (21290 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144991), _1144995), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144991), _1144997), _1144993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144991), _1144997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144991), _1144995), _1144993))))]]], (24621 ^ _777864) ^ [_1209787, _1209789] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1209787), _1209789) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1209787)), hAPP(c_Code__Numeral_Onat__of, _1209789))))], (44380 ^ _777864) ^ [_1649726, _1649728, _1649730, _1649732] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649726, _1649726)), _1649728), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1649726, _1649726), tc_HOL_Obool), _1649730), _1649732))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649726, _1649726)), _1649728), c_Transitive__Closure_Ortrancl(_1649726, _1649732))))], (47022 ^ _777864) ^ [_1715737, _1715739, _1715741, _1715743, _1715745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715737), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715739)), _1715741))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715737), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715743)), _1715745))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1715739, _1715743)), hAPP(hAPP(c_List_Ozip(_1715739, _1715743), _1715741), _1715745)), _1715737) = hAPP(hAPP(c_Product__Type_OPair(_1715739, _1715743), hAPP(hAPP(c_List_Onth(_1715739), _1715741), _1715737)), hAPP(hAPP(c_List_Onth(_1715743), _1715745), _1715737)))], (20174 ^ _777864) ^ [_1125638, _1125640, _1125642, _1125644] : [class_Rings_Odivision__ring(_1125638), -(_1125640 = c_Groups_Ozero__class_Ozero(_1125638)), _1125642 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125638), _1125644), _1125640), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125638), _1125642), _1125640) = _1125644)], (10368 ^ _777864) ^ [_950892, _950894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950892), _950894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950894))))], (47972 ^ _777864) ^ [_1738282, _1738284, _1738286, _1738288] : [-(hBOOL(hAPP(hAPP(c_member(_1738282), _1738284), hAPP(c_List_Oset(_1738282), _1738286)))), -(c_List_Oremove1(_1738282, _1738284, hAPP(hAPP(c_List_Oappend(_1738282), _1738286), _1738288)) = hAPP(hAPP(c_List_Oappend(_1738282), _1738286), c_List_Oremove1(_1738282, _1738284, _1738288)))], (48792 ^ _777864) ^ [_1758573, _1758575, _1758577] : [-(hAPP(hAPP(c_List_Otake(_1758573), _1758575), hAPP(c_List_Otl(_1758573), _1758577)) = hAPP(c_List_Otl(_1758573), hAPP(hAPP(c_List_Otake(_1758573), hAPP(c_Nat_OSuc, _1758575)), _1758577)))], (38388 ^ _777864) ^ [_1498378] : [class_Lattices_Oboolean__algebra(_1498378), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1498378), c_Orderings_Otop__class_Otop(_1498378)) = c_Orderings_Obot__class_Obot(_1498378))], (48834 ^ _777864) ^ [_1759424, _1759426, _1759428] : [-(hAPP(c_List_Orotate(_1759424, hAPP(c_Nat_OSuc, _1759426)), _1759428) = hAPP(c_List_Orotate1(_1759424), hAPP(c_List_Orotate(_1759424, _1759426), _1759428)))], (49864 ^ _777864) ^ [_1782357, _1782359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1782357), _1782359)), -(c_List_Oupt(_1782357, hAPP(c_Nat_OSuc, _1782359)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1782357, _1782359)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1782359), c_List_Olist_ONil(tc_Nat_Onat))))], (4560 ^ _777864) ^ [_847560, _847562, _847564, _847566, _847568, _847570] : [-(c_List_Olist_Olist__size(_847570, _847566, _847562) = c_List_Olist_Olist__size(_847568, _847564, _847560)), _847570 = _847568, _847566 = _847564, _847562 = _847560], (51491 ^ _777864) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (5598 ^ _777864) ^ [_867216, _867218, _867220, _867222, _867224] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _867216)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867218), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_867220, _867218))), _867222)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_867224, _867216, _867220)), _867218), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867222), hAPP(c_Natural_Ogetlocs, _867218))), _867224), hAPP(hAPP(c_Natural_Ogetlocs, _867222), c_Com_ORes)))))], (47538 ^ _777864) ^ [_1728274] : [-(hAPP(c_List_Oset(_1728274), c_List_Olist_ONil(_1728274)) = c_Orderings_Obot__class_Obot(tc_fun(_1728274, tc_HOL_Obool)))], (44792 ^ _777864) ^ [_1659674, _1659676, _1659678, _1659680] : [-(hAPP(c_Set_Ovimage(_1659674, _1659676, _1659678), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659676, tc_HOL_Obool), _1659680)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659676, tc_HOL_Obool), tc_fun(_1659674, tc_HOL_Obool)), _1659680), c_Set_Ovimage(_1659674, _1659676, _1659678)))], (51159 ^ _777864) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (32843 ^ _777864) ^ [_1380019, _1380021, _1380023, _1380025] : [class_Rings_Ocomm__semiring__1(_1380019), class_Rings_Ono__zero__divisors(_1380019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380021), _1380023)), 32854 ^ _777864 : [(32864 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380021, _1380019), _1380025), _1380023) = c_Groups_Ozero__class_Ozero(_1380019)), 32865 ^ _777864 : [(32866 ^ _777864) ^ [_1380397] : [hBOOL(hAPP(hAPP(c_member(_1380021), _1380397), _1380023)), hAPP(_1380025, _1380397) = c_Groups_Ozero__class_Ozero(_1380019)]]], (32855 ^ _777864) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380021, _1380019), _1380025), _1380023) = c_Groups_Ozero__class_Ozero(_1380019), 32859 ^ _777864 : [(32862 ^ _777864) ^ [] : [-(hAPP(_1380025, 32858 ^ [_1380019, _1380021, _1380023, _1380025]) = c_Groups_Ozero__class_Ozero(_1380019))], (32860 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380021), 32858 ^ [_1380019, _1380021, _1380023, _1380025]), _1380023)))]]]]], (48920 ^ _777864) ^ [_1761331, _1761333] : [class_Groups_Omonoid__add(_1761331), -(hAPP(c_List_Ofoldl(_1761331, _1761331, c_Groups_Oplus__class_Oplus(_1761331), c_Groups_Ozero__class_Ozero(_1761331)), _1761333) = c_List_Ofoldr(_1761331, _1761331, c_Groups_Oplus__class_Oplus(_1761331), _1761333, c_Groups_Ozero__class_Ozero(_1761331)))], (49930 ^ _777864) ^ [_1783592, _1783594] : [c_List_Oupt(_1783592, _1783594) = c_List_Olist_ONil(tc_Nat_Onat), -(_1783594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1783594), _1783592)))], (16532 ^ _777864) ^ [_1061806, _1061808, _1061810] : [class_Rings_Ocomm__semiring__1(_1061806), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061806), hAPP(hAPP(c_Power_Opower__class_Opower(_1061806), _1061808), _1061810)), _1061808) = hAPP(hAPP(c_Power_Opower__class_Opower(_1061806), _1061808), hAPP(c_Nat_OSuc, _1061810)))], (40532 ^ _777864) ^ [_1552809, _1552811, _1552813] : [class_Lattices_Odistrib__lattice(_1552809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552809), _1552811)), -(_1552811 = c_Orderings_Obot__class_Obot(tc_fun(_1552809, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1552809), _1552813), c_Big__Operators_Olattice__class_OSup__fin(_1552809, _1552811)) = c_Big__Operators_Olattice__class_OSup__fin(_1552809, hAPP(c_Set_OCollect(_1552809), hAPP(hAPP(c_COMBB(tc_fun(_1552809, tc_HOL_Obool), tc_HOL_Obool, _1552809), c_HOL_OEx(_1552809)), hAPP(hAPP(c_COMBC(_1552809, tc_fun(_1552809, tc_HOL_Obool), tc_fun(_1552809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552809, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1552809, tc_HOL_Obool), tc_fun(_1552809, tc_HOL_Obool)), _1552809), c_COMBS(_1552809, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552809, tc_HOL_Obool), tc_fun(_1552809, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1552809), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1552809), c_fconj)), hAPP(hAPP(c_COMBC(_1552809, tc_fun(_1552809, _1552809), tc_fun(_1552809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1552809, tc_HOL_Obool), tc_fun(tc_fun(_1552809, _1552809), tc_fun(_1552809, tc_HOL_Obool)), _1552809), c_COMBB(_1552809, tc_HOL_Obool, _1552809)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1552809), _1552813))))), hAPP(hAPP(c_COMBC(_1552809, tc_fun(_1552809, tc_HOL_Obool), tc_HOL_Obool), c_member(_1552809)), _1552811))))))], (17224 ^ _777864) ^ [_1074902, _1074904] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1074902), c_Groups_Ozero__class_Ozero(_1074902)), hAPP(c_Nat_OSuc, _1074904)) = c_Groups_Ozero__class_Ozero(_1074902)), class_Power_Opower(_1074902), class_Rings_Osemiring__0(_1074902)], (12806 ^ _777864) ^ [_992863, _992865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992863)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _992865)))), 12809 ^ _777864 : [(12812 ^ _777864) ^ [] : [-(_992865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12810 ^ _777864) ^ [] : [-(_992863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (26381 ^ _777864) ^ [_1242497, _1242499, _1242501] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242497), _1242499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242497), _1242501))), -(_1242497 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242499), _1242501)))], (39476 ^ _777864) ^ [_1525142, _1525144, _1525146] : [class_Lattices_Oab__semigroup__idem__mult(_1525142), -(_1525144 = c_Orderings_Obot__class_Obot(tc_fun(_1525142, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525142), _1525144)), -(hAPP(c_Finite__Set_Ofold1(_1525142, c_Groups_Otimes__class_Otimes(_1525142)), hAPP(hAPP(c_Set_Oinsert(_1525142), _1525146), _1525144)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1525142), _1525146), hAPP(c_Finite__Set_Ofold1(_1525142, c_Groups_Otimes__class_Otimes(_1525142)), _1525144)))], (50118 ^ _777864) ^ [_1786484, _1786486] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1786484, _1786486)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1786484), hAPP(c_Nat_OSuc, _1786486)))], (46206 ^ _777864) ^ [_1693250, _1693252, _1693254, _1693256, _1693258, _1693260, _1693262, _1693264] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693250)), _1693252) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693254)), _1693256), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693250)), _1693258) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693254)), _1693256), -(hBOOL(hAPP(hAPP(c_member(_1693254), _1693260), hAPP(c_List_Oset(_1693254), _1693256)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693254, tc_Option_Ooption(_1693250)), c_Map_Omap__of(_1693254, _1693250, hAPP(hAPP(c_List_Ozip(_1693254, _1693250), _1693256), _1693252))), _1693260), hAPP(c_Option_Ooption_OSome(_1693250), _1693262)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693254, tc_Option_Ooption(_1693250)), c_Map_Omap__of(_1693254, _1693250, hAPP(hAPP(c_List_Ozip(_1693254, _1693250), _1693256), _1693258))), _1693260), hAPP(c_Option_Ooption_OSome(_1693250), _1693264)), -(c_Map_Omap__of(_1693254, _1693250, hAPP(hAPP(c_List_Ozip(_1693254, _1693250), _1693256), _1693252)) = c_Map_Omap__of(_1693254, _1693250, hAPP(hAPP(c_List_Ozip(_1693254, _1693250), _1693256), _1693258)))], (50544 ^ _777864) ^ [_1795921, _1795923, _1795925, _1795927] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795921)), _1795923) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795925)), _1795927), -(hAPP(hAPP(c_List_Ozip(_1795921, _1795925), hAPP(c_List_Orev(_1795921), _1795923)), hAPP(c_List_Orev(_1795925), _1795927)) = hAPP(c_List_Orev(tc_prod(_1795921, _1795925)), hAPP(hAPP(c_List_Ozip(_1795921, _1795925), _1795923), _1795927)))], (32177 ^ _777864) ^ [_1365945, _1365947, _1365949] : [class_Orderings_Olinorder(_1365945), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365945), _1365947)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365945), _1365949)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365945, tc_HOL_Obool)), _1365947), _1365949) = c_Orderings_Obot__class_Obot(tc_fun(_1365945, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365945), c_Big__Operators_Olattice_OInf__fin(_1365945, c_Orderings_Oord__class_Omin(_1365945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365945, tc_HOL_Obool)), _1365947), _1365949))), c_Big__Operators_Olattice_OInf__fin(_1365945, c_Orderings_Oord__class_Omin(_1365945), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365945, tc_HOL_Obool)), _1365947), _1365949))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365945), c_Big__Operators_Olattice_OInf__fin(_1365945, c_Orderings_Oord__class_Omin(_1365945), _1365947)), c_Big__Operators_Olattice_OInf__fin(_1365945, c_Orderings_Oord__class_Omin(_1365945), _1365949)))], (7316 ^ _777864) ^ [_898304, _898306, _898308, _898310, _898312] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_898304, _898306, _898308)), _898310), _898312)), 7321 ^ _777864 : [(7324 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898306), _898310), _898312)))], (7322 ^ _777864) ^ [] : [-(hBOOL(hAPP(_898304, _898310)))]], 7325 ^ _777864 : [(7328 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898308), _898310), _898312)))], (7326 ^ _777864) ^ [] : [hBOOL(hAPP(_898304, _898310))]]], (27075 ^ _777864) ^ [_1256135, _1256137, _1256139, _1256141] : [hAPP(hAPP(c_COMBC(_1256135, tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_fun(_1256137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256137, tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_fun(_1256137, tc_HOL_Obool)), _1256135), c_COMBC(_1256137, tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256137, tc_prod(_1256135, _1256137)), tc_fun(_1256137, tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), _1256135), hAPP(c_COMBB(tc_prod(_1256135, _1256137), tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool), _1256137), c_member(tc_prod(_1256135, _1256137)))), c_Product__Type_OPair(_1256135, _1256137)))), _1256139) = hAPP(hAPP(c_COMBC(_1256135, tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_fun(_1256137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256137, tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_fun(_1256137, tc_HOL_Obool)), _1256135), c_COMBC(_1256137, tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256137, tc_prod(_1256135, _1256137)), tc_fun(_1256137, tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool)), _1256135), hAPP(c_COMBB(tc_prod(_1256135, _1256137), tc_fun(tc_fun(tc_prod(_1256135, _1256137), tc_HOL_Obool), tc_HOL_Obool), _1256137), c_member(tc_prod(_1256135, _1256137)))), c_Product__Type_OPair(_1256135, _1256137)))), _1256141), -(_1256139 = _1256141)], (22773 ^ _777864) ^ [_1172112, _1172114, _1172116, _1172118, _1172120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172112, tc_HOL_Obool)), _1172114), _1172116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172112, tc_HOL_Obool)), _1172118), _1172120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172112, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172112, tc_HOL_Obool)), _1172114), _1172120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172112, tc_HOL_Obool)), _1172116), _1172118))))], (30905 ^ _777864) ^ [_1342923, _1342925, _1342927] : [class_Orderings_Olinorder(_1342923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342923), _1342925)), hBOOL(hAPP(hAPP(c_member(_1342923), _1342927), _1342925)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342923), _1342927), c_Big__Operators_Olinorder__class_OMax(_1342923, _1342925)) = c_Big__Operators_Olinorder__class_OMax(_1342923, _1342925))], (39053 ^ _777864) ^ [_1514661, _1514663, _1514665, _1514667, _1514669] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1514661, _1514663, hAPP(hAPP(c_Set_Oinsert(_1514661), _1514665), _1514667)), _1514669))), 39054 ^ _777864 : [(39055 ^ _777864) ^ [_1514765, _1514767] : [hAPP(hAPP(c_Set_Oinsert(_1514661), _1514665), _1514667) = hAPP(hAPP(c_Set_Oinsert(_1514661), _1514767), _1514765), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1514661, _1514661, _1514663, _1514767, _1514765), _1514669)), -(hBOOL(hAPP(hAPP(c_member(_1514661), _1514767), _1514765)))]]], (46392 ^ _777864) ^ [_1698124, _1698126, _1698128] : [_1698124 = _1698126, 46395 ^ _777864 : [(46398 ^ _777864) ^ [_1698280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1698128, _1698128)), _1698280), hAPP(c_List_Oset(tc_prod(_1698128, _1698128)), hAPP(hAPP(c_List_Ozip(_1698128, _1698128), _1698124), _1698126)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1698128, _1698128, tc_HOL_Obool), c_fequal), _1698280)))], (46396 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698128)), _1698124) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698128)), _1698126))]]], (24335 ^ _777864) ^ [_1203954, _1203956] : [-(c_Nitpick_Onumber__of__frac(_1203954, _1203956) = c_Nitpick_OAbs__Frac(_1203954, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1203956), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (11957 ^ _777864) ^ [_977878, _977880, _977882] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977878), _977880)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _977882), _977880)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _977880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977878), _977882))], (21000 ^ _777864) ^ [_1139908, _1139910, _1139912, _1139914] : [class_Fields_Ofield__inverse__zero(_1139908), class_Int_Onumber(_1139908), 21007 ^ _777864 : [(21008 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139908), _1139910), hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912)) = _1139914, 21011 ^ _777864 : [(21018 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912) = c_Groups_Ozero__class_Ozero(_1139908), -(_1139914 = c_Groups_Ozero__class_Ozero(_1139908))], (21012 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912) = c_Groups_Ozero__class_Ozero(_1139908)), -(_1139910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139908), _1139914), hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912)))]]], (21024 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139908), _1139910), hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912)) = _1139914), 21027 ^ _777864 : [(21030 ^ _777864) ^ [] : [_1139910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139908), _1139914), hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912))], (21028 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912) = c_Groups_Ozero__class_Ozero(_1139908)]], 21031 ^ _777864 : [(21034 ^ _777864) ^ [] : [_1139914 = c_Groups_Ozero__class_Ozero(_1139908)], (21032 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1139908), _1139912) = c_Groups_Ozero__class_Ozero(_1139908))]]]]], (5190 ^ _777864) ^ [_857297, _857299] : [_857299 = _857297, -(c_Finite__Set_Ocard(_857299) = c_Finite__Set_Ocard(_857297))], (8614 ^ _777864) ^ [_920775, _920777, _920779] : [class_Rings_Oring(_920775), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920775), _920777), _920779)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920775), hAPP(c_Groups_Ouminus__class_Ouminus(_920775), _920777)), _920779))], (11809 ^ _777864) ^ [_975328, _975330, _975332, _975334, _975336] : [class_Groups_Oordered__cancel__ab__semigroup__add(_975328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975328), _975330), _975332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975328), _975334), _975336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975328), _975330), _975334)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975328), _975332), _975336))))], (8466 ^ _777864) ^ [_918164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _918164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918164)))], (2524 ^ _777864) ^ [_815188, _815190, _815192, _815194] : [-(tc_Nitpick_Opair__box(_815194, _815190) = tc_Nitpick_Opair__box(_815192, _815188)), _815194 = _815192, _815190 = _815188], (30591 ^ _777864) ^ [_1337198, _1337200, _1337202, _1337204, _1337206, _1337208] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337198, tc_fun(_1337200, tc_HOL_Obool))), _1337202), _1337204), _1337206), _1337208)), -(hBOOL(hAPP(hAPP(_1337204, _1337206), _1337208)))], (38770 ^ _777864) ^ [_1508092, _1508094, _1508096, _1508098] : [hAPP(c_Set_Oimage(_1508092, _1508094, _1508096), c_Orderings_Otop__class_Otop(tc_fun(_1508092, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1508094, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1508092, _1508094, _1508096), hAPP(c_Set_Ovimage(_1508092, _1508094, _1508096), _1508098)) = _1508098)], (35262 ^ _777864) ^ [_1433551, _1433553] : [35270 ^ _777864 : [(35273 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1433553, 35269 ^ [_1433551, _1433553])))], (35271 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35269 ^ [_1433551, _1433553]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1433551))))]], 35263 ^ _777864 : [(35264 ^ _777864) ^ [_1433620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1433620), _1433551)), hBOOL(hAPP(_1433553, _1433620))]]], (18394 ^ _777864) ^ [_1094115, _1094117] : [class_Int_Onumber__ring(_1094115), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1094115), c_Groups_Oone__class_Oone(_1094115)), hAPP(c_Int_Onumber__class_Onumber__of(_1094115), _1094117)) = hAPP(c_Int_Onumber__class_Onumber__of(_1094115), 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), _1094117))))], (2414 ^ _777864) ^ [_813455, _813457, _813459, _813461] : [-(c_Nitpick_Oint__lcm(_813461, _813457) = c_Nitpick_Oint__lcm(_813459, _813455)), _813461 = _813459, _813457 = _813455], (9660 ^ _777864) ^ [_939306, _939308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939306)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939308))))], (36322 ^ _777864) ^ [] : [-(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)))], (34091 ^ _777864) ^ [_1409341, _1409343] : [-(c_Relation_OId__on(_1409341, _1409343) = hAPP(c_Product__Type_Oprod_Oprod__case(_1409341, _1409341, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1409341, tc_HOL_Obool, tc_fun(_1409341, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409341, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1409341, tc_HOL_Obool)), _1409341), c_COMBC(_1409341, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409341, tc_HOL_Obool), tc_fun(_1409341, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1409341), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1409341), c_fconj)), c_fequal))), _1409343)))], (7852 ^ _777864) ^ [_908467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _908467)), -(_908467 = hAPP(c_Nat_OSuc, 7855 ^ [_908467]))], (24677 ^ _777864) ^ [_1210726] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1210726)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1210726))], (15248 ^ _777864) ^ [_1036674, _1036676, _1036678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036674), _1036676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036678), _1036676)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036678), _1036674))))], (37771 ^ _777864) ^ [_1486546, _1486548, _1486550] : [class_Orderings_Olinorder(_1486546), 37774 ^ _777864 : [(37781 ^ _777864) ^ [] : [_1486548 = _1486550, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486546), _1486548) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486546), _1486550))], (37775 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486546), _1486548) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486546), _1486550), -(_1486548 = _1486550)]]], (47234 ^ _777864) ^ [_1721041, _1721043, _1721045, _1721047] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721041), tc_List_Olist(_1721041))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721041), tc_List_Olist(_1721041)), _1721043), _1721045)), c_List_Olistrel(_1721041, _1721047))), 47237 ^ _777864 : [(47240 ^ _777864) ^ [_1721270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721270), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721041)), _1721043))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1721041, _1721041)), hAPP(hAPP(c_Product__Type_OPair(_1721041, _1721041), hAPP(hAPP(c_List_Onth(_1721041), _1721043), _1721270)), hAPP(hAPP(c_List_Onth(_1721041), _1721045), _1721270))), _1721047)))], (47238 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721041)), _1721043) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721041)), _1721045))]]], (7536 ^ _777864) ^ [_902734, _902736, _902738, _902740] : [class_Rings_Ocomm__semiring__1(_902734), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902734), _902736), _902738)), _902740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902734), _902736), _902740)), _902738))], (40442 ^ _777864) ^ [_1549324, _1549326] : [-(c_Fun_Oinj__on(tc_fun(_1549324, _1549326), tc_fun(tc_prod(_1549324, _1549326), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1549324, _1549326), tc_HOL_Obool), tc_fun(tc_prod(_1549324, _1549326), tc_HOL_Obool), tc_fun(_1549324, _1549326)), c_Set_OCollect(tc_prod(_1549324, _1549326))), hAPP(hAPP(c_COMBB(tc_fun(_1549324, tc_fun(_1549326, tc_HOL_Obool)), tc_fun(tc_prod(_1549324, _1549326), tc_HOL_Obool), tc_fun(_1549324, _1549326)), c_Product__Type_Oprod_Oprod__case(_1549324, _1549326, tc_HOL_Obool)), hAPP(c_COMBB(_1549326, tc_fun(_1549326, tc_HOL_Obool), _1549324), hAPP(c_COMBC(_1549326, _1549326, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1549324, _1549326), tc_HOL_Obool))))], (26969 ^ _777864) ^ [_1254149, _1254151, _1254153, _1254155] : [hBOOL(hAPP(hAPP(c_member(_1254149), _1254151), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254149, tc_HOL_Obool)), _1254153), _1254155))), hBOOL(hAPP(hAPP(c_member(_1254149), _1254151), _1254155))], (48286 ^ _777864) ^ [_1745615, _1745617] : [-(c_List_Olistrel1(_1745615, hAPP(c_Relation_Oconverse(_1745615, _1745615), _1745617)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1745615), tc_List_Olist(_1745615)), c_List_Olistrel1(_1745615, _1745617)))], (39848 ^ _777864) ^ [_1533211, _1533213, _1533215] : [-(hAPP(c_Product__Type_Omap__pair(_1533211, _1533211, _1533213, _1533213, c_COMBI(_1533211), c_COMBI(_1533213)), _1533215) = _1533215)], (51237 ^ _777864) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (26933 ^ _777864) ^ [_1253368, _1253370, _1253372] : [hBOOL(hAPP(hAPP(c_member(_1253368), _1253370), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1253368, tc_HOL_Obool)), _1253372))), hBOOL(hAPP(hAPP(c_member(_1253368), _1253370), _1253372))], (8914 ^ _777864) ^ [_925951, _925953] : [class_Groups_Olinordered__ab__group__add(_925951), 8917 ^ _777864 : [(8924 ^ _777864) ^ [] : [_925953 = c_Groups_Ozero__class_Ozero(_925951), -(hAPP(c_Groups_Ouminus__class_Ouminus(_925951), _925953) = _925953)], (8918 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_925951), _925953) = _925953, -(_925953 = c_Groups_Ozero__class_Ozero(_925951))]]], (36152 ^ _777864) ^ [_1450760] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1450760)) = hAPP(c_Nat_OSuc, _1450760))], (32497 ^ _777864) ^ [_1372497, _1372499, _1372501] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372497), _1372499)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372497), _1372501)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372497, tc_HOL_Obool)), _1372499), _1372501) = c_Orderings_Obot__class_Obot(tc_fun(_1372497, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1372497), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372497, tc_HOL_Obool)), _1372499), _1372501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1372497), _1372499)), hAPP(c_Finite__Set_Ocard(_1372497), _1372501)))], (12019 ^ _777864) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39217 ^ _777864) ^ [_1519422, _1519424, _1519426, _1519428, _1519430, _1519432] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519422, _1519424)), hAPP(hAPP(c_Product__Type_OPair(_1519422, _1519424), _1519426), _1519428)), hAPP(hAPP(c_Product__Type_OSigma(_1519422, _1519424), _1519430), _1519432)))), hBOOL(hAPP(hAPP(c_member(_1519422), _1519426), _1519430)), hBOOL(hAPP(hAPP(c_member(_1519424), _1519428), hAPP(_1519432, _1519426)))], (40993 ^ _777864) ^ [] : [-(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)))))], (12264 ^ _777864) ^ [_983163, _983165] : [12265 ^ _777864 : [(12266 ^ _777864) ^ [_983216] : [_983165 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _983163), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _983216))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _983163), _983165)))], (17170 ^ _777864) ^ [_1074044, _1074046, _1074048] : [class_Rings_Olinordered__semidom(_1074044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074044), c_Groups_Ozero__class_Ozero(_1074044)), _1074046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074044), c_Groups_Ozero__class_Ozero(_1074044)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074044), _1074046), _1074048))))], (47840 ^ _777864) ^ [_1734990, _1734992, _1734994, _1734996, _1734998] : [-(c_Map_Odom(_1734990, _1734992, c_Map_Omap__upds(_1734990, _1734992, _1734994, _1734996, _1734998)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1734990, tc_HOL_Obool)), hAPP(c_List_Oset(_1734990), hAPP(hAPP(c_List_Otake(_1734990), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734992)), _1734998)), _1734996))), c_Map_Odom(_1734990, _1734992, _1734994)))], (33877 ^ _777864) ^ [_1404056] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1404056) = 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, _1404056)), 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))))))))], (50989 ^ _777864) ^ [_1806518, _1806520, _1806522, _1806524] : [hBOOL(hAPP(_1806518, _1806520)), -(c_List_OdropWhile(_1806522, _1806518, hAPP(hAPP(c_List_Olist_OCons(_1806522), _1806520), _1806524)) = c_List_OdropWhile(_1806522, _1806518, _1806524))], (4880 ^ _777864) ^ [_852480, _852482, _852484, _852486] : [-(c_List_Orotate(_852486, _852482) = c_List_Orotate(_852484, _852480)), _852486 = _852484, _852482 = _852480], (11993 ^ _777864) ^ [_978549, _978551] : [-(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), _978549), _978551)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978551))], (25743 ^ _777864) ^ [_1229456, _1229458, _1229460] : [class_Rings_Odvd(_1229456), class_Rings_Osemiring__0(_1229456), 25750 ^ _777864 : [(25760 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1229458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229456), _1229460), 25767 ^ [_1229456, _1229458, _1229460])))), 25761 ^ _777864 : [(25762 ^ _777864) ^ [_1229785] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229456), _1229460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229456), _1229785), c_Groups_Ozero__class_Ozero(_1229456)))), hBOOL(hAPP(_1229458, _1229785))]]], (25751 ^ _777864) ^ [] : [25752 ^ _777864 : [(25753 ^ _777864) ^ [_1229648] : [hBOOL(hAPP(_1229458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229456), _1229460), _1229648)))]], 25755 ^ _777864 : [(25758 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1229458, 25754 ^ [_1229456, _1229458, _1229460])))], (25756 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1229456), _1229460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229456), 25754 ^ [_1229456, _1229458, _1229460]), c_Groups_Ozero__class_Ozero(_1229456)))))]]]]], (40777 ^ _777864) ^ [_1562102, _1562104, _1562106, _1562108] : [hAPP(hAPP(c_Relation_Orel__comp(_1562102, _1562102, _1562102), _1562104), _1562106) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1562102, _1562102), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1562102, _1562102, _1562102), _1562104), _1562108) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1562102, _1562102), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1562102, _1562102, _1562102), _1562104), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562102, _1562102), tc_HOL_Obool)), _1562106), _1562108)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1562102, _1562102), tc_HOL_Obool)))], (1522 ^ _777864) ^ [_799657, _799659] : [-(class_Groups_Oab__semigroup__add(_799657)), _799659 = _799657, class_Groups_Oab__semigroup__add(_799659)], (35632 ^ _777864) ^ [_1440734, _1440736] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1440734), _1440736))))], (42712 ^ _777864) ^ [_1608511, _1608513, _1608515, _1608517, _1608519] : [class_Complete__Lattice_Ocomplete__lattice(_1608511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608513), _1608515)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1608511), _1608517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1608513, _1608511), _1608515), _1608519)) = hAPP(hAPP(c_Finite__Set_Ofold(_1608513, _1608511, hAPP(hAPP(c_COMBB(_1608511, tc_fun(_1608511, _1608511), _1608513), c_Lattices_Osemilattice__sup__class_Osup(_1608511)), _1608519)), _1608517), _1608515))], (18206 ^ _777864) ^ [_1091044, _1091046] : [18207 ^ _777864 : [(18210 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091044), c_Int_OPls))], (18208 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091044), _1091046))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091044)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091046))))], (41513 ^ _777864) ^ [_1580737, _1580739, _1580741] : [-(c_Relation_Orefl__on(_1580737, _1580739, _1580741)), 41517 ^ _777864 : [(41520 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1580737, _1580737, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1580737, tc_fun(_1580737, tc_HOL_Obool), tc_fun(_1580737, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1580737, tc_HOL_Obool), tc_fun(_1580737, tc_HOL_Obool)), _1580737), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1580737)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580737), c_fconj), hAPP(hAPP(c_COMBC(_1580737, tc_fun(_1580737, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580737)), _1580739)))), hAPP(hAPP(c_COMBC(_1580737, tc_fun(_1580737, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580737)), _1580739))), 41516 ^ [_1580737, _1580739, _1580741]))], (41518 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580737, _1580737)), 41516 ^ [_1580737, _1580739, _1580741]), _1580741)))]], 41522 ^ _777864 : [(41525 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580737, _1580737)), hAPP(hAPP(c_Product__Type_OPair(_1580737, _1580737), 41521 ^ [_1580737, _1580739, _1580741]), 41521 ^ [_1580737, _1580739, _1580741])), _1580741))], (41523 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1580737), 41521 ^ [_1580737, _1580739, _1580741]), _1580739)))]]], (15739 ^ _777864) ^ [_1046825, _1046827, _1046829] : [hBOOL(hAPP(_1046825, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046827), _1046829))), 15742 ^ _777864 : [(15749 ^ _777864) ^ [_1047010] : [_1046827 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046829), _1047010), -(hBOOL(hAPP(_1046825, _1047010)))], (15743 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046827), _1046829)), -(hBOOL(hAPP(_1046825, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (22330 ^ _777864) ^ [_1163799, _1163801, _1163803] : [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), _1163799), _1163801))), -(hBOOL(hAPP(hAPP(_1163803, _1163799), _1163801))), 22337 ^ _777864 : [(22340 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1163803, 22335 ^ [_1163799, _1163801, _1163803]), 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)))), 22336 ^ [_1163799, _1163801, _1163803])))), -(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), 22335 ^ [_1163799, _1163801, _1163803]), 22336 ^ [_1163799, _1163801, _1163803])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22336 ^ [_1163799, _1163801, _1163803]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22350 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1163803, 22335 ^ [_1163799, _1163801, _1163803]), 22336 ^ [_1163799, _1163801, _1163803]))], (22338 ^ _777864) ^ [] : [-(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), 22335 ^ [_1163799, _1163801, _1163803]), 22336 ^ [_1163799, _1163801, _1163803]))))]]], (35428 ^ _777864) ^ [_1436700, _1436702, _1436704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436700)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436702), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1436704)), 35438 ^ _777864 : [(35444 ^ _777864) ^ [] : [-(_1436702 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35440 ^ [_1436700, _1436702, _1436704]), 35437 ^ [_1436700, _1436702, _1436704]))], (35442 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35440 ^ [_1436700, _1436702, _1436704]), _1436704)))], (35439 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35437 ^ [_1436700, _1436702, _1436704]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1436700))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436702), _1436700) = _1436702)], (18356 ^ _777864) ^ [_1093533, _1093535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093533), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093535)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1093533), _1093535)))], (39173 ^ _777864) ^ [_1518158, _1518160, _1518162, _1518164] : [-(hAPP(c_Set_Oimage(tc_prod(_1518158, _1518160), tc_prod(_1518160, _1518158), hAPP(c_Product__Type_Oprod_Oprod__case(_1518158, _1518160, tc_prod(_1518160, _1518158)), hAPP(c_COMBC(_1518160, _1518158, tc_prod(_1518160, _1518158)), c_Product__Type_OPair(_1518160, _1518158)))), hAPP(hAPP(c_Product__Type_OSigma(_1518158, _1518160), _1518162), hAPP(c_COMBK(tc_fun(_1518160, tc_HOL_Obool), _1518158), _1518164))) = hAPP(hAPP(c_Product__Type_OSigma(_1518160, _1518158), _1518164), hAPP(c_COMBK(tc_fun(_1518158, tc_HOL_Obool), _1518160), _1518162)))], (40671 ^ _777864) ^ [_1559088, _1559090] : [-(hAPP(c_Set_Ovimage(_1559088, _1559088, c_Fun_Oid(_1559088)), _1559090) = _1559090)], (43249 ^ _777864) ^ [_1619844, _1619846, _1619848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1619844, _1619844), tc_HOL_Obool)), _1619846), _1619848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1619844, _1619844), tc_HOL_Obool)), _1619848), c_Transitive__Closure_Ortrancl(_1619844, _1619846))), -(c_Transitive__Closure_Ortrancl(_1619844, _1619848) = c_Transitive__Closure_Ortrancl(_1619844, _1619846))], (40434 ^ _777864) ^ [_1549161, _1549163, _1549165, _1549167, _1549169, _1549171] : [hBOOL(hAPP(hAPP(c_member(_1549161), _1549163), _1549165)), -(hAPP(c_Fun_Ooverride__on(_1549161, _1549167, _1549169, _1549171, _1549165), _1549163) = hAPP(_1549171, _1549163))], (22190 ^ _777864) ^ [_1161539, _1161541, _1161543] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1161539, _1161539), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1161541), _1161543))), -(_1161539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1161543 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18098 ^ _777864) ^ [_1089396] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089396), 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), _1089396)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1089396)))], (36758 ^ _777864) ^ [_1464255, _1464257, _1464259] : [class_Groups_Ocomm__monoid__add(_1464255), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464255), _1464257), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1464259))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464255), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464255), _1464257), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1464259))), hAPP(_1464257, hAPP(c_Nat_OSuc, _1464259))))], (8514 ^ _777864) ^ [_919053, _919055, _919057] : [class_Rings_Ocomm__semiring__1(_919053), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919053), _919055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919053), _919057), _919055)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919053), _919057), c_Groups_Oone__class_Oone(_919053))), _919055))], (13317 ^ _777864) ^ [_1001573, _1001575, _1001577, _1001579] : [_1001573 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1001575), _1001577)), _1001579), -(_1001575 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1001573, _1001575) = _1001579), 13324 ^ _777864 : [(13327 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001579), _1001575))], (13325 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001575)))]], 13332 ^ _777864 : [(13335 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1001575), _1001579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1001579), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (13333 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1001575))]]], (20430 ^ _777864) ^ [_1129662, _1129664, _1129666] : [class_Fields_Olinordered__field(_1129662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129662), _1129664), c_Groups_Ozero__class_Ozero(_1129662))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129662), c_Groups_Ozero__class_Ozero(_1129662)), _1129666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129662), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129662), _1129664), _1129666)), c_Groups_Ozero__class_Ozero(_1129662))))], (42611 ^ _777864) ^ [_1606424, _1606426, _1606428, _1606430] : [-(hAPP(c_Finite__Set_Ofold__image(_1606424, _1606426, _1606428), _1606430) = c_Finite__Set_Ofold(_1606426, _1606424, hAPP(hAPP(c_COMBB(_1606424, tc_fun(_1606424, _1606424), _1606426), _1606428), _1606430)))], (44354 ^ _777864) ^ [_1649141, _1649143, _1649145] : [c_Relation_Ototal__on(_1649141, _1649143, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1649141, _1649141), tc_HOL_Obool)), _1649145), c_Relation_OId(_1649141))), -(c_Relation_Ototal__on(_1649141, _1649143, _1649145))], (45557 ^ _777864) ^ [_1677664, _1677666, _1677668] : [-(c_Smallcheck_Oorelse(_1677664, _1677666, _1677668) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1677664), _1677664, _1677668, c_Option_Ooption_OSome(_1677664)), _1677666))], (2606 ^ _777864) ^ [_816565, _816567, _816569, _816571] : [-(c_Divides_Odivmod__nat__rel(_816571, _816567) = c_Divides_Odivmod__nat__rel(_816569, _816565)), _816571 = _816569, _816567 = _816565], (18674 ^ _777864) ^ [_1098805] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1098805)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1098805)))], (46052 ^ _777864) ^ [_1689331, _1689333] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1689331, _1689333) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1689331), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1689333)))], (20154 ^ _777864) ^ [_1125310, _1125312, _1125314, _1125316] : [class_Rings_Odivision__ring(_1125310), -(_1125312 = c_Groups_Ozero__class_Ozero(_1125310)), 20161 ^ _777864 : [(20168 ^ _777864) ^ [] : [_1125314 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125310), _1125316), _1125312), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125310), _1125314), _1125312) = _1125316)], (20162 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1125310), _1125314), _1125312) = _1125316, -(_1125314 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125310), _1125316), _1125312))]]], (42774 ^ _777864) ^ [_1609736, _1609738, _1609740, _1609742] : [class_Orderings_Olinorder(_1609736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609736), _1609738)), hBOOL(hAPP(hAPP(c_member(_1609736), _1609740), _1609738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609736), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1609736), _1609740), _1609742)), hAPP(hAPP(c_Finite__Set_Ofold(_1609736, _1609736, c_Orderings_Oord__class_Omax(_1609736)), _1609742), _1609738))))], (28304 ^ _777864) ^ [_1283243, _1283245, _1283247, _1283249] : [hBOOL(hAPP(hAPP(c_member(_1283243), _1283249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283243, tc_HOL_Obool)), _1283245), _1283247))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283243, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1283243, tc_fun(_1283243, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283243)), _1283245)), hAPP(hAPP(c_COMBC(_1283243, tc_fun(_1283243, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283243)), _1283247)), _1283249)))], (18612 ^ _777864) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (15536 ^ _777864) ^ [_1042366, _1042368, _1042370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042366), _1042368)), 15539 ^ _777864 : [(15546 ^ _777864) ^ [] : [_1042368 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042370), _1042366), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042368), _1042366) = _1042370)], (15540 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042368), _1042366) = _1042370, -(_1042368 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042370), _1042366))]]], (12688 ^ _777864) ^ [_990964, _990966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990966), _990964))))], (5398 ^ _777864) ^ [_860433, _860435, _860437, _860439] : [-(tc_prod(_860439, _860435) = tc_prod(_860437, _860433)), _860439 = _860437, _860435 = _860433], (38462 ^ _777864) ^ [_1499816, _1499818] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499816), c_Orderings_Otop__class_Otop(tc_fun(_1499816, tc_HOL_Obool)))), c_Fun_Oinj__on(_1499816, _1499816, _1499818, c_Orderings_Otop__class_Otop(tc_fun(_1499816, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1499816, _1499816, _1499818), c_Orderings_Otop__class_Otop(tc_fun(_1499816, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1499816, tc_HOL_Obool)))], (17092 ^ _777864) ^ [_1072512, _1072514, _1072516] : [class_Rings_Oring__1__no__zero__divisors(_1072512), -(_1072514 = c_Groups_Ozero__class_Ozero(_1072512)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072512), _1072514), _1072516) = c_Groups_Ozero__class_Ozero(_1072512)], (34199 ^ _777864) ^ [_1411778, _1411780, _1411782, _1411784] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1411778), _1411780)), -(hAPP(c_Set_Oimage(_1411778, _1411782, _1411784), _1411780) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1411782, tc_HOL_Obool), _1411778, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411782, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1411778, tc_fun(_1411782, tc_HOL_Obool), tc_fun(_1411782, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1411782, tc_fun(tc_fun(_1411782, tc_HOL_Obool), tc_fun(_1411782, tc_HOL_Obool)), _1411778), c_Set_Oinsert(_1411782)), _1411784)), c_Orderings_Obot__class_Obot(tc_fun(_1411782, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1411782, tc_HOL_Obool))), _1411780))], (13186 ^ _777864) ^ [_999283, _999285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999283), _999285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999285), _999283)), -(_999283 = _999285)], (18992 ^ _777864) ^ [_1104304, _1104306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104304)), c_Int_OBit1(_1104306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104304), _1104306)))], (23249 ^ _777864) ^ [_1182052, _1182054] : [class_Rings_Oring__1(_1182052), 23252 ^ _777864 : [(23259 ^ _777864) ^ [] : [-(_1182054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23262 ^ _777864 : [(23269 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182054), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1182052), _1182054) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1182052), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1182052, _1182052)), tc_fun(tc_Int_Oint, _1182052)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1182052, _1182052), _1182052), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1182052, _1182052)), tc_fun(tc_Int_Oint, _1182052)), tc_Int_Oint), c_COMBB(tc_fun(_1182052, _1182052), _1182052, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1182052, tc_fun(tc_fun(_1182052, _1182052), _1182052), tc_Int_Oint), c_HOL_OLet(_1182052, _1182052)), c_Int_Oring__1__class_Oof__int(_1182052)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1182052, _1182052), tc_fun(_1182052, _1182052)), hAPP(hAPP(c_COMBB(tc_fun(_1182052, tc_fun(_1182052, _1182052)), tc_fun(tc_fun(_1182052, _1182052), tc_fun(_1182052, _1182052)), tc_Int_Oint), c_COMBS(_1182052, _1182052, _1182052)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1182052, _1182052), tc_fun(_1182052, tc_fun(_1182052, _1182052))), hAPP(hAPP(c_COMBB(tc_fun(_1182052, tc_fun(_1182052, _1182052)), tc_fun(tc_fun(_1182052, _1182052), tc_fun(_1182052, tc_fun(_1182052, _1182052))), tc_Int_Oint), c_COMBB(_1182052, tc_fun(_1182052, _1182052), _1182052)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1182052, tc_fun(_1182052, _1182052)), tc_Int_Oint), c_If(_1182052)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBS(_1182052, _1182052, _1182052), c_Groups_Oplus__class_Oplus(_1182052)), c_COMBI(_1182052))))), hAPP(hAPP(c_COMBC(_1182052, _1182052, _1182052), hAPP(hAPP(c_COMBB(_1182052, tc_fun(_1182052, _1182052), _1182052), c_Groups_Oplus__class_Oplus(_1182052)), hAPP(hAPP(c_COMBS(_1182052, _1182052, _1182052), c_Groups_Oplus__class_Oplus(_1182052)), c_COMBI(_1182052)))), c_Groups_Oone__class_Oone(_1182052))))), c_Divides_Odivmod__int(_1182054, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (23263 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182054), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1182052), _1182054) = hAPP(c_Groups_Ouminus__class_Ouminus(_1182052), hAPP(c_Int_Oring__1__class_Oof__int(_1182052), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182054))))]]], (23253 ^ _777864) ^ [] : [_1182054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1182052), _1182054) = c_Groups_Ozero__class_Ozero(_1182052))]]], (16808 ^ _777864) ^ [_1067412] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067412), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1067412) = _1067412)], (45908 ^ _777864) ^ [_1686074, _1686076, _1686078, _1686080] : [hAPP(c_Map_Omap__of(_1686074, _1686076, _1686078), _1686080) = c_Option_Ooption_ONone(_1686076), hBOOL(hAPP(hAPP(c_member(_1686074), _1686080), hAPP(c_Set_Oimage(tc_prod(_1686074, _1686076), _1686074, c_Product__Type_Ofst(_1686074, _1686076)), hAPP(c_List_Oset(tc_prod(_1686074, _1686076)), _1686078))))], (2256 ^ _777864) ^ [_811098, _811100, _811102, _811104, _811106, _811108] : [-(c_Nat_Onat_Onat__rec(_811108, _811104, _811100) = c_Nat_Onat_Onat__rec(_811106, _811102, _811098)), _811108 = _811106, _811104 = _811102, _811100 = _811098], (49398 ^ _777864) ^ [_1771744, _1771746, _1771748] : [hBOOL(hAPP(hAPP(c_member(_1771744), _1771746), hAPP(c_List_Oset(_1771744), c_List_Obutlast(_1771744, _1771748)))), -(hBOOL(hAPP(hAPP(c_member(_1771744), _1771746), hAPP(c_List_Oset(_1771744), _1771748))))], (48480 ^ _777864) ^ [_1751594, _1751596, _1751598, _1751600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751594), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751596)), _1751598))), -(hAPP(hAPP(c_List_Olist__update(_1751596, _1751598), _1751594), _1751600) = hAPP(hAPP(c_List_Oappend(_1751596), hAPP(hAPP(c_List_Otake(_1751596), _1751594), _1751598)), hAPP(hAPP(c_List_Olist_OCons(_1751596), _1751600), hAPP(hAPP(c_List_Odrop(_1751596), hAPP(c_Nat_OSuc, _1751594)), _1751598))))], (30925 ^ _777864) ^ [_1343265, _1343267] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343265), _1343267))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343265, _1343267))], (11313 ^ _777864) ^ [_966401, _966403] : [class_Rings_Olinordered__idom(_966401), 11316 ^ _777864 : [(11323 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _966403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966401), c_Groups_Ozero__class_Ozero(_966401)), hAPP(c_Int_Oring__1__class_Oof__int(_966401), _966403))))], (11317 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966401), c_Groups_Ozero__class_Ozero(_966401)), hAPP(c_Int_Oring__1__class_Oof__int(_966401), _966403))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _966403)))]]], (43905 ^ _777864) ^ [_1636881, _1636883, _1636885, _1636887, _1636889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636881, _1636883)), hAPP(hAPP(c_Product__Type_OPair(_1636881, _1636883), _1636885), _1636887)), hAPP(c_Relation_Oconverse(_1636883, _1636881), _1636889))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1636883, _1636881)), hAPP(hAPP(c_Product__Type_OPair(_1636883, _1636881), _1636887), _1636885)), _1636889)))], (13102 ^ _777864) ^ [_997820, _997822, _997824, _997826, _997828] : [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), _997820), _997822)), _997824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _997820), _997826)), _997828))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997828), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997820), _997828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997820), _997824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997826), _997822)))], (49380 ^ _777864) ^ [_1771501, _1771503, _1771505] : [-(_1771501 = c_List_Olist_ONil(_1771503)), -(c_List_Obutlast(_1771503, hAPP(hAPP(c_List_Oappend(_1771503), _1771505), _1771501)) = hAPP(hAPP(c_List_Oappend(_1771503), _1771505), c_List_Obutlast(_1771503, _1771501)))], (15072 ^ _777864) ^ [_1033462, _1033464, _1033466] : [class_Groups_Ogroup__add(_1033462), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033462), _1033464), _1033466)), _1033466) = _1033464)], (11361 ^ _777864) ^ [_967142] : [class_Groups_Osgn__if(_967142), -(c_Groups_Osgn__class_Osgn(_967142, c_Groups_Ozero__class_Ozero(_967142)) = c_Groups_Ozero__class_Ozero(_967142))], (284 ^ _777864) ^ [_782140, _782142, _782144, _782146, _782148, _782150, _782152, _782154, _782156, _782158] : [-(c_Big__Operators_Ocomm__monoid__big(_782156, _782152, _782148, _782144, _782140)), c_Big__Operators_Ocomm__monoid__big(_782158, _782154, _782150, _782146, _782142), _782158 = _782156, _782154 = _782152, _782150 = _782148, _782146 = _782144, _782142 = _782140], (11022 ^ _777864) ^ [_961472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961472)), _961472))], (26835 ^ _777864) ^ [_1251634, _1251636, _1251638, _1251640] : [hBOOL(hAPP(hAPP(c_member(_1251634), _1251636), hAPP(hAPP(c_Set_Oinsert(_1251634), _1251638), _1251640))), -(_1251636 = _1251638), -(hBOOL(hAPP(hAPP(c_member(_1251634), _1251636), _1251640)))], (50386 ^ _777864) ^ [_1792625, _1792627] : [c_List_Olist_ONil(_1792625) = hAPP(c_List_Orev(_1792625), _1792627), -(_1792627 = c_List_Olist_ONil(_1792625))], (36934 ^ _777864) ^ [_1468173, _1468175, _1468177, _1468179] : [class_Groups_Ocomm__monoid__add(_1468173), 36937 ^ _777864 : [(36944 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1468175), _1468177))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468173), _1468179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1468177), hAPP(c_Nat_OSuc, _1468175))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468173), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468173), _1468179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1468177), _1468175))), hAPP(_1468179, _1468175)))], (36938 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1468175), _1468177)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468173), _1468179), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1468177), hAPP(c_Nat_OSuc, _1468175))) = c_Groups_Ozero__class_Ozero(_1468173))]]], (49496 ^ _777864) ^ [_1773905, _1773907, _1773909] : [hAPP(c_List_Ofilter(_1773905, _1773907), _1773909) = c_List_Olist_ONil(_1773905), 49499 ^ _777864 : [(49500 ^ _777864) ^ [_1774002] : [hBOOL(hAPP(hAPP(c_member(_1773905), _1774002), hAPP(c_List_Oset(_1773905), _1773909))), hBOOL(hAPP(_1773907, _1774002))]]], (29868 ^ _777864) ^ [_1320152, _1320154, _1320156, _1320158] : [hBOOL(hAPP(hAPP(c_member(_1320152), _1320154), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320152, tc_HOL_Obool)), _1320156), _1320158))), -(hBOOL(hAPP(hAPP(c_member(_1320152), _1320154), _1320158)))], (38631 ^ _777864) ^ [_1505023, _1505025] : [c_Equiv__Relations_Oequivp(_1505023, _1505025), 38634 ^ _777864 : [(38641 ^ _777864) ^ [_1505216, _1505218] : [hAPP(_1505025, _1505218) = hAPP(_1505025, _1505216), -(hBOOL(hAPP(hAPP(_1505025, _1505218), _1505216)))], (38635 ^ _777864) ^ [_1505117, _1505119] : [hBOOL(hAPP(hAPP(_1505025, _1505119), _1505117)), -(hAPP(_1505025, _1505119) = hAPP(_1505025, _1505117))]]], (28576 ^ _777864) ^ [_1292184, _1292186, _1292188, _1292190, _1292192] : [-(hAPP(c_Relation_OImage(_1292184, _1292186, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292184, _1292186), tc_HOL_Obool)), _1292188), _1292190)), _1292192) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292186, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1292184, _1292186, _1292188), _1292192)), hAPP(c_Relation_OImage(_1292184, _1292186, _1292190), _1292192)))], (32805 ^ _777864) ^ [_1379166, _1379168, _1379170] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379166, tc_Nat_Onat), _1379168), _1379170)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379166, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1379166), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1379168)), _1379170))], (33192 ^ _777864) ^ [_1387224, _1387226, _1387228, _1387230, _1387232] : [class_Groups_Ocomm__monoid__mult(_1387224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387226), _1387228)), hBOOL(hAPP(hAPP(c_member(_1387226), _1387230), _1387228)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387226, _1387224), _1387232), _1387228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387224), hAPP(_1387232, _1387230)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387226, _1387224), _1387232), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1387226, tc_HOL_Obool)), _1387228), hAPP(hAPP(c_Set_Oinsert(_1387226), _1387230), c_Orderings_Obot__class_Obot(tc_fun(_1387226, tc_HOL_Obool)))))))], (4918 ^ _777864) ^ [_853071, _853073, _853075, _853077] : [-(c_List_Olist__update(_853077, _853073) = c_List_Olist__update(_853075, _853071)), _853077 = _853075, _853073 = _853071], (31503 ^ _777864) ^ [_1353520, _1353522] : [class_Lattices_Olattice(_1353520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353520), _1353522)), -(_1353522 = c_Orderings_Obot__class_Obot(tc_fun(_1353520, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1353520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1353520), 31516 ^ [_1353520, _1353522]), 31517 ^ [_1353520, _1353522])), hAPP(hAPP(c_Set_Oinsert(_1353520), 31516 ^ [_1353520, _1353522]), hAPP(hAPP(c_Set_Oinsert(_1353520), 31517 ^ [_1353520, _1353522]), c_Orderings_Obot__class_Obot(tc_fun(_1353520, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1353520), c_Big__Operators_Olattice__class_OInf__fin(_1353520, _1353522)), _1353522)))], (17590 ^ _777864) ^ [_1081418] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081418)))], (6438 ^ _777864) ^ [_884075, _884077, _884079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884075), _884077)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884075), _884079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884077), _884079)))], (39862 ^ _777864) ^ [_1533676, _1533678, _1533680, _1533682, _1533684, _1533686, _1533688, _1533690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533676, _1533678)), _1533680), hAPP(c_Set_Oimage(tc_prod(_1533682, _1533684), tc_prod(_1533676, _1533678), c_Product__Type_Omap__pair(_1533682, _1533676, _1533684, _1533678, _1533686, _1533688)), _1533690))), 39867 ^ _777864 : [(39870 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533682, _1533684)), hAPP(hAPP(c_Product__Type_OPair(_1533682, _1533684), 39865 ^ [_1533676, _1533678, _1533680, _1533682, _1533684, _1533686, _1533688, _1533690]), 39866 ^ [_1533676, _1533678, _1533680, _1533682, _1533684, _1533686, _1533688, _1533690])), _1533690)))], (39868 ^ _777864) ^ [] : [-(_1533680 = hAPP(hAPP(c_Product__Type_OPair(_1533676, _1533678), hAPP(_1533686, 39865 ^ [_1533676, _1533678, _1533680, _1533682, _1533684, _1533686, _1533688, _1533690])), hAPP(_1533688, 39866 ^ [_1533676, _1533678, _1533680, _1533682, _1533684, _1533686, _1533688, _1533690])))]]], (29143 ^ _777864) ^ [_1305339, _1305341, _1305343] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305339), _1305341)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305339), hAPP(hAPP(c_Set_Oinsert(_1305339), _1305343), _1305341))))], (18912 ^ _777864) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (19302 ^ _777864) ^ [_1109719] : [-(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)))), _1109719) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1109719)))], (36456 ^ _777864) ^ [_1456734, _1456736, _1456738] : [class_Orderings_Olinorder(_1456734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456734), _1456736), _1456738)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456734, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1456734), _1456736)), c_SetInterval_Oord__class_OatLeastAtMost(_1456734, _1456736, _1456738)) = hAPP(c_SetInterval_Oord__class_OatMost(_1456734), _1456738))], (41578 ^ _777864) ^ [_1582699, _1582701] : [41580 ^ _777864 : [(41583 ^ _777864) ^ [] : [hBOOL(hAPP(_1582699, hAPP(c_Int_OAbs__Integ, 41579 ^ [_1582699, _1582701])))], (41581 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 41579 ^ [_1582699, _1582701]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1582699, _1582701)))], (14600 ^ _777864) ^ [_1024543, _1024545, _1024547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024543)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024547), _1024543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024545), _1024547)), _1024543))], (48886 ^ _777864) ^ [_1760625, _1760627, _1760629, _1760631, _1760633] : [-(c_List_Olist_Olist__size(_1760625, _1760627, hAPP(hAPP(c_List_Omap(_1760629, _1760625), _1760631), _1760633)) = c_List_Olist_Olist__size(_1760629, hAPP(c_Fun_Ocomp(_1760625, tc_Nat_Onat, _1760629, _1760627), _1760631), _1760633))], (12618 ^ _777864) ^ [_989793, _989795, _989797] : [class_Rings_Olinordered__idom(_989793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989793), c_Groups_Ozero__class_Ozero(_989793)), _989795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989793), c_Groups_Ozero__class_Ozero(_989793)), _989797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989793), _989797), c_Groups_Oone__class_Oone(_989793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989793), _989795), _989797)), _989795)))], (12073 ^ _777864) ^ [_979983, _979985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979983), _979985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979983), hAPP(c_Nat_OSuc, _979985))))], (29648 ^ _777864) ^ [_1316200, _1316202, _1316204] : [class_Lattices_Olattice(_1316200), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316200), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316200), _1316202), _1316204)), _1316202)))], (128 ^ _777864) ^ [_779632, _779634, _779636, _779638, _779640, _779642] : [-(c_Nitpick_Oless__eq__frac(_779640, _779636, _779632)), c_Nitpick_Oless__eq__frac(_779642, _779638, _779634), _779642 = _779640, _779638 = _779636, _779634 = _779632], (6747 ^ _777864) ^ [_888987, _888989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _888987)), hAPP(c_Nat_OSuc, _888989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888987), _888989)))], (40128 ^ _777864) ^ [_1539500, _1539502, _1539504] : [hBOOL(hAPP(hAPP(c_member(_1539500), _1539502), hAPP(c_Set_OCollect(_1539500), _1539504))), -(hBOOL(hAPP(_1539504, _1539502)))], (47046 ^ _777864) ^ [_1716355, _1716357, _1716359] : [-(hAPP(hAPP(c_List_Onth(_1716355), hAPP(hAPP(c_List_Olist_OCons(_1716355), _1716357), _1716359)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1716357)], (22540 ^ _777864) ^ [_1167496, _1167498, _1167500, _1167502, _1167504] : [hAPP(c_Product__Type_Osnd(_1167496, _1167498), hAPP(hAPP(c_Product__Type_OPair(_1167496, _1167498), _1167500), _1167502)) = _1167504, -(_1167502 = _1167504)], (41914 ^ _777864) ^ [_1590507, _1590509, _1590511, _1590513, _1590515, _1590517, _1590519] : [class_Groups_Oab__semigroup__mult(_1590507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590509), _1590511)), c_Fun_Oinj__on(_1590509, _1590513, _1590515, _1590511), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1590507, _1590513, c_Groups_Otimes__class_Otimes(_1590507)), _1590517), _1590519), hAPP(c_Set_Oimage(_1590509, _1590513, _1590515), _1590511)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1590507, _1590509, c_Groups_Otimes__class_Otimes(_1590507)), hAPP(c_Fun_Ocomp(_1590513, _1590507, _1590509, _1590517), _1590515)), _1590519), _1590511))], (18146 ^ _777864) ^ [_1090081] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090081), c_Int_OPls)))], (24861 ^ _777864) ^ [_1214412, _1214414, _1214416, _1214418] : [class_Divides_Osemiring__div(_1214412), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), _1214414), _1214416)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), _1214414), _1214418)), 24872 ^ _777864 : [(24879 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), _1214416), _1214418)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214412), _1214416), _1214414)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214412), _1214418), _1214414))))], (24873 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214412), _1214416), _1214414)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1214412), _1214418), _1214414))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214412), _1214416), _1214418)))]]], (6248 ^ _777864) ^ [_880754, _880756, _880758, _880760] : [class_Groups_Oordered__cancel__ab__semigroup__add(_880754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880754), _880756), _880758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880754), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880754), _880760), _880756)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880754), _880760), _880758))))], (35700 ^ _777864) ^ [_1441877, _1441879] : [35702 ^ _777864 : [(35705 ^ _777864) ^ [] : [hBOOL(hAPP(_1441879, 35701 ^ [_1441877, _1441879]))], (35703 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35701 ^ [_1441877, _1441879]), _1441877)))]], 35706 ^ _777864 : [(35707 ^ _777864) ^ [_1442027] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1442027), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1441877))), -(hBOOL(hAPP(_1441879, _1442027)))]]], (37576 ^ _777864) ^ [_1482586, _1482588, _1482590, _1482592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1482586), _1482588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482586, tc_HOL_Obool)), _1482588), _1482590)), hBOOL(hAPP(_1482592, c_Orderings_Obot__class_Obot(tc_fun(_1482586, tc_HOL_Obool)))), 37591 ^ _777864 : [(37592 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1482586), 37590 ^ [_1482586, _1482588, _1482590, _1482592])))], (37596 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1482586), 37589 ^ [_1482586, _1482588, _1482590, _1482592]), 37590 ^ [_1482586, _1482588, _1482590, _1482592]))], (37600 ^ _777864) ^ [] : [hBOOL(hAPP(_1482592, hAPP(hAPP(c_Set_Oinsert(_1482586), 37589 ^ [_1482586, _1482588, _1482590, _1482592]), 37590 ^ [_1482586, _1482588, _1482590, _1482592])))], (37598 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1482592, 37590 ^ [_1482586, _1482588, _1482590, _1482592])))], (37594 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482586), 37589 ^ [_1482586, _1482588, _1482590, _1482592]), _1482590)))]], -(hBOOL(hAPP(_1482592, _1482588)))], (26927 ^ _777864) ^ [_1253306, _1253308, _1253310] : [-(hBOOL(hAPP(hAPP(c_member(_1253306), _1253308), _1253310))), -(hBOOL(hAPP(hAPP(c_member(_1253306), _1253308), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1253306, tc_HOL_Obool)), _1253310))))], (17580 ^ _777864) ^ [_1081295] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1081295)))], (15788 ^ _777864) ^ [_1047774, _1047776, _1047778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047774), _1047776)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047776), _1047774))), _1047778) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1047776)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047774), _1047778)))], (34713 ^ _777864) ^ [_1422374, _1422376, _1422378] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422374), _1422376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422374, tc_HOL_Obool)), _1422376), hAPP(c_Set_Oimage(_1422374, _1422374, _1422378), _1422376))), -(c_Fun_Oinj__on(_1422374, _1422374, _1422378, _1422376))], (14183 ^ _777864) ^ [_1017824, _1017826] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017824, _1017826)) = _1017826), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1017824), _1017826) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017824, _1017826)))], (41406 ^ _777864) ^ [_1578499, _1578501, _1578503, _1578505] : [41407 ^ _777864 : [(41408 ^ _777864) ^ [_1578553] : [hBOOL(hAPP(hAPP(_1578503, _1578505), _1578553))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1578499, _1578501, _1578503), _1578505)))], (3220 ^ _777864) ^ [_826584, _826586, _826588, _826590, _826592, _826594, _826596, _826598] : [-(c_Sum__Type_OPlus(_826598, _826594, _826590, _826586) = c_Sum__Type_OPlus(_826596, _826592, _826588, _826584)), _826598 = _826596, _826594 = _826592, _826590 = _826588, _826586 = _826584], (48778 ^ _777864) ^ [_1758327] : [-(hAPP(c_List_Otl(_1758327), c_List_Olist_ONil(_1758327)) = c_List_Olist_ONil(_1758327))], (10932 ^ _777864) ^ [_959844] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _959844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39239 ^ _777864) ^ [_1519975, _1519977, _1519979, _1519981, _1519983, _1519985] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519975, _1519977)), hAPP(hAPP(c_Product__Type_OPair(_1519975, _1519977), _1519979), _1519981)), hAPP(hAPP(c_Product__Type_OSigma(_1519975, _1519977), _1519983), _1519985))), 39242 ^ _777864 : [(39245 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519977), _1519981), hAPP(_1519985, _1519979))))], (39243 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519975), _1519979), _1519983)))]]], (40286 ^ _777864) ^ [_1543034, _1543036, _1543038] : [-(hAPP(c_Set_OCollect(_1543034), hAPP(hAPP(c_COMBS(_1543034, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543034), c_fimplies), _1543036)), _1543038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543034, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1543034, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1543034), _1543036))), hAPP(c_Set_OCollect(_1543034), _1543038)))], (15816 ^ _777864) ^ [_1048515, _1048517, _1048519, _1048521, _1048523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048515), _1048517)), 15819 ^ _777864 : [(15826 ^ _777864) ^ [] : [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), _1048517), _1048515)), _1048519)), _1048521) = _1048523, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048517), _1048519)), _1048521) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048515), _1048519)), _1048523))], (15820 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048517), _1048519)), _1048521) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048515), _1048519)), _1048523), -(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), _1048517), _1048515)), _1048519)), _1048521) = _1048523)]]], (8104 ^ _777864) ^ [_912708, _912710, _912712] : [class_Orderings_Olinorder(_912708), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912708), _912710), _912712))), -(_912710 = _912712), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912708), _912712), _912710)))], (45735 ^ _777864) ^ [_1681772, _1681774, _1681776, _1681778, _1681780, _1681782, _1681784] : [-(c_List_Ofoldr(_1681772, _1681774, _1681776, hAPP(hAPP(c_List_Omap(_1681778, _1681772), _1681780), _1681782), _1681784) = c_List_Ofoldr(_1681778, _1681774, hAPP(c_Fun_Ocomp(_1681772, tc_fun(_1681774, _1681774), _1681778, _1681776), _1681780), _1681782, _1681784))], (48550 ^ _777864) ^ [_1753244, _1753246, _1753248, _1753250, _1753252] : [hAPP(hAPP(c_List_Odrop(_1753244), _1753246), _1753248) = hAPP(hAPP(c_List_Olist_OCons(_1753244), _1753250), _1753252), -(hAPP(hAPP(c_List_Onth(_1753244), _1753248), _1753246) = _1753250)], (26057 ^ _777864) ^ [_1235572, _1235574, _1235576] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235572), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235574, _1235576))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235572), _1235576)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235572), _1235574)))], (39207 ^ _777864) ^ [_1519137, _1519139] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519137, _1519139), c_Orderings_Otop__class_Otop(tc_fun(_1519137, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1519139, tc_HOL_Obool), _1519137), c_Orderings_Otop__class_Otop(tc_fun(_1519139, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1519137, _1519139), tc_HOL_Obool)))], (23665 ^ _777864) ^ [_1191156, _1191158, _1191160, _1191162] : [class_Orderings_Olinorder(_1191156), 23668 ^ _777864 : [(23669 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191156), _1191158), _1191160)), _1191162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), _1191158), _1191162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), _1191160), _1191162)))], (23679 ^ _777864) ^ [] : [23680 ^ _777864 : [(23683 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), _1191160), _1191162))], (23681 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), _1191158), _1191162))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191156), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191156), _1191158), _1191160)), _1191162)))]]], (15402 ^ _777864) ^ [_1039867, _1039869, _1039871] : [class_Rings_Ocomm__ring__1(_1039867), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039867), _1039869), _1039871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039867), _1039869), hAPP(c_Groups_Ouminus__class_Ouminus(_1039867), _1039871)))], (4368 ^ _777864) ^ [_844692, _844694] : [_844694 = _844692, -(c_Groups_Otimes__class_Otimes(_844694) = c_Groups_Otimes__class_Otimes(_844692))], (47424 ^ _777864) ^ [_1725844, _1725846, _1725848, _1725850] : [-(hAPP(hAPP(c_List_Otake(_1725844), _1725846), hAPP(hAPP(c_List_Olist_OCons(_1725844), _1725848), _1725850)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1725844), c_List_Olist_ONil(_1725844), hAPP(hAPP(c_COMBB(tc_List_Olist(_1725844), tc_List_Olist(_1725844), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1725844), _1725848)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1725844), tc_List_Olist(_1725844)), c_List_Otake(_1725844)), _1725850)), _1725846))], (3046 ^ _777864) ^ [_823767, _823769] : [_823769 = _823767, -(c_Int_Oring__1__class_OInts(_823769) = c_Int_Oring__1__class_OInts(_823767))], (41051 ^ _777864) ^ [_1569173] : [class_Orderings_Owellorder(_1569173), -(c_Wellfounded_Owf(_1569173, hAPP(c_Set_OCollect(tc_prod(_1569173, _1569173)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569173, _1569173, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1569173)))))], (17820 ^ _777864) ^ [_1084986, _1084988] : [class_Int_Onumber__ring(_1084986), 17823 ^ _777864 : [(17830 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084988)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084986), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084988)) = hAPP(c_Int_Onumber__class_Onumber__of(_1084986), _1084988))], (17824 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084988))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084986), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084988)) = c_Groups_Ozero__class_Ozero(_1084986))]]], (13537 ^ _777864) ^ [_1005835] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1005835) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50901 ^ _777864) ^ [_1804592, _1804594] : [hBOOL(hAPP(c_List_Odistinct(_1804592), _1804594)), -(c_List_Oremdups(_1804592, _1804594) = _1804594)], (44860 ^ _777864) ^ [_1661338, _1661340] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661338, tc_HOL_Obool), hAPP(c_Set_OPow(_1661338), _1661340)) = _1661340)], (1482 ^ _777864) ^ [_799157, _799159] : [-(class_Rings_Olinordered__semiring(_799157)), _799159 = _799157, class_Rings_Olinordered__semiring(_799159)], (21930 ^ _777864) ^ [_1157201, _1157203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1157201)), 21933 ^ _777864 : [(21940 ^ _777864) ^ [] : [-(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), _1157203), _1157201)))), -(c_Divides_OnegDivAlg(_1157203, _1157201) = hAPP(c_Divides_Oadjust(_1157201), c_Divides_OnegDivAlg(_1157203, 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)))), _1157201))))], (21934 ^ _777864) ^ [] : [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), _1157203), _1157201))), -(c_Divides_OnegDivAlg(_1157203, _1157201) = 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), _1157203), _1157201)))]]], (21884 ^ _777864) ^ [_1156397, _1156399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156397), 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)), _1156399)), -(c_Divides_OnegDivAlg(_1156397, _1156399) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1156397), _1156399)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1156397, _1156399)))], (45677 ^ _777864) ^ [_1680495, _1680497, _1680499, _1680501, _1680503] : [hAPP(hAPP(c_List_Omap(_1680495, _1680497), _1680499), _1680501) = hAPP(hAPP(c_List_Omap(_1680495, _1680497), _1680499), _1680503), c_Fun_Oinj__on(_1680495, _1680497, _1680499, c_Orderings_Otop__class_Otop(tc_fun(_1680495, tc_HOL_Obool))), -(_1680501 = _1680503)], (50156 ^ _777864) ^ [_1787230, _1787232, _1787234, _1787236] : [class_Groups_Ocomm__monoid__add(_1787230), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1787230), _1787232), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1787234, _1787236))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1787230), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1787230), _1787232), c_List_Oupt(_1787234, _1787236))))], (6546 ^ _777864) ^ [_885922, _885924] : [6547 ^ _777864 : [(6550 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885924))], (6548 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885922))]], -(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), _885922), _885924))))], (33251 ^ _777864) ^ [_1388586, _1388588, _1388590, _1388592, _1388594] : [class_Groups_Ocomm__monoid__mult(_1388586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388588), _1388590)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388588), _1388592)), 33265 ^ _777864 : [(33268 ^ _777864) ^ [] : [hAPP(_1388594, 33264 ^ [_1388586, _1388588, _1388590, _1388592, _1388594]) = c_Groups_Oone__class_Oone(_1388586)], (33266 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388588), 33264 ^ [_1388586, _1388588, _1388590, _1388592, _1388594]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388588, tc_HOL_Obool)), _1388590), _1388592))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388588, _1388586), _1388594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388588, tc_HOL_Obool)), _1388590), _1388592)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388586), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388588, _1388586), _1388594), _1388590)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388588, _1388586), _1388594), _1388592)))], (48856 ^ _777864) ^ [_1759914, _1759916] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759914)), hAPP(c_List_Otl(_1759914), _1759916)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759914)), _1759916)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (14800 ^ _777864) ^ [_1028606, _1028608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028608)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1028606), hAPP(c_Int_Onat, _1028608)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028606, _1028608)))], (51127 ^ _777864) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (50941 ^ _777864) ^ [_1805341, _1805343, _1805345] : [-(hBOOL(hAPP(hAPP(c_member(_1805341), _1805343), hAPP(c_List_Oset(_1805341), _1805345)))), -(c_List_Oremdups(_1805341, hAPP(hAPP(c_List_Olist_OCons(_1805341), _1805343), _1805345)) = hAPP(hAPP(c_List_Olist_OCons(_1805341), _1805343), c_List_Oremdups(_1805341, _1805345)))], (35922 ^ _777864) ^ [_1446133, _1446135, _1446137, _1446139] : [class_Orderings_Olinorder(_1446133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446133), _1446135), _1446137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446133), _1446137), _1446139)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446133, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446133, _1446135, _1446137)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446133, _1446137), _1446139)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1446133, _1446135, _1446139))], (17284 ^ _777864) ^ [_1076047, _1076049, _1076051, _1076053] : [class_Rings_Olinordered__semidom(_1076047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076047), hAPP(hAPP(c_Power_Opower__class_Opower(_1076047), _1076049), _1076051)), hAPP(hAPP(c_Power_Opower__class_Opower(_1076047), _1076053), _1076051))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076047), c_Groups_Ozero__class_Ozero(_1076047)), _1076053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076047), _1076049), _1076053)))], (36124 ^ _777864) ^ [_1450219, _1450221, _1450223, _1450225, _1450227, _1450229] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450219, _1450221), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450219, _1450221), _1450223), _1450225), _1450227)), _1450225), _1450229) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450219, _1450221), _1450223), _1450225), _1450229))], (28424 ^ _777864) ^ [_1288772, _1288774] : [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)), _1288772), _1288774)), 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)), _1288772), 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)), _1288774), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (41485 ^ _777864) ^ [_1579923, _1579925] : [-(c_Nitpick_Owf_H(_1579923, _1579925)), c_Wellfounded_Oacyclic(_1579923, _1579925), 41490 ^ _777864 : [(41493 ^ _777864) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (41491 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579923, _1579923)), _1579925))]]], (48249 ^ _777864) ^ [_1744587, _1744589, _1744591, _1744593, _1744595, _1744597] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744587), tc_List_Olist(_1744587))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744587), tc_List_Olist(_1744587)), hAPP(hAPP(c_List_Oappend(_1744587), _1744589), hAPP(hAPP(c_List_Olist_OCons(_1744587), _1744591), c_List_Olist_ONil(_1744587)))), hAPP(hAPP(c_List_Oappend(_1744587), _1744593), hAPP(hAPP(c_List_Olist_OCons(_1744587), _1744595), c_List_Olist_ONil(_1744587))))), c_List_Olistrel1(_1744587, _1744597)))), 48250 ^ _777864 : [(48257 ^ _777864) ^ [] : [_1744589 = _1744593, hBOOL(hAPP(hAPP(c_member(tc_prod(_1744587, _1744587)), hAPP(hAPP(c_Product__Type_OPair(_1744587, _1744587), _1744591), _1744595)), _1744597))], (48251 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1744587), tc_List_Olist(_1744587))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1744587), tc_List_Olist(_1744587)), _1744589), _1744593)), c_List_Olistrel1(_1744587, _1744597))), _1744591 = _1744595]]], (854 ^ _777864) ^ [_791035, _791037, _791039, _791041, _791043, _791045] : [-(c_Finite__Set_Ofun__left__comm__idem(_791043, _791039, _791035)), c_Finite__Set_Ofun__left__comm__idem(_791045, _791041, _791037), _791045 = _791043, _791041 = _791039, _791037 = _791035], (44212 ^ _777864) ^ [_1645693, _1645695] : [-(c_Transitive__Closure_Ortrancl(_1645693, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1645693, _1645693), tc_HOL_Obool)), _1645695), c_Relation_OId(_1645693))) = c_Transitive__Closure_Ortrancl(_1645693, _1645695))], (42583 ^ _777864) ^ [_1605944, _1605946] : [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), _1605944), _1605946)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1605944), _1605946)))], (23967 ^ _777864) ^ [_1196873, _1196875, _1196877, _1196879] : [class_Orderings_Olinorder(_1196873), 23970 ^ _777864 : [(23979 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196873), _1196875), _1196877)), _1196879))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), _1196875), _1196879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), _1196877), _1196879))], (23971 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196873), _1196875), _1196877)), _1196879)), 23974 ^ _777864 : [(23977 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), _1196877), _1196879)))], (23975 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196873), _1196875), _1196879)))]]]]], (6613 ^ _777864) ^ [_887036] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887036), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _887036)], (16150 ^ _777864) ^ [_1054792, _1054794] : [-(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), _1054792)), _1054794))))], (45848 ^ _777864) ^ [_1684603, _1684605, _1684607, _1684609, _1684611, _1684613, _1684615] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1684603), tc_Option_Ooption(_1684605), _1684607, hAPP(c_Option_Omap(_1684603, _1684605), _1684609)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1684607, tc_Option_Ooption(_1684603)), _1684611), _1684613), hAPP(c_Option_Ooption_OSome(_1684603), _1684615))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1684607, tc_Option_Ooption(_1684605)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1684603), tc_Option_Ooption(_1684605), _1684607, hAPP(c_Option_Omap(_1684603, _1684605), _1684609)), _1684611)), _1684613), hAPP(c_Option_Ooption_OSome(_1684605), hAPP(_1684609, _1684615))))], (6783 ^ _777864) ^ [_889527, _889529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889529), hAPP(c_Nat_OSuc, _889527))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889527), _889529))], (41331 ^ _777864) ^ [_1575900, _1575902, _1575904] : [-(hAPP(c_Set_Oimage(tc_prod(_1575900, _1575902), _1575900, c_Product__Type_Ofst(_1575900, _1575902)), _1575904) = hAPP(c_Relation_ODomain(_1575900, _1575902), _1575904))], (9314 ^ _777864) ^ [_933023, _933025, _933027, _933029] : [class_Rings_Olinordered__ring__strict(_933023), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933023), _933025), _933027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933023), _933029), c_Groups_Ozero__class_Ozero(_933023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933023), _933027), _933029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933023), _933025), _933029))))], (37931 ^ _777864) ^ [_1489663, _1489665, _1489667, _1489669] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489663, _1489665, _1489667, _1489669, c_Orderings_Obot__class_Obot(tc_fun(_1489663, tc_HOL_Obool))), _1489669)))], (51497 ^ _777864) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (17330 ^ _777864) ^ [_1076924, _1076926, _1076928] : [class_Rings_Olinordered__semidom(_1076924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076924), c_Groups_Oone__class_Oone(_1076924)), _1076926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076924), c_Groups_Oone__class_Oone(_1076924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076924), _1076926), hAPP(hAPP(c_Power_Opower__class_Opower(_1076924), _1076926), _1076928)))))], (10067 ^ _777864) ^ [_946104] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946104), _946104))))], (34613 ^ _777864) ^ [_1420704, _1420706, _1420708] : [class_Orderings_Oorder(_1420704), 34616 ^ _777864 : [(34623 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420704), _1420706), _1420708))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1420704, _1420706, _1420708) = c_Orderings_Obot__class_Obot(tc_fun(_1420704, tc_HOL_Obool)))], (34617 ^ _777864) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1420704, _1420706, _1420708) = c_Orderings_Obot__class_Obot(tc_fun(_1420704, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420704), _1420706), _1420708))]]], (20226 ^ _777864) ^ [_1126547, _1126549, _1126551, _1126553] : [class_Fields_Ofield__inverse__zero(_1126547), -(_1126549 = c_Groups_Ozero__class_Ozero(_1126547)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126547), _1126549), _1126551)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126547), _1126549), _1126553)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126547), _1126551), _1126553))], (31255 ^ _777864) ^ [_1348717, _1348719, _1348721] : [class_Lattices_Olattice(_1348717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348717), _1348719)), -(hBOOL(hAPP(hAPP(c_member(_1348717), _1348721), _1348719))), -(_1348719 = c_Orderings_Obot__class_Obot(tc_fun(_1348717, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1348717, hAPP(hAPP(c_Set_Oinsert(_1348717), _1348721), _1348719)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1348717), _1348721), c_Big__Operators_Olattice__class_OInf__fin(_1348717, _1348719)))], (42391 ^ _777864) ^ [_1601602, _1601604] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1601602), _1601604)), 42397 ^ _777864 : [(42400 ^ _777864) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42398 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601602), 42396 ^ [_1601602, _1601604]), _1601604)))]], -(hAPP(c_Finite__Set_Ocard(_1601602), _1601604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47456 ^ _777864) ^ [_1726603, _1726605, _1726607, _1726609, _1726611, _1726613] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1726603, _1726605), hAPP(hAPP(c_List_Ozip(_1726603, _1726605), _1726607), _1726609)), _1726611), _1726613) = hAPP(hAPP(c_List_Ozip(_1726603, _1726605), hAPP(hAPP(c_List_Olist__update(_1726603, _1726607), _1726611), hAPP(c_Product__Type_Ofst(_1726603, _1726605), _1726613))), hAPP(hAPP(c_List_Olist__update(_1726605, _1726609), _1726611), hAPP(c_Product__Type_Osnd(_1726603, _1726605), _1726613))))], (44800 ^ _777864) ^ [_1659964, _1659966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1659964), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659964, tc_HOL_Obool), _1659966))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1659964, tc_HOL_Obool)), _1659966)))], (40622 ^ _777864) ^ [_1556681] : [-(c_Int_Oint__ge__less__than(_1556681) = 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), _1556681)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (51493 ^ _777864) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (21832 ^ _777864) ^ [_1155695, _1155697] : [_1155695 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1155695, _1155697) = _1155697)], (4690 ^ _777864) ^ [_849561, _849563, _849565, _849567, _849569, _849571] : [-(c_List_Osublist(_849571, _849567, _849563) = c_List_Osublist(_849569, _849565, _849561)), _849571 = _849569, _849567 = _849565, _849563 = _849561], (18842 ^ _777864) ^ [_1101718, _1101720] : [class_Rings_Osemiring__1(_1101718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101720)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1101718), 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)))), _1101720))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101718), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1101718), hAPP(c_Int_Onat, _1101720))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1101718), hAPP(c_Int_Onat, _1101720))))], (5525 ^ _777864) ^ [_865110, _865112, _865114, _865116] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _865110), _865112, hAPP(c_Nat_OSuc, _865114), _865116), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _865110)), _865112, _865114, _865116))], (44103 ^ _777864) ^ [_1642332, _1642334, _1642336, _1642338, _1642340] : [-(_1642332 = c_Orderings_Obot__class_Obot(tc_fun(_1642334, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642334, tc_fun(_1642336, tc_HOL_Obool)), _1642332), hAPP(hAPP(c_COMBB(tc_fun(_1642336, tc_HOL_Obool), tc_fun(_1642336, tc_HOL_Obool), _1642334), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1642336, tc_HOL_Obool)), _1642338)), _1642340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1642336, tc_HOL_Obool)), _1642338), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1642334, tc_fun(_1642336, tc_HOL_Obool)), _1642332), _1642340)))], (49146 ^ _777864) ^ [_1766638] : [-(c_List_Olists(_1766638, c_Orderings_Obot__class_Obot(tc_fun(_1766638, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1766638)), c_List_Olist_ONil(_1766638)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1766638), tc_HOL_Obool))))], (5114 ^ _777864) ^ [_856161, _856163, _856165, _856167] : [-(c_List_Olast(_856167, _856163) = c_List_Olast(_856165, _856161)), _856167 = _856165, _856163 = _856161], (17056 ^ _777864) ^ [_1071903, _1071905] : [-(_1071903 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071905), _1071903) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1071905), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071905), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071903), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (2996 ^ _777864) ^ [_823006, _823008, _823010, _823012, _823014, _823016] : [-(c_Com_Ocom_OLocal(_823016, _823012, _823008) = c_Com_Ocom_OLocal(_823014, _823010, _823006)), _823016 = _823014, _823012 = _823010, _823008 = _823006], (11170 ^ _777864) ^ [_963777, _963779] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963777), _963779))))], (46332 ^ _777864) ^ [_1696168, _1696170, _1696172, _1696174, _1696176] : [class_Orderings_Olinorder(_1696168), 46335 ^ _777864 : [(46344 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696170), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696170, _1696168, _1696172), _1696174), _1696176)))), -(hBOOL(hAPP(hAPP(c_member(_1696170), _1696174), hAPP(c_List_Oset(_1696170), _1696176)))), hBOOL(hAPP(c_List_Odistinct(_1696170), _1696176))], (46336 ^ _777864) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1696170), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696170, _1696168, _1696172), _1696174), _1696176))), 46339 ^ _777864 : [(46342 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696170), _1696176)))], (46340 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1696170), _1696174), hAPP(c_List_Oset(_1696170), _1696176)))]]]]], (29874 ^ _777864) ^ [_1320283, _1320285, _1320287, _1320289] : [hBOOL(hAPP(hAPP(c_member(_1320283), _1320285), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320283, tc_HOL_Obool)), _1320287), _1320289))), -(hBOOL(hAPP(hAPP(c_member(_1320283), _1320285), _1320287)))], (44584 ^ _777864) ^ [_1654899, _1654901, _1654903, _1654905] : [hBOOL(hAPP(hAPP(c_member(_1654899), _1654901), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1654899, tc_HOL_Obool), _1654903))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1654899, tc_HOL_Obool)), _1654905), _1654903)), -(hBOOL(hAPP(hAPP(c_member(_1654899), _1654901), _1654905)))], (48832 ^ _777864) ^ [_1759375, _1759377, _1759379] : [-(hAPP(c_List_Orotate1(_1759375), hAPP(c_List_Orotate(_1759375, _1759377), _1759379)) = hAPP(c_List_Orotate(_1759375, _1759377), hAPP(c_List_Orotate1(_1759375), _1759379)))], (22530 ^ _777864) ^ [_1167305, _1167307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1167305), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1167307), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1167305), _1167307) = 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), _1167305), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1167307)))))], (40044 ^ _777864) ^ [_1537737] : [class_Lattices_Osemilattice__sup(_1537737), -(c_Finite__Set_Ofun__left__comm__idem(_1537737, _1537737, c_Lattices_Osemilattice__sup__class_Osup(_1537737)))], (8866 ^ _777864) ^ [_925261, _925263] : [class_Groups_Ogroup__add(_925261), 8869 ^ _777864 : [(8876 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(_925261) = _925263, -(c_Groups_Ozero__class_Ozero(_925261) = hAPP(c_Groups_Ouminus__class_Ouminus(_925261), _925263))], (8870 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(_925261) = hAPP(c_Groups_Ouminus__class_Ouminus(_925261), _925263), -(c_Groups_Ozero__class_Ozero(_925261) = _925263)]]], (43178 ^ _777864) ^ [_1618010, _1618012, _1618014, _1618016, _1618018, _1618020] : [c_Finite__Set_Ofun__left__comm(_1618010, _1618012, _1618014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618010), _1618016)), -(hBOOL(hAPP(hAPP(c_member(_1618010), _1618018), _1618016))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618010, _1618012, _1618014), _1618020), hAPP(hAPP(c_Set_Oinsert(_1618010), _1618018), _1618016)) = hAPP(hAPP(c_Finite__Set_Ofold(_1618010, _1618012, _1618014), hAPP(hAPP(_1618014, _1618018), _1618020)), _1618016))], (14966 ^ _777864) ^ [_1031615, _1031617, _1031619, _1031621, _1031623] : [class_Groups_Ominus(_1031615), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031617, _1031615)), _1031619), _1031621), _1031623) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031615), hAPP(_1031619, _1031623)), hAPP(_1031621, _1031623)))], (42295 ^ _777864) ^ [_1599435, _1599437] : [-(c_Hilbert__Choice_OEps(_1599435, hAPP(c_fequal, _1599437)) = _1599437)], (50478 ^ _777864) ^ [_1794554, _1794556, _1794558, _1794560] : [-(hAPP(hAPP(c_List_Omap(_1794554, _1794556), _1794558), c_List_Oconcat(_1794554, _1794560)) = c_List_Oconcat(_1794556, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1794554), tc_List_Olist(_1794556)), hAPP(c_List_Omap(_1794554, _1794556), _1794558)), _1794560)))], (45822 ^ _777864) ^ [_1684054, _1684056, _1684058, _1684060, _1684062] : [-(hAPP(hAPP(c_Option_Omap(_1684054, _1684056), _1684058), _1684060) = hAPP(c_Option_Ooption_OSome(_1684056), _1684062)), 45823 ^ _777864 : [(45824 ^ _777864) ^ [_1684122] : [_1684060 = hAPP(c_Option_Ooption_OSome(_1684054), _1684122), hAPP(_1684058, _1684122) = _1684062]]], (51529 ^ _777864) ^ [_1812237, _1812239, _1812241, _1812243, _1812245, _1812247] : [-(hAPP(hAPP(hAPP(c_COMBS(_1812237, _1812239, _1812241), _1812243), _1812245), _1812247) = hAPP(hAPP(_1812243, _1812247), hAPP(_1812245, _1812247)))], (29370 ^ _777864) ^ [_1310278, _1310280, _1310282, _1310284] : [c_Finite__Set_Ofolding__one(_1310278, _1310280, _1310282), -(hAPP(_1310282, hAPP(hAPP(c_Set_Oinsert(_1310278), _1310284), c_Orderings_Obot__class_Obot(tc_fun(_1310278, tc_HOL_Obool)))) = _1310284)], (43694 ^ _777864) ^ [_1629983, _1629985, _1629987, _1629989, _1629991] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629983, tc_fun(_1629985, tc_HOL_Obool)), _1629987), hAPP(hAPP(c_COMBB(tc_fun(_1629985, tc_HOL_Obool), tc_fun(_1629985, tc_HOL_Obool), _1629983), hAPP(c_Set_Oinsert(_1629985), _1629989)), _1629991)) = hAPP(hAPP(c_Set_Oinsert(_1629985), _1629989), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629983, tc_fun(_1629985, tc_HOL_Obool)), _1629987), _1629991)))], (46976 ^ _777864) ^ [_1714434, _1714436, _1714438, _1714440, _1714442] : [class_Orderings_Olinorder(_1714434), hBOOL(hAPP(hAPP(c_member(_1714434), hAPP(_1714436, _1714438)), hAPP(c_Set_Oimage(_1714440, _1714434, _1714436), hAPP(c_List_Oset(_1714440), _1714442)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1714440, _1714434, _1714436, _1714438, _1714442) = _1714442)], (8706 ^ _777864) ^ [_922316, _922318] : [class_Groups_Oone(_922316), 8709 ^ _777864 : [(8716 ^ _777864) ^ [] : [_922318 = c_Groups_Oone__class_Oone(_922316), -(c_Groups_Oone__class_Oone(_922316) = _922318)], (8710 ^ _777864) ^ [] : [c_Groups_Oone__class_Oone(_922316) = _922318, -(_922318 = c_Groups_Oone__class_Oone(_922316))]]], (2700 ^ _777864) ^ [_818026, _818028, _818030, _818032, _818034, _818036, _818038, _818040] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_818040, _818036, _818032, _818028) = c_New__Random__Sequence_Opos__not__random__dseq(_818038, _818034, _818030, _818026)), _818040 = _818038, _818036 = _818034, _818032 = _818030, _818028 = _818026], (24537 ^ _777864) ^ [_1208526] : [-(_1208526 = 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)), _1208526)))], (47956 ^ _777864) ^ [_1737802, _1737804, _1737806, _1737808] : [-(hAPP(hAPP(c_List_Oappend(_1737802), hAPP(hAPP(c_List_Olist_OCons(_1737802), _1737804), _1737806)), _1737808) = hAPP(hAPP(c_List_Olist_OCons(_1737802), _1737804), hAPP(hAPP(c_List_Oappend(_1737802), _1737806), _1737808)))], (25665 ^ _777864) ^ [_1228102, _1228104, _1228106, _1228108] : [class_Divides_Osemiring__div(_1228102), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228102), _1228104), _1228106)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1228102), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1228102), _1228106), _1228104)), _1228108) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1228102), hAPP(hAPP(c_Power_Opower__class_Opower(_1228102), _1228106), _1228108)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228102), _1228104), _1228108)))], (49677 ^ _777864) ^ [_1778542, _1778544, _1778546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778542), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1778544))), c_List_Otranspose(_1778544, _1778546)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1778544)), c_List_Otranspose(_1778544, _1778546)), _1778542) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1778544), _1778544), hAPP(hAPP(c_COMBC(tc_List_Olist(_1778544), tc_Nat_Onat, _1778544), c_List_Onth(_1778544)), _1778542)), hAPP(c_List_Ofilter(tc_List_Olist(_1778544), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1778544)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1778542)), c_Nat_Osize__class_Osize(tc_List_Olist(_1778544)))), _1778546)))], (8794 ^ _777864) ^ [_924125, _924127] : [class_Rings_Ocomm__semiring__1(_924125), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924125), c_Groups_Oone__class_Oone(_924125)), _924127) = _924127)], (48065 ^ _777864) ^ [_1740490, _1740492, _1740494] : [-(hAPP(c_List_Oset(_1740490), hAPP(hAPP(c_List_Oappend(_1740490), _1740492), _1740494)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1740490, tc_HOL_Obool)), hAPP(c_List_Oset(_1740490), _1740492)), hAPP(c_List_Oset(_1740490), _1740494)))], (50574 ^ _777864) ^ [_1796722, _1796724, _1796726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796722), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796724)), _1796726))), -(hAPP(hAPP(c_List_Onth(_1796724), hAPP(c_List_Orev(_1796724), _1796726)), _1796722) = hAPP(hAPP(c_List_Onth(_1796724), _1796726), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796724)), _1796726)), hAPP(c_Nat_OSuc, _1796722))))], (8214 ^ _777864) ^ [_914167, _914169, _914171] : [class_Orderings_Olinorder(_914167), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914167), _914169), _914171))), -(_914169 = _914171), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914167), _914171), _914169)))], (51019 ^ _777864) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (6312 ^ _777864) ^ [_881916, _881918, _881920, _881922] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_881916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881916), _881918), _881920)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881916), _881918), _881922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881916), _881920), _881922)))], (11082 ^ _777864) ^ [_962403, _962405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _962403)), _962405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962403), _962405)))], (33320 ^ _777864) ^ [_1390274, _1390276] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1390274, _1390276))))], (46795 ^ _777864) ^ [_1710121, _1710123, _1710125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1710121), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710123), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1710123)), _1710125)))), -(hBOOL(hAPP(hAPP(c_member(_1710123), hAPP(c_Random_Opick(_1710123, _1710125), _1710121)), hAPP(c_List_Oset(_1710123), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710123), _1710123), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1710123)), _1710125)))))], (28032 ^ _777864) ^ [_1277430] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1277430) = c_Orderings_Oord__class_Omax(_1277430)), class_Lattices_Osemilattice__sup(_1277430), class_Orderings_Olinorder(_1277430)], (22274 ^ _777864) ^ [_1162647, _1162649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1162649)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162647, _1162649), c_Divides_OposDivAlg(_1162647, _1162649))))], (37322 ^ _777864) ^ [_1477292, _1477294, _1477296, _1477298] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477292), _1477294)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477292), _1477296)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477292, tc_Nat_Onat), _1477298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477292, tc_HOL_Obool)), _1477294), _1477296)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477292, tc_Nat_Onat), _1477298), _1477294)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477292, tc_Nat_Onat), _1477298), _1477296))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477292, tc_Nat_Onat), _1477298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477292, tc_HOL_Obool)), _1477294), _1477296))))], (27175 ^ _777864) ^ [_1259288, _1259290, _1259292, _1259294] : [hBOOL(hAPP(hAPP(c_member(_1259288), _1259290), _1259292)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259288, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1259288), _1259290), _1259294)), _1259292) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259288, tc_HOL_Obool)), _1259294), _1259292))], (23293 ^ _777864) ^ [_1183687, _1183689, _1183691, _1183693, _1183695, _1183697] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183687, _1183689, _1183691), _1183693), hAPP(hAPP(c_Product__Type_OPair(_1183687, _1183689), _1183695), _1183697)) = hAPP(hAPP(_1183693, _1183695), _1183697))], (46152 ^ _777864) ^ [_1691563, _1691565, _1691567, _1691569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1691563, _1691563)), hAPP(hAPP(c_Product__Type_OPair(_1691563, _1691563), _1691565), _1691567)), hAPP(c_List_Oset(tc_prod(_1691563, _1691563)), hAPP(hAPP(c_List_Ozip(_1691563, _1691563), _1691569), _1691569)))), 46155 ^ _777864 : [(46158 ^ _777864) ^ [] : [-(_1691565 = _1691567)], (46156 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1691563), _1691565), hAPP(c_List_Oset(_1691563), _1691569))))]]], (41968 ^ _777864) ^ [_1591959, _1591961, _1591963, _1591965, _1591967] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1591959, _1591961, _1591963), _1591965), _1591967))), hBOOL(hAPP(hAPP(_1591961, _1591965), _1591967)), hBOOL(hAPP(_1591963, _1591967))], (49644 ^ _777864) ^ [_1777657, _1777659] : [-(c_List_Otranspose(_1777657, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1777657)), c_List_Olist_ONil(_1777657)), _1777659)) = c_List_Otranspose(_1777657, _1777659))], (21068 ^ _777864) ^ [_1141103, _1141105, _1141107] : [class_Fields_Olinordered__field__inverse__zero(_1141103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141103), c_Groups_Ozero__class_Ozero(_1141103)), _1141105)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141103), hAPP(c_Groups_Oabs__class_Oabs(_1141103), _1141107)), _1141105) = hAPP(c_Groups_Oabs__class_Oabs(_1141103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141103), _1141107), _1141105)))], (22633 ^ _777864) ^ [_1169341, _1169343, _1169345] : [hBOOL(hAPP(_1169341, hAPP(hAPP(c_Product__Type_OPair(_1169343, _1169345), 22634 ^ [_1169341, _1169343, _1169345]), 22635 ^ [_1169341, _1169343, _1169345]))), 22638 ^ _777864 : [(22639 ^ _777864) ^ [_1169488] : [-(hBOOL(hAPP(_1169341, _1169488)))]]], (34107 ^ _777864) ^ [_1409719, _1409721, _1409723, _1409725, _1409727] : [class_Groups_Ocomm__monoid__mult(_1409719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409721), _1409723)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1409719, _1409721, c_Groups_Otimes__class_Otimes(_1409719)), hAPP(hAPP(c_COMBS(_1409721, _1409719, _1409719), hAPP(hAPP(c_COMBB(_1409719, tc_fun(_1409719, _1409719), _1409721), c_Groups_Otimes__class_Otimes(_1409719)), _1409725)), _1409727)), c_Groups_Oone__class_Oone(_1409719)), _1409723) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409719), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1409719, _1409721, c_Groups_Otimes__class_Otimes(_1409719)), _1409725), c_Groups_Oone__class_Oone(_1409719)), _1409723)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1409719, _1409721, c_Groups_Otimes__class_Otimes(_1409719)), _1409727), c_Groups_Oone__class_Oone(_1409719)), _1409723)))], (26137 ^ _777864) ^ [_1237461, _1237463, _1237465, _1237467] : [c_Hoare__Mirabelle_Ohoare__derivs(_1237461, _1237463, _1237465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237461), tc_HOL_Obool)), _1237463), _1237467)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1237461, _1237467, _1237465))], (25021 ^ _777864) ^ [_1217074, _1217076] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217074), _1217076)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217076), _1217074))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217076), _1217074)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217074), _1217076)))], (10800 ^ _777864) ^ [_957557, _957559, _957561, _957563] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_957557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957557), _957559), _957561)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957557), _957563), _957561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957557), _957559), _957563)))], (48506 ^ _777864) ^ [_1752243, _1752245, _1752247, _1752249] : [hBOOL(hAPP(hAPP(c_member(_1752243), _1752245), hAPP(c_List_Oset(_1752243), hAPP(hAPP(c_List_Odrop(_1752243), _1752247), _1752249)))), -(hBOOL(hAPP(hAPP(c_member(_1752243), _1752245), hAPP(c_List_Oset(_1752243), _1752249))))], (38754 ^ _777864) ^ [_1507612, _1507614, _1507616, _1507618, _1507620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507612, tc_HOL_Obool)), _1507614), _1507616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1507618, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1507618, _1507612, _1507620), _1507614)), hAPP(c_Set_Ovimage(_1507618, _1507612, _1507620), _1507616))))], (44786 ^ _777864) ^ [_1659487, _1659489, _1659491, _1659493] : [-(hAPP(c_Set_Oimage(_1659487, _1659489, _1659491), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659487, tc_HOL_Obool), _1659493)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659487, tc_HOL_Obool), tc_fun(_1659489, tc_HOL_Obool)), _1659493), c_Set_Oimage(_1659487, _1659489, _1659491)))], (10958 ^ _777864) ^ [_960296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960296)))], (12976 ^ _777864) ^ [_995638, _995640] : [class_Rings_Oring__1(_995638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995640)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_995638), hAPP(c_Int_Onat, _995640)) = hAPP(c_Int_Oring__1__class_Oof__int(_995638), _995640))], (26147 ^ _777864) ^ [_1237626, _1237628, _1237630, _1237632] : [c_Hoare__Mirabelle_Ohoare__derivs(_1237626, _1237628, _1237630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237626), tc_HOL_Obool)), _1237632), _1237630)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1237626, _1237628, _1237632))], (41171 ^ _777864) ^ [_1572023, _1572025, _1572027, _1572029] : [-(hAPP(c_Relation_ORange(_1572023, _1572025), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572023, _1572025), tc_HOL_Obool)), _1572027), _1572029)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572025, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1572023, _1572025), _1572027)), hAPP(c_Relation_ORange(_1572023, _1572025), _1572029)))], (12776 ^ _777864) ^ [_992277, _992279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992277), _992279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992277), c_Groups_Oone__class_Oone(tc_Int_Oint))), _992279)))], (45646 ^ _777864) ^ [_1679785, _1679787, _1679789, _1679791, _1679793, _1679795] : [hAPP(_1679785, _1679787) = c_Option_Ooption_ONone(_1679789), -(c_Map_Omap__comp(_1679789, _1679791, _1679793, _1679795, _1679785, _1679787) = c_Option_Ooption_ONone(_1679791))], (41317 ^ _777864) ^ [_1575564, _1575566, _1575568, _1575570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575564, _1575566), tc_HOL_Obool)), _1575568), _1575570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575564, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1575564, _1575566), _1575568)), hAPP(c_Relation_ODomain(_1575564, _1575566), _1575570))))], (14155 ^ _777864) ^ [_1017376] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1017376), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1017376)], (24385 ^ _777864) ^ [_1204976, _1204978, _1204980, _1204982, _1204984, _1204986] : [hBOOL(hAPP(hAPP(_1204976, _1204978), _1204980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204982, tc_fun(_1204984, tc_HOL_Obool))), _1204976), _1204986)), -(hBOOL(hAPP(hAPP(_1204986, _1204978), _1204980)))], (44780 ^ _777864) ^ [_1659217, _1659219, _1659221, _1659223] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659217, tc_fun(_1659219, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659217, tc_HOL_Obool), _1659221)), _1659223) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659217, tc_HOL_Obool), tc_fun(_1659219, tc_HOL_Obool)), _1659221), hAPP(hAPP(c_COMBC(tc_fun(_1659217, tc_HOL_Obool), tc_fun(_1659217, tc_fun(_1659219, tc_HOL_Obool)), tc_fun(_1659219, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1659217, tc_fun(_1659219, tc_HOL_Obool))), _1659223)))], (9576 ^ _777864) ^ [_937858, _937860] : [class_Rings_Olinordered__ring(_937858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937858), _937860), _937860)), c_Groups_Ozero__class_Ozero(_937858)))], (9508 ^ _777864) ^ [_936646, _936648, _936650, _936652] : [class_Rings_Olinordered__ring__strict(_936646), 9511 ^ _777864 : [(9526 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936646), _936648), _936650)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936646), _936648), _936652)))), 9527 ^ _777864 : [(9534 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936648), c_Groups_Ozero__class_Ozero(_936646))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936652), _936650))], (9528 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), c_Groups_Ozero__class_Ozero(_936646)), _936648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936650), _936652))]]], (9512 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936646), _936648), _936650)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936646), _936648), _936652))), 9517 ^ _777864 : [(9520 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936650), _936652)))], (9518 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), c_Groups_Ozero__class_Ozero(_936646)), _936648)))]], 9521 ^ _777864 : [(9524 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936652), _936650)))], (9522 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936646), _936648), c_Groups_Ozero__class_Ozero(_936646))))]]]]], (42283 ^ _777864) ^ [_1599194, _1599196, _1599198] : [-(c_Hilbert__Choice_OEps(tc_prod(_1599194, _1599196), hAPP(c_Product__Type_Oprod_Oprod__case(_1599194, _1599196, tc_HOL_Obool), _1599198)) = c_Hilbert__Choice_OEps(tc_prod(_1599194, _1599196), hAPP(hAPP(c_COMBS(tc_prod(_1599194, _1599196), _1599196, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1599194, tc_fun(_1599196, tc_HOL_Obool), tc_prod(_1599194, _1599196)), _1599198), c_Product__Type_Ofst(_1599194, _1599196))), c_Product__Type_Osnd(_1599194, _1599196))))], (43611 ^ _777864) ^ [_1628114, _1628116, _1628118, _1628120] : [-(_1628114 = c_Orderings_Obot__class_Obot(tc_fun(_1628116, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628116, tc_fun(_1628118, tc_HOL_Obool)), _1628114), hAPP(c_COMBK(tc_fun(_1628118, tc_HOL_Obool), _1628116), _1628120)) = _1628120)], (5924 ^ _777864) ^ [_875220, _875222] : [_875220 = _875222, -(hAPP(c_Nat_OSuc, _875220) = hAPP(c_Nat_OSuc, _875222))], (18130 ^ _777864) ^ [_1089852] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1089852) = c_Int_Opred(_1089852))], (24147 ^ _777864) ^ [_1200486, _1200488, _1200490, _1200492, _1200494] : [-(hAPP(c_Product__Type_Osnd(_1200486, _1200488), hAPP(c_Product__Type_Oapfst(_1200490, _1200486, _1200488, _1200492), _1200494)) = hAPP(c_Product__Type_Osnd(_1200490, _1200488), _1200494))], (31743 ^ _777864) ^ [_1357895, _1357897, _1357899] : [class_Orderings_Olinorder(_1357895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357895), _1357897)), -(_1357897 = c_Orderings_Obot__class_Obot(tc_fun(_1357895, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357895), _1357899)), -(_1357899 = c_Orderings_Obot__class_Obot(tc_fun(_1357895, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1357895, tc_HOL_Obool)), _1357897), _1357899) = c_Orderings_Obot__class_Obot(tc_fun(_1357895, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1357895, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357895, tc_HOL_Obool)), _1357897), _1357899)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1357895), c_Big__Operators_Olinorder__class_OMin(_1357895, _1357897)), c_Big__Operators_Olinorder__class_OMin(_1357895, _1357899)))], (38576 ^ _777864) ^ [_1503557, _1503559, _1503561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503557, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503557, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38577 ^ [_1503557, _1503559, _1503561])), _1503559)), _1503561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1503557, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503557, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1503559)), _1503561)))], (18092 ^ _777864) ^ [_1089305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089305), 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), _1089305)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18122 ^ _777864) ^ [_1089718, _1089720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1089718)), _1089720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089718), _1089720)))], (6474 ^ _777864) ^ [_884763, _884765, _884767] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884763), _884765)), _884767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884765), _884767)))], (19184 ^ _777864) ^ [_1107691, _1107693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107691)), c_Int_OBit0(_1107693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107691), _1107693)))], (5008 ^ _777864) ^ [_854484, _854486, _854488, _854490] : [-(c_List_Otranspose(_854490, _854486) = c_List_Otranspose(_854488, _854484)), _854490 = _854488, _854486 = _854484], (51219 ^ _777864) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (18900 ^ _777864) ^ [_1102786, _1102788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102786)), c_Int_OBit0(_1102788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102786), _1102788)))], (6368 ^ _777864) ^ [_882940, _882942, _882944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882940), _882942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882940), _882944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882942), _882944))))], (51581 ^ _777864) ^ [_1812936, _1812938] : [hBOOL(_1812936), -(hBOOL(hAPP(hAPP(c_fdisj, _1812936), _1812938)))], (4504 ^ _777864) ^ [_846730, _846732] : [_846732 = _846730, -(c_Orderings_Otop__class_Otop(_846732) = c_Orderings_Otop__class_Otop(_846730))], (35140 ^ _777864) ^ [_1431032, _1431034, _1431036, _1431038, _1431040] : [c_Fun_Oinj__on(_1431032, _1431034, _1431036, _1431038), c_Fun_Oinj__on(_1431032, _1431034, _1431036, _1431040), -(c_Fun_Oinj__on(_1431032, _1431034, _1431036, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431032, tc_HOL_Obool)), _1431038), _1431040)))], (36274 ^ _777864) ^ [_1453150, _1453152, _1453154, _1453156, _1453158] : [c_Fun_Oinj__on(_1453150, _1453152, _1453154, _1453156), hBOOL(hAPP(hAPP(c_member(_1453152), _1453158), hAPP(c_Set_Oimage(_1453150, _1453152, _1453154), _1453156))), -(hAPP(_1453154, hAPP(c_Fun_Othe__inv__into(_1453150, _1453152, _1453156, _1453154), _1453158)) = _1453158)], (930 ^ _777864) ^ [_792195, _792197] : [-(c_List_Onat__list(_792195)), _792197 = _792195, c_List_Onat__list(_792197)], (15140 ^ _777864) ^ [_1034775, _1034777, _1034779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1034775)), _1034777)), hAPP(c_Nat_OSuc, _1034779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034775), _1034777)), _1034779))], (24901 ^ _777864) ^ [_1215101, _1215103, _1215105, _1215107] : [class_Rings_Ocomm__semiring__1(_1215101), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215101), _1215103), _1215105)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215101), _1215105), _1215107)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215101), _1215103), _1215107)))], (43056 ^ _777864) ^ [_1615376, _1615378, _1615380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615376, _1615376), tc_HOL_Obool)), _1615378), hAPP(hAPP(c_Product__Type_OSigma(_1615376, _1615376), _1615380), hAPP(c_COMBK(tc_fun(_1615376, tc_HOL_Obool), _1615376), _1615380)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1615376, _1615376), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1615376, _1615378)), hAPP(hAPP(c_Product__Type_OSigma(_1615376, _1615376), _1615380), hAPP(c_COMBK(tc_fun(_1615376, tc_HOL_Obool), _1615376), _1615380)))))], (42271 ^ _777864) ^ [_1598898, _1598900, _1598902, _1598904] : [-(c_New__Random__Sequence_Oneg__map(_1598898, _1598900, _1598902, _1598904) = c_New__Random__Sequence_Oneg__bind(_1598898, _1598900, _1598904, hAPP(c_Fun_Ocomp(_1598900, 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(_1598900)))))), _1598898, c_New__Random__Sequence_Oneg__single(_1598900)), _1598902)))], (17650 ^ _777864) ^ [_1082265] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1082265), hAPP(c_Int_Onumber__class_Onumber__of(_1082265), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1082265)), class_Int_Onumber__ring(_1082265), class_Rings_Olinordered__idom(_1082265)], (49525 ^ _777864) ^ [_1774445, _1774447, _1774449] : [49527 ^ _777864 : [(49530 ^ _777864) ^ [] : [hBOOL(hAPP(_1774447, 49526 ^ [_1774445, _1774447, _1774449]))], (49528 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774445), 49526 ^ [_1774445, _1774447, _1774449]), hAPP(c_List_Oset(_1774445), _1774449))))]], -(hAPP(c_List_Ofilter(_1774445, _1774447), _1774449) = _1774449)], (7148 ^ _777864) ^ [_895341, _895343, _895345, _895347, _895349] : [hBOOL(hAPP(_895341, _895343)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895345), _895343), _895347)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_895341, _895345, _895349)), _895343), _895347)))], (2082 ^ _777864) ^ [_808281, _808283, _808285, _808287, _808289, _808291] : [-(c_Random_Ominus__shift(_808291, _808287, _808283) = c_Random_Ominus__shift(_808289, _808285, _808281)), _808291 = _808289, _808287 = _808285, _808283 = _808281], (36376 ^ _777864) ^ [_1454982, _1454984, _1454986, _1454988, _1454990, _1454992, _1454994] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1454982, tc_Option_Ooption(_1454984)), _1454986), _1454988), hAPP(c_Option_Ooption_OSome(_1454984), _1454990)), _1454992) = hAPP(c_Option_Ooption_OSome(_1454984), _1454994), 36381 ^ _777864 : [(36384 ^ _777864) ^ [] : [-(_1454990 = _1454994)], (36382 ^ _777864) ^ [] : [-(_1454992 = _1454988)]], 36385 ^ _777864 : [(36388 ^ _777864) ^ [] : [-(hAPP(_1454986, _1454992) = hAPP(c_Option_Ooption_OSome(_1454984), _1454994))], (36386 ^ _777864) ^ [] : [_1454992 = _1454988]]], (30174 ^ _777864) ^ [_1327058, _1327060, _1327062, _1327064] : [hBOOL(hAPP(hAPP(c_member(_1327058), _1327060), _1327062)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327058, tc_HOL_Obool)), _1327062), hAPP(hAPP(c_Set_Oinsert(_1327058), _1327060), _1327064)) = hAPP(hAPP(c_Set_Oinsert(_1327058), _1327060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327058, tc_HOL_Obool)), _1327062), _1327064)))], (29986 ^ _777864) ^ [_1323153, _1323155, _1323157] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323153, tc_HOL_Obool)), _1323155), _1323157) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323153, tc_HOL_Obool)), _1323157), _1323155))], (15040 ^ _777864) ^ [_1032917, _1032919] : [class_Groups_Ogroup__add(_1032917), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032917), _1032919), _1032919) = c_Groups_Ozero__class_Ozero(_1032917))], (26765 ^ _777864) ^ [_1250414, _1250416, _1250418, _1250420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1250414, tc_HOL_Obool)), _1250416), _1250418)), hBOOL(hAPP(hAPP(c_member(_1250414), _1250420), _1250416)), -(hBOOL(hAPP(hAPP(c_member(_1250414), _1250420), _1250418)))], (45949 ^ _777864) ^ [_1686854, _1686856, _1686858] : [hBOOL(hAPP(c_List_Odistinct(_1686854), hAPP(hAPP(c_List_Omap(tc_prod(_1686854, _1686856), _1686854), c_Product__Type_Ofst(_1686854, _1686856)), _1686858))), -(hAPP(c_List_Oset(tc_prod(_1686854, _1686856)), _1686858) = hAPP(c_Set_OCollect(tc_prod(_1686854, _1686856)), hAPP(c_Product__Type_Oprod_Oprod__case(_1686854, _1686856, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1686854, tc_fun(_1686856, tc_Option_Ooption(_1686856)), tc_fun(_1686856, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1686856), tc_HOL_Obool), tc_fun(tc_fun(_1686856, tc_Option_Ooption(_1686856)), tc_fun(_1686856, tc_HOL_Obool)), _1686854), c_COMBB(tc_Option_Ooption(_1686856), tc_HOL_Obool, _1686856)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1686856), tc_fun(tc_Option_Ooption(_1686856), tc_HOL_Obool), _1686854), c_fequal), c_Map_Omap__of(_1686854, _1686856, _1686858)))), c_Option_Ooption_OSome(_1686856)))))], (51259 ^ _777864) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (50460 ^ _777864) ^ [_1794132, _1794134, _1794136] : [hAPP(hAPP(c_List_Olist_OCons(_1794132), _1794134), c_List_Olist_ONil(_1794132)) = hAPP(c_List_Orev(_1794132), _1794136), -(_1794136 = hAPP(hAPP(c_List_Olist_OCons(_1794132), _1794134), c_List_Olist_ONil(_1794132)))], (45225 ^ _777864) ^ [_1670054, _1670056, _1670058] : [45227 ^ _777864 : [(45230 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1670054), _1670058), 45226 ^ [_1670054, _1670056, _1670058]))], (45228 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1670054, tc_HOL_Obool)), 45226 ^ [_1670054, _1670056, _1670058]), _1670056)))]], -(hBOOL(hAPP(hAPP(c_member(_1670054), _1670058), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1670054, tc_HOL_Obool), _1670056))))], (29185 ^ _777864) ^ [_1305973, _1305975] : [class_Finite__Set_Ofinite(_1305973), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305973), _1305975)))], (18948 ^ _777864) ^ [_1103545, _1103547] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1103545)), c_Int_OBit0(_1103547)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1103545), _1103547)))], (30126 ^ _777864) ^ [_1326018, _1326020, _1326022] : [class_Lattices_Oboolean__algebra(_1326018), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1326018), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1326018), _1326020), _1326022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1326018), hAPP(c_Groups_Ouminus__class_Ouminus(_1326018), _1326020)), hAPP(c_Groups_Ouminus__class_Ouminus(_1326018), _1326022)))], (48450 ^ _777864) ^ [_1750662, _1750664, _1750666, _1750668] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1750662), tc_List_Olist(_1750662))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1750662), tc_List_Olist(_1750662)), _1750664), _1750666)), c_List_Olistrel1(_1750662, _1750668)))), 48451 ^ _777864 : [(48452 ^ _777864) ^ [_1750795, _1750797] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1750662, _1750662)), hAPP(hAPP(c_Product__Type_OPair(_1750662, _1750662), hAPP(hAPP(c_List_Onth(_1750662), _1750664), _1750795)), _1750797)), _1750668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750795), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750662)), _1750664))), _1750666 = hAPP(hAPP(c_List_Olist__update(_1750662, _1750664), _1750795), _1750797)]]], (30959 ^ _777864) ^ [_1343729] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343729, _1343729) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1343729), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (6190 ^ _777864) ^ [_879680, _879682, _879684, _879686] : [class_Groups_Ocancel__semigroup__add(_879680), 6193 ^ _777864 : [(6200 ^ _777864) ^ [] : [_879682 = _879686, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879680), _879682), _879684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879680), _879686), _879684))], (6194 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879680), _879682), _879684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879680), _879686), _879684), -(_879682 = _879686)]]], (2056 ^ _777864) ^ [_807898, _807900] : [_807900 = _807898, -(c_Int_Osucc(_807900) = c_Int_Osucc(_807898))], (24569 ^ _777864) ^ [_1208900, _1208902] : [_1208900 = _1208902, -(hAPP(c_Code__Numeral_Oof__nat, _1208900) = hAPP(c_Code__Numeral_Oof__nat, _1208902))], (49484 ^ _777864) ^ [_1773578, _1773580, _1773582, _1773584, _1773586] : [c_List_Opartition(_1773578, _1773580, _1773582) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773578), tc_List_Olist(_1773578)), _1773584), _1773586), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1773578, tc_HOL_Obool)), hAPP(c_List_Oset(_1773578), _1773584)), hAPP(c_List_Oset(_1773578), _1773586)) = hAPP(c_List_Oset(_1773578), _1773582))], (16596 ^ _777864) ^ [_1063111, _1063113, _1063115, _1063117] : [class_Rings_Ocomm__semiring__1(_1063111), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063111), hAPP(hAPP(c_Power_Opower__class_Opower(_1063111), _1063113), _1063115)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063111), _1063113), _1063117)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1063111), _1063113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063115), _1063117)))], (37991 ^ _777864) ^ [_1490831, _1490833, _1490835, _1490837, _1490839] : [hAPP(_1490831, _1490833) = c_Option_Ooption_ONone(_1490835), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490837, tc_HOL_Obool)), c_Map_Odom(_1490837, _1490835, _1490831)), hAPP(hAPP(c_Set_Oinsert(_1490837), _1490833), _1490839)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1490837, tc_HOL_Obool)), c_Map_Odom(_1490837, _1490835, _1490831)), _1490839))], (36638 ^ _777864) ^ [_1461369, _1461371, _1461373, _1461375, _1461377] : [class_Groups_Ocomm__monoid__add(_1461369), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461369), _1461371), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1461373), _1461375)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1461377), _1461375))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461369), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1461369, tc_Nat_Onat), _1461371), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1461375))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1461373), _1461377)))], (46104 ^ _777864) ^ [_1690268, _1690270, _1690272] : [hBOOL(hAPP(c_List_Odistinct(_1690268), _1690270)), -(hBOOL(hAPP(c_List_Odistinct(_1690268), c_List_Oremove1(_1690268, _1690272, _1690270))))], (23035 ^ _777864) ^ [_1177351, _1177353, _1177355] : [-(hAPP(c_Divides_Oadjust(_1177351), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177353), _1177355)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177355), _1177351)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1177353)), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1177353)), _1177355))))], (24131 ^ _777864) ^ [_1200039, _1200041, _1200043, _1200045, _1200047, _1200049] : [-(hAPP(c_Product__Type_Oapfst(_1200039, _1200041, _1200043, _1200045), hAPP(hAPP(c_Product__Type_OPair(_1200039, _1200043), _1200047), _1200049)) = hAPP(hAPP(c_Product__Type_OPair(_1200041, _1200043), hAPP(_1200045, _1200047)), _1200049))], (16628 ^ _777864) ^ [_1063732, _1063734, _1063736] : [class_Int_Onumber__ring(_1063732), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063732), hAPP(c_Int_Onumber__class_Onumber__of(_1063732), _1063734)), hAPP(c_Int_Onumber__class_Onumber__of(_1063732), _1063736)) = hAPP(c_Int_Onumber__class_Onumber__of(_1063732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1063734), _1063736)))], (32491 ^ _777864) ^ [_1372320, _1372322, _1372324] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372320), _1372322)), -(hAPP(c_Finite__Set_Ocard(_1372320), hAPP(hAPP(c_Set_Oinsert(_1372320), _1372324), _1372322)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1372320), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372320, tc_HOL_Obool)), _1372322), hAPP(hAPP(c_Set_Oinsert(_1372320), _1372324), c_Orderings_Obot__class_Obot(tc_fun(_1372320, tc_HOL_Obool)))))))], (51277 ^ _777864) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (46573 ^ _777864) ^ [_1704179, _1704181, _1704183] : [-(hAPP(c_List_Oset(_1704179), hAPP(hAPP(c_List_Olist_OCons(_1704179), _1704181), _1704183)) = hAPP(hAPP(c_Set_Oinsert(_1704179), _1704181), hAPP(c_List_Oset(_1704179), _1704183)))], (45384 ^ _777864) ^ [_1673646, _1673648, _1673650, _1673652, _1673654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673646, tc_HOL_Obool)), _1673648), _1673650)), 45390 ^ _777864 : [(45395 ^ _777864) ^ [] : [hBOOL(hAPP(_1673654, 45389 ^ [_1673646, _1673648, _1673650, _1673652, _1673654]))], (45393 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1673652, 45389 ^ [_1673646, _1673648, _1673650, _1673652, _1673654])))], (45391 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673646), 45389 ^ [_1673646, _1673648, _1673650, _1673652, _1673654]), _1673648)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673646, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1673646, tc_HOL_Obool)), _1673648), hAPP(c_Set_OCollect(_1673646), _1673652))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1673646, tc_HOL_Obool)), _1673650), hAPP(c_Set_OCollect(_1673646), _1673654)))))], (45164 ^ _777864) ^ [_1668498, _1668500, _1668502, _1668504, _1668506] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1668498, _1668498)), hAPP(hAPP(c_Product__Type_OPair(_1668498, _1668498), _1668500), _1668502)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1668498, _1668498), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1668504)), _1668506))), 45168 ^ _777864 : [(45171 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668498, _1668498)), hAPP(hAPP(c_Product__Type_OPair(_1668498, _1668498), 45167 ^ [_1668498, _1668500, _1668502, _1668504, _1668506]), _1668502)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1668498, _1668498), tc_HOL_Obool), _1668504), _1668506))))], (45169 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668498, _1668498)), hAPP(hAPP(c_Product__Type_OPair(_1668498, _1668498), _1668500), 45167 ^ [_1668498, _1668500, _1668502, _1668504, _1668506])), _1668506)))]]], (30953 ^ _777864) ^ [_1343630, _1343632] : [_1343630 = _1343632, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343630, _1343632) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1343630), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (17496 ^ _777864) ^ [_1080010] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080010)))), -(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), _1080010)) = 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), _1080010))))], (46025 ^ _777864) ^ [_1688705, _1688707, _1688709, _1688711, _1688713] : [hBOOL(hAPP(c_List_Odistinct(_1688705), hAPP(hAPP(c_List_Omap(tc_prod(_1688705, _1688707), _1688705), c_Product__Type_Ofst(_1688705, _1688707)), _1688709))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1688705, _1688707)), hAPP(hAPP(c_Product__Type_OPair(_1688705, _1688707), _1688711), _1688713)), hAPP(c_List_Oset(tc_prod(_1688705, _1688707)), _1688709))), -(hAPP(c_Map_Omap__of(_1688705, _1688707, _1688709), _1688711) = hAPP(c_Option_Ooption_OSome(_1688707), _1688713))], (25163 ^ _777864) ^ [_1219350, _1219352] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219350), _1219352)), 25168 ^ _777864 : [(25171 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219352), _1219350))], (25169 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219350), _1219352)))]], -(_1219350 = _1219352)], (36032 ^ _777864) ^ [_1448538] : [-(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)), _1448538))))], (38194 ^ _777864) ^ [_1494624, _1494626] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494624, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1494624, tc_HOL_Obool))), _1494626) = _1494626)], (19160 ^ _777864) ^ [_1107245, _1107247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1107245)), c_Int_OBit1(_1107247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107245), _1107247)))], (12231 ^ _777864) ^ [_982553, _982555, _982557, _982559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982553), _982555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _982557), _982559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _982553), _982557)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _982555), _982559))))], (20314 ^ _777864) ^ [_1127859, _1127861] : [class_Rings_Odivision__ring__inverse__zero(_1127859), 20317 ^ _777864 : [(20324 ^ _777864) ^ [] : [-(_1127861 = c_Groups_Ozero__class_Ozero(_1127859)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127859), _1127861), _1127861) = c_Groups_Oone__class_Oone(_1127859))], (20318 ^ _777864) ^ [] : [_1127861 = c_Groups_Ozero__class_Ozero(_1127859), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1127859), _1127861), _1127861) = c_Groups_Ozero__class_Ozero(_1127859))]]], (40326 ^ _777864) ^ [_1544754, _1544756, _1544758, _1544760, _1544762, _1544764] : [class_Groups_Ocomm__monoid__add(_1544754), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544756), _1544758)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544756, _1544754), _1544760), _1544758) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544762, _1544754), hAPP(hAPP(c_COMBB(tc_fun(_1544756, tc_HOL_Obool), _1544754, _1544762), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544756, _1544754), _1544760)), hAPP(hAPP(c_COMBB(tc_fun(_1544756, tc_HOL_Obool), tc_fun(_1544756, tc_HOL_Obool), _1544762), c_Set_OCollect(_1544756)), hAPP(hAPP(c_COMBB(tc_fun(_1544756, tc_HOL_Obool), tc_fun(_1544756, tc_HOL_Obool), _1544762), hAPP(c_COMBS(_1544756, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544756), c_fconj), hAPP(hAPP(c_COMBC(_1544756, tc_fun(_1544756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544756)), _1544758)))), hAPP(c_COMBC(_1544756, _1544762, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1544762, tc_fun(_1544762, tc_HOL_Obool), _1544756), c_fequal), _1544764)))))), hAPP(c_Set_Oimage(_1544756, _1544762, _1544764), _1544758)))], (40172 ^ _777864) ^ [_1540407, _1540409, _1540411] : [-(hAPP(hAPP(c_Set_Oinsert(_1540407), _1540409), hAPP(c_Set_OCollect(_1540407), _1540411)) = hAPP(c_Set_OCollect(_1540407), hAPP(hAPP(c_COMBS(_1540407, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540407), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540407), c_fNot), hAPP(hAPP(c_COMBC(_1540407, _1540407, tc_HOL_Obool), c_fequal), _1540409)))), _1540411)))], (24653 ^ _777864) ^ [_1210317, _1210319] : [_1210317 = _1210319, -(hAPP(c_Code__Numeral_Onat__of, _1210317) = hAPP(c_Code__Numeral_Onat__of, _1210319))], (19166 ^ _777864) ^ [_1107346, _1107348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107346), _1107348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1107346)), c_Int_OBit1(_1107348))))], (31953 ^ _777864) ^ [_1361888, _1361890, _1361892] : [class_Orderings_Olinorder(_1361888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361888), _1361890)), -(_1361890 = c_Orderings_Obot__class_Obot(tc_fun(_1361888, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1361888, c_Orderings_Oord__class_Omax(_1361888), hAPP(hAPP(c_Set_Oinsert(_1361888), _1361892), _1361890)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1361888), _1361892), c_Big__Operators_Olattice_OSup__fin(_1361888, c_Orderings_Oord__class_Omax(_1361888), _1361890)))], (49207 ^ _777864) ^ [_1768137, _1768139, _1768141] : [_1768137 = c_List_Olist_ONil(_1768139), -(c_List_Olast(_1768139, hAPP(hAPP(c_List_Olist_OCons(_1768139), _1768141), _1768137)) = _1768141)], (50410 ^ _777864) ^ [_1793031, _1793033] : [c_List_Olist_ONil(_1793031) = c_List_Oconcat(_1793031, _1793033), 50413 ^ _777864 : [(50414 ^ _777864) ^ [_1793122] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1793031)), _1793122), hAPP(c_List_Oset(tc_List_Olist(_1793031)), _1793033))), -(_1793122 = c_List_Olist_ONil(_1793031))]]], (8788 ^ _777864) ^ [_924030, _924032] : [class_Rings_Ocomm__semiring__1(_924030), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924030), _924032), c_Groups_Oone__class_Oone(_924030)) = _924032)], (41576 ^ _777864) ^ [_1582664] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 41572 ^ [_1582664]), c_Int_OInteg)))], (704 ^ _777864) ^ [_788770, _788772, _788774, _788776] : [-(c_Relation_Oirrefl(_788774, _788770)), c_Relation_Oirrefl(_788776, _788772), _788776 = _788774, _788772 = _788770], (10834 ^ _777864) ^ [_958218, _958220, _958222, _958224] : [class_Groups_Oordered__ab__semigroup__add(_958218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), _958220), _958222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958218), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958218), _958220), _958224)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958218), _958222), _958224))))], (1952 ^ _777864) ^ [_806280, _806282] : [_806282 = _806280, -(c_Com_Ovname_OGlb(_806282) = c_Com_Ovname_OGlb(_806280))], (32315 ^ _777864) ^ [_1368835, _1368837] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1368835), _1368837))), -(hAPP(c_Finite__Set_Ocard(_1368835), _1368837) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17836 ^ _777864) ^ [_1085226, _1085228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1085226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085226), _1085228)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085226), _1085228) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (19140 ^ _777864) ^ [_1106833] : [-(c_Int_Osucc(c_Int_OBit0(_1106833)) = c_Int_OBit1(_1106833))], (49972 ^ _777864) ^ [_1784211] : [class_Orderings_Olinorder(_1784211), -(c_List_Olinorder__class_Osorted(_1784211, c_List_Olist_ONil(_1784211)))], (17956 ^ _777864) ^ [_1087383] : [class_Int_Onumber__ring(_1087383), -(c_Int_Oiszero(_1087383, hAPP(c_Int_Onumber__class_Onumber__of(_1087383), c_Int_OPls)))], (3382 ^ _777864) ^ [_829147, _829149, _829151, _829153, _829155, _829157] : [-(c_FunDef_Oin__rel(_829157, _829153, _829149) = c_FunDef_Oin__rel(_829155, _829151, _829147)), _829157 = _829155, _829153 = _829151, _829149 = _829147], (40068 ^ _777864) ^ [_1538129] : [class_Lattices_Oab__semigroup__idem__mult(_1538129), -(c_Finite__Set_Ofun__left__comm__idem(_1538129, _1538129, c_Groups_Otimes__class_Otimes(_1538129)))], (26873 ^ _777864) ^ [_1252277, _1252279, _1252281] : [_1252277 = c_Orderings_Obot__class_Obot(tc_fun(_1252279, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1252279), _1252281), _1252277))], (43307 ^ _777864) ^ [_1621281, _1621283] : [-(c_Transitive__Closure_Otrancl(_1621281, c_Transitive__Closure_Ortrancl(_1621281, _1621283)) = c_Transitive__Closure_Ortrancl(_1621281, _1621283))], (30216 ^ _777864) ^ [_1328244, _1328246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328244, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328244, tc_HOL_Obool)), _1328246)), _1328246) = c_Orderings_Obot__class_Obot(tc_fun(_1328244, tc_HOL_Obool)))], (26489 ^ _777864) ^ [_1244528, _1244530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244528, tc_HOL_Obool)), _1244530), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244528, tc_HOL_Obool)), _1244530))), -(_1244530 = c_Orderings_Obot__class_Obot(tc_fun(_1244528, tc_HOL_Obool)))], (21606 ^ _777864) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (16077 ^ _777864) ^ [_1053532] : [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), _1053532))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1053532) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1053532)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (17020 ^ _777864) ^ [_1071262, _1071264, _1071266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1071262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071262), _1071264)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071262), _1071266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1071264), _1071266)))], (17576 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (39836 ^ _777864) ^ [_1532801, _1532803, _1532805, _1532807, _1532809, _1532811, _1532813, _1532815, _1532817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532801, _1532803)), hAPP(hAPP(c_Product__Type_OPair(_1532801, _1532803), _1532805), _1532807)), _1532809)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532811, _1532813)), hAPP(hAPP(c_Product__Type_OPair(_1532811, _1532813), hAPP(_1532815, _1532805)), hAPP(_1532817, _1532807))), hAPP(c_Set_Oimage(tc_prod(_1532801, _1532803), tc_prod(_1532811, _1532813), c_Product__Type_Omap__pair(_1532801, _1532811, _1532803, _1532813, _1532815, _1532817)), _1532809))))], (51615 ^ _777864) ^ [_1813331, _1813333] : [hBOOL(hAPP(hAPP(c_fimplies, _1813331), _1813333)), hBOOL(_1813331), -(hBOOL(_1813333))], (43217 ^ _777864) ^ [_1619018, _1619020, _1619022] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619018, _1619018)), hAPP(hAPP(c_Product__Type_OPair(_1619018, _1619018), _1619020), _1619020)), c_Transitive__Closure_Ortrancl(_1619018, _1619022))))], (50773 ^ _777864) ^ [_1802234, _1802236, _1802238, _1802240] : [hBOOL(hAPP(_1802234, _1802236)), -(c_List_OtakeWhile(_1802238, _1802234, hAPP(hAPP(c_List_Olist_OCons(_1802238), _1802236), _1802240)) = hAPP(hAPP(c_List_Olist_OCons(_1802238), _1802236), c_List_OtakeWhile(_1802238, _1802234, _1802240)))], (234 ^ _777864) ^ [_781345, _781347] : [-(class_Fields_Olinordered__field(_781345)), _781347 = _781345, class_Fields_Olinordered__field(_781347)], (37032 ^ _777864) ^ [_1470463, _1470465, _1470467, _1470469, _1470471] : [class_Groups_Oab__group__add(_1470463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470465), 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470465, _1470463), _1470471), _1470467)), hAPP(_1470471, _1470469)))]]], (44228 ^ _777864) ^ [_1646126, _1646128, _1646130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1646126, _1646126), tc_HOL_Obool)), c_Relation_OId(_1646126)), _1646128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1646126, _1646126), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1646126, _1646126, _1646126), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1646126, _1646126), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1646126, _1646130)), _1646128)), _1646130)), _1646128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1646126, _1646126), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1646126, _1646130)), _1646128)))], (30789 ^ _777864) ^ [_1341081, _1341083] : [class_Lattices_Olattice(_1341081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341081), _1341083)), -(_1341083 = c_Orderings_Obot__class_Obot(tc_fun(_1341081, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341081), c_Big__Operators_Olattice__class_OInf__fin(_1341081, _1341083)), c_Big__Operators_Olattice__class_OSup__fin(_1341081, _1341083))))], (37695 ^ _777864) ^ [_1484948, _1484950, _1484952] : [class_Orderings_Olinorder(_1484948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484948), _1484950), _1484952)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484948, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1484948, _1484950), _1484952)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484948), _1484952)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1484948), _1484950))], (22036 ^ _777864) ^ [_1158817] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1158817) = 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)))], (33440 ^ _777864) ^ [_1392528, _1392530, _1392532, _1392534] : [-(hAPP(c_Relation_OImage(_1392528, _1392530, _1392532), _1392534) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1392528, tc_fun(_1392530, tc_HOL_Obool)), _1392534), hAPP(hAPP(c_COMBB(tc_fun(_1392528, tc_HOL_Obool), tc_fun(_1392530, tc_HOL_Obool), _1392528), c_Relation_OImage(_1392528, _1392530, _1392532)), hAPP(hAPP(c_COMBC(_1392528, tc_fun(_1392528, tc_HOL_Obool), tc_fun(_1392528, tc_HOL_Obool)), c_Set_Oinsert(_1392528)), c_Orderings_Obot__class_Obot(tc_fun(_1392528, tc_HOL_Obool))))))], (40851 ^ _777864) ^ [_1565310, _1565312, _1565314, _1565316] : [c_Wellfounded_Owf(_1565310, _1565312), c_Wellfounded_Owf(_1565314, _1565316), -(c_Wellfounded_Owf(tc_prod(_1565310, _1565314), c_Wellfounded_Olex__prod(_1565310, _1565314, _1565312, _1565316)))], (32345 ^ _777864) ^ [_1369293, _1369295, _1369297] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369293), _1369295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369293), _1369295)), hAPP(c_Finite__Set_Ocard(_1369293), hAPP(hAPP(c_Set_Oinsert(_1369293), _1369297), _1369295)))))], (36116 ^ _777864) ^ [_1450109, _1450111, _1450113, _1450115, _1450117, _1450119] : [-(_1450109 = _1450111), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450113, _1450115), _1450117), _1450111), _1450119), _1450109) = hAPP(_1450117, _1450109))], (19064 ^ _777864) ^ [_1105573, _1105575] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1105573)), c_Int_OBit1(_1105575)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105573), _1105575)))], (29574 ^ _777864) ^ [_1314411, _1314413] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314411), c_Orderings_Obot__class_Obot(tc_fun(_1314411, tc_HOL_Obool))), _1314413) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314411, tc_HOL_Obool), tc_HOL_Obool)))], (37923 ^ _777864) ^ [_1489512, _1489514, _1489516, _1489518, _1489520] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489512, _1489514, _1489516, _1489518, c_Orderings_Obot__class_Obot(tc_fun(_1489512, tc_HOL_Obool))), _1489520)), -(_1489520 = _1489518)], (49560 ^ _777864) ^ [_1775060, _1775062, _1775064] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1775060), tc_List_Olist(_1775060)), c_List_Opartition(_1775060, _1775062, _1775064)) = hAPP(c_List_Ofilter(_1775060, _1775062), _1775064))], (24501 ^ _777864) ^ [_1207371, _1207373, _1207375, _1207377] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1207371, _1207373, _1207375, c_Code__Numeral_OSuc__code__numeral(_1207377)) = hAPP(hAPP(_1207375, _1207377), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1207371, _1207373, _1207375, _1207377)))], (35336 ^ _777864) ^ [_1434989, _1434991, _1434993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434989)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1434991), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1434993)), 35346 ^ _777864 : [(35352 ^ _777864) ^ [] : [-(_1434991 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35348 ^ [_1434989, _1434991, _1434993]), 35345 ^ [_1434989, _1434991, _1434993]))], (35350 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35348 ^ [_1434989, _1434991, _1434993]), _1434993)))], (35347 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35345 ^ [_1434989, _1434991, _1434993]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1434989))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1434991), _1434989) = _1434991)], (49324 ^ _777864) ^ [_1770145, _1770147, _1770149] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770145)), _1770147), c_List_Olists(_1770145, _1770149)))), 49325 ^ _777864 : [(49328 ^ _777864) ^ [_1770273, _1770275] : [_1770147 = hAPP(hAPP(c_List_Olist_OCons(_1770145), _1770275), _1770273), hBOOL(hAPP(hAPP(c_member(_1770145), _1770275), _1770149)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770145)), _1770273), c_List_Olists(_1770145, _1770149)))], (49326 ^ _777864) ^ [] : [_1770147 = c_List_Olist_ONil(_1770145)]]], (8118 ^ _777864) ^ [_912839, _912841, _912843] : [class_Orderings_Olinorder(_912839), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912839), _912841), _912843))), 8125 ^ _777864 : [(8132 ^ _777864) ^ [] : [_912843 = _912841, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912839), _912843), _912841))], (8126 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912839), _912843), _912841))), -(_912843 = _912841)]]], (42992 ^ _777864) ^ [_1613818, _1613820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1613818, _1613818)), c_Transitive__Closure_Otrancl(_1613818, _1613820))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1613818, _1613818)), _1613820)))], (34913 ^ _777864) ^ [_1426068, _1426070, _1426072, _1426074, _1426076] : [c_Fun_Oinj__on(_1426068, _1426070, _1426072, _1426074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426070, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1426068, _1426070, _1426072), _1426074)), _1426076)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426070), _1426076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1426068), _1426074)), hAPP(c_Finite__Set_Ocard(_1426070), _1426076))))], (23055 ^ _777864) ^ [_1177762, _1177764, _1177766, _1177768, _1177770, _1177772, _1177774, _1177776, _1177778] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1177762, _1177764, _1177766, _1177768), hAPP(hAPP(c_Product__Type_Oscomp(_1177762, _1177770, _1177772, tc_prod(_1177764, _1177766)), _1177774), _1177776)), _1177778) = hAPP(hAPP(c_Product__Type_Oscomp(_1177762, _1177770, _1177772, _1177768), _1177774), hAPP(hAPP(c_COMBC(_1177770, tc_fun(_1177764, tc_fun(_1177766, _1177768)), tc_fun(_1177772, _1177768)), hAPP(hAPP(c_COMBB(tc_fun(_1177772, tc_prod(_1177764, _1177766)), tc_fun(tc_fun(_1177764, tc_fun(_1177766, _1177768)), tc_fun(_1177772, _1177768)), _1177770), c_Product__Type_Oscomp(_1177772, _1177764, _1177766, _1177768)), _1177776)), _1177778)))], (43981 ^ _777864) ^ [_1639255, _1639257, _1639259, _1639261, _1639263] : [-(_1639255 = c_Orderings_Obot__class_Obot(tc_fun(_1639257, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639257, tc_fun(_1639259, tc_HOL_Obool)), _1639255), hAPP(hAPP(c_COMBC(_1639257, tc_fun(_1639259, tc_HOL_Obool), tc_fun(_1639259, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639259, tc_HOL_Obool), tc_fun(tc_fun(_1639259, tc_HOL_Obool), tc_fun(_1639259, tc_HOL_Obool)), _1639257), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639259, tc_HOL_Obool))), _1639261)), _1639263)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639259, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639257, tc_fun(_1639259, tc_HOL_Obool)), _1639255), _1639261)), _1639263))], (11679 ^ _777864) ^ [_973003, _973005, _973007] : [class_Rings_Oordered__cancel__semiring(_973003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973003), c_Groups_Ozero__class_Ozero(_973003)), _973005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973003), _973007), c_Groups_Ozero__class_Ozero(_973003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973003), _973007), _973005)), c_Groups_Ozero__class_Ozero(_973003))))], (51631 ^ _777864) ^ [_1813557, _1813559] : [v_P(_1813559, _1813557), 51634 ^ _777864 : [(51635 ^ _777864) ^ [_1813643] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), _1813557, hAPP(c_Nat_OSuc, v_na), _1813643), -(v_Q(_1813559, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _1813643), hAPP(c_Natural_Ogetlocs, v_s_H))), v_X), hAPP(hAPP(c_Natural_Ogetlocs, _1813643), c_Com_ORes))))]]], (50831 ^ _777864) ^ [_1803329, _1803331, _1803333, _1803335, _1803337] : [class_Orderings_Olinorder(_1803329), c_List_Olinorder__class_Osorted(_1803329, hAPP(c_List_Orev(_1803329), hAPP(hAPP(c_List_Omap(_1803331, _1803329), _1803333), _1803335))), -(hAPP(c_List_Ofilter(_1803331, hAPP(hAPP(c_COMBB(_1803329, tc_HOL_Obool, _1803331), hAPP(c_Orderings_Oord__class_Oless(_1803329), _1803337)), _1803333)), _1803335) = c_List_OtakeWhile(_1803331, hAPP(hAPP(c_COMBB(_1803329, tc_HOL_Obool, _1803331), hAPP(c_Orderings_Oord__class_Oless(_1803329), _1803337)), _1803333), _1803335))], (45155 ^ _777864) ^ [_1668186, _1668188, _1668190, _1668192, _1668194] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1668186, _1668186)), hAPP(hAPP(c_Product__Type_OPair(_1668186, _1668186), _1668188), _1668190)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1668186, _1668186), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1668192)), _1668194))), 45159 ^ _777864 : [(45162 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668186, _1668186)), hAPP(hAPP(c_Product__Type_OPair(_1668186, _1668186), 45158 ^ [_1668186, _1668188, _1668190, _1668192, _1668194]), _1668190)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1668186, _1668186), tc_HOL_Obool), _1668192), _1668194))))], (45160 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1668186, _1668186)), hAPP(hAPP(c_Product__Type_OPair(_1668186, _1668186), _1668188), 45158 ^ [_1668186, _1668188, _1668190, _1668192, _1668194])), _1668194)))]]], (29390 ^ _777864) ^ [_1310637, _1310639, _1310641, _1310643, _1310645] : [c_Finite__Set_Ofolding__one(_1310637, _1310639, _1310641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310637), _1310643)), -(hBOOL(hAPP(hAPP(c_member(_1310637), _1310645), _1310643))), -(_1310643 = c_Orderings_Obot__class_Obot(tc_fun(_1310637, tc_HOL_Obool))), -(hAPP(_1310641, hAPP(hAPP(c_Set_Oinsert(_1310637), _1310645), _1310643)) = hAPP(hAPP(_1310639, _1310645), hAPP(_1310641, _1310643)))], (29520 ^ _777864) ^ [_1313383, _1313385, _1313387, _1313389] : [hBOOL(hAPP(_1313383, _1313385)), hBOOL(hAPP(_1313387, _1313385)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313389, tc_HOL_Obool)), _1313383), _1313387), _1313385)))], (2640 ^ _777864) ^ [_817100, _817102, _817104, _817106, _817108, _817110, _817112, _817114] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_817114, _817110, _817106, _817102) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_817112, _817108, _817104, _817100)), _817114 = _817112, _817110 = _817108, _817106 = _817104, _817102 = _817100], (46502 ^ _777864) ^ [_1701214, _1701216, _1701218, _1701220] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1701214), tc_List_Olist(_1701214))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701214), tc_List_Olist(_1701214)), _1701216), _1701218)), c_List_Olistrel(_1701214, _1701220)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701214)), _1701216) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701214)), _1701218), 46508 ^ _777864 : [(46511 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1701214, _1701214, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1701214, tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_fun(_1701214, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1701214, tc_fun(tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_fun(_1701214, tc_HOL_Obool)), _1701214), c_COMBC(_1701214, tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1701214, tc_prod(_1701214, _1701214)), tc_fun(_1701214, tc_fun(tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_HOL_Obool)), _1701214), hAPP(c_COMBB(tc_prod(_1701214, _1701214), tc_fun(tc_fun(tc_prod(_1701214, _1701214), tc_HOL_Obool), tc_HOL_Obool), _1701214), c_member(tc_prod(_1701214, _1701214)))), c_Product__Type_OPair(_1701214, _1701214)))), _1701220)), 46507 ^ [_1701214, _1701216, _1701218, _1701220]))], (46509 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1701214, _1701214)), 46507 ^ [_1701214, _1701216, _1701218, _1701220]), hAPP(c_List_Oset(tc_prod(_1701214, _1701214)), hAPP(hAPP(c_List_Ozip(_1701214, _1701214), _1701216), _1701218)))))]]], (50350 ^ _777864) ^ [_1791547, _1791549, _1791551] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1791547), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1791547))), _1791549))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1791551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1791547))), _1791549))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1791547), _1791547), hAPP(hAPP(c_COMBC(tc_List_Olist(_1791547), tc_Nat_Onat, _1791547), c_List_Onth(_1791547)), _1791551)), hAPP(c_List_Ofilter(tc_List_Olist(_1791547), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1791547)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1791551)), c_Nat_Osize__class_Osize(tc_List_Olist(_1791547)))), c_List_Otranspose(_1791547, _1791549))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1791547)), _1791549), _1791551))], (46629 ^ _777864) ^ [_1705386, _1705388, _1705390, _1705392] : [_1705386 = _1705388, -(c_List_Oremove1(_1705390, _1705386, hAPP(hAPP(c_List_Olist_OCons(_1705390), _1705388), _1705392)) = _1705392)], (21596 ^ _777864) ^ [_1151121, _1151123] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151121), hAPP(c_Int_Onumber__class_Onumber__of(_1151121), c_Int_OMin)), _1151123) = hAPP(c_Groups_Ouminus__class_Ouminus(_1151121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151121), c_Groups_Oone__class_Oone(_1151121)), _1151123))), class_Fields_Ofield__inverse__zero(_1151121), class_Int_Onumber__ring(_1151121)], (49075 ^ _777864) ^ [_1764965] : [-(c_List_Olists(_1764965, c_Orderings_Otop__class_Otop(tc_fun(_1764965, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1764965), tc_HOL_Obool)))], (36098 ^ _777864) ^ [_1449827, _1449829, _1449831, _1449833, _1449835, _1449837] : [-(_1449827 = _1449829), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449831, _1449833), _1449835), _1449829), _1449837), _1449827) = hAPP(_1449835, _1449827))], (36262 ^ _777864) ^ [_1452896, _1452898, _1452900] : [class_Orderings_Oorder(_1452896), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1452896, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1452896), _1452898)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1452896, _1452898, _1452900)) = c_Orderings_Obot__class_Obot(tc_fun(_1452896, tc_HOL_Obool)))], (17864 ^ _777864) ^ [_1085676] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085676)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085676)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1085676)))], (14268 ^ _777864) ^ [_1019107] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019107, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1019107)], (30114 ^ _777864) ^ [_1325794, _1325796] : [class_Lattices_Oboolean__algebra(_1325794), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325794), _1325796), hAPP(c_Groups_Ouminus__class_Ouminus(_1325794), _1325796)) = c_Orderings_Obot__class_Obot(_1325794))], (8626 ^ _777864) ^ [_921033, _921035] : [class_Rings_Oring__1(_921033), -(hAPP(c_Int_Oring__1__class_Oof__int(_921033), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _921035)) = hAPP(c_Groups_Ouminus__class_Ouminus(_921033), hAPP(c_Int_Oring__1__class_Oof__int(_921033), _921035)))], (10079 ^ _777864) ^ [_946240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946240), _946240)))], (23075 ^ _777864) ^ [_1178258, _1178260, _1178262] : [class_Int_Onumber__ring(_1178258), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178258), _1178260), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1178262))) = hAPP(hAPP(c_HOL_OLet(_1178258, _1178258), hAPP(hAPP(c_Power_Opower__class_Opower(_1178258), _1178260), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1178262))), hAPP(hAPP(c_COMBS(_1178258, _1178258, _1178258), c_Groups_Otimes__class_Otimes(_1178258)), c_COMBI(_1178258))))], (18048 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (17002 ^ _777864) ^ [_1071019, _1071021] : [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), _1071019), _1071021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1071019))), -(_1071021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31137 ^ _777864) ^ [_1346631, _1346633, _1346635] : [class_Orderings_Olinorder(_1346631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346631), _1346633)), -(_1346633 = c_Orderings_Obot__class_Obot(tc_fun(_1346631, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346631), _1346635)), -(_1346635 = c_Orderings_Obot__class_Obot(tc_fun(_1346631, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1346631, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346631, tc_HOL_Obool)), _1346633), _1346635)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1346631), c_Big__Operators_Olinorder__class_OMax(_1346631, _1346633)), c_Big__Operators_Olinorder__class_OMax(_1346631, _1346635)))], (43961 ^ _777864) ^ [_1638570, _1638572, _1638574, _1638576] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638570, tc_fun(_1638572, tc_HOL_Obool)), _1638574), _1638576) = hAPP(c_Set_OCollect(_1638572), hAPP(hAPP(c_COMBB(tc_fun(_1638570, tc_HOL_Obool), tc_HOL_Obool, _1638572), c_HOL_OAll(_1638570)), hAPP(hAPP(c_COMBB(tc_fun(_1638570, tc_HOL_Obool), tc_fun(_1638570, tc_HOL_Obool), _1638572), hAPP(c_COMBS(_1638570, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1638570), c_fimplies), hAPP(hAPP(c_COMBC(_1638570, tc_fun(_1638570, tc_HOL_Obool), tc_HOL_Obool), c_member(_1638570)), _1638574)))), hAPP(hAPP(c_COMBC(_1638572, tc_fun(_1638570, tc_fun(_1638572, tc_HOL_Obool)), tc_fun(_1638570, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1638572, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1638570, tc_fun(_1638572, tc_HOL_Obool)), tc_fun(_1638570, tc_HOL_Obool)), _1638572), c_COMBB(tc_fun(_1638572, tc_HOL_Obool), tc_HOL_Obool, _1638570)), c_member(_1638572))), _1638576)))))], (13844 ^ _777864) ^ [_1011239, _1011241, _1011243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011239)), 13847 ^ _777864 : [(13848 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1011241, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011243), _1011239)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011243, _1011239))), 13851 ^ _777864 : [(13852 ^ _777864) ^ [_1011440, _1011442] : [-(hBOOL(hAPP(hAPP(_1011241, _1011442), _1011440))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1011440), _1011239)), _1011243 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011239), _1011442)), _1011440)]]], (13866 ^ _777864) ^ [] : [13869 ^ _777864 : [(13872 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 13868 ^ [_1011239, _1011241, _1011243]), _1011239)))], (13874 ^ _777864) ^ [] : [-(_1011243 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1011239), 13867 ^ [_1011239, _1011241, _1011243])), 13868 ^ [_1011239, _1011241, _1011243]))], (13876 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1011241, 13867 ^ [_1011239, _1011241, _1011243]), 13868 ^ [_1011239, _1011241, _1011243]))], (13870 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13868 ^ [_1011239, _1011241, _1011243])))]], -(hBOOL(hAPP(hAPP(_1011241, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1011243), _1011239)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011243, _1011239))))]]], (28110 ^ _777864) ^ [_1278767, _1278769, _1278771] : [class_Lattices_Osemilattice__sup(_1278767), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278767), _1278769), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278767), _1278769), _1278771)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278767), _1278769), _1278771))], (19080 ^ _777864) ^ [_1105885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105885), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1105885)), c_Int_OMin)))], (1910 ^ _777864) ^ [_805593, _805595, _805597, _805599, _805601, _805603, _805605, _805607] : [-(c_Com_Ovname_Ovname__case(_805607, _805603, _805599, _805595) = c_Com_Ovname_Ovname__case(_805605, _805601, _805597, _805593)), _805607 = _805605, _805603 = _805601, _805599 = _805597, _805595 = _805593], (23779 ^ _777864) ^ [_1193296] : [class_Orderings_Oord(_1193296), -(c_Orderings_Oord__class_Omin(_1193296) = c_Orderings_Oord_Omin(_1193296, c_Orderings_Oord__class_Oless__eq(_1193296)))], (7128 ^ _777864) ^ [_895004, _895006, _895008, _895010, _895012, _895014] : [-(hBOOL(hAPP(_895004, _895006))), c_Natural_Oevaln(_895008, _895006, _895010, _895012), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_895004, _895014, _895008), _895006, _895010, _895012))], (47259 ^ _777864) ^ [_1721893, _1721895, _1721897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721893), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721895)), _1721897))), -(hAPP(c_Random_Opick(_1721895, hAPP(hAPP(c_List_Omap(_1721895, tc_prod(tc_Code__Numeral_Ocode__numeral, _1721895)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1721895), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1721897)), hAPP(c_Code__Numeral_Oof__nat, _1721893)) = hAPP(hAPP(c_List_Onth(_1721895), _1721897), _1721893))], (29622 ^ _777864) ^ [_1315615, _1315617, _1315619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315615, tc_HOL_Obool)), _1315617), _1315619)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315615, tc_HOL_Obool)), _1315619), _1315617) = _1315617)], (4704 ^ _777864) ^ [_849782, _849784] : [_849784 = _849782, -(c_Int_Onumber__class_Onumber__of(_849784) = c_Int_Onumber__class_Onumber__of(_849782))], (48147 ^ _777864) ^ [_1742008, _1742010, _1742012] : [c_List_Olist_ONil(_1742008) = hAPP(hAPP(c_List_Oappend(_1742008), _1742010), _1742012), 48150 ^ _777864 : [(48153 ^ _777864) ^ [] : [-(_1742012 = c_List_Olist_ONil(_1742008))], (48151 ^ _777864) ^ [] : [-(_1742010 = c_List_Olist_ONil(_1742008))]]], (2658 ^ _777864) ^ [_817401, _817403, _817405, _817407, _817409, _817411] : [-(c_Random__Sequence_Oempty(_817411, _817407, _817403) = c_Random__Sequence_Oempty(_817409, _817405, _817401)), _817411 = _817409, _817407 = _817405, _817403 = _817401], (43741 ^ _777864) ^ [_1631808, _1631810, _1631812] : [-(hAPP(c_Relation_Oconverse(_1631808, _1631810), hAPP(c_Relation_Oconverse(_1631810, _1631808), _1631812)) = _1631812)], (49267 ^ _777864) ^ [_1768886, _1768888, _1768890] : [-(c_List_Olast(_1768886, hAPP(hAPP(c_List_Oappend(_1768886), _1768888), hAPP(hAPP(c_List_Olist_OCons(_1768886), _1768890), c_List_Olist_ONil(_1768886)))) = _1768890)], (51395 ^ _777864) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (14838 ^ _777864) ^ [_1029263, _1029265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029263))), -(c_SMT_Oz3div(_1029265, _1029263) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029265), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1029263))))], (50536 ^ _777864) ^ [_1795732, _1795734] : [-(hAPP(c_List_Orev(_1795732), hAPP(c_List_Orev(_1795732), _1795734)) = _1795734)], (30230 ^ _777864) ^ [_1328686, _1328688] : [c_Nat__Transfer_Onat__set(_1328686), c_Nat__Transfer_Onat__set(_1328688), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1328686), _1328688) = 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), _1328686)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1328688))))], (5850 ^ _777864) ^ [_873920, _873922] : [_873920 = _873922, -(hAPP(c_Com_Ocom_OBODY, _873920) = hAPP(c_Com_Ocom_OBODY, _873922))], (10286 ^ _777864) ^ [_949458, _949460, _949462] : [class_Orderings_Oorder(_949458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949458), _949460), _949462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949458), _949462), _949460)), -(_949462 = _949460)], (16958 ^ _777864) ^ [_1070267, _1070269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1070267), _1070269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070267)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070269))))], (29478 ^ _777864) ^ [_1312383, _1312385, _1312387, _1312389, _1312391] : [c_Equiv__Relations_Oequiv(_1312383, _1312385, _1312387), hBOOL(hAPP(hAPP(c_member(_1312383), _1312389), _1312385)), hBOOL(hAPP(hAPP(c_member(_1312383), _1312391), _1312385)), 29489 ^ _777864 : [(29496 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1312383, _1312383)), hAPP(hAPP(c_Product__Type_OPair(_1312383, _1312383), _1312389), _1312391)), _1312387)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1312383), hAPP(hAPP(c_Set_Oinsert(_1312383), _1312389), c_Orderings_Obot__class_Obot(tc_fun(_1312383, tc_HOL_Obool)))), _1312387) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1312383), hAPP(hAPP(c_Set_Oinsert(_1312383), _1312391), c_Orderings_Obot__class_Obot(tc_fun(_1312383, tc_HOL_Obool)))), _1312387))], (29490 ^ _777864) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1312383), hAPP(hAPP(c_Set_Oinsert(_1312383), _1312389), c_Orderings_Obot__class_Obot(tc_fun(_1312383, tc_HOL_Obool)))), _1312387) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1312383), hAPP(hAPP(c_Set_Oinsert(_1312383), _1312391), c_Orderings_Obot__class_Obot(tc_fun(_1312383, tc_HOL_Obool)))), _1312387), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1312383, _1312383)), hAPP(hAPP(c_Product__Type_OPair(_1312383, _1312383), _1312389), _1312391)), _1312387)))]]], (29469 ^ _777864) ^ [_1312204] : [29471 ^ _777864 : [(29474 ^ _777864) ^ [_1312314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29470 ^ [_1312204, _1312314]), _1312314))], (29472 ^ _777864) ^ [_1312280] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29470 ^ [_1312204, _1312280]), _1312204)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1312204)))], (27470 ^ _777864) ^ [_1266864, _1266866, _1266868, _1266870, _1266872, _1266874, _1266876, _1266878] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1266864, _1266866), tc_prod(_1266864, _1266866))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1266864, _1266866), tc_prod(_1266864, _1266866)), hAPP(hAPP(c_Product__Type_OPair(_1266864, _1266866), _1266868), _1266870)), hAPP(hAPP(c_Product__Type_OPair(_1266864, _1266866), _1266872), _1266874))), c_Wellfounded_Olex__prod(_1266864, _1266866, _1266876, _1266878)))), 27471 ^ _777864 : [(27474 ^ _777864) ^ [] : [_1266868 = _1266872, hBOOL(hAPP(hAPP(c_member(tc_prod(_1266866, _1266866)), hAPP(hAPP(c_Product__Type_OPair(_1266866, _1266866), _1266870), _1266874)), _1266878))], (27472 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1266864, _1266864)), hAPP(hAPP(c_Product__Type_OPair(_1266864, _1266864), _1266868), _1266872)), _1266876))]]], (43453 ^ _777864) ^ [_1624713, _1624715, _1624717, _1624719] : [-(c_Wellfounded_Oacyclic(_1624713, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1624713, _1624713)), hAPP(hAPP(c_Product__Type_OPair(_1624713, _1624713), _1624715), _1624717)), _1624719))), c_Wellfounded_Oacyclic(_1624713, _1624719), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624713, _1624713)), hAPP(hAPP(c_Product__Type_OPair(_1624713, _1624713), _1624717), _1624715)), c_Transitive__Closure_Ortrancl(_1624713, _1624719))))], (8678 ^ _777864) ^ [_921885, _921887, _921889] : [class_Groups_Ogroup__add(_921885), 8681 ^ _777864 : [(8688 ^ _777864) ^ [] : [_921889 = hAPP(c_Groups_Ouminus__class_Ouminus(_921885), _921887), -(_921887 = hAPP(c_Groups_Ouminus__class_Ouminus(_921885), _921889))], (8682 ^ _777864) ^ [] : [_921887 = hAPP(c_Groups_Ouminus__class_Ouminus(_921885), _921889), -(_921889 = hAPP(c_Groups_Ouminus__class_Ouminus(_921885), _921887))]]], (1582 ^ _777864) ^ [_800407, _800409] : [-(class_Divides_Osemiring__div(_800407)), _800409 = _800407, class_Divides_Osemiring__div(_800409)], (48884 ^ _777864) ^ [_1760523, _1760525, _1760527, _1760529, _1760531, _1760533, _1760535] : [-(hAPP(c_List_Ofoldl(_1760523, _1760525, _1760527, _1760529), hAPP(hAPP(c_List_Omap(_1760531, _1760525), _1760533), _1760535)) = hAPP(c_List_Ofoldl(_1760523, _1760531, hAPP(hAPP(c_COMBC(_1760523, tc_fun(_1760531, _1760525), tc_fun(_1760531, _1760523)), hAPP(hAPP(c_COMBB(tc_fun(_1760525, _1760523), tc_fun(tc_fun(_1760531, _1760525), tc_fun(_1760531, _1760523)), _1760523), c_COMBB(_1760525, _1760523, _1760531)), _1760527)), _1760533), _1760529), _1760535))], (14810 ^ _777864) ^ [_1028777, _1028779, _1028781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1028777)), 14813 ^ _777864 : [(14814 ^ _777864) ^ [] : [-(_1028779 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028781), _1028777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028777), _1028779)), _1028781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028777), hAPP(c_Nat_OSuc, _1028779))))], (14824 ^ _777864) ^ [] : [_1028779 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028781), _1028777), 14827 ^ _777864 : [(14830 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028777), hAPP(c_Nat_OSuc, _1028779)))))], (14828 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028777), _1028779)), _1028781)))]]]]], (18310 ^ _777864) ^ [_1092686] : 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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)))))], (34211 ^ _777864) ^ [_1412153, _1412155] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1412153), _1412155))), -(hAPP(c_Finite__Set_Ocard(_1412153), _1412155) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27304 ^ _777864) ^ [_1263215, _1263217, _1263219, _1263221] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1263215, tc_fun(_1263217, tc_HOL_Obool))), _1263219), _1263221))], (7446 ^ _777864) ^ [_900762, _900764] : [hBOOL(hAPP(c_Com_OWT, _900762)), hBOOL(hAPP(c_Com_OWT, _900764)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_900762, _900764))))], (45567 ^ _777864) ^ [_1677852, _1677854, _1677856] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1677852), _1677854))), -(c_Smallcheck_Osmall_H(_1677856, _1677852, _1677854) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1677856, _1677852, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1677854), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1677856, _1677854)))], (30400 ^ _777864) ^ [_1332293, _1332295] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332293), 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)))), _1332295))), 30403 ^ _777864 : [(30406 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332295), _1332293))], (30404 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332293), _1332295)))]]], (33777 ^ _777864) ^ [_1401579, _1401581, _1401583, _1401585, _1401587] : [hBOOL(hAPP(hAPP(c_member(_1401579), _1401581), _1401583)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401585, tc_HOL_Obool)), hAPP(_1401587, _1401581)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401579, tc_fun(_1401585, tc_HOL_Obool)), _1401583), _1401587)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401579, tc_fun(_1401585, tc_HOL_Obool)), _1401583), _1401587))], (27117 ^ _777864) ^ [_1258087, _1258089, _1258091] : [_1258089 = _1258091, -(hBOOL(hAPP(hAPP(c_member(_1258087), _1258089), hAPP(hAPP(c_Set_Oinsert(_1258087), _1258091), c_Orderings_Obot__class_Obot(tc_fun(_1258087, tc_HOL_Obool))))))], (46260 ^ _777864) ^ [_1694590] : [class_Orderings_Olinorder(_1694590), -(c_Finite__Set_Ofun__left__comm(_1694590, tc_List_Olist(_1694590), c_List_Olinorder__class_Oinsort__key(_1694590, _1694590, c_COMBI(_1694590))))], (23071 ^ 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_1653646]), _1653642)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1653638, _1653638), tc_HOL_Obool), 44538 ^ [_1653638, _1653640, _1653642, _1653644, _1653646]), _1653646))))], (44542 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653638, _1653638)), hAPP(hAPP(c_Product__Type_OPair(_1653638, _1653638), _1653640), 44537 ^ [_1653638, _1653640, _1653642, _1653644, _1653646])), _1653646)))], (44540 ^ _777864) ^ [] : [-(_1653644 = hAPP(c_Nat_OSuc, 44538 ^ [_1653638, _1653640, _1653642, _1653644, _1653646]))]]], (39407 ^ _777864) ^ [_1523857, _1523859, _1523861] : [class_Lattices_Osemilattice__inf(_1523857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523857), _1523859)), hBOOL(hAPP(hAPP(c_member(_1523857), _1523861), _1523859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1523857), hAPP(c_Finite__Set_Ofold1(_1523857, c_Lattices_Osemilattice__inf__class_Oinf(_1523857)), _1523859)), _1523861)))], (14590 ^ _777864) ^ [_1024384, _1024386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1024386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024384), _1024386)), _1024384)))], (28578 ^ _777864) ^ [_1292261, _1292263, _1292265, _1292267, _1292269] : [hBOOL(hAPP(hAPP(c_member(_1292261), _1292263), _1292265)), -(hAPP(hAPP(c_Set_Oinsert(_1292267), hAPP(_1292269, _1292263)), hAPP(c_Set_Oimage(_1292261, _1292267, _1292269), _1292265)) = hAPP(c_Set_Oimage(_1292261, _1292267, _1292269), _1292265))], (48356 ^ _777864) ^ [_1747880, _1747882, _1747884, _1747886] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747880), tc_List_Olist(_1747880))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747880), tc_List_Olist(_1747880)), _1747882), _1747884)), c_List_Olistrel(_1747880, _1747886))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747880), tc_List_Olist(_1747880))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747880), tc_List_Olist(_1747880)), _1747882), _1747884)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1747880), c_List_Olistrel1(_1747880, _1747886)))))], (6076 ^ _777864) ^ [_877902, _877904] : [c_Com_Ovname_OLoc(_877902) = c_Com_Ovname_OGlb(_877904)], (8407 ^ _777864) ^ [_917119, _917121] : [class_Rings_Olinordered__idom(_917119), 8410 ^ _777864 : [(8417 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917121), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917119), hAPP(c_Int_Oring__1__class_Oof__int(_917119), _917121)), c_Groups_Ozero__class_Ozero(_917119))))], (8411 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_917119), hAPP(c_Int_Oring__1__class_Oof__int(_917119), _917121)), c_Groups_Ozero__class_Ozero(_917119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917121), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30002 ^ _777864) ^ [_1323518, _1323520, _1323522, _1323524] : [class_Lattices_Olattice(_1323518), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323518), _1323520), _1323522)), _1323524) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323518), _1323520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323518), _1323522), _1323524)))], (3910 ^ _777864) ^ [_837395, _837397, _837399, _837401, _837403, _837405] : [-(c_Smallcheck_Oorelse(_837405, _837401, _837397) = c_Smallcheck_Oorelse(_837403, _837399, _837395)), _837405 = _837403, _837401 = _837399, _837397 = _837395], (48700 ^ _777864) ^ [_1757010, _1757012, _1757014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757010), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757012)), _1757014))), -(_1757014 = hAPP(hAPP(c_List_Oappend(_1757012), hAPP(hAPP(c_List_Otake(_1757012), _1757010), _1757014)), hAPP(hAPP(c_List_Olist_OCons(_1757012), hAPP(hAPP(c_List_Onth(_1757012), _1757014), _1757010)), hAPP(hAPP(c_List_Odrop(_1757012), hAPP(c_Nat_OSuc, _1757010)), _1757014))))], (21664 ^ _777864) ^ [_1152434, _1152436, _1152438, _1152440] : [class_Fields_Olinordered__field__inverse__zero(_1152434), class_Int_Onumber(_1152434), 21671 ^ _777864 : [(21672 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152434), _1152438), _1152440))), 21675 ^ _777864 : [(21682 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), c_Groups_Ozero__class_Ozero(_1152434)), _1152440))), 21685 ^ _777864 : [(21692 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), _1152440), c_Groups_Ozero__class_Ozero(_1152434)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), c_Groups_Ozero__class_Ozero(_1152434))))], (21686 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), _1152440), c_Groups_Ozero__class_Ozero(_1152434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), _1152438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), _1152440))))]]], (21676 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), c_Groups_Ozero__class_Ozero(_1152434)), _1152440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), _1152440)), _1152438)))]]], (21698 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152434), _1152438), _1152440)))), 21701 ^ _777864 : [(21704 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), _1152440)), _1152438))], (21702 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), c_Groups_Ozero__class_Ozero(_1152434)), _1152440)))]], 21705 ^ _777864 : [(21708 ^ _777864) ^ [] : [21709 ^ _777864 : [(21712 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), _1152438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), _1152440)))], (21710 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), _1152440), c_Groups_Ozero__class_Ozero(_1152434))))]], 21713 ^ _777864 : [(21716 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152434), hAPP(c_Int_Onumber__class_Onumber__of(_1152434), _1152436)), c_Groups_Ozero__class_Ozero(_1152434)))], (21714 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), _1152440), c_Groups_Ozero__class_Ozero(_1152434)))]]], (21706 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152434), c_Groups_Ozero__class_Ozero(_1152434)), _1152440))]]]]], (23591 ^ _777864) ^ [_1189651, _1189653, _1189655, _1189657] : [class_Orderings_Olinorder(_1189651), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189651), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189651), _1189653), _1189655)), _1189657) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189651), _1189653), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189651), _1189655), _1189657)))], (38562 ^ _777864) ^ [_1502947, _1502949, _1502951, _1502953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502947, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1502947, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38563 ^ [_1502947, _1502949, _1502951, _1502953])), _1502949)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1502947, 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), 38563 ^ [_1502947, _1502949, _1502951, _1502953]), _1502951))), _1502953))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1502947, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1502947, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1502949)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1502947, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1502953))))], (7252 ^ _777864) ^ [_897160, _897162, _897164, _897166, _897168] : [c_Com_Ocom_OSemi(_897160, _897162) = c_Com_Ocom_OCond(_897164, _897166, _897168)], (40821 ^ _777864) ^ [_1564758, _1564760, _1564762] : [c_Wellfounded_Owf(_1564758, _1564760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564758, _1564758), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564758, _1564758, _1564758), _1564760), _1564762)), _1564760)), -(c_FunDef_Oreduction__pair(_1564758, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1564758, _1564758), tc_HOL_Obool), tc_fun(tc_prod(_1564758, _1564758), tc_HOL_Obool)), _1564760), _1564762)))], (9076 ^ _777864) ^ [_928628] : [class_Rings_Ozero__neq__one(_928628), c_Groups_Oone__class_Oone(_928628) = c_Groups_Ozero__class_Ozero(_928628)], (23603 ^ _777864) ^ [_1189937, _1189939, _1189941, _1189943] : [class_Orderings_Olinorder(_1189937), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189937), _1189939), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189937), _1189941), _1189943)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189937), _1189941), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189937), _1189939), _1189943)))], (48544 ^ _777864) ^ [_1753090, _1753092, _1753094] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753090)), hAPP(hAPP(c_List_Odrop(_1753090), _1753092), _1753094)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753090)), _1753094)), _1753092))], (10230 ^ _777864) ^ [_948574, _948576, _948578, _948580] : [class_Orderings_Oord(_948574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948574), _948576), _948578)), _948578 = _948580, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948574), _948576), _948580)))], (26403 ^ _777864) ^ [_1242897, _1242899, _1242901, _1242903, _1242905] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242897), _1242899)), 26406 ^ _777864 : [(26413 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242905), _1242899))), _1242903))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242901), _1242903))))], (26407 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242901), _1242903))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242905), _1242899))), _1242903))))]]], (23835 ^ _777864) ^ [_1194415, _1194417, _1194419, _1194421] : [class_Orderings_Olinorder(_1194415), 23838 ^ _777864 : [(23839 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194415), _1194419), _1194421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), _1194419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), _1194421)))], (23849 ^ _777864) ^ [] : [23850 ^ _777864 : [(23853 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), _1194421))], (23851 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), _1194419))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194415), _1194417), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194415), _1194419), _1194421))))]]], (13002 ^ _777864) ^ [_996042, _996044, _996046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996042)), _996042 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _996044), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _996042), _996046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996046), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (39977 ^ _777864) ^ [_1536342, _1536344, _1536346, _1536348, _1536350] : [c_Finite__Set_Ofolding__one__idem(_1536342, _1536344, _1536346), hAPP(_1536348, hAPP(hAPP(_1536344, 39982 ^ [_1536342, _1536344, _1536346, _1536348, _1536350]), 39983 ^ [_1536342, _1536344, _1536346, _1536348, _1536350])) = hAPP(hAPP(_1536344, hAPP(_1536348, 39982 ^ [_1536342, _1536344, _1536346, _1536348, _1536350])), hAPP(_1536348, 39983 ^ [_1536342, _1536344, _1536346, _1536348, _1536350])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536342), _1536350)), -(_1536350 = c_Orderings_Obot__class_Obot(tc_fun(_1536342, tc_HOL_Obool))), -(hAPP(_1536348, hAPP(_1536346, _1536350)) = hAPP(_1536346, hAPP(c_Set_Oimage(_1536342, _1536342, _1536348), _1536350)))], (5980 ^ _777864) ^ [_876127] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _876127)], (43231 ^ _777864) ^ [_1619358, _1619360] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1619358, _1619358, _1619358), _1619360), c_Transitive__Closure_Ortrancl(_1619358, _1619360)) = hAPP(hAPP(c_Relation_Orel__comp(_1619358, _1619358, _1619358), c_Transitive__Closure_Ortrancl(_1619358, _1619360)), _1619360))], (47564 ^ _777864) ^ [_1728739] : [class_Groups_Omonoid__add(_1728739), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1728739), c_List_Olist_ONil(_1728739)) = c_Groups_Ozero__class_Ozero(_1728739))], (23031 ^ _777864) ^ [_1177251, _1177253] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1177251, _1177253), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1177251), _1177253)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1177251, _1177253)))))], (42226 ^ _777864) ^ [_1597918, _1597920, _1597922, _1597924, _1597926, _1597928] : [c_Finite__Set_Ofolding__idem(_1597918, _1597920, _1597922, _1597924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597918), _1597926)), hBOOL(hAPP(hAPP(c_member(_1597918), _1597928), _1597926)), -(hAPP(c_Fun_Ocomp(_1597920, _1597920, _1597920, hAPP(_1597924, _1597926)), hAPP(_1597922, _1597928)) = hAPP(_1597924, _1597926))], (38583 ^ _777864) ^ [_1503783, _1503785] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1503783, tc_HOL_Obool)), _1503785)))], (30667 ^ _777864) ^ [_1338612, _1338614] : [30668 ^ _777864 : [(30671 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338614), _1338612))], (30669 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338612), _1338614)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338612, _1338614) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (9686 ^ _777864) ^ [_939718, _939720] : [9687 ^ _777864 : [(9690 ^ _777864) ^ [] : [_939718 = _939720], (9688 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _939718), _939720))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _939718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _939720), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (22596 ^ _777864) ^ [_1168587, _1168589, _1168591] : [-(hAPP(hAPP(c_Product__Type_OPair(_1168587, _1168589), hAPP(c_Product__Type_Ofst(_1168587, _1168589), _1168591)), hAPP(c_Product__Type_Osnd(_1168587, _1168589), _1168591)) = _1168591)], (45778 ^ _777864) ^ [_1682900, _1682902, _1682904, _1682906, _1682908] : [hAPP(hAPP(c_List_Omap(_1682900, _1682902), _1682904), _1682906) = hAPP(hAPP(c_List_Omap(_1682900, _1682902), _1682908), _1682906), 45781 ^ _777864 : [(45782 ^ _777864) ^ [_1683023] : [hBOOL(hAPP(hAPP(c_member(_1682900), _1683023), hAPP(c_List_Oset(_1682900), _1682906))), -(hAPP(_1682904, _1683023) = hAPP(_1682908, _1683023))]]], (48776 ^ _777864) ^ [_1758274, _1758276, _1758278] : [-(hAPP(c_List_Otl(_1758274), hAPP(hAPP(c_List_Odrop(_1758274), _1758276), _1758278)) = hAPP(hAPP(c_List_Odrop(_1758274), _1758276), hAPP(c_List_Otl(_1758274), _1758278)))], (8252 ^ _777864) ^ [_914695, _914697, _914699, _914701] : [class_Orderings_Opreorder(_914695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914695), _914697), _914699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914695), _914699), _914701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914695), _914697), _914701)))], (7776 ^ _777864) ^ [_906987, _906989] : [hBOOL(hAPP(c_Com_OWT, _906989)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_906987, _906989))))], (48318 ^ _777864) ^ [_1746630, _1746632, _1746634, _1746636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746630), tc_List_Olist(_1746630))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746630), tc_List_Olist(_1746630)), _1746632), _1746634)), c_List_Olistrel1(_1746630, _1746636))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746630)), _1746632) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746630)), _1746634))], (49490 ^ _777864) ^ [_1773747, _1773749, _1773751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773747)), hAPP(c_List_Ofilter(_1773747, _1773749), _1773751))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773747)), _1773751))))], (12003 ^ _777864) ^ [_978722, _978724, _978726] : [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, _978722)), _978724)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978722)), _978726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978724), _978726)))], (8812 ^ _777864) ^ [_924470] : [class_Rings_Osemiring__1(_924470), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924470), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_924470))], (41188 ^ _777864) ^ [_1572432, _1572434, _1572436, _1572438] : [41189 ^ _777864 : [(41190 ^ _777864) ^ [_1572507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572436, _1572432)), hAPP(hAPP(c_Product__Type_OPair(_1572436, _1572432), _1572507), _1572434)), _1572438))]], -(hBOOL(hAPP(hAPP(c_member(_1572432), _1572434), hAPP(c_Relation_ORange(_1572436, _1572432), _1572438))))], (25175 ^ _777864) ^ [_1219544, _1219546] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219544), _1219546)), 25178 ^ _777864 : [(25185 ^ _777864) ^ [] : [_1219546 = _1219544, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219546), _1219544)))], (25179 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219546), _1219544)), -(_1219546 = _1219544)]]], (24753 ^ _777864) ^ [_1212463, _1212465, _1212467, _1212469, _1212471] : [-(hAPP(c_New__DSequence_Oneg__bind(_1212463, _1212465, _1212467, _1212469), _1212471) = c_Lazy__Sequence_Ohb__bind(_1212463, _1212465, hAPP(_1212467, _1212471), hAPP(hAPP(c_COMBC(_1212463, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1212465))), _1212469), _1212471)))], (5574 ^ _777864) ^ [_866618, _866620, _866622, _866624, _866626] : [c_Hoare__Mirabelle_Otriple__valid(_866618, hAPP(c_Nat_OSuc, _866620), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866618), _866622), hAPP(c_Com_Ocom_OBODY, _866624)), _866626)), -(c_Hoare__Mirabelle_Otriple__valid(_866618, _866620, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_866618), _866622), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _866624))), _866626)))], (5856 ^ _777864) ^ [_874026, _874028] : [c_Com_Ovname_OLoc(_874026) = c_Com_Ovname_OLoc(_874028), -(_874026 = _874028)], (44011 ^ _777864) ^ [_1640062, _1640064, _1640066, _1640068, _1640070] : [_1640062 = c_Orderings_Obot__class_Obot(tc_fun(_1640064, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1640066, tc_HOL_Obool)), _1640068), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1640064, tc_fun(_1640066, tc_HOL_Obool)), _1640062), _1640070)) = _1640068)], (29944 ^ _777864) ^ [_1322134, _1322136, _1322138, _1322140] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322134, tc_HOL_Obool)), _1322136), _1322138), _1322140)), -(hBOOL(hAPP(_1322138, _1322140)))], (23157 ^ _777864) ^ [_1180001, _1180003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180001)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180003))), -(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(_1180003))), 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), _1180001)), c_Int_Onat))))))], (1092 ^ _777864) ^ [_794282, _794284] : [-(class_Groups_Oab__group__add(_794282)), _794284 = _794282, class_Groups_Oab__group__add(_794284)], (27217 ^ _777864) ^ [_1261136, _1261138, _1261140, _1261142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261136, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261136, tc_HOL_Obool)), _1261138), hAPP(hAPP(c_Set_Oinsert(_1261136), _1261140), c_Orderings_Obot__class_Obot(tc_fun(_1261136, tc_HOL_Obool))))), _1261142)), hBOOL(hAPP(hAPP(c_member(_1261136), _1261140), _1261138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261136, tc_HOL_Obool)), _1261138), hAPP(hAPP(c_Set_Oinsert(_1261136), _1261140), _1261142))))], (11162 ^ _777864) ^ [_963630, _963632, _963634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963630), _963632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963632), _963634))))], (36104 ^ _777864) ^ [_1449885, _1449887, _1449889, _1449891, _1449893, _1449895, _1449897] : [-(_1449885 = _1449887), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449889, _1449891), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449889, _1449891), _1449893), _1449885), _1449895)), _1449887), _1449897) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449889, _1449891), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449889, _1449891), _1449893), _1449887), _1449897)), _1449885), _1449895))], (32381 ^ _777864) ^ [_1369995, _1369997, _1369999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369995), _1369997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1369995, tc_HOL_Obool)), _1369999), _1369997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369995), _1369999)), hAPP(c_Finite__Set_Ocard(_1369995), _1369997))))], (32435 ^ _777864) ^ [_1370960, _1370962, _1370964] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370960), _1370962)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370960), _1370964)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1370960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1370960, tc_HOL_Obool)), _1370962), _1370964))), hAPP(c_Finite__Set_Ocard(_1370960), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370960, tc_HOL_Obool)), _1370962), _1370964))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1370960), _1370962)), hAPP(c_Finite__Set_Ocard(_1370960), _1370964)))], (8138 ^ _777864) ^ [_913098, _913100, _913102] : [class_Orderings_Olinorder(_913098), -(_913100 = _913102), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913098), _913100), _913102))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913098), _913102), _913100)))], (9588 ^ _777864) ^ [_938063] : [class_Rings_Olinordered__semidom(_938063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938063), c_Groups_Oone__class_Oone(_938063)), c_Groups_Ozero__class_Ozero(_938063)))], (43128 ^ _777864) ^ [_1617028, _1617030, _1617032, _1617034, _1617036] : [c_Finite__Set_Ofun__left__comm(_1617028, _1617030, _1617032), -(hAPP(c_Fun_Ocomp(_1617030, _1617030, _1617030, hAPP(_1617032, _1617034)), hAPP(_1617032, _1617036)) = hAPP(c_Fun_Ocomp(_1617030, _1617030, _1617030, hAPP(_1617032, _1617036)), hAPP(_1617032, _1617034)))], (48276 ^ _777864) ^ [_1745374, _1745376, _1745378, _1745380] : [hBOOL(hAPP(hAPP(c_member(_1745374), _1745376), c_Wellfounded_Oacc(_1745374, _1745378))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1745374)), _1745380), c_Wellfounded_Oacc(tc_List_Olist(_1745374), c_List_Olistrel1(_1745374, _1745378)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1745374)), hAPP(hAPP(c_List_Olist_OCons(_1745374), _1745376), _1745380)), c_Wellfounded_Oacc(tc_List_Olist(_1745374), c_List_Olistrel1(_1745374, _1745378)))))], (40310 ^ _777864) ^ [_1544230, _1544232, _1544234, _1544236] : [_1544230 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1544232, _1544234), 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)), _1544236))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544232), _1544230)))], (51145 ^ _777864) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (49340 ^ _777864) ^ [_1770511, _1770513, _1770515, _1770517] : [49342 ^ _777864 : [(49345 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1770515, 49341 ^ [_1770511, _1770513, _1770515, _1770517])), hAPP(_1770517, 49341 ^ [_1770511, _1770513, _1770515, _1770517])))], (49343 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770511), 49341 ^ [_1770511, _1770513, _1770515, _1770517]), hAPP(c_List_Oset(_1770511), _1770513))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1770511, _1770515, _1770513)), c_List_Olist_Olist__size(_1770511, _1770517, _1770513))))], (47540 ^ _777864) ^ [_1728324, _1728326] : [c_Orderings_Obot__class_Obot(tc_fun(_1728324, tc_HOL_Obool)) = hAPP(c_List_Oset(_1728324), _1728326), -(_1728326 = c_List_Olist_ONil(_1728324))], (8594 ^ _777864) ^ [_920376, _920378, _920380] : [class_Rings_Oring(_920376), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920376), hAPP(c_Groups_Ouminus__class_Ouminus(_920376), _920378)), _920380) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920376), _920378), hAPP(c_Groups_Ouminus__class_Ouminus(_920376), _920380)))], (14400 ^ _777864) ^ [_1021358, _1021360, _1021362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021358), _1021360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021358), _1021362)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021360), _1021362))))], (50486 ^ _777864) ^ [_1794768, _1794770, _1794772] : [-(hAPP(c_List_Orev(_1794768), hAPP(hAPP(c_List_Oappend(_1794768), _1794770), _1794772)) = hAPP(hAPP(c_List_Oappend(_1794768), hAPP(c_List_Orev(_1794768), _1794772)), hAPP(c_List_Orev(_1794768), _1794770)))], (15470 ^ _777864) ^ [_1041118, _1041120, _1041122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041118), _1041122)), _1041120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041120), _1041122))))], (49630 ^ _777864) ^ [_1777252, _1777254] : [-(c_List_Ofoldr(tc_List_Olist(_1777252), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1777252)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1777252))), c_List_Otranspose(_1777252, _1777254), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1777252))), hAPP(c_List_Ofilter(tc_List_Olist(_1777252), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1777252)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1777252), tc_List_Olist(_1777252), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1777252)))), _1777254)))], (17632 ^ _777864) ^ [_1081960, _1081962] : [class_Int_Onumber__ring(_1081960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081960), _1081962), hAPP(c_Int_Onumber__class_Onumber__of(_1081960), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1081960), _1081962))], (31183 ^ _777864) ^ [_1347475, _1347477, _1347479, _1347481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347475, _1347477)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347479, _1347481))), 31186 ^ _777864 : [(31187 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347475), _1347477)), 31190 ^ _777864 : [(31195 ^ _777864) ^ [] : [31196 ^ _777864 : [(31199 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347475), _1347479))], (31197 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347479), _1347475)))]], 31200 ^ _777864 : [(31203 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347481), _1347477))], (31201 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347477), _1347481)))]]], (31193 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347477), _1347481)))], (31191 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347479), _1347475)))]]], (31205 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347479), _1347481)))]]], (50502 ^ _777864) ^ [_1795099, _1795101] : [-(hAPP(c_List_Oset(_1795099), c_List_Oconcat(_1795099, _1795101)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1795099), tc_fun(_1795099, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1795099)), _1795101)), c_List_Oset(_1795099)))], (3214 ^ _777864) ^ [_826499, _826501] : [_826501 = _826499, -(c_Power_Opower__class_Opower(_826501) = c_Power_Opower__class_Opower(_826499))], (19414 ^ _777864) ^ [_1111667, _1111669, _1111671] : [class_Rings_Olinordered__idom(_1111667), 19417 ^ _777864 : [(19426 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111667), hAPP(hAPP(c_Power_Opower__class_Opower(_1111667), _1111669), 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(_1111667), _1111671), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1111667)), _1111669 = c_Groups_Ozero__class_Ozero(_1111667), _1111671 = c_Groups_Ozero__class_Ozero(_1111667)], (19418 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111667), hAPP(hAPP(c_Power_Opower__class_Opower(_1111667), _1111669), 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(_1111667), _1111671), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1111667), 19421 ^ _777864 : [(19424 ^ _777864) ^ [] : [-(_1111671 = c_Groups_Ozero__class_Ozero(_1111667))], (19422 ^ _777864) ^ [] : [-(_1111669 = c_Groups_Ozero__class_Ozero(_1111667))]]]]], (12678 ^ _777864) ^ [_990805, _990807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _990805), _990807))))], (41655 ^ _777864) ^ [_1584419, _1584421, _1584423] : [c_Wellfounded_OwfP(_1584419, hAPP(_1584421, 41656 ^ [_1584419, _1584421, _1584423])), 41663 ^ _777864 : [(41666 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584419, tc_HOL_Obool)), c_Predicate_ODomainP(_1584419, _1584419, hAPP(_1584421, 41661 ^ [_1584419, _1584421, _1584423]))), c_Predicate_ORangeP(_1584419, _1584419, hAPP(_1584421, 41662 ^ [_1584419, _1584421, _1584423]))) = c_Orderings_Obot__class_Obot(tc_fun(_1584419, tc_HOL_Obool))], (41664 ^ _777864) ^ [] : [hAPP(_1584421, 41661 ^ [_1584419, _1584421, _1584423]) = hAPP(_1584421, 41662 ^ [_1584419, _1584421, _1584423])]], -(c_Wellfounded_OwfP(_1584419, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1584423, tc_fun(_1584419, tc_fun(_1584419, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1584423, tc_HOL_Obool))), _1584421)))], (7804 ^ _777864) ^ [_907630, _907632, _907634, _907636, _907638] : [c_Com_Ocom_OWhile(_907630, _907632) = c_Com_Ocom_OLocal(_907634, _907636, _907638)], (8728 ^ _777864) ^ [_922628, _922630] : [class_Groups_Omonoid__mult(_922628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922628), c_Groups_Oone__class_Oone(_922628)), _922630) = _922630)], (28140 ^ _777864) ^ [_1279464, _1279466, _1279468, _1279470] : [class_Lattices_Olattice(_1279464), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279464), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279464), _1279466), _1279468)), _1279470) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279464), _1279466), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279464), _1279468), _1279470)))], (7330 ^ _777864) ^ [_898562, _898564, _898566, _898568, _898570] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_898562, _898564, _898566)), _898568), _898570))), 7331 ^ _777864 : [(7338 ^ _777864) ^ [] : [-(hBOOL(hAPP(_898562, _898568))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898566), _898568), _898570))], (7332 ^ _777864) ^ [] : [hBOOL(hAPP(_898562, _898568)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898564), _898568), _898570))]]], (14099 ^ _777864) ^ [_1016340] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016340) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31457 ^ _777864) ^ [_1352599, _1352601, _1352603] : [class_Orderings_Olinorder(_1352599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352599), _1352601)), -(_1352601 = c_Orderings_Obot__class_Obot(tc_fun(_1352599, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352599), _1352603)), -(_1352603 = c_Orderings_Obot__class_Obot(tc_fun(_1352599, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352599, tc_HOL_Obool)), _1352601), _1352603) = c_Orderings_Obot__class_Obot(tc_fun(_1352599, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1352599, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352599, tc_HOL_Obool)), _1352601), _1352603)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352599), c_Big__Operators_Olinorder__class_OMax(_1352599, _1352601)), c_Big__Operators_Olinorder__class_OMax(_1352599, _1352603)))], (42798 ^ _777864) ^ [_1610198, _1610200, _1610202] : [class_Lattices_Olattice(_1610198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610198), _1610200)), -(c_Big__Operators_Olattice__class_OSup__fin(_1610198, hAPP(hAPP(c_Set_Oinsert(_1610198), _1610202), _1610200)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610198, _1610198, c_Lattices_Osemilattice__sup__class_Osup(_1610198)), _1610202), _1610200))], (26631 ^ _777864) ^ [_1247515, _1247517] : [_1247517 = c_Option_Ooption_ONone(_1247515), -(c_Option_Oset(_1247515, _1247517) = c_Orderings_Obot__class_Obot(tc_fun(_1247515, tc_HOL_Obool)))], (9800 ^ _777864) ^ [_941615, _941617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _941615)), _941617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941615), hAPP(c_Int_Onat, _941617))))], (9446 ^ _777864) ^ [_935500, _935502, _935504] : [class_Rings_Olinordered__semiring__strict(_935500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935500), c_Groups_Ozero__class_Ozero(_935500)), _935502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935500), _935504), c_Groups_Ozero__class_Ozero(_935500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935500), _935504), _935502)), c_Groups_Ozero__class_Ozero(_935500))))], (26163 ^ _777864) ^ [_1237896, _1237898, _1237900, _1237902] : [c_Hoare__Mirabelle_Ohoare__derivs(_1237896, _1237898, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1237896)), _1237900), _1237902)), 26166 ^ _777864 : [(26169 ^ _777864) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1237896, _1237898, _1237902))], (26167 ^ _777864) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1237896, _1237898, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1237896)), _1237900), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237896), tc_HOL_Obool)))))]]], (40883 ^ _777864) ^ [_1565843, _1565845, _1565847, _1565849] : [c_Wellfounded_Owf(_1565843, _1565845), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565843, _1565843)), hAPP(hAPP(c_Product__Type_OPair(_1565843, _1565843), _1565847), _1565849)), _1565845)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565843, _1565843)), hAPP(hAPP(c_Product__Type_OPair(_1565843, _1565843), _1565849), _1565847)), _1565845))], (18858 ^ _777864) ^ [_1102015, _1102017] : [_1102015 = _1102017, -(c_Int_OBit0(_1102015) = c_Int_OBit0(_1102017))], (18788 ^ _777864) ^ [_1100553, _1100555] : [class_Int_Onumber__ring(_1100553), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100553), c_Groups_Oone__class_Oone(_1100553)), hAPP(c_Int_Onumber__class_Onumber__of(_1100553), _1100555)) = hAPP(c_Int_Onumber__class_Onumber__of(_1100553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1100555)))], (23311 ^ _777864) ^ [_1184155, _1184157, _1184159, _1184161] : [-(c_Nat_Onat_Onat__case(_1184155, _1184157, _1184159, hAPP(c_Nat_OSuc, _1184161)) = hAPP(_1184159, _1184161))], (6080 ^ _777864) ^ [_877974, _877976, _877978] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_877974, _877976, _877978)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_877978)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45766 ^ _777864) ^ [_1682457, _1682459, _1682461, _1682463, _1682465] : [-(c_Map_Omap__of(_1682457, _1682459, hAPP(hAPP(c_List_Omap(tc_prod(_1682457, _1682461), tc_prod(_1682457, _1682459)), hAPP(c_Product__Type_Oprod_Oprod__case(_1682457, _1682461, tc_prod(_1682457, _1682459)), hAPP(hAPP(c_COMBC(_1682457, tc_fun(_1682461, _1682459), tc_fun(_1682461, tc_prod(_1682457, _1682459))), hAPP(hAPP(c_COMBB(tc_fun(_1682459, tc_prod(_1682457, _1682459)), tc_fun(tc_fun(_1682461, _1682459), tc_fun(_1682461, tc_prod(_1682457, _1682459))), _1682457), c_COMBB(_1682459, tc_prod(_1682457, _1682459), _1682461)), c_Product__Type_OPair(_1682457, _1682459))), _1682463))), _1682465)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1682461), tc_Option_Ooption(_1682459), _1682457, hAPP(c_Option_Omap(_1682461, _1682459), _1682463)), c_Map_Omap__of(_1682457, _1682461, _1682465)))], (6963 ^ _777864) ^ [_892383] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _892383))), -(hAPP(c_Com_Obody, _892383) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6966 ^ [_892383]))], (16522 ^ _777864) ^ [_1061563, _1061565, _1061567, _1061569] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061563), hAPP(c_Int_Onumber__class_Onumber__of(_1061563), _1061565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061563), _1061567), _1061569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061563), hAPP(c_Int_Onumber__class_Onumber__of(_1061563), _1061565)), _1061567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061563), hAPP(c_Int_Onumber__class_Onumber__of(_1061563), _1061565)), _1061569))), class_Int_Onumber(_1061563), class_Rings_Osemiring(_1061563)], (47506 ^ _777864) ^ [_1727721, _1727723, _1727725, _1727727] : [_1727723 = c_List_Olist_ONil(_1727721), -(hAPP(hAPP(c_List_Olist__update(_1727721, _1727723), _1727725), _1727727) = c_List_Olist_ONil(_1727721))], (17732 ^ _777864) ^ [_1083478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083478)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1083478) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (48838 ^ _777864) ^ [_1759514, _1759516, _1759518] : [-(hAPP(c_List_Otl(_1759514), hAPP(hAPP(c_List_Oappend(_1759514), _1759516), _1759518)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1759514), _1759514, hAPP(c_List_Otl(_1759514), _1759518), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1759514), tc_List_Olist(_1759514)), _1759514), hAPP(hAPP(c_COMBC(tc_List_Olist(_1759514), tc_List_Olist(_1759514), tc_List_Olist(_1759514)), c_List_Oappend(_1759514)), _1759518))), _1759516))], (23361 ^ _777864) ^ [_1185447, _1185449] : [_1185447 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185447, _1185449) = 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)))], (32953 ^ _777864) ^ [_1381950, _1381952, _1381954, _1381956, _1381958] : [class_Fields_Ofield__inverse__zero(_1381950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381952), _1381954)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381952, _1381950), hAPP(hAPP(c_COMBS(_1381952, _1381950, _1381950), hAPP(hAPP(c_COMBB(_1381950, tc_fun(_1381950, _1381950), _1381952), c_Rings_Oinverse__class_Odivide(_1381950)), _1381956)), _1381958)), _1381954) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381950), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381952, _1381950), _1381956), _1381954)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381952, _1381950), _1381958), _1381954)))], (34723 ^ _777864) ^ [_1422553, _1422555, _1422557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422553), _1422555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422553, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1422553, _1422553, _1422557), _1422555)), _1422555)), c_Fun_Oinj__on(_1422553, _1422553, _1422557, _1422555), -(hAPP(c_Set_Oimage(_1422553, _1422553, _1422557), _1422555) = _1422555)], (19312 ^ _777864) ^ [_1109883, _1109885] : [class_Rings_Oring__1(_1109883), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1109883), hAPP(c_Groups_Ouminus__class_Ouminus(_1109883), _1109885)), 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(_1109883), _1109885), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19848 ^ _777864) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (822 ^ _777864) ^ [_790557, _790559, _790561, _790563, _790565, _790567, _790569, _790571] : [-(c_List_Olistrelp(_790569, _790565, _790561, _790557)), c_List_Olistrelp(_790571, _790567, _790563, _790559), _790571 = _790569, _790567 = _790565, _790563 = _790561, _790559 = _790557], (36590 ^ _777864) ^ [_1460009, _1460011, _1460013, _1460015, _1460017] : [class_Groups_Ocomm__monoid__add(_1460009), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460011, _1460009), hAPP(hAPP(c_COMBS(_1460011, _1460009, _1460009), hAPP(hAPP(c_COMBB(_1460009, tc_fun(_1460009, _1460009), _1460011), c_Groups_Oplus__class_Oplus(_1460009)), _1460013)), _1460015)), _1460017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460009), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460011, _1460009), _1460013), _1460017)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460011, _1460009), _1460015), _1460017)))], (33351 ^ _777864) ^ [_1390938, _1390940, _1390942, _1390944, _1390946, _1390948] : [-(hAPP(c_Relation_OImage(_1390938, _1390940, _1390942), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390944, tc_fun(_1390938, tc_HOL_Obool)), _1390946), _1390948)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390944, tc_fun(_1390940, tc_HOL_Obool)), _1390946), hAPP(hAPP(c_COMBB(tc_fun(_1390938, tc_HOL_Obool), tc_fun(_1390940, tc_HOL_Obool), _1390944), c_Relation_OImage(_1390938, _1390940, _1390942)), _1390948)))], (4176 ^ _777864) ^ [_841692, _841694, _841696, _841698] : [-(c_List_Olex(_841698, _841694) = c_List_Olex(_841696, _841692)), _841698 = _841696, _841694 = _841692], (30937 ^ _777864) ^ [_1343420, _1343422] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343420), _1343422))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343420, _1343422) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (45788 ^ _777864) ^ [_1683144, _1683146, _1683148, _1683150, _1683152] : [45790 ^ _777864 : [(45793 ^ _777864) ^ [] : [hAPP(_1683148, 45789 ^ [_1683144, _1683146, _1683148, _1683150, _1683152]) = hAPP(_1683152, 45789 ^ [_1683144, _1683146, _1683148, _1683150, _1683152])], (45791 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683144), 45789 ^ [_1683144, _1683146, _1683148, _1683150, _1683152]), hAPP(c_List_Oset(_1683144), _1683150))))]], -(hAPP(hAPP(c_List_Omap(_1683144, _1683146), _1683148), _1683150) = hAPP(hAPP(c_List_Omap(_1683144, _1683146), _1683152), _1683150))], (1332 ^ _777864) ^ [_797282, _797284] : [-(class_Orderings_Obot(_797282)), _797284 = _797282, class_Orderings_Obot(_797284)], (14362 ^ _777864) ^ [_1020671, _1020673, _1020675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1020671)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020671), _1020673)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1020671), _1020675)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1020673), _1020675))], (8162 ^ _777864) ^ [_913388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913388)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17998 ^ _777864) ^ [_1087913] : [class_Rings_Osemiring__1(_1087913), -(c_Int_Oiszero(_1087913, c_Groups_Ozero__class_Ozero(_1087913)))], (3568 ^ _777864) ^ [_832094, _832096, _832098, _832100, _832102, _832104, _832106, _832108] : [-(c_Random__Sequence_Obind(_832108, _832104, _832100, _832096) = c_Random__Sequence_Obind(_832106, _832102, _832098, _832094)), _832108 = _832106, _832104 = _832102, _832100 = _832098, _832096 = _832094], (3762 ^ _777864) ^ [_835139, _835141, _835143, _835145] : [-(c_HOL_OThe(_835145, _835141) = c_HOL_OThe(_835143, _835139)), _835145 = _835143, _835141 = _835139], (16446 ^ _777864) ^ [_1060189, _1060191, _1060193] : [class_Groups_Oordered__ab__group__add__abs(_1060189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060189), _1060191), _1060193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060189), hAPP(c_Groups_Ouminus__class_Ouminus(_1060189), _1060191)), _1060193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060189), hAPP(c_Groups_Oabs__class_Oabs(_1060189), _1060191)), _1060193)))], (14668 ^ _777864) ^ [_1025987, _1025989, _1025991] : [class_Divides_Osemiring__div(_1025987), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025987), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025987), _1025989), _1025991)), _1025991)), c_Divides_Odiv__class_Omod(_1025987, _1025989, _1025991)) = _1025989)], (9857 ^ _777864) ^ [_942649, _942651] : [class_Groups_Osgn__if(_942649), 9860 ^ _777864 : [(9867 ^ _777864) ^ [] : [-(_942651 = c_Groups_Ozero__class_Ozero(_942649)), 9870 ^ _777864 : [(9877 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942649), c_Groups_Ozero__class_Ozero(_942649)), _942651))), -(c_Groups_Osgn__class_Osgn(_942649, _942651) = hAPP(c_Groups_Ouminus__class_Ouminus(_942649), c_Groups_Oone__class_Oone(_942649)))], (9871 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942649), c_Groups_Ozero__class_Ozero(_942649)), _942651)), -(c_Groups_Osgn__class_Osgn(_942649, _942651) = c_Groups_Oone__class_Oone(_942649))]]], (9861 ^ _777864) ^ [] : [_942651 = c_Groups_Ozero__class_Ozero(_942649), -(c_Groups_Osgn__class_Osgn(_942649, _942651) = c_Groups_Ozero__class_Ozero(_942649))]]], (6456 ^ _777864) ^ [_884436, _884438, _884440] : [_884436 = _884440, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884436), _884438) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884440), _884438))], (28042 ^ _777864) ^ [_1277559, _1277561] : [class_Lattices_Olattice(_1277559), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277559), _1277561), _1277561) = _1277561)], (29710 ^ _777864) ^ [_1317264, _1317266, _1317268, _1317270] : [class_Lattices_Osemilattice__inf(_1317264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317264), _1317266), _1317268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317264), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317264), _1317266), _1317270)), _1317268)))], (28501 ^ _777864) ^ [_1290569, _1290571, _1290573, _1290575, _1290577] : [hBOOL(hAPP(hAPP(c_member(_1290569), _1290571), hAPP(c_Set_Oimage(_1290573, _1290569, _1290575), _1290577))), 28505 ^ _777864 : [(28508 ^ _777864) ^ [] : [-(_1290571 = hAPP(_1290575, 28504 ^ [_1290569, _1290571, _1290573, _1290575, _1290577]))], (28506 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290573), 28504 ^ [_1290569, _1290571, _1290573, _1290575, _1290577]), _1290577)))]]], (51207 ^ _777864) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (4008 ^ _777864) ^ [_838998, _839000, _839002, _839004, _839006, _839008] : [-(c_Map_Oran(_839008, _839004, _839000) = c_Map_Oran(_839006, _839002, _838998)), _839008 = _839006, _839004 = _839002, _839000 = _838998], (20246 ^ _777864) ^ [_1126871, _1126873, _1126875, _1126877] : [class_Fields_Ofield__inverse__zero(_1126871), 20249 ^ _777864 : [(20250 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126871), _1126873), _1126875) = _1126877, 20253 ^ _777864 : [(20260 ^ _777864) ^ [] : [_1126875 = c_Groups_Ozero__class_Ozero(_1126871), -(_1126877 = c_Groups_Ozero__class_Ozero(_1126871))], (20254 ^ _777864) ^ [] : [-(_1126875 = c_Groups_Ozero__class_Ozero(_1126871)), -(_1126873 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126871), _1126877), _1126875))]]], (20266 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1126871), _1126873), _1126875) = _1126877), 20269 ^ _777864 : [(20272 ^ _777864) ^ [] : [_1126873 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126871), _1126877), _1126875)], (20270 ^ _777864) ^ [] : [_1126875 = c_Groups_Ozero__class_Ozero(_1126871)]], 20273 ^ _777864 : [(20276 ^ _777864) ^ [] : [_1126877 = c_Groups_Ozero__class_Ozero(_1126871)], (20274 ^ _777864) ^ [] : [-(_1126875 = c_Groups_Ozero__class_Ozero(_1126871))]]]]], (42864 ^ _777864) ^ [_1611587, _1611589, _1611591, _1611593, _1611595] : [c_Finite__Set_Ofolding__one(_1611587, _1611589, _1611591), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611587), _1611593)), -(hBOOL(hAPP(hAPP(c_member(_1611587), _1611595), _1611593))), -(hAPP(_1611591, hAPP(hAPP(c_Set_Oinsert(_1611587), _1611595), _1611593)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611587, _1611587, _1611589), _1611595), _1611593))], (22408 ^ _777864) ^ [_1165231, _1165233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165231))), 22411 ^ _777864 : [(22418 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165233))), -(c_Divides_Odivmod__int(_1165231, _1165233) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1165231), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1165233))))], (22412 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165233)), -(c_Divides_Odivmod__int(_1165231, _1165233) = c_Divides_OnegDivAlg(_1165231, _1165233))]]], (50261 ^ _777864) ^ [_1789239, _1789241] : [class_Orderings_Olinorder(_1789239), 50264 ^ _777864 : [(50265 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1789239, _1789241), 50268 ^ _777864 : [(50269 ^ _777864) ^ [_1789410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789410), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789239)), _1789241))), 50272 ^ _777864 : [(50273 ^ _777864) ^ [_1789527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1789527), _1789410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789239), hAPP(hAPP(c_List_Onth(_1789239), _1789241), _1789527)), hAPP(hAPP(c_List_Onth(_1789239), _1789241), _1789410))))]]]]], (50279 ^ _777864) ^ [] : [50281 ^ _777864 : [(50287 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789239), hAPP(hAPP(c_List_Onth(_1789239), _1789241), 50283 ^ [_1789239, _1789241])), hAPP(hAPP(c_List_Onth(_1789239), _1789241), 50280 ^ [_1789239, _1789241])))], (50285 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50283 ^ [_1789239, _1789241]), 50280 ^ [_1789239, _1789241])))], (50282 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50280 ^ [_1789239, _1789241]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1789239)), _1789241))))]], -(c_List_Olinorder__class_Osorted(_1789239, _1789241))]]], (9296 ^ _777864) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23209 ^ _777864) ^ [_1181250, _1181252] : [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), _1181250))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1181252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1181250))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1181252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181250))), 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), _1181252))), c_COMBI(tc_Int_Oint))))], (33586 ^ _777864) ^ [_1396403, _1396405, _1396407, _1396409, _1396411] : [class_Complete__Lattice_Ocomplete__lattice(_1396403), class_Orderings_Olinorder(_1396403), 33593 ^ _777864 : [(33603 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396403), _1396405), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396407, _1396403), _1396409), _1396411)))), 33604 ^ _777864 : [(33605 ^ _777864) ^ [_1396751] : [hBOOL(hAPP(hAPP(c_member(_1396407), _1396751), _1396409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396403), _1396405), hAPP(_1396411, _1396751)))]]], (33594 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396403), _1396405), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1396407, _1396403), _1396409), _1396411))), 33598 ^ _777864 : [(33601 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396403), _1396405), hAPP(_1396411, 33597 ^ [_1396403, _1396405, _1396407, _1396409, _1396411]))))], (33599 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1396407), 33597 ^ [_1396403, _1396405, _1396407, _1396409, _1396411]), _1396409)))]]]]], (31665 ^ _777864) ^ [_1356491, _1356493, _1356495] : [class_Orderings_Olinorder(_1356491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356491), _1356493)), -(_1356493 = c_Orderings_Obot__class_Obot(tc_fun(_1356491, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356491), _1356495)), -(_1356495 = c_Orderings_Obot__class_Obot(tc_fun(_1356491, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1356491, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1356491, tc_HOL_Obool)), _1356493), _1356495)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1356491), c_Big__Operators_Olinorder__class_OMin(_1356491, _1356493)), c_Big__Operators_Olinorder__class_OMin(_1356491, _1356495)))], (51379 ^ _777864) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (42980 ^ _777864) ^ [_1613556, _1613558, _1613560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613556, _1613556)), _1613558), _1613560)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613556, _1613556)), _1613558), c_Transitive__Closure_Otrancl(_1613556, _1613560))))], (11623 ^ _777864) ^ [_971955, _971957, _971959, _971961] : [class_Rings_Oordered__semiring(_971955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971955), _971957), _971959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971955), c_Groups_Ozero__class_Ozero(_971955)), _971961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971955), _971961), _971957)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971955), _971961), _971959))))], (20380 ^ _777864) ^ [_1128793, _1128795, _1128797, _1128799] : [class_Fields_Ofield(_1128793), -(_1128795 = c_Groups_Ozero__class_Ozero(_1128793)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128793), _1128797), _1128795)), _1128799) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128793), hAPP(hAPP(c_Power_Opower__class_Opower(_1128793), _1128797), _1128799)), hAPP(hAPP(c_Power_Opower__class_Opower(_1128793), _1128795), _1128799)))], (19112 ^ _777864) ^ [_1106431] : [-(c_Int_Opred(c_Int_OBit0(_1106431)) = c_Int_OBit1(c_Int_Opred(_1106431)))], (41136 ^ _777864) ^ [_1571245, _1571247] : [-(hAPP(c_List_Olexn(_1571245, _1571247), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1571245), tc_List_Olist(_1571245)), tc_HOL_Obool)))], (35818 ^ _777864) ^ [_1443913, _1443915, _1443917, _1443919] : [class_Orderings_Olinorder(_1443913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443913), _1443915), _1443917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443913), _1443917), _1443919)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443913, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443913, _1443915), _1443917)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443913, _1443917), _1443919)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443913, _1443915), _1443919))], (47396 ^ _777864) ^ [_1725342, _1725344, _1725346] : [47397 ^ _777864 : [(47400 ^ _777864) ^ [] : [_1725346 = c_List_Olist_ONil(_1725342)], (47398 ^ _777864) ^ [] : [_1725344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1725342), _1725344), _1725346) = c_List_Olist_ONil(_1725342))], (12958 ^ _777864) ^ [_995327, _995329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995329)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _995327), _995329)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _995327)), hAPP(c_Int_Onat, _995329)))], (42878 ^ _777864) ^ [_1611809, _1611811, _1611813, _1611815] : [class_Complete__Lattice_Ocomplete__lattice(_1611809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611811), _1611813)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611811, _1611809), _1611813), _1611815) = hAPP(hAPP(c_Finite__Set_Ofold(_1611811, _1611809, hAPP(hAPP(c_COMBB(_1611809, tc_fun(_1611809, _1611809), _1611811), c_Lattices_Osemilattice__sup__class_Osup(_1611809)), _1611815)), c_Orderings_Obot__class_Obot(_1611809)), _1611813))], (32455 ^ _777864) ^ [_1371474, _1371476, _1371478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371474), _1371476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371474, tc_HOL_Obool)), _1371476), _1371478)), -(hAPP(c_Finite__Set_Ocard(_1371474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371474, tc_HOL_Obool)), _1371478), _1371476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1371474), _1371478)), hAPP(c_Finite__Set_Ocard(_1371474), _1371476)))], (19568 ^ _777864) ^ [_1114466, _1114468, _1114470] : [class_Rings_Olinordered__idom(_1114466), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1114466), c_Groups_Ozero__class_Ozero(_1114466)), hAPP(hAPP(c_Power_Opower__class_Opower(_1114466), _1114468), 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)))), _1114470)))))], (46009 ^ _777864) ^ [_1688325, _1688327, _1688329, _1688331, _1688333] : [hBOOL(hAPP(c_List_Odistinct(_1688325), hAPP(hAPP(c_List_Omap(tc_prod(_1688325, _1688327), _1688325), c_Product__Type_Ofst(_1688325, _1688327)), _1688329))), 46012 ^ _777864 : [(46019 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1688325, _1688327)), hAPP(hAPP(c_Product__Type_OPair(_1688325, _1688327), _1688331), _1688333)), hAPP(c_List_Oset(tc_prod(_1688325, _1688327)), _1688329))), -(hAPP(c_Map_Omap__of(_1688325, _1688327, _1688329), _1688331) = hAPP(c_Option_Ooption_OSome(_1688327), _1688333))], (46013 ^ _777864) ^ [] : [hAPP(c_Map_Omap__of(_1688325, _1688327, _1688329), _1688331) = hAPP(c_Option_Ooption_OSome(_1688327), _1688333), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1688325, _1688327)), hAPP(hAPP(c_Product__Type_OPair(_1688325, _1688327), _1688331), _1688333)), hAPP(c_List_Oset(tc_prod(_1688325, _1688327)), _1688329))))]]], (22430 ^ _777864) ^ [_1165591, _1165593] : [c_Code__Numeral_OSuc__code__numeral(_1165591) = c_Code__Numeral_OSuc__code__numeral(_1165593), -(_1165591 = _1165593)], (38238 ^ _777864) ^ [_1495370, _1495372, _1495374, _1495376] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1495370, _1495372, _1495374), _1495376)), _1495374 = c_Orderings_Obot__class_Obot(tc_fun(_1495370, tc_HOL_Obool))], (49355 ^ _777864) ^ [_1770914, _1770916, _1770918, _1770920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1770914), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770916)), _1770918))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1770914), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770916)), _1770920))), 49365 ^ _777864 : [(49368 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Onth(_1770916), _1770918), 49364 ^ [_1770914, _1770916, _1770918, _1770920]) = hAPP(hAPP(c_List_Onth(_1770916), _1770920), 49364 ^ [_1770914, _1770916, _1770918, _1770920])], (49366 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49364 ^ [_1770914, _1770916, _1770918, _1770920]), _1770914)))]], -(hAPP(hAPP(c_List_Otake(_1770916), _1770914), _1770918) = hAPP(hAPP(c_List_Otake(_1770916), _1770914), _1770920))], (37084 ^ _777864) ^ [_1471774, _1471776, _1471778, _1471780, _1471782, _1471784] : [hBOOL(hAPP(hAPP(c_member(_1471774), _1471776), _1471778)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1471774, tc_Option_Ooption(_1471780)), c_Map_Orestrict__map(_1471774, _1471780, _1471782, _1471778)), _1471776), _1471784) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1471774, tc_Option_Ooption(_1471780)), c_Map_Orestrict__map(_1471774, _1471780, _1471782, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471774, tc_HOL_Obool)), _1471778), hAPP(hAPP(c_Set_Oinsert(_1471774), _1471776), c_Orderings_Obot__class_Obot(tc_fun(_1471774, tc_HOL_Obool)))))), _1471776), _1471784))], (45850 ^ _777864) ^ [_1684715, _1684717, _1684719, _1684721, _1684723] : [hAPP(hAPP(c_List_Omap(_1684715, _1684717), _1684719), _1684721) = hAPP(hAPP(c_List_Omap(_1684715, _1684717), _1684719), _1684723), c_Fun_Oinj__on(_1684715, _1684717, _1684719, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1684715, tc_HOL_Obool)), hAPP(c_List_Oset(_1684715), _1684721)), hAPP(c_List_Oset(_1684715), _1684723))), -(_1684721 = _1684723)], (43933 ^ _777864) ^ [_1637668, _1637670, _1637672, _1637674, _1637676, _1637678] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637668, tc_fun(_1637670, tc_HOL_Obool)), _1637672), hAPP(hAPP(c_COMBC(_1637668, tc_fun(_1637674, tc_fun(_1637670, tc_HOL_Obool)), tc_fun(_1637670, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637674, tc_HOL_Obool), tc_fun(tc_fun(_1637674, tc_fun(_1637670, tc_HOL_Obool)), tc_fun(_1637670, tc_HOL_Obool)), _1637668), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637674, tc_fun(_1637670, tc_HOL_Obool))), _1637676)), _1637678)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637674, tc_fun(_1637670, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637668, tc_fun(_1637674, tc_HOL_Obool)), _1637672), _1637676)), _1637678))], (39041 ^ _777864) ^ [_1514270, _1514272, _1514274, _1514276, _1514278] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1514270, _1514272, hAPP(hAPP(c_Set_Oinsert(_1514270), _1514274), _1514276)), _1514278)), 39046 ^ _777864 : [(39051 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1514270), 39044 ^ [_1514270, _1514272, _1514274, _1514276, _1514278]), 39045 ^ [_1514270, _1514272, _1514274, _1514276, _1514278]))], (39049 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1514270, _1514270, _1514272, 39044 ^ [_1514270, _1514272, _1514274, _1514276, _1514278], 39045 ^ [_1514270, _1514272, _1514274, _1514276, _1514278]), _1514278)))], (39047 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1514270), _1514274), _1514276) = hAPP(hAPP(c_Set_Oinsert(_1514270), 39044 ^ [_1514270, _1514272, _1514274, _1514276, _1514278]), 39045 ^ [_1514270, _1514272, _1514274, _1514276, _1514278]))]]], (41206 ^ _777864) ^ [_1573199, _1573201, _1573203, _1573205] : [hBOOL(hAPP(hAPP(c_member(_1573201), _1573205), hAPP(c_Relation_ORange(_1573199, _1573201), _1573203))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1573199, _1573201, hAPP(hAPP(c_COMBC(_1573199, tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_fun(_1573201, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573201, tc_fun(tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_fun(_1573201, tc_HOL_Obool)), _1573199), c_COMBC(_1573201, tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573201, tc_prod(_1573199, _1573201)), tc_fun(_1573201, tc_fun(tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_HOL_Obool)), _1573199), hAPP(c_COMBB(tc_prod(_1573199, _1573201), tc_fun(tc_fun(tc_prod(_1573199, _1573201), tc_HOL_Obool), tc_HOL_Obool), _1573201), c_member(tc_prod(_1573199, _1573201)))), c_Product__Type_OPair(_1573199, _1573201)))), _1573203)), _1573205)))], (34575 ^ _777864) ^ [_1420126, _1420128, _1420130, _1420132] : [c_Fun_Oinj__on(_1420126, _1420128, _1420130, _1420132), -(hAPP(c_Finite__Set_Ocard(_1420128), hAPP(c_Set_Oimage(_1420126, _1420128, _1420130), _1420132)) = hAPP(c_Finite__Set_Ocard(_1420126), _1420132))], (6030 ^ _777864) ^ [_877105, _877107, _877109, _877111] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_877105, _877107), _877109, _877111, hAPP(hAPP(hAPP(c_Natural_Oupdate, _877109), _877105), hAPP(_877107, _877109))))], (2818 ^ _777864) ^ [_820007, _820009, _820011, _820013, _820015, _820017, _820019, _820021] : [-(c_Product__Type_Ocurry(_820021, _820017, _820013, _820009) = c_Product__Type_Ocurry(_820019, _820015, _820011, _820007)), _820021 = _820019, _820017 = _820015, _820013 = _820011, _820009 = _820007], (46084 ^ _777864) ^ [_1689871, _1689873, _1689875, _1689877] : [-(_1689871 = _1689873), 46087 ^ _777864 : [(46094 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1689875), _1689871), hAPP(c_List_Oset(_1689875), _1689877))), -(hBOOL(hAPP(hAPP(c_member(_1689875), _1689871), hAPP(c_List_Oset(_1689875), c_List_Oremove1(_1689875, _1689873, _1689877)))))], (46088 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1689875), _1689871), hAPP(c_List_Oset(_1689875), c_List_Oremove1(_1689875, _1689873, _1689877)))), -(hBOOL(hAPP(hAPP(c_member(_1689875), _1689871), hAPP(c_List_Oset(_1689875), _1689877))))]]], (1392 ^ _777864) ^ [_798032, _798034] : [-(class_Rings_Olinordered__comm__semiring__strict(_798032)), _798034 = _798032, class_Rings_Olinordered__comm__semiring__strict(_798034)], (17542 ^ _777864) ^ [_1080738, _1080740] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080738))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080738)), _1080740) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1080740))], (41431 ^ _777864) ^ [_1579188, _1579190] : [c_Wellfounded_Owf(_1579188, _1579190), -(c_Wellfounded_Oacyclic(_1579188, _1579190))], (49948 ^ _777864) ^ [_1783827, _1783829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1783827), _1783829)), -(c_List_Oupt(_1783829, _1783827) = c_List_Olist_ONil(tc_Nat_Onat))], (18170 ^ _777864) ^ [] : [-(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))))], (8930 ^ _777864) ^ [_926177, _926179, _926181] : [class_Groups_Oordered__ab__group__add(_926177), 8933 ^ _777864 : [(8940 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926177), _926181), hAPP(c_Groups_Ouminus__class_Ouminus(_926177), _926179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926177), _926179), hAPP(c_Groups_Ouminus__class_Ouminus(_926177), _926181))))], (8934 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926177), _926179), hAPP(c_Groups_Ouminus__class_Ouminus(_926177), _926181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926177), _926181), hAPP(c_Groups_Ouminus__class_Ouminus(_926177), _926179))))]]], (4940 ^ _777864) ^ [_853390, _853392, _853394, _853396, _853398, _853400, _853402, _853404, _853406, _853408] : [-(c_List_Ofoldr(_853408, _853404, _853400, _853396, _853392) = c_List_Ofoldr(_853406, _853402, _853398, _853394, _853390)), _853408 = _853406, _853404 = _853402, _853400 = _853398, _853396 = _853394, _853392 = _853390], (38228 ^ _777864) ^ [_1495212] : [c_Orderings_Otop__class_Otop(tc_fun(_1495212, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1495212, tc_HOL_Obool))], (29253 ^ _777864) ^ [_1307189, _1307191, _1307193] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307189), _1307191)), 29256 ^ _777864 : [(29263 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307189), _1307193)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307189, tc_HOL_Obool)), _1307193), _1307191))))], (29257 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307189, tc_HOL_Obool)), _1307193), _1307191))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307189), _1307193)))]]], (26109 ^ _777864) ^ [_1236538, _1236540, _1236542, _1236544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236538, tc_HOL_Obool)), _1236540), _1236542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236538, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1236538), _1236544), _1236540)), hAPP(hAPP(c_Set_Oinsert(_1236538), _1236544), _1236542))))], (13375 ^ _777864) ^ [_1002568, _1002570, _1002572, _1002574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002570), _1002572)), -(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), _1002572), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002574, _1002568))), _1002570)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1002572), _1002568))))], (17644 ^ _777864) ^ [_1082168] : [class_Int_Onumber__ring(_1082168), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082168), c_Groups_Oone__class_Oone(_1082168)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082168), c_Int_OMin))], (51085 ^ _777864) ^ [_1807828, _1807830] : [class_Lattices_Olattice(_1807828), -(class_Lattices_Olattice(tc_fun(_1807830, _1807828)))], (29856 ^ _777864) ^ [_1319991, _1319993, _1319995] : [29858 ^ _777864 : [(29864 ^ _777864) ^ [] : [-(29857 ^ [_1319991, _1319993, _1319995] = 29860 ^ [_1319991, _1319993, _1319995])], (29862 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319991), 29860 ^ [_1319991, _1319993, _1319995]), _1319995)))], (29859 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319991), 29857 ^ [_1319991, _1319993, _1319995]), _1319993)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319991, tc_HOL_Obool)), _1319993), _1319995) = c_Orderings_Obot__class_Obot(tc_fun(_1319991, tc_HOL_Obool)))], (14740 ^ _777864) ^ [_1027486, _1027488, _1027490] : [hBOOL(hAPP(_1027486, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027488, _1027490))), 14743 ^ _777864 : [(14750 ^ _777864) ^ [] : [-(_1027490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 14753 ^ _777864 : [(14754 ^ _777864) ^ [_1027734, _1027736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027734), _1027490)), _1027488 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027490), _1027736)), _1027734), -(hBOOL(hAPP(_1027486, _1027734)))]]], (14744 ^ _777864) ^ [] : [_1027490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1027486, _1027488)))]]], (45399 ^ _777864) ^ [_1674046, _1674048, _1674050] : [hBOOL(hAPP(hAPP(c_member(_1674046), _1674048), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674046, tc_HOL_Obool), _1674050))), 45403 ^ _777864 : [(45406 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674046, tc_HOL_Obool)), 45402 ^ [_1674046, _1674048, _1674050]), _1674050)))], (45404 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1674046), _1674048), 45402 ^ [_1674046, _1674048, _1674050])))]]], (7962 ^ _777864) ^ [_910457, _910459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910457), _910459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910457)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910459))))], (19810 ^ _777864) ^ [_1119288, _1119290, _1119292] : [class_Fields_Ofield__inverse__zero(_1119288), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1119288), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119288), _1119290), _1119292)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119288), _1119290), hAPP(c_Groups_Ouminus__class_Ouminus(_1119288), _1119292)))], (24509 ^ _777864) ^ [_1207564, _1207566, _1207568, _1207570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1207564), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1207566, _1207568, _1207564, _1207570) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1207566, 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(_1207566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1207568, _1207570)), 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(_1207566)))), 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(_1207566)))), 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(_1207566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1207566, 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(_1207566)))), 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(_1207566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1207566, _1207568, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1207564), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1207570))), 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(_1207566)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566)))), 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(_1207566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1207566, 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(_1207566)))), 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(_1207566)))), 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(_1207566))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566)))), 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(_1207566)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566))))), tc_prod(_1207566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1207566)), hAPP(hAPP(c_COMBB(_1207566, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1207566)))), tc_prod(_1207566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1207566)), c_Product__Type_Ofst(_1207566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (26625 ^ _777864) ^ [_1247422, _1247424] : [c_Option_Oset(_1247422, _1247424) = c_Orderings_Obot__class_Obot(tc_fun(_1247422, tc_HOL_Obool)), -(_1247424 = c_Option_Ooption_ONone(_1247422))], (34817 ^ _777864) ^ [_1424331, _1424333, _1424335, _1424337, _1424339] : [class_Orderings_Olinorder(_1424331), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424331, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424331, _1424333, _1424335)), c_SetInterval_Oord__class_OatLeastAtMost(_1424331, _1424337, _1424339)) = c_SetInterval_Oord__class_OatLeastAtMost(_1424331, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424331), _1424333), _1424337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424331), _1424335), _1424339)))], (44604 ^ _777864) ^ [_1655293, _1655295, _1655297] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1655293, tc_HOL_Obool)), _1655295), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1655293, tc_HOL_Obool), _1655297)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1655293, tc_HOL_Obool), tc_fun(_1655293, tc_HOL_Obool)), _1655297), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1655293, tc_HOL_Obool)), _1655295)))], (38200 ^ _777864) ^ [_1494757, _1494759] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494757, tc_HOL_Obool)), _1494759), c_Orderings_Otop__class_Otop(tc_fun(_1494757, tc_HOL_Obool)))))], (45427 ^ _777864) ^ [_1674715, _1674717, _1674719, _1674721, _1674723, _1674725] : [hAPP(c_Map_Omap__add(_1674715, _1674717, _1674719, _1674721), _1674723) = hAPP(c_Option_Ooption_OSome(_1674717), _1674725), -(hAPP(_1674721, _1674723) = hAPP(c_Option_Ooption_OSome(_1674717), _1674725)), 45434 ^ _777864 : [(45437 ^ _777864) ^ [] : [-(hAPP(_1674719, _1674723) = hAPP(c_Option_Ooption_OSome(_1674717), _1674725))], (45435 ^ _777864) ^ [] : [-(hAPP(_1674721, _1674723) = c_Option_Ooption_ONone(_1674717))]]], (6571 ^ _777864) ^ [_886389, _886391] : [class_Groups_Omonoid__add(_886389), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886389), c_Groups_Ozero__class_Ozero(_886389)), _886391) = _886391)], (34783 ^ _777864) ^ [_1423658, _1423660, _1423662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423658, tc_HOL_Obool)), _1423660), _1423662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1423658, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1423658, _1423660)), c_Predicate_OPowp(_1423658, _1423662))))], (43842 ^ _777864) ^ [_1635190, _1635192, _1635194, _1635196, _1635198] : [hBOOL(hAPP(hAPP(c_member(_1635190), _1635192), _1635194)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1635196, tc_HOL_Obool)), hAPP(_1635198, _1635192)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635190, tc_fun(_1635196, tc_HOL_Obool)), _1635194), _1635198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635190, tc_fun(_1635196, tc_HOL_Obool)), _1635194), _1635198))], (42595 ^ _777864) ^ [_1606160, _1606162, _1606164] : [class_Orderings_Olinorder(_1606160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1606160), _1606162)), -(hBOOL(hAPP(hAPP(c_member(_1606160), _1606164), _1606162))), -(c_Big__Operators_Olattice_OSup__fin(_1606160, c_Orderings_Oord__class_Omax(_1606160), hAPP(hAPP(c_Set_Oinsert(_1606160), _1606164), _1606162)) = hAPP(hAPP(c_Finite__Set_Ofold(_1606160, _1606160, c_Orderings_Oord__class_Omax(_1606160)), _1606164), _1606162))], (22881 ^ _777864) ^ [_1174355, _1174357] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1174355, _1174357) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1174355, _1174357)))], (28926 ^ _777864) ^ [_1300284, _1300286] : [c_Nat__Transfer_Onat__set(_1300284), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1300286), _1300284)), -(c_Nat__Transfer_Ois__nat(_1300286))], (26195 ^ _777864) ^ [_1238469, _1238471, _1238473] : [class_Orderings_Obot(_1238469), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1238471, _1238469)), _1238473) = c_Orderings_Obot__class_Obot(_1238469))], (28795 ^ _777864) ^ [_1298228, _1298230, _1298232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1298228, _1298228), tc_HOL_Obool)), _1298230), _1298232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298228, tc_HOL_Obool)), hAPP(c_Relation_OField(_1298228), _1298230)), hAPP(c_Relation_OField(_1298228), _1298232))))], (14346 ^ _777864) ^ [_1020385, _1020387, _1020389] : [class_Divides_Osemiring__div(_1020385), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020385), c_Divides_Odiv__class_Omod(_1020385, _1020387, _1020389)), _1020389) = c_Groups_Ozero__class_Ozero(_1020385))], (14139 ^ _777864) ^ [_1017074, _1017076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017074)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1017074), _1017076)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1017074)), hAPP(c_Int_Onat, _1017076)))], (8800 ^ _777864) ^ [_924220, _924222] : [class_Rings_Ocomm__ring__1(_924220), -(hAPP(c_Groups_Ouminus__class_Ouminus(_924220), _924222) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924220), hAPP(c_Groups_Ouminus__class_Ouminus(_924220), c_Groups_Oone__class_Oone(_924220))), _924222))], (11185 ^ _777864) ^ [_964067, _964069, _964071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964067), _964069)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964067), _964071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964069), _964071)))], (11132 ^ _777864) ^ [_963175, _963177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963175), _963177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963175), _963177)))], (29530 ^ _777864) ^ [_1313554, _1313556, _1313558, _1313560] : [hBOOL(hAPP(hAPP(c_member(_1313554), _1313556), _1313558)), hBOOL(hAPP(hAPP(c_member(_1313554), _1313556), _1313560)), -(hBOOL(hAPP(hAPP(c_member(_1313554), _1313556), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313554, tc_HOL_Obool)), _1313558), _1313560))))], (38208 ^ _777864) ^ [_1494890, _1494892] : [class_Lattices_Obounded__lattice__top(_1494890), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1494890), _1494892), c_Orderings_Otop__class_Otop(_1494890)) = c_Orderings_Otop__class_Otop(_1494890))], (30218 ^ _777864) ^ [_1328293, _1328295] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328293, tc_HOL_Obool)), _1328295), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328293, tc_HOL_Obool)), _1328295)) = c_Orderings_Obot__class_Obot(tc_fun(_1328293, tc_HOL_Obool)))], (43265 ^ _777864) ^ [_1620196, _1620198, _1620200] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1620196, _1620196), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620196, _1620196), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1620196, _1620198)), c_Transitive__Closure_Ortrancl(_1620196, _1620200))), c_Transitive__Closure_Ortrancl(_1620196, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1620196, _1620196), tc_HOL_Obool)), _1620198), _1620200)))))], (19732 ^ _777864) ^ [_1117584, _1117586, _1117588, _1117590] : [19734 ^ _777864 : [(19739 ^ _777864) ^ [] : [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(_1117588, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19733 ^ [_1117584, _1117586, _1117588, _1117590]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1117588, 19733 ^ [_1117584, _1117586, _1117588, _1117590])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19737 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19733 ^ [_1117584, _1117586, _1117588, _1117590]), _1117586)))], (19735 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117584), 19733 ^ [_1117584, _1117586, _1117588, _1117590])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1117584), _1117586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1117588, _1117584)), _1117590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117590), hAPP(_1117588, _1117586))), 19753 ^ _777864 : [(19758 ^ _777864) ^ [] : [-(hAPP(_1117588, 19752 ^ [_1117584, _1117586, _1117588, _1117590]) = _1117590)], (19756 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19752 ^ [_1117584, _1117586, _1117588, _1117590]), _1117586)))], (19754 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117584), 19752 ^ [_1117584, _1117586, _1117588, _1117590])))]]], (41703 ^ _777864) ^ [_1585719, _1585721, _1585723, _1585725] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585719, tc_Nat_Onat), _1585721), _1585723) = hAPP(c_Nat_OSuc, _1585725), 41707 ^ _777864 : [(41710 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1585721, 41706 ^ [_1585719, _1585721, _1585723, _1585725]))))], (41708 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585719), 41706 ^ [_1585719, _1585721, _1585723, _1585725]), _1585723)))]]], (13162 ^ _777864) ^ [_998963] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998963), _998963)))], (46657 ^ _777864) ^ [_1705951, _1705953, _1705955] : [hBOOL(hAPP(c_List_Odistinct(_1705951), hAPP(hAPP(c_List_Olist_OCons(_1705951), _1705953), _1705955))), 46660 ^ _777864 : [(46663 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1705951), _1705955)))], (46661 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1705951), _1705953), hAPP(c_List_Oset(_1705951), _1705955)))]]], (17952 ^ _777864) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (51377 ^ _777864) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (4596 ^ _777864) ^ [_848100, _848102, _848104, _848106, _848108, _848110] : [-(c_List_Opartition(_848110, _848106, _848102) = c_List_Opartition(_848108, _848104, _848100)), _848110 = _848108, _848106 = _848104, _848102 = _848100], (44029 ^ _777864) ^ [_1640484, _1640486, _1640488, _1640490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640484, _1640484)), hAPP(hAPP(c_Product__Type_OPair(_1640484, _1640484), _1640486), _1640488)), c_Transitive__Closure_Ortrancl(_1640484, hAPP(c_Relation_Oconverse(_1640484, _1640484), _1640490)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640484, _1640484)), hAPP(hAPP(c_Product__Type_OPair(_1640484, _1640484), _1640488), _1640486)), c_Transitive__Closure_Ortrancl(_1640484, _1640490))))], (46290 ^ _777864) ^ [_1695243, _1695245] : [hAPP(c_Finite__Set_Ocard(_1695243), hAPP(c_List_Oset(_1695243), _1695245)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695243)), _1695245), -(hBOOL(hAPP(c_List_Odistinct(_1695243), _1695245)))], (48145 ^ _777864) ^ [_1741955, _1741957] : [-(hAPP(hAPP(c_List_Oappend(_1741955), _1741957), c_List_Olist_ONil(_1741955)) = _1741957)], (14420 ^ _777864) ^ [_1021700, _1021702, _1021704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021700), 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)), _1021702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021702), _1021704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021700), _1021702)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021700), _1021704))))], (42978 ^ _777864) ^ [_1613487, _1613489] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613487, _1613487), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1613487, _1613489)), hAPP(hAPP(c_Product__Type_OSigma(_1613487, _1613487), hAPP(c_Relation_OField(_1613487), _1613489)), hAPP(c_COMBK(tc_fun(_1613487, tc_HOL_Obool), _1613487), hAPP(c_Relation_OField(_1613487), _1613489))))))], (4318 ^ _777864) ^ [_843923, _843925, _843927, _843929, _843931, _843933, _843935, _843937] : [-(c_Nat_Onat_Onat__case(_843937, _843933, _843929, _843925) = c_Nat_Onat_Onat__case(_843935, _843931, _843927, _843923)), _843937 = _843935, _843933 = _843931, _843929 = _843927, _843925 = _843923], (10930 ^ _777864) ^ [_959815] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959815), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17938 ^ _777864) ^ [_1087123, _1087125, _1087127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087123), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087125)), _1087127)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45292 ^ _777864) ^ [_1671674, _1671676] : [-(c_Wellfounded_Owf(_1671674, _1671676)), 45295 ^ _777864 : [(45298 ^ _777864) ^ [_1671894] : [hBOOL(hAPP(hAPP(c_member(_1671674), _1671894), 45293 ^ [_1671674, _1671676])), 45302 ^ _777864 : [(45305 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671674), 45301 ^ [_1671674, _1671676, _1671894]), 45293 ^ [_1671674, _1671676])))], (45303 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1671674, _1671674)), hAPP(hAPP(c_Product__Type_OPair(_1671674, _1671674), 45301 ^ [_1671674, _1671676, _1671894]), _1671894)), _1671676)))]]], (45296 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671674), 45294 ^ [_1671674, _1671676]), 45293 ^ [_1671674, _1671676])))]]], (30943 ^ _777864) ^ [_1343468, _1343470] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343470, _1343468) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343468), _1343470)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343470), _1343468)))], (42818 ^ _777864) ^ [_1610568, _1610570, _1610572] : [class_Orderings_Olinorder(_1610568), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610568), _1610570)), -(c_Big__Operators_Olinorder__class_OMin(_1610568, hAPP(hAPP(c_Set_Oinsert(_1610568), _1610572), _1610570)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610568, _1610568, c_Orderings_Oord__class_Omin(_1610568)), _1610572), _1610570))], (4358 ^ _777864) ^ [_844543, _844545, _844547, _844549] : [-(c_Finite__Set_Ofold1(_844549, _844545) = c_Finite__Set_Ofold1(_844547, _844543)), _844549 = _844547, _844545 = _844543], (48944 ^ _777864) ^ [_1761809, _1761811] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761809), _1761811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1761809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 48950 ^ _777864 : [(48953 ^ _777864) ^ [] : [48949 ^ [_1761809, _1761811] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48951 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 48949 ^ [_1761809, _1761811]), hAPP(c_List_Oset(tc_Nat_Onat), _1761811))))]]], (41291 ^ _777864) ^ [_1575077, _1575079] : [-(hAPP(c_Relation_ODomain(_1575077, _1575077), c_Relation_OId__on(_1575077, _1575079)) = _1575079)], (44794 ^ _777864) ^ [_1659735, _1659737, _1659739, _1659741] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1659735, tc_HOL_Obool), tc_fun(_1659737, tc_HOL_Obool)), _1659739), hAPP(hAPP(c_COMBC(tc_fun(_1659735, tc_HOL_Obool), tc_fun(_1659735, tc_fun(_1659737, tc_HOL_Obool)), tc_fun(_1659737, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659735, tc_fun(_1659737, tc_HOL_Obool))), _1659741)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659735, tc_fun(_1659737, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659735, tc_HOL_Obool), _1659739)), _1659741))], (47524 ^ _777864) ^ [_1728044, _1728046] : [-(c_List_Oremove1(_1728044, _1728046, c_List_Olist_ONil(_1728044)) = c_List_Olist_ONil(_1728044))], (6010 ^ _777864) ^ [_876748, _876750, _876752, _876754, _876756] : [c_Com_Ocom_OLocal(_876748, _876750, _876752) = c_Com_Ocom_OAss(_876754, _876756)], (146 ^ _777864) ^ [_779901, _779903, _779905, _779907, _779909, _779911, _779913, _779915] : [-(c_Orderings_Oorder_Ostrict__mono(_779913, _779909, _779905, _779901)), c_Orderings_Oorder_Ostrict__mono(_779915, _779911, _779907, _779903), _779915 = _779913, _779911 = _779909, _779907 = _779905, _779903 = _779901], (32131 ^ _777864) ^ [_1364962, _1364964, _1364966] : [class_Orderings_Olinorder(_1364962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364962), _1364964)), 32138 ^ _777864 : [(32145 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364962, tc_HOL_Obool)), _1364964), hAPP(hAPP(c_Set_Oinsert(_1364962), _1364966), c_Orderings_Obot__class_Obot(tc_fun(_1364962, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364962, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1364962, c_Orderings_Oord__class_Omax(_1364962), hAPP(hAPP(c_Set_Oinsert(_1364962), _1364966), _1364964)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364962), _1364966), c_Big__Operators_Olattice_OSup__fin(_1364962, c_Orderings_Oord__class_Omax(_1364962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364962, tc_HOL_Obool)), _1364964), hAPP(hAPP(c_Set_Oinsert(_1364962), _1364966), c_Orderings_Obot__class_Obot(tc_fun(_1364962, tc_HOL_Obool)))))))], (32139 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364962, tc_HOL_Obool)), _1364964), hAPP(hAPP(c_Set_Oinsert(_1364962), _1364966), c_Orderings_Obot__class_Obot(tc_fun(_1364962, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1364962, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1364962, c_Orderings_Oord__class_Omax(_1364962), hAPP(hAPP(c_Set_Oinsert(_1364962), _1364966), _1364964)) = _1364966)]]], (51373 ^ _777864) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (23787 ^ _777864) ^ [_1193455, _1193457] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1193455)), hAPP(c_Nat_OSuc, _1193457)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1193455))), 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, _1193457))), 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)), _1193457)))))], (19244 ^ _777864) ^ [_1108772, _1108774] : [class_Int_Onumber__ring(_1108772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108772), _1108774), hAPP(c_Int_Onumber__class_Onumber__of(_1108772), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108772), _1108774), _1108774))], (48300 ^ _777864) ^ [_1745961, _1745963, _1745965, _1745967, _1745969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745961), tc_List_Olist(_1745961))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745961), tc_List_Olist(_1745961)), _1745963), _1745965)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1745961), c_List_Olistrel1(_1745961, _1745967)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1745961), tc_List_Olist(_1745961))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1745961), tc_List_Olist(_1745961)), hAPP(hAPP(c_List_Olist_OCons(_1745961), _1745969), _1745963)), hAPP(hAPP(c_List_Olist_OCons(_1745961), _1745969), _1745965))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1745961), c_List_Olistrel1(_1745961, _1745967)))))], (12800 ^ _777864) ^ [_992737, _992739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992737), _992739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992739), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (28715 ^ _777864) ^ [_1296256, _1296258] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1296256), _1296258)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296256)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296258))))], (43629 ^ _777864) ^ [_1628383, _1628385, _1628387, _1628389, _1628391] : [_1628383 = c_Orderings_Obot__class_Obot(tc_fun(_1628385, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628387, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628385, tc_fun(_1628387, tc_HOL_Obool)), _1628383), _1628389)), _1628391) = _1628391)], (51139 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (24315 ^ _777864) ^ [_1203675, _1203677] : [-(c_Nitpick_Oint__lcm(_1203675, _1203677) = 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), _1203675)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1203677)))))], (34117 ^ _777864) ^ [_1410034, _1410036, _1410038, _1410040, _1410042, _1410044] : [class_Groups_Oab__semigroup__mult(_1410034), hBOOL(hAPP(c_Finite__Set_Ofinite(_1410036), _1410038)), -(hBOOL(hAPP(hAPP(c_member(_1410036), _1410040), _1410038))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1410034, _1410036, c_Groups_Otimes__class_Otimes(_1410034)), _1410042), _1410044), hAPP(hAPP(c_Set_Oinsert(_1410036), _1410040), _1410038)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410034), hAPP(_1410042, _1410040)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1410034, _1410036, c_Groups_Otimes__class_Otimes(_1410034)), _1410042), _1410044), _1410038)))], (19628 ^ _777864) ^ [_1115753, _1115755, _1115757] : [class_Rings_Olinordered__idom(_1115753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115753), c_Groups_Ozero__class_Ozero(_1115753)), hAPP(hAPP(c_Power_Opower__class_Opower(_1115753), _1115755), 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)))), _1115757))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1115753), c_Groups_Ozero__class_Ozero(_1115753)), _1115755)))], (39721 ^ _777864) ^ [_1530009, _1530011, _1530013, _1530015, _1530017, _1530019] : [class_Groups_Ocomm__monoid__add(_1530009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530011), _1530013)), 39731 ^ _777864 : [(39734 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530015), hAPP(_1530017, 39730 ^ [_1530009, _1530011, _1530013, _1530015, _1530017, _1530019])))], (39732 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530011), 39730 ^ [_1530009, _1530011, _1530013, _1530015, _1530017, _1530019]), _1530013)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530011, _1530009), hAPP(hAPP(c_COMBS(_1530011, tc_fun(_1530015, tc_HOL_Obool), _1530009), hAPP(hAPP(c_COMBB(tc_fun(_1530015, _1530009), tc_fun(tc_fun(_1530015, tc_HOL_Obool), _1530009), _1530011), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530015, _1530009)), _1530019)), _1530017)), _1530013) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1530011, _1530015), _1530009), hAPP(c_Product__Type_Oprod_Oprod__case(_1530011, _1530015, _1530009), _1530019)), hAPP(hAPP(c_Product__Type_OSigma(_1530011, _1530015), _1530013), _1530017)))], (45687 ^ _777864) ^ [_1680686, _1680688, _1680690] : [c_Fun_Oinj__on(tc_List_Olist(_1680686), tc_List_Olist(_1680688), hAPP(c_List_Omap(_1680686, _1680688), _1680690), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680686), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1680686, _1680688, _1680690, c_Orderings_Otop__class_Otop(tc_fun(_1680686, tc_HOL_Obool))))], (18906 ^ _777864) ^ [_1102887, _1102889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102887), _1102889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1102887)), c_Int_OBit0(_1102889))))], (27394 ^ _777864) ^ [_1265032, _1265034] : [class_Rings_Osemiring__1(_1265032), -(hBOOL(hAPP(hAPP(c_member(_1265032), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1265032), _1265034)), c_Nat_Osemiring__1__class_ONats(_1265032))))], (19338 ^ _777864) ^ [_1110351, _1110353] : [class_Rings_Olinordered__idom(_1110351), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1110351), hAPP(c_Groups_Oabs__class_Oabs(_1110351), _1110353)), 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(_1110351), _1110353), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44411 ^ _777864) ^ [_1650505, _1650507, _1650509] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650505, _1650505), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1650507)), _1650509) = hAPP(hAPP(c_Relation_Orel__comp(_1650505, _1650505, _1650505), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650505, _1650505), tc_HOL_Obool), _1650507), _1650509)), _1650509))], (28252 ^ _777864) ^ [_1282045, _1282047, _1282049, _1282051] : [hBOOL(hAPP(_1282045, _1282047)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282049, tc_HOL_Obool)), _1282045), _1282051), _1282047)))], (44220 ^ _777864) ^ [_1645852, _1645854] : [-(c_Transitive__Closure_Ortrancl(_1645852, _1645854) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645852, _1645852), tc_HOL_Obool)), c_Relation_OId(_1645852)), hAPP(hAPP(c_Relation_Orel__comp(_1645852, _1645852, _1645852), c_Transitive__Closure_Ortrancl(_1645852, _1645854)), _1645854)))], (41764 ^ _777864) ^ [_1587292, _1587294, _1587296, _1587298, _1587300, _1587302] : [-(hAPP(hAPP(c_Fun_Ocomp(_1587292, _1587294, _1587296, _1587298), _1587300), _1587302) = hAPP(_1587298, hAPP(_1587300, _1587302)))], (32311 ^ _777864) ^ [_1368774] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1368774) = 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)), _1368774)))], (35874 ^ _777864) ^ [_1445099, _1445101, _1445103, _1445105] : [class_Orderings_Oorder(_1445099), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445099, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445099, _1445101), _1445103)), c_SetInterval_Oord__class_OatLeastAtMost(_1445099, _1445103, _1445105)) = c_Orderings_Obot__class_Obot(tc_fun(_1445099, tc_HOL_Obool)))], (40978 ^ _777864) ^ [_1567606, _1567608] : [hBOOL(hAPP(hAPP(c_member(_1567606), 40979 ^ [_1567606, _1567608]), c_Wellfounded_Oacc(_1567606, _1567608))), -(c_Wellfounded_Owf(_1567606, _1567608))], (34517 ^ _777864) ^ [_1418767] : [-(hAPP(c_Set_OPow(_1418767), c_Orderings_Obot__class_Obot(tc_fun(_1418767, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1418767, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1418767, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1418767, tc_HOL_Obool), tc_HOL_Obool))))], (28318 ^ _777864) ^ [_1283671, _1283673, _1283675, _1283677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283671, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283671, tc_HOL_Obool)), _1283673), _1283675)), _1283677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283671, tc_HOL_Obool)), _1283673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283671, tc_HOL_Obool)), _1283675), _1283677))))], (28552 ^ _777864) ^ [_1291652, _1291654, _1291656] : [-(hAPP(c_Set_Oimage(_1291652, _1291654, _1291656), c_Orderings_Obot__class_Obot(tc_fun(_1291652, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1291654, tc_HOL_Obool)))], (33642 ^ _777864) ^ [_1397557, _1397559, _1397561, _1397563] : [c_Orderings_Obot__class_Obot(tc_fun(_1397557, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397559, tc_fun(_1397557, tc_HOL_Obool)), _1397561), _1397563), 33645 ^ _777864 : [(33646 ^ _777864) ^ [_1397673] : [hBOOL(hAPP(hAPP(c_member(_1397559), _1397673), _1397561)), -(hAPP(_1397563, _1397673) = c_Orderings_Obot__class_Obot(tc_fun(_1397557, tc_HOL_Obool)))]]], (17870 ^ _777864) ^ [_1085728, _1085730, _1085732] : [17872 ^ _777864 : [(17875 ^ _777864) ^ [] : [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(_1085730, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17871 ^ [_1085728, _1085730, _1085732]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1085730, 17871 ^ [_1085728, _1085730, _1085732])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17873 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17871 ^ [_1085728, _1085730, _1085732]), _1085728)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1085730, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1085732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085732), hAPP(_1085730, _1085728))), 17885 ^ _777864 : [(17888 ^ _777864) ^ [] : [-(hAPP(_1085730, 17884 ^ [_1085728, _1085730, _1085732]) = _1085732)], (17886 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17884 ^ [_1085728, _1085730, _1085732]), _1085728)))]]], (51131 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (50482 ^ _777864) ^ [_1794672, _1794674] : [-(c_List_Oconcat(_1794672, _1794674) = hAPP(c_List_Ofoldl(tc_List_Olist(_1794672), tc_List_Olist(_1794672), c_List_Oappend(_1794672), c_List_Olist_ONil(_1794672)), _1794674))], (38540 ^ _777864) ^ [] : [-(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))))], (20100 ^ _777864) ^ [_1124392, _1124394, _1124396] : [class_Fields_Olinordered__field__inverse__zero(_1124392), 20103 ^ _777864 : [(20118 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124392), _1124394), _1124396)))), 20119 ^ _777864 : [(20126 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), _1124394), c_Groups_Ozero__class_Ozero(_1124392))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), _1124396), c_Groups_Ozero__class_Ozero(_1124392)))], (20120 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), _1124394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), _1124396))]]], (20104 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124392), _1124394), _1124396))), 20109 ^ _777864 : [(20112 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), _1124396)))], (20110 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), c_Groups_Ozero__class_Ozero(_1124392)), _1124394)))]], 20113 ^ _777864 : [(20116 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), _1124396), c_Groups_Ozero__class_Ozero(_1124392))))], (20114 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124392), _1124394), c_Groups_Ozero__class_Ozero(_1124392))))]]]]], (22382 ^ _777864) ^ [_1164861, _1164863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164861)), 22385 ^ _777864 : [(22392 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164863))), 22395 ^ _777864 : [(22402 ^ _777864) ^ [] : [-(_1164861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1164861, _1164863) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164861), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1164863))))], (22396 ^ _777864) ^ [] : [_1164861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1164861, _1164863) = 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)))]]], (22386 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164863)), -(c_Divides_Odivmod__int(_1164861, _1164863) = c_Divides_OposDivAlg(_1164861, _1164863))]]], (26181 ^ _777864) ^ [_1238260, _1238262, _1238264, _1238266] : [c_Hoare__Mirabelle_Ohoare__derivs(_1238260, _1238262, _1238264), c_Hoare__Mirabelle_Ohoare__derivs(_1238260, _1238266, _1238262), -(c_Hoare__Mirabelle_Ohoare__derivs(_1238260, _1238266, _1238264))], (38840 ^ _777864) ^ [_1509648, _1509650, _1509652, _1509654] : [-(hAPP(c_Set_Ovimage(_1509648, _1509650, _1509652), _1509654) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509650, tc_fun(_1509648, tc_HOL_Obool)), _1509654), hAPP(hAPP(c_COMBB(tc_fun(_1509650, tc_HOL_Obool), tc_fun(_1509648, tc_HOL_Obool), _1509650), c_Set_Ovimage(_1509648, _1509650, _1509652)), hAPP(hAPP(c_COMBC(_1509650, tc_fun(_1509650, tc_HOL_Obool), tc_fun(_1509650, tc_HOL_Obool)), c_Set_Oinsert(_1509650)), c_Orderings_Obot__class_Obot(tc_fun(_1509650, tc_HOL_Obool))))))], (48073 ^ _777864) ^ [_1740690, _1740692, _1740694] : [_1740690 = _1740692, -(_1740690 = hAPP(hAPP(c_List_Oappend(_1740694), c_List_Olist_ONil(_1740694)), _1740692))], (19046 ^ _777864) ^ [_1105243, _1105245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105243), _1105245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105243)), c_Int_OBit0(_1105245))))], (27740 ^ _777864) ^ [_1271973, _1271975, _1271977, _1271979] : [27741 ^ _777864 : [(27744 ^ _777864) ^ [] : [hBOOL(hAPP(_1271977, _1271975))], (27742 ^ _777864) ^ [] : [hBOOL(hAPP(_1271973, _1271975))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271979, tc_HOL_Obool)), _1271977), _1271973), _1271975)))], (25257 ^ _777864) ^ [_1220873, _1220875] : [_1220873 = _1220875, 25260 ^ _777864 : [(25263 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220875), _1220873)))], (25261 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220873), _1220875)))]]], (24093 ^ _777864) ^ [_1199156] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1199156), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1199156)], (14636 ^ _777864) ^ [_1025325, _1025327, _1025329] : [class_Divides_Osemiring__div(_1025325), -(_1025327 = c_Groups_Ozero__class_Ozero(_1025325)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025325), _1025327), _1025329)), _1025327) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025325), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025325), _1025329), _1025327)), c_Groups_Oone__class_Oone(_1025325)))], (13443 ^ _777864) ^ [_1003830, _1003832, _1003834, _1003836] : [class_Divides_Osemiring__div(_1003830), -(c_Divides_Odiv__class_Omod(_1003830, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003830), _1003832), c_Divides_Odiv__class_Omod(_1003830, _1003834, _1003836)), _1003836) = c_Divides_Odiv__class_Omod(_1003830, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003830), _1003832), _1003834), _1003836))], (29576 ^ _777864) ^ [_1314475, _1314477, _1314479] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314475, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314475), _1314477), _1314479), -(_1314477 = c_Orderings_Obot__class_Obot(tc_fun(_1314475, tc_HOL_Obool)))], (43575 ^ _777864) ^ [_1627359, _1627361] : [-(c_Transitive__Closure_Ortrancl(_1627359, hAPP(c_Relation_Oconverse(_1627359, _1627359), _1627361)) = hAPP(c_Relation_Oconverse(_1627359, _1627359), c_Transitive__Closure_Ortrancl(_1627359, _1627361)))], (47188 ^ _777864) ^ [_1719771, _1719773, _1719775, _1719777] : [-(_1719771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1719773), hAPP(hAPP(c_List_Olist_OCons(_1719773), _1719775), _1719777)), _1719771) = hAPP(hAPP(c_List_Onth(_1719773), _1719777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1719771), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24785 ^ _777864) ^ [_1213030, _1213032, _1213034, _1213036] : [class_Rings_Ocomm__semiring__1(_1213030), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213030), _1213032), _1213034)), _1213036)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213030), _1213032), _1213036)))], (8472 ^ _777864) ^ [_918249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _918249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _918249))))], (17156 ^ _777864) ^ [_1073775, _1073777, _1073779, _1073781] : [class_Rings_Olinordered__semidom(_1073775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073775), _1073777), _1073779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073775), c_Groups_Ozero__class_Ozero(_1073775)), _1073777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073775), hAPP(hAPP(c_Power_Opower__class_Opower(_1073775), _1073777), _1073781)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073775), _1073779), _1073781))))], (46921 ^ _777864) ^ [_1713459, _1713461, _1713463, _1713465, _1713467] : [class_Orderings_Olinorder(_1713459), -(hBOOL(hAPP(hAPP(c_member(_1713459), hAPP(_1713461, _1713463)), hAPP(c_Set_Oimage(_1713465, _1713459, _1713461), hAPP(c_List_Oset(_1713465), _1713467))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1713465, _1713459, _1713461, _1713463, _1713467) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1713465, _1713459, _1713461), _1713463), _1713467))], (43309 ^ _777864) ^ [_1621315, _1621317] : [-(c_Transitive__Closure_Ortrancl(_1621315, c_Transitive__Closure_Otrancl(_1621315, _1621317)) = c_Transitive__Closure_Ortrancl(_1621315, _1621317))], (15552 ^ _777864) ^ [_1042625, _1042627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042625), _1042627)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042627), _1042625)), _1042625) = _1042627)], (38336 ^ _777864) ^ [_1497281, _1497283, _1497285, _1497287] : [hBOOL(hAPP(hAPP(c_member(_1497283), _1497287), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497281, tc_fun(_1497283, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1497281, tc_HOL_Obool))), _1497285))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497281, tc_fun(_1497283, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1497281, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1497283, tc_HOL_Obool), tc_fun(_1497283, tc_HOL_Obool), _1497281), hAPP(c_COMBC(_1497283, tc_fun(_1497283, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497283))), _1497285)), _1497287)))], (38902 ^ _777864) ^ [_1511316, _1511318, _1511320, _1511322, _1511324, _1511326] : [c_Typedef_Otype__definition(_1511316, _1511318, _1511320, _1511322, _1511324), -(hAPP(_1511322, hAPP(_1511320, _1511326)) = _1511326)], (6046 ^ _777864) ^ [_877426, _877428, _877430] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_877426, _877428, _877430)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27604 ^ _777864) ^ [_1269373, _1269375, _1269377, _1269379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1269373), _1269375)), -(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), _1269373), _1269377)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1269375), _1269379))), c_FunDef_Opair__less)))], (10448 ^ _777864) ^ [_952356, _952358, _952360] : [10449 ^ _777864 : [(10452 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952356), _952360))], (10450 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952358)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952356), _952358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952360), _952358))))], (6811 ^ _777864) ^ [_890027, _890029, _890031] : [c_Com_Ocom_OLocal(_890027, _890029, _890031) = c_Com_Ocom_OSKIP], (27279 ^ _777864) ^ [_1262662, _1262664] : [c_Nitpick_Orefl_H(_1262662, _1262664), 27282 ^ _777864 : [(27283 ^ _777864) ^ [_1262740] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1262662, _1262662)), hAPP(hAPP(c_Product__Type_OPair(_1262662, _1262662), _1262740), _1262740)), _1262664)))]]], (51509 ^ _777864) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (9594 ^ _777864) ^ [_938159, _938161, _938163, _938165, _938167, _938169] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_938159), -(_938161 = c_Groups_Ozero__class_Ozero(_938159)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938159), _938163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938159), _938161), _938167)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938159), _938165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938159), _938161), _938169)), _938163 = _938165, -(_938167 = _938169)], (37481 ^ _777864) ^ [_1480882, _1480884, _1480886, _1480888, _1480890] : [class_Groups_Ocomm__monoid__add(_1480882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480884), _1480886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480884, tc_HOL_Obool)), _1480888), _1480886)), 37495 ^ _777864 : [(37498 ^ _777864) ^ [] : [hAPP(_1480890, 37494 ^ [_1480882, _1480884, _1480886, _1480888, _1480890]) = c_Groups_Ozero__class_Ozero(_1480882)], (37496 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480884), 37494 ^ [_1480882, _1480884, _1480886, _1480888, _1480890]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1480884, tc_HOL_Obool)), _1480886), _1480888))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480884, _1480882), _1480890), _1480886) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480884, _1480882), _1480890), _1480888))], (39574 ^ _777864) ^ [_1526919, _1526921, _1526923] : [class_Orderings_Olinorder(_1526919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526919), _1526921)), -(_1526921 = c_Orderings_Obot__class_Obot(tc_fun(_1526919, tc_HOL_Obool))), 39585 ^ _777864 : [(39595 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1526919), hAPP(c_Finite__Set_Ofold1(_1526919, c_Orderings_Oord__class_Omin(_1526919)), _1526921)), _1526923))), 39596 ^ _777864 : [(39597 ^ _777864) ^ [_1527308] : [hBOOL(hAPP(hAPP(c_member(_1526919), _1527308), _1526921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1526919), _1527308), _1526923))]]], (39586 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1526919), hAPP(c_Finite__Set_Ofold1(_1526919, c_Orderings_Oord__class_Omin(_1526919)), _1526921)), _1526923)), 39590 ^ _777864 : [(39593 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1526919), 39589 ^ [_1526919, _1526921, _1526923]), _1526923)))], (39591 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526919), 39589 ^ [_1526919, _1526921, _1526923]), _1526921)))]]]]], (13573 ^ _777864) ^ [_1006555, _1006557] : [class_Divides_Osemiring__div(_1006555), -(c_Divides_Odiv__class_Omod(_1006555, _1006557, c_Groups_Oone__class_Oone(_1006555)) = c_Groups_Ozero__class_Ozero(_1006555))], (5452 ^ _777864) ^ [_861258, _861260, _861262, _861264, _861266, _861268] : [-(c_COMBS(_861268, _861264, _861260) = c_COMBS(_861266, _861262, _861258)), _861268 = _861266, _861264 = _861262, _861260 = _861258], (58 ^ _777864) ^ [_778635, _778637] : [-(class_Rings_Odivision__ring(_778635)), _778637 = _778635, class_Rings_Odivision__ring(_778637)], (10704 ^ _777864) ^ [_956133, _956135, _956137] : [class_Orderings_Opreorder(_956133), 10707 ^ _777864 : [(10716 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956133), _956135), _956137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956133), _956135), _956137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956133), _956137), _956135)))], (10708 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956133), _956135), _956137)), 10711 ^ _777864 : [(10714 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956133), _956137), _956135))], (10712 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956133), _956135), _956137)))]]]]], (908 ^ _777864) ^ [_791842, _791844, _791846, _791848, _791850, _791852, _791854, _791856] : [-(c_Fun_Oinj__on(_791854, _791850, _791846, _791842)), c_Fun_Oinj__on(_791856, _791852, _791848, _791844), _791856 = _791854, _791852 = _791850, _791848 = _791846, _791844 = _791842], (21846 ^ _777864) ^ [] : [-(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))], (18632 ^ _777864) ^ [_1098185] : [class_Int_Onumber__ring(_1098185), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098185), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1098185))], (51525 ^ _777864) ^ [_1812133, _1812135, _1812137, _1812139, _1812141, _1812143] : [-(hAPP(hAPP(hAPP(c_COMBB(_1812133, _1812135, _1812137), _1812139), _1812141), _1812143) = hAPP(_1812139, hAPP(_1812141, _1812143)))], (44427 ^ _777864) ^ [_1650898, _1650900, _1650902] : [c_Relation_Ototal__on(_1650898, _1650900, _1650902), -(c_Relation_Ototal__on(_1650898, _1650900, hAPP(c_Relation_Oconverse(_1650898, _1650898), _1650902)))], (3924 ^ _777864) ^ [_837616, _837618, _837620, _837622, _837624, _837626] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_837626, _837622, _837618) = c_Smallcheck_Ofull__small__class_Ofull__small(_837624, _837620, _837616)), _837626 = _837624, _837622 = _837620, _837618 = _837616], (5641 ^ _777864) ^ [_868691, _868693, _868695, _868697, _868699] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_868691), hAPP(hAPP(hAPP(c_Natural_Oupdate, _868693), c_Com_Ovname_OLoc(_868695)), hAPP(_868697, _868693))), _868699)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_868695, _868697, _868691)), _868693), hAPP(hAPP(hAPP(c_Natural_Oupdate, _868699), c_Com_Ovname_OLoc(_868695)), hAPP(hAPP(c_Natural_Ogetlocs, _868693), _868695)))))], (45515 ^ _777864) ^ [_1676406, _1676408, _1676410, _1676412] : [-(c_Map_Odom(_1676406, _1676408, c_Map_Omap__add(_1676406, _1676408, _1676410, _1676412)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1676406, tc_HOL_Obool)), c_Map_Odom(_1676406, _1676408, _1676412)), c_Map_Odom(_1676406, _1676408, _1676410)))], (16964 ^ _777864) ^ [_1070393, _1070395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070393)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070393), _1070395)))], (31237 ^ _777864) ^ [_1348480, _1348482, _1348484] : [class_Lattices_Olattice(_1348480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348480), _1348482)), -(hBOOL(hAPP(hAPP(c_member(_1348480), _1348484), _1348482))), -(_1348482 = c_Orderings_Obot__class_Obot(tc_fun(_1348480, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1348480, hAPP(hAPP(c_Set_Oinsert(_1348480), _1348484), _1348482)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1348480), _1348484), c_Big__Operators_Olattice__class_OSup__fin(_1348480, _1348482)))], (37689 ^ _777864) ^ [_1484837, _1484839] : [class_Orderings_Olinorder(_1484837), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484837, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1484837), _1484839)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1484837), _1484839))], (37865 ^ _777864) ^ [_1488264] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1488264)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1488264)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1488264)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (25675 ^ _777864) ^ [_1228343] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228343), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1228343 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25069 ^ _777864) ^ [_1217849, _1217851, _1217853] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217849), _1217851)), 25080 ^ _777864 : [(25083 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217853), _1217849))], (25081 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217849), _1217853)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217851), _1217853)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217853), _1217851)))], (47470 ^ _777864) ^ [_1726980, _1726982, _1726984, _1726986] : [-(hAPP(hAPP(c_List_Olist__update(_1726980, hAPP(hAPP(c_List_Olist_OCons(_1726980), _1726982), _1726984)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1726986) = hAPP(hAPP(c_List_Olist_OCons(_1726980), _1726986), _1726984))], (18472 ^ _777864) ^ [_1095606] : [c_Int_OBit1(_1095606) = c_Int_OPls], (3896 ^ _777864) ^ [_837174, _837176, _837178, _837180, _837182, _837184] : [-(c_Relation_Orel__comp(_837184, _837180, _837176) = c_Relation_Orel__comp(_837182, _837178, _837174)), _837184 = _837182, _837180 = _837178, _837176 = _837174], (51307 ^ _777864) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (51135 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (16544 ^ _777864) ^ [_1062068, _1062070, _1062072] : [class_Rings_Ocomm__semiring__1(_1062068), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062068), _1062070), hAPP(c_Nat_OSuc, _1062072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062068), _1062070), hAPP(hAPP(c_Power_Opower__class_Opower(_1062068), _1062070), _1062072)))], (24503 ^ _777864) ^ [_1207433, _1207435, _1207437, _1207439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1207433), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1207435, _1207437, _1207433, _1207439) = 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(_1207435)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1207435)))], (46831 ^ _777864) ^ [_1711289, _1711291, _1711293] : [class_Groups_Omonoid__add(_1711289), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711289), hAPP(hAPP(c_List_Omap(_1711291, _1711289), hAPP(c_COMBK(_1711289, _1711291), c_Groups_Ozero__class_Ozero(_1711289))), _1711293)) = c_Groups_Ozero__class_Ozero(_1711289))], (2404 ^ _777864) ^ [_813306, _813308, _813310, _813312] : [-(c_HOL_OLet(_813312, _813308) = c_HOL_OLet(_813310, _813306)), _813312 = _813310, _813308 = _813306], (35880 ^ _777864) ^ [_1445230, _1445232, _1445234, _1445236, _1445238] : [class_Orderings_Olinorder(_1445230), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445230, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445230, _1445232), _1445234)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445230, _1445236), _1445238)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445230, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1445230), _1445232), _1445236)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1445230), _1445234), _1445238)))], (49414 ^ _777864) ^ [_1772027] : [-(c_List_Obutlast(_1772027, c_List_Olist_ONil(_1772027)) = c_List_Olist_ONil(_1772027))], (41348 ^ _777864) ^ [_1576355, _1576357, _1576359, _1576361] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1576355, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1576355, _1576357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576355, _1576357), tc_HOL_Obool)), _1576359), _1576361))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1576355, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1576355, _1576357), _1576359)), hAPP(c_Relation_ODomain(_1576355, _1576357), _1576361)))))], (32417 ^ _777864) ^ [_1370653, _1370655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1370653), _1370655))), 32420 ^ _777864 : [(32423 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370653), _1370655)))], (32421 ^ _777864) ^ [] : [_1370655 = c_Orderings_Obot__class_Obot(tc_fun(_1370653, tc_HOL_Obool))]]], (26133 ^ _777864) ^ [_1237311, _1237313, _1237315, _1237317] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237311, tc_HOL_Obool)), _1237313), hAPP(hAPP(c_Set_Oinsert(_1237311), _1237315), _1237317)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237311, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237311, tc_HOL_Obool)), _1237313), hAPP(hAPP(c_Set_Oinsert(_1237311), _1237315), c_Orderings_Obot__class_Obot(tc_fun(_1237311, tc_HOL_Obool))))), _1237317))], (9154 ^ _777864) ^ [_930146, _930148, _930150, _930152] : [class_Rings_Ocomm__semiring(_930146), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930146), _930148), _930150)), _930152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930146), _930148), _930152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930146), _930150), _930152)))], (2672 ^ _777864) ^ [_817622, _817624] : [_817624 = _817622, -(c_DSequence_Oempty(_817624) = c_DSequence_Oempty(_817622))], (28627 ^ _777864) ^ [_1293432, _1293434, _1293436, _1293438, _1293440] : [hBOOL(hAPP(hAPP(c_member(_1293432), _1293434), _1293436)), -(hAPP(c_Set_Oimage(_1293432, _1293438, hAPP(c_COMBK(_1293438, _1293432), _1293440)), _1293436) = hAPP(hAPP(c_Set_Oinsert(_1293438), _1293440), c_Orderings_Obot__class_Obot(tc_fun(_1293438, tc_HOL_Obool))))], (19696 ^ _777864) ^ [_1116975, _1116977] : [class_Fields_Olinordered__field__inverse__zero(_1116975), class_Int_Onumber__ring(_1116975), 19703 ^ _777864 : [(19710 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116975), c_Groups_Ozero__class_Ozero(_1116975)), _1116977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116975), c_Groups_Ozero__class_Ozero(_1116975)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116975), _1116977), hAPP(c_Int_Onumber__class_Onumber__of(_1116975), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19704 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116975), c_Groups_Ozero__class_Ozero(_1116975)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1116975), _1116977), hAPP(c_Int_Onumber__class_Onumber__of(_1116975), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1116975), c_Groups_Ozero__class_Ozero(_1116975)), _1116977)))]]], (18742 ^ _777864) ^ [_1099807, _1099809] : [class_Int_Onumber__ring(_1099807), class_Rings_Olinordered__idom(_1099807), 18749 ^ _777864 : [(18756 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099809), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099807), hAPP(c_Int_Onumber__class_Onumber__of(_1099807), _1099809)), c_Groups_Oone__class_Oone(_1099807))))], (18750 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099807), hAPP(c_Int_Onumber__class_Onumber__of(_1099807), _1099809)), c_Groups_Oone__class_Oone(_1099807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099809), c_Int_OBit1(c_Int_OPls))))]]], (51115 ^ _777864) ^ [_1808223, _1808225] : [class_Groups_Ouminus(_1808223), -(class_Groups_Ouminus(tc_fun(_1808225, _1808223)))], (50720 ^ _777864) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (39203 ^ _777864) ^ [_1518963, _1518965, _1518967, _1518969, _1518971] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518963, _1518965), _1518967), hAPP(hAPP(c_COMBS(_1518963, tc_fun(_1518965, tc_HOL_Obool), tc_fun(_1518965, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518965, tc_HOL_Obool), tc_fun(tc_fun(_1518965, tc_HOL_Obool), tc_fun(_1518965, tc_HOL_Obool)), _1518963), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518965, tc_HOL_Obool))), _1518969)), _1518971)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518963, _1518965), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518963, _1518965), _1518967), _1518969)), hAPP(hAPP(c_Product__Type_OSigma(_1518963, _1518965), _1518967), _1518971)))], (28098 ^ _777864) ^ [_1278517, _1278519, _1278521] : [class_Lattices_Osemilattice__sup(_1278517), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278517), _1278519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278517), _1278519), _1278521)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278517), _1278519), _1278521))], (43719 ^ _777864) ^ [_1630771, _1630773, _1630775, _1630777, _1630779] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630771, tc_fun(_1630773, tc_HOL_Obool)), _1630775), hAPP(hAPP(c_COMBB(tc_fun(_1630773, tc_HOL_Obool), tc_fun(_1630773, tc_HOL_Obool), _1630771), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630773, tc_HOL_Obool)), _1630777)), _1630779)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1630773, tc_HOL_Obool)), _1630777), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630771, tc_fun(_1630773, tc_HOL_Obool)), _1630775), _1630779)))], (19540 ^ _777864) ^ [_1113876, _1113878, _1113880] : [class_Rings_Olinordered__idom(_1113876), 19543 ^ _777864 : [(19544 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113876), c_Groups_Ozero__class_Ozero(_1113876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113876), hAPP(hAPP(c_Power_Opower__class_Opower(_1113876), _1113878), 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(_1113876), _1113880), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1113878 = c_Groups_Ozero__class_Ozero(_1113876), _1113880 = c_Groups_Ozero__class_Ozero(_1113876)], (19554 ^ _777864) ^ [] : [19555 ^ _777864 : [(19558 ^ _777864) ^ [] : [-(_1113880 = c_Groups_Ozero__class_Ozero(_1113876))], (19556 ^ _777864) ^ [] : [-(_1113878 = c_Groups_Ozero__class_Ozero(_1113876))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113876), c_Groups_Ozero__class_Ozero(_1113876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113876), hAPP(hAPP(c_Power_Opower__class_Opower(_1113876), _1113878), 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(_1113876), _1113880), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (40691 ^ _777864) ^ [_1559427, _1559429, _1559431, _1559433] : [-(c_Product__Type_Oapsnd(_1559427, _1559429, _1559431, _1559433) = c_Product__Type_Omap__pair(_1559431, _1559431, _1559427, _1559429, c_Fun_Oid(_1559431), _1559433))], (23717 ^ _777864) ^ [_1192093, _1192095, _1192097, _1192099, _1192101, _1192103] : [-(hAPP(c_Product__Type_Oapsnd(_1192093, _1192095, _1192097, _1192099), hAPP(hAPP(c_Product__Type_OPair(_1192097, _1192093), _1192101), _1192103)) = hAPP(hAPP(c_Product__Type_OPair(_1192097, _1192095), _1192101), hAPP(_1192099, _1192103)))], (44688 ^ _777864) ^ [_1657042, _1657044] : [class_Complete__Lattice_Ocomplete__lattice(_1657042), -(c_Complete__Lattice_OInf__class_OInf(_1657042, hAPP(hAPP(c_Set_Oinsert(_1657042), _1657044), c_Orderings_Obot__class_Obot(tc_fun(_1657042, tc_HOL_Obool)))) = _1657044)], (50429 ^ _777864) ^ [_1793443, _1793445] : [c_List_Oconcat(_1793443, _1793445) = c_List_Olist_ONil(_1793443), 50432 ^ _777864 : [(50433 ^ _777864) ^ [_1793534] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1793443)), _1793534), hAPP(c_List_Oset(tc_List_Olist(_1793443)), _1793445))), -(_1793534 = c_List_Olist_ONil(_1793443))]]], (50152 ^ _777864) ^ [_1787160, _1787162] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1787160, _1787162) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1787160, hAPP(c_Nat_OSuc, _1787162))))], (38366 ^ _777864) ^ [_1497991] : [class_Nat_Osemiring__char__0(_1497991), -(c_Fun_Oinj__on(tc_Nat_Onat, _1497991, c_Nat_Osemiring__1__class_Oof__nat(_1497991), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (24969 ^ _777864) ^ [_1216226, _1216228, _1216230] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216226), _1216228)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216228), _1216226))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216228), _1216230)), 24980 ^ _777864 : [(24983 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216230), _1216226))], (24981 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216226), _1216230)))]]], (15384 ^ _777864) ^ [_1039510, _1039512, _1039514] : [class_Groups_Ogroup__add(_1039510), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039510), _1039512), hAPP(c_Groups_Ouminus__class_Ouminus(_1039510), _1039514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039510), _1039512), _1039514))], (24915 ^ _777864) ^ [_1215334, _1215336] : [class_Rings_Ocomm__semiring__1(_1215334), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1215334), _1215336), _1215336)))], (25221 ^ _777864) ^ [_1220260, _1220262] : [25228 ^ _777864 : [(25231 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220262), _1220260))], (25229 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220260), _1220262)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220260), _1220262)), -(_1220260 = _1220262)], (46462 ^ _777864) ^ [_1699653, _1699655, _1699657, _1699659] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699653)), _1699655) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699657)), _1699659), hBOOL(hAPP(c_List_Odistinct(_1699653), _1699655)), -(c_Map_Odom(_1699653, _1699657, c_Map_Omap__of(_1699653, _1699657, hAPP(hAPP(c_List_Ozip(_1699653, _1699657), _1699655), _1699659))) = hAPP(c_List_Oset(_1699653), _1699655))], (9418 ^ _777864) ^ [_934990, _934992, _934994] : [class_Rings_Olinordered__semiring__strict(_934990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934990), c_Groups_Ozero__class_Ozero(_934990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934990), _934992), _934994))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934990), c_Groups_Ozero__class_Ozero(_934990)), _934994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934990), c_Groups_Ozero__class_Ozero(_934990)), _934992)))], (30504 ^ _777864) ^ [_1335401, _1335403, _1335405, _1335407] : [hBOOL(hAPP(hAPP(c_member(_1335401), _1335403), c_SetInterval_Oord_OatMost(_1335401, _1335405, _1335407))), -(hBOOL(hAPP(hAPP(_1335405, _1335403), _1335407)))], (17578 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30603 ^ _777864) ^ [_1337479, _1337481] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1337479, _1337481), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337479), _1337481)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337481), _1337479)))], (30997 ^ _777864) ^ [_1344367, _1344369, _1344371] : [class_Lattices_Olattice(_1344367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344367), _1344369)), -(_1344369 = c_Orderings_Obot__class_Obot(tc_fun(_1344367, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1344367, hAPP(hAPP(c_Set_Oinsert(_1344367), _1344371), _1344369)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1344367), _1344371), c_Big__Operators_Olattice__class_OSup__fin(_1344367, _1344369)))], (46889 ^ _777864) ^ [_1712625, _1712627, _1712629, _1712631, _1712633] : [class_Groups_Ocomm__monoid__add(_1712625), hBOOL(hAPP(hAPP(c_member(_1712627), _1712629), hAPP(c_List_Oset(_1712627), _1712631))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1712625), hAPP(hAPP(c_List_Omap(_1712627, _1712625), _1712633), _1712631)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1712625), hAPP(_1712633, _1712629)), hAPP(c_List_Omonoid__add__class_Olistsum(_1712625), hAPP(hAPP(c_List_Omap(_1712627, _1712625), _1712633), c_List_Oremove1(_1712627, _1712629, _1712631)))))], (51167 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51013 ^ _777864) ^ [_1806864, _1806866, _1806868] : [-(c_List_OdropWhile(_1806864, _1806866, _1806868) = c_List_Olist_ONil(_1806864)), hBOOL(hAPP(_1806866, hAPP(c_List_Ohd(_1806864), c_List_OdropWhile(_1806864, _1806866, _1806868))))], (5972 ^ _777864) ^ [_875987] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _875987)], (18408 ^ _777864) ^ [_1094424, _1094426] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1094424)))), _1094426) = 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)))), _1094424)), _1094426))], (41535 ^ _777864) ^ [_1581503, _1581505, _1581507] : [hBOOL(hAPP(c_Predicate_OPowp(_1581503, _1581505), _1581507)), 41538 ^ _777864 : [(41539 ^ _777864) ^ [_1581587] : [hBOOL(hAPP(hAPP(c_member(_1581503), _1581587), _1581507)), -(hBOOL(hAPP(_1581505, _1581587)))]]], (29137 ^ _777864) ^ [_1305228, _1305230, _1305232, _1305234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1305228), _1305230)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305232), hAPP(c_Set_Oimage(_1305228, _1305232, _1305234), _1305230))))], (4672 ^ _777864) ^ [_849306, _849308] : [_849308 = _849306, -(c_If(_849308) = c_If(_849306))], (27816 ^ _777864) ^ [_1273335, _1273337] : [class_Lattices_Obounded__lattice__bot(_1273335), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273335), c_Orderings_Obot__class_Obot(_1273335)), _1273337) = _1273337)], (18620 ^ _777864) ^ [_1097983, _1097985] : [class_Int_Onumber__ring(_1097983), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097983), hAPP(c_Int_Onumber__class_Onumber__of(_1097983), c_Int_OBit1(c_Int_OPls))), _1097985) = _1097985)], (47468 ^ _777864) ^ [_1726883, _1726885, _1726887, _1726889, _1726891] : [-(hAPP(hAPP(c_List_Olist__update(_1726883, hAPP(hAPP(c_List_Olist_OCons(_1726883), _1726885), _1726887)), _1726889), _1726891) = c_Nat_Onat_Onat__case(tc_List_Olist(_1726883), hAPP(hAPP(c_List_Olist_OCons(_1726883), _1726891), _1726887), hAPP(hAPP(c_COMBB(tc_List_Olist(_1726883), tc_List_Olist(_1726883), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1726883), _1726885)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1726883, tc_List_Olist(_1726883)), c_List_Olist__update(_1726883, _1726887)), _1726891)), _1726889))], (40428 ^ _777864) ^ [_1549098, _1549100, _1549102, _1549104, _1549106, _1549108] : [-(hBOOL(hAPP(hAPP(c_member(_1549098), _1549100), _1549102))), -(hAPP(c_Fun_Ooverride__on(_1549098, _1549104, _1549106, _1549108, _1549102), _1549100) = hAPP(_1549106, _1549100))], (13614 ^ _777864) ^ [_1007218, _1007220] : [13615 ^ _777864 : [(13616 ^ _777864) ^ [_1007267] : [_1007218 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1007220), _1007267)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007218, _1007220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23789 ^ _777864) ^ [_1193521, _1193523, _1193525, _1193527, _1193529, _1193531, _1193533] : [-(hAPP(c_Product__Type_Oapfst(_1193521, _1193523, _1193525, _1193527), hAPP(c_Product__Type_Oapsnd(_1193529, _1193525, _1193521, _1193531), _1193533)) = hAPP(hAPP(c_Product__Type_OPair(_1193523, _1193525), hAPP(_1193527, hAPP(c_Product__Type_Ofst(_1193521, _1193529), _1193533))), hAPP(_1193531, hAPP(c_Product__Type_Osnd(_1193521, _1193529), _1193533))))], (7808 ^ _777864) ^ [_907745, _907747, _907749, _907751] : [c_Com_Ocom_OSemi(_907745, _907747) = c_Com_Ocom_OWhile(_907749, _907751)], (12257 ^ _777864) ^ [_983050, _983052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _983050), _983052)), -(_983052 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _983050), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12260 ^ [_983050, _983052])))], (47718 ^ _777864) ^ [_1731735, _1731737, _1731739, _1731741] : [hBOOL(hAPP(c_List_Odistinct(_1731735), _1731737)), -(hBOOL(hAPP(hAPP(c_member(_1731735), _1731739), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1731735, tc_HOL_Obool)), hAPP(c_List_Oset(_1731735), _1731737)), hAPP(hAPP(c_Set_Oinsert(_1731735), hAPP(hAPP(c_List_Onth(_1731735), _1731737), _1731741)), c_Orderings_Obot__class_Obot(tc_fun(_1731735, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1731735), hAPP(hAPP(c_List_Olist__update(_1731735, _1731737), _1731741), _1731739))))], (44451 ^ _777864) ^ [_1651509, _1651511, _1651513, _1651515, _1651517, _1651519] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651509, _1651509)), hAPP(hAPP(c_Product__Type_OPair(_1651509, _1651509), _1651511), _1651513)), _1651515)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1651509, _1651509)), hAPP(hAPP(c_Product__Type_OPair(_1651509, _1651509), _1651513), _1651517)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1651509, _1651509), tc_HOL_Obool), _1651519), _1651515))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651509, _1651509)), hAPP(hAPP(c_Product__Type_OPair(_1651509, _1651509), _1651511), _1651517)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1651509, _1651509), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1651519)), _1651515))))], (2172 ^ _777864) ^ [_809724, _809726, _809728, _809730] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_809730, _809726) = c_Code__Numeral_Odiv__mod__code__numeral(_809728, _809724)), _809730 = _809728, _809726 = _809724], (32681 ^ _777864) ^ [_1376530, _1376532, _1376534, _1376536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1376530, _1376532)), c_Sum__Type_OPlus(_1376530, _1376532, _1376534, _1376536))), 32684 ^ _777864 : [(32687 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376532), _1376536)))], (32685 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376530), _1376534)))]]], (35936 ^ _777864) ^ [_1446402, _1446404, _1446406] : [class_Orderings_Olinorder(_1446402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446402), _1446404), _1446406)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446402, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446402, _1446404), _1446406)), hAPP(hAPP(c_Set_Oinsert(_1446402), _1446406), c_Orderings_Obot__class_Obot(tc_fun(_1446402, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1446402, _1446404, _1446406))], (8898 ^ _777864) ^ [_925719, _925721] : [class_Groups_Ogroup__add(_925719), 8901 ^ _777864 : [(8908 ^ _777864) ^ [] : [_925721 = c_Groups_Ozero__class_Ozero(_925719), -(hAPP(c_Groups_Ouminus__class_Ouminus(_925719), _925721) = c_Groups_Ozero__class_Ozero(_925719))], (8902 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_925719), _925721) = c_Groups_Ozero__class_Ozero(_925719), -(_925721 = c_Groups_Ozero__class_Ozero(_925719))]]], (13632 ^ _777864) ^ [_1007510, _1007512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007510)), -(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, _1007512, _1007510))))], (42692 ^ _777864) ^ [_1608065, _1608067, _1608069, _1608071, _1608073, _1608075] : [c_Finite__Set_Ofun__left__comm__idem(_1608065, _1608067, _1608069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608065), _1608071)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1608065, _1608067, _1608069), _1608073), hAPP(hAPP(c_Set_Oinsert(_1608065), _1608075), _1608071)) = hAPP(hAPP(_1608069, _1608075), hAPP(hAPP(c_Finite__Set_Ofold(_1608065, _1608067, _1608069), _1608073), _1608071)))], (49055 ^ _777864) ^ [_1764439, _1764441, _1764443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1764439, _1764439), tc_HOL_Obool)), _1764441), hAPP(hAPP(c_Product__Type_OSigma(_1764439, _1764439), _1764443), hAPP(c_COMBK(tc_fun(_1764439, tc_HOL_Obool), _1764439), _1764443)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1764439), tc_List_Olist(_1764439)), tc_HOL_Obool)), c_List_Olistrel(_1764439, _1764441)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1764439), tc_List_Olist(_1764439)), c_List_Olists(_1764439, _1764443)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1764439), tc_HOL_Obool), tc_List_Olist(_1764439)), c_List_Olists(_1764439, _1764443))))))], (23121 ^ _777864) ^ [_1179309, _1179311] : [hAPP(c_Nat_OSuc, _1179309) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179311), -(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(_1179311))), 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)), _1179309))))))], (6072 ^ _777864) ^ [_877822] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(_877822)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38665 ^ _777864) ^ [_1505673] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1505673)), c_Int_OInteg)))], (28336 ^ _777864) ^ [_1284100, _1284102, _1284104] : [-(c_Wellfounded_Omlex__prod(_1284100, _1284102, _1284104) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1284100), _1284100), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1284100, c_Wellfounded_Oless__than, _1284104)), hAPP(hAPP(c_COMBS(_1284100, _1284100, tc_prod(tc_Nat_Onat, _1284100)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1284100, tc_prod(tc_Nat_Onat, _1284100)), _1284100), c_Product__Type_OPair(tc_Nat_Onat, _1284100)), _1284102)), c_COMBI(_1284100))))], (23385 ^ _777864) ^ [_1185870, _1185872] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1185870)), hAPP(c_Nat_OSuc, _1185872)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1185870))), 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)), _1185872)))))], (8451 ^ _777864) ^ [_917889, _917891] : [-(hBOOL(hAPP(_917889, hAPP(c_Int_Onat, _917891)))), 8455 ^ _777864 : [(8458 ^ _777864) ^ [] : [hBOOL(hAPP(_917889, 8454 ^ [_917889, _917891]))], (8456 ^ _777864) ^ [] : [-(_917891 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8454 ^ [_917889, _917891]))]], 8459 ^ _777864 : [(8462 ^ _777864) ^ [] : [hBOOL(hAPP(_917889, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8460 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (45754 ^ _777864) ^ [_1682192, _1682194, _1682196, _1682198, _1682200, _1682202] : [-(c_Map_Omap__comp(_1682192, _1682194, _1682196, _1682198, _1682200, _1682202) = c_Option_Ooption_ONone(_1682194)), 45755 ^ _777864 : [(45758 ^ _777864) ^ [_1682304] : [hAPP(_1682200, _1682202) = hAPP(c_Option_Ooption_OSome(_1682192), _1682304), hAPP(_1682198, _1682304) = c_Option_Ooption_ONone(_1682194)], (45756 ^ _777864) ^ [] : [hAPP(_1682200, _1682202) = c_Option_Ooption_ONone(_1682192)]]], (9182 ^ _777864) ^ [_930811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _930811)), -(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, _930811))))], (51317 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (26359 ^ _777864) ^ [_1241834, _1241836, _1241838, _1241840, _1241842, _1241844, _1241846, _1241848] : [c_Hoare__Mirabelle_Ohoare__derivs(_1241834, _1241836, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241834)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241834), _1241838), _1241840), hAPP(hAPP(c_COMBC(_1241834, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1241834), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1241842)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1241844))), hAPP(hAPP(c_Natural_Ogetlocs, _1241846), _1241844))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241834), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1241834, _1241836, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241834)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241834), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1241834), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1241846)))), hAPP(hAPP(c_COMBC(_1241834, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1241834), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1241838)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1241844))), _1241848)))), c_Com_Ocom_OLocal(_1241844, _1241848, _1241840)), _1241842)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241834), tc_HOL_Obool)))))], (49767 ^ _777864) ^ [_1780563, _1780565] : [class_Orderings_Olinorder(_1780563), -(_1780565 = c_List_Olist_ONil(_1780563)), c_List_Olinorder__class_Osorted(_1780563, _1780565), -(c_List_Olinorder__class_Osorted(_1780563, c_List_Obutlast(_1780563, _1780565)))], (28164 ^ _777864) ^ [_1280032, _1280034, _1280036, _1280038] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280032, tc_HOL_Obool)), _1280034), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280032, tc_HOL_Obool)), _1280036), _1280038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280032, tc_HOL_Obool)), _1280036), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280032, tc_HOL_Obool)), _1280034), _1280038)))], (19304 ^ _777864) ^ [_1109751] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109751), 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, _1109751)))], (28493 ^ _777864) ^ [_1290330, _1290332, _1290334, _1290336, _1290338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290330, tc_HOL_Obool)), _1290332), _1290334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290336, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1290330, _1290336, _1290338), _1290332)), hAPP(c_Set_Oimage(_1290330, _1290336, _1290338), _1290334))))], (21214 ^ _777864) ^ [_1143691, _1143693, _1143695, _1143697] : [class_Fields_Olinordered__field(_1143691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143691), c_Groups_Ozero__class_Ozero(_1143691)), _1143693)), 21221 ^ _777864 : [(21228 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143691), _1143695), _1143693)), _1143697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143691), _1143695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143691), _1143697), _1143693))))], (21222 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143691), _1143695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143691), _1143697), _1143693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143691), _1143695), _1143693)), _1143697)))]]], (30456 ^ _777864) ^ [_1333867, _1333869, _1333871, _1333873, _1333875, _1333877] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1333867, _1333869)), hAPP(hAPP(c_Product__Type_OPair(_1333867, _1333869), _1333875), _1333877)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool)), _1333871), _1333873))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333867, tc_fun(_1333869, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1333867, tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_fun(_1333869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333869, tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_fun(_1333869, tc_HOL_Obool)), _1333867), c_COMBC(_1333869, tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333869, tc_prod(_1333867, _1333869)), tc_fun(_1333869, tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), _1333867), hAPP(c_COMBB(tc_prod(_1333867, _1333869), tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool), _1333869), c_member(tc_prod(_1333867, _1333869)))), c_Product__Type_OPair(_1333867, _1333869)))), _1333871)), hAPP(hAPP(c_COMBC(_1333867, tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_fun(_1333869, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333869, tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_fun(_1333869, tc_HOL_Obool)), _1333867), c_COMBC(_1333869, tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333869, tc_prod(_1333867, _1333869)), tc_fun(_1333869, tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool)), _1333867), hAPP(c_COMBB(tc_prod(_1333867, _1333869), tc_fun(tc_fun(tc_prod(_1333867, _1333869), tc_HOL_Obool), tc_HOL_Obool), _1333869), c_member(tc_prod(_1333867, _1333869)))), c_Product__Type_OPair(_1333867, _1333869)))), _1333873)), _1333875), _1333877)))], (36514 ^ _777864) ^ [_1458081, _1458083, _1458085, _1458087, _1458089] : [-(c_Map_Orestrict__map(_1458081, _1458083, c_Map_Orestrict__map(_1458081, _1458083, _1458085, _1458087), _1458089) = c_Map_Orestrict__map(_1458081, _1458083, _1458085, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458081, tc_HOL_Obool)), _1458087), _1458089)))], (18952 ^ _777864) ^ [_1103630] : [c_Int_OMin = c_Int_OBit0(_1103630)], (5262 ^ _777864) ^ [_858393, _858395] : [_858395 = _858393, -(c_List_Orev(_858395) = c_List_Orev(_858393))], (3536 ^ _777864) ^ [_831572, _831574, _831576, _831578, _831580, _831582] : [-(c_Hoare__Mirabelle_Opeek__and(_831582, _831578, _831574) = c_Hoare__Mirabelle_Opeek__and(_831580, _831576, _831572)), _831582 = _831580, _831578 = _831576, _831574 = _831572], (17890 ^ _777864) ^ [_1086178, _1086180, _1086182] : [17892 ^ _777864 : [(17895 ^ _777864) ^ [] : [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(_1086180, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17891 ^ [_1086178, _1086180, _1086182]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1086180, 17891 ^ [_1086178, _1086180, _1086182])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17893 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17891 ^ [_1086178, _1086180, _1086182]), _1086178)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1086180, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1086182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086182), hAPP(_1086180, _1086178))), 17905 ^ _777864 : [(17908 ^ _777864) ^ [] : [-(hAPP(_1086180, 17904 ^ [_1086178, _1086180, _1086182]) = _1086182)], (17906 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17904 ^ [_1086178, _1086180, _1086182]), _1086178)))]]], (20798 ^ _777864) ^ [_1136546, _1136548, _1136550, _1136552, _1136554] : [class_Fields_Ofield(_1136546), -(_1136548 = c_Groups_Ozero__class_Ozero(_1136546)), -(_1136550 = c_Groups_Ozero__class_Ozero(_1136546)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136546), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136546), _1136552), _1136548)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136546), _1136554), _1136550)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136546), _1136552), _1136550)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136546), _1136554), _1136548))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136546), _1136548), _1136550)))], (21904 ^ _777864) ^ [_1156781, _1156783] : [-(c_Divides_OnegDivAlg(_1156781, _1156783) = hAPP(c_Divides_Oadjust(_1156783), c_Divides_OnegDivAlg(_1156781, 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)))), _1156783)))), -(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), _1156781), _1156783)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156783), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41130 ^ _777864) ^ [_1571150, _1571152, _1571154] : [c_Wellfounded_Owf(_1571150, _1571152), -(c_Wellfounded_Owf(tc_List_Olist(_1571150), hAPP(c_List_Olexn(_1571150, _1571152), _1571154)))], (35068 ^ _777864) ^ [_1429811, _1429813] : [-(c_Fun_Oinj__on(_1429811, _1429811, c_COMBI(_1429811), _1429813))], (47958 ^ _777864) ^ [_1737863, _1737865, _1737867, _1737869] : [-(hAPP(hAPP(c_List_Otake(_1737863), _1737865), hAPP(hAPP(c_List_Oappend(_1737863), _1737867), _1737869)) = hAPP(hAPP(c_List_Oappend(_1737863), hAPP(hAPP(c_List_Otake(_1737863), _1737865), _1737867)), hAPP(hAPP(c_List_Otake(_1737863), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1737865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737863)), _1737867))), _1737869)))], (7554 ^ _777864) ^ [_903164, _903166, _903168, _903170] : [-(c_Option_Ooption_Ooption__rec(_903164, _903166, _903168, _903170, c_Option_Ooption_ONone(_903166)) = _903168)], (40234 ^ _777864) ^ [_1541826, _1541828, _1541830] : [hBOOL(hAPP(_1541826, _1541828)), -(hAPP(c_Set_OCollect(_1541830), hAPP(hAPP(c_COMBS(_1541830, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541830), c_fconj), hAPP(hAPP(c_COMBC(_1541830, _1541830, tc_HOL_Obool), c_fequal), _1541828))), _1541826)) = hAPP(hAPP(c_Set_Oinsert(_1541830), _1541828), c_Orderings_Obot__class_Obot(tc_fun(_1541830, tc_HOL_Obool))))], (48989 ^ _777864) ^ [_1762699, _1762701, _1762703] : [class_Orderings_Olinorder(_1762699), -(c_Big__Operators_Olinorder__class_OMin(_1762699, hAPP(c_List_Oset(_1762699), hAPP(hAPP(c_List_Olist_OCons(_1762699), _1762701), _1762703))) = hAPP(c_List_Ofoldl(_1762699, _1762699, c_Orderings_Oord__class_Omin(_1762699), _1762701), _1762703))], (34509 ^ _777864) ^ [_1418541, _1418543, _1418545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1418541, tc_HOL_Obool)), _1418543), _1418545)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418541, tc_HOL_Obool)), _1418543), hAPP(c_Set_OPow(_1418541), _1418545))))], (40062 ^ _777864) ^ [_1538008, _1538010, _1538012, _1538014, _1538016] : [c_Finite__Set_Ofun__left__comm__idem(_1538008, _1538010, _1538012), -(hAPP(hAPP(_1538012, _1538014), hAPP(hAPP(_1538012, _1538014), _1538016)) = hAPP(hAPP(_1538012, _1538014), _1538016))], (2836 ^ 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(23899 ^ _777864) ^ [_1195625, _1195627, _1195629, _1195631] : [class_Orderings_Olinorder(_1195625), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195625), _1195627), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195625), _1195629), _1195631)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195625), _1195629), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195625), _1195627), _1195631)))], (40861 ^ _777864) ^ [_1565463, _1565465] : [-(c_Wellfounded_Owf(_1565463, hAPP(c_Wellfounded_Omeasure(_1565463), _1565465)))], (15420 ^ _777864) ^ [_1040217, _1040219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040219), _1040217)), _1040219)))], (40074 ^ _777864) ^ [_1538208] : [class_Orderings_Olinorder(_1538208), -(c_Finite__Set_Ofun__left__comm__idem(_1538208, _1538208, c_Orderings_Oord__class_Omin(_1538208)))], (30522 ^ _777864) ^ [_1335741, _1335743] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335743), _1335741)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335741), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335743))))], (32943 ^ _777864) ^ [_1381683, _1381685, _1381687, _1381689, _1381691] : [class_Groups_Ocomm__monoid__mult(_1381683), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381685), _1381687)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381685, _1381683), hAPP(hAPP(c_COMBS(_1381685, _1381683, _1381683), hAPP(hAPP(c_COMBB(_1381683, tc_fun(_1381683, _1381683), _1381685), c_Groups_Otimes__class_Otimes(_1381683)), _1381689)), _1381691)), _1381687) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381683), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381685, _1381683), _1381689), _1381687)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381685, _1381683), _1381691), _1381687)))], (26473 ^ _777864) ^ [_1244249, _1244251] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244249), _1244251)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1244251), _1244249)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244251)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244249)))], (32375 ^ _777864) ^ [_1369862, _1369864, _1369866, _1369868] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369862), _1369864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369866), hAPP(c_Set_Oimage(_1369862, _1369866, _1369868), _1369864))), hAPP(c_Finite__Set_Ocard(_1369862), _1369864))))], (26067 ^ _777864) ^ [_1235758, _1235760] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235758), _1235760)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235758)), _1235760)))], (11191 ^ _777864) ^ [_964186, _964188, _964190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964188), _964190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964186), _964188)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964186), _964190))))], (7492 ^ _777864) ^ [_901725, _901727, _901729] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_901725, _901727, _901729)], (49632 ^ _777864) ^ [_1777349, _1777351, _1777353, _1777355, _1777357, _1777359] : [hAPP(c_Map_Omap__of(_1777349, _1777351, _1777353), _1777355) = hAPP(c_Option_Ooption_OSome(_1777351), _1777357), hBOOL(hAPP(hAPP(_1777359, _1777355), _1777357)), -(hAPP(c_Map_Omap__of(_1777349, _1777351, hAPP(c_List_Ofilter(tc_prod(_1777349, _1777351), hAPP(c_Product__Type_Oprod_Oprod__case(_1777349, _1777351, tc_HOL_Obool), _1777359)), _1777353)), _1777355) = hAPP(c_Option_Ooption_OSome(_1777351), _1777357))], (23585 ^ _777864) ^ [_1189508, _1189510, _1189512, _1189514] : [class_Orderings_Olinorder(_1189508), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189508), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189508), _1189510), _1189512)), _1189514) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189508), _1189510), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189508), _1189512), _1189514)))], (9995 ^ _777864) ^ [_944882] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _944882)))], (51603 ^ _777864) ^ [_1813204, _1813206] : [-(hBOOL(_1813204)), -(hBOOL(hAPP(hAPP(c_fimplies, _1813204), _1813206)))], (46517 ^ _777864) ^ [_1702012, _1702014, _1702016, _1702018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702012), tc_List_Olist(_1702012))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702012), tc_List_Olist(_1702012)), _1702014), _1702016)), c_List_Olistrel(_1702012, _1702018))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702012)), _1702014) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702012)), _1702016))], (36866 ^ _777864) ^ [_1466481, _1466483, _1466485, _1466487] : [class_Groups_Ocomm__monoid__add(_1466481), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1466483), _1466485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466481), _1466487), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1466483, _1466485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1466481), hAPP(_1466487, _1466483)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466481), _1466487), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1466483), _1466485))))], (31075 ^ _777864) ^ [_1345619, _1345621, _1345623] : [class_Lattices_Olattice(_1345619), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345619), _1345621)), -(_1345621 = c_Orderings_Obot__class_Obot(tc_fun(_1345619, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345619), _1345623)), -(_1345623 = c_Orderings_Obot__class_Obot(tc_fun(_1345619, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1345619, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1345619, tc_HOL_Obool)), _1345621), _1345623)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1345619), c_Big__Operators_Olattice__class_OSup__fin(_1345619, _1345621)), c_Big__Operators_Olattice__class_OSup__fin(_1345619, _1345623)))], (17146 ^ _777864) ^ [_1073592, _1073594, _1073596] : [class_Rings_Olinordered__semidom(_1073592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073592), c_Groups_Ozero__class_Ozero(_1073592)), _1073594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1073592), c_Groups_Ozero__class_Ozero(_1073592)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073592), _1073594), _1073596))))], (48842 ^ _777864) ^ [_1759630, _1759632, _1759634] : [-(c_List_Orotate(_1759630, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1759632), _1759634)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1759630), tc_List_Olist(_1759630), tc_List_Olist(_1759630), c_List_Orotate(_1759630, _1759632)), c_List_Orotate(_1759630, _1759634)))], (27263 ^ _777864) ^ [_1262267, _1262269, _1262271, _1262273, _1262275] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1262267, _1262269)), hAPP(hAPP(c_Product__Type_OPair(_1262267, _1262269), _1262273), _1262275)), _1262271)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1262267, _1262269, _1262271), _1262273), _1262275)))], (23893 ^ _777864) ^ [_1195482, _1195484, _1195486, _1195488] : [class_Orderings_Olinorder(_1195482), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195482), _1195484), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195482), _1195486), _1195488)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195482), _1195486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195482), _1195484), _1195488)))], (37729 ^ _777864) ^ [_1485691, _1485693] : [class_Groups_Oordered__ab__group__add(_1485691), -(hAPP(c_Set_Oimage(_1485691, _1485691, c_Groups_Ouminus__class_Ouminus(_1485691)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485691), _1485693)) = hAPP(c_SetInterval_Oord__class_OatMost(_1485691), hAPP(c_Groups_Ouminus__class_Ouminus(_1485691), _1485693)))], (14113 ^ _777864) ^ [_1016589, _1016591, _1016593] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016589, _1016591)), _1016593) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016589), _1016593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016591), _1016593)))], (44666 ^ _777864) ^ [_1656574] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656574, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1656574, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1656574, tc_HOL_Obool)))], (9834 ^ _777864) ^ [_942245] : [class_Rings_Olinordered__semidom(_942245), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942245), c_Groups_Ozero__class_Ozero(_942245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942245), c_Groups_Oone__class_Oone(_942245)), c_Groups_Oone__class_Oone(_942245)))))], (49990 ^ _777864) ^ [_1784461, _1784463] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1784461, _1784463)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1784461), _1784463))], (5786 ^ _777864) ^ [_872491, _872493, _872495, _872497, _872499] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_872491, _872493, _872495)), _872497), _872499)), 5790 ^ _777864 : [(5793 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872495), hAPP(hAPP(hAPP(c_Natural_Oupdate, _872497), c_Com_Ovname_OLoc(_872491)), hAPP(_872493, _872497))), 5789 ^ [_872491, _872493, _872495, _872497, _872499])))], (5791 ^ _777864) ^ [] : [-(_872499 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 5789 ^ [_872491, _872493, _872495, _872497, _872499]), c_Com_Ovname_OLoc(_872491)), hAPP(hAPP(c_Natural_Ogetlocs, _872497), _872491)))]]], (40687 ^ _777864) ^ [_1559356, _1559358] : [-(c_Fun_Oinj__on(_1559356, _1559356, c_Fun_Oid(_1559356), _1559358))], (28701 ^ _777864) ^ [_1296036, _1296038] : [_1296036 = _1296038, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296036) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296038))], (31291 ^ _777864) ^ [_1349191, _1349193, _1349195] : [class_Lattices_Olattice(_1349191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349191), _1349193)), 31298 ^ _777864 : [(31305 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349191, tc_HOL_Obool)), _1349193), hAPP(hAPP(c_Set_Oinsert(_1349191), _1349195), c_Orderings_Obot__class_Obot(tc_fun(_1349191, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349191, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1349191, hAPP(hAPP(c_Set_Oinsert(_1349191), _1349195), _1349193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1349191), _1349195), c_Big__Operators_Olattice__class_OSup__fin(_1349191, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349191, tc_HOL_Obool)), _1349193), hAPP(hAPP(c_Set_Oinsert(_1349191), _1349195), c_Orderings_Obot__class_Obot(tc_fun(_1349191, tc_HOL_Obool)))))))], (31299 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349191, tc_HOL_Obool)), _1349193), hAPP(hAPP(c_Set_Oinsert(_1349191), _1349195), c_Orderings_Obot__class_Obot(tc_fun(_1349191, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1349191, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1349191, hAPP(hAPP(c_Set_Oinsert(_1349191), _1349195), _1349193)) = _1349195)]]], (51443 ^ _777864) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (34217 ^ _777864) ^ [_1412200, _1412202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1412200), _1412202)), -(hAPP(c_Finite__Set_Ocard(_1412200), _1412202) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1412200, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1412200), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1412202))], (17448 ^ _777864) ^ [_1079088, _1079090, _1079092] : [class_Rings_Oring__1(_1079088), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079088), hAPP(c_Groups_Ouminus__class_Ouminus(_1079088), _1079090)), _1079092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079088), hAPP(hAPP(c_Power_Opower__class_Opower(_1079088), hAPP(c_Groups_Ouminus__class_Ouminus(_1079088), c_Groups_Oone__class_Oone(_1079088))), _1079092)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079088), _1079090), _1079092)))], (3292 ^ _777864) ^ [_827750, _827752, _827754, _827756, _827758, _827760, _827762, _827764] : [-(c_Nitpick_Oprod(_827764, _827760, _827756, _827752) = c_Nitpick_Oprod(_827762, _827758, _827754, _827750)), _827764 = _827762, _827760 = _827758, _827756 = _827754, _827752 = _827750], (35275 ^ _777864) ^ [_1433781, _1433783] : [35283 ^ _777864 : [(35286 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1433783, 35282 ^ [_1433781, _1433783])))], (35284 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35282 ^ [_1433781, _1433783]), _1433781)))]], 35276 ^ _777864 : [(35277 ^ _777864) ^ [_1433850] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1433850), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1433781))), hBOOL(hAPP(_1433783, _1433850))]]], (16664 ^ _777864) ^ [_1064572, _1064574] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064572), _1064574)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1064572) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30919 ^ _777864) ^ [_1343173, _1343175] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343173, _1343175), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343173), _1343175))], (44798 ^ _777864) ^ [_1659915, _1659917] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1659915, tc_HOL_Obool), tc_HOL_Obool)), _1659917), hAPP(c_Set_OPow(_1659915), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659915, tc_HOL_Obool), _1659917)))))], (49190 ^ _777864) ^ [_1767701, _1767703, _1767705, _1767707, _1767709] : [class_Groups_Omonoid__add(_1767701), class_Groups_Oordered__ab__semigroup__add(_1767701), 49200 ^ _777864 : [(49203 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767701), hAPP(_1767707, 49199 ^ [_1767701, _1767703, _1767705, _1767707, _1767709])), hAPP(_1767709, 49199 ^ [_1767701, _1767703, _1767705, _1767707, _1767709])))], (49201 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767703), 49199 ^ [_1767701, _1767703, _1767705, _1767707, _1767709]), hAPP(c_List_Oset(_1767703), _1767705))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767701), hAPP(c_List_Omonoid__add__class_Olistsum(_1767701), hAPP(hAPP(c_List_Omap(_1767703, _1767701), _1767707), _1767705))), hAPP(c_List_Omonoid__add__class_Olistsum(_1767701), hAPP(hAPP(c_List_Omap(_1767703, _1767701), _1767709), _1767705)))))], (5976 ^ _777864) ^ [_876057] : [hAPP(c_Nat_OSuc, _876057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23315 ^ _777864) ^ [_1184254, _1184256, _1184258, _1184260, _1184262] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184254, _1184256, _1184258), _1184260), _1184262) = hAPP(hAPP(_1184260, hAPP(c_Product__Type_Ofst(_1184254, _1184256), _1184262)), hAPP(c_Product__Type_Osnd(_1184254, _1184256), _1184262)))], (38268 ^ _777864) ^ [_1495956, _1495958, _1495960, _1495962, _1495964] : [c_Fun_Oinj__on(_1495956, _1495958, _1495960, c_Orderings_Otop__class_Otop(tc_fun(_1495956, tc_HOL_Obool))), 38271 ^ _777864 : [(38278 ^ _777864) ^ [] : [_1495962 = _1495964, -(hAPP(c_Set_Oimage(_1495956, _1495958, _1495960), _1495962) = hAPP(c_Set_Oimage(_1495956, _1495958, _1495960), _1495964))], (38272 ^ _777864) ^ [] : [hAPP(c_Set_Oimage(_1495956, _1495958, _1495960), _1495962) = hAPP(c_Set_Oimage(_1495956, _1495958, _1495960), _1495964), -(_1495962 = _1495964)]]], (25597 ^ _777864) ^ [_1226806, _1226808, _1226810] : [class_Divides_Osemiring__div(_1226806), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226806), _1226808), _1226810)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226806), _1226808), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226806), _1226810), _1226808)) = _1226810)], (39275 ^ _777864) ^ [_1520840, _1520842, _1520844, _1520846, _1520848, _1520850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520840, _1520842), tc_HOL_Obool)), _1520844), hAPP(hAPP(c_Product__Type_OSigma(_1520840, _1520842), _1520846), hAPP(c_COMBK(tc_fun(_1520842, tc_HOL_Obool), _1520840), _1520848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520842, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1520840, _1520842, _1520844), _1520850)), _1520848)))], (51363 ^ _777864) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (39924 ^ _777864) ^ [_1535217, _1535219, _1535221, _1535223, _1535225] : [c_Relation_Orefl__on(_1535217, _1535219, _1535221), c_Relation_Orefl__on(_1535217, _1535223, _1535225), -(c_Relation_Orefl__on(_1535217, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535217, tc_HOL_Obool)), _1535219), _1535223), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535217, _1535217), tc_HOL_Obool)), _1535221), _1535225)))], (47990 ^ _777864) ^ [_1738731, _1738733, _1738735, _1738737, _1738739] : [-(hAPP(hAPP(c_List_Omap(_1738731, _1738733), _1738735), hAPP(hAPP(c_List_Oappend(_1738731), _1738737), _1738739)) = hAPP(hAPP(c_List_Oappend(_1738733), hAPP(hAPP(c_List_Omap(_1738731, _1738733), _1738735), _1738737)), hAPP(hAPP(c_List_Omap(_1738731, _1738733), _1738735), _1738739)))], (9274 ^ _777864) ^ [_932357, _932359, _932361] : [class_Groups_Ogroup__add(_932357), 9277 ^ _777864 : [(9284 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932357), _932359), _932361) = c_Groups_Ozero__class_Ozero(_932357), -(_932359 = hAPP(c_Groups_Ouminus__class_Ouminus(_932357), _932361))], (9278 ^ _777864) ^ [] : [_932359 = hAPP(c_Groups_Ouminus__class_Ouminus(_932357), _932361), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932357), _932359), _932361) = c_Groups_Ozero__class_Ozero(_932357))]]], (5795 ^ _777864) ^ [_872733, _872735, _872737, _872739, _872741, _872743] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_872733, _872735, _872737), _872739, _872741, _872743), 5799 ^ _777864 : [(5802 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_872737, hAPP(hAPP(hAPP(c_Natural_Oupdate, _872739), c_Com_Ovname_OLoc(_872733)), hAPP(_872735, _872739)), _872741, 5798 ^ [_872733, _872735, _872737, _872739, _872741, _872743]))], (5800 ^ _777864) ^ [] : [-(_872743 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 5798 ^ [_872733, _872735, _872737, _872739, _872741, _872743]), c_Com_Ovname_OLoc(_872733)), hAPP(hAPP(c_Natural_Ogetlocs, _872739), _872733)))]]], (8280 ^ _777864) ^ [_915147, _915149, _915151, _915153] : [class_Orderings_Oord(_915147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915147), _915149), _915151)), _915151 = _915153, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915147), _915149), _915153)))], (19216 ^ _777864) ^ [_1108237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108237), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1108237)), c_Int_OMin)))], (13932 ^ _777864) ^ [_1013007, _1013009, _1013011] : [hBOOL(hAPP(_1013007, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1013009), _1013011))), 13935 ^ _777864 : [(13960 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013011), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 13963 ^ _777864 : [(13964 ^ _777864) ^ [_1013671] : [-(hBOOL(hAPP(_1013007, _1013671))), 13965 ^ _777864 : [(13966 ^ _777864) ^ [_1013745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013011), _1013745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1013745), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1013009 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013011), _1013671)), _1013745)]]]]], (13942 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013011)), 13945 ^ _777864 : [(13946 ^ _777864) ^ [_1013341] : [-(hBOOL(hAPP(_1013007, _1013341))), 13947 ^ _777864 : [(13948 ^ _777864) ^ [_1013412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1013412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1013412), _1013011)), _1013009 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1013011), _1013341)), _1013412)]]]]], (13936 ^ _777864) ^ [] : [_1013011 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1013007, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (16058 ^ _777864) ^ [_1053170, _1053172, _1053174] : [16060 ^ _777864 : [(16065 ^ _777864) ^ [] : [hBOOL(hAPP(_1053172, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16059 ^ [_1053170, _1053172, _1053174]), _1053170)))], (16063 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1053172, 16059 ^ [_1053170, _1053172, _1053174])))], (16061 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16059 ^ [_1053170, _1053172, _1053174]), _1053170)))]], hBOOL(hAPP(_1053172, _1053174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053174), _1053170)), -(hBOOL(hAPP(_1053172, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6160 ^ _777864) ^ [_879157] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _879157), _879157)))], (16096 ^ _777864) ^ [_1053925, _1053927, _1053929] : [class_Rings_Oring__1(_1053925), -(hAPP(c_Int_Oring__1__class_Oof__int(_1053925), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1053927), _1053929)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1053925), hAPP(c_Int_Oring__1__class_Oof__int(_1053925), _1053927)), _1053929))], (5038 ^ _777864) ^ [_854931, _854933] : [_854933 = _854931, -(c_List_Otake(_854933) = c_List_Otake(_854931))], (23755 ^ _777864) ^ [_1192983, _1192985] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1192983)), _1192985) = 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), _1192983)), _1192985))], (43225 ^ _777864) ^ [_1619236, _1619238] : [-(hAPP(c_Relation_ODomain(_1619236, _1619236), c_Transitive__Closure_Ortrancl(_1619236, _1619238)) = c_Orderings_Otop__class_Otop(tc_fun(_1619236, tc_HOL_Obool)))], (36072 ^ _777864) ^ [_1449405, _1449407, _1449409, _1449411] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449405, _1449407), _1449409), _1449411), hAPP(_1449409, _1449411)) = _1449409)], (25905 ^ _777864) ^ [_1232692, _1232694, _1232696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232692)), 25908 ^ _777864 : [(25915 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232694), _1232696)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232692), _1232694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232692), _1232696))))], (25909 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232692), _1232694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232692), _1232696))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232694), _1232696)))]]], (41340 ^ _777864) ^ [_1576124, _1576126, _1576128, _1576130] : [41341 ^ _777864 : [(41342 ^ _777864) ^ [_1576199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576124, _1576128)), hAPP(hAPP(c_Product__Type_OPair(_1576124, _1576128), _1576126), _1576199)), _1576130))]], -(hBOOL(hAPP(hAPP(c_member(_1576124), _1576126), hAPP(c_Relation_ODomain(_1576124, _1576128), _1576130))))], (18244 ^ _777864) ^ [_1091665, _1091667] : [class_Int_Onumber__ring(_1091665), class_Rings_Olinordered__idom(_1091665), 18251 ^ _777864 : [(18258 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1091667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091665), c_Groups_Ozero__class_Ozero(_1091665)), hAPP(c_Int_Onumber__class_Onumber__of(_1091665), _1091667))))], (18252 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091665), c_Groups_Ozero__class_Ozero(_1091665)), hAPP(c_Int_Onumber__class_Onumber__of(_1091665), _1091667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1091667)))]]], (46282 ^ _777864) ^ [_1695087, _1695089, _1695091] : [class_Orderings_Olinorder(_1695087), -(c_List_Oremove1(_1695087, _1695089, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695087, _1695087, c_COMBI(_1695087)), _1695089), _1695091)) = _1695091)], (17582 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (50730 ^ _777864) ^ [_1801383, _1801385, _1801387, _1801389] : [hBOOL(hAPP(hAPP(c_member(_1801383), _1801385), hAPP(c_List_Oset(_1801383), c_List_OtakeWhile(_1801383, _1801387, _1801389)))), 50733 ^ _777864 : [(50736 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1801387, _1801385)))], (50734 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801383), _1801385), hAPP(c_List_Oset(_1801383), _1801389))))]]], (51287 ^ _777864) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (1172 ^ _777864) ^ [_795282, _795284] : [-(class_Groups_Osgn__if(_795282)), _795284 = _795282, class_Groups_Osgn__if(_795284)], (3998 ^ _777864) ^ [_838849, _838851, _838853, _838855] : [-(c_Option_Omap(_838855, _838851) = c_Option_Omap(_838853, _838849)), _838855 = _838853, _838851 = _838849], (40015 ^ _777864) ^ [_1537064, _1537066, _1537068, _1537070, _1537072, _1537074, _1537076, _1537078] : [c_Finite__Set_Ofolding__image__simple(_1537064, _1537066, _1537068, _1537070, _1537072, _1537074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537066), _1537076)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537066), _1537078)), 40029 ^ _777864 : [(40032 ^ _777864) ^ [] : [hAPP(_1537072, 40028 ^ [_1537064, _1537066, _1537068, _1537070, _1537072, _1537074, _1537076, _1537078]) = _1537070], (40030 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537066), 40028 ^ [_1537064, _1537066, _1537068, _1537070, _1537072, _1537074, _1537076, _1537078]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1537066, tc_HOL_Obool)), _1537076), _1537078))))]], -(hAPP(_1537074, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1537066, tc_HOL_Obool)), _1537076), _1537078)) = hAPP(hAPP(_1537068, hAPP(_1537074, _1537076)), hAPP(_1537074, _1537078)))], (31171 ^ _777864) ^ [_1347222, _1347224, _1347226, _1347228] : [-(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), _1347222, _1347224)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347226, _1347228)))), 31172 ^ _777864 : [(31175 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347226), _1347222)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347224), _1347228))], (31173 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347222), _1347224)))]]], (42486 ^ _777864) ^ [_1603863, _1603865, _1603867] : [class_Orderings_Olinorder(_1603863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603863), _1603865)), 42496 ^ _777864 : [(42499 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1603863), 42495 ^ [_1603863, _1603865, _1603867]), _1603867))], (42497 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603863), 42495 ^ [_1603863, _1603865, _1603867]), _1603865)))]], hBOOL(hAPP(hAPP(c_member(_1603863), _1603867), _1603865)), -(c_Big__Operators_Olinorder__class_OMax(_1603863, _1603865) = _1603867)], (50767 ^ _777864) ^ [_1802151, _1802153, _1802155, _1802157, _1802159] : [-(hBOOL(hAPP(_1802151, _1802153))), -(c_List_OtakeWhile(_1802155, _1802151, hAPP(hAPP(c_List_Oappend(_1802155), _1802157), hAPP(hAPP(c_List_Olist_OCons(_1802155), _1802153), _1802159))) = c_List_OtakeWhile(_1802155, _1802151, _1802157))], (19880 ^ _777864) ^ [_1120441, _1120443] : [c_Nat__Transfer_Ois__nat(_1120441), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1120441), _1120443)))], (42404 ^ _777864) ^ [_1601823, _1601825, _1601827, _1601829] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1601823, tc_HOL_Obool), tc_fun(_1601823, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1601823, tc_HOL_Obool), tc_fun(_1601823, tc_HOL_Obool)), _1601825), _1601827)), c_Wellfounded_Omax__ext(_1601823, _1601829))), 42407 ^ _777864 : [(42410 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1601823), _1601827)))], (42412 ^ _777864) ^ [] : [_1601827 = c_Orderings_Obot__class_Obot(tc_fun(_1601823, tc_HOL_Obool))], (42414 ^ _777864) ^ [_1602117] : [hBOOL(hAPP(hAPP(c_member(_1601823), _1602117), _1601825)), 42418 ^ _777864 : [(42421 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601823, _1601823)), hAPP(hAPP(c_Product__Type_OPair(_1601823, _1601823), _1602117), 42417 ^ [_1601823, _1601825, _1601827, _1601829, _1602117])), _1601829)))], (42419 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601823), 42417 ^ [_1601823, _1601825, _1601827, _1601829, _1602117]), _1601827)))]]], (42408 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1601823), _1601825)))]]], (51229 ^ _777864) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (38896 ^ _777864) ^ [_1511205, _1511207, _1511209, _1511211, _1511213, _1511215] : [c_Typedef_Otype__definition(_1511205, _1511207, _1511209, _1511211, _1511213), -(hBOOL(hAPP(hAPP(c_member(_1511207), hAPP(_1511209, _1511215)), _1511213)))], (24735 ^ _777864) ^ [_1211930, _1211932, _1211934, _1211936, _1211938] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1211930, _1211932, tc_HOL_Obool, _1211934), _1211936), _1211938)), -(hBOOL(hAPP(_1211934, hAPP(hAPP(c_Product__Type_OPair(_1211930, _1211932), _1211936), _1211938))))], (24775 ^ _777864) ^ [_1212851, _1212853, _1212855, _1212857] : [class_Rings_Ocomm__semiring__1(_1212851), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212851), _1212853), _1212855)), _1212857)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212851), _1212855), _1212857)))], (44417 ^ _777864) ^ [_1650721, _1650723] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650721, _1650721), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1650723) = _1650723)], (11096 ^ _777864) ^ [_962636, _962638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962636), _962638)), 11099 ^ _777864 : [(11102 ^ _777864) ^ [] : [_962636 = _962638], (11100 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962636), _962638)))]]], (1032 ^ _777864) ^ [_793532, _793534] : [-(class_Rings_Oring__no__zero__divisors(_793532)), _793534 = _793532, class_Rings_Oring__no__zero__divisors(_793534)], (44267 ^ _777864) ^ [_1647142, _1647144, _1647146, _1647148, _1647150] : [c_Relation_Osingle__valued(_1647142, _1647144, _1647146), c_Relation_Osingle__valued(_1647144, _1647148, _1647150), -(c_Relation_Osingle__valued(_1647142, _1647148, hAPP(hAPP(c_Relation_Orel__comp(_1647142, _1647144, _1647148), _1647146), _1647150)))], (16822 ^ _777864) ^ [_1067656, _1067658, _1067660] : [class_Int_Onumber__ring(_1067656), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067656), hAPP(c_Int_Onumber__class_Onumber__of(_1067656), _1067658)), hAPP(c_Int_Onumber__class_Onumber__of(_1067656), _1067660)) = hAPP(c_Int_Onumber__class_Onumber__of(_1067656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067658), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1067660))))], (44668 ^ _777864) ^ [_1656616, _1656618, _1656620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1656616, tc_HOL_Obool), tc_HOL_Obool)), _1656618), _1656620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1656616, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656616, tc_HOL_Obool), _1656620)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656616, tc_HOL_Obool), _1656618))))], (18946 ^ _777864) ^ [_1103504, _1103506] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1103504)), _1103506) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1103504), _1103506)))], (14127 ^ _777864) ^ [_1016880, _1016882] : [class_Divides_Osemiring__div(_1016880), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1016880), _1016882), c_Groups_Ozero__class_Ozero(_1016880)) = c_Groups_Ozero__class_Ozero(_1016880))], (41020 ^ _777864) ^ [_1568634, _1568636] : [41022 ^ _777864 : [(41023 ^ _777864) ^ [_1568659] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568634, _1568634)), hAPP(hAPP(c_Product__Type_OPair(_1568634, _1568634), hAPP(41021 ^ [_1568634, _1568636], hAPP(c_Nat_OSuc, _1568659))), hAPP(41021 ^ [_1568634, _1568636], _1568659))), _1568636)))]], -(c_Wellfounded_Owf(_1568634, _1568636))], (51303 ^ _777864) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (26305 ^ _777864) ^ [_1240664, _1240666] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240664, tc_HOL_Obool)), _1240666), _1240666) = c_Orderings_Obot__class_Obot(tc_fun(_1240664, tc_HOL_Obool)))], (22877 ^ _777864) ^ [_1174266, _1174268, _1174270] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174266, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174266, tc_HOL_Obool)), _1174268), _1174270)), _1174270) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1174266, tc_HOL_Obool)), _1174268), _1174270))], (12948 ^ _777864) ^ [_995148, _995150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995150)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _995148)), hAPP(c_Int_Onat, _995150)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _995148), _995150)))], (47196 ^ _777864) ^ [_1719984, _1719986, _1719988, _1719990] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719984) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1719986), hAPP(hAPP(c_List_Olist_OCons(_1719986), _1719988), _1719990)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719984)) = _1719988)], (24497 ^ _777864) ^ [_1207302, _1207304] : [-(c_HOL_OThe(_1207302, hAPP(hAPP(c_COMBC(_1207302, _1207302, tc_HOL_Obool), c_fequal), _1207304)) = _1207304)], (40707 ^ _777864) ^ [_1559749, _1559751, _1559753, _1559755] : [class_Groups_Ocomm__monoid__mult(_1559749), c_Fun_Oinj__on(_1559751, _1559749, _1559753, _1559755), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1559751, _1559749), _1559753), _1559755) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1559749, _1559749), c_Fun_Oid(_1559749)), hAPP(c_Set_Oimage(_1559751, _1559749, _1559753), _1559755)))], (49628 ^ _777864) ^ [_1777150, _1777152, _1777154, _1777156] : [-(c_List_Omap__filter(_1777150, _1777152, _1777154, _1777156) = hAPP(hAPP(c_List_Omap(_1777150, _1777152), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1777152), _1777152, _1777150, c_Option_Othe(_1777152)), _1777154)), hAPP(c_List_Ofilter(_1777150, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1777150), c_fNot), hAPP(hAPP(c_COMBC(_1777150, tc_Option_Ooption(_1777152), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1777152), tc_fun(tc_Option_Ooption(_1777152), tc_HOL_Obool), _1777150), c_fequal), _1777154)), c_Option_Ooption_ONone(_1777152)))), _1777156)))], (46226 ^ _777864) ^ [_1693862, _1693864, _1693866, _1693868, _1693870] : [class_Orderings_Olinorder(_1693862), -(hAPP(c_List_Oset(_1693864), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693864, _1693862, _1693866), _1693868), _1693870)) = hAPP(hAPP(c_Set_Oinsert(_1693864), _1693868), hAPP(c_List_Oset(_1693864), _1693870)))], (7968 ^ _777864) ^ [_910568, _910570, _910572] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910568)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910570)), _910572)) = 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), _910568), _910570))), _910572))], (5484 ^ _777864) ^ [_861734, _861736] : [_861736 = _861734, -(c_Com_Ovname_OLoc(_861736) = c_Com_Ovname_OLoc(_861734))], (7270 ^ _777864) ^ [_897483, _897485, _897487, _897489, _897491, _897493] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_897483, _897485, _897487), _897489, _897491, _897493)), 7271 ^ _777864 : [(7278 ^ _777864) ^ [] : [-(hBOOL(hAPP(_897483, _897489))), c_Natural_Oevaln(_897487, _897489, _897491, _897493)], (7272 ^ _777864) ^ [] : [hBOOL(hAPP(_897483, _897489)), c_Natural_Oevaln(_897485, _897489, _897491, _897493)]]], (7990 ^ _777864) ^ [_910966] : [class_Rings_Osemiring__1(_910966), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_910966), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_910966))], (41157 ^ _777864) ^ [_1571747, _1571749, _1571751] : [hAPP(c_Relation_ORange(_1571747, _1571749), _1571751) = c_Orderings_Obot__class_Obot(tc_fun(_1571749, tc_HOL_Obool)), -(_1571751 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1571747, _1571749), tc_HOL_Obool)))], (6152 ^ _777864) ^ [_879047, _879049, _879051] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _879047, _879049, _879051), -(_879051 = _879047)], (10614 ^ _777864) ^ [_954860, _954862, _954864] : [class_Orderings_Oorder(_954860), -(_954862 = _954864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954860), _954864), _954862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954860), _954864), _954862)))], (26365 ^ _777864) ^ [_1242220, _1242222, _1242224] : [-(_1242220 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26368 ^ _777864 : [(26375 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242220), _1242222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242220), _1242224))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242222), _1242224)))], (26369 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1242222), _1242224)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242220), _1242222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242220), _1242224))))]]], (34711 ^ _777864) ^ [_1422338, _1422340] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1422338), _1422340) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1422338, _1422340))], (15574 ^ _777864) ^ [_1043025, _1043027, _1043029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043025), _1043027)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043027), _1043025)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043029), _1043027)), _1043025))], (18588 ^ _777864) ^ [_1097449] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1097449)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1097449))))], (37530 ^ _777864) ^ [_1481793, _1481795, _1481797, _1481799, _1481801] : [c_Finite__Set_Ofolding__one__idem(_1481793, _1481795, _1481797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481793), _1481799)), hBOOL(hAPP(hAPP(c_member(_1481793), _1481801), _1481799)), -(hAPP(hAPP(_1481795, _1481801), hAPP(_1481797, _1481799)) = hAPP(_1481797, _1481799))], (22168 ^ _777864) ^ [_1161200, _1161202, _1161204, _1161206] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1161200, _1161202), _1161204)), hBOOL(hAPP(hAPP(_1161202, _1161206), _1161204)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1161200, _1161202), _1161206)))], (19092 ^ _777864) ^ [_1106081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1106081))))], (4644 ^ _777864) ^ [_848856, _848858, _848860, _848862] : [-(c_Random_Opick(_848862, _848858) = c_Random_Opick(_848860, _848856)), _848862 = _848860, _848858 = _848856], (14260 ^ _777864) ^ [_1018971, _1018973] : [14261 ^ _777864 : [(14262 ^ _777864) ^ [_1019020] : [_1018971 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018973), _1019020)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1018971, _1018973) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42104 ^ _777864) ^ [_1595091, _1595093, _1595095, _1595097, _1595099, _1595101] : [c_Finite__Set_Ofolding(_1595091, _1595093, _1595095, _1595097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595091), _1595099)), -(hBOOL(hAPP(hAPP(c_member(_1595091), _1595101), _1595099))), -(hAPP(_1595097, hAPP(hAPP(c_Set_Oinsert(_1595091), _1595101), _1595099)) = hAPP(c_Fun_Ocomp(_1595093, _1595093, _1595093, hAPP(_1595097, _1595099)), hAPP(_1595095, _1595101)))], (6142 ^ _777864) ^ [_878879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _878879), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26193 ^ _777864) ^ [_1238436, _1238438] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1238436, _1238438, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1238436), tc_HOL_Obool))))], (6058 ^ _777864) ^ [_877626, _877628] : [c_Com_Ovname_OGlb(_877626) = c_Com_Ovname_OGlb(_877628), -(_877626 = _877628)], (38070 ^ _777864) ^ [_1492450, _1492452, _1492454, _1492456, _1492458] : [-(hAPP(c_Set_Oimage(_1492450, _1492452, hAPP(hAPP(c_COMBB(_1492454, _1492452, _1492450), _1492456), _1492458)), c_Orderings_Otop__class_Otop(tc_fun(_1492450, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1492454, _1492452, _1492456), hAPP(c_Set_Oimage(_1492450, _1492454, _1492458), c_Orderings_Otop__class_Otop(tc_fun(_1492450, tc_HOL_Obool)))))], (39687 ^ _777864) ^ [_1528975, _1528977, _1528979, _1528981, _1528983, _1528985] : [class_Groups_Ocomm__monoid__mult(_1528975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528977), _1528979)), 39697 ^ _777864 : [(39700 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528981), hAPP(_1528983, 39696 ^ [_1528975, _1528977, _1528979, _1528981, _1528983, _1528985])))], (39698 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528977), 39696 ^ [_1528975, _1528977, _1528979, _1528981, _1528983, _1528985]), _1528979)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1528975, _1528977, c_Groups_Otimes__class_Otimes(_1528975)), hAPP(hAPP(c_COMBS(_1528977, tc_fun(_1528981, tc_HOL_Obool), _1528975), hAPP(hAPP(c_COMBC(_1528977, _1528975, tc_fun(tc_fun(_1528981, tc_HOL_Obool), _1528975)), hAPP(hAPP(c_COMBB(tc_fun(_1528981, _1528975), tc_fun(_1528975, tc_fun(tc_fun(_1528981, tc_HOL_Obool), _1528975)), _1528977), c_Finite__Set_Ofold__image(_1528975, _1528981, c_Groups_Otimes__class_Otimes(_1528975))), _1528985)), c_Groups_Oone__class_Oone(_1528975))), _1528983)), c_Groups_Oone__class_Oone(_1528975)), _1528979) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1528975, tc_prod(_1528977, _1528981), c_Groups_Otimes__class_Otimes(_1528975)), hAPP(c_Product__Type_Oprod_Oprod__case(_1528977, _1528981, _1528975), _1528985)), c_Groups_Oone__class_Oone(_1528975)), hAPP(hAPP(c_Product__Type_OSigma(_1528977, _1528981), _1528979), _1528983)))], (30268 ^ _777864) ^ [_1329583, _1329585, _1329587, _1329589, _1329591] : [c_Finite__Set_Ofolding__one(_1329583, _1329585, _1329587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329583), _1329589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329583), _1329591)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329583, tc_HOL_Obool)), _1329589), _1329591) = c_Orderings_Obot__class_Obot(tc_fun(_1329583, tc_HOL_Obool))), -(hAPP(hAPP(_1329585, hAPP(_1329587, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329583, tc_HOL_Obool)), _1329589), _1329591))), hAPP(_1329587, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329583, tc_HOL_Obool)), _1329589), _1329591))) = hAPP(hAPP(_1329585, hAPP(_1329587, _1329589)), hAPP(_1329587, _1329591)))], (15810 ^ _777864) ^ [_1048314, _1048316, _1048318, _1048320, _1048322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048314), _1048316)), -(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), _1048316), _1048318)), _1048320)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048314), _1048318)), _1048322)) = 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), _1048316), _1048314)), _1048318)), _1048320)), _1048322))], (13228 ^ _777864) ^ [_999954, _999956, _999958] : [13229 ^ _777864 : [(13232 ^ _777864) ^ [] : [_999956 = _999958], (13230 ^ _777864) ^ [] : [_999954 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999954), _999956) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _999954), _999958))], (11609 ^ _777864) ^ [_971686, _971688, _971690, _971692] : [class_Rings_Oordered__comm__semiring(_971686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971686), _971688), _971690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971686), c_Groups_Ozero__class_Ozero(_971686)), _971692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971686), _971692), _971688)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971686), _971692), _971690))))], (41872 ^ _777864) ^ [_1589594, _1589596, _1589598, _1589600, _1589602] : [class_Groups_Ocomm__monoid__add(_1589594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589596), _1589598)), c_Fun_Oinj__on(_1589596, _1589596, _1589600, _1589598), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1589596, _1589594), _1589602), hAPP(c_Set_Oimage(_1589596, _1589596, _1589600), _1589598)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1589596, _1589594), hAPP(c_Fun_Ocomp(_1589596, _1589594, _1589596, _1589602), _1589600)), _1589598))], (45002 ^ _777864) ^ [_1664124, _1664126, _1664128] : [45004 ^ _777864 : [(45007 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664124, tc_HOL_Obool)), 45003 ^ [_1664124, _1664126, _1664128]), _1664128))], (45005 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1664124, tc_HOL_Obool)), 45003 ^ [_1664124, _1664126, _1664128]), _1664126)))]], -(_1664126 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1664124, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664124, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1664124, tc_HOL_Obool), _1664126)), _1664128)))], (10043 ^ _777864) ^ [_945740] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945740), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _945740)], (26747 ^ _777864) ^ [_1250109, _1250111, _1250113, _1250115] : [hBOOL(hAPP(hAPP(c_member(_1250109), _1250111), hAPP(hAPP(c_Set_Oinsert(_1250109), _1250113), _1250115))), -(_1250111 = _1250113), -(hBOOL(hAPP(hAPP(c_member(_1250109), _1250111), _1250115)))], (36892 ^ _777864) ^ [_1467148, _1467150, _1467152, _1467154, _1467156] : [class_Groups_Ocomm__monoid__add(_1467148), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467150), _1467152)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467150, _1467148), _1467154), hAPP(hAPP(c_Set_Oinsert(_1467150), _1467156), _1467152)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467148), hAPP(_1467154, _1467156)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467150, _1467148), _1467154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467150, tc_HOL_Obool)), _1467152), hAPP(hAPP(c_Set_Oinsert(_1467150), _1467156), c_Orderings_Obot__class_Obot(tc_fun(_1467150, tc_HOL_Obool)))))))], (28264 ^ _777864) ^ [_1282267, _1282269, _1282271, _1282273] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282267, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1282267), _1282269), _1282271)), _1282273) = hAPP(hAPP(c_Set_Oinsert(_1282267), _1282269), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282267, tc_HOL_Obool)), _1282271), _1282273)))], (44182 ^ _777864) ^ [_1645090, _1645092] : [-(hAPP(c_Relation_OImage(_1645090, _1645090, c_Relation_OId(_1645090)), _1645092) = _1645092)], (16014 ^ _777864) ^ [_1052267, _1052269, _1052271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052267)), 16020 ^ _777864 : [(16023 ^ _777864) ^ [] : [hBOOL(hAPP(_1052269, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16019 ^ [_1052267, _1052269, _1052271]), _1052267)))], (16021 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1052269, 16019 ^ [_1052267, _1052269, _1052271])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052271)), 16028 ^ _777864 : [(16029 ^ _777864) ^ [_1052556] : [hBOOL(hAPP(_1052269, _1052556)), -(hBOOL(hAPP(_1052269, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1052271), _1052267)))))]]], (49882 ^ _777864) ^ [_1782658, _1782660, _1782662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1782658), _1782660)), -(c_List_Oupt(_1782658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1782660), _1782662)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1782658, _1782660)), c_List_Oupt(_1782660, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1782660), _1782662))))], (19330 ^ _777864) ^ [] : [-(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)))))], (43963 ^ _777864) ^ [_1638753, _1638755, _1638757, _1638759, _1638761] : [_1638753 = c_Orderings_Obot__class_Obot(tc_fun(_1638755, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638755, tc_fun(_1638757, tc_HOL_Obool)), _1638753), hAPP(hAPP(c_COMBB(tc_fun(_1638757, tc_HOL_Obool), tc_fun(_1638757, tc_HOL_Obool), _1638755), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638757, tc_HOL_Obool)), _1638759)), _1638761)) = c_Orderings_Otop__class_Otop(tc_fun(_1638757, tc_HOL_Obool)))], (18164 ^ _777864) ^ [_1090360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090360), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090360))], (38548 ^ _777864) ^ [] : [-(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))))], (48977 ^ _777864) ^ [_1762441, _1762443, _1762445] : [class_Lattices_Olattice(_1762441), -(c_Big__Operators_Olattice__class_OSup__fin(_1762441, hAPP(c_List_Oset(_1762441), hAPP(hAPP(c_List_Olist_OCons(_1762441), _1762443), _1762445))) = hAPP(c_List_Ofoldl(_1762441, _1762441, c_Lattices_Osemilattice__sup__class_Osup(_1762441), _1762443), _1762445))], (9370 ^ _777864) ^ [_934099, _934101, _934103] : [class_Rings_Olinordered__ring__strict(_934099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934099), _934101), c_Groups_Ozero__class_Ozero(_934099))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934099), _934103), c_Groups_Ozero__class_Ozero(_934099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934099), c_Groups_Ozero__class_Ozero(_934099)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934099), _934101), _934103))))], (39954 ^ _777864) ^ [_1535804, _1535806, _1535808, _1535810] : [c_Relation_Orefl__on(_1535804, _1535806, _1535808), hBOOL(hAPP(hAPP(c_member(_1535804), _1535810), _1535806)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1535804, _1535804)), hAPP(hAPP(c_Product__Type_OPair(_1535804, _1535804), _1535810), _1535810)), _1535808)))], (16768 ^ _777864) ^ [_1066714, _1066716] : [class_Groups_Oabs__if(_1066714), 16771 ^ _777864 : [(16778 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066714), _1066716), c_Groups_Ozero__class_Ozero(_1066714)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066714), _1066716) = _1066716)], (16772 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066714), _1066716), c_Groups_Ozero__class_Ozero(_1066714))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066714), _1066716) = hAPP(c_Groups_Ouminus__class_Ouminus(_1066714), _1066716))]]], (31615 ^ _777864) ^ [_1355663, _1355665, _1355667] : [class_Orderings_Olinorder(_1355663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355663, tc_HOL_Obool)), _1355665), _1355667)), -(_1355665 = c_Orderings_Obot__class_Obot(tc_fun(_1355663, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355663), _1355667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355663), c_Big__Operators_Olinorder__class_OMin(_1355663, _1355667)), c_Big__Operators_Olinorder__class_OMin(_1355663, _1355665))))], (48900 ^ _777864) ^ [_1760945, _1760947, _1760949] : [class_Groups_Omonoid__add(_1760945), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1760945), _1760947), hAPP(c_List_Ofoldl(_1760945, _1760945, c_Groups_Oplus__class_Oplus(_1760945), c_Groups_Ozero__class_Ozero(_1760945)), _1760949)) = hAPP(c_List_Ofoldl(_1760945, _1760945, c_Groups_Oplus__class_Oplus(_1760945), _1760947), _1760949))], (7464 ^ _777864) ^ [_901041, _901043] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_901041, _901043)))), hBOOL(hAPP(c_Com_OWT, _901041)), hBOOL(hAPP(c_Com_OWT, _901043))], (17514 ^ _777864) ^ [_1080275, _1080277] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080275)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080275)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080277)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080275)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080277))))], (10023 ^ _777864) ^ [_945449, _945451] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945449), _945451) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 10026 ^ _777864 : [(10029 ^ _777864) ^ [] : [-(_945451 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10027 ^ _777864) ^ [] : [-(_945449 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17786 ^ _777864) ^ [_1084376, _1084378, _1084380] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084376))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084378)), _1084380)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084378)), _1084380))], (6056 ^ _777864) ^ [_877582] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _877582)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27338 ^ _777864) ^ [_1264022, _1264024, _1264026, _1264028, _1264030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1264022, _1264024)), hAPP(_1264022, _1264026))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1264028, _1264028)), hAPP(hAPP(c_Product__Type_OPair(_1264028, _1264028), _1264024), _1264026)), c_Wellfounded_Omlex__prod(_1264028, _1264022, _1264030))))], (50540 ^ _777864) ^ [_1795824, _1795826, _1795828, _1795830, _1795832] : [-(hAPP(c_List_Ofoldl(_1795824, _1795826, _1795828, _1795830), _1795832) = c_List_Ofoldr(_1795826, _1795824, hAPP(c_COMBC(_1795824, _1795826, _1795824), _1795828), hAPP(c_List_Orev(_1795826), _1795832), _1795830))], (39127 ^ _777864) ^ [_1516588, _1516590, _1516592, _1516594, _1516596] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516588, _1516590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1516588, tc_HOL_Obool)), _1516592), _1516594)), _1516596) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1516588, _1516590), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516588, _1516590), _1516592), _1516596)), hAPP(hAPP(c_Product__Type_OSigma(_1516588, _1516590), _1516594), _1516596)))], (40038 ^ _777864) ^ [_1537658] : [class_Orderings_Olinorder(_1537658), -(c_Finite__Set_Ofun__left__comm__idem(_1537658, _1537658, c_Orderings_Oord__class_Omax(_1537658)))], (39147 ^ _777864) ^ [_1517170, _1517172, _1517174, _1517176] : [39148 ^ _777864 : [(39151 ^ _777864) ^ [] : [_1517176 = c_Orderings_Obot__class_Obot(tc_fun(_1517172, tc_HOL_Obool))], (39149 ^ _777864) ^ [] : [_1517174 = c_Orderings_Obot__class_Obot(tc_fun(_1517170, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1517170, _1517172), _1517174), hAPP(c_COMBK(tc_fun(_1517172, tc_HOL_Obool), _1517170), _1517176)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517170, _1517172), tc_HOL_Obool)))], (27712 ^ _777864) ^ [] : [-(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)))))], (28633 ^ _777864) ^ [_1293605, _1293607, _1293609, _1293611, _1293613] : [hBOOL(hAPP(hAPP(c_member(_1293605), _1293607), hAPP(c_Relation_OImage(_1293609, _1293605, _1293611), hAPP(hAPP(c_Set_Oinsert(_1293609), _1293613), c_Orderings_Obot__class_Obot(tc_fun(_1293609, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1293609, _1293605)), hAPP(hAPP(c_Product__Type_OPair(_1293609, _1293605), _1293613), _1293607)), _1293611)))], (43417 ^ _777864) ^ [_1623834, _1623836, _1623838, _1623840] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623834, _1623834)), hAPP(hAPP(c_Product__Type_OPair(_1623834, _1623834), _1623836), _1623838)), c_Transitive__Closure_Ortrancl(_1623834, _1623840))), hBOOL(hAPP(hAPP(c_member(_1623834), _1623838), c_Wellfounded_Oacc(_1623834, _1623840))), -(hBOOL(hAPP(hAPP(c_member(_1623834), _1623836), c_Wellfounded_Oacc(_1623834, _1623840))))], (16460 ^ _777864) ^ [_1060436, _1060438, _1060440] : [class_Groups_Oordered__ab__group__add__abs(_1060436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060436), hAPP(c_Groups_Oabs__class_Oabs(_1060436), _1060438)), _1060440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060436), hAPP(c_Groups_Ouminus__class_Ouminus(_1060436), _1060438)), _1060440)))], (30228 ^ _777864) ^ [_1328629, _1328631, _1328633] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328629, tc_HOL_Obool)), _1328631), _1328633) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328629, tc_HOL_Obool)), _1328631), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328629, tc_HOL_Obool)), _1328633)))], (51495 ^ _777864) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (18938 ^ _777864) ^ [_1103360, _1103362] : [c_Int_OBit0(_1103360) = c_Int_OBit1(_1103362)], (28116 ^ _777864) ^ [_1278892, _1278894, _1278896, _1278898] : [class_Lattices_Osemilattice__sup(_1278892), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278892), _1278894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278892), _1278896), _1278898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278892), _1278896), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278892), _1278894), _1278898)))], (4586 ^ _777864) ^ [_847951, _847953, _847955, _847957] : [-(c_Product__Type_OPair(_847957, _847953) = c_Product__Type_OPair(_847955, _847951)), _847957 = _847955, _847953 = _847951], (38669 ^ _777864) ^ [_1505722, _1505724, _1505726, _1505728] : [c_Fun_Oinj__on(_1505722, _1505724, _1505726, c_Orderings_Otop__class_Otop(tc_fun(_1505722, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505722, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1505722, _1505724, _1505726), hAPP(hAPP(c_Set_Oinsert(_1505724), _1505728), c_Orderings_Obot__class_Obot(tc_fun(_1505724, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1505722), c_HOL_OThe(_1505722, hAPP(hAPP(c_COMBC(_1505722, _1505724, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1505724, tc_fun(_1505724, tc_HOL_Obool), _1505722), c_fequal), _1505726)), _1505728))), c_Orderings_Obot__class_Obot(tc_fun(_1505722, tc_HOL_Obool))))))], (32425 ^ _777864) ^ [_1370794, _1370796] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1370794), _1370796)))), -(_1370796 = c_Orderings_Obot__class_Obot(tc_fun(_1370794, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370794), _1370796))], (19666 ^ _777864) ^ [_1116508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1116508)), -(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), _1116508), 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)))))))], (24477 ^ _777864) ^ [_1206744, _1206746, _1206748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1206744), c_Nitpick_Oplus__frac(_1206744, _1206746, c_Nitpick_Ouminus__frac(_1206744, _1206748)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1206744, _1206746, _1206748))], (40350 ^ _777864) ^ [_1545790, _1545792, _1545794, _1545796, _1545798, _1545800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545790), _1545792)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545794), _1545796)), 40360 ^ _777864 : [(40363 ^ _777864) ^ [] : [hAPP(c_Finite__Set_Ocard(_1545790), hAPP(c_Set_OCollect(_1545790), hAPP(hAPP(c_COMBS(_1545790, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545790), c_fconj), hAPP(hAPP(c_COMBC(_1545790, tc_fun(_1545790, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545790)), _1545792))), hAPP(hAPP(c_COMBC(_1545790, _1545794, tc_HOL_Obool), _1545798), 40359 ^ [_1545790, _1545792, _1545794, _1545796, _1545798, _1545800])))) = _1545800], (40361 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545794), 40359 ^ [_1545790, _1545792, _1545794, _1545796, _1545798, _1545800]), _1545796)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545790, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1545794, tc_HOL_Obool), tc_Nat_Onat, _1545790), c_Finite__Set_Ocard(_1545794)), hAPP(hAPP(c_COMBB(tc_fun(_1545794, tc_HOL_Obool), tc_fun(_1545794, tc_HOL_Obool), _1545790), c_Set_OCollect(_1545794)), hAPP(hAPP(c_COMBB(tc_fun(_1545794, tc_HOL_Obool), tc_fun(_1545794, tc_HOL_Obool), _1545790), hAPP(c_COMBS(_1545794, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545794), c_fconj), hAPP(hAPP(c_COMBC(_1545794, tc_fun(_1545794, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545794)), _1545796)))), _1545798)))), _1545792) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1545800), hAPP(c_Finite__Set_Ocard(_1545794), _1545796)))], (12400 ^ _777864) ^ [_985625, _985627, _985629, _985631, _985633] : [class_Rings_Olinordered__semiring__strict(_985625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985625), _985627), _985629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985625), _985631), _985633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985625), c_Groups_Ozero__class_Ozero(_985625)), _985629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_985625), c_Groups_Ozero__class_Ozero(_985625)), _985631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985625), _985627), _985631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985625), _985629), _985633))))], (23383 ^ _777864) ^ [_1185837] : [-(c_Hoare__Mirabelle_OMGT(_1185837) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1185837), c_Natural_Oevalc(_1185837)))], (6144 ^ _777864) ^ [_878907, _878909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _878907), _878909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _878907)), hAPP(c_Nat_OSuc, _878909))))], (14247 ^ _777864) ^ [_1018811] : [-(_1018811 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018811), _1018811) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (31483 ^ _777864) ^ [_1353076, _1353078] : [class_Orderings_Olinorder(_1353076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353076), _1353078)), -(_1353078 = c_Orderings_Obot__class_Obot(tc_fun(_1353076, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1353076), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1353076), 31496 ^ [_1353076, _1353078]), 31497 ^ [_1353076, _1353078])), hAPP(hAPP(c_Set_Oinsert(_1353076), 31496 ^ [_1353076, _1353078]), hAPP(hAPP(c_Set_Oinsert(_1353076), 31497 ^ [_1353076, _1353078]), c_Orderings_Obot__class_Obot(tc_fun(_1353076, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1353076), c_Big__Operators_Olinorder__class_OMax(_1353076, _1353078)), _1353078)))], (7806 ^ _777864) ^ [_907689, _907691, _907693, _907695, _907697] : [c_Com_Ocom_OWhile(_907689, _907691) = c_Com_Ocom_OCall(_907693, _907695, _907697)], (35024 ^ _777864) ^ [_1428801, _1428803, _1428805] : [-(c_Fun_Oinj__on(_1428801, _1428803, _1428805, c_Orderings_Obot__class_Obot(tc_fun(_1428801, tc_HOL_Obool))))], (19580 ^ _777864) ^ [_1114752, _1114754, _1114756] : [class_Groups_Omonoid__mult(_1114752), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114752), _1114754), 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)))), _1114756))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114752), _1114754), hAPP(hAPP(c_Power_Opower__class_Opower(_1114752), hAPP(hAPP(c_Power_Opower__class_Opower(_1114752), _1114754), _1114756)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (44476 ^ _777864) ^ [_1652200, _1652202, _1652204] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652200, _1652200)), _1652202), c_Transitive__Closure_Otrancl(_1652200, _1652204)))), 44477 ^ _777864 : [(44478 ^ _777864) ^ [_1652279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1652279)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1652200, _1652200)), _1652202), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1652200, _1652200), tc_HOL_Obool), _1652279), _1652204)))]]], (22765 ^ _777864) ^ [_1171913, _1171915, _1171917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171913, tc_HOL_Obool)), _1171915), _1171917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171913, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171913, tc_HOL_Obool)), _1171917)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1171913, tc_HOL_Obool)), _1171915))))], (18602 ^ _777864) ^ [_1097680, _1097682] : [c_Int_Oiszero(_1097680, hAPP(c_Int_Onumber__class_Onumber__of(_1097680), c_Int_OBit1(_1097682))), class_Int_Onumber__ring(_1097680), class_Int_Oring__char__0(_1097680)], (6206 ^ _777864) ^ [_879945, _879947, _879949, _879951] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_879945), 6209 ^ _777864 : [(6216 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879945), _879947), _879951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879945), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879945), _879947), _879949)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879945), _879951), _879949))))], (6210 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879945), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879945), _879947), _879949)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879945), _879951), _879949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_879945), _879947), _879951)))]]], (49924 ^ _777864) ^ [_1783440, _1783442, _1783444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1783440), _1783442)), _1783444)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1783442), c_List_Oupt(_1783440, _1783444)) = c_List_Oupt(_1783440, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1783440), _1783442)))], (24773 ^ _777864) ^ [_1212826] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1212826)))], (38232 ^ _777864) ^ [_1495293] : [-(hAPP(c_Set_OPow(_1495293), c_Orderings_Otop__class_Otop(tc_fun(_1495293, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1495293, tc_HOL_Obool), tc_HOL_Obool)))], (36876 ^ _777864) ^ [_1466706, _1466708, _1466710, _1466712, _1466714] : [class_Groups_Ocomm__monoid__add(_1466706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466708), _1466710)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466708, _1466706), _1466712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466708, tc_HOL_Obool)), _1466710), _1466714)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466708, _1466706), hAPP(hAPP(c_COMBC(_1466708, _1466706, _1466706), hAPP(hAPP(c_COMBS(_1466708, _1466706, tc_fun(_1466706, _1466706)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1466706, tc_fun(_1466706, _1466706)), _1466708), c_If(_1466706)), hAPP(hAPP(c_COMBC(_1466708, tc_fun(_1466708, tc_HOL_Obool), tc_HOL_Obool), c_member(_1466708)), _1466714))), _1466712)), c_Groups_Ozero__class_Ozero(_1466706))), _1466710))], (40991 ^ _777864) ^ [_1567838] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1567838)))], (43555 ^ _777864) ^ [_1626930, _1626932, _1626934, _1626936, _1626938, _1626940] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626930, tc_fun(_1626932, tc_HOL_Obool)), _1626934), _1626936), _1626938)), -(hBOOL(hAPP(hAPP(_1626936, _1626940), _1626938))), hBOOL(hAPP(hAPP(c_member(_1626930), _1626940), _1626934))], (51371 ^ _777864) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (16108 ^ _777864) ^ [_1054151, _1054153, _1054155] : [class_Int_Onumber__ring(_1054151), class_Int_Oring__char__0(_1054151), 16115 ^ _777864 : [(16122 ^ _777864) ^ [] : [_1054153 = _1054155, -(hAPP(c_Int_Onumber__class_Onumber__of(_1054151), _1054153) = hAPP(c_Int_Onumber__class_Onumber__of(_1054151), _1054155))], (16116 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054151), _1054153) = hAPP(c_Int_Onumber__class_Onumber__of(_1054151), _1054155), -(_1054153 = _1054155)]]], (14390 ^ _777864) ^ [_1021171, _1021173, _1021175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021171), _1021173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021175), 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), _1021173), _1021175)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021171), _1021175))))], (28677 ^ _777864) ^ [_1295574, _1295576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1295574), _1295576)), -(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)), _1295574)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1295576))))], (34473 ^ _777864) ^ [_1417664, _1417666, _1417668] : [-(hAPP(c_Set_OPow(_1417664), hAPP(hAPP(c_Set_Oinsert(_1417664), _1417666), _1417668)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1417664, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417664), _1417668)), hAPP(c_Set_Oimage(tc_fun(_1417664, tc_HOL_Obool), tc_fun(_1417664, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1417664), _1417666)), hAPP(c_Set_OPow(_1417664), _1417668))))], (32929 ^ _777864) ^ [_1381438, _1381440, _1381442] : [class_Groups_Ocomm__monoid__add(_1381438), class_Groups_Ocomm__monoid__mult(_1381438), c_Nat__Transfer_Onat__set(_1381440), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1381438), _1381442), _1381440) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1381438), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1381438, tc_Nat_Onat), _1381442), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1381440)))], (47883 ^ _777864) ^ [_1736137, _1736139, _1736141, _1736143, _1736145] : [-(hAPP(hAPP(c_List_Olist_OCons(_1736137), _1736139), _1736141) = hAPP(hAPP(c_List_Oappend(_1736137), _1736143), _1736145)), 47884 ^ _777864 : [(47891 ^ _777864) ^ [_1736320] : [hAPP(hAPP(c_List_Olist_OCons(_1736137), _1736139), _1736320) = _1736143, _1736141 = hAPP(hAPP(c_List_Oappend(_1736137), _1736320), _1736145)], (47885 ^ _777864) ^ [] : [_1736143 = c_List_Olist_ONil(_1736137), hAPP(hAPP(c_List_Olist_OCons(_1736137), _1736139), _1736141) = _1736145]]], (32783 ^ _777864) ^ [_1378702, _1378704, _1378706, _1378708] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1378702), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378704, tc_Int_Oint), _1378706), _1378708)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378704, _1378702), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1378702, _1378704), c_Int_Oring__1__class_Oof__int(_1378702)), _1378706)), _1378708)), class_Groups_Ocomm__monoid__mult(_1378702), class_Rings_Oring__1(_1378702)], (8228 ^ _777864) ^ [_914302, _914304, _914306] : [class_Orderings_Opreorder(_914302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914302), _914304), _914306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914302), _914306), _914304))], (18508 ^ _777864) ^ [_1096126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096126), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1096126)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (46224 ^ _777864) ^ [_1693794, _1693796, _1693798, _1693800] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1693794, _1693796))), hAPP(hAPP(c_List_Ozip(_1693794, _1693796), _1693798), _1693800)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693794)), _1693798)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693796)), _1693800)))], (23085 ^ _777864) ^ [_1178531, _1178533, _1178535] : [class_Int_Onumber__ring(_1178531), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178531), hAPP(c_Int_Onumber__class_Onumber__of(_1178531), _1178533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1178535))) = hAPP(hAPP(c_HOL_OLet(_1178531, _1178531), hAPP(hAPP(c_Power_Opower__class_Opower(_1178531), hAPP(c_Int_Onumber__class_Onumber__of(_1178531), _1178533)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1178535))), hAPP(hAPP(c_COMBS(_1178531, _1178531, _1178531), c_Groups_Otimes__class_Otimes(_1178531)), c_COMBI(_1178531))))], (12027 ^ _777864) ^ [_979203, _979205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979203), _979205)), 12030 ^ _777864 : [(12037 ^ _777864) ^ [] : [_979205 = _979203, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979205), hAPP(c_Nat_OSuc, _979203))))], (12031 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979205), hAPP(c_Nat_OSuc, _979203))), -(_979205 = _979203)]]], (5562 ^ _777864) ^ [_866348, _866350, _866352, _866354] : [c_Natural_Oevaln(_866348, _866350, _866352, _866354), -(c_Natural_Oevaln(_866348, _866350, hAPP(c_Nat_OSuc, _866352), _866354))], (49656 ^ _777864) ^ [_1777925, _1777927] : [49658 ^ _777864 : [(49661 ^ _777864) ^ [] : [49657 ^ [_1777925, _1777927] = c_List_Olist_ONil(_1777925)], (49659 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777925)), 49657 ^ [_1777925, _1777927]), hAPP(c_List_Oset(tc_List_Olist(_1777925)), _1777927))))]], -(c_List_Otranspose(_1777925, _1777927) = c_List_Olist_ONil(tc_List_Olist(_1777925)))], (27932 ^ _777864) ^ [_1275554, _1275556, _1275558, _1275560] : [class_Lattices_Osemilattice__sup(_1275554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275554), _1275556), _1275558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275554), _1275556), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275554), _1275558), _1275560))))], (37967 ^ _777864) ^ [_1490323, _1490325, _1490327, _1490329, _1490331, _1490333, _1490335] : [-(hBOOL(hAPP(hAPP(c_member(_1490323), _1490325), _1490327))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1490323, _1490329, _1490331, _1490333, _1490327), _1490335)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1490323, _1490329, _1490331, _1490333, hAPP(hAPP(c_Set_Oinsert(_1490323), _1490325), _1490327)), hAPP(hAPP(_1490331, _1490325), _1490335))))], (48590 ^ _777864) ^ [_1754174, _1754176, _1754178, _1754180] : [-(hAPP(hAPP(c_List_Oappend(_1754174), _1754176), _1754178) = _1754180), _1754176 = hAPP(hAPP(c_List_Otake(_1754174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754174)), _1754176)), _1754180), _1754178 = hAPP(hAPP(c_List_Odrop(_1754174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754174)), _1754176)), _1754180)], (34869 ^ _777864) ^ [_1425261, _1425263, _1425265, _1425267] : [class_Orderings_Olinorder(_1425261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425261), _1425263), _1425265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425261), _1425265), _1425267)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425261, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1425261, _1425263, _1425265)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1425261, _1425265, _1425267)) = c_SetInterval_Oord__class_OatLeastAtMost(_1425261, _1425263, _1425267))], (6044 ^ _777864) ^ [_877387, _877389, _877391, _877393] : [-(c_Com_Ovname_Ovname__rec(_877387, _877389, _877391, c_Com_Ovname_OGlb(_877393)) = hAPP(_877389, _877393))], (18004 ^ _777864) ^ [_1087990] : [class_Rings_Osemiring__1(_1087990), c_Int_Oiszero(_1087990, c_Groups_Oone__class_Oone(_1087990))], (29151 ^ _777864) ^ [_1305494] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1305494)), -(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)), _1305494))))], (6444 ^ _777864) ^ [_884194, _884196, _884198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884196), _884198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884194), _884196)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884194), _884198))))], (18060 ^ _777864) ^ [_1088781, _1088783] : [class_Int_Onumber__ring(_1088781), 18063 ^ _777864 : [(18070 ^ _777864) ^ [] : [c_Int_Oiszero(_1088781, hAPP(c_Int_Onumber__class_Onumber__of(_1088781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088783), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1088781), _1088783) = c_Groups_Ozero__class_Ozero(_1088781))], (18064 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1088781), _1088783) = c_Groups_Ozero__class_Ozero(_1088781), -(c_Int_Oiszero(_1088781, hAPP(c_Int_Onumber__class_Onumber__of(_1088781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088783), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (7026 ^ _777864) ^ [_893280, _893282, _893284] : [hAPP(c_Option_Ooption_OSome(_893280), _893282) = hAPP(c_Option_Ooption_OSome(_893280), _893284), -(_893282 = _893284)], (51397 ^ _777864) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (43593 ^ _777864) ^ [_1627786, _1627788] : [c_Wellfounded_Oacyclic(_1627786, hAPP(c_Relation_Oconverse(_1627786, _1627786), _1627788)), -(c_Wellfounded_Oacyclic(_1627786, _1627788))], (44891 ^ _777864) ^ [_1661897] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661897, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1661897, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1661897, tc_HOL_Obool)))], (28784 ^ _777864) ^ [_1297963, _1297965, _1297967, _1297969, _1297971] : [hBOOL(hAPP(hAPP(c_member(_1297963), _1297965), hAPP(c_Relation_OImage(_1297967, _1297963, _1297969), _1297971))), 28788 ^ _777864 : [(28791 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1297967), 28787 ^ [_1297963, _1297965, _1297967, _1297969, _1297971]), _1297971)))], (28789 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1297967, _1297963)), hAPP(hAPP(c_Product__Type_OPair(_1297967, _1297963), 28787 ^ [_1297963, _1297965, _1297967, _1297969, _1297971]), _1297965)), _1297969)))]]], (50466 ^ _777864) ^ [_1794257, _1794259, _1794261] : [_1794261 = hAPP(hAPP(c_List_Olist_OCons(_1794257), _1794259), c_List_Olist_ONil(_1794257)), -(hAPP(hAPP(c_List_Olist_OCons(_1794257), _1794259), c_List_Olist_ONil(_1794257)) = hAPP(c_List_Orev(_1794257), _1794261))], (43024 ^ _777864) ^ [_1614566, _1614568, _1614570, _1614572, _1614574] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614566, _1614566)), hAPP(hAPP(c_Product__Type_OPair(_1614566, _1614566), _1614568), _1614570)), c_Transitive__Closure_Otrancl(_1614566, _1614572))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614566, _1614566)), hAPP(hAPP(c_Product__Type_OPair(_1614566, _1614566), _1614570), _1614574)), _1614572)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614566, _1614566)), hAPP(hAPP(c_Product__Type_OPair(_1614566, _1614566), _1614568), _1614574)), c_Transitive__Closure_Otrancl(_1614566, _1614572))))], (40290 ^ _777864) ^ [_1543192, _1543194] : [-(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), _1543192)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1543194))))))], (18502 ^ _777864) ^ [_1096031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1096031)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1096031), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28536 ^ _777864) ^ [_1291295, _1291297, _1291299, _1291301, _1291303] : [-(hAPP(c_Set_Oimage(_1291295, _1291297, _1291299), hAPP(hAPP(c_Set_Oinsert(_1291295), _1291301), _1291303)) = hAPP(hAPP(c_Set_Oinsert(_1291297), hAPP(_1291299, _1291301)), hAPP(c_Set_Oimage(_1291295, _1291297, _1291299), _1291303)))], (40731 ^ _777864) ^ [_1560224, _1560226, _1560228, _1560230, _1560232] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1560224, _1560226, _1560228), _1560230), _1560232) = hAPP(c_Set_OCollect(tc_prod(_1560224, _1560228)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560224, _1560228, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1560228, tc_fun(_1560226, tc_HOL_Obool)), tc_fun(_1560228, tc_HOL_Obool), _1560224), hAPP(c_COMBB(tc_fun(_1560226, tc_HOL_Obool), tc_HOL_Obool, _1560228), c_HOL_OEx(_1560226))), hAPP(hAPP(c_COMBC(_1560224, tc_fun(_1560228, tc_fun(_1560226, tc_HOL_Obool)), tc_fun(_1560228, tc_fun(_1560226, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1560226, tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), tc_fun(tc_fun(_1560228, tc_fun(_1560226, tc_HOL_Obool)), tc_fun(_1560228, tc_fun(_1560226, tc_HOL_Obool))), _1560224), c_COMBB(tc_fun(_1560226, tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool), _1560228)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1560226, tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), _1560224), c_COMBS(_1560226, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_HOL_Obool), tc_fun(_1560226, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1560224), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560226), c_fconj)), hAPP(hAPP(c_COMBC(_1560224, tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_fun(tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), _1560224), c_COMBC(_1560226, tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_prod(_1560224, _1560226)), tc_fun(_1560226, tc_fun(tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_HOL_Obool)), _1560224), hAPP(c_COMBB(tc_prod(_1560224, _1560226), tc_fun(tc_fun(tc_prod(_1560224, _1560226), tc_HOL_Obool), tc_HOL_Obool), _1560226), c_member(tc_prod(_1560224, _1560226)))), c_Product__Type_OPair(_1560224, _1560226)))), _1560230))))), hAPP(hAPP(c_COMBC(_1560228, tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_fun(tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_fun(_1560226, tc_HOL_Obool)), _1560228), c_COMBC(_1560226, tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560226, tc_prod(_1560226, _1560228)), tc_fun(_1560226, tc_fun(tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_HOL_Obool)), _1560228), hAPP(c_COMBB(tc_prod(_1560226, _1560228), tc_fun(tc_fun(tc_prod(_1560226, _1560228), tc_HOL_Obool), tc_HOL_Obool), _1560226), c_member(tc_prod(_1560226, _1560228)))), hAPP(c_COMBC(_1560226, _1560228, tc_prod(_1560226, _1560228)), c_Product__Type_OPair(_1560226, _1560228))))), _1560232))))))], (41862 ^ _777864) ^ [_1589381, _1589383, _1589385, _1589387, _1589389, _1589391] : [class_Groups_Ocomm__monoid__mult(_1589381), c_Fun_Oinj__on(_1589383, _1589385, _1589387, _1589389), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589385, _1589381), _1589391), hAPP(c_Set_Oimage(_1589383, _1589385, _1589387), _1589389)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1589383, _1589381), hAPP(c_Fun_Ocomp(_1589385, _1589381, _1589383, _1589391), _1589387)), _1589389))], (14336 ^ _777864) ^ [_1020271, _1020273] : [class_Divides_Osemiring__div(_1020271), -(_1020273 = c_Groups_Ozero__class_Ozero(_1020271)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1020271), _1020273), _1020273) = c_Groups_Oone__class_Oone(_1020271))], (26203 ^ _777864) ^ [_1238636, _1238638, _1238640] : [hAPP(hAPP(c_Set_Oinsert(_1238636), _1238638), _1238640) = c_Orderings_Obot__class_Obot(tc_fun(_1238636, tc_HOL_Obool))], (51527 ^ _777864) ^ [_1812185, _1812187, _1812189, _1812191, _1812193, _1812195] : [-(hAPP(hAPP(hAPP(c_COMBC(_1812185, _1812187, _1812189), _1812191), _1812193), _1812195) = hAPP(hAPP(_1812191, _1812195), _1812193))], (43780 ^ _777864) ^ [_1632963, _1632965, _1632967, _1632969] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632963, tc_fun(_1632965, tc_HOL_Obool)), _1632967), _1632969) = c_Orderings_Otop__class_Otop(tc_fun(_1632965, tc_HOL_Obool)), 43783 ^ _777864 : [(43784 ^ _777864) ^ [_1633079] : [hBOOL(hAPP(hAPP(c_member(_1632963), _1633079), _1632967)), -(hAPP(_1632969, _1633079) = c_Orderings_Otop__class_Otop(tc_fun(_1632965, tc_HOL_Obool)))]]], (41437 ^ _777864) ^ [_1579265, _1579267, _1579269] : [c_Wellfounded_Oacyclic(_1579265, _1579267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1579265, _1579265), tc_HOL_Obool)), _1579269), _1579267)), -(c_Wellfounded_Oacyclic(_1579265, _1579269))], (44806 ^ _777864) ^ [_1660075, _1660077, _1660079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1660075, tc_HOL_Obool), tc_HOL_Obool)), _1660077), _1660079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660075, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1660075, tc_HOL_Obool), _1660077)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1660075, tc_HOL_Obool), _1660079))))], (46386 ^ _777864) ^ [_1697803, _1697805, _1697807] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1697803), _1697805)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1697803)), hAPP(c_Set_OCollect(tc_List_Olist(_1697803)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1697803), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1697803)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697803), tc_fun(_1697803, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1697803, tc_HOL_Obool), tc_fun(tc_fun(_1697803, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1697803)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1697803, tc_HOL_Obool))), c_List_Oset(_1697803))), _1697805))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697803), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1697803)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1697803)))), _1697807))))))], (8362 ^ _777864) ^ [_916416, _916418, _916420] : [class_Orderings_Opreorder(_916416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916416), _916418), _916420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916416), _916420), _916418))], (33669 ^ _777864) ^ [_1398226, _1398228, _1398230, _1398232] : [-(_1398226 = c_Orderings_Obot__class_Obot(tc_fun(_1398228, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398228, tc_fun(_1398230, tc_HOL_Obool)), _1398226), hAPP(c_COMBK(tc_fun(_1398230, tc_HOL_Obool), _1398228), _1398232)) = _1398232)], (38908 ^ _777864) ^ [_1511419, _1511421, _1511423, _1511425, _1511427, _1511429, _1511431] : [c_Typedef_Otype__definition(_1511419, _1511421, _1511423, _1511425, _1511427), 38911 ^ _777864 : [(38918 ^ _777864) ^ [] : [_1511429 = _1511431, -(hAPP(_1511423, _1511429) = hAPP(_1511423, _1511431))], (38912 ^ _777864) ^ [] : [hAPP(_1511423, _1511429) = hAPP(_1511423, _1511431), -(_1511429 = _1511431)]]], (24701 ^ _777864) ^ [_1211181, _1211183] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1211181), _1211183) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211181)), hAPP(c_Code__Numeral_Onat__of, _1211183))))], (28904 ^ _777864) ^ [_1299986] : [-(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)), _1299986)))], (40765 ^ _777864) ^ [_1561697, _1561699, _1561701, _1561703, _1561705, _1561707, _1561709] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561697, _1561699, _1561701), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561703, tc_fun(tc_prod(_1561697, _1561699), tc_HOL_Obool)), _1561705), _1561707)), _1561709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1561703, tc_fun(tc_prod(_1561697, _1561701), tc_HOL_Obool)), _1561705), hAPP(hAPP(c_COMBC(_1561703, tc_fun(tc_prod(_1561699, _1561701), tc_HOL_Obool), tc_fun(tc_prod(_1561697, _1561701), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1561697, _1561699), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1561699, _1561701), tc_HOL_Obool), tc_fun(tc_prod(_1561697, _1561701), tc_HOL_Obool)), _1561703), c_Relation_Orel__comp(_1561697, _1561699, _1561701)), _1561707)), _1561709)))], (11851 ^ _777864) ^ [_976064, _976066] : [class_Groups_Olinordered__ab__group__add(_976064), 11854 ^ _777864 : [(11861 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976064), _976066), c_Groups_Ozero__class_Ozero(_976064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976064), _976066), hAPP(c_Groups_Ouminus__class_Ouminus(_976064), _976066))))], (11855 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976064), _976066), hAPP(c_Groups_Ouminus__class_Ouminus(_976064), _976066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976064), _976066), c_Groups_Ozero__class_Ozero(_976064))))]]], (38716 ^ _777864) ^ [_1506787, _1506789, _1506791, _1506793, _1506795] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1506787, _1506789, _1506791), _1506793), _1506795)), -(hBOOL(hAPP(_1506793, hAPP(_1506791, _1506795))))], (46791 ^ _777864) ^ [_1710017, _1710019, _1710021] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710017, tc_HOL_Obool)), hAPP(c_List_Oset(_1710017), c_List_Osublist(_1710017, _1710019, _1710021))), hAPP(c_List_Oset(_1710017), _1710019))))], (16035 ^ _777864) ^ [_1052679, _1052681, _1052683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1052681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1052683), 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), _1052683), _1052681))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1052679)))))], (28086 ^ _777864) ^ [_1278299, _1278301, _1278303] : [class_Lattices_Olattice(_1278299), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278299), _1278301), _1278303) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278299), _1278303), _1278301))], (45943 ^ _777864) ^ [_1686679, _1686681, _1686683] : [hBOOL(hAPP(c_List_Odistinct(_1686679), hAPP(hAPP(c_List_Omap(tc_prod(_1686679, _1686681), _1686679), c_Product__Type_Ofst(_1686679, _1686681)), _1686683))), -(c_Map_Oran(_1686679, _1686681, c_Map_Omap__of(_1686679, _1686681, _1686683)) = hAPP(c_Set_Oimage(tc_prod(_1686679, _1686681), _1686681, c_Product__Type_Osnd(_1686679, _1686681)), hAPP(c_List_Oset(tc_prod(_1686679, _1686681)), _1686683)))], (22214 ^ _777864) ^ [_1161859, _1161861, _1161863, _1161865, _1161867, _1161869] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1161859, _1161861), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1161863), _1161865))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1161859, _1161861), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1161867), _1161869))), -(_1161861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1161865 = _1161869)], (18520 ^ _777864) ^ [_1096322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1096322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1096322))))], (42186 ^ _777864) ^ [_1597088, _1597090, _1597092, _1597094, _1597096, _1597098] : [c_Finite__Set_Ofolding__idem(_1597088, _1597090, _1597092, _1597094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597088), _1597096)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597088), _1597098)), -(hAPP(_1597094, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1597088, tc_HOL_Obool)), _1597096), _1597098)) = hAPP(c_Fun_Ocomp(_1597090, _1597090, _1597090, hAPP(_1597094, _1597096)), hAPP(_1597094, _1597098)))], (21470 ^ _777864) ^ [_1148654, _1148656, _1148658, _1148660] : [class_Fields_Olinordered__field__inverse__zero(_1148654), class_Int_Onumber(_1148654), 21477 ^ _777864 : [(21478 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148654), _1148656), _1148658)), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660))), 21481 ^ _777864 : [(21488 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), _1148658))), 21491 ^ _777864 : [(21498 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148658), c_Groups_Ozero__class_Ozero(_1148654)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660))))], (21492 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148658), c_Groups_Ozero__class_Ozero(_1148654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148654), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)), _1148658)), _1148656)))]]], (21482 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), _1148658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148654), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)), _1148658))))]]], (21504 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148654), _1148656), _1148658)), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)))), 21507 ^ _777864 : [(21510 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148654), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)), _1148658)))], (21508 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), _1148658)))]], 21511 ^ _777864 : [(21514 ^ _777864) ^ [] : [21515 ^ _777864 : [(21518 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148654), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)), _1148658)), _1148656))], (21516 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148658), c_Groups_Ozero__class_Ozero(_1148654))))]], 21519 ^ _777864 : [(21522 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), hAPP(c_Int_Onumber__class_Onumber__of(_1148654), _1148660)))], (21520 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), _1148658), c_Groups_Ozero__class_Ozero(_1148654)))]]], (21512 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148654), c_Groups_Ozero__class_Ozero(_1148654)), _1148658))]]]]], (34591 ^ _777864) ^ [_1420404, _1420406] : [c_Nat__Transfer_Ois__nat(_1420404), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1420404, _1420406)))], (9262 ^ _777864) ^ [_932147, _932149] : [class_Groups_Oab__group__add(_932147), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932147), hAPP(c_Groups_Ouminus__class_Ouminus(_932147), _932149)), _932149) = c_Groups_Ozero__class_Ozero(_932147))], (37052 ^ _777864) ^ [_1470933, _1470935, _1470937] : [class_Fields_Ofield(_1470933), -(_1470935 = c_Groups_Oone__class_Oone(_1470933)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1470933), hAPP(c_Power_Opower__class_Opower(_1470933), _1470935)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1470937)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1470933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1470933), hAPP(hAPP(c_Power_Opower__class_Opower(_1470933), _1470935), _1470937)), c_Groups_Oone__class_Oone(_1470933))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1470933), _1470935), c_Groups_Oone__class_Oone(_1470933))))], (43688 ^ _777864) ^ [_1629836, _1629838, _1629840, _1629842, _1629844] : [hBOOL(hAPP(hAPP(c_member(_1629836), _1629838), _1629840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1629842, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629836, tc_fun(_1629842, tc_HOL_Obool)), _1629840), _1629844)), hAPP(_1629844, _1629838))))], (28356 ^ _777864) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (7066 ^ _777864) ^ [_893939] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_893939)), c_Option_Ooption_ONone(_893939)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48965 ^ _777864) ^ [_1762211, _1762213] : [class_Complete__Lattice_Ocomplete__lattice(_1762211), -(c_Complete__Lattice_OSup__class_OSup(_1762211, hAPP(c_List_Oset(_1762211), _1762213)) = hAPP(c_List_Ofoldl(_1762211, _1762211, c_Lattices_Osemilattice__sup__class_Osup(_1762211), c_Orderings_Obot__class_Obot(_1762211)), _1762213))], (15242 ^ _777864) ^ [_1036551, _1036553, _1036555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036551), _1036553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036551), _1036555)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036553), _1036555))))], (25707 ^ _777864) ^ [_1228815, _1228817, _1228819] : [25708 ^ _777864 : [(25711 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228817), _1228819))], (25709 ^ _777864) ^ [] : [_1228815 = 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), _1228815), _1228817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228815), _1228819))))], (51515 ^ _777864) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (46472 ^ _777864) ^ [_1699870, _1699872, _1699874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1699870), _1699872)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1699870)), hAPP(c_Set_OCollect(tc_List_Olist(_1699870)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1699870), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1699870)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699870), tc_fun(_1699870, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1699870, tc_HOL_Obool), tc_fun(tc_fun(_1699870, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1699870)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1699870, tc_HOL_Obool))), c_List_Oset(_1699870))), _1699872))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699870), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1699870)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1699870)))), _1699874))))))], (47794 ^ _777864) ^ [_1733968, _1733970, _1733972, _1733974, _1733976, _1733978, _1733980] : [-(hBOOL(hAPP(hAPP(c_member(_1733968), _1733970), hAPP(c_List_Oset(_1733968), hAPP(hAPP(c_List_Otake(_1733968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733972)), _1733974)), _1733976))))), -(c_Map_Omap__upds(_1733968, _1733972, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1733968, tc_Option_Ooption(_1733972)), _1733978), _1733970), hAPP(c_Option_Ooption_OSome(_1733972), _1733980)), _1733976, _1733974) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1733968, tc_Option_Ooption(_1733972)), c_Map_Omap__upds(_1733968, _1733972, _1733978, _1733976, _1733974)), _1733970), hAPP(c_Option_Ooption_OSome(_1733972), _1733980)))], (33126 ^ _777864) ^ [_1385645, _1385647, _1385649, _1385651, _1385653] : [class_Groups_Ocomm__monoid__mult(_1385645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385647), _1385649)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385647), _1385651)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385645), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385647, _1385645), _1385653), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385647, tc_HOL_Obool)), _1385649), _1385651))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385647, _1385645), _1385653), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385647, tc_HOL_Obool)), _1385649), _1385651))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385645), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385647, _1385645), _1385653), _1385649)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1385647, _1385645), _1385653), _1385651)))], (15008 ^ _777864) ^ [_1032435, _1032437, _1032439] : [class_Groups_Ogroup__add(_1032435), 15011 ^ _777864 : [(15018 ^ _777864) ^ [] : [_1032437 = _1032439, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032435), _1032437), _1032439) = c_Groups_Ozero__class_Ozero(_1032435))], (15012 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032435), _1032437), _1032439) = c_Groups_Ozero__class_Ozero(_1032435), -(_1032437 = _1032439)]]], (18700 ^ _777864) ^ [] : [-(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)))))], (2012 ^ _777864) ^ [_807230, _807232, _807234, _807236] : [-(c_Int_Onat__aux(_807236, _807232) = c_Int_Onat__aux(_807234, _807230)), _807236 = _807234, _807232 = _807230], (6522 ^ _777864) ^ [_885526, _885528] : [6523 ^ _777864 : [(6526 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885528), _885526))], (6524 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885526), _885528))]], _885526 = _885528], (11138 ^ _777864) ^ [_963272, _963274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963272), _963274)), -(_963272 = _963274), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963272), _963274)))], (45799 ^ _777864) ^ [_1683472, _1683474, _1683476, _1683478, _1683480, _1683482] : [-(hAPP(hAPP(c_Option_Omap(_1683472, _1683474), _1683476), hAPP(hAPP(c_Option_Omap(_1683478, _1683472), _1683480), _1683482)) = hAPP(hAPP(c_Option_Omap(_1683478, _1683474), hAPP(c_Fun_Ocomp(_1683472, _1683474, _1683478, _1683476), _1683480)), _1683482))], (34299 ^ _777864) ^ [_1413886, _1413888, _1413890] : [class_Orderings_Olinorder(_1413886), hAPP(_1413888, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413886), 34304 ^ [_1413886, _1413888, _1413890]), 34305 ^ [_1413886, _1413888, _1413890])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413886), hAPP(_1413888, 34304 ^ [_1413886, _1413888, _1413890])), hAPP(_1413888, 34305 ^ [_1413886, _1413888, _1413890])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413886), _1413890)), -(_1413890 = c_Orderings_Obot__class_Obot(tc_fun(_1413886, tc_HOL_Obool))), -(hAPP(_1413888, c_Big__Operators_Olinorder__class_OMax(_1413886, _1413890)) = c_Big__Operators_Olinorder__class_OMax(_1413886, hAPP(c_Set_Oimage(_1413886, _1413886, _1413888), _1413890)))], (6428 ^ _777864) ^ [_884004, _884006] : [-(_884004 = _884006), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884004), _884006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _884006), _884004)))], (51441 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (3352 ^ _777864) ^ [_828676, _828678] : [_828678 = _828676, -(c_Wellfounded_Ofinite__psubset(_828678) = c_Wellfounded_Ofinite__psubset(_828676))], (39685 ^ _777864) ^ [_1528889, _1528891, _1528893, _1528895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528891, _1528889), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528889, tc_prod(_1528891, _1528889), 39681 ^ [_1528889, _1528891, _1528893, _1528895]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528891, tc_fun(_1528889, tc_HOL_Obool)), _1528893), _1528895))), hAPP(hAPP(c_Product__Type_OSigma(_1528891, _1528889), _1528893), _1528895))))], (4990 ^ _777864) ^ [_854183, _854185, _854187, _854189, _854191, _854193, _854195, _854197] : [-(c_List_Olist_Olist__case(_854197, _854193, _854189, _854185) = c_List_Olist_Olist__case(_854195, _854191, _854187, _854183)), _854197 = _854195, _854193 = _854191, _854189 = _854187, _854185 = _854183], (32880 ^ _777864) ^ [_1380661, _1380663, _1380665] : [class_Groups_Ocomm__monoid__mult(_1380661), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1380663, _1380661), _1380665), c_Orderings_Obot__class_Obot(tc_fun(_1380663, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1380661))], (25379 ^ _777864) ^ [_1222924, _1222926, _1222928, _1222930] : [class_Rings_Ocomm__ring__1(_1222924), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222924), _1222926), _1222928)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222924), _1222926), _1222930)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222924), _1222926), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1222924), _1222928), _1222930))))], (45439 ^ _777864) ^ [_1674951, _1674953, _1674955, _1674957, _1674959, _1674961] : [hAPP(c_Map_Omap__add(_1674951, _1674953, _1674955, _1674957), _1674959) = hAPP(c_Option_Ooption_OSome(_1674953), _1674961), -(hAPP(_1674957, _1674959) = hAPP(c_Option_Ooption_OSome(_1674953), _1674961)), 45446 ^ _777864 : [(45449 ^ _777864) ^ [] : [-(hAPP(_1674955, _1674959) = hAPP(c_Option_Ooption_OSome(_1674953), _1674961))], (45447 ^ _777864) ^ [] : [-(hAPP(_1674957, _1674959) = c_Option_Ooption_ONone(_1674953))]]], (51227 ^ _777864) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (26307 ^ _777864) ^ [_1240705, _1240707] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240705, tc_HOL_Obool)), _1240707), c_Orderings_Obot__class_Obot(tc_fun(_1240705, tc_HOL_Obool))) = _1240707)], (31115 ^ _777864) ^ [_1346282, _1346284, _1346286] : [class_Lattices_Olattice(_1346282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346282), _1346284)), -(_1346284 = c_Orderings_Obot__class_Obot(tc_fun(_1346282, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346282), _1346286)), -(_1346286 = c_Orderings_Obot__class_Obot(tc_fun(_1346282, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1346282, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346282, tc_HOL_Obool)), _1346284), _1346286)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1346282), c_Big__Operators_Olattice__class_OInf__fin(_1346282, _1346284)), c_Big__Operators_Olattice__class_OInf__fin(_1346282, _1346286)))], (26599 ^ _777864) ^ [_1246538, _1246540, _1246542, _1246544, _1246546] : [26602 ^ _777864 : [(26605 ^ _777864) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1246540, _1246542, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246540)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246540), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1246540), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 26601 ^ [_1246538, _1246540, _1246542, _1246544, _1246546]))), _1246544), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1246540), hAPP(_1246546, 26600 ^ [_1246538, _1246540, _1246542, _1246544, _1246546])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246540), tc_HOL_Obool))))], (26603 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1246538, 26600 ^ [_1246538, _1246540, _1246542, _1246544, _1246546]), 26601 ^ [_1246538, _1246540, _1246542, _1246544, _1246546])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1246540, _1246542, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246540)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246540), _1246538), _1246544), _1246546)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246540), tc_HOL_Obool)))))], (24885 ^ _777864) ^ [_1214859, _1214861] : [class_Rings_Ocomm__semiring__1(_1214859), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214859), c_Groups_Oone__class_Oone(_1214859)), _1214861)))], (45733 ^ _777864) ^ [_1681701, _1681703, _1681705, _1681707, _1681709] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1681701), tc_List_Olist(_1681703), tc_List_Olist(_1681705), hAPP(c_List_Omap(_1681701, _1681703), _1681707)), hAPP(c_List_Omap(_1681705, _1681701), _1681709)) = hAPP(c_List_Omap(_1681705, _1681703), hAPP(c_Fun_Ocomp(_1681701, _1681703, _1681705, _1681707), _1681709)))], (28885 ^ _777864) ^ [_1299681] : [c_Nat__Transfer_Onat__set(_1299681), 28888 ^ _777864 : [(28889 ^ _777864) ^ [_1299747] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1299747), _1299681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299747)))]]], (15870 ^ _777864) ^ [_1049838, _1049840] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049838, _1049840) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049838, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1049840)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16246 ^ _777864) ^ [_1056604, _1056606, _1056608] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1056604), _1056606)), _1056608) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1056604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1056606), _1056608)))], (958 ^ _777864) ^ [_792589, _792591, _792593, _792595] : [-(c_List_Olinorder__class_Osorted(_792593, _792589)), c_List_Olinorder__class_Osorted(_792595, _792591), _792595 = _792593, _792591 = _792589], (36236 ^ _777864) ^ [_1452297, _1452299, _1452301, _1452303, _1452305] : [-(hAPP(c_Fun_Othe__inv__into(_1452297, _1452299, _1452301, _1452303), _1452305) = c_HOL_OThe(_1452297, hAPP(hAPP(c_COMBS(_1452297, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1452297), c_fconj), hAPP(hAPP(c_COMBC(_1452297, tc_fun(_1452297, tc_HOL_Obool), tc_HOL_Obool), c_member(_1452297)), _1452301))), hAPP(hAPP(c_COMBC(_1452297, _1452299, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1452299, tc_fun(_1452299, tc_HOL_Obool), _1452297), c_fequal), _1452303)), _1452305))))], (46035 ^ _777864) ^ [_1688962, _1688964] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1688962, _1688964) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1688962), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1688964), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50205 ^ _777864) ^ [_1788214, _1788216] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1788214, _1788216) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1788214), _1788216)))], (11455 ^ _777864) ^ [_968789, _968791, _968793, _968795] : [class_Groups_Oordered__comm__monoid__add(_968789), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968789), c_Groups_Ozero__class_Ozero(_968789)), _968791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968789), _968793), _968795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968789), _968793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968789), _968791), _968795))))], (18882 ^ _777864) ^ [_1102441, _1102443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102441), _1102443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1102441)), c_Int_OBit0(_1102443))))], (14105 ^ _777864) ^ [_1016460, _1016462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016460), _1016462)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016460, _1016462) = _1016460)], (18926 ^ _777864) ^ [_1103192] : [c_Int_OBit0(_1103192) = c_Int_OPls, -(_1103192 = c_Int_OPls)], (25839 ^ _777864) ^ [_1231548, _1231550, _1231552, _1231554] : [class_Divides_Osemiring__div(_1231548), -(_1231550 = c_Groups_Ozero__class_Ozero(_1231548)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1231548), _1231550), _1231552)), 25850 ^ _777864 : [(25857 ^ _777864) ^ [] : [_1231552 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231548), _1231554), _1231550), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231548), _1231552), _1231550) = _1231554)], (25851 ^ _777864) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231548), _1231552), _1231550) = _1231554, -(_1231552 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231548), _1231554), _1231550))]]], (1572 ^ _777864) ^ [_800282, _800284] : [-(class_Groups_Osemigroup__add(_800282)), _800284 = _800282, class_Groups_Osemigroup__add(_800284)], (37106 ^ _777864) ^ [_1472485, _1472487, _1472489, _1472491] : [class_Rings_Ocomm__semiring__1(_1472485), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1472485), c_Groups_Oone__class_Oone(_1472485)), c_Groups_Oone__class_Oone(_1472485))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1472485), hAPP(hAPP(c_COMBB(_1472485, _1472485, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1472485), _1472487)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1472485, _1472485), hAPP(hAPP(c_COMBB(_1472485, tc_fun(_1472485, _1472485), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1472485)), c_Nat_Osemiring__1__class_Oof__nat(_1472485))), _1472489))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1472491))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472485), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1472485), _1472491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1472485), _1472487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1472485), _1472487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1472485), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1472485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1472491), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1472489)))))], (47744 ^ _777864) ^ [_1732225, _1732227, _1732229, _1732231, _1732233] : [_1732225 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1732227, _1732229, _1732231, _1732225), _1732233) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732229), _1732227), c_List_Olist_ONil(_1732229)), _1732233))], (40761 ^ _777864) ^ [_1561502, _1561504, _1561506, _1561508, _1561510, _1561512] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561502, _1561504, _1561506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561502, _1561504), tc_HOL_Obool)), _1561508), _1561510)), _1561512) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561502, _1561506), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1561502, _1561504, _1561506), _1561508), _1561512)), hAPP(hAPP(c_Relation_Orel__comp(_1561502, _1561504, _1561506), _1561510), _1561512)))], (5671 ^ _777864) ^ [_869336, _869338, _869340, _869342] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869336), _869338), _869340)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869336), _869338), _869342)), -(_869342 = _869340)], (26419 ^ _777864) ^ [_1243249, _1243251] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1243249), _1243251)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243249)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1243251))))], (41075 ^ _777864) ^ [_1569905, _1569907, _1569909, _1569911] : [c_FunDef_Oreduction__pair(_1569905, _1569907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool)), _1569909), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool), tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool)), _1569907))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool)), _1569911), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool), tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool)), _1569907))), c_Wellfounded_Owf(_1569905, _1569911), -(c_Wellfounded_Owf(_1569905, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569905, _1569905), tc_HOL_Obool)), _1569909), _1569911)))], (18050 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (32689 ^ _777864) ^ [_1376673, _1376675, _1376677, _1376679] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1376673, _1376675)), c_Sum__Type_OPlus(_1376673, _1376675, _1376677, _1376679)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376673), _1376677)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376675), _1376679))], (37194 ^ _777864) ^ [_1474599, _1474601] : [-(hAPP(c_Finite__Set_Ocard(_1474599), _1474601) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474599, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1474599), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1474601))], (12332 ^ _777864) ^ [_984353, _984355, _984357] : [class_Groups_Oordered__comm__monoid__add(_984353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984353), _984355), c_Groups_Ozero__class_Ozero(_984353))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984353), _984357), c_Groups_Ozero__class_Ozero(_984353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984353), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984353), _984355), _984357)), c_Groups_Ozero__class_Ozero(_984353))))], (46941 ^ _777864) ^ [_1713811] : [46943 ^ _777864 : [(46946 ^ _777864) ^ [] : [46942 ^ [_1713811] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46944 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46942 ^ [_1713811]), hAPP(c_List_Oset(tc_Nat_Onat), _1713811))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1713811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27063 ^ _777864) ^ [_1255886, _1255888] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1255886, tc_HOL_Obool)), _1255888)), -(hBOOL(hAPP(hAPP(c_member(_1255886), _1255888), c_Orderings_Obot__class_Obot(tc_fun(_1255886, tc_HOL_Obool)))))], (37735 ^ _777864) ^ [_1485814, _1485816] : [class_Groups_Oordered__ab__group__add(_1485814), -(hAPP(c_Set_Oimage(_1485814, _1485814, c_Groups_Ouminus__class_Ouminus(_1485814)), hAPP(c_SetInterval_Oord__class_OatMost(_1485814), _1485816)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1485814), hAPP(c_Groups_Ouminus__class_Ouminus(_1485814), _1485816)))], (11172 ^ _777864) ^ [_963828, _963830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963828), _963830)), -(_963830 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963828), 11175 ^ [_963828, _963830]))], (24845 ^ _777864) ^ [_1214110, _1214112, _1214114] : [class_Rings_Ocomm__semiring__1(_1214110), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214110), _1214112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214110), _1214112), _1214114))))], (1972 ^ _777864) ^ [_806586, _806588] : [_806588 = _806586, -(c_Nat_Onat_Onat__size(_806588) = c_Nat_Onat_Onat__size(_806586))], (50070 ^ _777864) ^ [_1785700, _1785702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785700), _1785702)), -(c_List_Oupt(_1785700, _1785702) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1785700), c_List_Oupt(hAPP(c_Nat_OSuc, _1785700), _1785702)))], (18116 ^ _777864) ^ [_1089621, _1089623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089621), _1089623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1089621)), _1089623)))], (50726 ^ _777864) ^ [_1801235, _1801237, _1801239, _1801241, _1801243] : [-(hAPP(hAPP(c_List_Ozip(_1801235, _1801237), _1801239), c_List_OtakeWhile(_1801237, _1801241, _1801243)) = c_List_OtakeWhile(tc_prod(_1801235, _1801237), hAPP(c_Fun_Ocomp(_1801237, tc_HOL_Obool, tc_prod(_1801235, _1801237), _1801241), c_Product__Type_Osnd(_1801235, _1801237)), hAPP(hAPP(c_List_Ozip(_1801235, _1801237), _1801239), _1801243)))], (13389 ^ _777864) ^ [_1002833, _1002835, _1002837] : [class_Divides_Osemiring__div(_1002833), -(c_Divides_Odiv__class_Omod(_1002833, c_Divides_Odiv__class_Omod(_1002833, _1002835, _1002837), _1002837) = c_Divides_Odiv__class_Omod(_1002833, _1002835, _1002837))], (37933 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (13455 ^ _777864) ^ [_1004100, _1004102, _1004104, _1004106, _1004108, _1004110] : [class_Divides_Osemiring__div(_1004100), c_Divides_Odiv__class_Omod(_1004100, _1004102, _1004104) = c_Divides_Odiv__class_Omod(_1004100, _1004106, _1004104), c_Divides_Odiv__class_Omod(_1004100, _1004108, _1004104) = c_Divides_Odiv__class_Omod(_1004100, _1004110, _1004104), -(c_Divides_Odiv__class_Omod(_1004100, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004100), _1004102), _1004108), _1004104) = c_Divides_Odiv__class_Omod(_1004100, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004100), _1004106), _1004110), _1004104))], (45932 ^ _777864) ^ [] : [45934 ^ _777864 : [(45937 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 45933 ^ []))], (45935 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 45933 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (5814 ^ _777864) ^ [_873271, _873273, _873275, _873277] : [hAPP(c_Com_Ocom_OBODY, _873271) = c_Com_Ocom_OCall(_873273, _873275, _873277)], (29826 ^ _777864) ^ [_1319369, _1319371] : [class_Lattices_Obounded__lattice__bot(_1319369), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319369), c_Orderings_Obot__class_Obot(_1319369)), _1319371) = c_Orderings_Obot__class_Obot(_1319369))], (5613 ^ _777864) ^ [_867820, _867822, _867824, _867826, _867828] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_867820, _867822, _867824)), _867826), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867828), hAPP(c_Natural_Ogetlocs, _867826))), _867820), hAPP(hAPP(c_Natural_Ogetlocs, _867828), c_Com_ORes))))), 5614 ^ _777864 : [(5615 ^ _777864) ^ [_867977] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867828), hAPP(c_Natural_Ogetlocs, _867826))), _867820), hAPP(hAPP(c_Natural_Ogetlocs, _867828), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867977), hAPP(c_Natural_Ogetlocs, _867826))), _867820), hAPP(hAPP(c_Natural_Ogetlocs, _867977), c_Com_ORes)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _867822)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867826), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_867824, _867826))), _867977))]]], (39852 ^ _777864) ^ [_1533375, _1533377, _1533379, _1533381, _1533383, _1533385, _1533387, _1533389, _1533391, _1533393] : [hAPP(c_Set_Oimage(_1533375, _1533377, _1533379), _1533381) = _1533383, hAPP(c_Set_Oimage(_1533385, _1533387, _1533389), _1533391) = _1533393, -(hAPP(c_Set_Oimage(tc_prod(_1533375, _1533385), tc_prod(_1533377, _1533387), c_Product__Type_Omap__pair(_1533375, _1533377, _1533385, _1533387, _1533379, _1533389)), hAPP(hAPP(c_Product__Type_OSigma(_1533375, _1533385), _1533381), hAPP(c_COMBK(tc_fun(_1533385, tc_HOL_Obool), _1533375), _1533391))) = hAPP(hAPP(c_Product__Type_OSigma(_1533377, _1533387), _1533383), hAPP(c_COMBK(tc_fun(_1533387, tc_HOL_Obool), _1533377), _1533393)))], (18338 ^ _777864) ^ [_1093171, _1093173] : [class_Int_Onumber__ring(_1093171), -(hAPP(c_Int_Onumber__class_Onumber__of(_1093171), c_Int_Osucc(_1093173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093171), c_Groups_Oone__class_Oone(_1093171)), hAPP(c_Int_Onumber__class_Onumber__of(_1093171), _1093173)))], (46825 ^ _777864) ^ [_1711086, _1711088, _1711090, _1711092, _1711094] : [class_Rings_Osemiring__0(_1711086), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711086), hAPP(hAPP(c_List_Omap(_1711088, _1711086), hAPP(hAPP(c_COMBC(_1711088, _1711086, _1711086), hAPP(hAPP(c_COMBB(_1711086, tc_fun(_1711086, _1711086), _1711088), c_Groups_Otimes__class_Otimes(_1711086)), _1711090)), _1711092)), _1711094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1711086), hAPP(c_List_Omonoid__add__class_Olistsum(_1711086), hAPP(hAPP(c_List_Omap(_1711088, _1711086), _1711090), _1711094))), _1711092))], (47728 ^ _777864) ^ [_1731953, _1731955] : [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), _1731953), _1731955))), 47731 ^ _777864 : [(47738 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1731953), _1731955))), -(c_List_Oupto(_1731953, _1731955) = c_List_Olist_ONil(tc_Int_Oint))], (47732 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1731953), _1731955)), -(c_List_Oupto(_1731953, _1731955) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1731953), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1731953), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1731955)))]]], (15442 ^ _777864) ^ [_1040595, _1040597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040595), _1040597)), hAPP(c_Nat_OSuc, _1040595))))], (40618 ^ _777864) ^ [_1556507, _1556509, _1556511, _1556513] : [-(c_Nitpick_Oprod(_1556507, _1556509, _1556511, _1556513) = hAPP(c_Set_OCollect(tc_prod(_1556507, _1556509)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556507, _1556509, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556507, tc_fun(_1556509, tc_HOL_Obool), tc_fun(_1556509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556509, tc_HOL_Obool), tc_fun(_1556509, tc_HOL_Obool)), _1556507), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556509)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556507), c_fconj), hAPP(hAPP(c_COMBC(_1556507, tc_fun(_1556507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1556507)), _1556511)))), hAPP(hAPP(c_COMBC(_1556509, tc_fun(_1556509, tc_HOL_Obool), tc_HOL_Obool), c_member(_1556509)), _1556513)))))], (7566 ^ _777864) ^ [_903366, _903368] : [c_Option_Ois__none(_903366, hAPP(c_Option_Ooption_OSome(_903366), _903368))], (40809 ^ _777864) ^ [_1563506, _1563508, _1563510, _1563512, _1563514, _1563516, _1563518] : [c_Predicate_Opred__comp(_1563506, _1563508, _1563510, hAPP(hAPP(c_COMBC(_1563506, tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_fun(_1563508, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563508, tc_fun(tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_fun(_1563508, tc_HOL_Obool)), _1563506), c_COMBC(_1563508, tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563508, tc_prod(_1563506, _1563508)), tc_fun(_1563508, tc_fun(tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_HOL_Obool)), _1563506), hAPP(c_COMBB(tc_prod(_1563506, _1563508), tc_fun(tc_fun(tc_prod(_1563506, _1563508), tc_HOL_Obool), tc_HOL_Obool), _1563508), c_member(tc_prod(_1563506, _1563508)))), c_Product__Type_OPair(_1563506, _1563508)))), _1563512), hAPP(hAPP(c_COMBC(_1563508, tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_fun(_1563510, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563510, tc_fun(tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_fun(_1563510, tc_HOL_Obool)), _1563508), c_COMBC(_1563510, tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563510, tc_prod(_1563508, _1563510)), tc_fun(_1563510, tc_fun(tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_HOL_Obool)), _1563508), hAPP(c_COMBB(tc_prod(_1563508, _1563510), tc_fun(tc_fun(tc_prod(_1563508, _1563510), tc_HOL_Obool), tc_HOL_Obool), _1563510), c_member(tc_prod(_1563508, _1563510)))), c_Product__Type_OPair(_1563508, _1563510)))), _1563514), _1563516, _1563518), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563506, _1563510)), hAPP(hAPP(c_Product__Type_OPair(_1563506, _1563510), _1563516), _1563518)), hAPP(hAPP(c_Relation_Orel__comp(_1563506, _1563508, _1563510), _1563512), _1563514))))], (18056 ^ _777864) ^ [] : [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)], (19816 ^ _777864) ^ [_1119417, _1119419, _1119421] : [class_Fields_Ofield__inverse__zero(_1119417), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119417), hAPP(c_Groups_Ouminus__class_Ouminus(_1119417), _1119419)), hAPP(c_Groups_Ouminus__class_Ouminus(_1119417), _1119421)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119417), _1119419), _1119421))], (40697 ^ _777864) ^ [_1559556, _1559558, _1559560, _1559562] : [class_Groups_Ocomm__monoid__add(_1559556), c_Fun_Oinj__on(_1559558, _1559556, _1559560, _1559562), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559558, _1559556), _1559560), _1559562) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559556, _1559556), c_Fun_Oid(_1559556)), hAPP(c_Set_Oimage(_1559558, _1559556, _1559560), _1559562)))], (33771 ^ _777864) ^ [_1401432, _1401434, _1401436, _1401438, _1401440] : [hBOOL(hAPP(hAPP(c_member(_1401432), _1401434), _1401436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1401438, tc_HOL_Obool)), hAPP(_1401440, _1401434)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401432, tc_fun(_1401438, tc_HOL_Obool)), _1401436), _1401440))))], (47214 ^ _777864) ^ [_1720317, _1720319, _1720321] : [-(hAPP(c_List_Oset(_1720317), c_List_Osublist(_1720317, _1720319, _1720321)) = hAPP(c_Set_OCollect(_1720317), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1720317), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1720317, 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)), _1720317), 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)), _1720317), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1720317, tc_fun(tc_Nat_Onat, _1720317), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1720317, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1720317), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1720317), c_COMBB(_1720317, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1720317), _1720319))))), 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(_1720317)), _1720319)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1720321))))))], (35910 ^ _777864) ^ [_1445958, _1445960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1445958), _1445960)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445958), hAPP(c_Nat_OSuc, _1445960)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1445960), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445958), _1445960)))], (27257 ^ _777864) ^ [_1262132, _1262134, _1262136, _1262138, _1262140] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1262132, _1262134, _1262136), _1262138), _1262140)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1262132, _1262134)), hAPP(hAPP(c_Product__Type_OPair(_1262132, _1262134), _1262138), _1262140)), _1262136)))], (50552 ^ _777864) ^ [_1796147, _1796149] : [-(_1796147 = c_List_Olist_ONil(_1796149)), -(c_List_Olast(_1796149, hAPP(c_List_Orev(_1796149), _1796147)) = hAPP(c_List_Ohd(_1796149), _1796147))], (48368 ^ _777864) ^ [_1748298, _1748300, _1748302, _1748304, _1748306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1748298, _1748298)), hAPP(hAPP(c_Product__Type_OPair(_1748298, _1748298), _1748300), _1748302)), _1748304)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748298), tc_List_Olist(_1748298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748298), tc_List_Olist(_1748298)), hAPP(hAPP(c_List_Olist_OCons(_1748298), _1748300), _1748306)), hAPP(hAPP(c_List_Olist_OCons(_1748298), _1748302), _1748306))), c_List_Olistrel1(_1748298, _1748304))))], (41554 ^ _777864) ^ [_1581887, _1581889, _1581891, _1581893] : [c_Equiv__Relations_Ocongruent(_1581887, _1581889, _1581891, _1581893), 41557 ^ _777864 : [(41558 ^ _777864) ^ [_1582032] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581887, _1581887)), _1582032), _1581891)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1581887, _1581887, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581887, tc_fun(_1581887, _1581889), tc_fun(_1581887, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581889, tc_HOL_Obool), tc_fun(tc_fun(_1581887, _1581889), tc_fun(_1581887, tc_HOL_Obool)), _1581887), c_COMBB(_1581889, tc_HOL_Obool, _1581887)), hAPP(hAPP(c_COMBB(_1581889, tc_fun(_1581889, tc_HOL_Obool), _1581887), c_fequal), _1581893))), _1581893)), _1582032)))]]], (8990 ^ _777864) ^ [_927304, _927306, _927308] : [class_Groups_Ogroup__add(_927304), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927304), _927306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927304), hAPP(c_Groups_Ouminus__class_Ouminus(_927304), _927306)), _927308)) = _927308)], (27193 ^ _777864) ^ [_1259698, _1259700, _1259702, _1259704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259698, tc_fun(_1259700, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1259698, tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_fun(_1259700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1259700, tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_fun(_1259700, tc_HOL_Obool)), _1259698), c_COMBC(_1259700, tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1259700, tc_prod(_1259698, _1259700)), tc_fun(_1259700, tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), _1259698), hAPP(c_COMBB(tc_prod(_1259698, _1259700), tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool), _1259700), c_member(tc_prod(_1259698, _1259700)))), c_Product__Type_OPair(_1259698, _1259700)))), _1259702)), hAPP(hAPP(c_COMBC(_1259698, tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_fun(_1259700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1259700, tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_fun(_1259700, tc_HOL_Obool)), _1259698), c_COMBC(_1259700, tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1259700, tc_prod(_1259698, _1259700)), tc_fun(_1259700, tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool)), _1259698), hAPP(c_COMBB(tc_prod(_1259698, _1259700), tc_fun(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool), tc_HOL_Obool), _1259700), c_member(tc_prod(_1259698, _1259700)))), c_Product__Type_OPair(_1259698, _1259700)))), _1259704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1259698, _1259700), tc_HOL_Obool)), _1259702), _1259704)))], (38021 ^ _777864) ^ [_1491513, _1491515, _1491517, _1491519, _1491521] : [_1491513 = c_Option_Ooption_ONone(_1491515), -(c_Map_Odom(_1491517, _1491515, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1491517, tc_Option_Ooption(_1491515)), _1491519), _1491521), _1491513)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491517, tc_HOL_Obool)), c_Map_Odom(_1491517, _1491515, _1491519)), hAPP(hAPP(c_Set_Oinsert(_1491517), _1491521), c_Orderings_Obot__class_Obot(tc_fun(_1491517, tc_HOL_Obool)))))], (50761 ^ _777864) ^ [_1802052, _1802054, _1802056] : [hBOOL(hAPP(c_List_Odistinct(_1802052), _1802054)), -(hBOOL(hAPP(c_List_Odistinct(_1802052), c_List_OtakeWhile(_1802052, _1802056, _1802054))))], (50981 ^ _777864) ^ [_1806350, _1806352, _1806354] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806350)), c_List_OdropWhile(_1806350, _1806352, _1806354))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806350)), _1806354))))], (26045 ^ _777864) ^ [_1235361, _1235363] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1235361, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1235361, tc_HOL_Obool))), _1235363)))], (38736 ^ _777864) ^ [_1507197, _1507199, _1507201, _1507203, _1507205] : [hBOOL(hAPP(hAPP(c_member(_1507197), _1507199), hAPP(c_Set_Ovimage(_1507197, _1507201, _1507203), _1507205))), -(hBOOL(hAPP(hAPP(c_member(_1507201), hAPP(_1507203, _1507199)), _1507205)))], (48888 ^ _777864) ^ [_1760681, _1760683, _1760685] : [class_Groups_Oab__semigroup__add(_1760681), -(c_List_Ofoldr(_1760681, _1760681, c_Groups_Oplus__class_Oplus(_1760681), _1760683, _1760685) = hAPP(c_List_Ofoldl(_1760681, _1760681, c_Groups_Oplus__class_Oplus(_1760681), _1760685), _1760683))], (28946 ^ _777864) ^ [_1300560] : [c_Nat__Transfer_Onat__set(_1300560), -(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), _1300560)) = _1300560)], (29350 ^ _777864) ^ [_1309844, _1309846, _1309848, _1309850, _1309852, _1309854, _1309856, _1309858] : [c_Finite__Set_Ofolding__image__simple(_1309844, _1309846, _1309848, _1309850, _1309852, _1309854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309846), _1309856)), hBOOL(hAPP(hAPP(c_member(_1309846), _1309858), _1309856)), -(hAPP(_1309854, _1309856) = hAPP(hAPP(_1309848, hAPP(_1309852, _1309858)), hAPP(_1309854, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309846, tc_HOL_Obool)), _1309856), hAPP(hAPP(c_Set_Oinsert(_1309846), _1309858), c_Orderings_Obot__class_Obot(tc_fun(_1309846, tc_HOL_Obool)))))))], (51345 ^ _777864) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (22502 ^ _777864) ^ [_1166798, _1166800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1166798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1166800)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166798, _1166800) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1166798, _1166800)))], (31633 ^ _777864) ^ [_1355969, _1355971, _1355973] : [class_Orderings_Olinorder(_1355969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355969), _1355971)), -(_1355971 = c_Orderings_Obot__class_Obot(tc_fun(_1355969, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1355969, hAPP(hAPP(c_Set_Oinsert(_1355969), _1355973), _1355971)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1355969), _1355973), c_Big__Operators_Olinorder__class_OMin(_1355969, _1355971)))], (8480 ^ _777864) ^ [_918382] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _918382)) = 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), _918382)))], (4616 ^ _777864) ^ [_848406, _848408, _848410, _848412, _848414, _848416, _848418, _848420] : [-(c_Option_Ooption_Ooption__case(_848420, _848416, _848412, _848408) = c_Option_Ooption_Ooption__case(_848418, _848414, _848410, _848406)), _848420 = _848418, _848416 = _848414, _848412 = _848410, _848408 = _848406], (39233 ^ _777864) ^ [_1519814, _1519816, _1519818, _1519820, _1519822, _1519824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519814, _1519816)), hAPP(hAPP(c_Product__Type_OPair(_1519814, _1519816), _1519818), _1519820)), hAPP(hAPP(c_Product__Type_OSigma(_1519814, _1519816), _1519822), _1519824))), -(hBOOL(hAPP(hAPP(c_member(_1519816), _1519820), hAPP(_1519824, _1519818))))], (8620 ^ _777864) ^ [_920904, _920906, _920908] : [class_Rings_Oring(_920904), -(hAPP(c_Groups_Ouminus__class_Ouminus(_920904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920904), _920906), _920908)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920904), _920906), hAPP(c_Groups_Ouminus__class_Ouminus(_920904), _920908)))], (2370 ^ _777864) ^ [_812787, _812789, _812791, _812793] : [-(c_Nitpick_Onat__gcd(_812793, _812789) = c_Nitpick_Onat__gcd(_812791, _812787)), _812793 = _812791, _812789 = _812787], (41780 ^ _777864) ^ [_1587792, _1587794, _1587796, _1587798] : [c_Finite__Set_Ofun__left__comm__idem(_1587792, _1587794, _1587796), -(hAPP(c_Fun_Ocomp(_1587794, _1587794, _1587794, hAPP(_1587796, _1587798)), hAPP(_1587796, _1587798)) = hAPP(_1587796, _1587798))], (18140 ^ _777864) ^ [_1090014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090014), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090014)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1090014)))], (38342 ^ _777864) ^ [_1497506, _1497508, _1497510, _1497512, _1497514] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497506), hAPP(c_Set_Oimage(_1497508, _1497506, _1497510), c_Orderings_Otop__class_Otop(tc_fun(_1497508, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497512), hAPP(c_Set_Oimage(_1497508, _1497512, hAPP(hAPP(c_COMBB(_1497506, _1497512, _1497508), _1497514), _1497510)), c_Orderings_Otop__class_Otop(tc_fun(_1497508, tc_HOL_Obool))))))], (40106 ^ _777864) ^ [_1538809, _1538811, _1538813] : [40107 ^ _777864 : [(40110 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538809), hAPP(c_Set_OCollect(_1538809), _1538813)))], (40108 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538809), hAPP(c_Set_OCollect(_1538809), _1538811)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1538809), hAPP(c_Set_OCollect(_1538809), hAPP(hAPP(c_COMBS(_1538809, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538809), c_fconj), _1538811)), _1538813)))))], (1652 ^ _777864) ^ [_801282, _801284] : [-(class_Groups_Omonoid__add(_801282)), _801284 = _801282, class_Groups_Omonoid__add(_801284)], (19230 ^ _777864) ^ [_1108494, _1108496] : [class_Int_Onumber__ring(_1108494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108494), c_Groups_Oone__class_Oone(_1108494)), c_Groups_Oone__class_Oone(_1108494))), hAPP(c_Int_Onumber__class_Onumber__of(_1108494), _1108496)) = hAPP(c_Int_Onumber__class_Onumber__of(_1108494), c_Int_OBit0(_1108496)))], (33713 ^ _777864) ^ [_1399319, _1399321, _1399323, _1399325, _1399327, _1399329] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399319, tc_fun(_1399321, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1399323, _1399319, _1399325), _1399327)), _1399329) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399323, tc_fun(_1399321, tc_HOL_Obool)), _1399327), hAPP(hAPP(c_COMBB(_1399319, tc_fun(_1399321, tc_HOL_Obool), _1399323), _1399329), _1399325)))], (39183 ^ _777864) ^ [_1518424, _1518426, _1518428, _1518430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1518424), _1518426)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518428), _1518430)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1518424, _1518428)), hAPP(hAPP(c_Product__Type_OSigma(_1518424, _1518428), _1518426), hAPP(c_COMBK(tc_fun(_1518428, tc_HOL_Obool), _1518424), _1518430)))))], (29740 ^ _777864) ^ [_1317783, _1317785, _1317787] : [class_Lattices_Osemilattice__inf(_1317783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317783), _1317785), _1317787)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317783), _1317787), _1317785) = _1317785)], (15046 ^ _777864) ^ [_1033012, _1033014] : [class_Groups_Ogroup__add(_1033012), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033012), _1033014), c_Groups_Ozero__class_Ozero(_1033012)) = _1033014)], (28226 ^ _777864) ^ [_1281444, _1281446, _1281448, _1281450] : [28230 ^ _777864 : [(28233 ^ _777864) ^ [] : [hBOOL(hAPP(_1281450, 28229 ^ [_1281444, _1281446, _1281448, _1281450]))], (28231 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281444), 28229 ^ [_1281444, _1281446, _1281448, _1281450]), _1281446)))]], 28235 ^ _777864 : [(28238 ^ _777864) ^ [] : [hBOOL(hAPP(_1281450, 28234 ^ [_1281444, _1281446, _1281448, _1281450]))], (28236 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281444), 28234 ^ [_1281444, _1281446, _1281448, _1281450]), _1281448)))]], 28239 ^ _777864 : [(28240 ^ _777864) ^ [_1281777] : [hBOOL(hAPP(hAPP(c_member(_1281444), _1281777), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281444, tc_HOL_Obool)), _1281446), _1281448))), -(hBOOL(hAPP(_1281450, _1281777)))]]], (23917 ^ _777864) ^ [_1196054, _1196056, _1196058, _1196060] : [class_Orderings_Olinorder(_1196054), 23920 ^ _777864 : [(23921 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196054), _1196058), _1196060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), _1196058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), _1196060)))], (23931 ^ _777864) ^ [] : [23932 ^ _777864 : [(23935 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), _1196060))], (23933 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), _1196058))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196054), _1196056), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196054), _1196058), _1196060))))]]], (21582 ^ _777864) ^ [_1150837, _1150839, _1150841, _1150843] : [class_Fields_Ofield(_1150837), -(_1150839 = c_Groups_Ozero__class_Ozero(_1150837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1150841), _1150843)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1150837), _1150839), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150843), _1150841)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150837), hAPP(hAPP(c_Power_Opower__class_Opower(_1150837), _1150839), _1150843)), hAPP(hAPP(c_Power_Opower__class_Opower(_1150837), _1150839), _1150841)))], (26845 ^ _777864) ^ [_1251768, _1251770, _1251772, _1251774] : [26846 ^ _777864 : [(26849 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1251768), _1251770), _1251774))], (26847 ^ _777864) ^ [] : [_1251770 = _1251772]], -(hBOOL(hAPP(hAPP(c_member(_1251768), _1251770), hAPP(hAPP(c_Set_Oinsert(_1251768), _1251772), _1251774))))], (20052 ^ _777864) ^ [_1123547, _1123549, _1123551] : [class_Fields_Olinordered__field(_1123547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123547), c_Groups_Ozero__class_Ozero(_1123547)), _1123549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123547), c_Groups_Ozero__class_Ozero(_1123547)), _1123551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123547), c_Groups_Ozero__class_Ozero(_1123547)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123547), _1123549), _1123551))))], (32673 ^ _777864) ^ [_1376409, _1376411, _1376413, _1376415] : [32674 ^ _777864 : [(32677 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376413), _1376415)))], (32675 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376409), _1376411)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1376409, _1376413)), c_Sum__Type_OPlus(_1376409, _1376413, _1376411, _1376415)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3406 ^ _777864) ^ [_829517, _829519, _829521, _829523, _829525, _829527] : [-(c_Predicate_ODomainP(_829527, _829523, _829519) = c_Predicate_ODomainP(_829525, _829521, _829517)), _829527 = _829525, _829523 = _829521, _829519 = _829517], (48514 ^ _777864) ^ [_1752428, _1752430, _1752432] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1752428, tc_HOL_Obool)), hAPP(c_List_Oset(_1752428), hAPP(hAPP(c_List_Odrop(_1752428), _1752430), _1752432))), hAPP(c_List_Oset(_1752428), _1752432))))], (35156 ^ _777864) ^ [_1431336, _1431338, _1431340] : [hAPP(c_Set_Oimage(_1431338, tc_fun(_1431338, tc_HOL_Obool), _1431336), _1431340) = hAPP(c_Set_OPow(_1431338), _1431340)], (6715 ^ _777864) ^ [_888489, _888491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888489), _888491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888489), hAPP(c_Nat_OSuc, _888491))))], (50542 ^ _777864) ^ [_1795881, _1795883] : [-(hAPP(c_List_Oset(_1795881), hAPP(c_List_Orev(_1795881), _1795883)) = hAPP(c_List_Oset(_1795881), _1795883))], (33745 ^ _777864) ^ [_1400827, _1400829, _1400831, _1400833, _1400835] : [class_Complete__Lattice_Ocomplete__lattice(_1400827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400829, tc_HOL_Obool)), _1400831), _1400833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400827), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400829, _1400827), _1400831), _1400835)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400829, _1400827), _1400833), _1400835))))], (18644 ^ _777864) ^ [_1098371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1098371)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098371), c_Int_OPls)))], (7970 ^ _777864) ^ [_910628, _910630] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910628)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _910630)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _910628), _910630)))], (43469 ^ _777864) ^ [_1625059, _1625061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1625059), _1625061)), -(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), _1625059), _1625061)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (29449 ^ _777864) ^ [_1311826] : [29451 ^ _777864 : [(29454 ^ _777864) ^ [_1311936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29450 ^ [_1311826, _1311936]), _1311936))], (29452 ^ _777864) ^ [_1311902] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29450 ^ [_1311826, _1311902]), _1311826)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1311826)))], (49097 ^ _777864) ^ [_1765449, _1765451, _1765453, _1765455] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765449)), hAPP(hAPP(c_List_Oappend(_1765449), _1765451), _1765453)), c_List_Olists(_1765449, _1765455)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765449)), _1765451), c_List_Olists(_1765449, _1765455))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765449)), _1765453), c_List_Olists(_1765449, _1765455)))], (32195 ^ _777864) ^ [_1366317, _1366319, _1366321] : [class_Orderings_Olinorder(_1366317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366317), _1366319)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366317), _1366321)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366317, tc_HOL_Obool)), _1366319), _1366321) = c_Orderings_Obot__class_Obot(tc_fun(_1366317, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366317), c_Big__Operators_Olattice_OSup__fin(_1366317, c_Orderings_Oord__class_Omax(_1366317), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366317, tc_HOL_Obool)), _1366319), _1366321))), c_Big__Operators_Olattice_OSup__fin(_1366317, c_Orderings_Oord__class_Omax(_1366317), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366317, tc_HOL_Obool)), _1366319), _1366321))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366317), c_Big__Operators_Olattice_OSup__fin(_1366317, c_Orderings_Oord__class_Omax(_1366317), _1366319)), c_Big__Operators_Olattice_OSup__fin(_1366317, c_Orderings_Oord__class_Omax(_1366317), _1366321)))], (43951 ^ _777864) ^ [_1638361, _1638363, _1638365, _1638367, _1638369] : [class_Complete__Lattice_Ocomplete__lattice(_1638361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1638363, tc_HOL_Obool)), _1638365), _1638367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1638361), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638363, _1638361), _1638367), _1638369)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638363, _1638361), _1638365), _1638369))))], (29121 ^ _777864) ^ [_1304830, _1304832, _1304834, _1304836, _1304838] : [c_Equiv__Relations_Oequiv(_1304830, _1304832, _1304834), hBOOL(hAPP(hAPP(c_member(tc_prod(_1304830, _1304830)), hAPP(hAPP(c_Product__Type_OPair(_1304830, _1304830), _1304836), _1304838)), _1304834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304830, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1304830, _1304830, _1304834), hAPP(hAPP(c_Set_Oinsert(_1304830), _1304836), c_Orderings_Obot__class_Obot(tc_fun(_1304830, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1304830, _1304830, _1304834), hAPP(hAPP(c_Set_Oinsert(_1304830), _1304838), c_Orderings_Obot__class_Obot(tc_fun(_1304830, tc_HOL_Obool)))))))], (37635 ^ _777864) ^ [_1483925, _1483927, _1483929] : [class_Orderings_Olinorder(_1483925), 37638 ^ _777864 : [(37645 ^ _777864) ^ [] : [_1483927 = _1483929, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1483925), _1483927) = hAPP(c_SetInterval_Oord__class_OatLeast(_1483925), _1483929))], (37639 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1483925), _1483927) = hAPP(c_SetInterval_Oord__class_OatLeast(_1483925), _1483929), -(_1483927 = _1483929)]]], (40120 ^ _777864) ^ [_1539203, _1539205, _1539207, _1539209] : [-(hAPP(c_Set_OCollect(tc_prod(_1539203, _1539205)), hAPP(c_Product__Type_Oprod_Oprod__case(_1539203, _1539205, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1539203, tc_fun(_1539205, tc_HOL_Obool), tc_fun(_1539205, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539205, tc_HOL_Obool), tc_fun(_1539205, tc_HOL_Obool)), _1539203), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539205)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539203), c_fconj), _1539207))), _1539209))) = hAPP(hAPP(c_Product__Type_OSigma(_1539203, _1539205), hAPP(c_Set_OCollect(_1539203), _1539207)), hAPP(hAPP(c_COMBB(tc_fun(_1539205, tc_HOL_Obool), tc_fun(_1539205, tc_HOL_Obool), _1539203), c_Set_OCollect(_1539205)), _1539209)))], (35832 ^ _777864) ^ [_1444190, _1444192, _1444194, _1444196] : [class_Orderings_Olinorder(_1444190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444190), _1444192), _1444194)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1444190, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444190, _1444192), _1444196)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444190, _1444192), _1444194)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444190, _1444194), _1444196))], (23627 ^ _777864) ^ [_1190439, _1190441, _1190443] : [class_Orderings_Olinorder(_1190439), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190439), _1190441), _1190443) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190439), _1190443), _1190441))], (43357 ^ _777864) ^ [_1622506, _1622508, _1622510, _1622512, _1622514] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622506, _1622506)), hAPP(hAPP(c_Product__Type_OPair(_1622506, _1622506), _1622508), _1622510)), _1622512)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1622506, _1622506)), hAPP(hAPP(c_Product__Type_OPair(_1622506, _1622506), _1622510), _1622514)), c_Transitive__Closure_Ortrancl(_1622506, _1622512))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622506, _1622506)), hAPP(hAPP(c_Product__Type_OPair(_1622506, _1622506), _1622508), _1622514)), c_Transitive__Closure_Otrancl(_1622506, _1622512))))], (51553 ^ _777864) ^ [_1812588] : [-(hBOOL(_1812588)), -(hBOOL(hAPP(c_fNot, _1812588)))], (16982 ^ _777864) ^ [_1070751, _1070753] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1070751), _1070753) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1070753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1070751 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24095 ^ _777864) ^ [_1199185, _1199187, _1199189] : [class_Orderings_Olinorder(_1199185), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199185), _1199187), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199185), _1199187), _1199189)) = _1199187)], (39462 ^ _777864) ^ [_1524905, _1524907, _1524909] : [class_Orderings_Olinorder(_1524905), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524905), _1524907)), hBOOL(hAPP(hAPP(c_member(_1524905), _1524909), _1524907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1524905), hAPP(c_Finite__Set_Ofold1(_1524905, c_Orderings_Oord__class_Omin(_1524905)), _1524907)), _1524909)))], (41109 ^ _777864) ^ [_1570584, _1570586, _1570588, _1570590] : [41111 ^ _777864 : [(41114 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1570586, hAPP(_1570588, 41110 ^ [_1570584, _1570586, _1570588, _1570590]))), hAPP(_1570586, 41110 ^ [_1570584, _1570586, _1570588, _1570590])))], (41112 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1570584, 41110 ^ [_1570584, _1570586, _1570588, _1570590])))]], -(c_Wellfounded_Owf(_1570590, hAPP(c_Set_OCollect(tc_prod(_1570590, _1570590)), hAPP(c_Product__Type_Oprod_Oprod__case(_1570590, _1570590, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1570590, tc_HOL_Obool), tc_fun(_1570590, tc_HOL_Obool), _1570590), hAPP(c_COMBS(_1570590, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570590), c_fconj), _1570584))), hAPP(hAPP(c_COMBC(_1570590, tc_fun(_1570590, _1570590), tc_fun(_1570590, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1570590, tc_HOL_Obool), tc_fun(tc_fun(_1570590, _1570590), tc_fun(_1570590, tc_HOL_Obool)), _1570590), c_COMBB(_1570590, tc_HOL_Obool, _1570590)), c_fequal)), _1570588))))))], (44316 ^ _777864) ^ [_1648267, _1648269, _1648271, _1648273, _1648275, _1648277] : [c_Relation_Osingle__valued(_1648267, _1648269, _1648271), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648267, _1648269)), hAPP(hAPP(c_Product__Type_OPair(_1648267, _1648269), _1648273), _1648275)), _1648271)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648267, _1648269)), hAPP(hAPP(c_Product__Type_OPair(_1648267, _1648269), _1648273), _1648277)), _1648271)), -(_1648275 = _1648277)], (44095 ^ _777864) ^ [] : [-(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)))], (4484 ^ _777864) ^ [_846432, _846434, _846436, _846438] : [-(c_Fun_Ofun__upd(_846438, _846434) = c_Fun_Ofun__upd(_846436, _846432)), _846438 = _846436, _846434 = _846432], (30156 ^ _777864) ^ [_1326707, _1326709, _1326711, _1326713] : [-(hBOOL(hAPP(hAPP(c_member(_1326707), _1326709), _1326711))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326707, tc_HOL_Obool)), _1326711), hAPP(hAPP(c_Set_Oinsert(_1326707), _1326709), _1326713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326707, tc_HOL_Obool)), _1326711), _1326713))], (47348 ^ _777864) ^ [_1724469, _1724471, _1724473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1724471))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1724471), _1724469), _1724473)) = 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), _1724471)), _1724473)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1724471), _1724469)))], (16736 ^ _777864) ^ [_1066118, _1066120, _1066122] : [class_Groups_Oordered__ab__group__add__abs(_1066118), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066118), hAPP(c_Groups_Oabs__class_Oabs(_1066118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1066118), _1066120), _1066122))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066118), hAPP(c_Groups_Oabs__class_Oabs(_1066118), _1066120)), hAPP(c_Groups_Oabs__class_Oabs(_1066118), _1066122)))))], (4520 ^ _777864) ^ [_846964, _846966, _846968, _846970] : [-(c_Wellfounded_Oacc(_846970, _846966) = c_Wellfounded_Oacc(_846968, _846964)), _846970 = _846968, _846966 = _846964], (24597 ^ _777864) ^ [_1209391, _1209393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1209391)), hAPP(c_Code__Numeral_Oof__nat, _1209393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209391), _1209393)))], (16041 ^ _777864) ^ [_1052826, _1052828, _1052830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1052828), 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), _1052828), _1052830))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1052826))), _1052830)))], (43790 ^ _777864) ^ [_1633192, _1633194, _1633196, _1633198] : [43792 ^ _777864 : [(43795 ^ _777864) ^ [] : [hAPP(_1633198, 43791 ^ [_1633192, _1633194, _1633196, _1633198]) = c_Orderings_Otop__class_Otop(tc_fun(_1633194, tc_HOL_Obool))], (43793 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633192), 43791 ^ [_1633192, _1633194, _1633196, _1633198]), _1633196)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1633192, tc_fun(_1633194, tc_HOL_Obool)), _1633196), _1633198) = c_Orderings_Otop__class_Otop(tc_fun(_1633194, tc_HOL_Obool)))], (30050 ^ _777864) ^ [_1324608, _1324610, _1324612] : [class_Lattices_Osemilattice__inf(_1324608), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324608), _1324610), _1324612) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324608), _1324612), _1324610))], (18836 ^ _777864) ^ [_1101591, _1101593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101591)), -(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)))), _1101593)), 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)))), _1101591)) = 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, _1101593, _1101591))))], (40995 ^ _777864) ^ [_1567881, _1567883] : [hAPP(hAPP(c_Relation_Orel__comp(_1567881, _1567881, _1567881), _1567883), _1567883) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567881, _1567881), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1567881, _1567883))], (35682 ^ _777864) ^ [_1441555, _1441557, _1441559, _1441561, _1441563] : [class_Orderings_Olinorder(_1441555), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441555, _1441557), _1441559) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441555, _1441561), _1441563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441555), _1441557), _1441559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441555), _1441561), _1441563)), -(_1441559 = _1441563)], (45234 ^ _777864) ^ [_1670270, _1670272, _1670274, _1670276] : [class_Lattices_Osemilattice__inf(_1670270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1670270), _1670272)), 45244 ^ _777864 : [(45247 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670270), _1670274), 45243 ^ [_1670270, _1670272, _1670274, _1670276]))], (45245 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670270), 45243 ^ [_1670270, _1670272, _1670274, _1670276]), _1670272)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1670270), _1670274), _1670276)), hAPP(hAPP(c_Finite__Set_Ofold(_1670270, _1670270, c_Lattices_Osemilattice__inf__class_Oinf(_1670270)), _1670276), _1670272))))], (9088 ^ _777864) ^ [] : [-(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))], (14790 ^ _777864) ^ [_1028435, _1028437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028437)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1028435, _1028437)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1028435), hAPP(c_Int_Onat, _1028437)))], (51409 ^ _777864) ^ [_1810958] : [class_Finite__Set_Ofinite(_1810958), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1810958)))], (28000 ^ _777864) ^ [_1276732, _1276734, _1276736, _1276738, _1276740] : [class_Lattices_Osemilattice__sup(_1276732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276732), _1276734), _1276736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276732), _1276738), _1276740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276732), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276732), _1276734), _1276738)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276732), _1276736), _1276740))))], (4890 ^ _777864) ^ [_852629, _852631, _852633, _852635, _852637, _852639] : [-(c_Divides_Odiv__class_Omod(_852639, _852635, _852631) = c_Divides_Odiv__class_Omod(_852637, _852633, _852629)), _852639 = _852637, _852635 = _852633, _852631 = _852629], (8978 ^ _777864) ^ [_927026, _927028, _927030] : [class_Groups_Oab__group__add(_927026), -(hAPP(c_Groups_Ouminus__class_Ouminus(_927026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927026), _927028), _927030)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927026), hAPP(c_Groups_Ouminus__class_Ouminus(_927026), _927028)), hAPP(c_Groups_Ouminus__class_Ouminus(_927026), _927030)))], (19172 ^ _777864) ^ [_1107468, _1107470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107468)), c_Int_OBit0(_1107470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107468), _1107470)))], (48995 ^ _777864) ^ [_1762828, _1762830, _1762832] : [class_Orderings_Olinorder(_1762828), -(c_Big__Operators_Olinorder__class_OMax(_1762828, hAPP(c_List_Oset(_1762828), hAPP(hAPP(c_List_Olist_OCons(_1762828), _1762830), _1762832))) = hAPP(c_List_Ofoldl(_1762828, _1762828, c_Orderings_Oord__class_Omax(_1762828), _1762830), _1762832))], (37831 ^ _777864) ^ [_1487569, _1487571, _1487573] : [class_Orderings_Oorder(_1487569), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487569, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1487569, _1487571, _1487573)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487569), _1487573)) = c_Orderings_Obot__class_Obot(tc_fun(_1487569, tc_HOL_Obool)))], (1824 ^ _777864) ^ [_803494, _803496, _803498, _803500, _803502, _803504, _803506, _803508] : [-(c_Natural_Oevaln(_803506, _803502, _803498, _803494)), c_Natural_Oevaln(_803508, _803504, _803500, _803496), _803508 = _803506, _803504 = _803502, _803500 = _803498, _803496 = _803494], (7646 ^ _777864) ^ [_904574, _904576, _904578, _904580] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_904574, _904576), _904578, _904580, _904578), hBOOL(hAPP(_904574, _904578)), 7654 ^ _777864 : [(7657 ^ _777864) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_904574, _904576), 7653 ^ [_904574, _904576, _904578, _904580], _904580, _904578))], (7655 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_904576, _904578, _904580, 7653 ^ [_904574, _904576, _904578, _904580]))]]], (23757 ^ _777864) ^ [_1193028, _1193030] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1193028), hAPP(c_Nat_OSuc, _1193030)) = 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)), _1193030)), _1193028))], (13638 ^ _777864) ^ [_1007603, _1007605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1007603)), 13641 ^ _777864 : [(13644 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1007605, _1007603)), _1007603)))], (13642 ^ _777864) ^ [] : [-(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, _1007605, _1007603))))]]], (32075 ^ _777864) ^ [_1363976, _1363978, _1363980] : [class_Orderings_Olinorder(_1363976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363976), _1363978)), -(hBOOL(hAPP(hAPP(c_member(_1363976), _1363980), _1363978))), -(_1363978 = c_Orderings_Obot__class_Obot(tc_fun(_1363976, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1363976, c_Orderings_Oord__class_Omin(_1363976), hAPP(hAPP(c_Set_Oinsert(_1363976), _1363980), _1363978)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363976), _1363980), c_Big__Operators_Olattice_OInf__fin(_1363976, c_Orderings_Oord__class_Omin(_1363976), _1363978)))], (1946 ^ _777864) ^ [_806195, _806197] : [_806197 = _806195, -(c_Com_Ovname_Ovname__size(_806197) = c_Com_Ovname_Ovname__size(_806195))], (24195 ^ _777864) ^ [_1201596, _1201598, _1201600, _1201602, _1201604, _1201606, _1201608] : [-(hAPP(c_Product__Type_Oapsnd(_1201596, _1201598, _1201600, _1201602), hAPP(c_Product__Type_Oapfst(_1201604, _1201600, _1201596, _1201606), _1201608)) = hAPP(c_Product__Type_Oapfst(_1201604, _1201600, _1201598, _1201606), hAPP(c_Product__Type_Oapsnd(_1201596, _1201598, _1201604, _1201602), _1201608)))], (35713 ^ _777864) ^ [_1442128, _1442130] : [35715 ^ _777864 : [(35718 ^ _777864) ^ [] : [hBOOL(hAPP(_1442130, 35714 ^ [_1442128, _1442130]))], (35716 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35714 ^ [_1442128, _1442130]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1442128))))]], 35719 ^ _777864 : [(35720 ^ _777864) ^ [_1442281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1442281), _1442128)), -(hBOOL(hAPP(_1442130, _1442281)))]]], (42631 ^ _777864) ^ [_1606799, _1606801, _1606803] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1606799), _1606801)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606799, tc_HOL_Obool)), _1606801), _1606803) = hAPP(hAPP(c_Finite__Set_Ofold(_1606799, tc_fun(_1606799, tc_HOL_Obool), c_Set_Oinsert(_1606799)), _1606803), _1606801))], (17214 ^ _777864) ^ [_1074719, _1074721, _1074723] : [class_Rings_Olinordered__semidom(_1074719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074719), c_Groups_Oone__class_Oone(_1074719)), _1074721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074719), c_Groups_Oone__class_Oone(_1074719)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074719), _1074721), _1074723))))], (19846 ^ _777864) ^ [_1119997] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1119997)))], (48328 ^ _777864) ^ [_1746947, _1746949, _1746951, _1746953, _1746955, _1746957] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746947), tc_List_Olist(_1746947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746947), tc_List_Olist(_1746947)), hAPP(hAPP(c_List_Oappend(_1746947), _1746949), _1746955)), hAPP(hAPP(c_List_Oappend(_1746947), _1746951), _1746957))), c_List_Olistrel1(_1746947, _1746953)))), 48329 ^ _777864 : [(48336 ^ _777864) ^ [] : [_1746949 = _1746951, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746947), tc_List_Olist(_1746947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746947), tc_List_Olist(_1746947)), _1746955), _1746957)), c_List_Olistrel1(_1746947, _1746953)))], (48330 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746947), tc_List_Olist(_1746947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746947), tc_List_Olist(_1746947)), _1746949), _1746951)), c_List_Olistrel1(_1746947, _1746953))), _1746955 = _1746957]]], (41238 ^ _777864) ^ [_1574080, _1574082, _1574084] : [c_Wellfounded_Owf(_1574080, _1574082), c_Wellfounded_Owf(_1574080, _1574084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574080, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1574080, _1574080), _1574082)), hAPP(c_Relation_ORange(_1574080, _1574080), _1574084)) = c_Orderings_Obot__class_Obot(tc_fun(_1574080, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1574080, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574080, _1574080), tc_HOL_Obool)), _1574082), _1574084)))], (16646 ^ _777864) ^ [_1064133, _1064135, _1064137, _1064139] : [class_Int_Onumber__ring(_1064133), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064133), hAPP(c_Int_Onumber__class_Onumber__of(_1064133), _1064135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064133), hAPP(c_Int_Onumber__class_Onumber__of(_1064133), _1064137)), _1064139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064133), hAPP(c_Int_Onumber__class_Onumber__of(_1064133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064135), _1064137))), _1064139))], (51193 ^ _777864) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (3108 ^ _777864) ^ [_824744, _824746, _824748, _824750, _824752, _824754] : [-(c_SetInterval_Oord_OatMost(_824754, _824750, _824746) = c_SetInterval_Oord_OatMost(_824752, _824748, _824744)), _824754 = _824752, _824750 = _824748, _824746 = _824744], (43591 ^ _777864) ^ [_1627687, _1627689, _1627691, _1627693, _1627695, _1627697] : [-(hAPP(c_Set_Ovimage(_1627687, _1627689, _1627691), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627693, tc_fun(_1627689, tc_HOL_Obool)), _1627695), _1627697)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627693, tc_fun(_1627687, tc_HOL_Obool)), _1627695), hAPP(hAPP(c_COMBB(tc_fun(_1627689, tc_HOL_Obool), tc_fun(_1627687, tc_HOL_Obool), _1627693), c_Set_Ovimage(_1627687, _1627689, _1627691)), _1627697)))], (29364 ^ _777864) ^ [_1310169, _1310171, _1310173, _1310175, _1310177, _1310179] : [c_Finite__Set_Ofolding__image__simple(_1310169, _1310171, _1310173, _1310175, _1310177, _1310179), -(hAPP(_1310179, c_Orderings_Obot__class_Obot(tc_fun(_1310171, tc_HOL_Obool))) = _1310175)], (15910 ^ _777864) ^ [_1050399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1050399)), -(_1050399 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050399), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33272 ^ _777864) ^ [_1389081, _1389083, _1389085, _1389087, _1389089] : [class_Groups_Ocomm__monoid__mult(_1389081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389083), _1389085)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389083), _1389087)), 33286 ^ _777864 : [(33289 ^ _777864) ^ [] : [hAPP(_1389089, 33285 ^ [_1389081, _1389083, _1389085, _1389087, _1389089]) = c_Groups_Oone__class_Oone(_1389081)], (33287 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389083), 33285 ^ [_1389081, _1389083, _1389085, _1389087, _1389089]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389083, tc_HOL_Obool)), _1389085), _1389087))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389083, _1389081), _1389089), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1389083, tc_HOL_Obool)), _1389085), _1389087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389081), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389083, _1389081), _1389089), _1389085)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389083, _1389081), _1389089), _1389087)))], (15134 ^ _777864) ^ [_1034677] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034677), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1034677)], (10726 ^ _777864) ^ [_956490, _956492, _956494] : [class_Orderings_Oorder(_956490), 10729 ^ _777864 : [(10738 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956490), _956492), _956494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956490), _956492), _956494)), -(_956492 = _956494)], (10730 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956490), _956492), _956494)), 10733 ^ _777864 : [(10736 ^ _777864) ^ [] : [_956492 = _956494], (10734 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956490), _956492), _956494)))]]]]], (38766 ^ _777864) ^ [_1507995, _1507997, _1507999] : [-(hAPP(c_Set_Ovimage(_1507995, _1507997, _1507999), c_Orderings_Otop__class_Otop(tc_fun(_1507997, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1507995, tc_HOL_Obool)))], (49888 ^ _777864) ^ [_1782801, _1782803, _1782805, _1782807] : [class_Orderings_Olinorder(_1782801), 49891 ^ _777864 : [(49900 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1782801, hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782803), hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782805), _1782807)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1782801), _1782803), _1782805)), c_List_Olinorder__class_Osorted(_1782801, hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782805), _1782807))], (49892 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1782801, hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782803), hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782805), _1782807))), 49895 ^ _777864 : [(49898 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1782801, hAPP(hAPP(c_List_Olist_OCons(_1782801), _1782805), _1782807)))], (49896 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1782801), _1782803), _1782805)))]]]]], (49231 ^ _777864) ^ [_1768459, _1768461, _1768463] : [_1768459 = c_List_Olist_ONil(_1768461), -(c_List_Olast(_1768461, hAPP(hAPP(c_List_Oappend(_1768461), _1768463), _1768459)) = c_List_Olast(_1768461, _1768463))], (18128 ^ _777864) ^ [_1089821] : [-(c_Int_Opred(_1089821) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1089821), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11517 ^ _777864) ^ [_969926, _969928, _969930] : [class_Rings_Oordered__ring(_969926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969926), c_Groups_Ozero__class_Ozero(_969926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_969926), _969928), _969930)))), 11522 ^ _777864 : [(11529 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969926), _969928), c_Groups_Ozero__class_Ozero(_969926))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969926), _969930), c_Groups_Ozero__class_Ozero(_969926)))], (11523 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969926), c_Groups_Ozero__class_Ozero(_969926)), _969928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969926), c_Groups_Ozero__class_Ozero(_969926)), _969930))]]], (2354 ^ _777864) ^ [_812553, _812555] : [_812555 = _812553, -(c_Nitpick_Oone__frac(_812555) = c_Nitpick_Oone__frac(_812553))], (18442 ^ _777864) ^ [_1095044, _1095046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095044), _1095046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1095044)), c_Int_OBit1(_1095046))))], (43854 ^ _777864) ^ [_1635603, _1635605, _1635607, _1635609] : [hBOOL(hAPP(hAPP(c_member(_1635605), _1635609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635603, tc_fun(_1635605, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1635603, tc_HOL_Obool))), _1635607))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635603, tc_fun(_1635605, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1635603, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1635605, tc_HOL_Obool), tc_fun(_1635605, tc_HOL_Obool), _1635603), hAPP(c_COMBC(_1635605, tc_fun(_1635605, tc_HOL_Obool), tc_HOL_Obool), c_member(_1635605))), _1635607)), _1635609)))], (29908 ^ _777864) ^ [_1321280, _1321282, _1321284, _1321286] : [class_Lattices_Odistrib__lattice(_1321280), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321280), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321280), _1321282), _1321284)), _1321286) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321280), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321280), _1321282), _1321286)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321280), _1321284), _1321286)))], (16492 ^ _777864) ^ [_1060993, _1060995, _1060997] : [class_Int_Onumber(_1060993), class_Orderings_Olinorder(_1060993), 16499 ^ _777864 : [(16506 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060993), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060997)), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060995)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060993), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060995)), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060997))))], (16500 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060993), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060995)), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060997))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060993), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060997)), hAPP(c_Int_Onumber__class_Onumber__of(_1060993), _1060995)))]]], (6976 ^ _777864) ^ [_892626, _892628] : [-(_892626 = hAPP(c_Option_Ooption_OSome(_892628), 6977 ^ [_892626, _892628])), -(_892626 = c_Option_Ooption_ONone(_892628))], (35492 ^ _777864) ^ [_1437919, _1437921, _1437923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437919)), 35495 ^ _777864 : [(35496 ^ _777864) ^ [_1438053] : [35498 ^ _777864 : [(35504 ^ _777864) ^ [] : [-(_1438053 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35500 ^ [_1437919, _1437921, _1437923, _1438053]), 35497 ^ [_1437919, _1437921, _1437923, _1438053]))], (35502 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35500 ^ [_1437919, _1437921, _1437923, _1438053]), _1437921)))], (35499 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35497 ^ [_1437919, _1437921, _1437923, _1438053]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1437919))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437923), _1438053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1438053), _1437919))))]]], (43054 ^ _777864) ^ [_1615321, _1615323] : [-(c_Transitive__Closure_Otrancl(_1615321, _1615323) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1615321, _1615321), tc_HOL_Obool)), _1615323), hAPP(hAPP(c_Relation_Orel__comp(_1615321, _1615321, _1615321), c_Transitive__Closure_Otrancl(_1615321, _1615323)), _1615323)))], (40180 ^ _777864) ^ [_1540668] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1540668, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1540668), hAPP(c_COMBK(tc_HOL_Obool, _1540668), c_fFalse)))], (46577 ^ _777864) ^ [_1704306, _1704308, _1704310] : [_1704306 = hAPP(hAPP(c_List_Olist_OCons(_1704308), _1704310), _1704306)], (17974 ^ _777864) ^ [_1087607] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1087607), c_Int_OPls) = _1087607)], (17978 ^ _777864) ^ [] : [c_Int_OMin = c_Int_OPls], (49404 ^ _777864) ^ [_1771876, _1771878] : [-(_1771876 = c_List_Olist_ONil(_1771878)), hBOOL(hAPP(c_List_Odistinct(_1771878), _1771876)), -(hBOOL(hAPP(c_List_Odistinct(_1771878), c_List_Obutlast(_1771878, _1771876))))], (2556 ^ _777864) ^ [_815726, _815728, _815730, _815732, _815734, _815736, _815738, _815740, _815742, _815744] : [-(c_Nitpick_Opair__box_Opair__box__rec(_815744, _815740, _815736, _815732, _815728) = c_Nitpick_Opair__box_Opair__box__rec(_815742, _815738, _815734, _815730, _815726)), _815744 = _815742, _815740 = _815738, _815736 = _815734, _815732 = _815730, _815728 = _815726], (18594 ^ _777864) ^ [_1097544] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1097544))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1097544)))))], (30014 ^ _777864) ^ [_1323804, _1323806, _1323808, _1323810] : [class_Lattices_Osemilattice__inf(_1323804), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323804), _1323806), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323804), _1323808), _1323810)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323804), _1323808), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323804), _1323806), _1323810)))], (27910 ^ _777864) ^ [_1275174, _1275176, _1275178, _1275180] : [class_Lattices_Osemilattice__sup(_1275174), 27913 ^ _777864 : [(27922 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275174), _1275176), _1275178)), _1275180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), _1275176), _1275180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), _1275178), _1275180))], (27914 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275174), _1275176), _1275178)), _1275180)), 27917 ^ _777864 : [(27920 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), _1275178), _1275180)))], (27918 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275174), _1275176), _1275180)))]]]]], (21776 ^ _777864) ^ [_1154572, _1154574, _1154576, _1154578] : [class_Fields_Olinordered__field__inverse__zero(_1154572), class_Int_Onumber(_1154572), 21783 ^ _777864 : [(21784 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154572), _1154574), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))), _1154578)), 21787 ^ _777864 : [(21794 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)))), 21797 ^ _777864 : [(21804 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)), c_Groups_Ozero__class_Ozero(_1154572)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), _1154578)))], (21798 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)), c_Groups_Ozero__class_Ozero(_1154572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154572), _1154578), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))), _1154574)))]]], (21788 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), _1154574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154572), _1154578), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)))))]]], (21810 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154572), _1154574), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))), _1154578))), 21813 ^ _777864 : [(21816 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), _1154574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154572), _1154578), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))))], (21814 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))))]], 21817 ^ _777864 : [(21820 ^ _777864) ^ [] : [21821 ^ _777864 : [(21824 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154572), _1154578), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576))), _1154574))], (21822 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)), c_Groups_Ozero__class_Ozero(_1154572))))]], 21825 ^ _777864 : [(21828 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), _1154578))], (21826 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)), c_Groups_Ozero__class_Ozero(_1154572)))]]], (21818 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154572), c_Groups_Ozero__class_Ozero(_1154572)), hAPP(c_Int_Onumber__class_Onumber__of(_1154572), _1154576)))]]]]], (47812 ^ _777864) ^ [_1734286, _1734288, _1734290, _1734292, _1734294, _1734296, _1734298] : [-(c_Map_Omap__upds(_1734286, _1734288, _1734290, hAPP(hAPP(c_List_Olist_OCons(_1734286), _1734292), _1734294), hAPP(hAPP(c_List_Olist_OCons(_1734288), _1734296), _1734298)) = c_Map_Omap__upds(_1734286, _1734288, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1734286, tc_Option_Ooption(_1734288)), _1734290), _1734292), hAPP(c_Option_Ooption_OSome(_1734288), _1734296)), _1734294, _1734298))], (38286 ^ _777864) ^ [_1496278] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496278, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1496278, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1496278, tc_HOL_Obool)))], (50628 ^ _777864) ^ [_1798553, _1798555, _1798557, _1798559] : [class_Orderings_Olinorder(_1798553), c_List_Olinorder__class_Osorted(_1798553, hAPP(c_List_Orev(_1798553), _1798555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1798557), _1798559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1798559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798553)), _1798555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798553), hAPP(hAPP(c_List_Onth(_1798553), _1798555), _1798559)), hAPP(hAPP(c_List_Onth(_1798553), _1798555), _1798557))))], (43987 ^ _777864) ^ [_1639400, _1639402, _1639404, _1639406, _1639408] : [_1639400 = c_Orderings_Obot__class_Obot(tc_fun(_1639402, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639404, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639402, tc_fun(_1639404, tc_HOL_Obool)), _1639400), _1639406)), _1639408) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639404, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1639404, tc_HOL_Obool))), _1639408))], (13714 ^ _777864) ^ [_1008850, _1008852, _1008854, _1008856] : [class_Groups_Ouminus(_1008850), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008852, _1008850)), _1008854), _1008856) = hAPP(c_Groups_Ouminus__class_Ouminus(_1008850), hAPP(_1008854, _1008856)))], (38868 ^ _777864) ^ [_1510474, _1510476, _1510478, _1510480, _1510482, _1510484] : [-(hBOOL(hAPP(hAPP(c_member(_1510474), _1510476), _1510478))), 38871 ^ _777864 : [(38878 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510474), _1510480), _1510478))), -(hAPP(c_Set_Ovimage(_1510482, _1510474, hAPP(hAPP(c_COMBC(_1510482, _1510474, _1510474), hAPP(hAPP(c_COMBC(_1510482, _1510474, tc_fun(_1510474, _1510474)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1510474, tc_fun(_1510474, _1510474)), _1510482), c_If(_1510474)), hAPP(hAPP(c_COMBC(_1510482, tc_fun(_1510482, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510482)), _1510484))), _1510476)), _1510480)), _1510478) = c_Orderings_Obot__class_Obot(tc_fun(_1510482, tc_HOL_Obool)))], (38872 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1510474), _1510480), _1510478)), -(hAPP(c_Set_Ovimage(_1510482, _1510474, hAPP(hAPP(c_COMBC(_1510482, _1510474, _1510474), hAPP(hAPP(c_COMBC(_1510482, _1510474, tc_fun(_1510474, _1510474)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1510474, tc_fun(_1510474, _1510474)), _1510482), c_If(_1510474)), hAPP(hAPP(c_COMBC(_1510482, tc_fun(_1510482, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510482)), _1510484))), _1510476)), _1510480)), _1510478) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1510482, tc_HOL_Obool)), _1510484))]]], (14434 ^ _777864) ^ [_1021945, _1021947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021945), 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)), _1021947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021945), _1021947)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51559 ^ _777864) ^ [_1812623, _1812625] : [hBOOL(_1812623), hBOOL(_1812625), -(hBOOL(hAPP(hAPP(c_fconj, _1812623), _1812625)))], (9846 ^ _777864) ^ [] : [-(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))], (11036 ^ _777864) ^ [_961678, _961680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961678), hAPP(c_Nat_OSuc, _961680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961678), _961680))), -(_961678 = hAPP(c_Nat_OSuc, _961680))], (32581 ^ _777864) ^ [_1374393, _1374395, _1374397] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1374393), _1374395)), hBOOL(hAPP(hAPP(c_member(_1374393), _1374397), _1374395)), -(hAPP(c_Finite__Set_Ocard(_1374393), _1374395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1374393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374393, tc_HOL_Obool)), _1374395), hAPP(hAPP(c_Set_Oinsert(_1374393), _1374397), c_Orderings_Obot__class_Obot(tc_fun(_1374393, tc_HOL_Obool)))))))], (16900 ^ _777864) ^ [_1069182, _1069184, _1069186, _1069188] : [class_Rings_Olinordered__semidom(_1069182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069184), _1069186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069182), c_Groups_Ozero__class_Ozero(_1069182)), _1069188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069182), _1069188), c_Groups_Oone__class_Oone(_1069182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069182), hAPP(hAPP(c_Power_Opower__class_Opower(_1069182), _1069188), _1069186)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069182), _1069188), _1069184))))], (47372 ^ _777864) ^ [_1724982, _1724984, _1724986] : [-(hAPP(hAPP(c_List_Olist__update(_1724982, _1724984), _1724986), hAPP(hAPP(c_List_Onth(_1724982), _1724984), _1724986)) = _1724984)], (44606 ^ _777864) ^ [_1655360, _1655362, _1655364] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1655360, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1655360, tc_HOL_Obool)), _1655362), _1655364)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1655360, tc_HOL_Obool)), _1655362), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1655360, tc_HOL_Obool), _1655364)))], (18538 ^ _777864) ^ [_1096619] : [-(c_Int_OBit1(_1096619) = 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)), _1096619)), _1096619))], (28298 ^ _777864) ^ [_1283044, _1283046, _1283048, _1283050] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283044, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1283044, tc_fun(_1283044, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283044)), _1283046)), hAPP(hAPP(c_COMBC(_1283044, tc_fun(_1283044, tc_HOL_Obool), tc_HOL_Obool), c_member(_1283044)), _1283048)), _1283050)), -(hBOOL(hAPP(hAPP(c_member(_1283044), _1283050), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283044, tc_HOL_Obool)), _1283046), _1283048))))], (6653 ^ _777864) ^ [_887627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _887627)), _887627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27876 ^ _777864) ^ [_1274597, _1274599, _1274601] : [class_Lattices_Osemilattice__sup(_1274597), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274597), _1274599), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274597), _1274599), _1274601))))], (41372 ^ _777864) ^ [_1577296, _1577298, _1577300] : [-(hAPP(c_Relation_ODomain(_1577296, _1577298), hAPP(c_Set_OCollect(tc_prod(_1577296, _1577298)), hAPP(c_Product__Type_Oprod_Oprod__case(_1577296, _1577298, tc_HOL_Obool), _1577300))) = hAPP(c_Set_OCollect(_1577296), hAPP(hAPP(c_COMBB(tc_fun(_1577298, tc_HOL_Obool), tc_HOL_Obool, _1577296), c_HOL_OEx(_1577298)), _1577300)))], (44171 ^ _777864) ^ [_1644797, _1644799, _1644801, _1644803, _1644805, _1644807, _1644809] : [44173 ^ _777864 : [(44176 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1644805, 44172 ^ [_1644797, _1644799, _1644801, _1644803, _1644805, _1644807, _1644809]), _1644807), _1644809))], (44174 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1644797), 44172 ^ [_1644797, _1644799, _1644801, _1644803, _1644805, _1644807, _1644809]), _1644803)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644797, tc_fun(_1644799, tc_fun(_1644801, tc_HOL_Obool))), _1644803), _1644805), _1644807), _1644809)))], (11215 ^ _777864) ^ [_964656, _964658, _964660, _964662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964656), _964658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964660), _964662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964656), _964660)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _964658), _964662))))], (41194 ^ _777864) ^ [_1572592, _1572594, _1572596, _1572598, _1572600] : [-(hAPP(c_Relation_ORange(_1572592, _1572594), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1572592, _1572594)), hAPP(hAPP(c_Product__Type_OPair(_1572592, _1572594), _1572596), _1572598)), _1572600)) = hAPP(hAPP(c_Set_Oinsert(_1572594), _1572598), hAPP(c_Relation_ORange(_1572592, _1572594), _1572600)))], (26325 ^ _777864) ^ [_1241326, _1241328] : [class_Orderings_Obot(_1241326), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241326), c_Orderings_Obot__class_Obot(_1241326)), _1241328)))], (28713 ^ _777864) ^ [_1296212] : [-(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)), _1296212)) = _1296212)], (45693 ^ _777864) ^ [_1680817, _1680819, _1680821, _1680823, _1680825] : [c_Fun_Oinj__on(_1680817, _1680819, _1680821, c_Orderings_Otop__class_Otop(tc_fun(_1680817, tc_HOL_Obool))), 45696 ^ _777864 : [(45703 ^ _777864) ^ [] : [_1680823 = _1680825, -(hAPP(hAPP(c_List_Omap(_1680817, _1680819), _1680821), _1680823) = hAPP(hAPP(c_List_Omap(_1680817, _1680819), _1680821), _1680825))], (45697 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Omap(_1680817, _1680819), _1680821), _1680823) = hAPP(hAPP(c_List_Omap(_1680817, _1680819), _1680821), _1680825), -(_1680823 = _1680825)]]], (36738 ^ _777864) ^ [_1463852, _1463854, _1463856, _1463858, _1463860] : [-(hBOOL(hAPP(hAPP(c_member(_1463852), _1463854), _1463856))), -(hAPP(c_Map_Orestrict__map(_1463852, _1463858, _1463860, _1463856), _1463854) = c_Option_Ooption_ONone(_1463858))], (37853 ^ _777864) ^ [_1488014, _1488016] : [class_Groups_Oordered__ab__group__add(_1488014), -(hAPP(c_Set_Oimage(_1488014, _1488014, c_Groups_Ouminus__class_Ouminus(_1488014)), hAPP(c_SetInterval_Oord__class_OlessThan(_1488014), _1488016)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1488014), hAPP(c_Groups_Ouminus__class_Ouminus(_1488014), _1488016)))], (5302 ^ _777864) ^ [_859013, _859015, _859017, _859019, _859021, _859023] : [-(c_List_OtakeWhile(_859023, _859019, _859015) = c_List_OtakeWhile(_859021, _859017, _859013)), _859023 = _859021, _859019 = _859017, _859015 = _859013], (40681 ^ _777864) ^ [_1559244, _1559246] : [-(hAPP(c_Fun_Oid(_1559244), _1559246) = _1559246)], (25111 ^ _777864) ^ [_1218550, _1218552] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218550), _1218552)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218552), _1218550)), -(_1218550 = _1218552)], (51531 ^ _777864) ^ [_1812292, _1812294] : [hBOOL(hAPP(hAPP(c_fequal, _1812292), _1812294)), -(_1812292 = _1812294)], (44401 ^ _777864) ^ [_1650281, _1650283, _1650285] : [c_Wellfounded_Owf(_1650281, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650281, _1650281), tc_HOL_Obool), _1650283), _1650285)), -(c_Wellfounded_Owf(_1650281, _1650285))], (32365 ^ _777864) ^ [_1369671, _1369673, _1369675] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369671), _1369673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1369671, tc_HOL_Obool)), _1369675), _1369673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1369671), _1369675)), hAPP(c_Finite__Set_Ocard(_1369671), _1369673))))], (49275 ^ _777864) ^ [_1769061, _1769063] : [-(_1769061 = c_List_Olist_ONil(_1769063)), -(c_List_Olast(_1769063, _1769061) = hAPP(hAPP(c_List_Onth(_1769063), _1769061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769063)), _1769061)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (19256 ^ _777864) ^ [_1109006] : [class_Int_Onumber__ring(_1109006), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109006), c_Groups_Oone__class_Oone(_1109006)), c_Groups_Oone__class_Oone(_1109006)) = hAPP(c_Int_Onumber__class_Onumber__of(_1109006), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (50550 ^ _777864) ^ [_1796102, _1796104, _1796106] : [-(hAPP(c_List_Orev(_1796102), hAPP(c_List_Ofilter(_1796102, _1796104), _1796106)) = hAPP(c_List_Ofilter(_1796102, _1796104), hAPP(c_List_Orev(_1796102), _1796106)))], (28058 ^ _777864) ^ [_1277829, _1277831, _1277833, _1277835] : [class_Lattices_Osemilattice__sup(_1277829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277829), _1277831), _1277833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277829), _1277831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277829), _1277835), _1277833))))], (34557 ^ _777864) ^ [_1419783, _1419785] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1419783, _1419785))))], (22248 ^ _777864) ^ [_1162305, _1162307, _1162309, _1162311] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162305, _1162307), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1162309), _1162311))), -(_1162307 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1162305), _1162307) = _1162309)], (37316 ^ _777864) ^ [_1477201, _1477203, _1477205, _1477207] : [-(hBOOL(hAPP(hAPP(c_member(_1477201), _1477203), _1477205))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477201, tc_Nat_Onat), _1477207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477201, tc_HOL_Obool)), _1477205), hAPP(hAPP(c_Set_Oinsert(_1477201), _1477203), c_Orderings_Obot__class_Obot(tc_fun(_1477201, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477201, tc_Nat_Onat), _1477207), _1477205))], (9612 ^ _777864) ^ [_938497, _938499, _938501] : [class_Rings_Olinordered__ring__strict(_938497), 9615 ^ _777864 : [(9624 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938497), _938499), _938499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938497), _938501), _938501)) = c_Groups_Ozero__class_Ozero(_938497)), _938499 = c_Groups_Ozero__class_Ozero(_938497), _938501 = c_Groups_Ozero__class_Ozero(_938497)], (9616 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938497), _938499), _938499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938497), _938501), _938501)) = c_Groups_Ozero__class_Ozero(_938497), 9619 ^ _777864 : [(9622 ^ _777864) ^ [] : [-(_938501 = c_Groups_Ozero__class_Ozero(_938497))], (9620 ^ _777864) ^ [] : [-(_938499 = c_Groups_Ozero__class_Ozero(_938497))]]]]], (42200 ^ _777864) ^ [_1597369, _1597371, _1597373, _1597375, _1597377, _1597379] : [c_Finite__Set_Ofolding__idem(_1597369, _1597371, _1597373, _1597375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597369), _1597377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597369, tc_HOL_Obool)), _1597379), _1597377)), -(hAPP(c_Fun_Ocomp(_1597371, _1597371, _1597371, hAPP(_1597375, _1597377)), hAPP(_1597375, _1597379)) = hAPP(_1597375, _1597377))], (44989 ^ _777864) ^ [_1663863, _1663865, _1663867, _1663869] : [-(_1663863 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1663865, tc_HOL_Obool), tc_HOL_Obool))), 44995 ^ _777864 : [(44998 ^ _777864) ^ [] : [c_Fun_Oinj__on(_1663865, _1663867, _1663869, 44994 ^ [_1663863, _1663865, _1663867, _1663869])], (44996 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1663865, tc_HOL_Obool)), 44994 ^ [_1663863, _1663865, _1663867, _1663869]), _1663863)))]], -(c_Fun_Oinj__on(_1663865, _1663867, _1663869, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1663865, tc_HOL_Obool), _1663863)))], (12794 ^ _777864) ^ [_992632, _992634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992634), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _992632), _992634)))], (21162 ^ _777864) ^ [_1142738, _1142740, _1142742, _1142744] : [class_Fields_Olinordered__field__inverse__zero(_1142738), 21165 ^ _777864 : [(21166 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142738), _1142740), _1142742)), _1142744)), 21169 ^ _777864 : [(21176 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142742))), 21179 ^ _777864 : [(21186 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), _1142742), c_Groups_Ozero__class_Ozero(_1142738)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142744)))], (21180 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), _1142742), c_Groups_Ozero__class_Ozero(_1142738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142738), _1142744), _1142742)), _1142740)))]]], (21170 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), _1142740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142738), _1142744), _1142742))))]]], (21192 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142738), _1142740), _1142742)), _1142744))), 21195 ^ _777864 : [(21198 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), _1142740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142738), _1142744), _1142742)))], (21196 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142742)))]], 21199 ^ _777864 : [(21202 ^ _777864) ^ [] : [21203 ^ _777864 : [(21206 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142738), _1142744), _1142742)), _1142740))], (21204 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), _1142742), c_Groups_Ozero__class_Ozero(_1142738))))]], 21207 ^ _777864 : [(21210 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142744))], (21208 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), _1142742), c_Groups_Ozero__class_Ozero(_1142738)))]]], (21200 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142738), c_Groups_Ozero__class_Ozero(_1142738)), _1142742))]]]]], (34030 ^ _777864) ^ [_1407839, _1407841, _1407843, _1407845, _1407847, _1407849, _1407851] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407839, tc_fun(_1407841, tc_fun(_1407843, tc_HOL_Obool))), _1407845), _1407847), _1407849), _1407851)), 34034 ^ _777864 : [(34037 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1407847, 34033 ^ [_1407839, _1407841, _1407843, _1407845, _1407847, _1407849, _1407851]), _1407849), _1407851)))], (34035 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407839), 34033 ^ [_1407839, _1407841, _1407843, _1407845, _1407847, _1407849, _1407851]), _1407845)))]]], (44204 ^ _777864) ^ [_1645532] : [-(hAPP(c_Relation_ORange(_1645532, _1645532), c_Relation_OId(_1645532)) = c_Orderings_Otop__class_Otop(tc_fun(_1645532, tc_HOL_Obool)))], (11867 ^ _777864) ^ [_976332, _976334] : [class_Groups_Oordered__ab__group__add(_976332), 11870 ^ _777864 : [(11877 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976332), c_Groups_Ozero__class_Ozero(_976332)), _976334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976332), hAPP(c_Groups_Ouminus__class_Ouminus(_976332), _976334)), c_Groups_Ozero__class_Ozero(_976332))))], (11871 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976332), hAPP(c_Groups_Ouminus__class_Ouminus(_976332), _976334)), c_Groups_Ozero__class_Ozero(_976332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976332), c_Groups_Ozero__class_Ozero(_976332)), _976334)))]]], (36554 ^ _777864) ^ [_1458753, _1458755, _1458757, _1458759] : [class_Rings_Oring__1(_1458753), -(hAPP(c_Int_Oring__1__class_Oof__int(_1458753), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458755, tc_Int_Oint), _1458757), _1458759)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458755, _1458753), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1458753, _1458755), c_Int_Oring__1__class_Oof__int(_1458753)), _1458757)), _1458759))], (17114 ^ _777864) ^ [_1072971, _1072973] : [class_Groups_Omonoid__mult(_1072971), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1072971), c_Groups_Oone__class_Oone(_1072971)), _1072973) = c_Groups_Oone__class_Oone(_1072971))], (41712 ^ _777864) ^ [_1585901, _1585903, _1585905] : [-(hAPP(c_Fun_Ocomp(_1585901, _1585903, _1585901, _1585905), c_Fun_Oid(_1585901)) = _1585905)], (8054 ^ _777864) ^ [_912110, _912112] : [class_Orderings_Opreorder(_912110), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912110), _912112), _912112))], (49135 ^ _777864) ^ [_1766340, _1766342, _1766344] : [49137 ^ _777864 : [(49140 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1766340), 49136 ^ [_1766340, _1766342, _1766344]), _1766344))], (49138 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766340), 49136 ^ [_1766340, _1766342, _1766344]), hAPP(c_List_Oset(_1766340), _1766342))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1766340)), _1766342), c_List_Olists(_1766340, _1766344))))], (44463 ^ _777864) ^ [_1651878, _1651880, _1651882, _1651884] : [-(hAPP(hAPP(c_Nat_Ocompow(_1651878, _1651878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651880), _1651882)), _1651884) = hAPP(c_Fun_Ocomp(_1651878, _1651878, _1651878, hAPP(hAPP(c_Nat_Ocompow(_1651878, _1651878), _1651880), _1651884)), hAPP(hAPP(c_Nat_Ocompow(_1651878, _1651878), _1651882), _1651884)))], (49243 ^ _777864) ^ [_1768616, _1768618, _1768620] : [-(_1768616 = c_List_Olist_ONil(_1768618)), -(c_List_Olast(_1768618, hAPP(hAPP(c_List_Oappend(_1768618), _1768620), _1768616)) = c_List_Olast(_1768618, _1768616))], (11156 ^ _777864) ^ [_963519, _963521, _963523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963519), _963521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963523), _963521))))], (1262 ^ _777864) ^ [_796407, _796409] : [-(class_Lattices_Obounded__lattice__bot(_796407)), _796409 = _796407, class_Lattices_Obounded__lattice__bot(_796409)], (9300 ^ _777864) ^ [_932754, _932756, _932758, _932760] : [class_Rings_Olinordered__ring__strict(_932754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932754), _932756), _932758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932754), _932760), c_Groups_Ozero__class_Ozero(_932754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932754), _932760), _932758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932754), _932760), _932756))))], (29006 ^ _777864) ^ [_1302155, _1302157, _1302159, _1302161] : [c_Equiv__Relations_Oequiv(_1302155, _1302157, _1302159), hBOOL(hAPP(hAPP(c_member(_1302155), _1302161), _1302157)), -(hBOOL(hAPP(hAPP(c_member(_1302155), _1302161), hAPP(c_Relation_OImage(_1302155, _1302155, _1302159), hAPP(hAPP(c_Set_Oinsert(_1302155), _1302161), c_Orderings_Obot__class_Obot(tc_fun(_1302155, tc_HOL_Obool)))))))], (34471 ^ _777864) ^ [_1417597, _1417599, _1417601] : [-(hAPP(c_Set_OPow(_1417597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417597, tc_HOL_Obool)), _1417599), _1417601)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1417597, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1417597), _1417599)), hAPP(c_Set_OPow(_1417597), _1417601)))], (4424 ^ _777864) ^ [_845522, _845524, _845526, _845528] : [-(c_Big__Operators_Olinorder__class_OMax(_845528, _845524) = c_Big__Operators_Olinorder__class_OMax(_845526, _845522)), _845528 = _845526, _845524 = _845522], (44889 ^ _777864) ^ [_1661834, _1661836] : [-(hAPP(c_Relation_OField(_1661834), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1661834, _1661834), tc_HOL_Obool), _1661836)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1661834, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1661834, _1661834), tc_HOL_Obool), tc_fun(_1661834, tc_HOL_Obool), c_Relation_OField(_1661834)), _1661836)))], (20786 ^ _777864) ^ [_1136394] : [c_Nat__Transfer_Ois__nat(_1136394), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136394)))], (5268 ^ _777864) ^ [_858478, _858480, _858482, _858484] : [-(c_List_Omap(_858484, _858480) = c_List_Omap(_858482, _858478)), _858484 = _858482, _858480 = _858478], (23493 ^ _777864) ^ [_1187951, _1187953, _1187955, _1187957] : [class_Orderings_Olinorder(_1187951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187951), _1187953), _1187955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187951), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187951), _1187957), _1187953)), _1187955)))], (35448 ^ _777864) ^ [_1437039, _1437041, _1437043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437039)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1437041), _1437043)), 35455 ^ _777864 : [(35456 ^ _777864) ^ [_1437235] : [35458 ^ _777864 : [(35464 ^ _777864) ^ [] : [-(_1437235 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35460 ^ [_1437039, _1437041, _1437043, _1437235]), 35457 ^ [_1437039, _1437041, _1437043, _1437235]))], (35462 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35460 ^ [_1437039, _1437041, _1437043, _1437235]), _1437043)))], (35459 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35457 ^ [_1437039, _1437041, _1437043, _1437235]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1437039))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437235), _1437041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437235), _1437039)), _1437041)))]]], (38550 ^ _777864) ^ [_1501975, _1501977, _1501979, _1501981, _1501983, _1501985] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501975, tc_fun(_1501977, tc_fun(_1501979, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1501975, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_fun(_1501977, tc_fun(_1501979, tc_HOL_Obool)), _1501975), hAPP(c_COMBC(_1501977, tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_fun(_1501979, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501979, tc_fun(tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_fun(_1501979, tc_HOL_Obool)), _1501977), c_COMBC(_1501979, tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501979, tc_prod(_1501977, _1501979)), tc_fun(_1501979, tc_fun(tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_HOL_Obool)), _1501977), hAPP(c_COMBB(tc_prod(_1501977, _1501979), tc_fun(tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool), tc_HOL_Obool), _1501979), c_member(tc_prod(_1501977, _1501979)))), c_Product__Type_OPair(_1501977, _1501979))))), _1501981)), _1501983), _1501985)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501977, _1501979)), hAPP(hAPP(c_Product__Type_OPair(_1501977, _1501979), _1501983), _1501985)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501975, tc_fun(tc_prod(_1501977, _1501979), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1501975, tc_HOL_Obool))), _1501981))))], (51143 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51069 ^ _777864) ^ [_1807620, _1807622] : [class_Orderings_Opreorder(_1807620), -(class_Orderings_Opreorder(tc_fun(_1807622, _1807620)))], (5472 ^ _777864) ^ [_861564, _861566] : [_861566 = _861564, -(tc_Hoare__Mirabelle_Otriple(_861566) = tc_Hoare__Mirabelle_Otriple(_861564))], (49835 ^ _777864) ^ [_1781823, _1781825, _1781827] : [class_Orderings_Olinorder(_1781823), 49838 ^ _777864 : [(49851 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781823, hAPP(hAPP(c_List_Olist_OCons(_1781823), _1781825), _1781827))), c_List_Olinorder__class_Osorted(_1781823, _1781827), 49857 ^ _777864 : [(49860 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781823), _1781825), 49856 ^ [_1781823, _1781825, _1781827]))], (49858 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781823), 49856 ^ [_1781823, _1781825, _1781827]), hAPP(c_List_Oset(_1781823), _1781827))))]]], (49839 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1781823, hAPP(hAPP(c_List_Olist_OCons(_1781823), _1781825), _1781827)), 49842 ^ _777864 : [(49845 ^ _777864) ^ [_1782009] : [hBOOL(hAPP(hAPP(c_member(_1781823), _1782009), hAPP(c_List_Oset(_1781823), _1781827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1781823), _1781825), _1782009)))], (49843 ^ _777864) ^ [] : [-(c_List_Olinorder__class_Osorted(_1781823, _1781827))]]]]], (27962 ^ _777864) ^ [_1276073, _1276075, _1276077] : [class_Lattices_Osemilattice__sup(_1276073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276073), _1276075), _1276077)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276073), _1276077), _1276075) = _1276077)], (3952 ^ _777864) ^ [_838058, _838060, _838062, _838064, _838066, _838068] : [-(c_Smallcheck_Osmall_H(_838068, _838064, _838060) = c_Smallcheck_Osmall_H(_838066, _838062, _838058)), _838068 = _838066, _838064 = _838062, _838060 = _838058], (45832 ^ _777864) ^ [_1684266, _1684268, _1684270] : [-(hAPP(hAPP(c_Option_Omap(_1684266, _1684268), _1684270), c_Option_Ooption_ONone(_1684266)) = c_Option_Ooption_ONone(_1684268))], (40222 ^ _777864) ^ [_1541518, _1541520, _1541522, _1541524] : [-(hBOOL(hAPP(hAPP(c_member(_1541518), _1541520), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541518, tc_HOL_Obool)), _1541522), hAPP(c_Set_OCollect(_1541518), _1541524))))), hBOOL(hAPP(hAPP(c_member(_1541518), _1541520), _1541522)), hBOOL(hAPP(_1541524, _1541520))], (24535 ^ _777864) ^ [_1208482, _1208484] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1208482), _1208484) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1208482, 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)))), _1208484))))], (12918 ^ _777864) ^ [_994732, _994734] : [_994732 = hAPP(c_Int_Onat, _994734), 12921 ^ _777864 : [(12928 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994734))), -(_994732 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12922 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994734)), -(_994734 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994732))]]], (50488 ^ _777864) ^ [_1794826, _1794828, _1794830] : [-(c_List_Oconcat(_1794826, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1794826)), _1794828), _1794830)) = hAPP(hAPP(c_List_Oappend(_1794826), c_List_Oconcat(_1794826, _1794828)), c_List_Oconcat(_1794826, _1794830)))], (33632 ^ _777864) ^ [_1397402, _1397404, _1397406, _1397408] : [class_Complete__Lattice_Ocomplete__lattice(_1397402), -(_1397404 = c_Orderings_Obot__class_Obot(tc_fun(_1397406, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397406, _1397402), _1397404), hAPP(c_COMBK(_1397402, _1397406), _1397408)) = _1397408)], (50243 ^ _777864) ^ [_1788912, _1788914, _1788916, _1788918] : [class_Orderings_Olinorder(_1788912), c_List_Olinorder__class_Osorted(_1788912, _1788914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1788916), _1788918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1788918), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788912)), _1788914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1788912), hAPP(hAPP(c_List_Onth(_1788912), _1788914), _1788916)), hAPP(hAPP(c_List_Onth(_1788912), _1788914), _1788918))))], (14616 ^ _777864) ^ [_1024969, _1024971, _1024973, _1024975] : [class_Divides_Osemiring__div(_1024969), -(_1024971 = c_Groups_Ozero__class_Ozero(_1024969)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024969), _1024973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024969), _1024975), _1024971))), _1024971) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1024969), _1024975), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1024969), _1024973), _1024971)))], (51039 ^ _777864) ^ [_1807225, _1807227] : [class_Lattices_Obounded__lattice(_1807225), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1807227, _1807225)))], (12782 ^ _777864) ^ [_992401, _992403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992401), c_Groups_Oone__class_Oone(tc_Int_Oint))), _992403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992401), _992403)))], (43134 ^ _777864) ^ [_1617169, _1617171, _1617173, _1617175, _1617177, _1617179] : [c_Finite__Set_Ofun__left__comm(_1617169, _1617171, _1617173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617169), _1617175)), -(hAPP(hAPP(_1617173, _1617177), hAPP(hAPP(c_Finite__Set_Ofold(_1617169, _1617171, _1617173), _1617179), _1617175)) = hAPP(hAPP(c_Finite__Set_Ofold(_1617169, _1617171, _1617173), hAPP(hAPP(_1617173, _1617177), _1617179)), _1617175))], (42465 ^ _777864) ^ [_1603367, _1603369, _1603371, _1603373, _1603375, _1603377] : [class_Rings_Ocomm__semiring__1(_1603367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603369), _1603371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603369, tc_HOL_Obool)), _1603373), _1603371)), 42479 ^ _777864 : [(42482 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1603367), hAPP(_1603375, 42478 ^ [_1603367, _1603369, _1603371, _1603373, _1603375, _1603377])), hAPP(_1603377, 42478 ^ [_1603367, _1603369, _1603371, _1603373, _1603375, _1603377])))], (42480 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603369), 42478 ^ [_1603367, _1603369, _1603371, _1603373, _1603375, _1603377]), _1603373)))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1603367), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1603369, _1603367), _1603375), _1603373)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1603369, _1603367), _1603377), _1603371))))], (40927 ^ _777864) ^ [_1566690, _1566692, _1566694] : [c_Wellfounded_Owf(_1566690, _1566692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566690, _1566690), tc_HOL_Obool)), _1566694), _1566692)), -(c_Wellfounded_Owf(_1566690, _1566694))], (1512 ^ _777864) ^ [_799532, _799534] : [-(class_Groups_Ocomm__monoid__mult(_799532)), _799534 = _799532, class_Groups_Ocomm__monoid__mult(_799534)], (516 ^ _777864) ^ [_785872, _785874] : [-(c_Nitpick_Ounknown(_785872)), _785874 = _785872, c_Nitpick_Ounknown(_785874)], (36990 ^ _777864) ^ [_1469488, _1469490, _1469492, _1469494, _1469496] : [class_Groups_Ocomm__monoid__add(_1469488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469490), _1469492)), hBOOL(hAPP(hAPP(c_member(_1469490), _1469494), _1469492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469490, _1469488), _1469496), _1469492) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469488), hAPP(_1469496, _1469494)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469490, _1469488), _1469496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469490, tc_HOL_Obool)), _1469492), hAPP(hAPP(c_Set_Oinsert(_1469490), _1469494), c_Orderings_Obot__class_Obot(tc_fun(_1469490, tc_HOL_Obool)))))))], (43937 ^ _777864) ^ [_1637906, _1637908, _1637910, _1637912, _1637914] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637906, tc_fun(_1637908, tc_HOL_Obool)), _1637910), hAPP(hAPP(c_COMBB(tc_fun(_1637908, tc_HOL_Obool), tc_fun(_1637908, tc_HOL_Obool), _1637906), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1637908, tc_HOL_Obool)), _1637912)), _1637914)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1637908, tc_HOL_Obool)), _1637912), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637906, tc_fun(_1637908, tc_HOL_Obool)), _1637910), _1637914)))], (15476 ^ _777864) ^ [_1041239, _1041241] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041239), _1041241))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041239), _1041241)) = _1041239)], (38124 ^ _777864) ^ [_1493309, _1493311] : [class_Lattices_Obounded__lattice__top(_1493309), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493309), _1493311), c_Orderings_Otop__class_Otop(_1493309)) = _1493311)], (29988 ^ _777864) ^ [_1323202, _1323204] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323202, tc_HOL_Obool)), _1323204), _1323204) = _1323204)], (19224 ^ _777864) ^ [_1108371] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1108371)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1108371)))], (40170 ^ _777864) ^ [_1540368] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1540368, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1540368), hAPP(c_COMBK(tc_HOL_Obool, _1540368), c_fTrue)))], (45487 ^ _777864) ^ [_1675900, _1675902, _1675904, _1675906, _1675908] : [-(c_Map_Omap__add(_1675900, _1675902, _1675904, c_Map_Omap__add(_1675900, _1675902, _1675906, _1675908)) = c_Map_Omap__add(_1675900, _1675902, c_Map_Omap__add(_1675900, _1675902, _1675904, _1675906), _1675908))], (26135 ^ _777864) ^ [_1237394, _1237396, _1237398] : [-(hAPP(hAPP(c_Set_Oinsert(_1237394), _1237396), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1237394, tc_HOL_Obool)), _1237398), hAPP(hAPP(c_Set_Oinsert(_1237394), _1237396), c_Orderings_Obot__class_Obot(tc_fun(_1237394, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1237394), _1237396), _1237398))], (48796 ^ _777864) ^ [_1758690, _1758692, _1758694] : [hBOOL(hAPP(c_List_Odistinct(_1758690), hAPP(c_List_Orotate(_1758690, _1758692), _1758694))), -(hBOOL(hAPP(c_List_Odistinct(_1758690), _1758694)))], (37935 ^ _777864) ^ [_1489723, _1489725, _1489727, _1489729, _1489731, _1489733] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489723, _1489725, _1489727, _1489729, _1489731), _1489733)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1489723), _1489731)))], (40679 ^ _777864) ^ [_1559214, _1559216] : [-(hAPP(c_Fun_Oid(_1559214), _1559216) = _1559216)], (28408 ^ _777864) ^ [_1288095, _1288097, _1288099, _1288101, _1288103, _1288105] : [c_Hoare__Mirabelle_Ohoare__derivs(_1288095, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1288095), tc_HOL_Obool)), _1288097), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1288095), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095))), hAPP(hAPP(c_COMBB(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1288095)), _1288099)), c_Com_Ocom_OBODY)), _1288101)), _1288103)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1288095), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095))), hAPP(hAPP(c_COMBB(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1288095, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1288095))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1288095)), _1288099)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _1288101)), _1288103)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1288105), _1288103)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1288095, _1288097, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1288095)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1288095), hAPP(_1288099, _1288105)), hAPP(c_Com_Ocom_OBODY, _1288105)), hAPP(_1288101, _1288105))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1288095), tc_HOL_Obool)))))], (40669 ^ _777864) ^ [_1559054, _1559056] : [-(hAPP(c_Set_Oimage(_1559054, _1559054, c_Fun_Oid(_1559054)), _1559056) = _1559056)], (45553 ^ _777864) ^ [_1677348, _1677350, _1677352] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1677348)), hAPP(c_Set_Oimage(_1677350, tc_Option_Ooption(_1677348), c_Map_Omap__of(_1677350, _1677348, _1677352)), c_Orderings_Otop__class_Otop(tc_fun(_1677350, tc_HOL_Obool))))))], (11665 ^ _777864) ^ [_972748, _972750, _972752] : [class_Rings_Oordered__cancel__semiring(_972748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972748), _972750), c_Groups_Ozero__class_Ozero(_972748))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972748), c_Groups_Ozero__class_Ozero(_972748)), _972752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972748), _972750), _972752)), c_Groups_Ozero__class_Ozero(_972748))))], (46635 ^ _777864) ^ [_1705485, _1705487, _1705489, _1705491] : [-(_1705485 = _1705487), -(c_List_Oremove1(_1705489, _1705485, hAPP(hAPP(c_List_Olist_OCons(_1705489), _1705487), _1705491)) = hAPP(hAPP(c_List_Olist_OCons(_1705489), _1705487), c_List_Oremove1(_1705489, _1705485, _1705491)))], (25393 ^ _777864) ^ [_1223173, _1223175, _1223177] : [class_Rings_Olinordered__idom(_1223173), 25396 ^ _777864 : [(25403 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223173), _1223175), _1223177)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223173), _1223175), hAPP(c_Groups_Oabs__class_Oabs(_1223173), _1223177))))], (25397 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223173), _1223175), hAPP(c_Groups_Oabs__class_Oabs(_1223173), _1223177))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223173), _1223175), _1223177)))]]], (26009 ^ _777864) ^ [_1234520, _1234522] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1234520)), _1234522)), 26012 ^ _777864 : [(26019 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234520))), -(_1234522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26013 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234520)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234520), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234522))))]]], (51499 ^ _777864) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (44085 ^ _777864) ^ [_1641972, _1641974] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1641972, _1641972)), _1641974)), c_Wellfounded_Oacyclic(_1641972, _1641974), -(c_Wellfounded_Owf(_1641972, hAPP(c_Relation_Oconverse(_1641972, _1641972), _1641974)))], (50983 ^ _777864) ^ [_1806400, _1806402, _1806404] : [hBOOL(hAPP(c_List_Odistinct(_1806400), _1806402)), -(hBOOL(hAPP(c_List_Odistinct(_1806400), c_List_OdropWhile(_1806400, _1806404, _1806402))))], (19022 ^ _777864) ^ [_1104842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104842), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1104842)), c_Int_OPls)))], (40008 ^ _777864) ^ [_1536959] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1536959), c_Int_OInteg)), -(_1536959 = hAPP(c_Int_ORep__Integ, 40011 ^ [_1536959]))], (17340 ^ _777864) ^ [_1077123, _1077125, _1077127] : [class_Rings_Olinordered__semidom(_1077123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077123), c_Groups_Oone__class_Oone(_1077123)), _1077125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077123), hAPP(hAPP(c_Power_Opower__class_Opower(_1077123), _1077125), _1077127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077123), _1077125), hAPP(hAPP(c_Power_Opower__class_Opower(_1077123), _1077125), _1077127)))))], (30821 ^ _777864) ^ [_1341588, _1341590, _1341592] : [class_Orderings_Olinorder(_1341588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341588), _1341590)), hBOOL(hAPP(hAPP(c_member(_1341588), _1341592), _1341590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341588), _1341592), c_Big__Operators_Olinorder__class_OMax(_1341588, _1341590))))], (18920 ^ _777864) ^ [_1103099] : [c_Int_OPls = _1103099, -(c_Int_OPls = c_Int_OBit0(_1103099))], (48165 ^ _777864) ^ [_1742300, _1742302] : [-(hAPP(hAPP(c_List_Oappend(_1742300), c_List_Olist_ONil(_1742300)), _1742302) = _1742302)], (34515 ^ _777864) ^ [_1418672, _1418674, _1418676, _1418678] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1418672, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418674, tc_fun(tc_fun(_1418672, tc_HOL_Obool), tc_HOL_Obool)), _1418676), hAPP(hAPP(c_COMBB(tc_fun(_1418672, tc_HOL_Obool), tc_fun(tc_fun(_1418672, tc_HOL_Obool), tc_HOL_Obool), _1418674), c_Set_OPow(_1418672)), _1418678))), hAPP(c_Set_OPow(_1418672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418674, tc_fun(_1418672, tc_HOL_Obool)), _1418676), _1418678)))))], (27630 ^ _777864) ^ [_1270001, _1270003, _1270005, _1270007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270001), _1270003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270005), _1270007)), -(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), _1270001), _1270005)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1270003), _1270007))), c_FunDef_Opair__leq)))], (10628 ^ _777864) ^ [_955076, _955078, _955080] : [class_Orderings_Oorder(_955076), -(_955078 = _955080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955076), _955078), _955080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955076), _955078), _955080)))], (48464 ^ _777864) ^ [_1751095, _1751097, _1751099, _1751101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1751095), tc_List_Olist(_1751095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751095), tc_List_Olist(_1751095)), _1751097), _1751099)), c_List_Olistrel1(_1751095, _1751101))), 48469 ^ _777864 : [(48476 ^ _777864) ^ [] : [-(_1751099 = hAPP(hAPP(c_List_Oappend(_1751095), 48471 ^ [_1751095, _1751097, _1751099, _1751101]), hAPP(hAPP(c_List_Olist_OCons(_1751095), 48468 ^ [_1751095, _1751097, _1751099, _1751101]), 48472 ^ [_1751095, _1751097, _1751099, _1751101])))], (48474 ^ _777864) ^ [] : [-(_1751097 = hAPP(hAPP(c_List_Oappend(_1751095), 48471 ^ [_1751095, _1751097, _1751099, _1751101]), hAPP(hAPP(c_List_Olist_OCons(_1751095), 48467 ^ [_1751095, _1751097, _1751099, _1751101]), 48472 ^ [_1751095, _1751097, _1751099, _1751101])))], (48470 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751095, _1751095)), hAPP(hAPP(c_Product__Type_OPair(_1751095, _1751095), 48467 ^ [_1751095, _1751097, _1751099, _1751101]), 48468 ^ [_1751095, _1751097, _1751099, _1751101])), _1751101)))]]], (36662 ^ _777864) ^ [_1461961, _1461963, _1461965, _1461967, _1461969] : [-(c_Map_Orestrict__map(_1461961, _1461963, _1461965, hAPP(hAPP(c_Set_Oinsert(_1461961), _1461967), _1461969)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1461961, tc_Option_Ooption(_1461963)), c_Map_Orestrict__map(_1461961, _1461963, _1461965, _1461969)), _1461967), hAPP(_1461965, _1461967)))], (37502 ^ _777864) ^ [_1481333, _1481335, _1481337, _1481339, _1481341] : [c_Finite__Set_Ofolding__one__idem(_1481333, _1481335, _1481337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481333), _1481339)), -(_1481339 = c_Orderings_Obot__class_Obot(tc_fun(_1481333, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481333), _1481341)), -(_1481341 = c_Orderings_Obot__class_Obot(tc_fun(_1481333, tc_HOL_Obool))), -(hAPP(_1481337, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481333, tc_HOL_Obool)), _1481339), _1481341)) = hAPP(hAPP(_1481335, hAPP(_1481337, _1481339)), hAPP(_1481337, _1481341)))], (16752 ^ _777864) ^ [_1066436, _1066438] : [class_Groups_Oordered__ab__group__add__abs(_1066436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066436), hAPP(c_Groups_Ouminus__class_Ouminus(_1066436), hAPP(c_Groups_Oabs__class_Oabs(_1066436), _1066438))), c_Groups_Ozero__class_Ozero(_1066436))))], (9342 ^ _777864) ^ [_933561, _933563, _933565, _933567] : [class_Rings_Olinordered__semiring__strict(_933561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933561), _933563), _933565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933561), c_Groups_Ozero__class_Ozero(_933561)), _933567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933561), _933567), _933563)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933561), _933567), _933565))))], (18500 ^ _777864) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (43969 ^ _777864) ^ [_1638922, _1638924, _1638926, _1638928, _1638930] : [-(_1638922 = c_Orderings_Obot__class_Obot(tc_fun(_1638924, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638924, tc_fun(_1638926, tc_HOL_Obool)), _1638922), hAPP(hAPP(c_COMBB(tc_fun(_1638926, tc_HOL_Obool), tc_fun(_1638926, tc_HOL_Obool), _1638924), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638926, tc_HOL_Obool)), _1638928)), _1638930)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638926, tc_HOL_Obool)), _1638928), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638924, tc_fun(_1638926, tc_HOL_Obool)), _1638922), _1638930)))], (10374 ^ _777864) ^ [_951018, _951020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _951018)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _951020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951018), _951020)))], (21952 ^ _777864) ^ [_1157592, _1157594, _1157596] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1157592), _1157594))), -(c_Random_Ominus__shift(_1157596, _1157592, _1157594) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1157592), _1157594))], (15648 ^ _777864) ^ [_1044681, _1044683, _1044685, _1044687, _1044689, _1044691] : [class_Rings_Oordered__ring(_1044681), 15651 ^ _777864 : [(15658 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044681), _1044683), _1044689)), _1044685)), _1044687)), _1044691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), _1044683), _1044685)), _1044687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), _1044689), _1044685)), _1044691))))], (15652 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), _1044683), _1044685)), _1044687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), _1044689), _1044685)), _1044691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044681), _1044683), _1044689)), _1044685)), _1044687)), _1044691)))]]], (18962 ^ _777864) ^ [_1103796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103796), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1103796)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41587 ^ _777864) ^ [_1582868, _1582870, _1582872] : [41589 ^ _777864 : [(41592 ^ _777864) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1582868, hAPP(c_Nat_OSuc, _1582872), 41588 ^ [_1582868, _1582870, _1582872])], (41590 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582868)), 41588 ^ [_1582868, _1582870, _1582872]), _1582870)))]], 41593 ^ _777864 : [(41594 ^ _777864) ^ [_1583041] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582868)), _1583041), _1582870)), -(c_Hoare__Mirabelle_Otriple__valid(_1582868, _1582872, _1583041))]]], (32731 ^ _777864) ^ [_1377487, _1377489, _1377491, _1377493] : [c_Sum__Type_OPlus(_1377487, _1377489, _1377491, _1377493) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1377487, _1377489), tc_HOL_Obool)), 32734 ^ _777864 : [(32737 ^ _777864) ^ [] : [-(_1377493 = c_Orderings_Obot__class_Obot(tc_fun(_1377489, tc_HOL_Obool)))], (32735 ^ _777864) ^ [] : [-(_1377491 = c_Orderings_Obot__class_Obot(tc_fun(_1377487, tc_HOL_Obool)))]]], (2690 ^ _777864) ^ [_817877, _817879, _817881, _817883] : [-(c_Quickcheck_Obeyond(_817883, _817879) = c_Quickcheck_Obeyond(_817881, _817877)), _817883 = _817881, _817879 = _817877], (36664 ^ _777864) ^ [_1462027, _1462029, _1462031, _1462033, _1462035] : [class_Groups_Ocomm__monoid__add(_1462027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462029), _1462031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462031), _1462033)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1462027), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462027), _1462035), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462029), _1462031))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462027), _1462035), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462031), _1462033))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1462027), _1462035), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1462029), _1462033)))], (46761 ^ _777864) ^ [_1709423, _1709425, _1709427, _1709429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1709423), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1709425), _1709427))), -(hAPP(c_Random_Opick(_1709425, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709425)), _1709427), _1709429)), _1709423) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1709425), _1709427))], (49669 ^ _777864) ^ [_1778190, _1778192, _1778194, _1778196, _1778198] : [-(c_List_Omap__filter(_1778190, _1778192, _1778194, hAPP(hAPP(c_List_Olist_OCons(_1778190), _1778196), _1778198)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1778192), _1778192, c_List_Omap__filter(_1778190, _1778192, _1778194, _1778198), hAPP(hAPP(c_COMBC(_1778192, tc_List_Olist(_1778192), tc_List_Olist(_1778192)), c_List_Olist_OCons(_1778192)), c_List_Omap__filter(_1778190, _1778192, _1778194, _1778198))), hAPP(_1778194, _1778196)))], (24691 ^ _777864) ^ [_1210989] : [-(hAPP(c_Code__Numeral_Onat__of, _1210989) = c_Code__Numeral_Onat__of__aux(_1210989, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24609 ^ _777864) ^ [_1209607, _1209609] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1209607)), hAPP(c_Code__Numeral_Oof__nat, _1209609)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209607), _1209609)))], (14290 ^ _777864) ^ [_1019547, _1019549, _1019551, _1019553] : [class_Divides_Osemiring__div(_1019547), -(_1019549 = c_Groups_Ozero__class_Ozero(_1019547)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019547), _1019551), _1019549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019547), _1019553), _1019549)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019547), _1019551), _1019553))], (29594 ^ _777864) ^ [_1314850, _1314852, _1314854] : [_1314852 = c_Orderings_Obot__class_Obot(tc_fun(_1314850, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314850), _1314852), _1314854) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314850, tc_HOL_Obool), tc_HOL_Obool)))], (18626 ^ _777864) ^ [_1098084, _1098086] : [class_Int_Onumber__ring(_1098084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098084), _1098086), hAPP(c_Int_Onumber__class_Onumber__of(_1098084), c_Int_OBit1(c_Int_OPls))) = _1098086)], (37711 ^ _777864) ^ [_1485278, _1485280, _1485282, _1485284] : [class_Orderings_Olinorder(_1485278), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485278, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485278), _1485280)), c_SetInterval_Oord__class_OatLeastAtMost(_1485278, _1485282, _1485284)) = c_SetInterval_Oord__class_OatLeastAtMost(_1485278, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1485278), _1485280), _1485282), _1485284))], (33074 ^ _777864) ^ [_1384585, _1384587, _1384589, _1384591] : [class_Groups_Ocomm__monoid__mult(_1384585), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384587), _1384589)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384587, _1384585), hAPP(c_COMBK(_1384585, _1384587), _1384591)), _1384589) = hAPP(hAPP(c_Power_Opower__class_Opower(_1384585), _1384591), hAPP(c_Finite__Set_Ocard(_1384587), _1384589)))], (29614 ^ _777864) ^ [_1315446, _1315448, _1315450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315446, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315446, tc_HOL_Obool)), _1315448), _1315450)), _1315450)))], (19786 ^ _777864) ^ [_1118728, _1118730, _1118732, _1118734, _1118736] : [class_Fields_Ofield__inverse__zero(_1118728), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118728), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118728), _1118730), _1118732)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118728), _1118734), _1118736)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118728), _1118730), _1118734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118728), _1118732), _1118736)))], (2062 ^ _777864) ^ [_807983, _807985, _807987, _807989] : [-(c_Nat__Transfer_Otsub(_807989, _807985) = c_Nat__Transfer_Otsub(_807987, _807983)), _807989 = _807987, _807985 = _807983], (48350 ^ _777864) ^ [_1747645, _1747647, _1747649, _1747651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747645), tc_List_Olist(_1747645))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747645), tc_List_Olist(_1747645)), _1747647), _1747649)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1747645), tc_List_Olist(_1747645)), c_List_Olistrel1(_1747645, _1747651)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747645), tc_List_Olist(_1747645))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747645), tc_List_Olist(_1747645)), _1747647), _1747649)), c_List_Olistrel1(_1747645, hAPP(c_Relation_Oconverse(_1747645, _1747645), _1747651)))))], (2390 ^ _777864) ^ [_813085, _813087, _813089, _813091, _813093, _813095] : [-(c_Product__Type_Ointernal__split(_813095, _813091, _813087) = c_Product__Type_Ointernal__split(_813093, _813089, _813085)), _813095 = _813093, _813091 = _813089, _813087 = _813085], (38667 ^ _777864) ^ [] : [-(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))], (51297 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (22586 ^ _777864) ^ [_1168382, _1168384, _1168386, _1168388] : [-(hAPP(c_Product__Type_Ofst(_1168382, _1168384), hAPP(hAPP(c_Product__Type_OPair(_1168382, _1168384), _1168386), _1168388)) = _1168386)], (17926 ^ _777864) ^ [_1086923] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1086923)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1086923) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18672 ^ _777864) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (36440 ^ _777864) ^ [_1456362, _1456364, _1456366] : [class_Orderings_Oorder(_1456362), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456362, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1456362), _1456364)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456362, _1456364), _1456366)) = c_Orderings_Obot__class_Obot(tc_fun(_1456362, tc_HOL_Obool)))], (17272 ^ _777864) ^ [_1075753, _1075755, _1075757, _1075759] : [class_Groups_Omonoid__mult(_1075753), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075753), _1075755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1075757), _1075759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075753), hAPP(hAPP(c_Power_Opower__class_Opower(_1075753), _1075755), _1075757)), hAPP(hAPP(c_Power_Opower__class_Opower(_1075753), _1075755), _1075759)))], (2770 ^ _777864) ^ [_819235, _819237, _819239, _819241, _819243, _819245, _819247, _819249] : [-(c_New__DSequence_Opos__decr__bind(_819249, _819245, _819241, _819237) = c_New__DSequence_Opos__decr__bind(_819247, _819243, _819239, _819235)), _819249 = _819247, _819245 = _819243, _819241 = _819239, _819237 = _819235], (39683 ^ _777864) ^ [_1528835, _1528837, _1528839, _1528841] : [-(c_Fun_Oinj__on(_1528835, tc_prod(_1528837, _1528835), 39681 ^ [_1528835, _1528837, _1528839, _1528841], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528837, tc_fun(_1528835, tc_HOL_Obool)), _1528839), _1528841)))], (7950 ^ _777864) ^ [_910211, _910213] : [7951 ^ _777864 : [(7952 ^ _777864) ^ [_910267] : [_910213 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _910211), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _910267)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _910211), _910213)))], (50933 ^ _777864) ^ [_1805159, _1805161, _1805163] : [-(c_List_Oremdups(_1805159, hAPP(c_List_Ofilter(_1805159, _1805161), _1805163)) = hAPP(c_List_Ofilter(_1805159, _1805161), c_List_Oremdups(_1805159, _1805163)))], (16570 ^ _777864) ^ [_1062685, _1062687, _1062689] : [class_Int_Onumber__ring(_1062685), class_Rings_Olinordered__idom(_1062685), 16577 ^ _777864 : [(16584 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1062687), _1062689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062685), hAPP(c_Int_Onumber__class_Onumber__of(_1062685), _1062687)), hAPP(c_Int_Onumber__class_Onumber__of(_1062685), _1062689))))], (16578 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1062685), hAPP(c_Int_Onumber__class_Onumber__of(_1062685), _1062687)), hAPP(c_Int_Onumber__class_Onumber__of(_1062685), _1062689))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1062687), _1062689)))]]], (6857 ^ _777864) ^ [_890682, _890684] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890682), _890684) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6858 ^ _777864 : [(6865 ^ _777864) ^ [] : [_890682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _890684 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6859 ^ _777864) ^ [] : [_890682 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _890684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43535 ^ _777864) ^ [_1626512, _1626514, _1626516, _1626518, _1626520, _1626522] : [hBOOL(hAPP(hAPP(c_member(_1626512), _1626514), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1626516, tc_fun(_1626512, tc_HOL_Obool)), _1626518), _1626520))), -(hBOOL(hAPP(hAPP(c_member(_1626512), _1626514), hAPP(_1626520, _1626522)))), hBOOL(hAPP(hAPP(c_member(_1626516), _1626522), _1626518))], (34581 ^ _777864) ^ [_1420245, _1420247] : [c_Nat__Transfer_Ois__nat(_1420245), c_Nat__Transfer_Ois__nat(_1420247), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1420245, _1420247) = 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, _1420245), hAPP(c_Int_Onat, _1420247))))], (3144 ^ _777864) ^ [_825354, _825356, _825358, _825360, _825362, _825364, _825366, _825368, _825370, _825372] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_825372, _825368, _825364, _825360, _825356) = c_SetInterval_Oord_OgreaterThanAtMost(_825370, _825366, _825362, _825358, _825354)), _825372 = _825370, _825368 = _825366, _825364 = _825362, _825360 = _825358, _825356 = _825354], (19900 ^ _777864) ^ [_1120795, _1120797, _1120799, _1120801] : [class_Fields_Olinordered__field__inverse__zero(_1120795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120795), _1120797), _1120799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120795), c_Groups_Ozero__class_Ozero(_1120795)), _1120801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120795), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120795), _1120797), _1120801)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120795), _1120799), _1120801))))], (18696 ^ _777864) ^ [_1099117] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1099117))) = 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)))), _1099117))], (5810 ^ _777864) ^ [_873163, _873165, _873167, _873169] : [c_Com_Ocom_OCall(_873163, _873165, _873167) = hAPP(c_Com_Ocom_OBODY, _873169)], (9716 ^ _777864) ^ [_940180, _940182] : [class_Int_Oring__char__0(_940180), 9719 ^ _777864 : [(9726 ^ _777864) ^ [] : [_940182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_940180), _940182) = c_Groups_Ozero__class_Ozero(_940180))], (9720 ^ _777864) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_940180), _940182) = c_Groups_Ozero__class_Ozero(_940180), -(_940182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (34976 ^ _777864) ^ [_1427617, _1427619, _1427621, _1427623, _1427625] : [c_Fun_Oinj__on(_1427617, _1427619, _1427621, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427617, tc_HOL_Obool)), _1427623), _1427625)), 34979 ^ _777864 : [(34984 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427619, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427617, _1427619, _1427621), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427617, tc_HOL_Obool)), _1427623), _1427625))), hAPP(c_Set_Oimage(_1427617, _1427619, _1427621), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427617, tc_HOL_Obool)), _1427625), _1427623))) = c_Orderings_Obot__class_Obot(tc_fun(_1427619, tc_HOL_Obool)))], (34982 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1427617, _1427619, _1427621, _1427625))], (34980 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1427617, _1427619, _1427621, _1427623))]]], (12728 ^ _777864) ^ [_991610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _991610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991610)))], (50052 ^ _777864) ^ [_1785390, _1785392] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1785390), _1785392)) = c_List_Oupt(_1785390, _1785392))], (8176 ^ _777864) ^ [_913625, _913627] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913625) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913627), -(_913625 = _913627)], (37741 ^ _777864) ^ [_1485937] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1485937)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1485937)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1485937), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (43379 ^ _777864) ^ [_1623052, _1623054, _1623056, _1623058] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623052, _1623052)), hAPP(hAPP(c_Product__Type_OPair(_1623052, _1623052), _1623054), _1623056)), c_Transitive__Closure_Ortrancl(_1623052, _1623058)))), 43380 ^ _777864 : [(43383 ^ _777864) ^ [] : [-(_1623054 = _1623056), hBOOL(hAPP(hAPP(c_member(tc_prod(_1623052, _1623052)), hAPP(hAPP(c_Product__Type_OPair(_1623052, _1623052), _1623054), _1623056)), c_Transitive__Closure_Otrancl(_1623052, _1623058)))], (43381 ^ _777864) ^ [] : [_1623054 = _1623056]]], (40452 ^ _777864) ^ [_1549610, _1549612, _1549614, _1549616, _1549618, _1549620] : [-(hBOOL(hAPP(hAPP(c_member(_1549610), _1549612), _1549614))), -(hAPP(c_Fun_Ooverride__on(_1549610, _1549616, _1549618, _1549620, _1549614), _1549612) = hAPP(_1549618, _1549612))], (23535 ^ _777864) ^ [_1188689, _1188691, _1188693] : [class_Orderings_Olinorder(_1188689), 23538 ^ _777864 : [(23545 ^ _777864) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188689), _1188691), _1188693) = _1188691, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188689), _1188691), _1188693)))], (23539 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188689), _1188691), _1188693)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188689), _1188691), _1188693) = _1188691)]]], (48388 ^ _777864) ^ [_1748908, _1748910, _1748912, _1748914, _1748916, _1748918] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748908), tc_List_Olist(_1748908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748908), tc_List_Olist(_1748908)), hAPP(hAPP(c_List_Olist_OCons(_1748908), _1748910), _1748912)), hAPP(hAPP(c_List_Olist_OCons(_1748908), _1748914), _1748916))), c_List_Olistrel1(_1748908, _1748918)))), 48389 ^ _777864 : [(48396 ^ _777864) ^ [] : [_1748910 = _1748914, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748908), tc_List_Olist(_1748908))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748908), tc_List_Olist(_1748908)), _1748912), _1748916)), c_List_Olistrel1(_1748908, _1748918)))], (48390 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1748908, _1748908)), hAPP(hAPP(c_Product__Type_OPair(_1748908, _1748908), _1748910), _1748914)), _1748918)), _1748912 = _1748916]]], (35130 ^ _777864) ^ [_1430863, _1430865, _1430867, _1430869, _1430871] : [c_Fun_Oinj__on(_1430863, _1430865, _1430867, _1430869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430863, tc_HOL_Obool)), _1430871), _1430869)), -(c_Fun_Oinj__on(_1430863, _1430865, _1430867, _1430871))], (29458 ^ _777864) ^ [_1312017] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1312017)), 29462 ^ _777864 : [(29463 ^ _777864) ^ [_1312097] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1312097), _1312017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1312097), 29461 ^ [_1312017])))]]], (18362 ^ _777864) ^ [_1093597, _1093599] : [class_Int_Onumber__ring(_1093597), 18365 ^ _777864 : [(18372 ^ _777864) ^ [] : [c_Int_Oiszero(_1093597, hAPP(c_Int_Onumber__class_Onumber__of(_1093597), 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), _1093599)))), -(c_Groups_Oone__class_Oone(_1093597) = hAPP(c_Int_Onumber__class_Onumber__of(_1093597), _1093599))], (18366 ^ _777864) ^ [] : [c_Groups_Oone__class_Oone(_1093597) = hAPP(c_Int_Onumber__class_Onumber__of(_1093597), _1093599), -(c_Int_Oiszero(_1093597, hAPP(c_Int_Onumber__class_Onumber__of(_1093597), 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), _1093599)))))]]], (8764 ^ _777864) ^ [_923492, _923494, _923496, _923498] : [class_Rings_Ocomm__semiring__1(_923492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923492), _923494), _923496)), _923498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923492), _923494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923492), _923496), _923498)))], (26239 ^ _777864) ^ [_1239411, _1239413, _1239415, _1239417] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1239411), _1239413), _1239415), _1239417)), -(_1239413 = _1239417), -(hBOOL(hAPP(_1239415, _1239417)))], (37959 ^ _777864) ^ [_1490140, _1490142, _1490144, _1490146, _1490148] : [hAPP(_1490140, _1490142) = hAPP(c_Option_Ooption_OSome(_1490144), _1490146), -(hAPP(hAPP(c_Set_Oinsert(_1490148), _1490142), c_Map_Odom(_1490148, _1490144, _1490140)) = c_Map_Odom(_1490148, _1490144, _1490140))], (47804 ^ _777864) ^ [_1734163, _1734165, _1734167, _1734169, _1734171, _1734173] : [-(hBOOL(hAPP(hAPP(c_member(_1734163), _1734165), hAPP(c_List_Oset(_1734163), _1734167)))), -(hAPP(c_Map_Omap__upds(_1734163, _1734169, _1734171, _1734167, _1734173), _1734165) = hAPP(_1734171, _1734165))], (26597 ^ _777864) ^ [_1246492, _1246494] : [-(c_Option_Oset(_1246492, hAPP(c_Option_Ooption_OSome(_1246492), _1246494)) = hAPP(hAPP(c_Set_Oinsert(_1246492), _1246494), c_Orderings_Obot__class_Obot(tc_fun(_1246492, tc_HOL_Obool))))], (5513 ^ _777864) ^ [_864887, _864889, _864891] : [c_Hoare__Mirabelle_Otriple__valid(_864887, hAPP(c_Nat_OSuc, _864889), _864891), -(c_Hoare__Mirabelle_Otriple__valid(_864887, _864889, _864891))], (35380 ^ _777864) ^ [_1435778, _1435780, _1435782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435778)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1435780), _1435782)), 35387 ^ _777864 : [(35388 ^ _777864) ^ [_1435968] : [35390 ^ _777864 : [(35396 ^ _777864) ^ [] : [-(_1435968 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35392 ^ [_1435778, _1435780, _1435782, _1435968]), 35389 ^ [_1435778, _1435780, _1435782, _1435968]))], (35394 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35392 ^ [_1435778, _1435780, _1435782, _1435968]), _1435782)))], (35391 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35389 ^ [_1435778, _1435780, _1435782, _1435968]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1435778))))]], -(_1435968 = _1435780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1435968), _1435778) = _1435780]]], (36412 ^ _777864) ^ [_1455714, _1455716, _1455718, _1455720, _1455722, _1455724, _1455726] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1455714, tc_Option_Ooption(_1455716)), _1455718), _1455720), hAPP(c_Option_Ooption_OSome(_1455716), _1455722)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1455714, tc_Option_Ooption(_1455716)), _1455724), _1455720), hAPP(c_Option_Ooption_OSome(_1455716), _1455726)), -(_1455722 = _1455726)], (46767 ^ _777864) ^ [_1709566, _1709568, _1709570, _1709572] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1709566), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1709568), _1709570)))), -(hAPP(c_Random_Opick(_1709568, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709568)), _1709570), _1709572)), _1709566) = hAPP(c_Random_Opick(_1709568, _1709572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1709566), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1709568), _1709570))))], (51343 ^ _777864) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (28246 ^ _777864) ^ [_1281908, _1281910, _1281912, _1281914, _1281916] : [class_Lattices_Olattice(_1281908), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281910, _1281908)), _1281912), _1281914), _1281916) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281908), hAPP(_1281912, _1281916)), hAPP(_1281914, _1281916)))], (46072 ^ _777864) ^ [_1689695, _1689697, _1689699] : [-(hBOOL(hAPP(hAPP(c_member(_1689695), _1689697), hAPP(c_List_Oset(_1689695), _1689699)))), -(c_List_Oremove1(_1689695, _1689697, _1689699) = _1689699)], (8082 ^ _777864) ^ [_912454, _912456, _912458] : [class_Orderings_Olinorder(_912454), 8085 ^ _777864 : [(8086 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912454), _912456), _912458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912454), _912458), _912456))), -(_912456 = _912458)], (8096 ^ _777864) ^ [] : [8097 ^ _777864 : [(8100 ^ _777864) ^ [] : [_912456 = _912458], (8098 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912454), _912458), _912456))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912454), _912456), _912458))]]], (40767 ^ _777864) ^ [_1561829, _1561831, _1561833, _1561835] : [hAPP(hAPP(c_Relation_Orel__comp(_1561829, _1561829, _1561829), _1561831), _1561833) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561829, _1561829), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1561829, _1561829, _1561829), _1561835), _1561833) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561829, _1561829), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1561829, _1561829, _1561829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561829, _1561829), tc_HOL_Obool)), _1561831), _1561835)), _1561833) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1561829, _1561829), tc_HOL_Obool)))], (46950 ^ _777864) ^ [_1713967, _1713969, _1713971, _1713973, _1713975] : [class_Orderings_Olinorder(_1713967), hBOOL(hAPP(c_List_Odistinct(_1713969), _1713971)), -(hBOOL(hAPP(c_List_Odistinct(_1713969), c_List_Olinorder__class_Oinsort__insert__key(_1713969, _1713967, _1713973, _1713975, _1713971))))], (21038 ^ _777864) ^ [_1140518, _1140520, _1140522] : [class_Fields_Olinordered__field(_1140518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140518), _1140520), _1140522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140518), _1140520), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140518), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140518), _1140520), _1140522)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140518), c_Groups_Oone__class_Oone(_1140518)), c_Groups_Oone__class_Oone(_1140518))))))], (16742 ^ _777864) ^ [_1066271, _1066273] : [class_Groups_Oordered__ab__group__add__abs(_1066271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066271), _1066273), c_Groups_Ozero__class_Ozero(_1066271))), -(hAPP(c_Groups_Oabs__class_Oabs(_1066271), _1066273) = hAPP(c_Groups_Ouminus__class_Ouminus(_1066271), _1066273))], (41812 ^ _777864) ^ [_1588388, _1588390, _1588392, _1588394, _1588396, _1588398] : [c_Fun_Oinj__on(_1588388, _1588390, hAPP(c_Fun_Ocomp(_1588392, _1588390, _1588388, _1588394), _1588396), _1588398), -(c_Fun_Oinj__on(_1588392, _1588390, _1588394, hAPP(c_Set_Oimage(_1588388, _1588392, _1588396), _1588398)))], (3816 ^ _777864) ^ [_835926, _835928, _835930, _835932] : [-(c_Relation_ODomain(_835932, _835928) = c_Relation_ODomain(_835930, _835926)), _835932 = _835930, _835928 = _835926], (46665 ^ _777864) ^ [_1706118, _1706120, _1706122] : [-(hBOOL(hAPP(c_List_Odistinct(_1706118), hAPP(hAPP(c_List_Olist_OCons(_1706118), _1706120), _1706122)))), -(hBOOL(hAPP(hAPP(c_member(_1706118), _1706120), hAPP(c_List_Oset(_1706118), _1706122)))), hBOOL(hAPP(c_List_Odistinct(_1706118), _1706122))], (51121 ^ _777864) ^ [_1808302, _1808304] : [class_Groups_Ominus(_1808302), -(class_Groups_Ominus(tc_fun(_1808304, _1808302)))], (12049 ^ _777864) ^ [_979547, _979549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979547), _979549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979547), hAPP(c_Nat_OSuc, _979549))))], (13176 ^ _777864) ^ [_999120, _999122, _999124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999120), _999122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999122), _999124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999120), _999124)))], (6450 ^ _777864) ^ [_884337, _884339, _884341] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884337), _884339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884341), _884339), -(_884337 = _884341)], (22258 ^ _777864) ^ [_1162435, _1162437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162435), 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)), _1162437)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162435, _1162437), c_Divides_OnegDivAlg(_1162435, _1162437))))], (13298 ^ _777864) ^ [_1001183, _1001185] : [-(hBOOL(hAPP(_1001183, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1001183, _1001185)), 13306 ^ _777864 : [(13309 ^ _777864) ^ [_1001421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001421), 13305 ^ [_1001183, _1001185])), hBOOL(hAPP(_1001183, _1001421))], (13315 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1001183, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13305 ^ [_1001183, _1001185]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13307 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13305 ^ [_1001183, _1001185]), _1001185)))]]], (10069 ^ _777864) ^ [_946138, _946140] : [_946138 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _946138), _946140), -(_946140 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_946138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46132 ^ _777864) ^ [_1690846, _1690848, _1690850, _1690852] : [hBOOL(hAPP(c_List_Odistinct(_1690846), _1690848)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1690850, _1690846)), hAPP(hAPP(c_List_Ozip(_1690850, _1690846), _1690852), _1690848))))], (22677 ^ _777864) ^ [_1170169, _1170171, _1170173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170169, tc_HOL_Obool)), _1170171), _1170173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170169, tc_HOL_Obool)), _1170171), _1170173)))], (10140 ^ _777864) ^ [_947179, _947181, _947183] : [class_Orderings_Oorder(_947179), 10143 ^ _777864 : [(10152 ^ _777864) ^ [] : [-(_947181 = _947183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947179), _947181), _947183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947179), _947183), _947181))], (10144 ^ _777864) ^ [] : [_947181 = _947183, 10147 ^ _777864 : [(10150 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947179), _947183), _947181)))], (10148 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947179), _947181), _947183)))]]]]], (28667 ^ _777864) ^ [_1295203, _1295205, _1295207, _1295209] : [-(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), _1295203), _1295205)), 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), _1295207), _1295209)), 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), _1295203), _1295207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295205), _1295209))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295203), _1295209)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1295205), _1295207)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (51261 ^ _777864) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (43325 ^ _777864) ^ [_1621704, _1621706, _1621708, _1621710, _1621712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621704, _1621704)), hAPP(hAPP(c_Product__Type_OPair(_1621704, _1621704), _1621706), _1621708)), c_Transitive__Closure_Otrancl(_1621704, _1621710))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621704, _1621704)), hAPP(hAPP(c_Product__Type_OPair(_1621704, _1621704), _1621708), _1621712)), c_Transitive__Closure_Ortrancl(_1621704, _1621710))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621704, _1621704)), hAPP(hAPP(c_Product__Type_OPair(_1621704, _1621704), _1621706), _1621712)), c_Transitive__Closure_Otrancl(_1621704, _1621710))))], (45463 ^ _777864) ^ [_1675407, _1675409, _1675411, _1675413, _1675415] : [-(hAPP(c_Map_Omap__add(_1675407, _1675409, _1675411, _1675413), _1675415) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1675409), _1675409, hAPP(_1675411, _1675415), c_Option_Ooption_OSome(_1675409)), hAPP(_1675413, _1675415)))], (12544 ^ _777864) ^ [_988393, _988395, _988397, _988399] : [class_Rings_Olinordered__semiring__strict(_988393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988393), _988395), _988397)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988393), _988399), _988397))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988393), c_Groups_Ozero__class_Ozero(_988393)), _988397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988393), _988395), _988399)))], (1462 ^ _777864) ^ [_798907, _798909] : [-(class_Rings_Oordered__comm__semiring(_798907)), _798909 = _798907, class_Rings_Oordered__comm__semiring(_798909)], (48536 ^ _777864) ^ [_1752846, _1752848, _1752850, _1752852] : [-(hAPP(hAPP(c_List_Odrop(_1752846), _1752848), hAPP(hAPP(c_List_Odrop(_1752846), _1752850), _1752852)) = hAPP(hAPP(c_List_Odrop(_1752846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752848), _1752850)), _1752852))], (21322 ^ _777864) ^ [_1145753, _1145755, _1145757, _1145759] : [class_Fields_Olinordered__field(_1145753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145753), _1145755), _1145757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145753), c_Groups_Ozero__class_Ozero(_1145753)), _1145759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145753), c_Groups_Ozero__class_Ozero(_1145753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145753), _1145757), _1145755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145753), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145753), _1145759), _1145757)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145753), _1145759), _1145755))))], (29376 ^ _777864) ^ [_1310393, _1310395, _1310397, _1310399, _1310401, _1310403, _1310405, _1310407] : [c_Finite__Set_Ofolding__image__simple(_1310393, _1310395, _1310397, _1310399, _1310401, _1310403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310395), _1310405)), -(hBOOL(hAPP(hAPP(c_member(_1310395), _1310407), _1310405))), -(hAPP(_1310403, hAPP(hAPP(c_Set_Oinsert(_1310395), _1310407), _1310405)) = hAPP(hAPP(_1310397, hAPP(_1310401, _1310407)), hAPP(_1310403, _1310405)))], (5948 ^ _777864) ^ [_875617, _875619, _875621, _875623] : [c_Com_Ocom_OAss(_875617, _875619) = c_Com_Ocom_OAss(_875621, _875623), 5951 ^ _777864 : [(5954 ^ _777864) ^ [] : [-(_875619 = _875623)], (5952 ^ _777864) ^ [] : [-(_875617 = _875621)]]], (50448 ^ _777864) ^ [_1793858, _1793860, _1793862] : [hAPP(c_List_Orev(_1793858), _1793860) = hAPP(hAPP(c_List_Olist_OCons(_1793858), _1793862), c_List_Olist_ONil(_1793858)), -(_1793860 = hAPP(hAPP(c_List_Olist_OCons(_1793858), _1793862), c_List_Olist_ONil(_1793858)))], (46533 ^ _777864) ^ [_1702520, _1702522, _1702524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1702520, _1702520), tc_HOL_Obool)), _1702522), _1702524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1702520), tc_List_Olist(_1702520)), tc_HOL_Obool)), c_List_Olistrel(_1702520, _1702522)), c_List_Olistrel(_1702520, _1702524))))], (48221 ^ _777864) ^ [_1743629, _1743631, _1743633, _1743635] : [-(c_List_Osublist(_1743629, hAPP(hAPP(c_List_Oappend(_1743629), _1743631), _1743633), _1743635) = hAPP(hAPP(c_List_Oappend(_1743629), c_List_Osublist(_1743629, _1743631, _1743635)), c_List_Osublist(_1743629, _1743633, 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(_1743629)), _1743631)))), _1743635)))))], (41103 ^ _777864) ^ [_1570497, _1570499] : [c_Wellfounded_Owf(_1570497, _1570499), -(c_Wellfounded_Owf(tc_List_Olist(_1570497), c_List_Olenlex(_1570497, _1570499)))], (24851 ^ _777864) ^ [_1214217, _1214219, _1214221, _1214223] : [class_Rings_Ocomm__semiring__1(_1214217), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214217), _1214219), _1214221)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214217), hAPP(hAPP(c_Power_Opower__class_Opower(_1214217), _1214219), _1214223)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214217), _1214221), _1214223))))], (40460 ^ _777864) ^ [_1549835, _1549837, _1549839] : [-(c_Map_Oran(_1549835, _1549837, _1549839) = hAPP(c_Set_OCollect(_1549837), hAPP(hAPP(c_COMBB(tc_fun(_1549835, tc_HOL_Obool), tc_HOL_Obool, _1549837), c_HOL_OEx(_1549835)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1549837), tc_fun(_1549835, tc_HOL_Obool), _1549837), hAPP(c_COMBC(_1549835, tc_Option_Ooption(_1549837), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1549837), tc_fun(tc_Option_Ooption(_1549837), tc_HOL_Obool), _1549835), c_fequal), _1549839))), c_Option_Ooption_OSome(_1549837)))))], (36566 ^ _777864) ^ [_1459175, _1459177, _1459179, _1459181] : [class_Rings_Osemiring__1(_1459175), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1459175), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459177, tc_Nat_Onat), _1459179), _1459181)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459177, _1459175), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1459175, _1459177), c_Nat_Osemiring__1__class_Oof__nat(_1459175)), _1459179)), _1459181))], (10216 ^ _777864) ^ [_948355, _948357, _948359, _948361] : [class_Orderings_Oorder(_948355), _948357 = _948359, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948355), _948361), _948359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948355), _948361), _948357)))], (27041 ^ _777864) ^ [_1255490, _1255492, _1255494] : [hBOOL(hAPP(hAPP(c_member(_1255490), _1255492), hAPP(c_fequal, _1255494))), -(_1255492 = _1255494)], (26807 ^ _777864) ^ [_1251216, _1251218] : [-(hBOOL(hAPP(hAPP(c_member(_1251216), 26808 ^ [_1251216, _1251218]), _1251218))), -(_1251218 = c_Orderings_Obot__class_Obot(tc_fun(_1251216, tc_HOL_Obool)))], (40395 ^ _777864) ^ [_1547754, _1547756] : [-(hAPP(c_Set_OPow(_1547754), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1547754, tc_HOL_Obool)), _1547756)) = hAPP(c_Set_OCollect(tc_fun(_1547754, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1547754, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1547754, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1547754, tc_HOL_Obool), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1547754, tc_HOL_Obool)), c_COMBS(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1547754, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1547754, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1547754, tc_HOL_Obool), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_fun(_1547754, tc_HOL_Obool)), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_fun(_1547754, tc_HOL_Obool)), tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1547754, tc_HOL_Obool)), c_COMBB(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1547754, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1547754, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1547754, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1547754, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1547754, tc_HOL_Obool)), _1547756)), c_Set_OPow(_1547754))))))], (26783 ^ _777864) ^ [_1250778, _1250780, _1250782, _1250784] : [hBOOL(hAPP(hAPP(c_member(_1250778), _1250780), _1250782)), -(hBOOL(hAPP(hAPP(c_member(_1250778), _1250780), _1250784))), -(hBOOL(hAPP(hAPP(c_member(_1250778), _1250780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250778, tc_HOL_Obool)), _1250782), _1250784))))], (36920 ^ _777864) ^ [_1467812, _1467814, _1467816, _1467818, _1467820] : [class_Groups_Oab__group__add(_1467812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467814), _1467816)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467814), _1467818)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467814, _1467812), _1467820), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467814, tc_HOL_Obool)), _1467816), _1467818)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1467812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467812), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467814, _1467812), _1467820), _1467816)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467814, _1467812), _1467820), _1467818))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467814, _1467812), _1467820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467814, tc_HOL_Obool)), _1467816), _1467818))))], (35754 ^ _777864) ^ [_1442900] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442900), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (17572 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (8308 ^ _777864) ^ [_915585, _915587, _915589, _915591] : [class_Orderings_Oord(_915585), _915587 = _915589, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915585), _915589), _915591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915585), _915587), _915591)))], (25059 ^ _777864) ^ [_1217696, _1217698] : [_1217696 = _1217698, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217696), _1217698)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1217698), _1217696)))], (40717 ^ _777864) ^ [_1559957, _1559959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559957), _1559959)), -(_1559959 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1559957, 40721 ^ [_1559957, _1559959]), 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)), 40720 ^ [_1559957, _1559959]))))], (14014 ^ _777864) ^ [_1014681, _1014683, _1014685, _1014687] : [_1014681 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014683), _1014685)), _1014687), -(_1014683 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1014681), _1014683) = _1014685), 14021 ^ _777864 : [(14024 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014687), _1014683))], (14022 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014683)))]], 14029 ^ _777864 : [(14032 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014683), _1014687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1014687), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14030 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1014683))]]], (50136 ^ _777864) ^ [_1786822, _1786824, _1786826, _1786828, _1786830, _1786832] : [class_Orderings_Olinorder(_1786822), c_List_Olinorder__class_Osorted(_1786822, hAPP(hAPP(c_List_Omap(_1786824, _1786822), _1786826), _1786828)), hBOOL(hAPP(_1786830, _1786832)), -(hAPP(c_List_Ofilter(_1786824, _1786830), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1786824, _1786822, _1786826), _1786832), _1786828)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1786824, _1786822, _1786826), _1786832), hAPP(c_List_Ofilter(_1786824, _1786830), _1786828)))], (23409 ^ _777864) ^ [_1186406] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8482 ^ _777864) ^ [_918429] : [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)), _918429)), _918429)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _918429), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34823 ^ _777864) ^ [_1424490, _1424492, _1424494, _1424496, _1424498] : [class_Orderings_Oorder(_1424490), 34826 ^ _777864 : [(34847 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1424490, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424490, _1424492, _1424494)), c_SetInterval_Oord__class_OatLeastAtMost(_1424490, _1424496, _1424498)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424496), _1424498)), 34850 ^ _777864 : [(34853 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424496), _1424492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424494), _1424498)), 34860 ^ _777864 : [(34863 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424490), _1424494), _1424498))], (34861 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424490), _1424496), _1424492))]]], (34851 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424492), _1424494)))]]], (34827 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1424490, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1424490, _1424492, _1424494)), c_SetInterval_Oord__class_OatLeastAtMost(_1424490, _1424496, _1424498))), 34830 ^ _777864 : [(34831 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424492), _1424494)), 34834 ^ _777864 : [(34839 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424490), _1424496), _1424492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424490), _1424494), _1424498)))], (34837 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424494), _1424498)))], (34835 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424496), _1424492)))]]], (34845 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424490), _1424496), _1424498)))]]]]], (38246 ^ _777864) ^ [_1495527, _1495529, _1495531, _1495533, _1495535] : [_1495527 = hAPP(_1495529, _1495531), -(hBOOL(hAPP(hAPP(c_member(_1495533), _1495527), hAPP(c_Set_Oimage(_1495535, _1495533, _1495529), c_Orderings_Otop__class_Otop(tc_fun(_1495535, tc_HOL_Obool))))))], (27328 ^ _777864) ^ [_1263775, _1263777, _1263779, _1263781, _1263783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1263775, _1263777)), hAPP(_1263775, _1263779))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1263781, _1263781)), hAPP(hAPP(c_Product__Type_OPair(_1263781, _1263781), _1263777), _1263779)), _1263783)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263781, _1263781)), hAPP(hAPP(c_Product__Type_OPair(_1263781, _1263781), _1263777), _1263779)), c_Wellfounded_Omlex__prod(_1263781, _1263775, _1263783))))], (9915 ^ _777864) ^ [_943555] : [-(_943555 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9918 ^ _777864 : [(9925 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943555))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _943555) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9919 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943555)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _943555) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (29582 ^ _777864) ^ [_1314592, _1314594, _1314596] : [_1314594 = c_Orderings_Obot__class_Obot(tc_fun(_1314592, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314592, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1314592), _1314594), _1314596))], (27724 ^ _777864) ^ [_1271732, _1271734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1271732), _1271734)), -(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), _1271732), _1271734)), c_Wellfounded_Oless__than)))], (872 ^ _777864) ^ [_791304, _791306, _791308, _791310, _791312, _791314] : [-(c_Relation_Orefl__on(_791312, _791308, _791304)), c_Relation_Orefl__on(_791314, _791310, _791306), _791314 = _791312, _791310 = _791308, _791306 = _791304], (47474 ^ _777864) ^ [_1727117, _1727119, _1727121] : [hAPP(hAPP(c_List_Olist_OCons(_1727117), _1727119), _1727121) = c_List_Olist_ONil(_1727117)], (6641 ^ _777864) ^ [_887466, _887468] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887466)), _887468) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887466), _887468)))], (48698 ^ _777864) ^ [_1756903, _1756905, _1756907, _1756909, _1756911] : [-(hAPP(hAPP(c_List_Ozip(_1756903, _1756905), _1756907), hAPP(hAPP(c_List_Oappend(_1756905), _1756909), _1756911)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1756903, _1756905)), hAPP(hAPP(c_List_Ozip(_1756903, _1756905), hAPP(hAPP(c_List_Otake(_1756903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756905)), _1756909)), _1756907)), _1756909)), hAPP(hAPP(c_List_Ozip(_1756903, _1756905), hAPP(hAPP(c_List_Odrop(_1756903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756905)), _1756909)), _1756907)), _1756911)))], (35946 ^ _777864) ^ [_1446615, _1446617, _1446619] : [class_Orderings_Olinorder(_1446615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446615), _1446617), _1446619)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446615, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1446615), _1446617), c_Orderings_Obot__class_Obot(tc_fun(_1446615, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1446615, _1446617, _1446619)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1446615, _1446617), _1446619))], (24765 ^ _777864) ^ [_1212705] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1212705), _1212705)))], (35570 ^ _777864) ^ [_1439429, _1439431, _1439433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1439429)), 35573 ^ _777864 : [(35574 ^ _777864) ^ [_1439563] : [35576 ^ _777864 : [(35582 ^ _777864) ^ [] : [-(_1439563 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35578 ^ [_1439429, _1439431, _1439433, _1439563]), 35575 ^ [_1439429, _1439431, _1439433, _1439563]))], (35580 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35578 ^ [_1439429, _1439431, _1439433, _1439563]), _1439431)))], (35577 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35575 ^ [_1439429, _1439431, _1439433, _1439563]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1439429))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439433), _1439563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439433), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1439563), _1439429))))]]], (18224 ^ _777864) ^ [_1091351, _1091353] : [class_Int_Onumber__ring(_1091351), class_Rings_Olinordered__idom(_1091351), 18231 ^ _777864 : [(18238 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091353), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091351), hAPP(c_Int_Onumber__class_Onumber__of(_1091351), _1091353)), c_Groups_Ozero__class_Ozero(_1091351))))], (18232 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091351), hAPP(c_Int_Onumber__class_Onumber__of(_1091351), _1091353)), c_Groups_Ozero__class_Ozero(_1091351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091353), c_Int_OPls)))]]], (18614 ^ _777864) ^ [_1097838, _1097840] : [class_Int_Onumber__ring(_1097838), -(hAPP(c_Int_Onumber__class_Onumber__of(_1097838), c_Int_OBit1(_1097840)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097838), c_Groups_Oone__class_Oone(_1097838)), hAPP(c_Int_Onumber__class_Onumber__of(_1097838), _1097840))), hAPP(c_Int_Onumber__class_Onumber__of(_1097838), _1097840)))], (29654 ^ _777864) ^ [_1316307, _1316309, _1316311] : [class_Lattices_Osemilattice__inf(_1316307), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316307), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316307), _1316309), _1316311)), _1316309)))], (31413 ^ _777864) ^ [_1351774, _1351776, _1351778] : [class_Lattices_Olattice(_1351774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351774), _1351776)), -(_1351776 = c_Orderings_Obot__class_Obot(tc_fun(_1351774, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351774), _1351778)), -(_1351778 = c_Orderings_Obot__class_Obot(tc_fun(_1351774, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351774, tc_HOL_Obool)), _1351776), _1351778) = c_Orderings_Obot__class_Obot(tc_fun(_1351774, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1351774, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351774, tc_HOL_Obool)), _1351776), _1351778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1351774), c_Big__Operators_Olattice__class_OInf__fin(_1351774, _1351776)), c_Big__Operators_Olattice__class_OInf__fin(_1351774, _1351778)))], (39405 ^ _777864) ^ [_1523577, _1523579, _1523581, _1523583] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523577, _1523579), _1523581), _1523583) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523577, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), _1523581), hAPP(hAPP(c_COMBS(_1523577, tc_fun(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523579, tc_HOL_Obool), tc_fun(tc_fun(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), _1523577), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), _1523583)), hAPP(hAPP(c_COMBC(_1523577, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523579, tc_fun(tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), _1523577), c_COMBC(_1523579, tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1523579, tc_prod(_1523577, _1523579)), tc_fun(_1523579, tc_fun(tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))), _1523577), hAPP(c_COMBB(tc_prod(_1523577, _1523579), tc_fun(tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool), tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool)), _1523579), c_Set_Oinsert(tc_prod(_1523577, _1523579)))), c_Product__Type_OPair(_1523577, _1523579)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523577, _1523579), tc_HOL_Obool))))))], (14205 ^ _777864) ^ [_1018135, _1018137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018135), 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)), _1018137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018135), _1018137)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27826 ^ _777864) ^ [_1273544, _1273546, _1273548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273544, tc_HOL_Obool)), _1273546), _1273548)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273544, tc_HOL_Obool)), _1273546), _1273548) = _1273548)], (27205 ^ _777864) ^ [_1260902, _1260904, _1260906] : [-(hBOOL(hAPP(hAPP(c_member(_1260902), _1260904), _1260906))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260902, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1260902), _1260904), _1260906)), hAPP(hAPP(c_Set_Oinsert(_1260902), _1260904), c_Orderings_Obot__class_Obot(tc_fun(_1260902, tc_HOL_Obool)))) = _1260906)], (18042 ^ _777864) ^ [_1088522, _1088524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1088522)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1088524)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088522)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1088524), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1088522))))], (7360 ^ _777864) ^ [_899137, _899139, _899141, _899143, _899145] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_899137, _899139, _899141)), _899143), _899145))), 7361 ^ _777864 : [(7368 ^ _777864) ^ [] : [-(hBOOL(hAPP(_899137, _899143))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899141), _899143), _899145))], (7362 ^ _777864) ^ [] : [hBOOL(hAPP(_899137, _899143)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899139), _899143), _899145))]]], (39105 ^ _777864) ^ [_1515961, _1515963, _1515965, _1515967, _1515969, _1515971] : [hBOOL(hAPP(hAPP(c_member(_1515961), _1515963), _1515965)), 39108 ^ _777864 : [(39115 ^ _777864) ^ [] : [_1515969 = _1515971, -(hAPP(hAPP(c_Product__Type_OSigma(_1515967, _1515961), _1515969), hAPP(c_COMBK(tc_fun(_1515961, tc_HOL_Obool), _1515967), _1515965)) = hAPP(hAPP(c_Product__Type_OSigma(_1515967, _1515961), _1515971), hAPP(c_COMBK(tc_fun(_1515961, tc_HOL_Obool), _1515967), _1515965)))], (39109 ^ _777864) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1515967, _1515961), _1515969), hAPP(c_COMBK(tc_fun(_1515961, tc_HOL_Obool), _1515967), _1515965)) = hAPP(hAPP(c_Product__Type_OSigma(_1515967, _1515961), _1515971), hAPP(c_COMBK(tc_fun(_1515961, tc_HOL_Obool), _1515967), _1515965)), -(_1515969 = _1515971)]]], (33909 ^ _777864) ^ [_1404718, _1404720] : [_1404718 = _1404720, -(hAPP(c_Int_ORep__Integ, _1404718) = hAPP(c_Int_ORep__Integ, _1404720))], (28266 ^ _777864) ^ [_1282334, _1282336, _1282338, _1282340] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282334, tc_HOL_Obool)), _1282336), hAPP(hAPP(c_Set_Oinsert(_1282334), _1282338), _1282340)) = hAPP(hAPP(c_Set_Oinsert(_1282334), _1282338), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282334, tc_HOL_Obool)), _1282336), _1282340)))], (19070 ^ _777864) ^ [_1105692, _1105694] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1105692)), c_Int_OBit0(_1105694)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1105692), _1105694)))], (6272 ^ _777864) ^ [_881220, _881222, _881224, _881226] : [class_Groups_Ocancel__semigroup__add(_881220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881220), _881222), _881224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881220), _881222), _881226), -(_881224 = _881226)], (45535 ^ _777864) ^ [_1676877, _1676879, _1676881, _1676883] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1676877)), hAPP(c_Set_Oimage(_1676879, tc_Option_Ooption(_1676877), _1676881), c_Orderings_Otop__class_Otop(tc_fun(_1676879, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1676877)), hAPP(c_Set_Oimage(_1676879, tc_Option_Ooption(_1676877), c_Map_Omap__add(_1676879, _1676877, _1676881, c_Map_Omap__of(_1676879, _1676877, _1676883))), c_Orderings_Otop__class_Otop(tc_fun(_1676879, tc_HOL_Obool))))))], (45774 ^ _777864) ^ [_1682787, _1682789] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1682787), hAPP(c_List_Oset(_1682787), _1682789))))], (1792 ^ _777864) ^ [_803032, _803034, _803036, _803038, _803040, _803042] : [-(c_Hoare__Mirabelle_Otriple__valid(_803040, _803036, _803032)), c_Hoare__Mirabelle_Otriple__valid(_803042, _803038, _803034), _803042 = _803040, _803038 = 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[-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (29672 ^ _777864) ^ [_1316628, _1316630, _1316632] : [class_Lattices_Osemilattice__inf(_1316628), 29675 ^ _777864 : [(29682 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316628), _1316630), _1316632) = _1316630, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316628), _1316630), _1316632)))], (29676 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316628), _1316630), _1316632)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316628), _1316630), _1316632) = _1316630)]]], (13401 ^ _777864) ^ [_1003025, _1003027] : [class_Divides_Osemiring__div(_1003025), -(c_Divides_Odiv__class_Omod(_1003025, _1003027, c_Groups_Ozero__class_Ozero(_1003025)) = _1003027)], (3342 ^ _777864) ^ [_828527, _828529, _828531, _828533] : [-(c_Wellfounded_Omin__ext(_828533, _828529) = c_Wellfounded_Omin__ext(_828531, _828527)), _828533 = _828531, _828529 = _828527], (13044 ^ _777864) ^ 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_824533 = _824531, _824529 = _824527, _824525 = _824523], (24485 ^ _777864) ^ [_1206903, _1206905, _1206907, _1206909, _1206911, _1206913] : [-(c_Nitpick_Opair__box_Opair__box__case(_1206903, _1206905, _1206907, _1206909, c_Nitpick_Opair__box_OPairBox(_1206903, _1206905, _1206911, _1206913)) = hAPP(hAPP(_1206909, _1206911), _1206913))], (44720 ^ _777864) ^ [_1657773, _1657775, _1657777] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657773, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1657773, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657773, tc_HOL_Obool), _1657775)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657773, tc_HOL_Obool), _1657777))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657773, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1657773, tc_HOL_Obool), tc_HOL_Obool)), _1657775), _1657777)))))], (49045 ^ _777864) ^ [_1763967, _1763969, _1763971, _1763973, _1763975] : [-(c_Map_Omap__upds(_1763967, _1763969, _1763971, _1763973, _1763975) = hAPP(c_List_Ofoldl(tc_fun(_1763967, tc_Option_Ooption(_1763969)), tc_prod(_1763967, _1763969), hAPP(hAPP(c_COMBB(tc_fun(_1763967, tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969)))), tc_fun(tc_prod(_1763967, _1763969), tc_fun(_1763967, tc_Option_Ooption(_1763969))), tc_fun(_1763967, tc_Option_Ooption(_1763969))), c_Product__Type_Oprod_Oprod__case(_1763967, _1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969)))), hAPP(hAPP(c_COMBC(tc_fun(_1763967, tc_Option_Ooption(_1763969)), tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763967, tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969))))), hAPP(hAPP(c_COMBB(tc_fun(_1763967, tc_fun(tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969))))), tc_fun(tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763967, tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969))))), tc_fun(_1763967, tc_Option_Ooption(_1763969))), c_COMBC(_1763967, tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969))))), hAPP(hAPP(c_COMBB(tc_fun(_1763967, tc_fun(tc_Option_Ooption(_1763969), tc_fun(_1763967, tc_Option_Ooption(_1763969)))), tc_fun(_1763967, tc_fun(tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969))))), tc_fun(_1763967, tc_Option_Ooption(_1763969))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1763969), tc_fun(_1763967, tc_Option_Ooption(_1763969))), tc_fun(tc_fun(_1763969, tc_Option_Ooption(_1763969)), tc_fun(_1763969, tc_fun(_1763967, tc_Option_Ooption(_1763969)))), _1763967), c_COMBB(tc_Option_Ooption(_1763969), tc_fun(_1763967, tc_Option_Ooption(_1763969)), _1763969))), c_Fun_Ofun__upd(_1763967, tc_Option_Ooption(_1763969))))), c_Option_Ooption_OSome(_1763969))), _1763971), hAPP(hAPP(c_List_Ozip(_1763967, _1763969), _1763973), _1763975)))], (39169 ^ 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_1613328)), _1613330)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613324, _1613324)), hAPP(hAPP(c_Product__Type_OPair(_1613324, _1613324), _1613326), _1613328)), c_Transitive__Closure_Otrancl(_1613324, _1613330))))], (22669 ^ _777864) ^ [_1170010, _1170012, _1170014] : [22670 ^ _777864 : [(22673 ^ _777864) ^ [] : [_1170012 = _1170014], (22671 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170010, tc_HOL_Obool)), _1170012), _1170014))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170010, tc_HOL_Obool)), _1170012), _1170014)))], (49550 ^ _777864) ^ [_1774890, _1774892, _1774894, _1774896] : [-(hAPP(c_List_Ofilter(_1774890, _1774892), c_List_Oremove1(_1774890, _1774894, _1774896)) = c_List_Oremove1(_1774890, _1774894, hAPP(c_List_Ofilter(_1774890, _1774892), _1774896)))], (18152 ^ _777864) ^ [_1090168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090168), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090168) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49781 ^ _777864) ^ [_1780764, _1780766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780766))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780764), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780766)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780764)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780766))))], (28324 ^ _777864) ^ [_1283832, _1283834, _1283836, _1283838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283832, tc_HOL_Obool)), _1283834), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283832, tc_HOL_Obool)), _1283836), _1283838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283832, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283832, tc_HOL_Obool)), _1283834), _1283836)), _1283838)))], (36622 ^ _777864) ^ [_1460931, _1460933, _1460935, _1460937, _1460939] : [class_Groups_Ocomm__monoid__add(_1460931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460933), _1460935)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460933, _1460931), hAPP(hAPP(c_COMBS(_1460933, _1460931, _1460931), hAPP(hAPP(c_COMBB(_1460931, tc_fun(_1460931, _1460931), _1460933), c_Groups_Oplus__class_Oplus(_1460931)), _1460937)), _1460939)), _1460935) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460931), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460933, _1460931), _1460937), _1460935)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460933, _1460931), _1460939), _1460935)))], (12872 ^ _777864) ^ [_994027, _994029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994027)), 12875 ^ _777864 : [(12882 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _994027), _994029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _994027)), hAPP(c_Int_Onat, _994029))))], (12876 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _994027)), hAPP(c_Int_Onat, _994029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _994027), _994029)))]]], (19178 ^ _777864) ^ [_1107569, _1107571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107569), _1107571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107569)), c_Int_OBit0(_1107571))))], (1322 ^ _777864) ^ [_797157, _797159] : [-(class_Orderings_Otop(_797157)), _797159 = _797157, class_Orderings_Otop(_797159)], (24751 ^ _777864) ^ [_1212346, _1212348, _1212350, _1212352, _1212354, _1212356, _1212358] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1212346, _1212348, _1212350, _1212352), _1212354), _1212356), _1212358) = c_New__DSequence_Opos__bind(_1212346, _1212348, hAPP(hAPP(hAPP(_1212350, _1212354), _1212356), _1212358), hAPP(hAPP(c_COMBC(_1212346, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1212348))), hAPP(hAPP(c_COMBC(_1212346, 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(_1212348)))), hAPP(hAPP(c_COMBC(_1212346, 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(_1212348))))), _1212352), _1212354)), _1212356)), _1212358)))], (50360 ^ _777864) ^ [_1791874, _1791876] : [-(c_List_Oconcat(_1791874, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1791874), tc_List_Olist(_1791874)), c_List_Olist_Olist__case(tc_List_Olist(_1791874), _1791874, c_List_Olist_ONil(_1791874), hAPP(hAPP(c_COMBB(tc_List_Olist(_1791874), tc_fun(tc_List_Olist(_1791874), tc_List_Olist(_1791874)), _1791874), c_COMBK(tc_List_Olist(_1791874), tc_List_Olist(_1791874))), hAPP(hAPP(c_COMBC(_1791874, tc_List_Olist(_1791874), tc_List_Olist(_1791874)), c_List_Olist_OCons(_1791874)), c_List_Olist_ONil(_1791874))))), _1791876)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1791874), _1791874), c_List_Ohd(_1791874)), hAPP(c_List_Ofilter(tc_List_Olist(_1791874), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1791874)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1791874), tc_List_Olist(_1791874), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1791874)))), _1791876)))], (30210 ^ _777864) ^ [_1328030, _1328032, _1328034, _1328036] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328030, tc_HOL_Obool)), _1328032), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328030, tc_HOL_Obool)), _1328034), _1328036)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328030, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328030, tc_HOL_Obool)), _1328032), _1328034)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328030, tc_HOL_Obool)), _1328032), _1328036)))], (12138 ^ _777864) ^ [_981077] : [hBOOL(hAPP(_981077, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 12139 ^ [_981077]))), 12142 ^ _777864 : [(12143 ^ _777864) ^ [_981177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981177)), -(hBOOL(hAPP(_981077, _981177)))]]], (49001 ^ _777864) ^ [_1762957, _1762959, _1762961] : [class_Orderings_Olinorder(_1762957), -(c_Big__Operators_Olattice_OInf__fin(_1762957, c_Orderings_Oord__class_Omin(_1762957), hAPP(c_List_Oset(_1762957), hAPP(hAPP(c_List_Olist_OCons(_1762957), _1762959), _1762961))) = hAPP(c_List_Ofoldl(_1762957, _1762957, c_Orderings_Oord__class_Omin(_1762957), _1762959), _1762961))], (19982 ^ _777864) ^ [_1122244, _1122246, _1122248, _1122250] : [class_Fields_Olinordered__field(_1122244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122244), _1122246), _1122248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122244), _1122250), c_Groups_Ozero__class_Ozero(_1122244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122244), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122244), _1122248), _1122250)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122244), _1122246), _1122250))))], (7913 ^ _777864) ^ [_909646, _909648, _909650] : [class_Nat_Osemiring__char__0(_909646), 7916 ^ _777864 : [(7923 ^ _777864) ^ [] : [_909648 = _909650, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909646), _909648) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909646), _909650))], (7917 ^ _777864) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909646), _909648) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_909646), _909650), -(_909648 = _909650)]]], (50572 ^ _777864) ^ [_1796496, _1796498, _1796500, _1796502] : [-(c_List_Otranspose(_1796496, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1796496)), hAPP(hAPP(c_List_Olist_OCons(_1796496), _1796498), _1796500)), _1796502)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1796496)), hAPP(hAPP(c_List_Olist_OCons(_1796496), _1796498), c_List_Oconcat(_1796496, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796496), tc_List_Olist(_1796496)), c_List_Olist_Olist__case(tc_List_Olist(_1796496), _1796496, c_List_Olist_ONil(_1796496), hAPP(hAPP(c_COMBB(tc_List_Olist(_1796496), tc_fun(tc_List_Olist(_1796496), tc_List_Olist(_1796496)), _1796496), c_COMBK(tc_List_Olist(_1796496), tc_List_Olist(_1796496))), hAPP(hAPP(c_COMBC(_1796496, tc_List_Olist(_1796496), tc_List_Olist(_1796496)), c_List_Olist_OCons(_1796496)), c_List_Olist_ONil(_1796496))))), _1796502)))), c_List_Otranspose(_1796496, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1796496)), _1796500), c_List_Oconcat(tc_List_Olist(_1796496), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796496), tc_List_Olist(tc_List_Olist(_1796496))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1796496)), _1796496, c_List_Olist_ONil(tc_List_Olist(_1796496)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1796496), tc_List_Olist(tc_List_Olist(_1796496))), _1796496), hAPP(hAPP(c_COMBC(tc_List_Olist(_1796496), tc_List_Olist(tc_List_Olist(_1796496)), tc_List_Olist(tc_List_Olist(_1796496))), c_List_Olist_OCons(tc_List_Olist(_1796496))), c_List_Olist_ONil(tc_List_Olist(_1796496)))))), _1796502))))))], (43725 ^ _777864) ^ [_1631060, _1631062, _1631064, _1631066, _1631068] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631060, tc_HOL_Obool)), _1631062), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631064, tc_fun(_1631060, tc_HOL_Obool)), _1631066), _1631068)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631064, tc_fun(_1631060, tc_HOL_Obool)), _1631066), hAPP(hAPP(c_COMBB(tc_fun(_1631060, tc_HOL_Obool), tc_fun(_1631060, tc_HOL_Obool), _1631064), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631060, tc_HOL_Obool)), _1631062)), _1631068)))], (34205 ^ _777864) ^ [_1412026, _1412028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1412026), _1412028)), -(hAPP(c_Finite__Set_Ocard(_1412026), _1412028) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1412026, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1412026), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1412028))], (23063 ^ _777864) ^ [_1178006, _1178008, _1178010, _1178012, _1178014] : [class_Groups_Ominus(_1178006), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178008, _1178006)), _1178010), _1178012), _1178014) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178006), hAPP(_1178010, _1178014)), hAPP(_1178012, _1178014)))], (28605 ^ _777864) ^ [_1292998, _1293000, _1293002, _1293004, _1293006, _1293008] : [hBOOL(hAPP(hAPP(c_member(_1292998), _1293000), _1293002)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1292998, _1293004)), hAPP(hAPP(c_Product__Type_OPair(_1292998, _1293004), _1293000), _1293006)), _1293008)), -(hBOOL(hAPP(hAPP(c_member(_1293004), _1293006), hAPP(c_Relation_OImage(_1292998, _1293004, _1293008), _1293002))))], (49626 ^ _777864) ^ [_1777070, _1777072, _1777074] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777070)), hAPP(c_List_Ofilter(_1777070, _1777072), _1777074)) = 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(_1777070)), _1777074)))), hAPP(hAPP(c_COMBB(_1777070, tc_HOL_Obool, tc_Nat_Onat), _1777072), hAPP(c_List_Onth(_1777070), _1777074))))))], (42132 ^ _777864) ^ [_1595652, _1595654, _1595656, _1595658, _1595660, _1595662] : [c_Finite__Set_Ofolding(_1595652, _1595654, _1595656, _1595658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595652), _1595660)), -(hAPP(_1595658, hAPP(hAPP(c_Set_Oinsert(_1595652), _1595662), _1595660)) = hAPP(c_Fun_Ocomp(_1595654, _1595654, _1595654, hAPP(_1595658, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1595652, tc_HOL_Obool)), _1595660), hAPP(hAPP(c_Set_Oinsert(_1595652), _1595662), c_Orderings_Obot__class_Obot(tc_fun(_1595652, tc_HOL_Obool)))))), hAPP(_1595656, _1595662)))], (7636 ^ _777864) ^ [_904402, _904404, _904406, _904408] : [-(c_Com_Ocom_OWhile(_904402, _904404) = c_Com_Ocom_OWhile(_904406, _904408)), _904402 = _904406, _904404 = _904408], (45860 ^ _777864) ^ [_1684938, _1684940, _1684942, _1684944, _1684946] : [c_Fun_Oinj__on(_1684938, _1684940, _1684942, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1684938, tc_HOL_Obool)), hAPP(c_List_Oset(_1684938), _1684944)), hAPP(c_List_Oset(_1684938), _1684946))), 45863 ^ _777864 : [(45870 ^ _777864) ^ [] : [_1684944 = _1684946, -(hAPP(hAPP(c_List_Omap(_1684938, _1684940), _1684942), _1684944) = hAPP(hAPP(c_List_Omap(_1684938, _1684940), _1684942), _1684946))], (45864 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Omap(_1684938, _1684940), _1684942), _1684944) = hAPP(hAPP(c_List_Omap(_1684938, _1684940), _1684942), _1684946), -(_1684944 = _1684946)]]], (5804 ^ _777864) ^ [_872985, _872987, _872989, _872991, _872993, _872995] : [c_Com_Ocom_OCall(_872985, _872987, _872989) = c_Com_Ocom_OLocal(_872991, _872993, _872995)], (49083 ^ _777864) ^ [_1765102, _1765104, _1765106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1765102, tc_HOL_Obool)), _1765104), _1765106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1765102), tc_HOL_Obool)), c_List_Olists(_1765102, _1765104)), c_List_Olists(_1765102, _1765106))))], (35184 ^ _777864) ^ [_1431884, _1431886, _1431888, _1431890, _1431892, _1431894] : [c_Fun_Oinj__on(_1431884, _1431886, _1431888, _1431890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431884, tc_HOL_Obool)), _1431892), _1431890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431884, tc_HOL_Obool)), _1431894), _1431890)), -(hAPP(c_Set_Oimage(_1431884, _1431886, _1431888), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431884, tc_HOL_Obool)), _1431892), _1431894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431886, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1431884, _1431886, _1431888), _1431892)), hAPP(c_Set_Oimage(_1431884, _1431886, _1431888), _1431894)))], (11024 ^ _777864) ^ [_961512, _961514] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _961512), _961514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _961514)), _961512)))], (42858 ^ _777864) ^ [_1611320, _1611322, _1611324] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1611320), _1611322)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611320, tc_HOL_Obool)), _1611324), _1611322) = hAPP(hAPP(c_Finite__Set_Ofold(_1611320, tc_fun(_1611320, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1611320, tc_HOL_Obool), tc_fun(tc_fun(_1611320, tc_HOL_Obool), tc_fun(_1611320, tc_HOL_Obool)), _1611320), hAPP(c_COMBC(tc_fun(_1611320, tc_HOL_Obool), tc_fun(_1611320, tc_HOL_Obool), tc_fun(_1611320, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1611320, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1611320, tc_fun(_1611320, tc_HOL_Obool), tc_fun(_1611320, tc_HOL_Obool)), c_Set_Oinsert(_1611320)), c_Orderings_Obot__class_Obot(tc_fun(_1611320, tc_HOL_Obool))))), _1611324), _1611322))], (22020 ^ _777864) ^ [_1158577, _1158579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158577)), 22023 ^ _777864 : [(22030 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158579), _1158577))), -(c_Divides_OposDivAlg(_1158579, _1158577) = hAPP(c_Divides_Oadjust(_1158577), c_Divides_OposDivAlg(_1158579, 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)))), _1158577))))], (22024 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158579), _1158577)), -(c_Divides_OposDivAlg(_1158579, _1158577) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158579))]]], (43745 ^ _777864) ^ [_1631906, _1631908, _1631910, _1631912, _1631914, _1631916] : [class_Complete__Lattice_Ocomplete__lattice(_1631906), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631908, _1631906), _1631910), hAPP(hAPP(c_COMBB(tc_fun(_1631912, _1631906), _1631906, _1631908), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631912, _1631906), _1631914)), _1631916)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631912, _1631906), _1631914), hAPP(hAPP(c_COMBB(tc_fun(_1631908, _1631906), _1631906, _1631912), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631908, _1631906), _1631910)), hAPP(c_COMBC(_1631908, _1631912, _1631906), _1631916))))], (38730 ^ _777864) ^ [_1507066, _1507068, _1507070, _1507072, _1507074] : [hBOOL(hAPP(hAPP(c_member(_1507066), hAPP(_1507068, _1507070)), _1507072)), -(hBOOL(hAPP(hAPP(c_member(_1507074), _1507070), hAPP(c_Set_Ovimage(_1507074, _1507066, _1507068), _1507072))))], (48780 ^ _777864) ^ [_1758377, _1758379, _1758381] : [hAPP(c_List_Orotate(_1758377, _1758379), _1758381) = c_List_Olist_ONil(_1758377), -(_1758381 = c_List_Olist_ONil(_1758377))], (44142 ^ _777864) ^ [_1644079, _1644081, _1644083, _1644085, _1644087] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644079, tc_fun(_1644081, tc_HOL_Obool)), _1644083), _1644085), _1644087)), 44145 ^ _777864 : [(44146 ^ _777864) ^ [_1644188] : [hBOOL(hAPP(hAPP(c_member(_1644079), _1644188), _1644083)), -(hBOOL(hAPP(hAPP(_1644085, _1644188), _1644087)))]]], (10362 ^ _777864) ^ [_950787, _950789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950787)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _950789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950787), _950789)))], (3080 ^ _777864) ^ [_824302, _824304, _824306, _824308, _824310, _824312] : [-(c_SetInterval_Oord_OgreaterThan(_824312, _824308, _824304) = c_SetInterval_Oord_OgreaterThan(_824310, _824306, _824302)), _824312 = _824310, _824308 = _824306, _824304 = _824302], (49281 ^ _777864) ^ [_1769123, _1769125, _1769127, _1769129] : [49284 ^ _777864 : [(49289 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769123, _1769123)), hAPP(hAPP(c_Product__Type_OPair(_1769123, _1769123), 49283 ^ [_1769123, _1769125, _1769127, _1769129]), 49282 ^ [_1769123, _1769125, _1769127, _1769129])), _1769125))], (49287 ^ _777864) ^ [] : [49282 ^ [_1769123, _1769125, _1769127, _1769129] = 49283 ^ [_1769123, _1769125, _1769127, _1769129]], (49285 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769123, _1769123)), hAPP(hAPP(c_Product__Type_OPair(_1769123, _1769123), 49282 ^ [_1769123, _1769125, _1769127, _1769129]), 49283 ^ [_1769123, _1769125, _1769127, _1769129])), _1769125))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769123), tc_List_Olist(_1769123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769123), tc_List_Olist(_1769123)), _1769127), _1769129)), c_List_Olexord(_1769123, _1769125)))), -(_1769127 = _1769129), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769123), tc_List_Olist(_1769123))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769123), tc_List_Olist(_1769123)), _1769129), _1769127)), c_List_Olexord(_1769123, _1769125))))], (43004 ^ _777864) ^ [_1614038, _1614040, _1614042, _1614044, _1614046] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614038, _1614038)), hAPP(hAPP(c_Product__Type_OPair(_1614038, _1614038), _1614040), _1614042)), _1614044)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614038, _1614038)), hAPP(hAPP(c_Product__Type_OPair(_1614038, _1614038), _1614042), _1614046)), _1614044)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614038, _1614038)), hAPP(hAPP(c_Product__Type_OPair(_1614038, _1614038), _1614040), _1614046)), c_Transitive__Closure_Otrancl(_1614038, _1614044))))], (17966 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (26921 ^ _777864) ^ [_1253188, _1253190, _1253192] : [hBOOL(hAPP(hAPP(c_member(_1253188), _1253190), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1253188, tc_HOL_Obool)), _1253192))), hBOOL(hAPP(hAPP(c_member(_1253188), _1253190), _1253192))], (45809 ^ _777864) ^ [_1683723, _1683725, _1683727, _1683729, _1683731] : [-(c_Map_Odom(_1683723, _1683725, hAPP(hAPP(c_COMBS(_1683723, tc_Option_Ooption(_1683727), tc_Option_Ooption(_1683725)), hAPP(hAPP(c_COMBB(tc_fun(_1683727, _1683725), tc_fun(tc_Option_Ooption(_1683727), tc_Option_Ooption(_1683725)), _1683723), c_Option_Omap(_1683727, _1683725)), _1683729)), _1683731)) = c_Map_Odom(_1683723, _1683727, _1683731))], (49255 ^ _777864) ^ [_1768777, _1768779, _1768781, _1768783] : [-(_1768777 = c_List_Olist_ONil(_1768779)), -(c_List_Olast(_1768781, hAPP(hAPP(c_List_Omap(_1768779, _1768781), _1768783), _1768777)) = hAPP(_1768783, c_List_Olast(_1768779, _1768777)))], (44109 ^ _777864) ^ [_1642440, _1642442, _1642444] : [-(hAPP(c_Relation_Oconverse(_1642440, _1642442), _1642444) = hAPP(c_Set_OCollect(tc_prod(_1642442, _1642440)), hAPP(c_Product__Type_Oprod_Oprod__case(_1642442, _1642440, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1642442, tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_fun(_1642440, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1642440, tc_fun(tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_fun(_1642440, tc_HOL_Obool)), _1642442), c_COMBC(_1642440, tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1642440, tc_prod(_1642440, _1642442)), tc_fun(_1642440, tc_fun(tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_HOL_Obool)), _1642442), hAPP(c_COMBB(tc_prod(_1642440, _1642442), tc_fun(tc_fun(tc_prod(_1642440, _1642442), tc_HOL_Obool), tc_HOL_Obool), _1642440), c_member(tc_prod(_1642440, _1642442)))), hAPP(c_COMBC(_1642440, _1642442, tc_prod(_1642440, _1642442)), c_Product__Type_OPair(_1642440, _1642442))))), _1642444))))], (51241 ^ _777864) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (23163 ^ _777864) ^ [_1180146, _1180148] : [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(_1180148))), 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), _1180146)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180146)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180148))))], (14548 ^ _777864) ^ [_1023759, _1023761] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023759), _1023761) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1023761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14557 ^ _777864 : [(14560 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023759), _1023761)))], (14558 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023759)))]], 14561 ^ _777864 : [(14564 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023761), _1023759)))], (14562 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023759), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25333 ^ _777864) ^ [_1222147, _1222149, _1222151, _1222153] : [class_Divides_Osemiring__div(_1222147), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222147), _1222149), c_Divides_Odiv__class_Omod(_1222147, _1222151, _1222153))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222147), _1222149), _1222153)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222147), _1222149), _1222151)))], (46779 ^ _777864) ^ [_1709757, _1709759, _1709761, _1709763] : [hBOOL(hAPP(hAPP(c_member(_1709757), _1709759), hAPP(c_List_Oset(_1709757), c_List_Osublist(_1709757, _1709761, _1709763)))), -(hBOOL(hAPP(hAPP(c_member(_1709757), _1709759), hAPP(c_List_Oset(_1709757), _1709761))))], (38102 ^ _777864) ^ [_1492982, _1492984, _1492986] : [class_Lattices_Obounded__lattice__top(_1492982), 38105 ^ _777864 : [(38114 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492982), _1492984), _1492986) = c_Orderings_Otop__class_Otop(_1492982)), _1492984 = c_Orderings_Otop__class_Otop(_1492982), _1492986 = c_Orderings_Otop__class_Otop(_1492982)], (38106 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1492982), _1492984), _1492986) = c_Orderings_Otop__class_Otop(_1492982), 38109 ^ _777864 : [(38112 ^ _777864) ^ [] : [-(_1492986 = c_Orderings_Otop__class_Otop(_1492982))], (38110 ^ _777864) ^ [] : [-(_1492984 = c_Orderings_Otop__class_Otop(_1492982))]]]]], (9120 ^ _777864) ^ [_929416, _929418, _929420, _929422] : [class_Rings_Ocomm__semiring__1(_929416), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929416), _929418), _929420)), _929422) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929416), _929418), _929422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929416), _929420), _929422)))], (31395 ^ _777864) ^ [_1351426, _1351428, _1351430] : [class_Lattices_Olattice(_1351426), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351426), _1351428)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351426), _1351430)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351426, tc_HOL_Obool)), _1351428), _1351430) = c_Orderings_Obot__class_Obot(tc_fun(_1351426, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1351426), c_Big__Operators_Olattice__class_OInf__fin(_1351426, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351426, tc_HOL_Obool)), _1351428), _1351430))), c_Big__Operators_Olattice__class_OInf__fin(_1351426, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351426, tc_HOL_Obool)), _1351428), _1351430))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1351426), c_Big__Operators_Olattice__class_OInf__fin(_1351426, _1351428)), c_Big__Operators_Olattice__class_OInf__fin(_1351426, _1351430)))], (37979 ^ _777864) ^ [_1490599, _1490601, _1490603] : [c_Map_Odom(_1490599, _1490601, _1490603) = c_Orderings_Obot__class_Obot(tc_fun(_1490599, tc_HOL_Obool)), -(_1490603 = hAPP(c_COMBK(tc_Option_Ooption(_1490601), _1490599), c_Option_Ooption_ONone(_1490601)))], (44899 ^ _777864) ^ [_1662048, _1662050, _1662052] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662048, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1662048, tc_HOL_Obool), tc_HOL_Obool)), _1662050), _1662052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1662048, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662048, tc_HOL_Obool), _1662050)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662048, tc_HOL_Obool), _1662052)))], (36988 ^ _777864) ^ [_1469444, _1469446] : [-(c_Map_Oran(_1469444, _1469446, hAPP(c_COMBK(tc_Option_Ooption(_1469446), _1469444), c_Option_Ooption_ONone(_1469446))) = c_Orderings_Obot__class_Obot(tc_fun(_1469446, tc_HOL_Obool)))], (18932 ^ _777864) ^ [_1103267] : [_1103267 = c_Int_OPls, -(c_Int_OBit0(_1103267) = c_Int_OPls)], (17588 ^ _777864) ^ [_1081383] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1081383) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1081383))], (30815 ^ _777864) ^ [_1341481, _1341483] : [class_Lattices_Olattice(_1341481), -(c_Big__Operators_Olattice__class_OSup__fin(_1341481, hAPP(hAPP(c_Set_Oinsert(_1341481), _1341483), c_Orderings_Obot__class_Obot(tc_fun(_1341481, tc_HOL_Obool)))) = _1341483)], (25197 ^ _777864) ^ [_1219862, _1219864] : [-(_1219862 = _1219864), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219862), _1219864)), 25204 ^ _777864 : [(25207 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219864), _1219862))], (25205 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1219862), _1219864)))]]], (48031 ^ _777864) ^ [_1739812, _1739814, _1739816, _1739818] : [hAPP(hAPP(c_List_Oappend(_1739812), _1739814), _1739816) = hAPP(hAPP(c_List_Oappend(_1739812), _1739814), _1739818), -(_1739816 = _1739818)], (10790 ^ _777864) ^ [_957362, _957364, _957366, _957368] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_957362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957362), _957364), _957366)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957362), _957364), _957368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957362), _957366), _957368)))], (8322 ^ _777864) ^ [_915804, _915806, _915808] : [class_Orderings_Oorder(_915804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915804), _915806), _915808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915804), _915808), _915806))], (1052 ^ _777864) ^ [_793782, _793784] : [-(class_Groups_Oordered__ab__group__add(_793782)), _793784 = _793782, class_Groups_Oordered__ab__group__add(_793784)], (41266 ^ _777864) ^ [_1574616, _1574618, _1574620, _1574622, _1574624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574616, _1574618)), hAPP(hAPP(c_Product__Type_OPair(_1574616, _1574618), _1574620), _1574622)), _1574624)), -(hBOOL(hAPP(hAPP(c_member(_1574616), _1574620), hAPP(c_Relation_ODomain(_1574616, _1574618), _1574624))))], (718 ^ _777864) ^ [_788963, _788965, _788967, _788969, _788971, _788973] : [-(c_Relation_Osingle__valued(_788971, _788967, _788963)), c_Relation_Osingle__valued(_788973, _788969, _788965), _788973 = _788971, _788969 = _788967, _788965 = _788963], (15464 ^ _777864) ^ [_1040999, _1041001, _1041003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041001), _1041003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040999), _1041003)), _1041001)))], (8700 ^ _777864) ^ [_922221, _922223] : [class_Groups_Omonoid__mult(_922221), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922221), _922223), c_Groups_Oone__class_Oone(_922221)) = _922223)], (3794 ^ _777864) ^ [_835607, _835609] : [_835609 = _835607, -(c_Nat_Ofunpow(_835609) = c_Nat_Ofunpow(_835607))], (8946 ^ _777864) ^ [_926460, _926462, _926464] : [class_Groups_Oordered__ab__group__add(_926460), 8949 ^ _777864 : [(8956 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926460), hAPP(c_Groups_Ouminus__class_Ouminus(_926460), _926464)), _926462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926460), hAPP(c_Groups_Ouminus__class_Ouminus(_926460), _926462)), _926464)))], (8950 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926460), hAPP(c_Groups_Ouminus__class_Ouminus(_926460), _926462)), _926464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926460), hAPP(c_Groups_Ouminus__class_Ouminus(_926460), _926464)), _926462)))]]], (41386 ^ _777864) ^ [_1578093, _1578095, _1578097, _1578099] : [hBOOL(hAPP(hAPP(c_member(_1578093), _1578095), hAPP(c_Relation_ODomain(_1578093, _1578097), _1578099))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578093, _1578097)), hAPP(hAPP(c_Product__Type_OPair(_1578093, _1578097), _1578095), 41389 ^ [_1578093, _1578095, _1578097, _1578099])), _1578099)))], (4766 ^ _777864) ^ [_850775, _850777] : [_850777 = _850775, -(c_SetInterval_Oord__class_OlessThan(_850777) = c_SetInterval_Oord__class_OlessThan(_850775))], (8202 ^ _777864) ^ [_914077, _914079] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _914077), _914079))), -(_914077 = _914079), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _914079), _914077)))], (47344 ^ _777864) ^ [_1724362, _1724364, _1724366] : [-(c_List_Osublist(_1724362, _1724364, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1724366)) = hAPP(hAPP(c_List_Otake(_1724362), _1724366), _1724364))], (3434 ^ _777864) ^ [_829959, _829961, _829963, _829965, _829967, _829969, _829971, _829973] : [-(c_Product__Type_Oapfst(_829973, _829969, _829965, _829961) = c_Product__Type_Oapfst(_829971, _829967, _829963, _829959)), _829973 = _829971, _829969 = _829967, _829965 = _829963, _829961 = _829959], (5150 ^ _777864) ^ [_856693, _856695, _856697, _856699] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_856699, _856695) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_856697, _856693)), _856699 = _856697, _856695 = _856693], (24665 ^ _777864) ^ [_1210510, _1210512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1210510), _1210512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210510)), hAPP(c_Code__Numeral_Onat__of, _1210512))))], (8818 ^ _777864) ^ [_924557, _924559] : [class_Rings_Oring__1(_924557), 8821 ^ _777864 : [(8828 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924559), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_924557), _924559) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924557), hAPP(c_Int_Onat, _924559)))], (8822 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924559), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_924557), _924559) = hAPP(c_Groups_Ouminus__class_Ouminus(_924557), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924557), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _924559)))))]]], (39751 ^ _777864) ^ [_1530823, _1530825] : [class_Groups_Oab__semigroup__mult(_1530823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530823), _1530825)), -(_1530825 = c_Orderings_Obot__class_Obot(tc_fun(_1530823, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1530823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1530823), 39764 ^ [_1530823, _1530825]), 39765 ^ [_1530823, _1530825])), hAPP(hAPP(c_Set_Oinsert(_1530823), 39764 ^ [_1530823, _1530825]), hAPP(hAPP(c_Set_Oinsert(_1530823), 39765 ^ [_1530823, _1530825]), c_Orderings_Obot__class_Obot(tc_fun(_1530823, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1530823), hAPP(c_Finite__Set_Ofold1(_1530823, c_Groups_Otimes__class_Otimes(_1530823)), _1530825)), _1530825)))], (18954 ^ _777864) ^ [_1103664] : [c_Int_OBit0(_1103664) = c_Int_OMin], (47342 ^ _777864) ^ [_1724298, _1724300, _1724302, _1724304] : [-(hAPP(hAPP(c_List_Otake(_1724298), hAPP(c_Nat_OSuc, _1724300)), hAPP(hAPP(c_List_Olist_OCons(_1724298), _1724302), _1724304)) = hAPP(hAPP(c_List_Olist_OCons(_1724298), _1724302), hAPP(hAPP(c_List_Otake(_1724298), _1724300), _1724304)))], (25975 ^ _777864) ^ [_1233851, _1233853, _1233855, _1233857, _1233859, _1233861, _1233863] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1233851, _1233853, _1233855, _1233857), _1233859), _1233861), _1233863) = c_New__DSequence_Oneg__bind(_1233851, _1233853, hAPP(hAPP(hAPP(_1233855, _1233859), _1233861), _1233863), hAPP(hAPP(c_COMBC(_1233851, 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(_1233853)))), hAPP(hAPP(c_COMBC(_1233851, 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(_1233853))))), hAPP(hAPP(c_COMBC(_1233851, 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(_1233853)))))), _1233857), _1233859)), _1233861)), _1233863)))], (51463 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (40174 ^ _777864) ^ [_1540492, _1540494, _1540496] : [-(hAPP(c_Set_OCollect(_1540492), hAPP(hAPP(c_COMBS(_1540492, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540492), c_fconj), _1540494)), _1540496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1540492, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1540492), _1540494)), hAPP(c_Set_OCollect(_1540492), _1540496)))], (37819 ^ _777864) ^ [_1487347, _1487349] : [class_Orderings_Olinorder(_1487347), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487347, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1487347), _1487349)) = hAPP(c_SetInterval_Oord__class_OatMost(_1487347), _1487349))], (44407 ^ _777864) ^ [_1650384, _1650386, _1650388, _1650390] : [-(hAPP(hAPP(c_Nat_Ocompow(_1650384, _1650384), _1650386), hAPP(hAPP(c_Nat_Ocompow(_1650384, _1650384), _1650388), _1650390)) = hAPP(hAPP(c_Nat_Ocompow(_1650384, _1650384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1650388), _1650386)), _1650390))], (49168 ^ _777864) ^ [_1767228, _1767230, _1767232] : [49169 ^ _777864 : [(49170 ^ _777864) ^ [_1767317, _1767319] : [_1767230 = hAPP(hAPP(c_List_Olist_OCons(_1767228), _1767319), _1767317)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1767228), tc_List_Olist(_1767228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1767228), tc_List_Olist(_1767228)), c_List_Olist_ONil(_1767228)), _1767230)), c_List_Olexord(_1767228, _1767232))))], (51223 ^ _777864) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (8508 ^ _777864) ^ [_918908, _918910, _918912] : [class_Rings_Ocomm__semiring__1(_918908), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918908), _918910), _918912)), _918912) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918908), _918910), c_Groups_Oone__class_Oone(_918908))), _918912))], (26279 ^ _777864) ^ [_1240072, _1240074, _1240076, _1240078, _1240080] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1240072, _1240074, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1240072)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1240072), hAPP(hAPP(c_COMBC(_1240072, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1240072), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1240076)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1240078)), _1240080))), c_Com_Ocom_OAss(_1240078, _1240080)), _1240076)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1240072), tc_HOL_Obool)))))], (30486 ^ _777864) ^ [_1335020, _1335022, _1335024, _1335026] : [hBOOL(hAPP(hAPP(_1335024, _1335026), _1335022)), -(hBOOL(hAPP(hAPP(c_member(_1335020), _1335022), c_SetInterval_Oord_OgreaterThan(_1335020, _1335024, _1335026))))], (37348 ^ _777864) ^ [_1477911, _1477913, _1477915] : [37350 ^ _777864 : [(37353 ^ _777864) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1477915, 37349 ^ [_1477911, _1477913, _1477915]))], (37351 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477911), 37349 ^ [_1477911, _1477913, _1477915]), _1477913)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477911, tc_Int_Oint), _1477915), _1477913) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477911, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1477911), c_Int_Onat), _1477915)), _1477913)))], (29962 ^ _777864) ^ [_1322597, _1322599, _1322601, _1322603] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322597, tc_HOL_Obool)), _1322599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322597, tc_HOL_Obool)), _1322601), _1322603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322597, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322597, tc_HOL_Obool)), _1322599), _1322601)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322597, tc_HOL_Obool)), _1322599), _1322603)))], (9252 ^ _777864) ^ [_931986, _931988, _931990] : [class_Groups_Ogroup__add(_931986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931986), _931988), _931990) = c_Groups_Ozero__class_Ozero(_931986), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931986), _931988) = _931990)], (10063 ^ _777864) ^ [_946038] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _946038) = _946038)], (7984 ^ _777864) ^ [_910862, _910864] : [class_Rings_Olinordered__semidom(_910862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910862), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_910862), _910864)), c_Groups_Ozero__class_Ozero(_910862)))], (34565 ^ _777864) ^ [_1419955, _1419957, _1419959, _1419961] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1419955), hAPP(c_Set_Oimage(_1419957, _1419955, _1419959), _1419961))), c_Fun_Oinj__on(_1419957, _1419955, _1419959, _1419961), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1419957), _1419961)))], (5830 ^ _777864) ^ [_873597, _873599, _873601, _873603, _873605, _873607] : [-(c_Com_Ocom_OCall(_873597, _873599, _873601) = c_Com_Ocom_OCall(_873603, _873605, _873607)), _873597 = _873603, _873599 = _873605, _873601 = _873607], (47246 ^ _777864) ^ [_1721449, _1721451, _1721453, _1721455] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1721449), tc_List_Olist(_1721449))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1721449), tc_List_Olist(_1721449)), _1721451), _1721453)), c_List_Olistrel(_1721449, _1721455)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721449)), _1721451) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721449)), _1721453), 47252 ^ _777864 : [(47255 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1721449, _1721449)), hAPP(hAPP(c_Product__Type_OPair(_1721449, _1721449), hAPP(hAPP(c_List_Onth(_1721449), _1721451), 47251 ^ [_1721449, _1721451, _1721453, _1721455])), hAPP(hAPP(c_List_Onth(_1721449), _1721453), 47251 ^ [_1721449, _1721451, _1721453, _1721455]))), _1721455))], (47253 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47251 ^ [_1721449, _1721451, _1721453, _1721455]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721449)), _1721451))))]]], (310 ^ _777864) ^ [_782585, _782587] : [-(class_Fields_Ofield(_782585)), _782587 = _782585, class_Fields_Ofield(_782587)], (6795 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (30020 ^ _777864) ^ [_1323947, _1323949, _1323951, _1323953] : [class_Lattices_Olattice(_1323947), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323947), _1323949), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323947), _1323951), _1323953)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323947), _1323951), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323947), _1323949), _1323953)))], (32819 ^ _777864) ^ [_1379540, _1379542, _1379544, _1379546] : [class_Fields_Olinordered__field(_1379540), -(hAPP(c_Groups_Oabs__class_Oabs(_1379540), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379542, _1379540), _1379544), _1379546)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379542, _1379540), hAPP(hAPP(c_COMBB(_1379540, _1379540, _1379542), c_Groups_Oabs__class_Oabs(_1379540)), _1379544)), _1379546))], (2976 ^ _777864) ^ [_822708, _822710, _822712, _822714] : [-(c_Com_Ocom_OSemi(_822714, _822710) = c_Com_Ocom_OSemi(_822712, _822708)), _822714 = _822712, _822710 = _822708], (6158 ^ _777864) ^ [_879130, _879132] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _879130, _879132, _879130))], (44706 ^ _777864) ^ [_1657335, _1657337, _1657339] : [class_Complete__Lattice_Ocomplete__lattice(_1657335), -(c_Complete__Lattice_OInf__class_OInf(_1657335, hAPP(hAPP(c_Set_Oinsert(_1657335), _1657337), _1657339)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1657335), _1657337), c_Complete__Lattice_OInf__class_OInf(_1657335, _1657339)))], (50564 ^ _777864) ^ [_1796245, _1796247] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1796245), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1796245))), c_List_Otranspose(_1796245, _1796247)))))], (9909 ^ _777864) ^ [_943479] : [_943479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _943479) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48049 ^ _777864) ^ [_1740166, _1740168, _1740170, _1740172] : [_1740168 = _1740172, -(hAPP(hAPP(c_List_Oappend(_1740166), _1740168), _1740170) = hAPP(hAPP(c_List_Oappend(_1740166), _1740172), _1740170))], (15170 ^ _777864) ^ [_1035281, _1035283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035281), _1035283))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035281, _1035283) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035281), _1035283), _1035283))], (17180 ^ _777864) ^ [_1074227, _1074229, _1074231] : [class_Power_Opower(_1074227), class_Rings_Omult__zero(_1074227), class_Rings_Ono__zero__divisors(_1074227), class_Rings_Ozero__neq__one(_1074227), 17195 ^ _777864 : [(17204 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1074227), _1074229), _1074231) = c_Groups_Ozero__class_Ozero(_1074227)), _1074229 = c_Groups_Ozero__class_Ozero(_1074227), -(_1074231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17196 ^ _777864) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1074227), _1074229), _1074231) = c_Groups_Ozero__class_Ozero(_1074227), 17199 ^ _777864 : [(17202 ^ _777864) ^ [] : [_1074231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17200 ^ _777864) ^ [] : [-(_1074229 = c_Groups_Ozero__class_Ozero(_1074227))]]]]], (24515 ^ _777864) ^ [_1207943, _1207945, _1207947, _1207949, _1207951, _1207953, _1207955] : [hBOOL(hAPP(hAPP(_1207943, hAPP(c_Product__Type_Osnd(_1207945, _1207947), _1207949)), hAPP(c_Product__Type_Ofst(_1207945, _1207947), _1207949))), 24522 ^ _777864 : [(24525 ^ _777864) ^ [] : [hBOOL(hAPP(_1207951, hAPP(hAPP(_1207953, 24520 ^ [_1207943, _1207945, _1207947, _1207949, _1207951, _1207953, _1207955]), 24521 ^ [_1207943, _1207945, _1207947, _1207949, _1207951, _1207953, _1207955])))], (24523 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1207943, 24521 ^ [_1207943, _1207945, _1207947, _1207949, _1207951, _1207953, _1207955]), 24520 ^ [_1207943, _1207945, _1207947, _1207949, _1207951, _1207953, _1207955])))]], -(hBOOL(hAPP(_1207951, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1207945, _1207947, _1207955), _1207953), _1207949))))], (33735 ^ _777864) ^ [_1400458, _1400460, _1400462, _1400464, _1400466, _1400468] : [class_Complete__Lattice_Ocomplete__lattice(_1400458), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400460, tc_fun(_1400462, _1400458)), _1400464), _1400466), _1400468) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400460, _1400458), _1400464), hAPP(hAPP(c_COMBC(_1400460, _1400462, _1400458), _1400466), _1400468)))], (48298 ^ _777864) ^ [_1745908, _1745910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1745908), tc_List_Olist(_1745908)), tc_HOL_Obool)), c_List_Olistrel(_1745908, _1745910)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1745908), c_List_Olistrel1(_1745908, _1745910)))))], (47324 ^ _777864) ^ [_1723878, _1723880, _1723882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723878)), _1723880)), _1723882)), -(hAPP(hAPP(c_List_Otake(_1723878), _1723882), _1723880) = _1723880)], (48203 ^ _777864) ^ [_1743248, _1743250, _1743252, _1743254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743248), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743250)), _1743252)))), -(hAPP(hAPP(c_List_Onth(_1743250), hAPP(hAPP(c_List_Oappend(_1743250), _1743252), _1743254)), _1743248) = hAPP(hAPP(c_List_Onth(_1743250), _1743254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1743248), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743250)), _1743252))))], (18576 ^ _777864) ^ [_1097241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1097241)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1097241), c_Int_OMin)))], (1592 ^ _777864) ^ [_800532, _800534] : [-(class_Rings_Ocomm__semiring(_800532)), _800534 = _800532, class_Rings_Ocomm__semiring(_800534)], (11018 ^ _777864) ^ [_961349, _961351, _961353] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961349), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961351), _961353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961349), _961351)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _961349), _961353)))], (34260 ^ _777864) ^ [_1413144, _1413146, _1413148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1413144, _1413144)), _1413146), c_Relation_OId__on(_1413144, _1413148))), 34264 ^ _777864 : [(34267 ^ _777864) ^ [] : [-(_1413146 = hAPP(hAPP(c_Product__Type_OPair(_1413144, _1413144), 34263 ^ [_1413144, _1413146, _1413148]), 34263 ^ [_1413144, _1413146, _1413148]))], (34265 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413144), 34263 ^ [_1413144, _1413146, _1413148]), _1413148)))]]], (34269 ^ _777864) ^ [_1413343, _1413345, _1413347, _1413349, _1413351, _1413353, _1413355] : [c_Big__Operators_Ocomm__monoid__big(_1413343, _1413345, _1413347, _1413349, _1413351), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1413345), _1413353))), -(hAPP(hAPP(_1413351, _1413355), _1413353) = _1413349)], (5346 ^ _777864) ^ [_859659, _859661] : [_859661 = _859659, -(c_List_Olist_ONil(_859661) = c_List_Olist_ONil(_859659))], (27047 ^ _777864) ^ [_1255585, _1255587, _1255589] : [_1255587 = _1255589, -(hBOOL(hAPP(hAPP(c_member(_1255585), _1255587), hAPP(c_fequal, _1255589))))], (16374 ^ _777864) ^ [_1058665, _1058667] : [class_Groups_Oordered__ab__group__add__abs(_1058665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058665), hAPP(c_Groups_Oabs__class_Oabs(_1058665), _1058667)), c_Groups_Ozero__class_Ozero(_1058665)))], (46553 ^ _777864) ^ [_1703743, _1703745, _1703747, _1703749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703743)), _1703745)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703743)), _1703747))), _1703745 = hAPP(hAPP(c_List_Olist_OCons(_1703743), _1703749), _1703747)], (33480 ^ _777864) ^ [_1393428, _1393430, _1393432, _1393434] : [-(hAPP(c_Set_Oimage(_1393428, _1393430, _1393432), _1393434) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393428, tc_fun(_1393430, tc_HOL_Obool)), _1393434), hAPP(hAPP(c_COMBC(_1393428, tc_fun(_1393430, tc_HOL_Obool), tc_fun(_1393430, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1393430, tc_fun(tc_fun(_1393430, tc_HOL_Obool), tc_fun(_1393430, tc_HOL_Obool)), _1393428), c_Set_Oinsert(_1393430)), _1393432)), c_Orderings_Obot__class_Obot(tc_fun(_1393430, tc_HOL_Obool)))))], (33827 ^ _777864) ^ [_1402797, _1402799, _1402801, _1402803, _1402805] : [-(_1402797 = c_Orderings_Obot__class_Obot(tc_fun(_1402799, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402801, tc_HOL_Obool)), _1402803), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402799, tc_fun(_1402801, tc_HOL_Obool)), _1402797), _1402805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402799, tc_fun(_1402801, tc_HOL_Obool)), _1402797), hAPP(hAPP(c_COMBB(tc_fun(_1402801, tc_HOL_Obool), tc_fun(_1402801, tc_HOL_Obool), _1402799), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402801, tc_HOL_Obool)), _1402803)), _1402805)))], (43925 ^ _777864) ^ [_1637335, _1637337, _1637339, _1637341, _1637343, _1637345] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637335, tc_fun(_1637337, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1637339, _1637335, _1637341), _1637343)), _1637345) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637339, tc_fun(_1637337, tc_HOL_Obool)), _1637343), hAPP(hAPP(c_COMBB(_1637335, tc_fun(_1637337, tc_HOL_Obool), _1637339), _1637345), _1637341)))], (29842 ^ _777864) ^ [_1319677, _1319679, _1319681] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319677, tc_HOL_Obool)), _1319679), _1319681) = c_Orderings_Obot__class_Obot(tc_fun(_1319677, tc_HOL_Obool)), 29845 ^ _777864 : [(29846 ^ _777864) ^ [_1319801] : [hBOOL(hAPP(hAPP(c_member(_1319677), _1319801), _1319679)), 29849 ^ _777864 : [(29850 ^ _777864) ^ [_1319891] : [hBOOL(hAPP(hAPP(c_member(_1319677), _1319891), _1319681)), _1319801 = _1319891]]]]], (43577 ^ _777864) ^ [_1627402, _1627404] : [-(c_Transitive__Closure_Otrancl(_1627402, hAPP(c_Relation_Oconverse(_1627402, _1627402), _1627404)) = hAPP(c_Relation_Oconverse(_1627402, _1627402), c_Transitive__Closure_Otrancl(_1627402, _1627404)))], (33230 ^ _777864) ^ [_1388090, _1388092, _1388094, _1388096, _1388098] : [class_Fields_Ofield(_1388090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388092), _1388094)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388092), _1388096)), 33244 ^ _777864 : [(33247 ^ _777864) ^ [] : [-(hAPP(_1388098, 33243 ^ [_1388090, _1388092, _1388094, _1388096, _1388098]) = c_Groups_Ozero__class_Ozero(_1388090))], (33245 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388092), 33243 ^ [_1388090, _1388092, _1388094, _1388096, _1388098]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388092, tc_HOL_Obool)), _1388094), _1388096))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388092, _1388090), _1388098), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1388092, tc_HOL_Obool)), _1388094), _1388096)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388090), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388090), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388092, _1388090), _1388098), _1388094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388092, _1388090), _1388098), _1388096))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388092, _1388090), _1388098), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388092, tc_HOL_Obool)), _1388094), _1388096))))], (23939 ^ _777864) ^ [_1196403, _1196405, _1196407] : [class_Orderings_Olinorder(_1196403), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196403), _1196405), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196403), _1196405), _1196407))))], (50227 ^ _777864) ^ [_1788636] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1788636) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1788636))))], (33743 ^ _777864) ^ [_1400718, _1400720, _1400722, _1400724, _1400726] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400718, tc_fun(_1400720, tc_HOL_Obool)), _1400722), hAPP(hAPP(c_COMBC(_1400718, tc_fun(_1400720, tc_HOL_Obool), tc_fun(_1400720, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400720, tc_HOL_Obool), tc_fun(tc_fun(_1400720, tc_HOL_Obool), tc_fun(_1400720, tc_HOL_Obool)), _1400718), c_Groups_Ominus__class_Ominus(tc_fun(_1400720, tc_HOL_Obool))), _1400724)), _1400726)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1400720, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400718, tc_fun(_1400720, tc_HOL_Obool)), _1400722), _1400724)), _1400726))], (46266 ^ _777864) ^ [_1694681, _1694683, _1694685, _1694687, _1694689] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694681), tc_List_Olist(_1694681))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694681), tc_List_Olist(_1694681)), _1694683), _1694685)), hAPP(c_List_Olexn(_1694681, _1694687), _1694689))), 46269 ^ _777864 : [(46272 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694681)), _1694685) = _1694689)], (46270 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694681)), _1694683) = _1694689)]]], (50374 ^ _777864) ^ [_1792328, _1792330, _1792332, _1792334] : [_1792330 = hAPP(hAPP(c_List_Oappend(_1792328), hAPP(c_List_Orev(_1792328), _1792334)), hAPP(hAPP(c_List_Olist_OCons(_1792328), _1792332), c_List_Olist_ONil(_1792328))), -(hAPP(c_List_Orev(_1792328), _1792330) = hAPP(hAPP(c_List_Olist_OCons(_1792328), _1792332), _1792334))], (18956 ^ _777864) ^ [_1103701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1103701)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103701), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20406 ^ _777864) ^ [_1129278, _1129280] : [c_Nat__Transfer_Ois__nat(_1129278), c_Nat__Transfer_Ois__nat(_1129280), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1129278, _1129280)))], (26283 ^ _777864) ^ [_1240256, _1240258] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240256), _1240258)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1240258), _1240256)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1240256) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1240258))], (48562 ^ _777864) ^ [_1753516, _1753518, _1753520] : [hAPP(hAPP(c_List_Odrop(_1753516), _1753518), _1753520) = c_List_Olist_ONil(_1753516), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753516)), _1753520)), _1753518)))], (29045 ^ _777864) ^ [_1303088, _1303090, _1303092, _1303094, _1303096] : [c_Equiv__Relations_Oequiv(_1303088, _1303090, _1303092), hBOOL(hAPP(hAPP(c_member(tc_prod(_1303088, _1303088)), hAPP(hAPP(c_Product__Type_OPair(_1303088, _1303088), _1303094), _1303096)), _1303092)), -(hAPP(c_Relation_OImage(_1303088, _1303088, _1303092), hAPP(hAPP(c_Set_Oinsert(_1303088), _1303094), c_Orderings_Obot__class_Obot(tc_fun(_1303088, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1303088, _1303088, _1303092), hAPP(hAPP(c_Set_Oinsert(_1303088), _1303096), c_Orderings_Obot__class_Obot(tc_fun(_1303088, tc_HOL_Obool)))))], (46773 ^ _777864) ^ [_1709654, _1709656, _1709658] : [hBOOL(hAPP(c_List_Odistinct(_1709654), _1709656)), -(hBOOL(hAPP(c_List_Odistinct(_1709654), c_List_Osublist(_1709654, _1709656, _1709658))))], (43700 ^ _777864) ^ [_1630250, _1630252, _1630254, _1630256, _1630258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630250, tc_HOL_Obool)), _1630252), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1630254, tc_fun(_1630250, tc_HOL_Obool)), _1630256), _1630258))), 43703 ^ _777864 : [(43704 ^ _777864) ^ [_1630383] : [hBOOL(hAPP(hAPP(c_member(_1630254), _1630383), _1630256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630250, tc_HOL_Obool)), _1630252), hAPP(_1630258, _1630383))))]]], (11975 ^ _777864) ^ [_978228, _978230, _978232] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978228), _978230)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978228), _978232)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978230), _978232))], (7602 ^ _777864) ^ [_903872, _903874, _903876, _903878, _903880] : [hBOOL(hAPP(_903872, _903874)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_903876), _903874), _903878)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_903872, _903876)), _903878), _903880)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_903872, _903876)), _903874), _903880)))], (41766 ^ _777864) ^ [_1587342, _1587344, _1587346, _1587348, _1587350, _1587352, _1587354] : [hAPP(c_Fun_Ocomp(_1587342, _1587344, _1587346, _1587348), _1587350) = _1587352, -(hAPP(_1587348, hAPP(_1587350, _1587354)) = hAPP(_1587352, _1587354))], (51201 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (13579 ^ _777864) ^ [_1006646, _1006648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006646, _1006648)), _1006646)))], (13058 ^ _777864) ^ [_996972, _996974, _996976, _996978, _996980] : [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), _996972), _996974)), _996976)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _996972), _996978)), _996980))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996976), _996972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996980), _996972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996974), _996978)))], (50859 ^ _777864) ^ [_1803924] : [-(c_List_Oremdups(_1803924, c_List_Olist_ONil(_1803924)) = c_List_Olist_ONil(_1803924))], (14444 ^ _777864) ^ [_1022110, _1022112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022110), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14447 ^ _777864 : [(14454 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022112), 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), _1022112), _1022110))))], (14448 ^ _777864) ^ [] : [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), _1022112), _1022110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (38198 ^ _777864) ^ [_1494711, _1494713] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494711, tc_HOL_Obool)), _1494713), c_Orderings_Otop__class_Otop(tc_fun(_1494711, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1494711, tc_HOL_Obool)))], (45882 ^ _777864) ^ [_1685345, _1685347, _1685349, _1685351] : [c_Fun_Oinj__on(_1685345, _1685347, _1685349, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1685345, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1685345), tc_fun(_1685345, tc_HOL_Obool), c_List_Oset(_1685345)), _1685351))), -(c_Fun_Oinj__on(tc_List_Olist(_1685345), tc_List_Olist(_1685347), hAPP(c_List_Omap(_1685345, _1685347), _1685349), _1685351))], (27482 ^ _777864) ^ [_1267239, _1267241, _1267243, _1267245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267239), _1267241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1267243), _1267245)), -(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), _1267239), _1267243)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1267241), _1267245))), c_FunDef_Opair__less)))], (39161 ^ _777864) ^ [_1517605, _1517607, _1517609, _1517611, _1517613, _1517615] : [class_Groups_Ocomm__monoid__mult(_1517605), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517607, _1517605), hAPP(hAPP(c_COMBC(_1517607, tc_fun(_1517609, tc_HOL_Obool), _1517605), hAPP(hAPP(c_COMBB(tc_fun(_1517609, _1517605), tc_fun(tc_fun(_1517609, tc_HOL_Obool), _1517605), _1517607), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1517609, _1517605)), _1517611)), _1517613)), _1517615) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1517607, _1517609), _1517605), hAPP(c_Product__Type_Oprod_Oprod__case(_1517607, _1517609, _1517605), _1517611)), hAPP(hAPP(c_Product__Type_OSigma(_1517607, _1517609), _1517615), hAPP(c_COMBK(tc_fun(_1517609, tc_HOL_Obool), _1517607), _1517613))))], (49237 ^ _777864) ^ [_1768564, _1768566, _1768568] : [-(_1768564 = c_List_Olist_ONil(_1768566)), -(c_List_Olast(_1768566, hAPP(hAPP(c_List_Oappend(_1768566), _1768568), _1768564)) = c_List_Olast(_1768566, _1768564))], (33675 ^ _777864) ^ [_1398315, _1398317, _1398319, _1398321] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398315, tc_fun(_1398317, tc_HOL_Obool)), _1398319), _1398321) = c_Orderings_Obot__class_Obot(tc_fun(_1398317, tc_HOL_Obool)), 33678 ^ _777864 : [(33679 ^ _777864) ^ [_1398431] : [hBOOL(hAPP(hAPP(c_member(_1398315), _1398431), _1398319)), -(hAPP(_1398321, _1398431) = c_Orderings_Obot__class_Obot(tc_fun(_1398317, tc_HOL_Obool)))]]], (5392 ^ _777864) ^ [_860348, _860350] : [_860350 = _860348, -(tc_Option_Ooption(_860350) = tc_Option_Ooption(_860348))], (30038 ^ _777864) ^ [_1324358, _1324360, _1324362] : [class_Lattices_Olattice(_1324358), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324358), _1324360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324358), _1324360), _1324362)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324358), _1324360), _1324362))], (18448 ^ _777864) ^ [_1095166, _1095168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1095166)), c_Int_OBit1(_1095168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095166), _1095168)))], (50020 ^ _777864) ^ [_1784918, _1784920, _1784922] : [class_Orderings_Olinorder(_1784918), 50023 ^ _777864 : [(50030 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1784918, _1784922), -(c_List_Olinorder__class_Osorted(_1784918, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1784918, _1784918, c_COMBI(_1784918)), _1784920), _1784922)))], (50024 ^ _777864) ^ [] : [c_List_Olinorder__class_Osorted(_1784918, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1784918, _1784918, c_COMBI(_1784918)), _1784920), _1784922)), -(c_List_Olinorder__class_Osorted(_1784918, _1784922))]]], (47850 ^ _777864) ^ [_1735428, _1735430, _1735432, _1735434, _1735436] : [hAPP(hAPP(c_List_Oappend(_1735428), _1735430), hAPP(hAPP(c_List_Olist_OCons(_1735428), _1735432), c_List_Olist_ONil(_1735428))) = hAPP(hAPP(c_List_Oappend(_1735428), _1735434), hAPP(hAPP(c_List_Olist_OCons(_1735428), _1735436), c_List_Olist_ONil(_1735428))), 47853 ^ _777864 : [(47856 ^ _777864) ^ [] : [-(_1735432 = _1735436)], (47854 ^ _777864) ^ [] : [-(_1735430 = _1735434)]]], (44461 ^ _777864) ^ [_1651822, _1651824, _1651826] : [-(hAPP(hAPP(c_Nat_Ocompow(_1651822, _1651822), hAPP(c_Nat_OSuc, _1651824)), _1651826) = hAPP(c_Fun_Ocomp(_1651822, _1651822, _1651822, _1651826), hAPP(hAPP(c_Nat_Ocompow(_1651822, _1651822), _1651824), _1651826)))], (42507 ^ _777864) ^ [_1604235, _1604237, _1604239] : [class_Orderings_Olinorder(_1604235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604235), _1604237)), 42517 ^ _777864 : [(42520 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1604235), _1604239), 42516 ^ [_1604235, _1604237, _1604239]))], (42518 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604235), 42516 ^ [_1604235, _1604237, _1604239]), _1604237)))]], hBOOL(hAPP(hAPP(c_member(_1604235), _1604239), _1604237)), -(c_Big__Operators_Olinorder__class_OMin(_1604235, _1604237) = _1604239)], (22442 ^ _777864) ^ [_1165759, _1165761] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165759, _1165761) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1165759, _1165761)))], (51319 ^ _777864) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (5104 ^ _777864) ^ [_856012, _856014, _856016, _856018] : [-(c_List_Ozip(_856018, _856014) = c_List_Ozip(_856016, _856012)), _856018 = _856016, _856014 = _856012], (4852 ^ _777864) ^ [_852076, _852078] : [_852078 = _852076, -(c_Groups_Oplus__class_Oplus(_852078) = c_Groups_Oplus__class_Oplus(_852076))], (26209 ^ _777864) ^ [_1238812, _1238814, _1238816, _1238818, _1238820] : [hAPP(hAPP(c_Set_Oinsert(_1238812), _1238814), hAPP(hAPP(c_Set_Oinsert(_1238812), _1238816), c_Orderings_Obot__class_Obot(tc_fun(_1238812, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1238812), _1238818), hAPP(hAPP(c_Set_Oinsert(_1238812), _1238820), c_Orderings_Obot__class_Obot(tc_fun(_1238812, tc_HOL_Obool)))), 26214 ^ _777864 : [(26217 ^ _777864) ^ [] : [-(_1238816 = _1238820)], (26215 ^ _777864) ^ [] : [-(_1238814 = _1238818)]], 26218 ^ _777864 : [(26221 ^ _777864) ^ [] : [-(_1238816 = _1238818)], (26219 ^ _777864) ^ [] : [-(_1238814 = _1238820)]]], (42060 ^ _777864) ^ [_1594179, _1594181, _1594183, _1594185, _1594187, _1594189] : [c_Finite__Set_Ofolding(_1594179, _1594181, _1594183, _1594185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594179), _1594187)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594179), _1594189)), -(hAPP(c_Fun_Ocomp(_1594181, _1594181, _1594181, hAPP(_1594185, _1594189)), hAPP(_1594185, _1594187)) = hAPP(c_Fun_Ocomp(_1594181, _1594181, _1594181, hAPP(_1594185, _1594187)), hAPP(_1594185, _1594189)))], (29000 ^ _777864) ^ [_1302018, _1302020, _1302022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1302018, _1302018), tc_HOL_Obool)), _1302020), _1302022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1302018, tc_HOL_Obool)), c_Wellfounded_Oacc(_1302018, _1302022)), c_Wellfounded_Oacc(_1302018, _1302020))))], (19604 ^ _777864) ^ [_1115255] : [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, _1115255, 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, _1115255, 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))], (47914 ^ _777864) ^ [_1736801, _1736803, _1736805, _1736807, _1736809] : [-(hAPP(hAPP(c_List_Oappend(_1736801), _1736803), _1736805) = hAPP(hAPP(c_List_Olist_OCons(_1736801), _1736807), _1736809)), 47915 ^ _777864 : [(47922 ^ _777864) ^ [_1736984] : [_1736803 = hAPP(hAPP(c_List_Olist_OCons(_1736801), _1736807), _1736984), hAPP(hAPP(c_List_Oappend(_1736801), _1736984), _1736805) = _1736809], (47916 ^ _777864) ^ [] : [_1736803 = c_List_Olist_ONil(_1736801), _1736805 = hAPP(hAPP(c_List_Olist_OCons(_1736801), _1736807), _1736809)]]], (9582 ^ _777864) ^ [_937968] : [class_Rings_Olinordered__semidom(_937968), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937968), c_Groups_Ozero__class_Ozero(_937968)), c_Groups_Oone__class_Oone(_937968))))], (15262 ^ _777864) ^ [_1036948, _1036950, _1036952] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1036950), _1036952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036948), _1036950)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036948), _1036952)))], (28721 ^ _777864) ^ [_1296361, _1296363] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296361)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296363))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1296361), _1296363)))], (11269 ^ _777864) ^ [_965639, _965641, _965643, _965645, _965647] : [c_Natural_Oevaln(_965639, _965641, _965643, _965645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965643), _965647)), -(c_Natural_Oevaln(_965639, _965641, _965647, _965645))], (38192 ^ _777864) ^ [_1494583, _1494585] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494583, tc_HOL_Obool)), _1494585), c_Orderings_Otop__class_Otop(tc_fun(_1494583, tc_HOL_Obool))) = _1494585)], (31273 ^ _777864) ^ [_1348954, _1348956, _1348958] : [class_Orderings_Olinorder(_1348954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348954), _1348956)), -(hBOOL(hAPP(hAPP(c_member(_1348954), _1348958), _1348956))), -(_1348956 = c_Orderings_Obot__class_Obot(tc_fun(_1348954, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1348954, hAPP(hAPP(c_Set_Oinsert(_1348954), _1348958), _1348956)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1348954), _1348958), c_Big__Operators_Olinorder__class_OMax(_1348954, _1348956)))], (31967 ^ _777864) ^ [_1362108, _1362110, _1362112] : [class_Orderings_Olinorder(_1362108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362108), _1362110)), -(_1362112 = c_Orderings_Obot__class_Obot(tc_fun(_1362108, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1362108, tc_HOL_Obool)), _1362112), _1362110)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1362108), c_Big__Operators_Olattice_OInf__fin(_1362108, c_Orderings_Oord__class_Omin(_1362108), _1362112)), c_Big__Operators_Olattice_OInf__fin(_1362108, c_Orderings_Oord__class_Omin(_1362108), _1362110)) = c_Big__Operators_Olattice_OInf__fin(_1362108, c_Orderings_Oord__class_Omin(_1362108), _1362110))], (6492 ^ _777864) ^ [_885097, _885099, _885101] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885099), _885101)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885097), _885101)))], (12120 ^ _777864) ^ [_980759] : [12121 ^ _777864 : [(12122 ^ _777864) ^ [_980816] : [hBOOL(hAPP(_980759, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _980816)))]], 12124 ^ _777864 : [(12127 ^ _777864) ^ [] : [-(hBOOL(hAPP(_980759, 12123 ^ [_980759])))], (12125 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12123 ^ [_980759])))]]], (50757 ^ _777864) ^ [_1801952, _1801954, _1801956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801952)), c_List_OtakeWhile(_1801952, _1801954, _1801956))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801952)), _1801956))))], (40964 ^ _777864) ^ [_1567372, _1567374] : [c_Wellfounded_Owf(_1567372, _1567374), -(c_Wellfounded_Owf(tc_fun(_1567372, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1567372, _1567374)))], (12488 ^ _777864) ^ [_987317, _987319, _987321, _987323] : [class_Rings_Olinordered__semiring(_987317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987317), _987319), _987321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987317), _987323), _987321))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987317), c_Groups_Ozero__class_Ozero(_987317)), _987321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987317), _987319), _987323)))], (47316 ^ _777864) ^ [_1723684, _1723686, _1723688, _1723690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723684), _1723686)), -(hAPP(hAPP(c_List_Onth(_1723688), hAPP(hAPP(c_List_Otake(_1723688), _1723686), _1723690)), _1723684) = hAPP(hAPP(c_List_Onth(_1723688), _1723690), _1723684))], (25687 ^ _777864) ^ [_1228511, _1228513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228511), _1228513)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228513), _1228511))], (23073 ^ _777864) ^ [_1178212, _1178214, _1178216, _1178218] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1178212, _1178214, _1178216, tc_prod(_1178214, _1178216)), _1178218), c_Product__Type_OPair(_1178214, _1178216)) = _1178218)], (11899 ^ _777864) ^ [_976889, _976891] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _976889), _976891) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11902 ^ _777864 : [(11905 ^ _777864) ^ [] : [-(_976891 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11903 ^ _777864) ^ [] : [-(_976889 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (23857 ^ _777864) ^ [_1194764, _1194766, _1194768, _1194770] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1194764), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194764), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194764), _1194766), _1194768)), _1194770) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1194764), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194764), _1194766), _1194770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194764), _1194768), _1194770)))], (36522 ^ _777864) ^ [_1458247, _1458249, _1458251] : [class_Groups_Ocomm__monoid__add(_1458247), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458249, _1458247), _1458251), c_Orderings_Obot__class_Obot(tc_fun(_1458249, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1458247))], (4710 ^ _777864) ^ [_849867, _849869, _849871, _849873] : [-(c_List_Oupto(_849873, _849869) = c_List_Oupto(_849871, _849867)), _849873 = _849871, _849869 = _849867], (44053 ^ _777864) ^ [_1641266, _1641268, _1641270, _1641272, _1641274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641268, tc_HOL_Obool)), _1641272), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1641268, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1641266, _1641268, hAPP(c_Relation_Oconverse(_1641268, _1641266), _1641270)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1641266, tc_HOL_Obool)), _1641274))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641266, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1641268, _1641266, _1641270), _1641272)), _1641274)))], (16538 ^ _777864) ^ [_1061937, _1061939, _1061941] : [class_Rings_Ocomm__semiring__1(_1061937), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061937), _1061939), hAPP(hAPP(c_Power_Opower__class_Opower(_1061937), _1061939), _1061941)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1061937), _1061939), hAPP(c_Nat_OSuc, _1061941)))], (26263 ^ _777864) ^ [_1239801, _1239803, _1239805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239801, tc_HOL_Obool)), _1239803), hAPP(hAPP(c_Set_Oinsert(_1239801), _1239805), c_Orderings_Obot__class_Obot(tc_fun(_1239801, tc_HOL_Obool))))), -(_1239803 = c_Orderings_Obot__class_Obot(tc_fun(_1239801, tc_HOL_Obool))), -(_1239803 = hAPP(hAPP(c_Set_Oinsert(_1239801), _1239805), c_Orderings_Obot__class_Obot(tc_fun(_1239801, tc_HOL_Obool))))], (23019 ^ _777864) ^ [_1177025, _1177027, _1177029, _1177031] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1177025, _1177027), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1177029), _1177031))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1177025, _1177027) = _1177031)], (40464 ^ _777864) ^ [_1550170] : [-(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)))), _1550170)) = 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), _1550170), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (13916 ^ _777864) ^ [_1012687, _1012689, _1012691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012687)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012691), _1012687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012691), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1012689), _1012691), _1012687))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012689, _1012691)))], (6125 ^ _777864) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1302 ^ _777864) ^ [_796907, _796909] : [-(class_Lattices_Oboolean__algebra(_796907)), _796909 = _796907, class_Lattices_Oboolean__algebra(_796909)], (17970 ^ _777864) ^ [_1087555] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1087555) = _1087555)], (27584 ^ _777864) ^ [_1269062, _1269064] : [class_Int_Oring__char__0(_1269062), hBOOL(hAPP(hAPP(c_member(_1269062), _1269064), c_Int_Oring__1__class_OInts(_1269062))), 27591 ^ _777864 : [(27598 ^ _777864) ^ [] : [_1269064 = c_Groups_Ozero__class_Ozero(_1269062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269062), _1269064), _1269064) = c_Groups_Ozero__class_Ozero(_1269062))], (27592 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1269062), _1269064), _1269064) = c_Groups_Ozero__class_Ozero(_1269062), -(_1269064 = c_Groups_Ozero__class_Ozero(_1269062))]]], (49494 ^ _777864) ^ [_1773852, _1773854] : [-(hAPP(c_List_Ofilter(_1773852, _1773854), c_List_Olist_ONil(_1773852)) = c_List_Olist_ONil(_1773852))], (9642 ^ _777864) ^ [_939028, _939030] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939028)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _939030), 9645 ^ _777864 : [(9648 ^ _777864) ^ [] : [-(_939030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9646 ^ _777864) ^ [] : [-(_939028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4448 ^ _777864) ^ [_845892, _845894] : [_845894 = _845892, -(c_Orderings_Oord__class_Omin(_845894) = c_Orderings_Oord__class_Omin(_845892))], (37378 ^ _777864) ^ [_1478636, _1478638, _1478640, _1478642, _1478644] : [class_Groups_Ocomm__monoid__add(_1478636), class_Groups_Oordered__ab__semigroup__add(_1478636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478638), _1478640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478638, tc_HOL_Obool)), _1478642), _1478640)), 37396 ^ _777864 : [(37399 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1478636), c_Groups_Ozero__class_Ozero(_1478636)), hAPP(_1478644, 37395 ^ [_1478636, _1478638, _1478640, _1478642, _1478644])))], (37397 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478638), 37395 ^ [_1478636, _1478638, _1478640, _1478642, _1478644]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478638, tc_HOL_Obool)), _1478640), _1478642))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1478636), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478638, _1478636), _1478644), _1478642)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478638, _1478636), _1478644), _1478640))))], (32401 ^ _777864) ^ [_1370344, _1370346, _1370348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370344), _1370346)), 32404 ^ _777864 : [(32411 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370344), _1370348), _1370346))), -(hAPP(c_Finite__Set_Ocard(_1370344), hAPP(hAPP(c_Set_Oinsert(_1370344), _1370348), _1370346)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1370344), _1370346)))], (32405 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1370344), _1370348), _1370346)), -(hAPP(c_Finite__Set_Ocard(_1370344), hAPP(hAPP(c_Set_Oinsert(_1370344), _1370348), _1370346)) = hAPP(c_Finite__Set_Ocard(_1370344), _1370346))]]], (7622 ^ _777864) ^ [_904175, _904177] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_904175, _904177))), -(hBOOL(hAPP(c_Com_OWT, _904177)))], (20134 ^ _777864) ^ [_1124982, _1124984, _1124986, _1124988] : [class_Rings_Odivision__ring(_1124982), -(_1124984 = c_Groups_Ozero__class_Ozero(_1124982)), 20141 ^ _777864 : [(20148 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124982), _1124986), _1124984) = _1124988, -(_1124986 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124982), _1124988), _1124984))], (20142 ^ _777864) ^ [] : [_1124986 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1124982), _1124988), _1124984), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124982), _1124986), _1124984) = _1124988)]]], (12770 ^ _777864) ^ [_992233] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _992233))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _992233)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20360 ^ _777864) ^ [_1128497, _1128499, _1128501] : [class_Rings_Odivision__ring(_1128497), -(_1128499 = c_Groups_Ozero__class_Ozero(_1128497)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1128497), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128497), _1128501), _1128499)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128497), _1128501), hAPP(c_Groups_Ouminus__class_Ouminus(_1128497), _1128499)))], (51221 ^ _777864) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (10340 ^ _777864) ^ [_950358, _950360, _950362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950360), _950362)), -(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, _950358)), _950360)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950358)), _950362))))], (34131 ^ _777864) ^ [_1410312, _1410314, _1410316, _1410318] : [class_Groups_Ocomm__monoid__mult(_1410312), 34134 ^ _777864 : [(34141 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1410314), _1410316))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410314, _1410312), _1410318), _1410316) = c_Groups_Oone__class_Oone(_1410312))], (34135 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1410314), _1410316)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1410314, _1410312), _1410318), _1410316) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1410312, _1410314, c_Groups_Otimes__class_Otimes(_1410312)), _1410318), c_Groups_Oone__class_Oone(_1410312)), _1410316))]]], (4284 ^ _777864) ^ [_843404, _843406, _843408, _843410, _843412, _843414] : [-(c_Map_Odom(_843414, _843410, _843406) = c_Map_Odom(_843412, _843408, _843404)), _843414 = _843412, _843410 = _843408, _843406 = _843404], (37667 ^ _777864) ^ [_1484434, _1484436, _1484438] : [class_Orderings_Oorder(_1484434), 37670 ^ _777864 : [(37677 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484434), _1484438), _1484436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484434, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484434), _1484436)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484434), _1484438))))], (37671 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484434, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484434), _1484436)), hAPP(c_SetInterval_Oord__class_OatLeast(_1484434), _1484438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484434), _1484438), _1484436)))]]], (43211 ^ _777864) ^ [_1618893, _1618895, _1618897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618893, _1618893)), _1618895), _1618897)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618893, _1618893)), _1618895), c_Transitive__Closure_Ortrancl(_1618893, _1618897))))], (14380 ^ _777864) ^ [_1021012, _1021014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1021012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1021014), _1021012)), _1021014)))], (36132 ^ _777864) ^ [_1450421, _1450423, _1450425, _1450427, _1450429] : [hAPP(_1450425, _1450427) = _1450429, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450421, _1450423), _1450425), _1450427), _1450429) = _1450425)], (18406 ^ _777864) ^ [_1094369, _1094371] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1094369)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094371)) = 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)))), _1094369)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094371)))], (15408 ^ _777864) ^ [_1040001, _1040003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040001), _1040003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1040001), _1040003)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33418 ^ _777864) ^ [_1392098, _1392100, _1392102, _1392104] : [class_Orderings_Olinorder(_1392098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392098), _1392100), _1392102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392098), _1392102), _1392104)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392098, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392098, _1392100, _1392102)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392098, _1392102, _1392104)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1392098, _1392100, _1392104))], (19352 ^ _777864) ^ [_1110619] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110619), _1110619)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1110619)], (41574 ^ _777864) ^ [_1582636] : [-(_1582636 = hAPP(c_Int_OAbs__Integ, 41572 ^ [_1582636]))], (27354 ^ _777864) ^ [_1264332] : [class_Rings_Osemiring__1(_1264332), -(hBOOL(hAPP(hAPP(c_member(_1264332), c_Groups_Ozero__class_Ozero(_1264332)), c_Nat_Osemiring__1__class_ONats(_1264332))))], (41834 ^ _777864) ^ [_1588819, _1588821, _1588823, _1588825, _1588827, _1588829] : [class_Groups_Ocomm__monoid__add(_1588819), c_Fun_Oinj__on(_1588821, _1588823, _1588825, _1588827), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1588823, _1588819), _1588829), hAPP(c_Set_Oimage(_1588821, _1588823, _1588825), _1588827)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1588821, _1588819), hAPP(c_Fun_Ocomp(_1588823, _1588819, _1588821, _1588829), _1588825)), _1588827))], (45628 ^ _777864) ^ [_1679294, _1679296, _1679298, _1679300, _1679302, _1679304, _1679306] : [c_Fun_Oinj__on(_1679294, _1679296, _1679298, c_Orderings_Otop__class_Otop(tc_fun(_1679294, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1679294, _1679300, _1679302), _1679304) = hAPP(c_Option_Ooption_OSome(_1679300), _1679306), -(hAPP(c_Map_Omap__of(_1679296, _1679300, hAPP(hAPP(c_List_Omap(tc_prod(_1679294, _1679300), tc_prod(_1679296, _1679300)), hAPP(c_Product__Type_Oprod_Oprod__case(_1679294, _1679300, tc_prod(_1679296, _1679300)), hAPP(hAPP(c_COMBB(_1679296, tc_fun(_1679300, tc_prod(_1679296, _1679300)), _1679294), c_Product__Type_OPair(_1679296, _1679300)), _1679298))), _1679302)), hAPP(_1679298, _1679304)) = hAPP(c_Option_Ooption_OSome(_1679300), _1679306))], (12652 ^ _777864) ^ [_990384, _990386] : [class_Rings_Olinordered__idom(_990384), 12655 ^ _777864 : [(12662 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990384), _990386), c_Groups_Ozero__class_Ozero(_990384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990384), c_Groups_Osgn__class_Osgn(_990384, _990386)), c_Groups_Ozero__class_Ozero(_990384))))], (12656 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990384), c_Groups_Osgn__class_Osgn(_990384, _990386)), c_Groups_Ozero__class_Ozero(_990384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990384), _990386), c_Groups_Ozero__class_Ozero(_990384))))]]], (36042 ^ _777864) ^ [_1448732, _1448734] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448732), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1448734) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1448732, _1448734))], (43941 ^ _777864) ^ [_1638086, _1638088, _1638090, _1638092] : [-(hAPP(c_Set_OCollect(_1638086), hAPP(hAPP(c_COMBB(tc_fun(_1638088, tc_HOL_Obool), tc_HOL_Obool, _1638086), c_HOL_OAll(_1638088)), hAPP(hAPP(c_COMBB(tc_fun(_1638088, tc_HOL_Obool), tc_fun(_1638088, tc_HOL_Obool), _1638086), hAPP(c_COMBS(_1638088, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1638088), c_fimplies), hAPP(hAPP(c_COMBC(_1638088, tc_fun(_1638088, tc_HOL_Obool), tc_HOL_Obool), c_member(_1638088)), _1638090)))), _1638092))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638088, tc_fun(_1638086, tc_HOL_Obool)), _1638090), hAPP(hAPP(c_COMBB(tc_fun(_1638086, tc_HOL_Obool), tc_fun(_1638086, tc_HOL_Obool), _1638088), c_Set_OCollect(_1638086)), hAPP(c_COMBC(_1638086, _1638088, tc_HOL_Obool), _1638092))))], (9850 ^ _777864) ^ [_942536] : 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hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1324233), _1324235), _1324237))], (23053 ^ _777864) ^ [_1177689, _1177691, _1177693, _1177695, _1177697, _1177699, _1177701] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1177689, _1177691, _1177693, _1177695), _1177697), _1177699), _1177701) = hAPP(hAPP(_1177699, hAPP(c_Product__Type_Ofst(_1177691, _1177693), hAPP(_1177697, _1177701))), hAPP(c_Product__Type_Osnd(_1177691, _1177693), hAPP(_1177697, _1177701))))], (39672 ^ _777864) ^ [_1528672, _1528674, _1528676, _1528678] : [c_Big__Operators_Osemilattice__big(_1528672, _1528674, _1528676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528672), _1528678)), -(hAPP(_1528676, _1528678) = hAPP(c_Finite__Set_Ofold1(_1528672, _1528674), _1528678))], (19512 ^ _777864) ^ [_1113336, _1113338, _1113340] : [class_Rings_Olinordered__idom(_1113336), 19515 ^ _777864 : [(19524 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113336), hAPP(hAPP(c_Power_Opower__class_Opower(_1113336), _1113338), 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(_1113336), _1113340), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1113336)))), _1113338 = c_Groups_Ozero__class_Ozero(_1113336), _1113340 = c_Groups_Ozero__class_Ozero(_1113336)], (19516 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1113336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113336), hAPP(hAPP(c_Power_Opower__class_Opower(_1113336), _1113338), 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(_1113336), _1113340), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1113336))), 19519 ^ _777864 : [(19522 ^ _777864) ^ [] : [-(_1113340 = c_Groups_Ozero__class_Ozero(_1113336))], (19520 ^ _777864) ^ [] : [-(_1113338 = c_Groups_Ozero__class_Ozero(_1113336))]]]]], (43655 ^ _777864) ^ [_1628971, _1628973, _1628975, _1628977, _1628979] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628971, tc_fun(_1628973, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1628971, tc_HOL_Obool)), _1628975), _1628977)), _1628979) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628973, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628971, tc_fun(_1628973, tc_HOL_Obool)), _1628975), _1628979)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628971, tc_fun(_1628973, tc_HOL_Obool)), _1628977), _1628979)))], (30168 ^ _777864) ^ [_1326964, _1326966, _1326968, _1326970] : [-(hBOOL(hAPP(hAPP(c_member(_1326964), _1326966), _1326968))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326964, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1326964), _1326966), _1326970)), _1326968) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326964, tc_HOL_Obool)), _1326970), _1326968))], (6000 ^ _777864) ^ [_876469, _876471, _876473] : [c_Com_Ocom_OAss(_876469, _876471) = hAPP(c_Com_Ocom_OBODY, _876473)], (7404 ^ _777864) ^ [_899895, _899897, _899899, _899901] : [c_Com_Ocom_OCond(_899895, _899897, _899899) = hAPP(c_Com_Ocom_OBODY, _899901)], (24707 ^ _777864) ^ [_1211370, _1211372, _1211374, _1211376, _1211378] : [-(hAPP(c_New__DSequence_Opos__bind(_1211370, _1211372, _1211374, _1211376), _1211378) = c_Lazy__Sequence_Obind(_1211370, _1211372, hAPP(_1211374, _1211378), hAPP(hAPP(c_COMBC(_1211370, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1211372)), _1211376), _1211378)))], (36752 ^ _777864) ^ [_1464102, _1464104, _1464106] : [class_Groups_Ocomm__monoid__add(_1464102), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464102), _1464104), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1464106))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464102), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464102), _1464104), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1464106))), hAPP(_1464104, _1464106)))], (16640 ^ _777864) ^ [_1064036, _1064038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064036)), -(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), _1064036), _1064038))))], (10410 ^ _777864) ^ [_951649, _951651] : [-(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), _951649), _951651)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _951649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _951651))], (1878 ^ _777864) ^ [_805071, _805073, _805075, _805077, _805079, _805081, _805083, _805085] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_805085, _805081, _805077, _805073) = c_Hoare__Mirabelle_Otriple_Otriple__case(_805083, _805079, _805075, _805071)), _805085 = _805083, _805081 = _805079, _805077 = _805075, _805073 = _805071], (17972 ^ _777864) ^ [_1087581] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1087581) = c_Int_OPls)], (43817 ^ _777864) ^ [_1634186, _1634188, _1634190, _1634192, _1634194, _1634196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634188, _1634190)), hAPP(hAPP(c_Product__Type_OPair(_1634188, _1634190), _1634194), _1634196)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634186, tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1634186, tc_HOL_Obool))), _1634192))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1634186, tc_fun(_1634188, tc_fun(_1634190, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1634186, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_fun(_1634188, tc_fun(_1634190, tc_HOL_Obool)), _1634186), hAPP(c_COMBC(_1634188, tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_fun(_1634190, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634190, tc_fun(tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_fun(_1634190, tc_HOL_Obool)), _1634188), c_COMBC(_1634190, tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1634190, tc_prod(_1634188, _1634190)), tc_fun(_1634190, tc_fun(tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_HOL_Obool)), _1634188), hAPP(c_COMBB(tc_prod(_1634188, _1634190), tc_fun(tc_fun(tc_prod(_1634188, _1634190), tc_HOL_Obool), tc_HOL_Obool), _1634190), c_member(tc_prod(_1634188, _1634190)))), c_Product__Type_OPair(_1634188, _1634190))))), _1634192)), _1634194), _1634196)))], (2812 ^ _777864) ^ [_819922, _819924] : [_819924 = _819922, -(c_Lazy__Sequence_Ohit__bound(_819924) = c_Lazy__Sequence_Ohit__bound(_819922))], (6386 ^ _777864) ^ [_883285, _883287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _883285), _883287)), _883285 = _883287], (40178 ^ _777864) ^ [_1540638, _1540640] : [-(hAPP(c_Set_OCollect(_1540638), _1540640) = _1540640)], (45803 ^ _777864) ^ [_1683608] : [-(hAPP(c_Option_Omap(_1683608, _1683608), c_COMBI(_1683608)) = c_Fun_Oid(tc_Option_Ooption(_1683608)))], (22935 ^ _777864) ^ [_1175595, _1175597, _1175599] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175595, _1175597), _1175599)), 22938 ^ _777864 : [(22947 ^ _777864) ^ [] : [-(_1175597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22950 ^ _777864 : [(22959 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175597))), 22962 ^ _777864 : [(22965 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1175599)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22963 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1175597), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1175599))))]]], (22951 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175597)), 22954 ^ _777864 : [(22957 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1175599)), _1175597)))], (22955 ^ _777864) ^ [] : [-(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), _1175599))))]]]]], (22941 ^ _777864) ^ [] : [_1175597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1175599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22939 ^ _777864) ^ [] : [-(_1175595 = 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), _1175599)), _1175597)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1175599)))]]], (5896 ^ _777864) ^ [_874669, _874671, _874673, _874675] : [-(c_Hoare__Mirabelle_Otriple__valid(_874669, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_874669), _874671), hAPP(c_Com_Ocom_OBODY, _874673)), _874675)))], (28396 ^ _777864) ^ [_1287715, _1287717, _1287719, _1287721, _1287723, _1287725] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1287715, _1287715)), hAPP(hAPP(c_Product__Type_OPair(_1287715, _1287715), _1287717), _1287719)), hAPP(hAPP(c_Relation_Oinv__image(_1287721, _1287715), _1287723), _1287725))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1287721, _1287721)), hAPP(hAPP(c_Product__Type_OPair(_1287721, _1287721), hAPP(_1287725, _1287717)), hAPP(_1287725, _1287719))), _1287723)))], (4832 ^ _777864) ^ [_851770, _851772, _851774, _851776, _851778, _851780] : [-(c_List_Olinorder__class_Oinsort__key(_851780, _851776, _851772) = c_List_Olinorder__class_Oinsort__key(_851778, _851774, _851770)), _851780 = _851778, _851776 = _851774, _851772 = _851770], (47518 ^ _777864) ^ [_1727964, _1727966, _1727968, _1727970, _1727972, _1727974] : [-(_1727964 = _1727966), -(hAPP(hAPP(c_List_Olist__update(_1727968, hAPP(hAPP(c_List_Olist__update(_1727968, _1727970), _1727964), _1727972)), _1727966), _1727974) = hAPP(hAPP(c_List_Olist__update(_1727968, hAPP(hAPP(c_List_Olist__update(_1727968, _1727970), _1727966), _1727974)), _1727964), _1727972))], (1012 ^ _777864) ^ [_793282, _793284] : [-(class_Rings_Oring__1__no__zero__divisors(_793282)), _793284 = _793282, class_Rings_Oring__1__no__zero__divisors(_793284)], (10758 ^ _777864) ^ [_956944, _956946, _956948] : [class_Orderings_Olinorder(_956944), 10761 ^ _777864 : [(10768 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956944), _956948), _956946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956944), _956946), _956948))], (10762 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956944), _956946), _956948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956944), _956948), _956946)))]]], (36712 ^ _777864) ^ [_1463211, _1463213, _1463215, _1463217, _1463219] : [class_Groups_Ocomm__monoid__add(_1463211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463213), _1463215)), 36719 ^ _777864 : [(36726 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1463213), _1463217), _1463215))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463213, _1463211), hAPP(hAPP(c_COMBC(_1463213, _1463211, _1463211), hAPP(hAPP(c_COMBS(_1463213, _1463211, tc_fun(_1463211, _1463211)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1463211, tc_fun(_1463211, _1463211)), _1463213), c_If(_1463211)), hAPP(c_fequal, _1463217))), _1463219)), c_Groups_Ozero__class_Ozero(_1463211))), _1463215) = c_Groups_Ozero__class_Ozero(_1463211))], (36720 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1463213), _1463217), _1463215)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463213, _1463211), hAPP(hAPP(c_COMBC(_1463213, _1463211, _1463211), hAPP(hAPP(c_COMBS(_1463213, _1463211, tc_fun(_1463211, _1463211)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1463211, tc_fun(_1463211, _1463211)), _1463213), c_If(_1463211)), hAPP(c_fequal, _1463217))), _1463219)), c_Groups_Ozero__class_Ozero(_1463211))), _1463215) = hAPP(_1463219, _1463217))]]], (37004 ^ _777864) ^ [_1469813, _1469815, _1469817, _1469819, _1469821] : [class_Groups_Ocomm__monoid__add(_1469813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469815), _1469817)), hBOOL(hAPP(hAPP(c_member(_1469815), _1469819), _1469817)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469815, _1469813), _1469821), _1469817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469813), hAPP(_1469821, _1469819)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469815, _1469813), _1469821), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469815, tc_HOL_Obool)), _1469817), hAPP(hAPP(c_Set_Oinsert(_1469815), _1469819), c_Orderings_Obot__class_Obot(tc_fun(_1469815, tc_HOL_Obool)))))))], (4810 ^ _777864) ^ [_851451, _851453] : [_851453 = _851451, -(c_Finite__Set_Ofinite(_851453) = c_Finite__Set_Ofinite(_851451))], (41802 ^ _777864) ^ [_1588201, _1588203, _1588205, _1588207, _1588209, _1588211] : [c_Fun_Oinj__on(_1588201, _1588203, _1588205, _1588207), c_Fun_Oinj__on(_1588203, _1588209, _1588211, hAPP(c_Set_Oimage(_1588201, _1588203, _1588205), _1588207)), -(c_Fun_Oinj__on(_1588201, _1588209, hAPP(c_Fun_Ocomp(_1588203, _1588209, _1588201, _1588211), _1588205), _1588207))], (7941 ^ _777864) ^ [] : [-(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))], (41936 ^ _777864) ^ [_1591034, _1591036, _1591038, _1591040, _1591042, _1591044] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1591034, _1591036), _1591034, tc_prod(_1591038, _1591040), c_Product__Type_Ofst(_1591034, _1591036)), c_Product__Type_Omap__pair(_1591038, _1591034, _1591040, _1591036, _1591042, _1591044)) = hAPP(c_Fun_Ocomp(_1591038, _1591034, tc_prod(_1591038, _1591040), _1591042), c_Product__Type_Ofst(_1591038, _1591040)))], (48548 ^ _777864) ^ [_1753201, _1753203, _1753205] : [-(hAPP(hAPP(c_List_Odrop(_1753201), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1753201), _1753203), _1753205)) = _1753205)], (27730 ^ _777864) ^ [_1271843, _1271845, _1271847, _1271849] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271843, tc_HOL_Obool)), _1271845), _1271847), _1271849)), -(hBOOL(hAPP(_1271845, _1271849))), -(hBOOL(hAPP(_1271847, _1271849)))], (7488 ^ _777864) ^ [_901623, _901625, _901627, _901629, _901631, _901633] : [c_Com_Ocom_OLocal(_901623, _901625, _901627) = c_Com_Ocom_OCond(_901629, _901631, _901633)], (30675 ^ _777864) ^ [_1338760, _1338762] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338760), _1338762)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338762, _1338760) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51027 ^ _777864) ^ [_1807067, _1807069] : [class_Complete__Lattice_Ocomplete__lattice(_1807067), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1807069, _1807067)))], (1602 ^ _777864) ^ [_800657, _800659] : [-(class_Nat_Osemiring__char__0(_800657)), _800659 = _800657, class_Nat_Osemiring__char__0(_800659)], (50076 ^ _777864) ^ [_1785811, _1785813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1785811), _1785813))), -(c_List_Oupt(_1785811, _1785813) = c_List_Olist_ONil(tc_Nat_Onat))], (47088 ^ _777864) ^ [_1717407, _1717409, _1717411] : [-(_1717407 = _1717409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717411)), _1717407) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717411)), _1717409), 47094 ^ _777864 : [(47097 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Onth(_1717411), _1717407), 47093 ^ [_1717407, _1717409, _1717411]) = hAPP(hAPP(c_List_Onth(_1717411), _1717409), 47093 ^ [_1717407, _1717409, _1717411])], (47095 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47093 ^ [_1717407, _1717409, _1717411]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717411)), _1717407))))]]], (28739 ^ _777864) ^ [_1296735, _1296737] : [-(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), _1296735), _1296737)), 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), _1296735), _1296737))], (5180 ^ _777864) ^ [_857148, _857150, _857152, _857154] : [-(c_List_Ofilter(_857154, _857150) = c_List_Ofilter(_857152, _857148)), _857154 = _857152, _857150 = _857148], (8722 ^ _777864) ^ [_922533, _922535] : [class_Groups_Ocomm__monoid__mult(_922533), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922533), c_Groups_Oone__class_Oone(_922533)), _922535) = _922535)], (50935 ^ _777864) ^ [_1805216, _1805218, _1805220] : [hBOOL(hAPP(hAPP(c_member(_1805216), _1805218), hAPP(c_List_Oset(_1805216), _1805220))), -(c_List_Oremdups(_1805216, hAPP(hAPP(c_List_Olist_OCons(_1805216), _1805218), _1805220)) = c_List_Oremdups(_1805216, _1805220))], (6123 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10662 ^ _777864) ^ [_955595, _955597, _955599] : [class_Orderings_Olinorder(_955595), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955595), _955597), _955599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955595), _955599), _955597)))], (17000 ^ _777864) ^ [_1070978] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1070978) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43945 ^ _777864) ^ [_1638248, _1638250, _1638252] : [c_Equiv__Relations_Oequiv(_1638248, _1638250, _1638252), -(hAPP(hAPP(c_Relation_Orel__comp(_1638248, _1638248, _1638248), hAPP(c_Relation_Oconverse(_1638248, _1638248), _1638252)), _1638252) = _1638252)], (18940 ^ _777864) ^ [_1103401, _1103403] : [c_Int_OBit1(_1103401) = c_Int_OBit0(_1103403)], (41309 ^ _777864) ^ [_1575401, _1575403, _1575405] : [_1575405 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575401, _1575403), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1575401, _1575403), _1575405) = c_Orderings_Obot__class_Obot(tc_fun(_1575401, tc_HOL_Obool)))], (34883 ^ _777864) ^ [_1425526, _1425528, _1425530, _1425532] : [class_Orderings_Oorder(_1425526), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425526, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1425526, _1425528, _1425530)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1425526, _1425530, _1425532)) = c_Orderings_Obot__class_Obot(tc_fun(_1425526, tc_HOL_Obool)))], (36034 ^ _777864) ^ [_1448566, _1448568] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1448566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448568), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1448566, _1448568))], (330 ^ _777864) ^ [_782835, _782837, _782839, _782841] : [-(c_Equiv__Relations_Oequivp(_782839, _782835)), c_Equiv__Relations_Oequivp(_782841, _782837), _782841 = _782839, _782837 = _782835], (27123 ^ _777864) ^ [_1258208, _1258210, _1258212] : [hBOOL(hAPP(hAPP(c_member(_1258208), _1258210), hAPP(hAPP(c_Set_Oinsert(_1258208), _1258212), c_Orderings_Obot__class_Obot(tc_fun(_1258208, tc_HOL_Obool))))), -(_1258210 = _1258212)], (17964 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (16730 ^ _777864) ^ [_1065897, _1065899, _1065901, _1065903, _1065905] : [class_Groups_Oordered__ab__group__add__abs(_1065897), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065897), hAPP(c_Groups_Oabs__class_Oabs(_1065897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065897), _1065899), _1065901)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065897), _1065903), _1065905)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1065897), hAPP(c_Groups_Oabs__class_Oabs(_1065897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065897), _1065899), _1065903))), hAPP(c_Groups_Oabs__class_Oabs(_1065897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1065897), _1065901), _1065905))))))], (17032 ^ _777864) ^ [_1071472, _1071474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1071472)), -(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), _1071472), _1071474))))], (51163 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (14832 ^ _777864) ^ [_1029170, _1029172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029170)), -(c_SMT_Oz3div(_1029172, _1029170) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029172), _1029170))], (2788 ^ _777864) ^ [_819536, _819538] : [_819538 = _819536, -(c_Lazy__Sequence_Oempty(_819538) = c_Lazy__Sequence_Oempty(_819536))], (12091 ^ _777864) ^ [_980307] : [-(hAPP(c_Nat_OSuc, _980307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _980307), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44393 ^ _777864) ^ [_1650054, _1650056, _1650058] : [44394 ^ _777864 : [(44395 ^ _777864) ^ [_1650130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1650054, _1650054)), _1650056), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650054, _1650054), tc_HOL_Obool), _1650130), _1650058)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650054, _1650054)), _1650056), c_Transitive__Closure_Ortrancl(_1650054, _1650058))))], (43727 ^ _777864) ^ [_1631150, _1631152, _1631154, _1631156, _1631158] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631150, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631152, tc_fun(_1631150, tc_HOL_Obool)), _1631154), _1631156)), _1631158) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631152, tc_fun(_1631150, tc_HOL_Obool)), _1631154), hAPP(hAPP(c_COMBC(_1631152, tc_fun(_1631150, tc_HOL_Obool), tc_fun(_1631150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1631150, tc_HOL_Obool), tc_fun(tc_fun(_1631150, tc_HOL_Obool), tc_fun(_1631150, tc_HOL_Obool)), _1631152), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1631150, tc_HOL_Obool))), _1631156)), _1631158)))], (24795 ^ _777864) ^ [_1213209, _1213211, _1213213, _1213215] : [class_Rings_Odvd(_1213209), _1213211 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213209), _1213213), _1213215), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213209), _1213213), _1213211)))], (24491 ^ _777864) ^ [_1207084, _1207086, _1207088] : [-(c_HOL_OThe(tc_prod(_1207084, _1207086), _1207088) = c_HOL_OThe(tc_prod(_1207084, _1207086), hAPP(c_Product__Type_Oprod_Oprod__case(_1207084, _1207086, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1207086, tc_prod(_1207084, _1207086)), tc_fun(_1207086, tc_HOL_Obool), _1207084), hAPP(c_COMBB(tc_prod(_1207084, _1207086), tc_HOL_Obool, _1207086), _1207088)), c_Product__Type_OPair(_1207084, _1207086)))))], (28595 ^ _777864) ^ [_1292732, _1292734, _1292736, _1292738, _1292740] : [-(hBOOL(hAPP(hAPP(c_member(_1292732), _1292734), hAPP(c_Relation_OImage(_1292736, _1292732, _1292738), _1292740)))), 28596 ^ _777864 : [(28597 ^ _777864) ^ [_1292818] : [hBOOL(hAPP(hAPP(c_member(_1292736), _1292818), _1292740)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1292736, _1292732)), hAPP(hAPP(c_Product__Type_OPair(_1292736, _1292732), _1292818), _1292734)), _1292738))]]], (23633 ^ _777864) ^ [_1190548, _1190550] : [class_Orderings_Olinorder(_1190548), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190548), _1190550), _1190550) = _1190550)], (50472 ^ _777864) ^ [_1794388, _1794390, _1794392] : [-(c_List_Oconcat(_1794388, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1794388)), _1794390), _1794392)) = hAPP(hAPP(c_List_Oappend(_1794388), _1794390), c_List_Oconcat(_1794388, _1794392)))], (22853 ^ _777864) ^ [_1173790, _1173792] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173790, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173790, tc_HOL_Obool)), _1173792)) = _1173792)], (38488 ^ _777864) ^ [_1500352, _1500354, _1500356, _1500358, _1500360] : [c_Fun_Oinj__on(_1500352, _1500354, _1500356, c_Orderings_Otop__class_Otop(tc_fun(_1500352, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1500352, _1500354, _1500356), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500352, tc_HOL_Obool)), _1500358), _1500360)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500354, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1500352, _1500354, _1500356), _1500358)), hAPP(c_Set_Oimage(_1500352, _1500354, _1500356), _1500360)))], (12043 ^ _777864) ^ [_979444, _979446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979444), _979446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _979444)), _979446)))], (11917 ^ _777864) ^ [_977143, _977145] : [class_Rings_Olinordered__semidom(_977143), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977143), c_Groups_Ozero__class_Ozero(_977143)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_977143), _977145))))], (18702 ^ _777864) ^ [_1099188, _1099190] : [class_Int_Onumber__ring(_1099188), class_Rings_Olinordered__idom(_1099188), 18709 ^ _777864 : [(18716 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1099190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099188), c_Groups_Oone__class_Oone(_1099188)), hAPP(c_Int_Onumber__class_Onumber__of(_1099188), _1099190))))], (18710 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099188), c_Groups_Oone__class_Oone(_1099188)), hAPP(c_Int_Onumber__class_Onumber__of(_1099188), _1099190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1099190)))]]], (36856 ^ _777864) ^ [_1466248, _1466250, _1466252, _1466254] : [class_Groups_Ocomm__monoid__add(_1466248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466250), _1466252)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466248), _1466254), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1466250), _1466252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1466248), hAPP(_1466254, _1466250)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466248), _1466254), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1466250)), _1466252))))], (11090 ^ _777864) ^ [_962524, _962526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962524), _962526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962524), _962526)))], (47454 ^ _777864) ^ [_1726511, _1726513, _1726515, _1726517, _1726519, _1726521, _1726523] : [-(hAPP(hAPP(c_List_Ozip(_1726511, _1726513), hAPP(hAPP(c_List_Olist__update(_1726511, _1726515), _1726517), _1726519)), hAPP(hAPP(c_List_Olist__update(_1726513, _1726521), _1726517), _1726523)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1726511, _1726513), hAPP(hAPP(c_List_Ozip(_1726511, _1726513), _1726515), _1726521)), _1726517), hAPP(hAPP(c_Product__Type_OPair(_1726511, _1726513), _1726519), _1726523)))], (47830 ^ _777864) ^ [_1734711, _1734713, _1734715, _1734717, _1734719, _1734721] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734711)), _1734713) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734715)), _1734717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734711, tc_HOL_Obool)), hAPP(c_List_Oset(_1734711), _1734713)), _1734719)), -(c_Map_Orestrict__map(_1734711, _1734715, c_Map_Omap__upds(_1734711, _1734715, _1734721, _1734713, _1734717), _1734719) = c_Map_Omap__upds(_1734711, _1734715, c_Map_Orestrict__map(_1734711, _1734715, _1734721, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1734711, tc_HOL_Obool)), _1734719), hAPP(c_List_Oset(_1734711), _1734713))), _1734713, _1734717))], (21414 ^ _777864) ^ [_1147585, _1147587, _1147589, _1147591] : [class_Fields_Olinordered__field__inverse__zero(_1147585), class_Int_Onumber(_1147585), 21421 ^ _777864 : [(21422 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147585), _1147589), _1147591))), 21425 ^ _777864 : [(21432 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), c_Groups_Ozero__class_Ozero(_1147585)), _1147591))), 21435 ^ _777864 : [(21442 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147591), c_Groups_Ozero__class_Ozero(_1147585)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), c_Groups_Ozero__class_Ozero(_1147585))))], (21436 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147591), c_Groups_Ozero__class_Ozero(_1147585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), _1147591))))]]], (21426 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), c_Groups_Ozero__class_Ozero(_1147585)), _1147591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), _1147591)), _1147589)))]]], (21448 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147585), _1147589), _1147591)))), 21451 ^ _777864 : [(21454 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), _1147591)), _1147589))], (21452 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), c_Groups_Ozero__class_Ozero(_1147585)), _1147591)))]], 21455 ^ _777864 : [(21458 ^ _777864) ^ [] : [21459 ^ _777864 : [(21462 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), _1147591)))], (21460 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147591), c_Groups_Ozero__class_Ozero(_1147585))))]], 21463 ^ _777864 : [(21466 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), hAPP(c_Int_Onumber__class_Onumber__of(_1147585), _1147587)), c_Groups_Ozero__class_Ozero(_1147585)))], (21464 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), _1147591), c_Groups_Ozero__class_Ozero(_1147585)))]]], (21456 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147585), c_Groups_Ozero__class_Ozero(_1147585)), _1147591))]]]]], (32751 ^ _777864) ^ [_1377868, _1377870, _1377872, _1377874, _1377876, _1377878] : [class_Groups_Ocomm__monoid__mult(_1377868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377870), _1377872)), 32758 ^ _777864 : [(32765 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377870), _1377874), _1377872))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377870, _1377868), hAPP(hAPP(c_COMBC(_1377870, _1377868, _1377868), hAPP(hAPP(c_COMBS(_1377870, _1377868, tc_fun(_1377868, _1377868)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1377868, tc_fun(_1377868, _1377868)), _1377870), c_If(_1377868)), hAPP(hAPP(c_COMBC(_1377870, _1377870, tc_HOL_Obool), c_fequal), _1377874))), _1377876)), _1377878)), _1377872) = hAPP(hAPP(c_Power_Opower__class_Opower(_1377868), _1377878), hAPP(c_Finite__Set_Ocard(_1377870), _1377872)))], (32759 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1377870), _1377874), _1377872)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377870, _1377868), hAPP(hAPP(c_COMBC(_1377870, _1377868, _1377868), hAPP(hAPP(c_COMBS(_1377870, _1377868, tc_fun(_1377868, _1377868)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1377868, tc_fun(_1377868, _1377868)), _1377870), c_If(_1377868)), hAPP(hAPP(c_COMBC(_1377870, _1377870, tc_HOL_Obool), c_fequal), _1377874))), _1377876)), _1377878)), _1377872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377868), hAPP(_1377876, _1377874)), hAPP(hAPP(c_Power_Opower__class_Opower(_1377868), _1377878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1377870), _1377872)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (36058 ^ _777864) ^ [_1449118, _1449120, _1449122, _1449124, _1449126, _1449128] : [c_Fun_Oinj__on(_1449118, _1449120, _1449122, _1449124), hBOOL(hAPP(hAPP(c_member(_1449120), _1449126), hAPP(c_Set_Oimage(_1449118, _1449120, _1449122), _1449124))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449118, tc_HOL_Obool)), _1449124), _1449128)), -(hBOOL(hAPP(hAPP(c_member(_1449118), hAPP(c_Fun_Othe__inv__into(_1449118, _1449120, _1449124, _1449122), _1449126)), _1449128)))], (6599 ^ _777864) ^ [_886820, _886822] : [class_Groups_Omonoid__add(_886820), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886820), _886822), c_Groups_Ozero__class_Ozero(_886820)) = _886822)], (17428 ^ _777864) ^ [_1078702, _1078704, _1078706] : [class_Rings_Olinordered__idom(_1078702), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078702), c_Groups_Ozero__class_Ozero(_1078702)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078702), hAPP(c_Groups_Oabs__class_Oabs(_1078702), _1078704)), _1078706))))], (50580 ^ _777864) ^ [_1796899, _1796901, _1796903] : [c_List_Oconcat(_1796899, _1796901) = c_List_Oconcat(_1796899, _1796903), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1796899))), _1796901) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1796899))), _1796903), 50590 ^ _777864 : [(50593 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1796899), tc_List_Olist(_1796899), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1796899), tc_fun(tc_List_Olist(_1796899), tc_Nat_Onat), tc_fun(tc_List_Olist(_1796899), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1796899), tc_Nat_Onat), tc_fun(tc_List_Olist(_1796899), tc_HOL_Obool)), tc_List_Olist(_1796899)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1796899))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1796899)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1796899))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1796899)))), 50589 ^ [_1796899, _1796901, _1796903]))], (50591 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1796899), tc_List_Olist(_1796899))), 50589 ^ [_1796899, _1796901, _1796903]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1796899), tc_List_Olist(_1796899))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1796899), tc_List_Olist(_1796899)), _1796901), _1796903)))))]], -(_1796901 = _1796903)], (27942 ^ _777864) ^ [_1275733, _1275735, _1275737, _1275739] : [class_Lattices_Osemilattice__sup(_1275733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275733), _1275735), _1275737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275733), _1275735), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275733), _1275739), _1275737))))], (30470 ^ _777864) ^ [_1334703, _1334705, _1334707, _1334709, _1334711] : [-(hBOOL(hAPP(hAPP(c_member(_1334703), _1334705), c_SetInterval_Oord_OgreaterThanLessThan(_1334703, _1334707, _1334709, _1334711)))), hBOOL(hAPP(hAPP(_1334707, _1334709), _1334705)), hBOOL(hAPP(hAPP(_1334707, _1334705), _1334711))], (49719 ^ _777864) ^ [_1779626, _1779628, _1779630] : [class_Orderings_Olinorder(_1779626), -(c_List_Olinorder__class_Osorted(_1779626, hAPP(c_List_Ofilter(_1779626, hAPP(hAPP(c_COMBC(_1779626, _1779626, tc_HOL_Obool), c_fequal), hAPP(_1779628, _1779630))), _1779630)))], (32608 ^ _777864) ^ [_1374984, _1374986, _1374988] : [hAPP(c_Finite__Set_Ocard(_1374984), _1374986) = hAPP(c_Nat_OSuc, _1374988), 32613 ^ _777864 : [(32616 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1374984), 32611 ^ [_1374984, _1374986, _1374988]), 32612 ^ [_1374984, _1374986, _1374988]))], (32618 ^ _777864) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1374984), 32612 ^ [_1374984, _1374986, _1374988]) = _1374988)], (32620 ^ _777864) ^ [] : [_1374988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(32612 ^ [_1374984, _1374986, _1374988] = c_Orderings_Obot__class_Obot(tc_fun(_1374984, tc_HOL_Obool)))], (32614 ^ _777864) ^ [] : [-(_1374986 = hAPP(hAPP(c_Set_Oinsert(_1374984), 32611 ^ [_1374984, _1374986, _1374988]), 32612 ^ [_1374984, _1374986, _1374988]))]]], (37899 ^ _777864) ^ [_1488980, _1488982, _1488984, _1488986] : [37900 ^ _777864 : [(37901 ^ _777864) ^ [_1489069] : [_1488984 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1488980, tc_Option_Ooption(_1488982)), hAPP(c_COMBK(tc_Option_Ooption(_1488982), _1488980), c_Option_Ooption_ONone(_1488982))), _1488986), hAPP(c_Option_Ooption_OSome(_1488982), _1489069))]], -(c_Map_Odom(_1488980, _1488982, _1488984) = hAPP(hAPP(c_Set_Oinsert(_1488980), _1488986), c_Orderings_Obot__class_Obot(tc_fun(_1488980, tc_HOL_Obool))))], (4298 ^ _777864) ^ [_843625, _843627, _843629, _843631] : [-(c_Relation_Oconverse(_843631, _843627) = c_Relation_Oconverse(_843629, _843625)), _843631 = _843629, _843627 = _843625], (32053 ^ _777864) ^ [_1363609, _1363611, _1363613] : [class_Orderings_Olinorder(_1363609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363609), _1363611)), -(_1363611 = c_Orderings_Obot__class_Obot(tc_fun(_1363609, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363609), _1363613)), -(_1363613 = c_Orderings_Obot__class_Obot(tc_fun(_1363609, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1363609, c_Orderings_Oord__class_Omax(_1363609), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363609, tc_HOL_Obool)), _1363611), _1363613)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363609), c_Big__Operators_Olattice_OSup__fin(_1363609, c_Orderings_Oord__class_Omax(_1363609), _1363611)), c_Big__Operators_Olattice_OSup__fin(_1363609, c_Orderings_Oord__class_Omax(_1363609), _1363613)))], (33821 ^ _777864) ^ [_1402664, _1402666, _1402668, _1402670, _1402672] : [_1402664 = c_Orderings_Obot__class_Obot(tc_fun(_1402666, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402668, tc_HOL_Obool)), _1402670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402666, tc_fun(_1402668, tc_HOL_Obool)), _1402664), _1402672)) = _1402670)], (6054 ^ _777864) ^ [_877551, _877553] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_877551, _877553)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37941 ^ _777864) ^ [_1489853, _1489855, _1489857, _1489859] : [hBOOL(hAPP(hAPP(c_member(_1489853), _1489855), c_Map_Odom(_1489853, _1489857, _1489859))), hAPP(_1489859, _1489855) = c_Option_Ooption_ONone(_1489857)], (1642 ^ _777864) ^ [_801157, _801159] : [-(class_Groups_Omonoid__mult(_801157)), _801159 = _801157, class_Groups_Omonoid__mult(_801159)], (24113 ^ _777864) ^ [_1199562, _1199564, _1199566, _1199568] : [class_Orderings_Olinorder(_1199562), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199562), _1199564), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199562), _1199566), _1199568)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199562), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199562), _1199564), _1199566)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199562), _1199564), _1199568)))], (12422 ^ _777864) ^ [_986048, _986050, _986052, _986054, _986056] : [class_Rings_Olinordered__semiring__strict(_986048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986048), _986050), _986052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986048), _986054), _986056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986048), c_Groups_Ozero__class_Ozero(_986048)), _986050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986048), c_Groups_Ozero__class_Ozero(_986048)), _986054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986048), _986050), _986054)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986048), _986052), _986056))))], (6809 ^ _777864) ^ [_889981, _889983, _889985] : [c_Com_Ocom_OCall(_889981, _889983, _889985) = c_Com_Ocom_OSKIP], (43164 ^ _777864) ^ [_1617758, _1617760, _1617762, _1617764, _1617766, _1617768] : [c_Finite__Set_Ofun__left__comm(_1617758, _1617760, _1617762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617758), _1617764)), -(hBOOL(hAPP(hAPP(c_member(_1617758), _1617766), _1617764))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617758, _1617760, _1617762), _1617768), hAPP(hAPP(c_Set_Oinsert(_1617758), _1617766), _1617764)) = hAPP(hAPP(_1617762, _1617766), hAPP(hAPP(c_Finite__Set_Ofold(_1617758, _1617760, _1617762), _1617768), _1617764)))], (19586 ^ _777864) ^ [_1114905, _1114907] : [class_Rings_Oring__1(_1114905), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114905), hAPP(c_Groups_Ouminus__class_Ouminus(_1114905), c_Groups_Oone__class_Oone(_1114905))), 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)))), _1114907)) = c_Groups_Oone__class_Oone(_1114905))], (7286 ^ _777864) ^ [_897779, _897781, _897783, _897785, _897787, _897789] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_897779, _897781, _897783), _897785, _897787, _897789), 7291 ^ _777864 : [(7294 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_897781, _897785, _897787, _897789))], (7292 ^ _777864) ^ [] : [-(hBOOL(hAPP(_897779, _897785)))]], 7295 ^ _777864 : [(7298 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_897783, _897785, _897787, _897789))], (7296 ^ _777864) ^ [] : [hBOOL(hAPP(_897779, _897785))]]], (7256 ^ _777864) ^ [_897251, _897253, _897255, _897257, _897259, _897261] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_897251, _897253, _897255), _897257, _897259, _897261), 7261 ^ _777864 : [(7264 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_897253, _897257, _897259, _897261))], (7262 ^ _777864) ^ [] : [-(hBOOL(hAPP(_897251, _897257)))]], 7265 ^ _777864 : [(7268 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_897255, _897257, _897259, _897261))], (7266 ^ _777864) ^ [] : [hBOOL(hAPP(_897251, _897257))]]], (38782 ^ _777864) ^ [_1508398, _1508400, _1508402, _1508404, _1508406] : [hAPP(_1508404, _1508400) = _1508406, -(hBOOL(hAPP(hAPP(c_member(_1508398), _1508400), hAPP(c_Set_Ovimage(_1508398, _1508402, _1508404), hAPP(hAPP(c_Set_Oinsert(_1508402), _1508406), c_Orderings_Obot__class_Obot(tc_fun(_1508402, tc_HOL_Obool)))))))], (28729 ^ _777864) ^ [] : [-(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))))], (42356 ^ _777864) ^ [_1600797, _1600799, _1600801] : [42358 ^ _777864 : [(42361 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1600797), 42357 ^ [_1600797, _1600799, _1600801]), c_Wellfounded_Oacc(_1600797, _1600801)))], (42359 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600797, _1600797)), hAPP(hAPP(c_Product__Type_OPair(_1600797, _1600797), 42357 ^ [_1600797, _1600799, _1600801]), _1600799)), _1600801)))]], -(hBOOL(hAPP(hAPP(c_member(_1600797), _1600799), c_Wellfounded_Oacc(_1600797, _1600801))))], (33293 ^ _777864) ^ [_1389576, _1389578] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1389576, _1389578))))], (27498 ^ _777864) ^ [_1267537, _1267539, _1267541] : [class_Rings_Oring__1(_1267537), hBOOL(hAPP(hAPP(c_member(_1267537), _1267539), c_Int_Oring__1__class_OInts(_1267537))), hBOOL(hAPP(hAPP(c_member(_1267537), _1267541), c_Int_Oring__1__class_OInts(_1267537))), -(hBOOL(hAPP(hAPP(c_member(_1267537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1267537), _1267539), _1267541)), c_Int_Oring__1__class_OInts(_1267537))))], (37977 ^ _777864) ^ [_1490537, _1490539] : [-(c_Map_Odom(_1490537, _1490539, hAPP(c_COMBK(tc_Option_Ooption(_1490539), _1490537), c_Option_Ooption_ONone(_1490539))) = c_Orderings_Obot__class_Obot(tc_fun(_1490537, tc_HOL_Obool)))], (37133 ^ _777864) ^ [_1473294, _1473296, _1473298, _1473300, _1473302] : [class_Groups_Oordered__ab__semigroup__add(_1473294), class_Rings_Osemiring__1(_1473294), 37143 ^ _777864 : [(37146 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473294), hAPP(_1473300, 37142 ^ [_1473294, _1473296, _1473298, _1473300, _1473302])), _1473302))], (37144 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473296), 37142 ^ [_1473294, _1473296, _1473298, _1473300, _1473302]), _1473298)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473294), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473296, _1473294), _1473300), _1473298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1473294), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1473294), hAPP(c_Finite__Set_Ocard(_1473296), _1473298))), _1473302))))], (22460 ^ _777864) ^ [_1166082, _1166084] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1166082), _1166084)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1166082), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1166084)))], (10300 ^ _777864) ^ [_949671, _949673, _949675, _949677] : [class_Orderings_Oorder(_949671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949671), _949673), _949675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949671), _949677), _949673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949671), _949677), _949675)))], (24743 ^ _777864) ^ [_1212111, _1212113, _1212115, _1212117] : [-(c_Product__Type_Ocurry(_1212111, _1212113, _1212115, hAPP(c_Product__Type_Oprod_Oprod__case(_1212111, _1212113, _1212115), _1212117)) = _1212117)], (36220 ^ _777864) ^ [_1452014, _1452016, _1452018, _1452020] : [c_Fun_Oinj__on(_1452014, _1452016, _1452018, _1452020), -(hAPP(c_Set_Oimage(_1452016, _1452014, c_Fun_Othe__inv__into(_1452014, _1452016, _1452020, _1452018)), hAPP(c_Set_Oimage(_1452014, _1452016, _1452018), _1452020)) = _1452020)], (37300 ^ _777864) ^ [_1476804, _1476806, _1476808] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476804), _1476806), _1476808) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1476804), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1476804, tc_Int_Oint), _1476806), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1476808))), class_Groups_Ocomm__monoid__add(_1476804), class_Groups_Ocomm__monoid__mult(_1476804)], (22084 ^ _777864) ^ [_1159569, _1159571, _1159573, _1159575, _1159577] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1159569, _1159571), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1159573), _1159575))), -(_1159571 = 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)), _1159577)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1159569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1159571), _1159577)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1159573), _1159577)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1159571), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1159573, _1159577))), _1159575)))))], (47182 ^ _777864) ^ [_1719664, _1719666, _1719668, _1719670] : [_1719664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1719666), hAPP(hAPP(c_List_Olist_OCons(_1719666), _1719668), _1719670)), _1719664) = _1719668)], (22915 ^ _777864) ^ [_1175109, _1175111, _1175113, _1175115, _1175117, _1175119, _1175121] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175109, _1175111), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175113), _1175115))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1175117, _1175111), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1175119), _1175121))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175111)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175109), _1175117), _1175111), 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), _1175113), _1175119)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175115), _1175121)), _1175111))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175115), _1175121), _1175111)))))], (41681 ^ _777864) ^ [_1585011, _1585013, _1585015, _1585017, _1585019, _1585021] : [hBOOL(hAPP(hAPP(c_member(_1585011), _1585013), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1585015, _1585017, tc_fun(_1585011, tc_HOL_Obool)), _1585019), _1585021))), 41686 ^ _777864 : [(41689 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585011), _1585013), hAPP(hAPP(_1585019, 41684 ^ [_1585011, _1585013, _1585015, _1585017, _1585019, _1585021]), 41685 ^ [_1585011, _1585013, _1585015, _1585017, _1585019, _1585021]))))], (41687 ^ _777864) ^ [] : [-(_1585021 = hAPP(hAPP(c_Product__Type_OPair(_1585015, _1585017), 41684 ^ [_1585011, _1585013, _1585015, _1585017, _1585019, _1585021]), 41685 ^ [_1585011, _1585013, _1585015, _1585017, _1585019, _1585021]))]]], (28972 ^ _777864) ^ [_1301357, _1301359, _1301361] : [hBOOL(hAPP(hAPP(c_member(_1301357), _1301361), c_Wellfounded_Oacc(_1301357, _1301359))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1301357, hAPP(hAPP(c_COMBC(_1301357, tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_fun(_1301357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1301357, tc_fun(tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_fun(_1301357, tc_HOL_Obool)), _1301357), c_COMBC(_1301357, tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1301357, tc_prod(_1301357, _1301357)), tc_fun(_1301357, tc_fun(tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_HOL_Obool)), _1301357), hAPP(c_COMBB(tc_prod(_1301357, _1301357), tc_fun(tc_fun(tc_prod(_1301357, _1301357), tc_HOL_Obool), tc_HOL_Obool), _1301357), c_member(tc_prod(_1301357, _1301357)))), c_Product__Type_OPair(_1301357, _1301357)))), _1301359)), _1301361)))], (18540 ^ _777864) ^ [_1096665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1096665)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096665), c_Int_OMin)))], (51063 ^ _777864) ^ [_1807541, _1807543] : [class_Lattices_Oboolean__algebra(_1807541), -(class_Lattices_Oboolean__algebra(tc_fun(_1807543, _1807541)))], (47346 ^ _777864) ^ [_1724404, _1724406, _1724408, _1724410, _1724412] : [-(hAPP(hAPP(c_List_Otake(_1724404), _1724406), hAPP(hAPP(c_List_Omap(_1724408, _1724404), _1724410), _1724412)) = hAPP(hAPP(c_List_Omap(_1724408, _1724404), _1724410), hAPP(hAPP(c_List_Otake(_1724408), _1724406), _1724412)))], (34339 ^ _777864) ^ [_1414692, _1414694, _1414696] : [class_Lattices_Olattice(_1414692), hAPP(_1414694, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414692), 34344 ^ [_1414692, _1414694, _1414696]), 34345 ^ [_1414692, _1414694, _1414696])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414692), hAPP(_1414694, 34344 ^ [_1414692, _1414694, _1414696])), hAPP(_1414694, 34345 ^ [_1414692, _1414694, _1414696])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414692), _1414696)), -(_1414696 = c_Orderings_Obot__class_Obot(tc_fun(_1414692, tc_HOL_Obool))), -(hAPP(_1414694, c_Big__Operators_Olattice__class_OInf__fin(_1414692, _1414696)) = c_Big__Operators_Olattice__class_OInf__fin(_1414692, hAPP(c_Set_Oimage(_1414692, _1414692, _1414694), _1414696)))], (22659 ^ _777864) ^ [_1169882, _1169884, _1169886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1169882, tc_HOL_Obool)), _1169884), _1169886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1169882, tc_HOL_Obool)), _1169884), _1169886))), -(_1169884 = _1169886)], (40677 ^ _777864) ^ [_1559177, _1559179] : [-(c_Product__Type_Oapfst(_1559177, _1559177, _1559179, c_Fun_Oid(_1559177)) = c_Fun_Oid(tc_prod(_1559177, _1559179)))], (36076 ^ _777864) ^ [_1449477, _1449479, _1449481] : [class_Orderings_Olinorder(_1449477), 36079 ^ _777864 : [(36086 ^ _777864) ^ [] : [_1449479 = _1449481, -(hAPP(c_SetInterval_Oord__class_OatMost(_1449477), _1449479) = hAPP(c_SetInterval_Oord__class_OatMost(_1449477), _1449481))], (36080 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1449477), _1449479) = hAPP(c_SetInterval_Oord__class_OatMost(_1449477), _1449481), -(_1449479 = _1449481)]]], (10162 ^ _777864) ^ [_947506, _947508, _947510] : [class_Orderings_Opreorder(_947506), _947508 = _947510, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947506), _947508), _947510)))], (46456 ^ _777864) ^ [_1699583, _1699585, _1699587] : [-(hBOOL(hAPP(hAPP(c_member(_1699583), _1699585), hAPP(c_List_Oset(_1699583), _1699587)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699583)), c_List_Oremove1(_1699583, _1699585, _1699587)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699583)), _1699587))], (4580 ^ _777864) ^ [_847866, _847868] : [_847868 = _847866, -(c_Orderings_Obot__class_Obot(_847868) = c_Orderings_Obot__class_Obot(_847866))], (3322 ^ _777864) ^ [_828221, _828223] : [_828223 = _828221, -(c_Int_Oint__ge__less__than(_828223) = c_Int_Oint__ge__less__than(_828221))], (4414 ^ _777864) ^ [_845373, _845375, _845377, _845379] : [-(c_Big__Operators_Olinorder__class_OMin(_845379, _845375) = c_Big__Operators_Olinorder__class_OMin(_845377, _845373)), _845379 = _845377, _845375 = _845373], (11179 ^ _777864) ^ [_963935, _963937] : [11180 ^ _777864 : [(11181 ^ _777864) ^ [_963985] : [_963937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963935), _963985)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _963935), _963937)))], (18570 ^ _777864) ^ [_1097140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1097140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1097140))))], (35032 ^ _777864) ^ [_1428921, _1428923, _1428925] : [-(c_Fun_Oinj__on(tc_prod(_1428921, _1428923), tc_prod(_1428923, _1428921), hAPP(c_Product__Type_Oprod_Oprod__case(_1428921, _1428923, tc_prod(_1428923, _1428921)), hAPP(c_COMBC(_1428923, _1428921, tc_prod(_1428923, _1428921)), c_Product__Type_OPair(_1428923, _1428921))), _1428925))], (39872 ^ _777864) ^ [_1534027, _1534029, _1534031] : [c_Relation_Orefl__on(_1534027, _1534029, _1534031), 39875 ^ _777864 : [(39878 ^ _777864) ^ [_1534209] : [hBOOL(hAPP(hAPP(c_member(_1534027), _1534209), _1534029)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534027, _1534027)), hAPP(hAPP(c_Product__Type_OPair(_1534027, _1534027), _1534209), _1534209)), _1534031)))], (39876 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534027, _1534027), tc_HOL_Obool)), _1534031), hAPP(hAPP(c_Product__Type_OSigma(_1534027, _1534027), _1534029), hAPP(c_COMBK(tc_fun(_1534027, tc_HOL_Obool), _1534027), _1534029)))))]]], (30144 ^ _777864) ^ [_1326467, _1326469, _1326471, _1326473] : [hBOOL(hAPP(hAPP(c_member(_1326467), _1326469), _1326471)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326467, tc_HOL_Obool)), _1326471), hAPP(hAPP(c_Set_Oinsert(_1326467), _1326469), _1326473)) = hAPP(hAPP(c_Set_Oinsert(_1326467), _1326469), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326467, tc_HOL_Obool)), _1326471), _1326473)))], (19386 ^ _777864) ^ [_1111224, _1111226] : [class_Rings_Olinordered__idom(_1111224), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111224), c_Groups_Ozero__class_Ozero(_1111224)), hAPP(hAPP(c_Power_Opower__class_Opower(_1111224), _1111226), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34775 ^ _777864) ^ [_1423484, _1423486] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1423484, _1423486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423486)), _1423484))], (46701 ^ _777864) ^ [_1707052, _1707054, _1707056, _1707058, _1707060, _1707062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707052), tc_List_Olist(_1707052))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707052), tc_List_Olist(_1707052)), hAPP(hAPP(c_List_Olist_OCons(_1707052), _1707054), _1707056)), hAPP(hAPP(c_List_Olist_OCons(_1707052), _1707058), _1707060))), c_List_Olex(_1707052, _1707062))), 46706 ^ _777864 : [(46709 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707052)), _1707056) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707052)), _1707060))], (46707 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1707052, _1707052)), hAPP(hAPP(c_Product__Type_OPair(_1707052, _1707052), _1707054), _1707058)), _1707062)))]], 46710 ^ _777864 : [(46713 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707052), tc_List_Olist(_1707052))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707052), tc_List_Olist(_1707052)), _1707056), _1707060)), c_List_Olex(_1707052, _1707062))))], (46711 ^ _777864) ^ [] : [-(_1707054 = _1707058)]]], (39029 ^ _777864) ^ [_1513853, _1513855, _1513857, _1513859, _1513861] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1513853, _1513855, hAPP(hAPP(c_Set_Oinsert(_1513853), _1513857), _1513859)), _1513861)), 39034 ^ _777864 : [(39039 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1513853), 39032 ^ [_1513853, _1513855, _1513857, _1513859, _1513861]), 39033 ^ [_1513853, _1513855, _1513857, _1513859, _1513861]))], (39037 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1513853, _1513853, _1513855, 39032 ^ [_1513853, _1513855, _1513857, _1513859, _1513861], 39033 ^ [_1513853, _1513855, _1513857, _1513859, _1513861]), _1513861)))], (39035 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1513853), _1513857), _1513859) = hAPP(hAPP(c_Set_Oinsert(_1513853), 39032 ^ [_1513853, _1513855, _1513857, _1513859, _1513861]), 39033 ^ [_1513853, _1513855, _1513857, _1513859, _1513861]))]]], (41748 ^ _777864) ^ [_1586874, _1586876, _1586878, _1586880, _1586882, _1586884, _1586886, _1586888] : [hAPP(c_Fun_Ocomp(_1586874, _1586876, _1586878, _1586880), _1586882) = hAPP(c_Fun_Ocomp(_1586884, _1586876, _1586878, _1586886), _1586888), 41751 ^ _777864 : [(41752 ^ _777864) ^ [_1586989] : [-(hAPP(_1586880, hAPP(_1586882, _1586989)) = hAPP(_1586886, hAPP(_1586888, _1586989)))]]], (20842 ^ _777864) ^ [_1137327, _1137329, _1137331, _1137333] : [class_Fields_Ofield__inverse__zero(_1137327), -(_1137329 = c_Groups_Ozero__class_Ozero(_1137327)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137327), _1137331), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137327), _1137333), _1137329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137327), _1137333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137327), _1137331), _1137329))), _1137329))], (41691 ^ _777864) ^ [_1585280, _1585282, _1585284, _1585286, _1585288, _1585290] : [41694 ^ _777864 : [(41697 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1585286), _1585288), hAPP(hAPP(_1585290, 41692 ^ [_1585280, _1585282, _1585284, _1585286, _1585288, _1585290]), 41693 ^ [_1585280, _1585282, _1585284, _1585286, _1585288, _1585290])))], (41695 ^ _777864) ^ [] : [-(_1585280 = hAPP(hAPP(c_Product__Type_OPair(_1585282, _1585284), 41692 ^ [_1585280, _1585282, _1585284, _1585286, _1585288, _1585290]), 41693 ^ [_1585280, _1585282, _1585284, _1585286, _1585288, _1585290]))]], -(hBOOL(hAPP(hAPP(c_member(_1585286), _1585288), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1585282, _1585284, tc_fun(_1585286, tc_HOL_Obool)), _1585290), _1585280))))], (5862 ^ _777864) ^ [_874107, _874109] : [_874107 = _874109, -(c_Com_Ovname_OLoc(_874107) = c_Com_Ovname_OLoc(_874109))], (9953 ^ _777864) ^ [_944109, _944111, _944113, _944115, _944117, _944119] : [class_Rings_Olinordered__semiring__1__strict(_944109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944109), _944111), _944113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944109), _944115), _944113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944109), c_Groups_Ozero__class_Ozero(_944109)), _944117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944109), c_Groups_Ozero__class_Ozero(_944109)), _944119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944109), _944117), _944119) = c_Groups_Oone__class_Oone(_944109), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944109), _944117), _944111)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944109), _944119), _944115))), _944113)))], (11967 ^ _777864) ^ [_978079, _978081, _978083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978079), _978081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978079), _978083))), 11970 ^ _777864 : [(11973 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978081), _978083)))], (11971 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _978079)))]]], (46190 ^ _777864) ^ [_1692594, _1692596, _1692598, _1692600, _1692602, _1692604, _1692606, _1692608] : [-(hAPP(hAPP(c_List_Ozip(_1692594, _1692596), hAPP(hAPP(c_List_Omap(_1692598, _1692594), _1692600), _1692602)), hAPP(hAPP(c_List_Omap(_1692604, _1692596), _1692606), _1692608)) = hAPP(hAPP(c_List_Omap(tc_prod(_1692598, _1692604), tc_prod(_1692594, _1692596)), hAPP(c_Product__Type_Oprod_Oprod__case(_1692598, _1692604, tc_prod(_1692594, _1692596)), hAPP(hAPP(c_COMBC(_1692598, tc_fun(_1692604, _1692596), tc_fun(_1692604, tc_prod(_1692594, _1692596))), hAPP(hAPP(c_COMBB(tc_fun(_1692596, tc_prod(_1692594, _1692596)), tc_fun(tc_fun(_1692604, _1692596), tc_fun(_1692604, tc_prod(_1692594, _1692596))), _1692598), c_COMBB(_1692596, tc_prod(_1692594, _1692596), _1692604)), hAPP(hAPP(c_COMBB(_1692594, tc_fun(_1692596, tc_prod(_1692594, _1692596)), _1692598), c_Product__Type_OPair(_1692594, _1692596)), _1692600))), _1692606))), hAPP(hAPP(c_List_Ozip(_1692598, _1692604), _1692602), _1692608)))], (51347 ^ _777864) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (6322 ^ _777864) ^ [_882111, _882113, _882115] : [6323 ^ _777864 : [(6326 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_882115, _882113), _882111))], (6324 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882111), _882113)))]], 6329 ^ _777864 : [(6332 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_882115, _882113), _882111))], (6330 ^ _777864) ^ [] : [-(_882111 = _882113)]], 6335 ^ _777864 : [(6338 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_882115, _882113), _882111))], (6336 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882113), _882111)))]], -(hBOOL(hAPP(hAPP(_882115, _882113), _882111)))], (47406 ^ _777864) ^ [_1725520, _1725522] : [-(hAPP(hAPP(c_List_Otake(_1725520), _1725522), c_List_Olist_ONil(_1725520)) = c_List_Olist_ONil(_1725520))], (20886 ^ _777864) ^ [_1138108, _1138110, _1138112, _1138114] : [class_Fields_Ofield__inverse__zero(_1138108), class_Int_Onumber(_1138108), 20893 ^ _777864 : [(20894 ^ _777864) ^ [] : [_1138110 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138108), _1138112), hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114)), 20897 ^ _777864 : [(20904 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114) = c_Groups_Ozero__class_Ozero(_1138108), -(_1138110 = c_Groups_Ozero__class_Ozero(_1138108))], (20898 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114) = c_Groups_Ozero__class_Ozero(_1138108)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138108), _1138110), hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114)) = _1138112)]]], (20910 ^ _777864) ^ [] : [-(_1138110 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138108), _1138112), hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114))), 20913 ^ _777864 : [(20916 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138108), _1138110), hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114)) = _1138112], (20914 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114) = c_Groups_Ozero__class_Ozero(_1138108)]], 20917 ^ _777864 : [(20920 ^ _777864) ^ [] : [_1138110 = c_Groups_Ozero__class_Ozero(_1138108)], (20918 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1138108), _1138114) = c_Groups_Ozero__class_Ozero(_1138108))]]]]], (46877 ^ _777864) ^ [_1712323, _1712325, _1712327, _1712329] : [class_Groups_Ocomm__monoid__add(_1712323), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1712323), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1712323), _1712325), c_List_Oupto(_1712327, _1712329))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1712323), _1712325), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1712327, _1712329))))], (41600 ^ _777864) ^ [_1583166, _1583168, _1583170] : [c_Hoare__Mirabelle_Ohoare__valids(_1583166, _1583168, _1583170), 41603 ^ _777864 : [(41604 ^ _777864) ^ [_1583275] : [41606 ^ _777864 : [(41609 ^ _777864) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1583166, _1583275, 41605 ^ [_1583166, _1583168, _1583170, _1583275])], (41607 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583166)), 41605 ^ [_1583166, _1583168, _1583170, _1583275]), _1583168)))]], 41610 ^ _777864 : [(41611 ^ _777864) ^ [_1583447] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583166)), _1583447), _1583170)), -(c_Hoare__Mirabelle_Otriple__valid(_1583166, _1583275, _1583447))]]]]], (26799 ^ _777864) ^ [_1250994, _1250996, _1250998, _1251000, _1251002, _1251004, _1251006] : [hBOOL(hAPP(hAPP(c_member(_1250994), _1250996), hAPP(hAPP(_1250998, _1251000), _1251002))), -(hBOOL(hAPP(hAPP(c_member(_1250994), _1250996), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1251004, _1251006, tc_fun(_1250994, tc_HOL_Obool)), _1250998), hAPP(hAPP(c_Product__Type_OPair(_1251004, _1251006), _1251000), _1251002)))))], (17468 ^ _777864) ^ [_1079536, _1079538, _1079540, _1079542] : [class_Rings_Olinordered__semidom(_1079536), hAPP(hAPP(c_Power_Opower__class_Opower(_1079536), _1079538), _1079540) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079536), _1079542), _1079540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079536), c_Groups_Ozero__class_Ozero(_1079536)), _1079538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079536), c_Groups_Ozero__class_Ozero(_1079536)), _1079542)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1079540)), -(_1079538 = _1079542)], (43771 ^ _777864) ^ [_1632712, _1632714, _1632716, _1632718] : [43773 ^ _777864 : [(43776 ^ _777864) ^ [] : [hAPP(_1632718, 43772 ^ [_1632712, _1632714, _1632716, _1632718]) = c_Orderings_Otop__class_Otop(tc_fun(_1632712, tc_HOL_Obool))], (43774 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632714), 43772 ^ [_1632712, _1632714, _1632716, _1632718]), _1632716)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1632712, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1632714, tc_fun(_1632712, tc_HOL_Obool)), _1632716), _1632718))], (37965 ^ _777864) ^ [_1490271, _1490273, _1490275, _1490277] : [-(c_Map_Odom(_1490271, _1490273, c_Map_Orestrict__map(_1490271, _1490273, _1490275, _1490277)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490271, tc_HOL_Obool)), c_Map_Odom(_1490271, _1490273, _1490275)), _1490277))], (48344 ^ _777864) ^ [_1747416, _1747418, _1747420, _1747422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747416), tc_List_Olist(_1747416))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747416), tc_List_Olist(_1747416)), _1747418), _1747420)), c_List_Olistrel1(_1747416, hAPP(c_Relation_Oconverse(_1747416, _1747416), _1747422)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1747416), tc_List_Olist(_1747416))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1747416), tc_List_Olist(_1747416)), _1747418), _1747420)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1747416), tc_List_Olist(_1747416)), c_List_Olistrel1(_1747416, _1747422)))))], (10992 ^ _777864) ^ [_960887, _960889, _960891] : [class_Groups_Oordered__ab__group__add(_960887), 10995 ^ _777864 : [(11002 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960887), _960891), _960889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960887), hAPP(c_Groups_Ouminus__class_Ouminus(_960887), _960889)), hAPP(c_Groups_Ouminus__class_Ouminus(_960887), _960891))))], (10996 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960887), hAPP(c_Groups_Ouminus__class_Ouminus(_960887), _960889)), hAPP(c_Groups_Ouminus__class_Ouminus(_960887), _960891))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960887), _960891), _960889)))]]], (7484 ^ _777864) ^ [_901493, _901495, _901497, _901499, _901501, _901503] : [c_Com_Ocom_OCond(_901493, _901495, _901497) = c_Com_Ocom_OCall(_901499, _901501, _901503)], (29824 ^ _777864) ^ [_1319294, _1319296, _1319298, _1319300] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319294, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1319294), _1319296), _1319298)), hAPP(hAPP(c_Set_Oinsert(_1319294), _1319296), _1319300)) = hAPP(hAPP(c_Set_Oinsert(_1319294), _1319296), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319294, tc_HOL_Obool)), _1319298), _1319300)))], (26311 ^ _777864) ^ [_1240804, _1240806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1240804, tc_HOL_Obool)), _1240806), c_Orderings_Obot__class_Obot(tc_fun(_1240804, tc_HOL_Obool))))], (6070 ^ _777864) ^ [_877794] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OGlb(_877794)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28068 ^ _777864) ^ [_1278008, _1278010] : [class_Lattices_Osemilattice__sup(_1278008), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278008), _1278010), _1278010) = _1278010)], (19456 ^ _777864) ^ [] : [-(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))))], (36304 ^ _777864) ^ [_1453742, _1453744, _1453746] : [class_Orderings_Olinorder(_1453742), 36307 ^ _777864 : [(36314 ^ _777864) ^ [] : [_1453744 = _1453746, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1453742), _1453744) = hAPP(c_SetInterval_Oord__class_OlessThan(_1453742), _1453746))], (36308 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1453742), _1453744) = hAPP(c_SetInterval_Oord__class_OlessThan(_1453742), _1453746), -(_1453744 = _1453746)]]], (44140 ^ _777864) ^ [_1644009, _1644011] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1644009, _1644009)), hAPP(hAPP(c_Product__Type_OPair(_1644009, _1644009), _1644011), _1644011)), c_Relation_OId(_1644009))))], (36010 ^ _777864) ^ [_1448041, _1448043, _1448045, _1448047] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1448041), _1448043)), 36013 ^ _777864 : [(36014 ^ _777864) ^ [_1448195] : [36016 ^ _777864 : [(36022 ^ _777864) ^ [] : [-(_1448195 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36018 ^ [_1448041, _1448043, _1448045, _1448047, _1448195]), 36015 ^ [_1448041, _1448043, _1448045, _1448047, _1448195]))], (36020 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36018 ^ [_1448041, _1448043, _1448045, _1448047, _1448195]), _1448045)))], (36017 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36015 ^ [_1448041, _1448043, _1448045, _1448047, _1448195]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1448043))))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1448041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448195), _1448047))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1448041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448195), _1448043)), _1448047))))]]], (7588 ^ _777864) ^ [_903639, _903641, _903643, _903645, _903647, _903649] : [hBOOL(hAPP(_903639, _903641)), c_Natural_Oevaln(_903643, _903641, _903645, _903647), c_Natural_Oevaln(c_Com_Ocom_OWhile(_903639, _903643), _903647, _903645, _903649), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_903639, _903643), _903641, _903645, _903649))], (44238 ^ _777864) ^ [_1646401, _1646403, _1646405, _1646407, _1646409, _1646411] : [c_Relation_Osingle__valued(_1646401, _1646403, hAPP(c_Relation_Oconverse(_1646403, _1646401), _1646405)), -(_1646407 = c_Orderings_Obot__class_Obot(tc_fun(_1646409, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1646403, _1646401, _1646405), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646409, tc_fun(_1646403, tc_HOL_Obool)), _1646407), _1646411)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646409, tc_fun(_1646401, tc_HOL_Obool)), _1646407), hAPP(hAPP(c_COMBB(tc_fun(_1646403, tc_HOL_Obool), tc_fun(_1646401, tc_HOL_Obool), _1646409), c_Relation_OImage(_1646403, _1646401, _1646405)), _1646411)))], (19638 ^ _777864) ^ [_1115948, _1115950, _1115952] : [class_Rings_Olinordered__idom(_1115948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115948), _1115950), c_Groups_Ozero__class_Ozero(_1115948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1115948), hAPP(hAPP(c_Power_Opower__class_Opower(_1115948), _1115950), 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)))), _1115952)))), c_Groups_Ozero__class_Ozero(_1115948))))], (14061 ^ _777864) ^ [_1015472, _1015474, _1015476] : [-(hBOOL(hAPP(_1015472, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1015474), _1015476)))), 14062 ^ _777864 : [(14069 ^ _777864) ^ [_1015640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015476), _1015640)), _1015474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015476), hAPP(c_Nat_OSuc, _1015640)))), hBOOL(hAPP(_1015472, _1015640))], (14063 ^ _777864) ^ [] : [_1015476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1015472, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8984 ^ _777864) ^ [_927165, _927167, _927169] : [class_Groups_Ogroup__add(_927165), -(hAPP(c_Groups_Ouminus__class_Ouminus(_927165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927165), _927167), _927169)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927165), hAPP(c_Groups_Ouminus__class_Ouminus(_927165), _927169)), hAPP(c_Groups_Ouminus__class_Ouminus(_927165), _927167)))], (17108 ^ _777864) ^ [_1072812, _1072814, _1072816, _1072818] : [class_Groups_Ocomm__monoid__mult(_1072812), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1072812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072812), _1072814), _1072816)), _1072818) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072812), hAPP(hAPP(c_Power_Opower__class_Opower(_1072812), _1072814), _1072818)), hAPP(hAPP(c_Power_Opower__class_Opower(_1072812), _1072816), _1072818)))], (28458 ^ _777864) ^ [_1289443, _1289445, _1289447, _1289449, _1289451] : [-(hAPP(c_Relation_OImage(_1289443, _1289445, _1289447), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289443, tc_HOL_Obool)), _1289449), _1289451)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289445, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1289443, _1289445, _1289447), _1289449)), hAPP(c_Relation_OImage(_1289443, _1289445, _1289447), _1289451)))], (4266 ^ _777864) ^ [_843103, _843105, _843107, _843109, _843111, _843113, _843115, _843117] : [-(c_Map_Orestrict__map(_843117, _843113, _843109, _843105) = c_Map_Orestrict__map(_843115, _843111, _843107, _843103)), _843117 = _843115, _843113 = _843111, _843109 = _843107, _843105 = _843103], (35174 ^ _777864) ^ [_1431671, _1431673, _1431675, _1431677, _1431679] : [c_Fun_Oinj__on(_1431671, _1431673, _1431675, _1431677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1431671, tc_HOL_Obool)), _1431679), _1431677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1431673, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1431671, _1431673, _1431675), _1431679)), hAPP(c_Set_Oimage(_1431671, _1431673, _1431675), _1431677))))], (34039 ^ _777864) ^ [_1408057, _1408059, _1408061, _1408063, _1408065, _1408067, _1408069] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408057, tc_fun(_1408059, tc_fun(_1408061, tc_HOL_Obool))), _1408063), _1408065), _1408067), _1408069))), 34040 ^ _777864 : [(34041 ^ _777864) ^ [_1408142] : [hBOOL(hAPP(hAPP(c_member(_1408057), _1408142), _1408063)), hBOOL(hAPP(hAPP(hAPP(_1408065, _1408142), _1408067), _1408069))]]], (27137 ^ _777864) ^ [_1258521, _1258523, _1258525, _1258527] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258521, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1258521), _1258523), _1258525)), _1258527))), hBOOL(hAPP(hAPP(c_member(_1258521), _1258523), _1258527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258521, tc_HOL_Obool)), _1258525), _1258527))], (7406 ^ _777864) ^ [_899949, _899951, _899953, _899955] : [hAPP(c_Com_Ocom_OBODY, _899949) = c_Com_Ocom_OCond(_899951, _899953, _899955)], (31725 ^ _777864) ^ [_1357547, _1357549, _1357551] : [class_Orderings_Olinorder(_1357547), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357547), _1357549)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357547), _1357551)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1357547, tc_HOL_Obool)), _1357549), _1357551) = c_Orderings_Obot__class_Obot(tc_fun(_1357547, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1357547), c_Big__Operators_Olinorder__class_OMin(_1357547, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357547, tc_HOL_Obool)), _1357549), _1357551))), c_Big__Operators_Olinorder__class_OMin(_1357547, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1357547, tc_HOL_Obool)), _1357549), _1357551))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1357547), c_Big__Operators_Olinorder__class_OMin(_1357547, _1357549)), c_Big__Operators_Olinorder__class_OMin(_1357547, _1357551)))], (43116 ^ _777864) ^ [_1616814, _1616816, _1616818, _1616820, _1616822, _1616824] : [c_Finite__Set_Ofun__left__comm(_1616814, _1616816, _1616818), -(hAPP(hAPP(_1616818, _1616820), hAPP(hAPP(_1616818, _1616822), _1616824)) = hAPP(hAPP(_1616818, _1616822), hAPP(hAPP(_1616818, _1616820), _1616824)))], (14231 ^ _777864) ^ [_1018556, _1018558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018556)), 14234 ^ _777864 : [(14241 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018558), 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), _1018558), _1018556)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14235 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018558), _1018556)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018558), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (3586 ^ _777864) ^ [_832395, _832397] : [_832397 = _832395, -(c_Random__Sequence_Osingle(_832397) = c_Random__Sequence_Osingle(_832395))], (35150 ^ _777864) ^ [_1431207, _1431209, _1431211, _1431213, _1431215] : [c_Fun_Oinj__on(_1431207, _1431209, _1431211, _1431213), -(c_Fun_Oinj__on(_1431207, _1431209, _1431211, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1431207, tc_HOL_Obool)), _1431213), _1431215)))], (26079 ^ _777864) ^ [_1235977, _1235979] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235977), _1235979)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235977), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235979))))], (10314 ^ _777864) ^ [_949904, _949906, _949908, _949910, _949912] : [class_Orderings_Oord(_949904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949906, _949904)), _949908), _949910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949904), hAPP(_949908, _949912)), hAPP(_949910, _949912))))], (22967 ^ _777864) ^ [_1176131, _1176133, _1176135] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176131, _1176133), _1176135))), _1176131 = 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), _1176135)), _1176133)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1176135)), 22974 ^ _777864 : [(22977 ^ _777864) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1176135) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22975 ^ _777864) ^ [] : [-(_1176133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22978 ^ _777864 : [(22981 ^ _777864) ^ [] : [22982 ^ _777864 : [(22985 ^ _777864) ^ [] : [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), _1176135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1176135)), _1176133))], (22983 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176133)))]], 22990 ^ _777864 : [(22993 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1176133), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1176135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1176135)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22991 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176133))]]], (22979 ^ _777864) ^ [] : [_1176133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (7098 ^ _777864) ^ [_894451, _894453] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_894451, _894453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_894451)), c_Com_Ocom_Ocom__size(_894453))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16676 ^ _777864) ^ [_1064808, _1064810, _1064812] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1064808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064810), _1064812)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1064808), _1064810)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1064808), _1064812)))], (35112 ^ _777864) ^ [_1430550, _1430552, _1430554, _1430556, _1430558, _1430560] : [c_Fun_Oinj__on(_1430550, _1430552, _1430554, _1430556), -(_1430558 = _1430560), hBOOL(hAPP(hAPP(c_member(_1430550), _1430558), _1430556)), hBOOL(hAPP(hAPP(c_member(_1430550), _1430560), _1430556)), hAPP(_1430554, _1430558) = hAPP(_1430554, _1430560)], (15176 ^ _777864) ^ [_1035336, _1035338] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035336), _1035338)), _1035338) = _1035336)], (8192 ^ _777864) ^ [_913856, _913858, _913860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _913856), _913858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _913856), _913860)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _913858), _913860))))], (19196 ^ _777864) ^ [_1107899, _1107901] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1107899)), _1107901) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1107899), _1107901))), _1107901))], (36284 ^ _777864) ^ [_1453345, _1453347, _1453349] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453345, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1453347)), _1453349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1453345, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1453345, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1453347)), _1453349)), hAPP(_1453349, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38512 ^ _777864) ^ [_1501031, _1501033, _1501035, _1501037] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1501031, _1501033, hAPP(hAPP(c_Set_Oinsert(_1501031), _1501035), c_Orderings_Obot__class_Obot(tc_fun(_1501031, tc_HOL_Obool)))), _1501037)), -(_1501035 = _1501037)], (37062 ^ _777864) ^ [_1471135, _1471137] : [class_Rings_Ocomm__semiring__1(_1471135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1471135), c_Groups_Oone__class_Oone(_1471135)), c_Groups_Oone__class_Oone(_1471135))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1471135), c_Nat_Osemiring__1__class_Oof__nat(_1471135)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1471137))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471135), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1471135), _1471137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1471135), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1471135), _1471137)), c_Groups_Oone__class_Oone(_1471135))))], (23139 ^ _777864) ^ [_1179656] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179656)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1179656)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179656)), 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)))))], (33341 ^ _777864) ^ [_1390714, _1390716, _1390718, _1390720, _1390722] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390714, tc_fun(_1390716, tc_HOL_Obool)), _1390718), _1390720), _1390722))), 33342 ^ _777864 : [(33343 ^ _777864) ^ [_1390786] : [hBOOL(hAPP(hAPP(c_member(_1390714), _1390786), _1390718)), hBOOL(hAPP(hAPP(_1390720, _1390786), _1390722))]]], (24325 ^ _777864) ^ [_1203835, _1203837] : [-(_1203835 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1203837, _1203835) = c_Nitpick_Onat__gcd(_1203835, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1203837, _1203835)))], (15960 ^ _777864) ^ [_1051467, _1051469] : [-(_1051467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051467), _1051469) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051467), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1051469)))], (40232 ^ _777864) ^ [_1541721, _1541723, _1541725] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1541721, tc_HOL_Obool)), _1541723), _1541725) = hAPP(c_Set_OCollect(_1541721), hAPP(hAPP(c_COMBS(_1541721, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541721), c_fconj), hAPP(hAPP(c_COMBC(_1541721, tc_fun(_1541721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541721)), _1541723))), hAPP(hAPP(c_COMBC(_1541721, tc_fun(_1541721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541721)), _1541725))))], (46182 ^ _777864) ^ [_1692359, _1692361, _1692363, _1692365, _1692367, _1692369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1692359, _1692361)), hAPP(hAPP(c_Product__Type_OPair(_1692359, _1692361), _1692363), _1692365)), hAPP(c_List_Oset(tc_prod(_1692359, _1692361)), hAPP(hAPP(c_List_Ozip(_1692359, _1692361), _1692367), _1692369)))), 46185 ^ _777864 : [(46188 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692361), _1692365), hAPP(c_List_Oset(_1692361), _1692369))))], (46186 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1692359), _1692363), hAPP(c_List_Oset(_1692359), _1692367))))]]], (44421 ^ _777864) ^ [_1650807, _1650809, _1650811] : [c_Relation_Ototal__on(_1650807, _1650809, hAPP(c_Relation_Oconverse(_1650807, _1650807), _1650811)), -(c_Relation_Ototal__on(_1650807, _1650809, _1650811))], (47546 ^ _777864) ^ [_1728421, _1728423] : [_1728423 = c_List_Olist_ONil(_1728421), -(c_Orderings_Obot__class_Obot(tc_fun(_1728421, tc_HOL_Obool)) = hAPP(c_List_Oset(_1728421), _1728423))], (15938 ^ _777864) ^ [_1050984, _1050986, _1050988, _1050990, _1050992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050984), _1050986)), 15941 ^ _777864 : [(15948 ^ _777864) ^ [] : [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), _1050986), _1050984)), _1050988)), _1050990)), _1050992)), -(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), _1050986), _1050988)), _1050990)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050984), _1050988)), _1050992))))], (15942 ^ _777864) ^ [] : 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c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1471338, _1471340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1471336), hAPP(_1471342, _1471338)), hAPP(_1471342, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1471340), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (28683 ^ _777864) ^ [_1295679, _1295681] : [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)), _1295679)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1295681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1295679), _1295681)))], (10844 ^ _777864) ^ [_958413, _958415, _958417, _958419] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_958413), 10847 ^ _777864 : [(10854 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958413), _958417), _958419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958413), _958415), _958417)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958413), _958415), _958419))))], (10848 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958413), _958415), _958417)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958413), _958415), _958419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958413), _958417), _958419)))]]], (32465 ^ _777864) ^ [_1371699, _1371701, _1371703] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371699), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371699, tc_HOL_Obool)), _1371701), _1371703))), -(hAPP(c_Finite__Set_Ocard(_1371699), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371699, tc_HOL_Obool)), _1371701), _1371703)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1371699), _1371701)), hAPP(c_Finite__Set_Ocard(_1371699), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371699, tc_HOL_Obool)), _1371701), _1371703))))], (22823 ^ _777864) ^ [_1173132, _1173134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173132), _1173134)), -(c_Divides_Odivmod__nat(_1173134, _1173132) = 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), _1173134), _1173132)), _1173132))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1173134), _1173132), _1173132)))], (10258 ^ _777864) ^ [_949012, _949014, _949016] : [class_Orderings_Oorder(_949012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949012), _949014), _949016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949012), _949016), _949014)), -(_949014 = _949016)], (22771 ^ _777864) ^ [_1172064, _1172066, _1172068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172064, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172064, tc_HOL_Obool)), _1172066), _1172068)), _1172066)))], (686 ^ _777864) ^ [_788501, _788503, _788505, _788507, _788509, _788511] : [-(c_Finite__Set_Ofolding__one(_788509, _788505, _788501)), c_Finite__Set_Ofolding__one(_788511, _788507, _788503), _788511 = _788509, _788507 = _788505, _788503 = _788501], (17042 ^ _777864) ^ [_1071633, _1071635] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1071633)), _1071635) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071633), _1071635)))], (24459 ^ _777864) ^ [_1206387, _1206389, _1206391] : [c_Nitpick_Oless__frac(_1206387, 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[(28481 ^ _777864) ^ [] : [-(_1289883 = hAPP(c_Set_Oimage(_1289885, _1289881, _1289887), 28477 ^ [_1289881, _1289883, _1289885, _1289887, _1289889]))], (28479 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289885, tc_HOL_Obool)), 28477 ^ [_1289881, _1289883, _1289885, _1289887, _1289889]), _1289889)))]]], (6947 ^ _777864) ^ [_892100, _892102] : [class_Rings_Olinordered__idom(_892100), 6950 ^ _777864 : [(6957 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892100), _892102), c_Groups_Ozero__class_Ozero(_892100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892100), _892102), _892102)), c_Groups_Ozero__class_Ozero(_892100))))], (6951 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_892100), _892102), _892102)), c_Groups_Ozero__class_Ozero(_892100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_892100), _892102), c_Groups_Ozero__class_Ozero(_892100))))]]], (8016 ^ _777864) ^ [_911403, _911405, _911407] : [class_Rings_Olinordered__semidom(_911403), 8019 ^ _777864 : [(8026 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911405), _911407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911403), _911405)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911403), _911407))))], (8020 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911403), _911405)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911403), _911407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911405), _911407)))]]], (20538 ^ _777864) ^ [_1131696, _1131698, _1131700, _1131702] : [class_Fields_Olinordered__field(_1131696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131696), _1131698), _1131700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131696), _1131702), c_Groups_Ozero__class_Ozero(_1131696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131696), c_Groups_Ozero__class_Ozero(_1131696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131696), _1131698), _1131700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131696), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131696), _1131702), _1131698)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131696), _1131702), _1131700))))], (39357 ^ _777864) ^ [_1522360, _1522362] : [class_Orderings_Olinorder(_1522360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522360), _1522362)), -(c_Big__Operators_Olinorder__class_OMax(_1522360, _1522362) = hAPP(c_Finite__Set_Ofold1(_1522360, c_Orderings_Oord__class_Omax(_1522360)), _1522362))], (35848 ^ _777864) ^ [_1444532, _1444534] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1444532)), _1444534) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1444532, _1444534))], (38884 ^ _777864) ^ [_1510979, _1510981, _1510983, _1510985, _1510987] : [c_Typedef_Otype__definition(_1510979, _1510981, _1510983, _1510985, _1510987), -(hAPP(c_Set_Oimage(_1510979, _1510981, _1510983), c_Orderings_Otop__class_Otop(tc_fun(_1510979, tc_HOL_Obool))) = _1510987)], (47648 ^ _777864) ^ [_1730506, _1730508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1730506), _1730508)), -(c_List_Oupto(_1730506, _1730508) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1730506), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1730506), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1730508)))], (12572 ^ _777864) ^ [_988931, _988933, _988935] : [class_Rings_Olinordered__ring__strict(_988931), 12575 ^ _777864 : [(12584 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988931), _988933), _988933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988931), _988935), _988935))), c_Groups_Ozero__class_Ozero(_988931)))), _988933 = c_Groups_Ozero__class_Ozero(_988931), _988935 = c_Groups_Ozero__class_Ozero(_988931)], (12576 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_988931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988931), _988933), _988933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988931), _988935), _988935))), c_Groups_Ozero__class_Ozero(_988931))), 12579 ^ _777864 : [(12582 ^ _777864) ^ [] : [-(_988935 = c_Groups_Ozero__class_Ozero(_988931))], (12580 ^ _777864) ^ [] : [-(_988933 = c_Groups_Ozero__class_Ozero(_988931))]]]]], (21058 ^ _777864) ^ [_1140948, _1140950] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140948), _1140950), hAPP(c_Int_Onumber__class_Onumber__of(_1140948), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1140948)), class_Fields_Ofield__inverse__zero(_1140948), class_Int_Onumber__ring(_1140948)], (27972 ^ _777864) ^ [_1276234, _1276236, _1276238, _1276240] : [class_Lattices_Osemilattice__sup(_1276234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276234), _1276236), _1276238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276234), _1276240), _1276238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276234), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276234), _1276236), _1276240)), _1276238)))], (29016 ^ _777864) ^ [_1302380, _1302382, _1302384] : [hBOOL(hAPP(hAPP(c_member(_1302380), _1302382), c_Wellfounded_Oacc(_1302380, _1302384))), 29019 ^ _777864 : [(29020 ^ _777864) ^ [_1302494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1302380, _1302380)), hAPP(hAPP(c_Product__Type_OPair(_1302380, _1302380), _1302494), _1302382)), _1302384)), -(hBOOL(hAPP(hAPP(c_member(_1302380), _1302494), c_Wellfounded_Oacc(_1302380, _1302384))))]]], (22546 ^ _777864) ^ [_1167609, _1167611, _1167613, _1167615] : [-(hAPP(c_Product__Type_Osnd(_1167609, _1167611), hAPP(hAPP(c_Product__Type_OPair(_1167609, _1167611), _1167613), _1167615)) = _1167615)], (3506 ^ _777864) ^ [_831117, _831119, _831121, _831123, _831125, _831127] : [-(c_Com_Ocom_OCond(_831127, _831123, _831119) = c_Com_Ocom_OCond(_831125, _831121, _831117)), _831127 = _831125, _831123 = _831121, _831119 = _831117], (22354 ^ _777864) ^ [_1164294, _1164296, _1164298] : [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), _1164294), _1164296))), -(hBOOL(hAPP(hAPP(_1164298, _1164294), _1164296))), 22361 ^ _777864 : [(22364 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1164298, 22359 ^ [_1164294, _1164296, _1164298]), 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)))), 22360 ^ [_1164294, _1164296, _1164298])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 22359 ^ [_1164294, _1164296, _1164298]), 22360 ^ [_1164294, _1164296, _1164298]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22360 ^ [_1164294, _1164296, _1164298]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22374 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1164298, 22359 ^ [_1164294, _1164296, _1164298]), 22360 ^ [_1164294, _1164296, _1164298]))], (22362 ^ _777864) ^ [] : [-(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), 22359 ^ [_1164294, _1164296, _1164298]), 22360 ^ [_1164294, _1164296, _1164298]))))]]], (6583 ^ _777864) ^ [_886579, _886581] : [class_Groups_Olinordered__ab__group__add(_886579), 6586 ^ _777864 : [(6593 ^ _777864) ^ [] : [_886581 = c_Groups_Ozero__class_Ozero(_886579), -(c_Groups_Ozero__class_Ozero(_886579) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886579), _886581), _886581))], (6587 ^ _777864) ^ [] : [c_Groups_Ozero__class_Ozero(_886579) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_886579), _886581), _886581), -(_886581 = c_Groups_Ozero__class_Ozero(_886579))]]], (43659 ^ _777864) ^ [_1629137, _1629139, _1629141, _1629143, _1629145] : [class_Complete__Lattice_Ocomplete__lattice(_1629137), 43662 ^ _777864 : [(43663 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1629137), _1629139), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629141, _1629137), _1629143), _1629145))), 43666 ^ _777864 : [(43667 ^ _777864) ^ [_1629318] : [hBOOL(hAPP(hAPP(c_member(_1629141), _1629318), _1629143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1629137), _1629139), hAPP(_1629145, _1629318))))]]], (43673 ^ _777864) ^ [] : [43675 ^ _777864 : [(43678 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1629137), _1629139), hAPP(_1629145, 43674 ^ [_1629137, _1629139, _1629141, _1629143, _1629145])))], (43676 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629141), 43674 ^ [_1629137, _1629139, _1629141, _1629143, _1629145]), _1629143)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1629137), _1629139), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629141, _1629137), _1629143), _1629145))))]]], (50476 ^ _777864) ^ [_1794497, _1794499, _1794501, _1794503] : [-(hAPP(c_List_Orev(_1794497), hAPP(hAPP(c_List_Omap(_1794499, _1794497), _1794501), _1794503)) = hAPP(hAPP(c_List_Omap(_1794499, _1794497), _1794501), hAPP(c_List_Orev(_1794499), _1794503)))], (19288 ^ _777864) ^ [_1109487, _1109489] : [class_Rings_Ocomm__semiring__1(_1109487), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109487), _1109489), _1109489) = hAPP(hAPP(c_Power_Opower__class_Opower(_1109487), _1109489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (6886 ^ _777864) ^ [_891123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891123), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_891123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29956 ^ _777864) ^ [_1322356, _1322358, _1322360, _1322362] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322356, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322356, tc_HOL_Obool)), _1322358), _1322360)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322356, tc_HOL_Obool)), _1322362), _1322360)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322356, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322356, tc_HOL_Obool)), _1322358), _1322360)), _1322362))], (33839 ^ _777864) ^ [_1403130, _1403132, _1403134, _1403136, _1403138] : [-(_1403130 = c_Orderings_Obot__class_Obot(tc_fun(_1403132, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403132, tc_fun(_1403134, tc_HOL_Obool)), _1403130), hAPP(hAPP(c_COMBC(_1403132, tc_fun(_1403134, tc_HOL_Obool), tc_fun(_1403134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1403134, tc_HOL_Obool), tc_fun(tc_fun(_1403134, tc_HOL_Obool), tc_fun(_1403134, tc_HOL_Obool)), _1403132), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403134, tc_HOL_Obool))), _1403136)), _1403138)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403134, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403132, tc_fun(_1403134, tc_HOL_Obool)), _1403130), _1403136)), _1403138))], (15708 ^ _777864) ^ [_1046222, _1046224, _1046226] : [hBOOL(hAPP(_1046222, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046224), _1046226))), 15711 ^ _777864 : [(15718 ^ _777864) ^ [_1046413] : [_1046224 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1046226), _1046413), -(hBOOL(hAPP(_1046222, _1046413)))], (15712 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046224), _1046226)), -(hBOOL(hAPP(_1046222, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (22783 ^ _777864) ^ [_1172357, _1172359, _1172361, _1172363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172357, tc_HOL_Obool)), _1172359), _1172361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1172357, tc_HOL_Obool)), _1172361), _1172363)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172357, tc_HOL_Obool)), _1172361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172357, tc_HOL_Obool)), _1172363), _1172359)) = _1172359)], (15848 ^ _777864) ^ [_1049267, _1049269, _1049271, _1049273, _1049275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049267), _1049269)), -(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), _1049267), _1049271)), _1049273)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049269), _1049271)), _1049275)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049273), 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), _1049269), _1049267)), _1049271)), _1049275)))], (35596 ^ _777864) ^ [_1440001, _1440003, _1440005] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1440001), _1440003))), 35599 ^ _777864 : [(35606 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1440005), _1440003))), -(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)), _1440001)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1440005), _1440003)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (35600 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1440005), _1440003)), -(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)), _1440001)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1440005), _1440003)) = 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))))]]], (47684 ^ _777864) ^ [_1731079, _1731081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731079)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731081))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731079), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731081)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731079)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731079)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1731081))))], (23389 ^ _777864) ^ [_1185990, _1185992, _1185994, _1185996, _1185998] : [hBOOL(hAPP(hAPP(_1185990, _1185992), _1185994)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1185996, _1185998, tc_HOL_Obool), _1185990), hAPP(hAPP(c_Product__Type_OPair(_1185996, _1185998), _1185992), _1185994))))], (42312 ^ _777864) ^ [_1599724, _1599726] : [42313 ^ _777864 : [(42314 ^ _777864) ^ [_1599770] : [hBOOL(hAPP(_1599724, _1599770))]], -(hBOOL(hAPP(_1599724, c_Hilbert__Choice_OEps(_1599726, _1599724))))], (32906 ^ _777864) ^ [_1381018, _1381020, _1381022] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381018), _1381020)), 32909 ^ _777864 : [(32910 ^ _777864) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381018, tc_Nat_Onat), _1381022), _1381020) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 32913 ^ _777864 : [(32914 ^ _777864) ^ [_1381180] : [hBOOL(hAPP(hAPP(c_member(_1381018), _1381180), _1381020)), -(hAPP(_1381022, _1381180) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (32920 ^ _777864) ^ [] : [32922 ^ _777864 : [(32925 ^ _777864) ^ [] : [hAPP(_1381022, 32921 ^ [_1381018, _1381020, _1381022]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (32923 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381018), 32921 ^ [_1381018, _1381020, _1381022]), _1381020)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381018, tc_Nat_Onat), _1381022), _1381020) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (20524 ^ _777864) ^ [_1131441, _1131443, _1131445] : [class_Fields_Olinordered__field(_1131441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131441), c_Groups_Ozero__class_Ozero(_1131441)), _1131443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131441), c_Groups_Ozero__class_Ozero(_1131441)), _1131445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131441), c_Groups_Ozero__class_Ozero(_1131441)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131441), _1131443), _1131445))))], (48766 ^ _777864) ^ [_1758100, _1758102, _1758104] : [-(_1758100 = c_List_Olist_ONil(_1758102)), -(hAPP(c_List_Ohd(_1758102), hAPP(c_List_Orotate(_1758102, _1758104), _1758100)) = hAPP(hAPP(c_List_Onth(_1758102), _1758100), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1758104, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758102)), _1758100))))], (36154 ^ _777864) ^ [_1450792] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1450792)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1450792)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1450792)))], (320 ^ _777864) ^ [_782710, _782712] : [-(c_Nat__Transfer_Ois__nat(_782710)), _782712 = _782710, c_Nat__Transfer_Ois__nat(_782712)], (16992 ^ _777864) ^ [_1070849, _1070851] : [16993 ^ _777864 : [(16996 ^ _777864) ^ [] : [_1070849 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16994 ^ _777864) ^ [] : [_1070851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1070849), _1070851) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6898 ^ _777864) ^ [_891306, _891308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _891306), hAPP(c_Nat_OSuc, _891308))), -(_891306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6906 ^ _777864 : [(6909 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 6905 ^ [_891306, _891308]), _891308)))], (6907 ^ _777864) ^ [] : [-(_891306 = hAPP(c_Nat_OSuc, 6905 ^ [_891306, _891308]))]]], (4384 ^ _777864) ^ [_844926, _844928, _844930, _844932] : [-(c_Complete__Lattice_OInf__class_OInf(_844932, _844928) = c_Complete__Lattice_OInf__class_OInf(_844930, _844926)), _844932 = _844930, _844928 = _844926], (15586 ^ _777864) ^ [_1043273, _1043275, _1043277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043273), _1043275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043277), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043275), _1043277)), _1043273))))], (50050 ^ _777864) ^ [_1785362, _1785364] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1785362, _1785364)))], (46899 ^ _777864) ^ [_1712874, _1712876, _1712878] : [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, _1712874), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1712874)), _1712876)))), -(hBOOL(hAPP(hAPP(c_member(_1712874), hAPP(c_Product__Type_Ofst(_1712874, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1712874, _1712876), _1712878))), hAPP(c_List_Oset(_1712874), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1712874), _1712874), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1712874)), _1712876)))))], (50849 ^ _777864) ^ [_1803723, _1803725] : [-(hBOOL(hAPP(c_List_Odistinct(_1803723), c_List_Oremdups(_1803723, _1803725))))], (44465 ^ _777864) ^ [_1651948, _1651950] : [-(hAPP(hAPP(c_Nat_Ocompow(_1651948, _1651948), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1651950) = c_Fun_Oid(_1651948))], (42279 ^ _777864) ^ [_1599110, _1599112, _1599114, _1599116, _1599118] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1599110), _1599112), _1599114), _1599116), _1599118) = c_New__DSequence_Opos__single(_1599110, _1599112))], (1492 ^ _777864) ^ [_799282, _799284] : [-(class_Rings_Olinordered__semidom(_799282)), _799284 = _799282, class_Rings_Olinordered__semidom(_799284)], (29548 ^ _777864) ^ [_1313930, _1313932, _1313934] : [29549 ^ _777864 : [(29552 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313930), _1313934))], (29550 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1313930), _1313932))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1313930), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313930, tc_HOL_Obool)), _1313932), _1313934))))], (47848 ^ _777864) ^ [_1735317, _1735319, _1735321, _1735323] : [-(c_List_Osublist(_1735317, hAPP(hAPP(c_List_Olist_OCons(_1735317), _1735319), _1735321), _1735323) = hAPP(hAPP(c_List_Oappend(_1735317), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1735317)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1735323)), hAPP(hAPP(c_List_Olist_OCons(_1735317), _1735319), c_List_Olist_ONil(_1735317))), c_List_Olist_ONil(_1735317))), c_List_Osublist(_1735317, _1735321, 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)), _1735323)))))], (50291 ^ _777864) ^ [_1789963, _1789965, _1789967, _1789969, _1789971] : [class_Orderings_Olinorder(_1789963), c_Fun_Oinj__on(_1789965, _1789963, _1789967, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1789965, tc_HOL_Obool)), hAPP(c_List_Oset(_1789965), _1789969)), hAPP(c_List_Oset(_1789965), _1789971))), c_List_Olinorder__class_Osorted(_1789963, hAPP(hAPP(c_List_Omap(_1789965, _1789963), _1789967), _1789969)), hBOOL(hAPP(c_List_Odistinct(_1789963), hAPP(hAPP(c_List_Omap(_1789965, _1789963), _1789967), _1789969))), c_List_Olinorder__class_Osorted(_1789963, hAPP(hAPP(c_List_Omap(_1789965, _1789963), _1789967), _1789971)), hBOOL(hAPP(c_List_Odistinct(_1789963), hAPP(hAPP(c_List_Omap(_1789965, _1789963), _1789967), _1789971))), hAPP(c_List_Oset(_1789965), _1789969) = hAPP(c_List_Oset(_1789965), _1789971), -(_1789969 = _1789971)], (34455 ^ _777864) ^ [_1417181, _1417183] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417181, tc_HOL_Obool)), _1417183), hAPP(c_Set_OPow(_1417181), _1417183))))], (51251 ^ _777864) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (25131 ^ _777864) ^ [_1218848, _1218850, _1218852] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218848), _1218850)), _1218850 = _1218852, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1218848), _1218852)))], (12698 ^ _777864) ^ [_991135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _991135)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_991135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13016 ^ _777864) ^ [_996271, _996273, _996275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996271)), _996271 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _996273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _996271), _996275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _996273), _996271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _996275)))], (33833 ^ _777864) ^ [_1402923, _1402925, _1402927, _1402929, _1402931] : [_1402923 = c_Orderings_Obot__class_Obot(tc_fun(_1402925, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402925, tc_fun(_1402927, tc_HOL_Obool)), _1402923), hAPP(hAPP(c_COMBC(_1402925, tc_fun(_1402927, tc_HOL_Obool), tc_fun(_1402927, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1402927, tc_HOL_Obool), tc_fun(tc_fun(_1402927, tc_HOL_Obool), tc_fun(_1402927, tc_HOL_Obool)), _1402925), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402927, tc_HOL_Obool))), _1402929)), _1402931)) = c_Orderings_Obot__class_Obot(tc_fun(_1402927, tc_HOL_Obool)))], (33537 ^ _777864) ^ [_1395006, _1395008, _1395010, _1395012, _1395014, _1395016] : [class_Complete__Lattice_Ocomplete__lattice(_1395006), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395008, _1395006), _1395010), hAPP(hAPP(c_COMBB(tc_fun(_1395012, _1395006), _1395006, _1395008), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395012, _1395006), _1395014)), _1395016)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395012, _1395006), _1395014), hAPP(hAPP(c_COMBB(tc_fun(_1395008, _1395006), _1395006, _1395012), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395008, _1395006), _1395010)), hAPP(c_COMBC(_1395008, _1395012, _1395006), _1395016))))], (28390 ^ _777864) ^ [_1287297, _1287299, _1287301, _1287303] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1287297, tc_HOL_Obool), tc_fun(_1287297, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1287297, tc_HOL_Obool), tc_fun(_1287297, tc_HOL_Obool)), _1287301), _1287303)), c_Wellfounded_Omax__ext(_1287297, _1287299))), -(c_Wellfounded_Omax__extp(_1287297, hAPP(hAPP(c_COMBC(_1287297, tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_fun(_1287297, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287297, tc_fun(tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_fun(_1287297, tc_HOL_Obool)), _1287297), c_COMBC(_1287297, tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1287297, tc_prod(_1287297, _1287297)), tc_fun(_1287297, tc_fun(tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_HOL_Obool)), _1287297), hAPP(c_COMBB(tc_prod(_1287297, _1287297), tc_fun(tc_fun(tc_prod(_1287297, _1287297), tc_HOL_Obool), tc_HOL_Obool), _1287297), c_member(tc_prod(_1287297, _1287297)))), c_Product__Type_OPair(_1287297, _1287297)))), _1287299), _1287301, _1287303))], (24281 ^ _777864) ^ [_1202961, _1202963] : [class_Orderings_Olinorder(_1202961), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1202961), _1202963), _1202963) = _1202963)], (3784 ^ _777864) ^ [_835458, _835460, _835462, _835464] : [-(c_Relation_OId__on(_835464, _835460) = c_Relation_OId__on(_835462, _835458)), _835464 = _835462, _835460 = _835458], (18676 ^ _777864) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (36138 ^ _777864) ^ [_1450557, _1450559, _1450561, _1450563, _1450565, _1450567] : [_1450557 = _1450559, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450561, _1450563), _1450565), _1450559), _1450567), _1450557) = _1450567)], (24767 ^ _777864) ^ [_1212733, _1212735] : [class_Rings_Ocomm__semiring__1(_1212733), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1212733), _1212735), c_Groups_Ozero__class_Ozero(_1212733))))], (40466 ^ _777864) ^ [_1550211] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1550211) = 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), _1550211), c_Int_Onat)))))], (43599 ^ _777864) ^ [_1627871, _1627873] : [c_Wellfounded_Oacyclic(_1627871, _1627873), -(c_Wellfounded_Oacyclic(_1627871, hAPP(c_Relation_Oconverse(_1627871, _1627871), _1627873)))], (47992 ^ _777864) ^ [_1738805, _1738807, _1738809, _1738811] : [-(hAPP(hAPP(c_List_Onth(_1738805), hAPP(hAPP(c_List_Oappend(_1738805), _1738807), _1738809)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738805)), _1738807)), _1738811)) = hAPP(hAPP(c_List_Onth(_1738805), _1738809), _1738811))], (41272 ^ _777864) ^ [_1574778, _1574780] : [c_Wellfounded_OwfP(_1574778, _1574780), 41275 ^ _777864 : [(41276 ^ _777864) ^ [_1574842] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1574778, _1574780), _1574842)))]]], (20682 ^ _777864) ^ [_1134476, _1134478, _1134480, _1134482] : [class_Fields_Olinordered__field__inverse__zero(_1134476), 20685 ^ _777864 : [(20686 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134476), _1134478), _1134480)), _1134482)), 20689 ^ _777864 : [(20696 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134480))), 20699 ^ _777864 : [(20706 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134480), c_Groups_Ozero__class_Ozero(_1134476)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134482)))], (20700 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134480), c_Groups_Ozero__class_Ozero(_1134476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134476), _1134482), _1134480)), _1134478)))]]], (20690 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134476), _1134482), _1134480))))]]], (20712 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134476), _1134478), _1134480)), _1134482))), 20715 ^ _777864 : [(20718 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134476), _1134482), _1134480)))], (20716 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134480)))]], 20719 ^ _777864 : [(20722 ^ _777864) ^ [] : [20723 ^ _777864 : [(20726 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134476), _1134482), _1134480)), _1134478))], (20724 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134480), c_Groups_Ozero__class_Ozero(_1134476))))]], 20727 ^ _777864 : [(20730 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134482))], (20728 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), _1134480), c_Groups_Ozero__class_Ozero(_1134476)))]]], (20720 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134476), c_Groups_Ozero__class_Ozero(_1134476)), _1134480))]]]]], (17584 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1978 ^ _777864) ^ [_806671, _806673, _806675, _806677, _806679, _806681, _806683, _806685, _806687, _806689] : [-(c_Option_Ooption_Ooption__rec(_806689, _806685, _806681, _806677, _806673) = c_Option_Ooption_Ooption__rec(_806687, _806683, _806679, _806675, _806671)), _806689 = _806687, _806685 = 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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)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100940), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1100938))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41007 ^ _777864) ^ [_1568211, _1568213, _1568215] : [c_Wellfounded_Owf(_1568211, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568211, _1568211), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568211, _1568211), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1568211, _1568211, _1568211), _1568213), _1568213)), hAPP(hAPP(c_Relation_Orel__comp(_1568211, _1568211, _1568211), _1568215), _1568213))), _1568215)), -(c_Wellfounded_Owf(_1568211, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568211, _1568211), tc_HOL_Obool)), _1568213), _1568215)))], (22745 ^ _777864) ^ 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1184488)), _1184490)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1184488), _1184490)))], (12079 ^ _777864) ^ [_980103, _980105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980103), _980105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _980103)), _980105)))], (31985 ^ _777864) ^ [_1362440, _1362442, _1362444] : [class_Orderings_Olinorder(_1362440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362440), _1362442)), -(_1362444 = c_Orderings_Obot__class_Obot(tc_fun(_1362440, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1362440, tc_HOL_Obool)), _1362444), _1362442)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362440), c_Big__Operators_Olattice_OSup__fin(_1362440, c_Orderings_Oord__class_Omax(_1362440), _1362444)), c_Big__Operators_Olattice_OSup__fin(_1362440, 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tc_prod(_1515024, _1515026)), _1515022), c_Product__Type_OPair(_1515024, _1515026)), _1515028)), _1515030)), _1515032) = hAPP(hAPP(c_Product__Type_OSigma(_1515024, _1515026), hAPP(c_Set_Oimage(_1515022, _1515024, _1515028), _1515032)), hAPP(hAPP(c_COMBB(tc_fun(_1515022, tc_HOL_Obool), tc_fun(_1515026, tc_HOL_Obool), _1515024), c_Set_Oimage(_1515022, _1515026, _1515030)), hAPP(hAPP(c_COMBC(_1515024, tc_fun(_1515022, tc_HOL_Obool), tc_fun(_1515022, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515022, tc_HOL_Obool), tc_fun(tc_fun(_1515022, tc_HOL_Obool), tc_fun(_1515022, tc_HOL_Obool)), _1515024), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515022, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1515024, tc_HOL_Obool), tc_fun(_1515022, tc_HOL_Obool), _1515024), c_Set_Ovimage(_1515022, _1515024, _1515028)), hAPP(hAPP(c_COMBC(_1515024, tc_fun(_1515024, tc_HOL_Obool), tc_fun(_1515024, tc_HOL_Obool)), c_Set_Oinsert(_1515024)), c_Orderings_Obot__class_Obot(tc_fun(_1515024, tc_HOL_Obool)))))), _1515032))))], (51271 ^ _777864) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (18350 ^ _777864) ^ [_1093428, _1093430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093428), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093428)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093430)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30108 ^ _777864) ^ [_1325689, _1325691] : [class_Lattices_Oboolean__algebra(_1325689), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325689), hAPP(c_Groups_Ouminus__class_Ouminus(_1325689), _1325691)), _1325691) = c_Orderings_Obot__class_Obot(_1325689))], (24293 ^ _777864) ^ [_1203153, _1203155] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1203153), _1203155) = 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), _1203153)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1203155)))))], (27129 ^ _777864) ^ [_1258348, _1258350, _1258352, _1258354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258348, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1258348), _1258350), _1258352)), _1258354)), 27132 ^ _777864 : [(27135 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1258348, tc_HOL_Obool)), _1258352), _1258354)))], (27133 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258348), _1258350), _1258354)))]]], (29628 ^ _777864) ^ [_1315736, _1315738, _1315740, _1315742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315736, tc_HOL_Obool)), _1315738), _1315740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315736, tc_HOL_Obool)), _1315738), _1315742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315736, tc_HOL_Obool)), _1315738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315736, tc_HOL_Obool)), _1315740), _1315742))))], (15488 ^ _777864) ^ [_1041415, _1041417, _1041419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041415), _1041417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041415), _1041419)), 15495 ^ _777864 : [(15502 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041417), _1041419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041417), _1041415)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041419), _1041415))))], (15496 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041417), _1041415)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041419), _1041415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1041417), _1041419)))]]], (46859 ^ _777864) ^ [_1711897, _1711899] : 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c_Random_Opick(_1711897, _1711899))))], (2312 ^ _777864) ^ [_811936, _811938] : [_811938 = _811936, -(c_Int_Opred(_811938) = c_Int_Opred(_811936))], (26025 ^ _777864) ^ [_1234732, _1234734] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1234732)), _1234734))), 26028 ^ _777864 : [(26031 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1234732), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234734)))], (26029 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234732)))]], 26032 ^ _777864 : [(26035 ^ _777864) ^ [] : [_1234734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26033 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234732))]]], (48983 ^ _777864) ^ [_1762570, _1762572, _1762574] : [class_Lattices_Olattice(_1762570), -(c_Big__Operators_Olattice__class_OInf__fin(_1762570, hAPP(c_List_Oset(_1762570), hAPP(hAPP(c_List_Olist_OCons(_1762570), _1762572), _1762574))) = hAPP(c_List_Ofoldl(_1762570, _1762570, c_Lattices_Osemilattice__inf__class_Oinf(_1762570), _1762572), _1762574))], (51389 ^ _777864) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (29920 ^ _777864) ^ [_1321598, _1321600, _1321602, _1321604] : [class_Lattices_Odistrib__lattice(_1321598), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321598), _1321600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321598), _1321602), _1321604)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321598), _1321600), _1321602)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321598), _1321600), _1321604)))], (8572 ^ _777864) ^ [_920006, _920008, _920010] : [class_Rings_Oring(_920006), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920006), hAPP(c_Groups_Ouminus__class_Ouminus(_920006), _920008)), hAPP(c_Groups_Ouminus__class_Ouminus(_920006), _920010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_920006), _920008), _920010))], (7394 ^ _777864) ^ [_899722, _899724, _899726] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_899722, _899724, _899726)))), hBOOL(hAPP(c_Com_OWT, _899724)), hBOOL(hAPP(c_Com_OWT, _899726))], (41232 ^ _777864) ^ [_1573962, _1573964, _1573966, _1573968] : [41233 ^ _777864 : [(41234 ^ _777864) ^ [_1574016] : [hBOOL(hAPP(hAPP(_1573966, _1574016), _1573968))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1573962, _1573964, _1573966), _1573968)))], (5256 ^ _777864) ^ [_858308, _858310] : [_858310 = _858308, -(c_List_Oset(_858310) = c_List_Oset(_858308))], (45408 ^ _777864) ^ [_1674234, _1674236, _1674238, _1674240, _1674242, _1674244] : [-(hBOOL(hAPP(hAPP(c_member(_1674234), _1674236), c_Map_Odom(_1674234, _1674238, _1674240)))), -(c_Map_Omap__add(_1674234, _1674238, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1674234, tc_Option_Ooption(_1674238)), _1674242), _1674236), hAPP(c_Option_Ooption_OSome(_1674238), _1674244)), _1674240) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1674234, tc_Option_Ooption(_1674238)), c_Map_Omap__add(_1674234, _1674238, _1674242, _1674240)), _1674236), hAPP(c_Option_Ooption_OSome(_1674238), _1674244)))], (34563 ^ _777864) ^ [_1419898, _1419900, _1419902] : [-(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)), _1419898)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1419900, _1419902)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419900), _1419898), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1419902), _1419898)))], (5028 ^ _777864) ^ [_854782, _854784, _854786, _854788] : [-(c_Product__Type_Ofst(_854788, _854784) = c_Product__Type_Ofst(_854786, _854782)), _854788 = _854786, _854784 = _854782], (2474 ^ _777864) ^ [_814435, _814437, _814439, _814441] : [-(c_Nitpick_Oinverse__frac(_814441, _814437) = c_Nitpick_Oinverse__frac(_814439, _814435)), _814441 = _814439, _814437 = _814435], (43929 ^ _777864) ^ [_1637494, _1637496, _1637498, _1637500] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1637494, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637496, tc_fun(_1637494, tc_HOL_Obool)), _1637498), _1637500)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637496, tc_fun(_1637494, tc_HOL_Obool)), _1637498), hAPP(hAPP(c_COMBB(tc_fun(_1637494, tc_HOL_Obool), tc_fun(_1637494, tc_HOL_Obool), _1637496), c_Groups_Ouminus__class_Ouminus(tc_fun(_1637494, tc_HOL_Obool))), _1637500)))], (45941 ^ _777864) ^ [_1686596, _1686598, _1686600, _1686602] : [-(c_Map_Omap__of(_1686596, _1686598, hAPP(hAPP(c_List_Omap(_1686596, tc_prod(_1686596, _1686598)), hAPP(hAPP(c_COMBS(_1686596, _1686598, tc_prod(_1686596, _1686598)), c_Product__Type_OPair(_1686596, _1686598)), _1686600)), _1686602)) = c_Map_Orestrict__map(_1686596, _1686598, hAPP(c_Fun_Ocomp(_1686598, tc_Option_Ooption(_1686598), _1686596, c_Option_Ooption_OSome(_1686598)), _1686600), hAPP(c_List_Oset(_1686596), _1686602)))], (4772 ^ _777864) ^ [_850860, _850862, _850864, _850866] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850866, _850862) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850864, _850860)), _850866 = _850864, _850862 = _850860], (11373 ^ _777864) ^ [_967356, _967358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _967356), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _967356), _967358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _967356))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _967358))))], (46354 ^ _777864) ^ [_1696570, _1696572, _1696574] : [hBOOL(hAPP(hAPP(c_member(_1696570), _1696572), hAPP(c_List_Oset(_1696570), _1696574))), -(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(_1696570)), _1696574))))], (8606 ^ _777864) ^ [_920614] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _920614) = _920614)], (50082 ^ _777864) ^ [_1785857, _1785859] : [class_Orderings_Olinorder(_1785857), c_List_Olinorder__class_Osorted(_1785857, _1785859), -(c_List_Olinorder__class_Osorted(_1785857, hAPP(c_List_Otl(_1785857), _1785859)))], (44184 ^ _777864) ^ [_1645124, _1645126, _1645128] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1645124, _1645126, _1645126), _1645128), c_Relation_OId(_1645126)) = _1645128)], (20574 ^ _777864) ^ [_1132414, _1132416, _1132418, _1132420] : [class_Fields_Olinordered__field(_1132414), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132414), _1132416), c_Groups_Ozero__class_Ozero(_1132414))), 20581 ^ _777864 : [(20588 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132414), _1132420), _1132416)), _1132418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132414), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132414), _1132418), _1132416)), _1132420)))], (20582 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132414), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132414), _1132418), _1132416)), _1132420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132414), _1132420), _1132416)), _1132418)))]]], (17764 ^ _777864) ^ [_1083963, _1083965] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083963) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1083965)), 17767 ^ _777864 : [(17770 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083965)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17768 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083963))))]], 17771 ^ _777864 : [(17774 ^ _777864) ^ [] : [17775 ^ _777864 : [(17778 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083963) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17776 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083965))))]], 17779 ^ _777864 : [(17782 ^ _777864) ^ [] : [_1083963 = _1083965], (17780 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083965)))]]], (17772 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083963)))]]], (7542 ^ _777864) ^ [_902877, _902879, _902881, _902883, _902885] : [class_Rings_Ocomm__semiring__1(_902877), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), _902879), _902881)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), _902883), _902885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), _902879), _902883)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902877), _902881), _902885)))], (39912 ^ _777864) ^ [_1534983] : [-(c_Relation_Orefl__on(_1534983, c_Orderings_Obot__class_Obot(tc_fun(_1534983, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1534983, _1534983), tc_HOL_Obool))))], (26479 ^ _777864) ^ [_1244378, _1244380] : [class_Orderings_Oorder(_1244378), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1244378, 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)))), _1244380), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1244378, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1244380))], (50931 ^ _777864) ^ [_1805125, _1805127] : [-(c_List_Oremdups(_1805125, c_List_Oremdups(_1805125, _1805127)) = c_List_Oremdups(_1805125, _1805127))], (49741 ^ _777864) ^ [_1780091, _1780093] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1780091, _1780093)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1780093), _1780091))], (11755 ^ _777864) ^ [_974358, _974360, _974362] : [class_Rings_Olinordered__ring__strict(_974358), 11758 ^ _777864 : [(11773 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974358), _974360), _974362)))), 11774 ^ _777864 : [(11781 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), _974360), c_Groups_Ozero__class_Ozero(_974358))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), _974362), c_Groups_Ozero__class_Ozero(_974358)))], (11775 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), _974360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), _974362))]]], (11759 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974358), _974360), _974362))), 11764 ^ _777864 : [(11767 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), _974362)))], (11765 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), c_Groups_Ozero__class_Ozero(_974358)), _974360)))]], 11768 ^ _777864 : [(11771 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), _974362), c_Groups_Ozero__class_Ozero(_974358))))], (11769 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974358), _974360), c_Groups_Ozero__class_Ozero(_974358))))]]]]], (28207 ^ _777864) ^ [_1281022, _1281024, _1281026, _1281028] : [28209 ^ _777864 : [(28212 ^ _777864) ^ [] : [hBOOL(hAPP(_1281028, 28208 ^ [_1281022, _1281024, _1281026, _1281028]))], (28210 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1281022), 28208 ^ [_1281022, _1281024, _1281026, _1281028]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281022, tc_HOL_Obool)), _1281024), _1281026))))]], 28213 ^ _777864 : [(28220 ^ _777864) ^ [_1281339] : [hBOOL(hAPP(hAPP(c_member(_1281022), _1281339), _1281026)), -(hBOOL(hAPP(_1281028, _1281339)))], (28214 ^ _777864) ^ [_1281242] : [hBOOL(hAPP(hAPP(c_member(_1281022), _1281242), _1281024)), -(hBOOL(hAPP(_1281028, _1281242)))]]], (39095 ^ _777864) ^ [_1515726, _1515728, _1515730, _1515732, _1515734, _1515736] : [hBOOL(hAPP(hAPP(c_member(_1515726), _1515728), _1515730)), hBOOL(hAPP(hAPP(c_member(_1515732), _1515734), hAPP(_1515736, _1515728))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515726, _1515732)), hAPP(hAPP(c_Product__Type_OPair(_1515726, _1515732), _1515728), _1515734)), hAPP(hAPP(c_Product__Type_OSigma(_1515726, _1515732), _1515730), _1515736))))], (30510 ^ _777864) ^ [_1335510, _1335512, _1335514, _1335516] : [hBOOL(hAPP(hAPP(_1335514, _1335512), _1335516)), -(hBOOL(hAPP(hAPP(c_member(_1335510), _1335512), c_SetInterval_Oord_OatMost(_1335510, _1335514, _1335516))))], (12788 ^ _777864) ^ [_992506, _992508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _992506), _992508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _992506), c_Groups_Oone__class_Oone(tc_Int_Oint))), _992508)))], (18216 ^ _777864) ^ [_1091236] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1091236), c_Int_OMin) = c_Int_Osucc(_1091236))], (34175 ^ _777864) ^ [_1411156, _1411158, _1411160, _1411162] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1411156, _1411156)), hAPP(hAPP(c_Product__Type_OPair(_1411156, _1411156), _1411158), _1411160)), c_Relation_OId__on(_1411156, _1411162)))), _1411158 = _1411160, hBOOL(hAPP(hAPP(c_member(_1411156), _1411158), _1411162))], (23305 ^ _777864) ^ [_1184037, _1184039, _1184041] : [-(hAPP(c_Nat_Onat_Onat__rec(_1184037, _1184039, _1184041), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1184039)], (38043 ^ _777864) ^ [_1491918, _1491920, _1491922, _1491924, _1491926] : [hBOOL(hAPP(hAPP(c_member(_1491918), _1491920), c_Map_Oran(_1491922, _1491918, c_Map_Orestrict__map(_1491922, _1491918, _1491924, _1491926)))), 38047 ^ _777864 : [(38050 ^ _777864) ^ [] : [-(hAPP(_1491924, 38046 ^ [_1491918, _1491920, _1491922, _1491924, _1491926]) = hAPP(c_Option_Ooption_OSome(_1491918), _1491920))], (38048 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491922), 38046 ^ [_1491918, _1491920, _1491922, _1491924, _1491926]), _1491926)))]]], (51285 ^ _777864) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (22268 ^ _777864) ^ [_1162590, _1162592] : [-(_1162590 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1162592, _1162590), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1162592), _1162590)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1162592, _1162590)))))], (2490 ^ _777864) ^ [_814669, _814671, _814673, _814675] : [-(c_Nitpick_OAbs__Frac(_814675, _814671) = c_Nitpick_OAbs__Frac(_814673, _814669)), _814675 = _814673, _814671 = _814669], (27986 ^ _777864) ^ [_1276483, _1276485, _1276487, _1276489] : [class_Lattices_Osemilattice__sup(_1276483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276483), _1276485), _1276487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276483), _1276489), _1276487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276483), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276483), _1276485), _1276489)), _1276487)))], (19480 ^ _777864) ^ [_1112652, _1112654, _1112656] : [class_Rings_Ocomm__semiring__1(_1112652), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1112652), _1112654), 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)))), _1112656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1112652), hAPP(hAPP(c_Power_Opower__class_Opower(_1112652), _1112654), _1112656)), hAPP(hAPP(c_Power_Opower__class_Opower(_1112652), _1112654), _1112656)))], (49534 ^ _777864) ^ [_1774637, _1774639, _1774641, _1774643, _1774645, _1774647] : [class_Orderings_Olinorder(_1774637), -(hBOOL(hAPP(_1774639, _1774641))), -(hAPP(c_List_Ofilter(_1774643, _1774639), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1774643, _1774637, _1774645), _1774641), _1774647)) = hAPP(c_List_Ofilter(_1774643, _1774639), _1774647))], (18980 ^ _777864) ^ [_1104093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104093)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104093), c_Int_OPls)))], (24671 ^ _777864) ^ [_1210615, _1210617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210615)), hAPP(c_Code__Numeral_Onat__of, _1210617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1210615), _1210617)))], (47516 ^ _777864) ^ [_1727910, _1727912, _1727914, _1727916, _1727918] : [-(hAPP(hAPP(c_List_Olist__update(_1727910, hAPP(hAPP(c_List_Olist__update(_1727910, _1727912), _1727914), _1727916)), _1727914), _1727918) = hAPP(hAPP(c_List_Olist__update(_1727910, _1727912), _1727914), _1727918))], (32771 ^ _777864) ^ [_1378480, _1378482] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1378480, _1378482))))], (41978 ^ _777864) ^ [_1592134, _1592136, _1592138, _1592140, _1592142] : [c_Hoare__Mirabelle_Ohoare__derivs(_1592134, _1592136, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1592134)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1592134), c_Hoare__Mirabelle_Opeek__and(_1592134, _1592138, _1592140)), _1592142), _1592138)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1592134), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1592134, _1592136, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1592134)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1592134), _1592138), c_Com_Ocom_OWhile(_1592140, _1592142)), c_Hoare__Mirabelle_Opeek__and(_1592134, _1592138, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1592140)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1592134), tc_HOL_Obool)))))], (47536 ^ _777864) ^ [_1728243, _1728245] : [-(c_List_Olistrelp(_1728243, _1728245, c_List_Olist_ONil(_1728243), c_List_Olist_ONil(_1728243)))], (46996 ^ _777864) ^ [_1714812, _1714814, _1714816, _1714818, _1714820, _1714822] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714812), tc_List_Olist(_1714812))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714812), tc_List_Olist(_1714812)), hAPP(hAPP(c_List_Olist_OCons(_1714812), _1714814), _1714816)), hAPP(hAPP(c_List_Olist_OCons(_1714812), _1714818), _1714820))), c_List_Olexord(_1714812, _1714822))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714812, _1714812)), hAPP(hAPP(c_Product__Type_OPair(_1714812, _1714812), _1714814), _1714818)), _1714822))), 47003 ^ _777864 : [(47006 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714812), tc_List_Olist(_1714812))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714812), tc_List_Olist(_1714812)), _1714816), _1714820)), c_List_Olexord(_1714812, _1714822))))], (47004 ^ _777864) ^ [] : [-(_1714814 = _1714818)]]], (68 ^ _777864) ^ [_778760, _778762] : [-(class_Fields_Olinordered__field__inverse__zero(_778760)), _778762 = _778760, class_Fields_Olinordered__field__inverse__zero(_778762)], (10087 ^ _777864) ^ [_946357, _946359] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946357), _946359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _946359), _946357)))], (23387 ^ _777864) ^ [_1185927, _1185929] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1185927)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1185929)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1185929))), 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), _1185927)), c_Int_Onat)))))], (51313 ^ _777864) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (16802 ^ _777864) ^ [_1067321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067321), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1067321) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1067321))], (6088 ^ _777864) ^ [_878065] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _878065))), -(hAPP(c_Com_Obody, _878065) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6091 ^ [_878065]))], (42299 ^ _777864) ^ [_1599519, _1599521] : [hBOOL(hAPP(_1599519, c_Hilbert__Choice_OEps(_1599521, _1599519))), -(hBOOL(hAPP(_1599519, 42302 ^ [_1599519, _1599521])))], (39291 ^ _777864) ^ [_1521185, _1521187, _1521189, _1521191] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521185, _1521187)), hAPP(hAPP(c_Product__Type_OSigma(_1521185, _1521187), _1521189), hAPP(c_COMBK(tc_fun(_1521187, tc_HOL_Obool), _1521185), _1521191)))), -(_1521189 = c_Orderings_Obot__class_Obot(tc_fun(_1521185, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521187), _1521191)))], (23187 ^ _777864) ^ [_1180732, _1180734] : [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(_1180734))), 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), _1180732)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1180732)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180734))))], (14656 ^ _777864) ^ [_1025653, _1025655, _1025657, _1025659] : [class_Divides_Osemiring__div(_1025653), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025653), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1025653), _1025655), _1025657)), _1025657)), c_Divides_Odiv__class_Omod(_1025653, _1025655, _1025657))), _1025659) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025653), _1025655), _1025659))], (30080 ^ _777864) ^ [_1325117, _1325119] : [class_Lattices_Olattice(_1325117), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325117), _1325119), _1325119) = _1325119)], (51381 ^ _777864) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (30408 ^ _777864) ^ [_1332438, _1332440] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332438), 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)))), _1332440)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332438), _1332440)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332440), _1332438)))], (48668 ^ _777864) ^ [_1756148, _1756150, _1756152, _1756154] : [-(hAPP(c_List_Orotate1(_1756148), c_List_Olist_ONil(_1756148)) = c_List_Olist_ONil(_1756148))], (37090 ^ _777864) ^ [_1472018, _1472020, _1472022, _1472024, _1472026, _1472028] : [hBOOL(hAPP(hAPP(c_member(_1472018), _1472020), _1472022)), -(c_Map_Orestrict__map(_1472018, _1472024, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472018, tc_Option_Ooption(_1472024)), _1472026), _1472020), _1472028), _1472022) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472018, tc_Option_Ooption(_1472024)), c_Map_Orestrict__map(_1472018, _1472024, _1472026, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472018, tc_HOL_Obool)), _1472022), hAPP(hAPP(c_Set_Oinsert(_1472018), _1472020), c_Orderings_Obot__class_Obot(tc_fun(_1472018, tc_HOL_Obool)))))), _1472020), _1472028))], (49025 ^ _777864) ^ [_1763569, _1763571, _1763573, _1763575, _1763577] : [hBOOL(hAPP(hAPP(c_member(_1763569), _1763571), hAPP(c_List_Oset(_1763569), _1763573))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763575), hAPP(_1763577, _1763571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763575), c_List_Olist_Olist__size(_1763569, _1763577, _1763573))))], (8526 ^ _777864) ^ [_919329, _919331, _919333] : [class_Rings_Oidom(_919329), 8529 ^ _777864 : [(8530 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919329), _919331), _919331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919329), _919333), _919333), -(_919331 = _919333), -(_919331 = hAPP(c_Groups_Ouminus__class_Ouminus(_919329), _919333))], (8540 ^ _777864) ^ [] : [8541 ^ _777864 : [(8544 ^ _777864) ^ [] : [_919331 = hAPP(c_Groups_Ouminus__class_Ouminus(_919329), _919333)], (8542 ^ _777864) ^ [] : [_919331 = _919333]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919329), _919331), _919331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919329), _919333), _919333))]]], (9732 ^ _777864) ^ [_940406, _940408, _940410] : [class_Rings_Olinordered__idom(_940406), 9735 ^ _777864 : [(9742 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _940408), _940410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940406), hAPP(c_Int_Oring__1__class_Oof__int(_940406), _940408)), hAPP(c_Int_Oring__1__class_Oof__int(_940406), _940410))))], (9736 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940406), hAPP(c_Int_Oring__1__class_Oof__int(_940406), _940408)), hAPP(c_Int_Oring__1__class_Oof__int(_940406), _940410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _940408), _940410)))]]], (48488 ^ _777864) ^ [_1751869, _1751871] : [-(hAPP(hAPP(c_List_Odrop(_1751869), _1751871), c_List_Olist_ONil(_1751869)) = c_List_Olist_ONil(_1751869))], (35898 ^ _777864) ^ [_1445679, _1445681, _1445683] : [class_Groups_Oordered__ab__group__add(_1445679), -(hAPP(c_Set_Oimage(_1445679, _1445679, c_Groups_Ouminus__class_Ouminus(_1445679)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1445679, _1445681, _1445683)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1445679, hAPP(c_Groups_Ouminus__class_Ouminus(_1445679), _1445683)), hAPP(c_Groups_Ouminus__class_Ouminus(_1445679), _1445681)))], (49458 ^ _777864) ^ [_1772970, _1772972, _1772974, _1772976] : [hAPP(hAPP(c_List_Oappend(_1772970), _1772972), hAPP(hAPP(c_List_Olist_OCons(_1772970), _1772974), c_List_Olist_ONil(_1772970))) = _1772976, 49461 ^ _777864 : [(49466 ^ _777864) ^ [] : [-(c_List_Olast(_1772970, _1772976) = _1772974)], (49464 ^ _777864) ^ [] : [-(c_List_Obutlast(_1772970, _1772976) = _1772972)], (49462 ^ _777864) ^ [] : [_1772976 = c_List_Olist_ONil(_1772970)]]], (844 ^ _777864) ^ [_790910, _790912] : [-(class_Lattices_Oab__semigroup__idem__mult(_790910)), _790912 = _790910, class_Lattices_Oab__semigroup__idem__mult(_790912)], (5942 ^ _777864) ^ [_875501, _875503, _875505] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_875501, _875503, _875505))), -(hBOOL(hAPP(c_Com_OWT, _875505)))], (38764 ^ _777864) ^ [_1507911, _1507913, _1507915, _1507917, _1507919, _1507921] : [-(hAPP(c_Set_Ovimage(_1507911, _1507913, _1507915), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507917, tc_fun(_1507913, tc_HOL_Obool)), _1507919), _1507921)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507917, tc_fun(_1507911, tc_HOL_Obool)), _1507919), hAPP(hAPP(c_COMBB(tc_fun(_1507913, tc_HOL_Obool), tc_fun(_1507911, tc_HOL_Obool), _1507917), c_Set_Ovimage(_1507911, _1507913, _1507915)), _1507921)))], (6661 ^ _777864) ^ [_887746, _887748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _887746), _887748)), _887748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48742 ^ _777864) ^ [_1757875, _1757877, _1757879, _1757881] : [-(_1757875 = c_List_Olist_ONil(_1757877)), -(hAPP(c_List_Ohd(_1757879), hAPP(hAPP(c_List_Omap(_1757877, _1757879), _1757881), _1757875)) = hAPP(_1757881, hAPP(c_List_Ohd(_1757877), _1757875)))], (16232 ^ _777864) ^ [_1056328, _1056330] : [class_Rings_Olinordered__idom(_1056328), -(hAPP(c_Groups_Oabs__class_Oabs(_1056328), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056328), _1056330)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056328), _1056330))], (12968 ^ _777864) ^ [_995506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _995506)), -(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)), _995506))))], (26257 ^ _777864) ^ [_1239670, _1239672, _1239674] : [hAPP(hAPP(c_Set_Oinsert(_1239670), _1239672), c_Orderings_Obot__class_Obot(tc_fun(_1239670, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1239670), _1239674), c_Orderings_Obot__class_Obot(tc_fun(_1239670, tc_HOL_Obool))), -(_1239672 = _1239674)], (51625 ^ _777864) ^ [_1813470] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _1813470), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, hAPP(c_Nat_OSuc, v_na), _1813470))], (8662 ^ _777864) ^ [_921644, _921646, _921648] : [class_Groups_Ogroup__add(_921644), 8665 ^ _777864 : [(8672 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_921644), _921648) = _921646, -(hAPP(c_Groups_Ouminus__class_Ouminus(_921644), _921646) = _921648)], (8666 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_921644), _921646) = _921648, -(hAPP(c_Groups_Ouminus__class_Ouminus(_921644), _921648) = _921646)]]], (39131 ^ _777864) ^ [_1516742, _1516744, _1516746, _1516748, _1516750, _1516752] : [class_Groups_Ocomm__monoid__add(_1516742), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516744, _1516742), hAPP(hAPP(c_COMBC(_1516744, tc_fun(_1516746, tc_HOL_Obool), _1516742), hAPP(hAPP(c_COMBB(tc_fun(_1516746, _1516742), tc_fun(tc_fun(_1516746, tc_HOL_Obool), _1516742), _1516744), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1516746, _1516742)), _1516748)), _1516750)), _1516752) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1516744, _1516746), _1516742), hAPP(c_Product__Type_Oprod_Oprod__case(_1516744, _1516746, _1516742), _1516748)), hAPP(hAPP(c_Product__Type_OSigma(_1516744, _1516746), _1516752), hAPP(c_COMBK(tc_fun(_1516746, tc_HOL_Obool), _1516744), _1516750))))], (5372 ^ _777864) ^ [_860050, _860052, _860054, _860056] : [-(tc_fun(_860056, _860052) = tc_fun(_860054, _860050)), _860056 = _860054, _860052 = _860050], (43267 ^ _777864) ^ [_1620273, _1620275, _1620277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620273, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1620273, _1620273, _1620275), _1620277)), _1620277)), -(hAPP(c_Relation_OImage(_1620273, _1620273, c_Transitive__Closure_Ortrancl(_1620273, _1620275)), _1620277) = _1620277)], (39175 ^ _777864) ^ [_1518259, _1518261, _1518263, _1518265] : [_1518259 = c_Finite__Set_Ofold1(_1518261, _1518263), -(hAPP(_1518259, hAPP(hAPP(c_Set_Oinsert(_1518261), _1518265), c_Orderings_Obot__class_Obot(tc_fun(_1518261, tc_HOL_Obool)))) = _1518265)], (17046 ^ _777864) ^ [_1071719, _1071721] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1071719)), _1071721) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071719), _1071721)))], (47768 ^ _777864) ^ [_1733256, _1733258, _1733260] : [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), _1733256), _1733258))), -(hBOOL(hAPP(hAPP(_1733260, _1733256), _1733258))), 47775 ^ _777864 : [(47778 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 47773 ^ [_1733256, _1733258, _1733260]), 47774 ^ [_1733256, _1733258, _1733260])), -(hBOOL(hAPP(hAPP(_1733260, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 47773 ^ [_1733256, _1733258, _1733260]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 47774 ^ [_1733256, _1733258, _1733260])))], (47784 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1733260, 47773 ^ [_1733256, _1733258, _1733260]), 47774 ^ [_1733256, _1733258, _1733260]))], (47776 ^ _777864) ^ [] : [-(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), 47773 ^ [_1733256, _1733258, _1733260]), 47774 ^ [_1733256, _1733258, _1733260]))))]]], (40212 ^ _777864) ^ [_1541237, _1541239, _1541241] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1541237, tc_HOL_Obool)), _1541239), _1541241) = hAPP(c_Set_OCollect(_1541237), hAPP(hAPP(c_COMBS(_1541237, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541237), c_fdisj), hAPP(hAPP(c_COMBC(_1541237, tc_fun(_1541237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541237)), _1541239))), hAPP(hAPP(c_COMBC(_1541237, tc_fun(_1541237, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541237)), _1541241))))], (9204 ^ _777864) ^ [_931170, _931172] : [class_Groups_Oordered__ab__group__add(_931170), 9207 ^ _777864 : [(9214 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931170), c_Groups_Ozero__class_Ozero(_931170)), _931172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931170), hAPP(c_Groups_Ouminus__class_Ouminus(_931170), _931172)), c_Groups_Ozero__class_Ozero(_931170))))], (9208 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931170), hAPP(c_Groups_Ouminus__class_Ouminus(_931170), _931172)), c_Groups_Ozero__class_Ozero(_931170))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931170), c_Groups_Ozero__class_Ozero(_931170)), _931172)))]]], (38926 ^ _777864) ^ [_1511698, _1511700, _1511702, _1511704, _1511706, _1511708, _1511710] : [c_Typedef_Otype__definition(_1511698, _1511700, _1511702, _1511704, _1511706), hBOOL(hAPP(hAPP(c_member(_1511700), _1511708), _1511706)), hBOOL(hAPP(hAPP(c_member(_1511700), _1511710), _1511706)), 38937 ^ _777864 : [(38944 ^ _777864) ^ [] : [_1511708 = _1511710, -(hAPP(_1511704, _1511708) = hAPP(_1511704, _1511710))], (38938 ^ _777864) ^ [] : [hAPP(_1511704, _1511708) = hAPP(_1511704, _1511710), -(_1511708 = _1511710)]]], (12180 ^ _777864) ^ [_981726] : [-(hBOOL(hAPP(_981726, 12187 ^ [_981726]))), 12181 ^ _777864 : [(12182 ^ _777864) ^ [_981778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _981778)), hBOOL(hAPP(_981726, hAPP(c_Int_Onat, _981778)))]]], (50857 ^ _777864) ^ [_1803886, _1803888] : [-(hAPP(c_List_Oset(_1803886), c_List_Oremdups(_1803886, _1803888)) = hAPP(c_List_Oset(_1803886), _1803888))], (17012 ^ _777864) ^ [_1071125, _1071127] : [17013 ^ _777864 : [(17016 ^ _777864) ^ [] : [_1071127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17014 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1071125))]], -(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), _1071125), _1071127))))], (49440 ^ _777864) ^ [_1772681, _1772683, _1772685, _1772687] : [_1772681 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772683)), _1772685)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1772683, hAPP(hAPP(c_List_Olist__update(_1772683, _1772685), _1772681), _1772687)) = c_List_Obutlast(_1772683, _1772685))], (15558 ^ _777864) ^ [_1042736, _1042738, _1042740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042736), _1042738)), 15561 ^ _777864 : [(15568 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042740), _1042736)), _1042738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042738), _1042736))))], (15562 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042740), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042738), _1042736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042740), _1042736)), _1042738)))]]], (41646 ^ _777864) ^ [_1584244, _1584246] : [41648 ^ _777864 : [(41651 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1584246), 41647 ^ [_1584244, _1584246]))], (41649 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 41647 ^ [_1584244, _1584246]), _1584244)))]], -(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)), _1584246), _1584244))], (26731 ^ _777864) ^ [_1249797, _1249799, _1249801, _1249803] : [_1249797 = _1249799, 26736 ^ _777864 : [(26739 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249801), _1249803), _1249799)))], (26737 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1249801), _1249803), _1249797)))]], 26740 ^ _777864 : [(26743 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1249801), _1249803), _1249799))], (26741 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1249801), _1249803), _1249797))]]], (10386 ^ _777864) ^ [_951234, _951236, _951238] : [class_Rings_Olinordered__idom(_951234), 10389 ^ _777864 : [(10396 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _951236), _951238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951234), hAPP(c_Int_Oring__1__class_Oof__int(_951234), _951236)), hAPP(c_Int_Oring__1__class_Oof__int(_951234), _951238))))], (10390 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951234), hAPP(c_Int_Oring__1__class_Oof__int(_951234), _951236)), hAPP(c_Int_Oring__1__class_Oof__int(_951234), _951238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _951236), _951238)))]]], (26281 ^ _777864) ^ [_1240164, _1240166, _1240168, _1240170, _1240172] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1240164, _1240166, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1240164)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1240164), hAPP(hAPP(c_COMBC(_1240164, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1240164), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1240168)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1240170)), _1240172))), c_Com_Ocom_OAss(_1240170, _1240172)), _1240168)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1240164), tc_HOL_Obool)))))], (3628 ^ _777864) ^ [_833082, _833084] : [_833084 = _833082, -(c_New__Random__Sequence_Oneg__single(_833084) = c_New__Random__Sequence_Oneg__single(_833082))], (9754 ^ _777864) ^ [_940818, _940820] : [class_Rings_Oring__1(_940818), -(hAPP(c_Int_Oring__1__class_Oof__int(_940818), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _940820)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_940818), _940820))], (36156 ^ _777864) ^ [_1450833, _1450835, _1450837] : [class_Orderings_Oord(_1450833), 36159 ^ _777864 : [(36166 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450833), _1450835), _1450837)), -(hBOOL(hAPP(hAPP(c_member(_1450833), _1450835), hAPP(c_SetInterval_Oord__class_OatMost(_1450833), _1450837))))], (36160 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1450833), _1450835), hAPP(c_SetInterval_Oord__class_OatMost(_1450833), _1450837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1450833), _1450835), _1450837)))]]], (47966 ^ _777864) ^ [_1738135, _1738137, _1738139, _1738141] : [hBOOL(hAPP(hAPP(c_member(_1738135), _1738137), hAPP(c_List_Oset(_1738135), _1738139))), -(c_List_Oremove1(_1738135, _1738137, hAPP(hAPP(c_List_Oappend(_1738135), _1738139), _1738141)) = hAPP(hAPP(c_List_Oappend(_1738135), c_List_Oremove1(_1738135, _1738137, _1738139)), _1738141))], (39137 ^ _777864) ^ [_1517008, _1517010, _1517012, _1517014] : [hAPP(hAPP(c_Product__Type_OSigma(_1517008, _1517010), _1517012), hAPP(c_COMBK(tc_fun(_1517010, tc_HOL_Obool), _1517008), _1517014)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517008, _1517010), tc_HOL_Obool)), -(_1517012 = c_Orderings_Obot__class_Obot(tc_fun(_1517008, tc_HOL_Obool))), -(_1517014 = c_Orderings_Obot__class_Obot(tc_fun(_1517010, tc_HOL_Obool)))], (9768 ^ _777864) ^ [_941069, _941071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _941069)), hAPP(c_Int_Onat, _941071)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _941071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _941069), _941071))], (15268 ^ _777864) ^ [_1037119, _1037121, _1037123] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037119), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1037121), _1037123)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037119), _1037121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1037119), _1037123)))], (6150 ^ _777864) ^ [_879016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _879016), hAPP(c_Nat_OSuc, _879016))))], (48037 ^ _777864) ^ [_1739921, _1739923, _1739925, _1739927] : [_1739925 = _1739927, -(hAPP(hAPP(c_List_Oappend(_1739921), _1739923), _1739925) = hAPP(hAPP(c_List_Oappend(_1739921), _1739923), _1739927))], (48111 ^ _777864) ^ [_1741364, _1741366, _1741368] : [-(hAPP(hAPP(c_List_Oappend(_1741364), _1741366), _1741368) = c_List_Olist_ONil(_1741364)), _1741366 = c_List_Olist_ONil(_1741364), _1741368 = c_List_Olist_ONil(_1741364)], (14410 ^ _777864) ^ [_1021539, _1021541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021539), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021541), _1021539)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1021539), _1021541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24187 ^ _777864) ^ [_1201414, _1201416, _1201418] : [class_Groups_Olinordered__ab__group__add(_1201414), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1201414), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201414), _1201416), _1201418)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201414), hAPP(c_Groups_Ouminus__class_Ouminus(_1201414), _1201416)), hAPP(c_Groups_Ouminus__class_Ouminus(_1201414), _1201418)))], (32646 ^ _777864) ^ [_1375824, _1375826, _1375828, _1375830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375824), _1375826)), c_Equiv__Relations_Oequiv(_1375824, _1375826, _1375828), 32656 ^ _777864 : [(32659 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375830), hAPP(c_Finite__Set_Ocard(_1375824), 32655 ^ [_1375824, _1375826, _1375828, _1375830])))], (32657 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1375824, tc_HOL_Obool)), 32655 ^ [_1375824, _1375826, _1375828, _1375830]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1375824), _1375826), _1375828))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1375830), hAPP(c_Finite__Set_Ocard(_1375824), _1375826))))], (39804 ^ _777864) ^ [_1531987, _1531989, _1531991, _1531993, _1531995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531987, _1531989)), _1531991), hAPP(hAPP(c_Product__Type_OSigma(_1531987, _1531989), _1531993), _1531995))), 39808 ^ _777864 : [(39814 ^ _777864) ^ [] : [-(_1531991 = hAPP(hAPP(c_Product__Type_OPair(_1531987, _1531989), 39807 ^ [_1531987, _1531989, _1531991, _1531993, _1531995]), 39810 ^ [_1531987, _1531989, _1531991, _1531993, _1531995]))], (39812 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531989), 39810 ^ [_1531987, _1531989, _1531991, _1531993, _1531995]), hAPP(_1531995, 39807 ^ [_1531987, _1531989, _1531991, _1531993, _1531995]))))], (39809 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531987), 39807 ^ [_1531987, _1531989, _1531991, _1531993, _1531995]), _1531993)))]]], (13272 ^ _777864) ^ [_1000722, _1000724, _1000726] : [class_Lattices_Oboolean__algebra(_1000722), 13275 ^ _777864 : [(13282 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000722), _1000726), _1000724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000722), hAPP(c_Groups_Ouminus__class_Ouminus(_1000722), _1000724)), hAPP(c_Groups_Ouminus__class_Ouminus(_1000722), _1000726))))], (13276 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000722), hAPP(c_Groups_Ouminus__class_Ouminus(_1000722), _1000724)), hAPP(c_Groups_Ouminus__class_Ouminus(_1000722), _1000726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000722), _1000726), _1000724)))]]], (46970 ^ _777864) ^ [_1714305, _1714307, _1714309] : [class_Orderings_Olinorder(_1714305), -(hAPP(c_List_Oset(_1714305), c_List_Olinorder__class_Oinsort__insert__key(_1714305, _1714305, c_COMBI(_1714305), _1714307, _1714309)) = hAPP(hAPP(c_Set_Oinsert(_1714305), _1714307), hAPP(c_List_Oset(_1714305), _1714309)))], (17526 ^ _777864) ^ [_1080456, _1080458] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080456)))), 17529 ^ _777864 : [(17536 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080458)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080458)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080458))))], (17530 ^ _777864) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080458))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080458)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080456))]]], (22793 ^ _777864) ^ [_1172578, _1172580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172578), 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)), _1172580)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1172578), _1172580) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1172578, _1172580)))], (23989 ^ _777864) ^ [_1197253, _1197255, _1197257, _1197259] : [class_Orderings_Olinorder(_1197253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197253), _1197255), _1197257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197253), _1197255), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197253), _1197257), _1197259))))], (34525 ^ _777864) ^ [_1418987, _1418989, _1418991] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418987, tc_HOL_Obool)), _1418991), hAPP(c_Set_OPow(_1418987), _1418989))), -(hBOOL(hAPP(c_Predicate_OPowp(_1418987, hAPP(hAPP(c_COMBC(_1418987, tc_fun(_1418987, tc_HOL_Obool), tc_HOL_Obool), c_member(_1418987)), _1418989)), _1418991)))], (50821 ^ _777864) ^ [_1803132, _1803134] : [-(_1803132 = c_List_Olist_ONil(_1803134)), hBOOL(hAPP(c_List_Odistinct(_1803134), _1803132)), -(c_List_OtakeWhile(_1803134, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1803134), c_fNot), hAPP(hAPP(c_COMBC(_1803134, _1803134, tc_HOL_Obool), c_fequal), c_List_Olast(_1803134, _1803132))), _1803132) = c_List_Obutlast(_1803134, _1803132))], (18264 ^ _777864) ^ [_1091970, _1091972] : [class_Int_Onumber__ring(_1091970), class_Rings_Olinordered__idom(_1091970), 18271 ^ _777864 : [(18278 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1091972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091970), c_Groups_Ozero__class_Ozero(_1091970)), hAPP(c_Int_Onumber__class_Onumber__of(_1091970), _1091972))))], (18272 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1091970), c_Groups_Ozero__class_Ozero(_1091970)), hAPP(c_Int_Onumber__class_Onumber__of(_1091970), _1091972))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1091972)))]]], (23237 ^ _777864) ^ [_1181868, _1181870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181868), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181870)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181868)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1181870))], (40695 ^ _777864) ^ [_1559513, _1559515] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1559513, _1559515, tc_prod(_1559513, _1559515)), c_Product__Type_OPair(_1559513, _1559515)) = c_Fun_Oid(tc_prod(_1559513, _1559515)))], (44564 ^ _777864) ^ [_1654522, _1654524] : [class_Complete__Lattice_Ocomplete__lattice(_1654522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1654522), _1654524)), -(c_Complete__Lattice_OInf__class_OInf(_1654522, _1654524) = hAPP(hAPP(c_Finite__Set_Ofold(_1654522, _1654522, c_Lattices_Osemilattice__inf__class_Oinf(_1654522)), c_Orderings_Otop__class_Otop(_1654522)), _1654524))], (14310 ^ _777864) ^ [_1019837, _1019839, _1019841] : [class_Divides_Osemiring__div(_1019837), -(_1019839 = c_Groups_Ozero__class_Ozero(_1019837)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1019837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019837), _1019841), _1019839)), _1019839) = _1019841)], (47438 ^ _777864) ^ [_1726166, _1726168, _1726170] : [-(hAPP(hAPP(c_List_Omap(_1726166, _1726168), _1726170), c_List_Olist_ONil(_1726166)) = c_List_Olist_ONil(_1726168))], (22641 ^ _777864) ^ [_1169537, _1169539, _1169541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1169537, tc_HOL_Obool)), _1169539), _1169541)), 22644 ^ _777864 : [(22647 ^ _777864) ^ [] : [_1169539 = _1169541], (22645 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1169537, tc_HOL_Obool)), _1169539), _1169541)))]]], (14163 ^ _777864) ^ [_1017516, _1017518, _1017520] : [_1017516 = 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), _1017516), _1017518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1017516), _1017520)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22558 ^ _777864) ^ [_1167859, _1167861, _1167863, _1167865] : [_1167859 = _1167861, 22561 ^ _777864 : [(22564 ^ _777864) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1167863, _1167865), _1167859) = hAPP(c_Product__Type_Osnd(_1167863, _1167865), _1167861))], (22562 ^ _777864) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1167863, _1167865), _1167859) = hAPP(c_Product__Type_Ofst(_1167863, _1167865), _1167861))]]], (20614 ^ _777864) ^ [_1133176, _1133178, _1133180, _1133182] : [class_Fields_Olinordered__field(_1133176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), c_Groups_Ozero__class_Ozero(_1133176)), _1133178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133176), _1133180), _1133178)), _1133182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133176), _1133180), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133176), _1133182), _1133178))))], (36190 ^ _777864) ^ [_1451475, _1451477, _1451479, _1451481, _1451483, _1451485] : [c_Fun_Oinj__on(_1451475, _1451477, _1451479, _1451481), hAPP(_1451479, _1451483) = _1451485, hBOOL(hAPP(hAPP(c_member(_1451475), _1451483), _1451481)), -(hAPP(c_Fun_Othe__inv__into(_1451475, _1451477, _1451481, _1451479), _1451485) = _1451483)], (34069 ^ _777864) ^ [_1408877, _1408879, _1408881] : [class_Orderings_Olinorder(_1408877), hAPP(_1408879, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1408877), 34074 ^ [_1408877, _1408879, _1408881]), 34075 ^ [_1408877, _1408879, _1408881])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1408877), hAPP(_1408879, 34074 ^ [_1408877, _1408879, _1408881])), hAPP(_1408879, 34075 ^ [_1408877, _1408879, _1408881])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408877), _1408881)), -(_1408881 = c_Orderings_Obot__class_Obot(tc_fun(_1408877, tc_HOL_Obool))), -(hAPP(_1408879, c_Big__Operators_Olattice_OSup__fin(_1408877, c_Orderings_Oord__class_Omax(_1408877), _1408881)) = c_Big__Operators_Olattice_OSup__fin(_1408877, c_Orderings_Oord__class_Omax(_1408877), hAPP(c_Set_Oimage(_1408877, _1408877, _1408879), _1408881)))], (32511 ^ _777864) ^ [_1372796, _1372798, _1372800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1372796), _1372798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1372796), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372796, tc_HOL_Obool)), _1372798), hAPP(hAPP(c_Set_Oinsert(_1372796), _1372800), c_Orderings_Obot__class_Obot(tc_fun(_1372796, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1372796), _1372798))))], (2300 ^ _777864) ^ [_811766, _811768] : [_811768 = _811766, -(c_Hoare__Mirabelle_OMGT(_811768) = c_Hoare__Mirabelle_OMGT(_811766))], (33915 ^ _777864) ^ [_1404809] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1404809)) = _1404809)], (17614 ^ _777864) ^ [_1081726] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081726)), -(hAPP(c_Int_Onat, _1081726) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50724 ^ _777864) ^ [_1801207] : [-(c_List_Oreturn__list(_1801207) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1801207))], (46641 ^ _777864) ^ [_1705551, _1705553, _1705555, _1705557, _1705559, _1705561] : [class_Orderings_Olinorder(_1705551), 46644 ^ _777864 : [(46651 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1705551), hAPP(_1705553, _1705555)), hAPP(_1705553, _1705557)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705559, _1705551, _1705553), _1705555), hAPP(hAPP(c_List_Olist_OCons(_1705559), _1705557), _1705561)) = hAPP(hAPP(c_List_Olist_OCons(_1705559), _1705557), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705559, _1705551, _1705553), _1705555), _1705561)))], (46645 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1705551), hAPP(_1705553, _1705555)), hAPP(_1705553, _1705557))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705559, _1705551, _1705553), _1705555), hAPP(hAPP(c_List_Olist_OCons(_1705559), _1705557), _1705561)) = hAPP(hAPP(c_List_Olist_OCons(_1705559), _1705555), hAPP(hAPP(c_List_Olist_OCons(_1705559), _1705557), _1705561)))]]], (23309 ^ _777864) ^ [_1184123, _1184125, _1184127] : [-(c_Nat_Onat_Onat__case(_1184123, _1184125, _1184127, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1184125)], (39771 ^ _777864) ^ [_1531277, _1531279, _1531281, _1531283] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531277), _1531279)), 39777 ^ _777864 : [(39780 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531281), hAPP(_1531283, 39776 ^ [_1531277, _1531279, _1531281, _1531283])))], (39778 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531277), 39776 ^ [_1531277, _1531279, _1531281, _1531283]), _1531279)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1531277, _1531281)), hAPP(hAPP(c_Product__Type_OSigma(_1531277, _1531281), _1531279), _1531283))))], (39636 ^ _777864) ^ [_1528047, _1528049, _1528051] : [class_Groups_Oab__semigroup__mult(_1528047), -(_1528049 = c_Orderings_Obot__class_Obot(tc_fun(_1528047, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528047), _1528049)), -(hBOOL(hAPP(hAPP(c_member(_1528047), _1528051), _1528049))), -(hAPP(c_Finite__Set_Ofold1(_1528047, c_Groups_Otimes__class_Otimes(_1528047)), hAPP(hAPP(c_Set_Oinsert(_1528047), _1528051), _1528049)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1528047), _1528051), hAPP(c_Finite__Set_Ofold1(_1528047, c_Groups_Otimes__class_Otimes(_1528047)), _1528049)))], (23193 ^ _777864) ^ [_1180883, _1180885, _1180887] : [class_Int_Onumber__ring(_1180883), 23196 ^ _777864 : [(23203 ^ _777864) ^ [] : [-(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), _1180885)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1180883), _1180887), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1180885))) = c_Groups_Oone__class_Oone(_1180883))], (23197 ^ _777864) ^ [] : [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), _1180885))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1180883), _1180887), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1180885))) = hAPP(hAPP(c_HOL_OLet(_1180883, _1180883), hAPP(hAPP(c_Power_Opower__class_Opower(_1180883), _1180887), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180885))), hAPP(hAPP(c_COMBS(_1180883, _1180883, _1180883), hAPP(hAPP(c_COMBB(_1180883, tc_fun(_1180883, _1180883), _1180883), c_Groups_Otimes__class_Otimes(_1180883)), hAPP(c_Groups_Otimes__class_Otimes(_1180883), _1180887))), c_COMBI(_1180883))))]]], (10922 ^ _777864) ^ [_959686, _959688] : [10923 ^ _777864 : [(10926 ^ _777864) ^ [] : [_959688 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10924 ^ _777864) ^ [] : [_959686 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959686), _959688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40338 ^ _777864) ^ [_1545268, _1545270, _1545272, _1545274, _1545276, _1545278] : [class_Groups_Ocomm__monoid__add(_1545268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545270), _1545272)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545270, _1545268), hAPP(hAPP(c_COMBS(_1545270, _1545268, _1545268), hAPP(hAPP(c_COMBS(_1545270, _1545268, tc_fun(_1545268, _1545268)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1545268, tc_fun(_1545268, _1545268)), _1545270), c_If(_1545268)), _1545274)), _1545276)), _1545278)), _1545272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1545268), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545270, _1545268), _1545276), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545270, tc_HOL_Obool)), _1545272), hAPP(c_Set_OCollect(_1545270), _1545274)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1545270, _1545268), _1545278), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545270, tc_HOL_Obool)), _1545272), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1545270, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1545270), _1545274))))))], (13547 ^ _777864) ^ [_1006049, _1006051] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006049, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1006051)) = 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), _1006049), _1006051)))], (17660 ^ _777864) ^ [_1082410] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1082410, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (190 ^ _777864) ^ [_780607, _780609, _780611, _780613] : [-(c_Nitpick_Orefl_H(_780611, _780607)), c_Nitpick_Orefl_H(_780613, _780609), _780613 = _780611, _780609 = _780607], (30537 ^ _777864) ^ [_1336103, _1336105, _1336107, _1336109, _1336111, _1336113] : [hBOOL(hAPP(hAPP(c_member(_1336103), _1336105), c_SetInterval_Oord_OgreaterThanAtMost(_1336103, _1336107, _1336109, _1336111, _1336113))), 30540 ^ _777864 : [(30543 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336107, _1336105), _1336113)))], (30541 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336109, _1336111), _1336105)))]]], (51305 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (20510 ^ _777864) ^ [_1131186, _1131188, _1131190] : [class_Fields_Olinordered__field(_1131186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131186), c_Groups_Ozero__class_Ozero(_1131186)), _1131188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1131186), _1131190), c_Groups_Ozero__class_Ozero(_1131186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131186), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131186), _1131188), _1131190)), c_Groups_Ozero__class_Ozero(_1131186))))], (2106 ^ _777864) ^ [_808651, _808653] : [_808653 = _808651, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808653) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808651))], (43943 ^ _777864) ^ [_1638220] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638220, tc_HOL_Obool) = c_Set_OBall(_1638220))], (28560 ^ _777864) ^ [_1291828, _1291830, _1291832, _1291834] : [_1291834 = c_Orderings_Obot__class_Obot(tc_fun(_1291828, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1291828, _1291830, _1291832), _1291834) = c_Orderings_Obot__class_Obot(tc_fun(_1291830, tc_HOL_Obool)))], (43096 ^ _777864) ^ [_1616456, _1616458, _1616460, _1616462, _1616464, _1616466, _1616468] : [c_Finite__Set_Ofun__left__comm(_1616456, _1616458, _1616460), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1616456, _1616458, _1616460, _1616462, _1616464), _1616466)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1616456, _1616458, _1616460, _1616462, _1616464), _1616468)), -(_1616468 = _1616466)], (28707 ^ _777864) ^ [_1296121, _1296123] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296121) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1296123), -(_1296121 = _1296123)], (27093 ^ _777864) ^ [_1257417, _1257419, _1257421, _1257423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1257417, _1257419)), hAPP(hAPP(c_Product__Type_OPair(_1257417, _1257419), _1257421), _1257423)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1257417, _1257419), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1257417, tc_fun(_1257419, tc_HOL_Obool))), _1257421), _1257423)))], (31573 ^ _777864) ^ [_1355021, _1355023, _1355025] : [class_Orderings_Olinorder(_1355021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355021), _1355023)), hBOOL(hAPP(hAPP(c_member(_1355021), _1355025), _1355023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355021), c_Big__Operators_Olinorder__class_OMin(_1355021, _1355023)), _1355025)))], (50404 ^ _777864) ^ [_1792919, _1792921] : [_1792921 = c_List_Olist_ONil(_1792919), -(hAPP(c_List_Orev(_1792919), _1792921) = c_List_Olist_ONil(_1792919))], (30220 ^ _777864) ^ [_1328342, _1328344, _1328346, _1328348, _1328350] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328342, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1328344, _1328342, _1328346), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328344, tc_HOL_Obool)), _1328348), _1328350))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328342, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1328344, _1328342, _1328346), _1328348)), hAPP(c_Relation_OImage(_1328344, _1328342, _1328346), _1328350)))))], (28268 ^ _777864) ^ [_1282422, _1282424, _1282426, _1282428] : [hBOOL(hAPP(hAPP(c_member(_1282422), _1282424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282422, tc_HOL_Obool)), _1282426), _1282428))), -(hBOOL(hAPP(hAPP(c_member(_1282422), _1282424), _1282426))), -(hBOOL(hAPP(hAPP(c_member(_1282422), _1282424), _1282428)))], (42685 ^ _777864) ^ [_1607991, _1607993] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607991, _1607991)), hAPP(hAPP(c_Product__Type_OPair(_1607991, _1607991), 42686 ^ [_1607991, _1607993]), 42686 ^ [_1607991, _1607993])), c_Transitive__Closure_Otrancl(_1607991, _1607993)))), -(c_Wellfounded_Oacyclic(_1607991, _1607993))], (19250 ^ _777864) ^ [_1108889, _1108891] : [class_Int_Onumber__ring(_1108889), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108889), hAPP(c_Int_Onumber__class_Onumber__of(_1108889), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1108891) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108889), _1108891), _1108891))], (36502 ^ _777864) ^ [_1457823, _1457825, _1457827, _1457829] : [class_Groups_Oordered__ab__group__add__abs(_1457823), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457823), c_Groups_Ozero__class_Ozero(_1457823)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457825, _1457823), hAPP(hAPP(c_COMBB(_1457823, _1457823, _1457825), c_Groups_Oabs__class_Oabs(_1457823)), _1457827)), _1457829))))], (3696 ^ _777864) ^ [_834152, _834154] : [_834154 = _834152, -(c_New__Random__Sequence_Opos__single(_834154) = c_New__Random__Sequence_Opos__single(_834152))], (44486 ^ _777864) ^ [_1652468, _1652470, _1652472] : [c_Relation_Ototal__on(_1652468, _1652470, _1652472), 44489 ^ _777864 : [(44490 ^ _777864) ^ [_1652612] : [hBOOL(hAPP(hAPP(c_member(_1652468), _1652612), _1652470)), 44493 ^ _777864 : [(44494 ^ _777864) ^ [_1652752] : [hBOOL(hAPP(hAPP(c_member(_1652468), _1652752), _1652470)), -(_1652612 = _1652752), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652468, _1652468)), hAPP(hAPP(c_Product__Type_OPair(_1652468, _1652468), _1652612), _1652752)), _1652472))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652468, _1652468)), hAPP(hAPP(c_Product__Type_OPair(_1652468, _1652468), _1652752), _1652612)), _1652472)))]]]]], (6302 ^ _777864) ^ [_881721, _881723, _881725, _881727] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_881721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881721), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881721), _881723), _881725)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881721), _881727), _881725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_881721), _881723), _881727)))], (48662 ^ _777864) ^ [_1755977, _1755979, _1755981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755977), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755979)), _1755981))), -(hAPP(hAPP(c_List_Olist_OCons(_1755979), hAPP(hAPP(c_List_Onth(_1755979), _1755981), _1755977)), hAPP(hAPP(c_List_Odrop(_1755979), hAPP(c_Nat_OSuc, _1755977)), _1755981)) = hAPP(hAPP(c_List_Odrop(_1755979), _1755977), _1755981))], (47496 ^ _777864) ^ [_1727515, _1727517, _1727519] : [-(hAPP(c_Map_Omap__of(_1727515, _1727517, c_List_Olist_ONil(tc_prod(_1727515, _1727517))), _1727519) = c_Option_Ooption_ONone(_1727517))], (51213 ^ _777864) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (26201 ^ _777864) ^ [_1238581, _1238583, _1238585] : [c_Orderings_Obot__class_Obot(tc_fun(_1238581, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1238581), _1238583), _1238585)], (24705 ^ _777864) ^ [_1211338, _1211340] : [-(hAPP(c_New__DSequence_Opos__empty(_1211338), _1211340) = c_Lazy__Sequence_Oempty(_1211338))], (47322 ^ _777864) ^ [_1723823, _1723825, _1723827] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1723823, tc_HOL_Obool)), hAPP(c_List_Oset(_1723823), hAPP(hAPP(c_List_Otake(_1723823), _1723825), _1723827))), hAPP(c_List_Oset(_1723823), _1723827))))], (24483 ^ _777864) ^ [_1206861, _1206863, _1206865, _1206867] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1206861, _1206863)), c_Nitpick_Opair__box_OPairBox(_1206861, _1206863, _1206865, _1206867)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48512 ^ _777864) ^ [_1752388, _1752390] : [-(hAPP(c_List_Oset(_1752388), hAPP(c_List_Orotate1(_1752388), _1752390)) = hAPP(c_List_Oset(_1752388), _1752390))], (6050 ^ _777864) ^ [_877489] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _877489)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28813 ^ _777864) ^ [_1298607, _1298609] : [c_Nat__Transfer_Onat__set(_1298607), c_Nat__Transfer_Onat__set(_1298609), 28820 ^ _777864 : [(28827 ^ _777864) ^ [] : [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), _1298607)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1298609))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298607), _1298609)))], (28821 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298607), _1298609)), -(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), _1298607)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1298609))))]]], (5777 ^ _777864) ^ [_872208, _872210, _872212, _872214, _872216] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_872208, _872210, _872212)), _872214), _872216)), 5781 ^ _777864 : [(5784 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _872210)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _872214), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_872212, _872214))), 5780 ^ [_872208, _872210, _872212, _872214, _872216])))], (5782 ^ _777864) ^ [] : [-(_872216 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 5780 ^ [_872208, _872210, _872212, _872214, _872216]), hAPP(c_Natural_Ogetlocs, _872214))), _872208), hAPP(hAPP(c_Natural_Ogetlocs, 5780 ^ [_872208, _872210, _872212, _872214, _872216]), c_Com_ORes)))]]], (7889 ^ _777864) ^ [_909166, _909168, _909170, _909172] : [class_Orderings_Oorder(_909166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909166), hAPP(_909168, 7894 ^ [_909166, _909168, _909170, _909172])), hAPP(_909168, hAPP(c_Nat_OSuc, 7894 ^ [_909166, _909168, _909170, _909172])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909170), _909172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909166), hAPP(_909168, _909170)), hAPP(_909168, _909172))))], (19086 ^ _777864) ^ [_1105998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1105998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1105998)))], (17566 ^ _777864) ^ [_1081103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081103)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1081103) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1081103), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30394 ^ _777864) ^ [_1332181, _1332183] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332181), _1332183)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1332183, _1332181) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23911 ^ _777864) ^ [_1195911, _1195913, _1195915, _1195917] : [class_Orderings_Olinorder(_1195911), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195911), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195911), _1195913), _1195915)), _1195917) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195911), _1195913), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195911), _1195915), _1195917)))], (44774 ^ _777864) ^ [_1659016, _1659018] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1659016, tc_HOL_Obool), _1659018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1659016, tc_HOL_Obool), tc_fun(_1659016, tc_HOL_Obool)), _1659018), c_COMBI(tc_fun(_1659016, tc_HOL_Obool))))], (23951 ^ _777864) ^ [_1196617, _1196619, _1196621] : [class_Orderings_Olinorder(_1196617), 23954 ^ _777864 : [(23961 ^ _777864) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196617), _1196619), _1196621) = _1196621, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196617), _1196619), _1196621)))], (23955 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196617), _1196619), _1196621)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1196617), _1196619), _1196621) = _1196621)]]], (18830 ^ _777864) ^ [_1101468, _1101470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1101468)), -(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)))), _1101470))), 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)))), _1101468)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1101470), _1101468))], (41350 ^ _777864) ^ [_1576437, _1576439, _1576441, _1576443] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1576437, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1576437, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1576437, _1576439), _1576441)), hAPP(c_Relation_ODomain(_1576437, _1576439), _1576443))), hAPP(c_Relation_ODomain(_1576437, _1576439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576437, _1576439), tc_HOL_Obool)), _1576441), _1576443)))))], (21844 ^ _777864) ^ [] : [-(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))], (46194 ^ _777864) ^ [_1692869, _1692871, _1692873, _1692875, _1692877, _1692879] : [-(hAPP(hAPP(c_List_Ozip(_1692869, _1692871), _1692873), hAPP(hAPP(c_List_Omap(_1692875, _1692871), _1692877), _1692879)) = hAPP(hAPP(c_List_Omap(tc_prod(_1692869, _1692875), tc_prod(_1692869, _1692871)), hAPP(c_Product__Type_Oprod_Oprod__case(_1692869, _1692875, tc_prod(_1692869, _1692871)), hAPP(hAPP(c_COMBC(_1692869, tc_fun(_1692875, _1692871), tc_fun(_1692875, tc_prod(_1692869, _1692871))), hAPP(hAPP(c_COMBB(tc_fun(_1692871, tc_prod(_1692869, _1692871)), tc_fun(tc_fun(_1692875, _1692871), tc_fun(_1692875, tc_prod(_1692869, _1692871))), _1692869), c_COMBB(_1692871, tc_prod(_1692869, _1692871), _1692875)), c_Product__Type_OPair(_1692869, _1692871))), _1692877))), hAPP(hAPP(c_List_Ozip(_1692869, _1692875), _1692873), _1692879)))], (23057 ^ _777864) ^ [_1177889, _1177891, _1177893, _1177895] : [class_Groups_Ouminus(_1177889), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1177891, _1177889)), _1177893), _1177895) = hAPP(c_Groups_Ouminus__class_Ouminus(_1177889), hAPP(_1177893, _1177895)))], (51349 ^ _777864) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (488 ^ _777864) ^ [_785486, _785488, _785490, _785492] : [-(c_FunDef_Oreduction__pair(_785490, _785486)), c_FunDef_Oreduction__pair(_785492, _785488), _785492 = _785490, _785488 = _785486], (42277 ^ _777864) ^ [_1599074, _1599076, _1599078] : [-(hAPP(c_New__DSequence_Oneg__single(_1599074, _1599076), _1599078) = c_Lazy__Sequence_Ohb__single(_1599074, _1599076))], (41778 ^ _777864) ^ [_1587703, _1587705, _1587707, _1587709, _1587711, _1587713, _1587715, _1587717, _1587719, _1587721, _1587723] : [-(hAPP(c_Product__Type_Omap__pair(_1587703, _1587705, _1587707, _1587709, _1587711, _1587713), hAPP(c_Product__Type_Omap__pair(_1587715, _1587703, _1587717, _1587707, _1587719, _1587721), _1587723)) = hAPP(c_Product__Type_Omap__pair(_1587715, _1587705, _1587717, _1587709, hAPP(c_Fun_Ocomp(_1587703, _1587705, _1587715, _1587711), _1587719), hAPP(c_Fun_Ocomp(_1587707, _1587709, _1587717, _1587713), _1587721)), _1587723))], (41225 ^ _777864) ^ [_1573847, _1573849, _1573851, _1573853] : [hBOOL(hAPP(c_Predicate_ORangeP(_1573847, _1573849, _1573851), _1573853)), -(hBOOL(hAPP(hAPP(_1573851, 41228 ^ [_1573847, _1573849, _1573851, _1573853]), _1573853)))], (45551 ^ _777864) ^ [_1677309, _1677311, _1677313] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1677309), c_Map_Odom(_1677309, _1677311, c_Map_Omap__of(_1677309, _1677311, _1677313)))))], (8694 ^ _777864) ^ [_922126, _922128] : [class_Groups_Ocomm__monoid__mult(_922126), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_922126), _922128), c_Groups_Oone__class_Oone(_922126)) = _922128)], (9236 ^ _777864) ^ [_931718, _931720] : [class_Rings_Olinordered__idom(_931718), 9239 ^ _777864 : [(9246 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931718), _931720), c_Groups_Ozero__class_Ozero(_931718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931718), _931720), hAPP(c_Groups_Ouminus__class_Ouminus(_931718), _931720))))], (9240 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931718), _931720), hAPP(c_Groups_Ouminus__class_Ouminus(_931718), _931720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931718), _931720), c_Groups_Ozero__class_Ozero(_931718))))]]], (25347 ^ _777864) ^ [_1222388, _1222390, _1222392] : [class_Rings_Ocomm__ring__1(_1222388), 25350 ^ _777864 : [(25357 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222388), _1222390), _1222392)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222388), _1222390), hAPP(c_Groups_Ouminus__class_Ouminus(_1222388), _1222392))))], (25351 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222388), _1222390), hAPP(c_Groups_Ouminus__class_Ouminus(_1222388), _1222392))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1222388), _1222390), _1222392)))]]], (47374 ^ _777864) ^ [_1725022, _1725024, _1725026, _1725028, _1725030] : [-(_1725022 = _1725024), -(hAPP(hAPP(c_List_Onth(_1725026), hAPP(hAPP(c_List_Olist__update(_1725026, _1725028), _1725022), _1725030)), _1725024) = hAPP(hAPP(c_List_Onth(_1725026), _1725028), _1725024))], (3122 ^ _777864) ^ [_824965, _824967, _824969, _824971, _824973, _824975, _824977, _824979, _824981, _824983] : [-(c_SetInterval_Oord_OatLeastLessThan(_824983, _824979, _824975, _824971, _824967) = c_SetInterval_Oord_OatLeastLessThan(_824981, _824977, _824973, _824969, _824965)), _824983 = _824981, _824979 = _824977, _824975 = _824973, _824971 = _824969, _824967 = _824965], (26309 ^ _777864) ^ [_1240746, _1240748] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240746, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1240746, tc_HOL_Obool))), _1240748) = c_Orderings_Obot__class_Obot(tc_fun(_1240746, tc_HOL_Obool)))], (25513 ^ _777864) ^ [_1225176, _1225178, _1225180] : [class_Divides_Osemiring__div(_1225176), 25516 ^ _777864 : [(25523 ^ _777864) ^ [] : [c_Divides_Odiv__class_Omod(_1225176, _1225180, _1225178) = c_Groups_Ozero__class_Ozero(_1225176), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225176), _1225178), _1225180)))], (25517 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225176), _1225178), _1225180)), -(c_Divides_Odiv__class_Omod(_1225176, _1225180, _1225178) = c_Groups_Ozero__class_Ozero(_1225176))]]], (9176 ^ _777864) ^ [_930726] : [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, _930726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _930726)))], (2460 ^ _777864) ^ [_814214, _814216, _814218, _814220, _814222, _814224] : [-(c_Nitpick_Oof__frac(_814224, _814220, _814216) = c_Nitpick_Oof__frac(_814222, _814218, _814214)), _814224 = _814222, _814220 = _814218, _814216 = _814214], (45015 ^ _777864) ^ [_1664386, _1664388] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1664386, tc_HOL_Obool), _1664388) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1664386, tc_HOL_Obool), tc_fun(_1664386, tc_HOL_Obool)), _1664388), c_COMBI(tc_fun(_1664386, tc_HOL_Obool))))], (8882 ^ _777864) ^ [_925493, _925495] : [class_Groups_Olinordered__ab__group__add(_925493), 8885 ^ _777864 : [(8892 ^ _777864) ^ [] : [_925495 = c_Groups_Ozero__class_Ozero(_925493), -(_925495 = hAPP(c_Groups_Ouminus__class_Ouminus(_925493), _925495))], (8886 ^ _777864) ^ [] : [_925495 = hAPP(c_Groups_Ouminus__class_Ouminus(_925493), _925495), -(_925495 = c_Groups_Ozero__class_Ozero(_925493))]]], (16272 ^ _777864) ^ [_1057037, _1057039] : [class_Int_Onumber__ring(_1057037), -(hAPP(c_Int_Onumber__class_Onumber__of(_1057037), _1057039) = hAPP(c_Int_Oring__1__class_Oof__int(_1057037), _1057039))], (14470 ^ _777864) ^ [_1022521, _1022523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022523), 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), _1022521), _1022523)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50162 ^ _777864) ^ [_1787373, _1787375, _1787377, _1787379] : [class_Groups_Ocomm__monoid__add(_1787373), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1787373), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1787373), _1787375), c_List_Oupt(_1787377, _1787379))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1787373), _1787375), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1787377, _1787379))))], (36172 ^ _777864) ^ [_1451101, _1451103, _1451105] : [class_Orderings_Oorder(_1451101), 36175 ^ _777864 : [(36182 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1451101), _1451103), _1451105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451101, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1451101), _1451103)), hAPP(c_SetInterval_Oord__class_OatMost(_1451101), _1451105))))], (36176 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451101, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1451101), _1451103)), hAPP(c_SetInterval_Oord__class_OatMost(_1451101), _1451105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1451101), _1451103), _1451105)))]]], (1292 ^ _777864) ^ [_796782, _796784] : [-(class_Lattices_Odistrib__lattice(_796782)), _796784 = _796782, class_Lattices_Odistrib__lattice(_796784)], (42930 ^ _777864) ^ [_1612676, _1612678, _1612680] : [class_Orderings_Olinorder(_1612676), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612676), _1612678)), -(hBOOL(hAPP(hAPP(c_member(_1612676), _1612680), _1612678))), -(c_Big__Operators_Olinorder__class_OMin(_1612676, hAPP(hAPP(c_Set_Oinsert(_1612676), _1612680), _1612678)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612676, _1612676, c_Orderings_Oord__class_Omin(_1612676)), _1612680), _1612678))], (51587 ^ _777864) ^ [_1813023, _1813025] : [hBOOL(_1813023), -(hBOOL(hAPP(hAPP(c_fdisj, _1813025), _1813023)))], (30252 ^ _777864) ^ [_1329163, _1329165, _1329167, _1329169, _1329171, _1329173, _1329175, _1329177] : [c_Finite__Set_Ofolding__image__simple(_1329163, _1329165, _1329167, _1329169, _1329171, _1329173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329165), _1329175)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329165), _1329177)), -(hAPP(hAPP(_1329167, hAPP(_1329173, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329165, tc_HOL_Obool)), _1329175), _1329177))), hAPP(_1329173, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329165, tc_HOL_Obool)), _1329175), _1329177))) = hAPP(hAPP(_1329167, hAPP(_1329173, _1329175)), hAPP(_1329173, _1329177)))], (42250 ^ _777864) ^ [_1598390, _1598392, _1598394, _1598396, _1598398, _1598400, _1598402, _1598404] : [class_Groups_Ocomm__monoid__mult(_1598390), c_Fun_Oinj__on(_1598392, _1598394, _1598396, _1598398), _1598400 = hAPP(c_Set_Oimage(_1598392, _1598394, _1598396), _1598398), 42264 ^ _777864 : [(42267 ^ _777864) ^ [] : [hAPP(_1598402, 42263 ^ [_1598390, _1598392, _1598394, _1598396, _1598398, _1598400, _1598402, _1598404]) = hAPP(hAPP(c_Fun_Ocomp(_1598394, _1598390, _1598392, _1598404), _1598396), 42263 ^ [_1598390, _1598392, _1598394, _1598396, _1598398, _1598400, _1598402, _1598404])], (42265 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598392), 42263 ^ [_1598390, _1598392, _1598394, _1598396, _1598398, _1598400, _1598402, _1598404]), _1598398)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1598394, _1598390), _1598404), _1598400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1598392, _1598390), _1598402), _1598398))], (9014 ^ _777864) ^ [_927740, _927742] : [class_Rings_Omult__zero(_927740), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927740), c_Groups_Ozero__class_Ozero(_927740)), _927742) = c_Groups_Ozero__class_Ozero(_927740))], (7138 ^ _777864) ^ [_895164, _895166, _895168, _895170, _895172] : [-(hBOOL(hAPP(_895164, _895166))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895168), _895166), _895170)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_895164, _895172, _895168)), _895166), _895170)))], (1132 ^ _777864) ^ [_794782, _794784] : [-(class_Divides_Oring__div(_794782)), _794784 = _794782, class_Divides_Oring__div(_794784)], (27888 ^ _777864) ^ [_1274811, _1274813, _1274815] : [class_Lattices_Osemilattice__sup(_1274811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274811), _1274813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274811), _1274815), _1274813))))], (45638 ^ _777864) ^ [_1679599, _1679601, _1679603, _1679605, _1679607, _1679609] : [-(c_Map_Omap__comp(_1679599, _1679601, _1679603, _1679605, _1679607, _1679609) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1679601), _1679599, c_Option_Ooption_ONone(_1679601), _1679605), hAPP(_1679607, _1679609)))], (24891 ^ _777864) ^ [_1214952, _1214954] : [class_Rings_Ocomm__semiring__1(_1214952), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1214952), c_Groups_Ozero__class_Ozero(_1214952)), _1214954)), -(_1214954 = c_Groups_Ozero__class_Ozero(_1214952))], (31331 ^ _777864) ^ [_1350131, _1350133, _1350135] : [class_Lattices_Olattice(_1350131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350131), _1350133)), -(_1350133 = c_Orderings_Obot__class_Obot(tc_fun(_1350131, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350131), _1350135)), -(_1350135 = c_Orderings_Obot__class_Obot(tc_fun(_1350131, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350131, tc_HOL_Obool)), _1350133), _1350135) = c_Orderings_Obot__class_Obot(tc_fun(_1350131, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1350131, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350131, tc_HOL_Obool)), _1350133), _1350135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1350131), c_Big__Operators_Olattice__class_OSup__fin(_1350131, _1350133)), c_Big__Operators_Olattice__class_OSup__fin(_1350131, _1350135)))], (22159 ^ _777864) ^ [_1161014, _1161016, _1161018] : [22161 ^ _777864 : [(22164 ^ _777864) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1161014, _1161016), 22160 ^ [_1161014, _1161016, _1161018]))], (22162 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1161016, 22160 ^ [_1161014, _1161016, _1161018]), _1161018)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1161014, _1161016), _1161018)))], (40458 ^ _777864) ^ [_1549675] : [-(c_Wellfounded_Ofinite__psubset(_1549675) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1549675, tc_HOL_Obool), tc_fun(_1549675, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1549675, tc_HOL_Obool), tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1549675, tc_HOL_Obool), tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1549675, tc_HOL_Obool)), c_COMBS(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549675, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1549675, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1549675, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1549675, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1549675)))))], (38190 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (15888 ^ _777864) ^ [_1050092, _1050094] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050092, _1050094) = 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), _1050092), _1050094) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050094), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050092, _1050094)))], (5250 ^ _777864) ^ [_858223, _858225] : [_858225 = _858223, -(c_List_Otl(_858225) = c_List_Otl(_858223))], (6827 ^ _777864) ^ [_890257, _890259] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _890257), _890259)), 6828 ^ _777864 : [(6835 ^ _777864) ^ [] : [_890257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _890259 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6829 ^ _777864) ^ [] : [_890257 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _890259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (24119 ^ _777864) ^ [_1199721, _1199723, _1199725, _1199727] : [class_Orderings_Olinorder(_1199721), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199721), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199721), _1199723), _1199725)), _1199727) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199721), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199721), _1199723), _1199727)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1199721), _1199725), _1199727)))], (44796 ^ _777864) ^ [_1659825, _1659827, _1659829, _1659831] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659825, tc_fun(_1659827, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659825, tc_HOL_Obool), _1659829)), _1659831) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1659825, tc_HOL_Obool), tc_fun(_1659827, tc_HOL_Obool)), _1659829), hAPP(hAPP(c_COMBC(tc_fun(_1659825, tc_HOL_Obool), tc_fun(_1659825, tc_fun(_1659827, tc_HOL_Obool)), tc_fun(_1659827, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659825, tc_fun(_1659827, tc_HOL_Obool))), _1659831)))], (8770 ^ _777864) ^ [_923635, _923637, _923639, _923641] : [class_Rings_Ocomm__semiring__1(_923635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923635), _923637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923635), _923639), _923641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923635), _923637), _923639)), _923641))], (43391 ^ _777864) ^ [_1623317, _1623319, _1623321, _1623323] : [-(hBOOL(hAPP(hAPP(c_member(_1623317), _1623319), hAPP(c_Relation_ODomain(_1623317, _1623317), _1623321)))), 43394 ^ _777864 : [(43401 ^ _777864) ^ [] : [_1623319 = _1623323, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623317, _1623317)), hAPP(hAPP(c_Product__Type_OPair(_1623317, _1623317), _1623319), _1623323)), c_Transitive__Closure_Ortrancl(_1623317, _1623321))))], (43395 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623317, _1623317)), hAPP(hAPP(c_Product__Type_OPair(_1623317, _1623317), _1623319), _1623323)), c_Transitive__Closure_Ortrancl(_1623317, _1623321))), -(_1623319 = _1623323)]]], (48882 ^ _777864) ^ [_1760460, _1760462, _1760464, _1760466, _1760468, _1760470] : [-(hAPP(c_List_Ofoldl(_1760460, _1760462, _1760464, _1760466), hAPP(hAPP(c_List_Olist_OCons(_1760462), _1760468), _1760470)) = hAPP(c_List_Ofoldl(_1760460, _1760462, _1760464, hAPP(hAPP(_1760464, _1760466), _1760468)), _1760470))], (20416 ^ _777864) ^ [_1129407, _1129409, _1129411] : [class_Fields_Olinordered__field(_1129407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129407), _1129409), c_Groups_Ozero__class_Ozero(_1129407))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129407), _1129411), c_Groups_Ozero__class_Ozero(_1129407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129407), c_Groups_Ozero__class_Ozero(_1129407)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129407), _1129409), _1129411))))], (28803 ^ _777864) ^ [_1298440, _1298442] : [c_Nat__Transfer_Onat__set(_1298440), c_Nat__Transfer_Onat__set(_1298442), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1298440), _1298442) = 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), _1298440)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1298442))))], (5490 ^ _777864) ^ [_861819, _861821] : [_861821 = _861819, -(v_a(_861821) = v_a(_861819))], (42142 ^ _777864) ^ [_1595907, _1595909, _1595911, _1595913, _1595915, _1595917] : [c_Finite__Set_Ofolding(_1595907, _1595909, _1595911, _1595913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595907), _1595915)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595907), _1595917)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1595907, tc_HOL_Obool)), _1595915), _1595917) = c_Orderings_Obot__class_Obot(tc_fun(_1595907, tc_HOL_Obool)), -(hAPP(_1595913, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1595907, tc_HOL_Obool)), _1595915), _1595917)) = hAPP(c_Fun_Ocomp(_1595909, _1595909, _1595909, hAPP(_1595913, _1595915)), hAPP(_1595913, _1595917)))], (9026 ^ _777864) ^ [_927938, _927940, _927942] : [class_Rings_Oring__no__zero__divisors(_927938), 9029 ^ _777864 : [(9030 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927938), _927940), _927942) = c_Groups_Ozero__class_Ozero(_927938), -(_927940 = c_Groups_Ozero__class_Ozero(_927938)), -(_927942 = c_Groups_Ozero__class_Ozero(_927938))], (9040 ^ _777864) ^ [] : [9041 ^ _777864 : [(9044 ^ _777864) ^ [] : [_927942 = c_Groups_Ozero__class_Ozero(_927938)], (9042 ^ _777864) ^ [] : [_927940 = c_Groups_Ozero__class_Ozero(_927938)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927938), _927940), _927942) = c_Groups_Ozero__class_Ozero(_927938))]]], (45495 ^ _777864) ^ [_1676074, _1676076, _1676078, _1676080, _1676082] : [-(hBOOL(hAPP(hAPP(c_member(_1676074), _1676076), c_Map_Odom(_1676074, _1676078, _1676080)))), -(hAPP(c_Map_Omap__add(_1676074, _1676078, _1676080, _1676082), _1676076) = hAPP(_1676082, _1676076))], (768 ^ _777864) ^ [_789694, _789696, _789698, _789700] : [-(c_Wellfounded_Owf(_789698, _789694)), c_Wellfounded_Owf(_789700, _789696), _789700 = _789698, _789696 = _789694], (47408 ^ _777864) ^ [_1725557] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725557)), c_List_Olist_ONil(_1725557)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2890 ^ _777864) ^ [_821283, _821285, _821287, _821289, _821291, _821293, _821295, _821297] : [-(c_New__DSequence_Oneg__decr__bind(_821297, _821293, _821289, _821285) = c_New__DSequence_Oneg__decr__bind(_821295, _821291, _821287, _821283)), _821297 = _821295, _821293 = _821291, _821289 = _821287, _821285 = _821283], (6052 ^ _777864) ^ [_877517, _877519, _877521] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_877517, _877519, _877521)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50480 ^ _777864) ^ [_1794617, _1794619] : [-(hAPP(c_List_Orev(_1794617), _1794619) = hAPP(c_List_Ofoldl(tc_List_Olist(_1794617), _1794617, hAPP(c_COMBC(_1794617, tc_List_Olist(_1794617), tc_List_Olist(_1794617)), c_List_Olist_OCons(_1794617)), c_List_Olist_ONil(_1794617)), _1794619))], (33018 ^ _777864) ^ [_1383243, _1383245, _1383247] : [class_Orderings_Oorder(_1383243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383243), _1383245), _1383247)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1383243, _1383247, _1383245) = c_Orderings_Obot__class_Obot(tc_fun(_1383243, tc_HOL_Obool)))], (21914 ^ _777864) ^ [_1156853, _1156855] : [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), _1156853))), 21917 ^ _777864 : [(21924 ^ _777864) ^ [] : [-(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), _1156855)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156855), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156855), 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), _1156853)))))], (21918 ^ _777864) ^ [] : [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), _1156855)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156855), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853)) = 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), _1156855)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156853))))]]], (38356 ^ _777864) ^ [_1497831, _1497833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1497831, _1497833)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1497831, _1497833), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1497833), c_Orderings_Otop__class_Otop(tc_fun(_1497833, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497831), c_Orderings_Otop__class_Otop(tc_fun(_1497831, tc_HOL_Obool)))))], (16684 ^ _777864) ^ [_1064976, _1064978] : [class_Int_Onumber__ring(_1064976), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064976), hAPP(c_Int_Onumber__class_Onumber__of(_1064976), _1064978)) = hAPP(c_Int_Onumber__class_Onumber__of(_1064976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1064978)))], (40146 ^ _777864) ^ [_1539819, _1539821, _1539823] : [hBOOL(hAPP(hAPP(c_member(_1539819), _1539821), hAPP(c_Set_OCollect(_1539819), _1539823))), -(hBOOL(hAPP(_1539823, _1539821)))], (5719 ^ _777864) ^ [_870568, _870570, _870572, _870574, _870576] : [c_Hoare__Mirabelle_Otriple__valid(_870568, _870570, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_870568), _870572), _870574), _870576)), 5722 ^ _777864 : [(5723 ^ _777864) ^ [_870689, _870691] : [hBOOL(hAPP(hAPP(_870572, _870691), _870689)), 5726 ^ _777864 : [(5727 ^ _777864) ^ [_870779] : [c_Natural_Oevaln(_870574, _870689, _870570, _870779), -(hBOOL(hAPP(hAPP(_870576, _870691), _870779)))]]]]], (24543 ^ _777864) ^ [_1208558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1208558)), _1208558 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8435 ^ _777864) ^ [_917626, _917628] : [hBOOL(hAPP(_917626, hAPP(c_Int_Onat, _917628))), 8438 ^ _777864 : [(8445 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _917628), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_917626, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8439 ^ _777864) ^ [_917726] : [_917628 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _917726), -(hBOOL(hAPP(_917626, _917726)))]]], (49077 ^ _777864) ^ [_1765003, _1765005, _1765007] : [c_Equiv__Relations_Oequiv(_1765003, _1765005, _1765007), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1765003), c_List_Olists(_1765003, _1765005), c_List_Olistrel(_1765003, _1765007)))], (28188 ^ _777864) ^ [_1280598, _1280600, _1280602, _1280604] : [28202 ^ _777864 : [(28205 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1280604, 28201 ^ [_1280598, _1280600, _1280602, _1280604])))], (28203 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1280598), 28201 ^ [_1280598, _1280600, _1280602, _1280604]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280598, tc_HOL_Obool)), _1280600), _1280602))))]], 28189 ^ _777864 : [(28196 ^ _777864) ^ [_1280807] : [hBOOL(hAPP(hAPP(c_member(_1280598), _1280807), _1280602)), hBOOL(hAPP(_1280604, _1280807))], (28190 ^ _777864) ^ [_1280711] : [hBOOL(hAPP(hAPP(c_member(_1280598), _1280711), _1280600)), hBOOL(hAPP(_1280604, _1280711))]]], (34927 ^ _777864) ^ [_1426343, _1426345, _1426347, _1426349] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426343), _1426345)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426347), _1426349)), 34934 ^ _777864 : [(34935 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1426343), _1426345)), hAPP(c_Finite__Set_Ocard(_1426347), _1426349)))), 34936 ^ _777864 : [(34937 ^ _777864) ^ [_1426554] : [c_Fun_Oinj__on(_1426343, _1426347, _1426554, _1426345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426347, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1426343, _1426347, _1426554), _1426345)), _1426349))]]], (34945 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1426343), _1426345)), hAPP(c_Finite__Set_Ocard(_1426347), _1426349))), 34949 ^ _777864 : [(34952 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426347, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1426343, _1426347, 34948 ^ [_1426343, _1426345, _1426347, _1426349]), _1426345)), _1426349)))], (34950 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1426343, _1426347, 34948 ^ [_1426343, _1426345, _1426347, _1426349], _1426345))]]]]], (41938 ^ _777864) ^ [_1591105, _1591107, _1591109, _1591111, _1591113, _1591115, _1591117] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1591105, _1591107, _1591109), hAPP(c_Fun_Ocomp(_1591111, tc_fun(_1591107, _1591109), _1591105, _1591113), _1591115)), _1591117) = hAPP(hAPP(_1591113, hAPP(_1591115, hAPP(c_Product__Type_Ofst(_1591105, _1591107), _1591117))), hAPP(c_Product__Type_Osnd(_1591105, _1591107), _1591117)))], (21894 ^ _777864) ^ [_1156578] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1156578) = 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), _1156578), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40056 ^ _777864) ^ [_1537895, _1537897, _1537899, _1537901, _1537903] : [c_Finite__Set_Ofun__left__comm__idem(_1537895, _1537897, _1537899), -(c_Finite__Set_Ofun__left__comm__idem(_1537901, _1537897, hAPP(hAPP(c_COMBB(_1537895, tc_fun(_1537897, _1537897), _1537901), _1537899), _1537903)))], (48502 ^ _777864) ^ [_1752109, _1752111, _1752113, _1752115] : [-(hAPP(hAPP(c_List_Odrop(_1752109), _1752111), hAPP(hAPP(c_List_Otake(_1752109), _1752113), _1752115)) = hAPP(hAPP(c_List_Otake(_1752109), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1752113), _1752111)), hAPP(hAPP(c_List_Odrop(_1752109), _1752111), _1752115)))], (33353 ^ _777864) ^ [_1391022, _1391024, _1391026, _1391028] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391022), _1391024)), 33356 ^ _777864 : [(33357 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391026), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391022, tc_fun(_1391026, tc_HOL_Obool)), _1391024), _1391028))), 33360 ^ _777864 : [(33361 ^ _777864) ^ [_1391206] : [hBOOL(hAPP(hAPP(c_member(_1391022), _1391206), _1391024)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391026), hAPP(_1391028, _1391206))))]]], (33367 ^ _777864) ^ [] : [33369 ^ _777864 : [(33372 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391026), hAPP(_1391028, 33368 ^ [_1391022, _1391024, _1391026, _1391028])))], (33370 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391022), 33368 ^ [_1391022, _1391024, _1391026, _1391028]), _1391024)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391026), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1391022, tc_fun(_1391026, tc_HOL_Obool)), _1391024), _1391028))))]]], (12600 ^ _777864) ^ [_989470, _989472, _989474] : [class_Rings_Olinordered__idom(_989470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989470), c_Groups_Ozero__class_Ozero(_989470)), _989472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989470), c_Groups_Ozero__class_Ozero(_989470)), _989474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989470), _989474), c_Groups_Oone__class_Oone(_989470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989470), _989474), _989472)), _989472)))], (13686 ^ _777864) ^ [_1008427, _1008429] : [class_Lattices_Oab__semigroup__idem__mult(_1008427), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008427), _1008429), _1008429) = _1008429)], (38615 ^ _777864) ^ [_1504762, _1504764, _1504766, _1504768] : [c_Equiv__Relations_Oequivp(_1504762, _1504764), hBOOL(hAPP(hAPP(_1504764, _1504766), _1504768)), -(hBOOL(hAPP(hAPP(_1504764, _1504768), _1504766)))], (17120 ^ _777864) ^ [_1073070, _1073072, _1073074] : [class_Rings_Osemiring__1(_1073070), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1073070), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1073072), _1073074)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1073070), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1073070), _1073072)), _1073074))], (7800 ^ _777864) ^ [_907512, _907514, _907516, _907518, _907520] : [c_Com_Ocom_OLocal(_907512, _907514, _907516) = c_Com_Ocom_OWhile(_907518, _907520)], (27420 ^ _777864) ^ [_1265548, _1265550, _1265552, _1265554, _1265556, _1265558, _1265560] : [c_Nitpick_Ofold__graph_H(_1265548, _1265550, _1265552, _1265554, _1265556, hAPP(hAPP(_1265552, _1265558), _1265560)), 27425 ^ _777864 : [(27428 ^ _777864) ^ [] : [-(hAPP(hAPP(_1265552, _1265558), _1265560) = _1265554)], (27426 ^ _777864) ^ [] : [-(_1265556 = c_Orderings_Obot__class_Obot(tc_fun(_1265548, tc_HOL_Obool)))]], 27431 ^ _777864 : [(27436 ^ _777864) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1265548, _1265550, _1265552, _1265554, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265548, 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[hBOOL(_1813244), -(hBOOL(hAPP(hAPP(c_fimplies, _1813246), _1813244)))], (18818 ^ _777864) ^ [_1101245, _1101247] : [-(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), _1101245)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1101247)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1101245))) = 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), _1101247)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1101245)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (43154 ^ _777864) ^ [_1617571, _1617573, _1617575, _1617577, _1617579] : [c_Finite__Set_Ofun__left__comm(_1617571, _1617573, _1617575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617571), _1617577)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1617571, _1617573, _1617575, _1617579, _1617577), hAPP(hAPP(c_Finite__Set_Ofold(_1617571, _1617573, _1617575), _1617579), _1617577))))], (23483 ^ _777864) ^ [_1187790, _1187792, _1187794] : [class_Orderings_Olinorder(_1187790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187790), _1187792), _1187794)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187790), _1187792), _1187794) = _1187792)], (24133 ^ _777864) ^ [_1200128, _1200130, _1200132, _1200134, _1200136, _1200138] : [hAPP(c_Product__Type_Oapfst(_1200128, _1200130, _1200132, _1200134), _1200136) = hAPP(c_Product__Type_Oapfst(_1200128, _1200130, _1200132, _1200138), _1200136), -(hAPP(_1200134, hAPP(c_Product__Type_Ofst(_1200128, _1200132), _1200136)) = hAPP(_1200138, hAPP(c_Product__Type_Ofst(_1200128, _1200132), _1200136)))], (29191 ^ _777864) ^ [_1306056] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1306056), c_Orderings_Obot__class_Obot(tc_fun(_1306056, tc_HOL_Obool)))))], (40869 ^ _777864) ^ [_1565601, _1565603] : [c_Wellfounded_Owf(_1565601, hAPP(hAPP(c_Relation_Orel__comp(_1565601, _1565601, _1565601), _1565603), _1565603)), -(c_Wellfounded_Owf(_1565601, _1565603))], (35356 ^ _777864) ^ [_1435328, _1435330, _1435332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1435328)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1435330), _1435332)), 35363 ^ _777864 : [(35364 ^ _777864) ^ [_1435518] : [35366 ^ _777864 : [(35372 ^ _777864) ^ [] : [-(_1435518 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35368 ^ [_1435328, _1435330, _1435332, _1435518]), 35365 ^ [_1435328, _1435330, _1435332, _1435518]))], (35370 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35368 ^ [_1435328, _1435330, _1435332, _1435518]), _1435332)))], (35367 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35365 ^ [_1435328, _1435330, _1435332, _1435518]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1435328))))]], -(_1435518 = _1435330), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1435518), _1435328) = _1435330]]], (9999 ^ _777864) ^ [_944946, _944948, _944950, _944952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944946), _944948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944950), _944952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _944946), _944950)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _944948), _944952))))], (39319 ^ _777864) ^ [_1521771, _1521773, _1521775, _1521777] : [-(_1521771 = c_Orderings_Obot__class_Obot(tc_fun(_1521773, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1521773, _1521775), _1521775, c_Product__Type_Osnd(_1521773, _1521775)), hAPP(hAPP(c_Product__Type_OSigma(_1521773, _1521775), _1521771), hAPP(c_COMBK(tc_fun(_1521775, tc_HOL_Obool), _1521773), _1521777))) = _1521777)], (43192 ^ _777864) ^ [_1618262, _1618264, _1618266, _1618268, _1618270, _1618272, _1618274] : [c_Finite__Set_Ofun__left__comm(_1618262, _1618264, _1618266), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618262, _1618264, _1618266, _1618268, _1618270), _1618272)), hBOOL(hAPP(hAPP(c_member(_1618262), _1618274), _1618270)), 43204 ^ _777864 : [(43207 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618262, _1618264, _1618266, _1618268, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1618262, tc_HOL_Obool)), _1618270), hAPP(hAPP(c_Set_Oinsert(_1618262), _1618274), c_Orderings_Obot__class_Obot(tc_fun(_1618262, tc_HOL_Obool))))), 43203 ^ [_1618262, _1618264, _1618266, _1618268, _1618270, _1618272, _1618274])))], (43205 ^ _777864) ^ [] : [-(_1618272 = hAPP(hAPP(_1618266, _1618274), 43203 ^ [_1618262, _1618264, _1618266, _1618268, _1618270, _1618272, _1618274]))]]], (38852 ^ _777864) ^ [_1509983, _1509985, _1509987, _1509989, _1509991, _1509993] : [hBOOL(hAPP(hAPP(c_member(_1509983), _1509985), _1509987)), 38855 ^ _777864 : [(38862 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509983), _1509989), _1509987))), -(hAPP(c_Set_Ovimage(_1509991, _1509983, hAPP(hAPP(c_COMBC(_1509991, _1509983, _1509983), hAPP(hAPP(c_COMBC(_1509991, _1509983, tc_fun(_1509983, _1509983)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1509983, tc_fun(_1509983, _1509983)), _1509991), c_If(_1509983)), hAPP(hAPP(c_COMBC(_1509991, tc_fun(_1509991, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509991)), _1509993))), _1509985)), _1509989)), _1509987) = _1509993)], (38856 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1509983), _1509989), _1509987)), -(hAPP(c_Set_Ovimage(_1509991, _1509983, hAPP(hAPP(c_COMBC(_1509991, _1509983, _1509983), hAPP(hAPP(c_COMBC(_1509991, _1509983, tc_fun(_1509983, _1509983)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1509983, tc_fun(_1509983, _1509983)), _1509991), c_If(_1509983)), hAPP(hAPP(c_COMBC(_1509991, tc_fun(_1509991, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509991)), _1509993))), _1509985)), _1509989)), _1509987) = c_Orderings_Otop__class_Otop(tc_fun(_1509991, tc_HOL_Obool)))]]], (16214 ^ _777864) ^ [_1055973] : [class_Rings_Olinordered__idom(_1055973), -(hAPP(c_Groups_Oabs__class_Oabs(_1055973), c_Groups_Oone__class_Oone(_1055973)) = c_Groups_Oone__class_Oone(_1055973))], (11379 ^ _777864) ^ [_967497, _967499] : [class_Groups_Olinordered__ab__group__add(_967497), 11382 ^ _777864 : [(11389 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967497), c_Groups_Ozero__class_Ozero(_967497)), _967499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967497), c_Groups_Ozero__class_Ozero(_967497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967497), _967499), _967499))))], (11383 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967497), c_Groups_Ozero__class_Ozero(_967497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967497), _967499), _967499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967497), c_Groups_Ozero__class_Ozero(_967497)), _967499)))]]], (40348 ^ _777864) ^ [_1545651, _1545653, _1545655, _1545657, _1545659] : [-(c_Map_Odom(_1545651, _1545653, c_Fun_Ooverride__on(_1545651, tc_Option_Ooption(_1545653), _1545655, _1545657, _1545659)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545651, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1545651, tc_HOL_Obool)), c_Map_Odom(_1545651, _1545653, _1545655)), hAPP(c_Set_OCollect(_1545651), hAPP(hAPP(c_COMBC(_1545651, tc_fun(_1545651, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545651)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1545651, tc_HOL_Obool)), _1545659), c_Map_Odom(_1545651, _1545653, _1545657)))))), hAPP(c_Set_OCollect(_1545651), hAPP(hAPP(c_COMBC(_1545651, tc_fun(_1545651, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545651)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545651, tc_HOL_Obool)), _1545659), c_Map_Odom(_1545651, _1545653, _1545657))))))], (32471 ^ _777864) ^ [_1371894, _1371896, _1371898] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371894), _1371896)), -(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(_1371894), _1371898)), hAPP(c_Finite__Set_Ocard(_1371894), _1371896))), hAPP(c_Finite__Set_Ocard(_1371894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371894, tc_HOL_Obool)), _1371898), _1371896)))))], (51169 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (3470 ^ _777864) ^ [_830561, _830563, _830565, _830567, _830569, _830571, _830573, _830575] : [-(c_Fun_Othe__inv__into(_830575, _830571, _830567, _830563) = c_Fun_Othe__inv__into(_830573, _830569, _830565, _830561)), _830575 = _830573, _830571 = _830569, _830567 = _830565, _830563 = _830561], (3494 ^ _777864) ^ [_830947, _830949] : [_830949 = _830947, -(c_Nitpick_Onum(_830949) = c_Nitpick_Onum(_830947))], (15178 ^ _777864) ^ [_1035373, _1035375] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035373), _1035375)), _1035373) = _1035375)], (18172 ^ _777864) ^ [_1090486, _1090488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090486)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090488))), 18175 ^ _777864 : [(18176 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090486), _1090488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1090488)))], (18182 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090486), _1090488)))]]], (50392 ^ _777864) ^ [_1792716, _1792718] : [_1792718 = c_List_Olist_ONil(_1792716), -(c_List_Olist_ONil(_1792716) = hAPP(c_List_Orev(_1792716), _1792718))], (22608 ^ _777864) ^ [_1168850, _1168852, _1168854, _1168856, _1168858, _1168860] : [hAPP(hAPP(c_Product__Type_OPair(_1168850, _1168852), _1168854), _1168856) = hAPP(hAPP(c_Product__Type_OPair(_1168850, _1168852), _1168858), _1168860), 22611 ^ _777864 : [(22614 ^ _777864) ^ [] : [-(_1168856 = _1168860)], (22612 ^ _777864) ^ [] : [-(_1168854 = _1168858)]]], (51269 ^ _777864) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (9634 ^ _777864) ^ [_938872, _938874] : [class_Rings_Olinordered__semidom(_938872), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938872), _938874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938872), _938874), c_Groups_Oone__class_Oone(_938872)))))], (25469 ^ _777864) ^ [_1224460, _1224462, _1224464, _1224466] : [class_Rings_Oidom(_1224460), 25472 ^ _777864 : [(25473 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224460), _1224462), _1224464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224460), _1224466), _1224464))), -(_1224464 = c_Groups_Ozero__class_Ozero(_1224460)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224460), _1224462), _1224466)))], (25483 ^ _777864) ^ [] : [25484 ^ _777864 : [(25487 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224460), _1224462), _1224466))], (25485 ^ _777864) ^ [] : [_1224464 = c_Groups_Ozero__class_Ozero(_1224460)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1224460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224460), _1224462), _1224464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224460), _1224466), _1224464))))]]], (7935 ^ _777864) ^ [_909976] : [_909976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _909976) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8152 ^ _777864) ^ [_913233, _913235, _913237] : [class_Orderings_Oorder(_913233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913233), _913235), _913237)), _913235 = _913237], (51281 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (9748 ^ _777864) ^ [_940683, _940685, _940687] : [class_Rings_Oring__1(_940683), -(hAPP(c_Int_Oring__1__class_Oof__int(_940683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _940685), _940687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940683), hAPP(c_Int_Oring__1__class_Oof__int(_940683), _940685)), hAPP(c_Int_Oring__1__class_Oof__int(_940683), _940687)))], (15102 ^ _777864) ^ [_1034069, _1034071, _1034073, _1034075] : [class_Divides_Oring__div(_1034069), -(c_Divides_Odiv__class_Omod(_1034069, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034069), _1034071), _1034073), _1034075) = c_Divides_Odiv__class_Omod(_1034069, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034069), c_Divides_Odiv__class_Omod(_1034069, _1034071, _1034075)), c_Divides_Odiv__class_Omod(_1034069, _1034073, _1034075)), _1034075))], (28128 ^ _777864) ^ [_1279178, _1279180, _1279182, _1279184] : [class_Lattices_Osemilattice__sup(_1279178), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279178), _1279180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279178), _1279182), _1279184)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279178), _1279182), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279178), _1279180), _1279184)))], (24355 ^ _777864) ^ [_1204250, _1204252, _1204254] : [-(c_Product__Type_Ointernal__split(_1204250, _1204252, _1204254) = c_Product__Type_Oprod_Oprod__case(_1204250, _1204252, _1204254))], (6970 ^ _777864) ^ [_892494, _892496] : [-(hAPP(c_Option_Othe(_892494), hAPP(c_Option_Ooption_OSome(_892494), _892496)) = _892496)], (13481 ^ _777864) ^ [_1004653, _1004655, _1004657, _1004659] : [class_Divides_Osemiring__div(_1004653), -(c_Divides_Odiv__class_Omod(_1004653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004653), _1004655), _1004657), _1004659) = c_Divides_Odiv__class_Omod(_1004653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004653), c_Divides_Odiv__class_Omod(_1004653, _1004655, _1004659)), c_Divides_Odiv__class_Omod(_1004653, _1004657, _1004659)), _1004659))], (23719 ^ _777864) ^ [_1192155, _1192157, _1192159, _1192161, _1192163] : [-(hAPP(c_Product__Type_Ofst(_1192155, _1192157), hAPP(c_Product__Type_Oapsnd(_1192159, _1192157, _1192155, _1192161), _1192163)) = hAPP(c_Product__Type_Ofst(_1192155, _1192159), _1192163))], (19190 ^ _777864) ^ [_1107792, _1107794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107792), _1107794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1107792)), c_Int_OBit0(_1107794))))], (51293 ^ _777864) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (16790 ^ _777864) ^ [_1067053] : [_1067053 = 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), _1067053)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7770 ^ _777864) ^ [_906900, _906902] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_906900, _906902))), -(hBOOL(hAPP(c_Com_OWT, _906902)))], (14117 ^ _777864) ^ [_1016695, _1016697] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1016695), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016697)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016695)), _1016697))], (34789 ^ _777864) ^ [_1423795, _1423797] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1423795), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1423797) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1423795, _1423797))], (50490 ^ _777864) ^ [_1794895, _1794897] : [hBOOL(hAPP(c_List_Odistinct(_1794895), hAPP(c_List_Orev(_1794895), _1794897))), -(hBOOL(hAPP(c_List_Odistinct(_1794895), _1794897)))], (29157 ^ _777864) ^ [_1305579] : [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)), _1305579))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1305579)))], (51283 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51091 ^ _777864) ^ [_1807907, _1807909] : [class_Orderings_Oorder(_1807907), -(class_Orderings_Oorder(tc_fun(_1807909, _1807907)))], (6168 ^ _777864) ^ [_879272, _879274, _879276, _879278] : [class_Groups_Oab__semigroup__add(_879272), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879272), _879274), _879276)), _879278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879272), _879274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_879272), _879276), _879278)))], (50538 ^ _777864) ^ [_1795767, _1795769, _1795771, _1795773, _1795775] : [-(c_List_Ofoldr(_1795767, _1795769, _1795771, _1795773, _1795775) = hAPP(c_List_Ofoldl(_1795769, _1795767, hAPP(c_COMBC(_1795767, _1795769, _1795769), _1795771), _1795775), hAPP(c_List_Orev(_1795767), _1795773)))], (46250 ^ _777864) ^ [_1694400, _1694402, _1694404, _1694406, _1694408, _1694410] : [class_Orderings_Olinorder(_1694400), -(hAPP(_1694402, _1694404) = hAPP(_1694402, _1694406)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694408, _1694400, _1694402), _1694406), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694408, _1694400, _1694402), _1694404), _1694410)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694408, _1694400, _1694402), _1694404), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694408, _1694400, _1694402), _1694406), _1694410)))], (45541 ^ _777864) ^ [_1677056, _1677058, _1677060, _1677062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1677056, _1677058)), _1677060), hAPP(c_Relation_Oconverse(_1677058, _1677056), _1677062))), 45546 ^ _777864 : [(45549 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1677058, _1677056)), hAPP(hAPP(c_Product__Type_OPair(_1677058, _1677056), 45544 ^ [_1677056, _1677058, _1677060, _1677062]), 45545 ^ [_1677056, _1677058, _1677060, _1677062])), _1677062)))], (45547 ^ _777864) ^ [] : [-(_1677060 = hAPP(hAPP(c_Product__Type_OPair(_1677056, _1677058), 45545 ^ [_1677056, _1677058, _1677060, _1677062]), 45544 ^ [_1677056, _1677058, _1677060, _1677062]))]]], (32749 ^ _777864) ^ [_1377821, _1377823] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1377821, _1377823)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1377823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1377821), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40749 ^ _777864) ^ [_1561144, _1561146, _1561148, _1561150, _1561152, _1561154, _1561156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561144, _1561146), tc_HOL_Obool)), _1561148), _1561150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561146, _1561152), tc_HOL_Obool)), _1561154), _1561156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561144, _1561152), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1561144, _1561146, _1561152), _1561148), _1561154)), hAPP(hAPP(c_Relation_Orel__comp(_1561144, _1561146, _1561152), _1561150), _1561156))))], (41354 ^ _777864) ^ [_1576572, _1576574] : [c_Wellfounded_Owf(_1576572, _1576574), -(c_Wellfounded_OwfP(_1576572, c_FunDef_Oin__rel(_1576572, _1576572, _1576574)))], (28080 ^ _777864) ^ [_1278190, _1278192, _1278194] : [class_Lattices_Osemilattice__sup(_1278190), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278190), _1278192), _1278194) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278190), _1278194), _1278192))], (3772 ^ _777864) ^ [_835288, _835290] : [_835290 = _835288, -(c_Set_OBall(_835290) = c_Set_OBall(_835288))], (33725 ^ _777864) ^ [_1399857, _1399859, _1399861, _1399863, _1399865] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399857, tc_fun(_1399859, tc_HOL_Obool)), _1399861), hAPP(hAPP(c_COMBC(_1399857, tc_fun(_1399859, tc_HOL_Obool), tc_fun(_1399859, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1399859, tc_HOL_Obool), tc_fun(tc_fun(_1399859, tc_HOL_Obool), tc_fun(_1399859, tc_HOL_Obool)), _1399857), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399859, tc_HOL_Obool))), _1399863)), _1399865)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399859, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399857, tc_fun(_1399859, tc_HOL_Obool)), _1399861), _1399863)), _1399865))], (4022 ^ _777864) ^ [_839219, _839221, _839223, _839225] : [-(c_List_Olenlex(_839225, _839221) = c_List_Olenlex(_839223, _839219)), _839225 = _839223, _839221 = _839219], (33316 ^ _777864) ^ [_1390087, _1390089, _1390091] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1390087), _1390089), _1390091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1390087, tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool)), _1390089), hAPP(hAPP(c_COMBC(_1390087, tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1390087, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool)), _1390087), c_Set_Oinsert(tc_fun(_1390087, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1390087, tc_HOL_Obool), tc_fun(_1390087, tc_HOL_Obool), _1390087), c_Relation_OImage(_1390087, _1390087, _1390091)), hAPP(hAPP(c_COMBC(_1390087, tc_fun(_1390087, tc_HOL_Obool), tc_fun(_1390087, tc_HOL_Obool)), c_Set_Oinsert(_1390087)), c_Orderings_Obot__class_Obot(tc_fun(_1390087, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1390087, tc_HOL_Obool), tc_HOL_Obool)))))], (50626 ^ _777864) ^ [_1798466, _1798468, _1798470, _1798472] : [-(c_List_Oconcat(_1798466, hAPP(hAPP(c_List_Omap(_1798468, tc_List_Olist(_1798466)), hAPP(hAPP(c_COMBC(_1798468, tc_List_Olist(_1798466), tc_List_Olist(_1798466)), hAPP(hAPP(c_COMBB(_1798466, tc_fun(tc_List_Olist(_1798466), tc_List_Olist(_1798466)), _1798468), c_List_Olist_OCons(_1798466)), _1798470)), c_List_Olist_ONil(_1798466))), _1798472)) = hAPP(hAPP(c_List_Omap(_1798468, _1798466), _1798470), _1798472))], (51339 ^ _777864) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (28158 ^ _777864) ^ [_1279887, _1279889] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279887, tc_HOL_Obool)), _1279889), _1279889) = _1279889)], (24465 ^ _777864) ^ [_1206498, _1206500, _1206502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1206498), c_Nitpick_Oplus__frac(_1206498, _1206500, c_Nitpick_Ouminus__frac(_1206498, _1206502)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1206498, _1206500, _1206502))], (24175 ^ _777864) ^ [_1201102, _1201104, _1201106, _1201108] : [class_Orderings_Olinorder(_1201102), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201102), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201102), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201102), _1201104), _1201106)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201102), _1201104), _1201108))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201102), _1201104), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1201102), _1201106), _1201108)))))], (26073 ^ _777864) ^ [_1235857, _1235859] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1235857)), _1235859)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1235857), _1235859)))], (1102 ^ _777864) ^ [_794407, _794409] : [-(class_Rings_Oordered__ring(_794407)), _794409 = _794407, class_Rings_Oordered__ring(_794409)], (32017 ^ _777864) ^ [_1363007, _1363009, _1363011] : [class_Orderings_Olinorder(_1363007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363007), _1363009)), hBOOL(hAPP(hAPP(c_member(_1363007), _1363011), _1363009)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363007), _1363011), c_Big__Operators_Olattice_OSup__fin(_1363007, c_Orderings_Oord__class_Omax(_1363007), _1363009)) = _1363011)], (6117 ^ _777864) ^ [_878497, _878499, _878501, _878503] : [class_Rings_Osemiring__1(_878497), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_878497, _878499, hAPP(c_Nat_OSuc, _878501), _878503) = c_Nat_Osemiring__1__class_Oof__nat__aux(_878497, _878499, _878501, hAPP(_878499, _878503)))], (4106 ^ _777864) ^ [_840601, _840603] : [_840603 = _840601, -(c_Groups_Oabs__class_Oabs(_840603) = c_Groups_Oabs__class_Oabs(_840601))], (42944 ^ _777864) ^ [_1612890, _1612892, _1612894] : [class_Orderings_Olinorder(_1612890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612890), _1612892)), -(hBOOL(hAPP(hAPP(c_member(_1612890), _1612894), _1612892))), -(c_Big__Operators_Olinorder__class_OMax(_1612890, hAPP(hAPP(c_Set_Oinsert(_1612890), _1612894), _1612892)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612890, _1612890, c_Orderings_Oord__class_Omax(_1612890)), _1612894), _1612892))], (7943 ^ _777864) ^ [_910092, _910094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _910092), _910094)), -(_910094 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _910092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 7946 ^ [_910092, _910094]))))], (31543 ^ _777864) ^ [_1354408, _1354410, _1354412] : [class_Orderings_Olinorder(_1354408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354408), _1354410)), hBOOL(hAPP(hAPP(c_member(_1354408), _1354412), _1354410)), 31554 ^ _777864 : [(31561 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354408, tc_HOL_Obool)), _1354410), hAPP(hAPP(c_Set_Oinsert(_1354408), _1354412), c_Orderings_Obot__class_Obot(tc_fun(_1354408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354408, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1354408, _1354410) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1354408), _1354412), c_Big__Operators_Olinorder__class_OMin(_1354408, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354408, tc_HOL_Obool)), _1354410), hAPP(hAPP(c_Set_Oinsert(_1354408), _1354412), c_Orderings_Obot__class_Obot(tc_fun(_1354408, tc_HOL_Obool)))))))], (31555 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354408, tc_HOL_Obool)), _1354410), hAPP(hAPP(c_Set_Oinsert(_1354408), _1354412), c_Orderings_Obot__class_Obot(tc_fun(_1354408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1354408, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1354408, _1354410) = _1354412)]]], (45640 ^ _777864) ^ [_1679654, _1679656, _1679658] : [c_Fun_Oinj__on(_1679654, _1679656, _1679658, c_Orderings_Otop__class_Otop(tc_fun(_1679654, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1679654), tc_List_Olist(_1679656), hAPP(c_List_Omap(_1679654, _1679656), _1679658), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1679654), tc_HOL_Obool))))], (43939 ^ _777864) ^ [_1637996, _1637998, _1638000, _1638002, _1638004] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1637996, tc_HOL_Obool)), _1637998), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638000, tc_fun(_1637996, tc_HOL_Obool)), _1638002), _1638004)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1638000, tc_fun(_1637996, tc_HOL_Obool)), _1638002), hAPP(hAPP(c_COMBB(tc_fun(_1637996, tc_HOL_Obool), tc_fun(_1637996, tc_HOL_Obool), _1638000), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1637996, tc_HOL_Obool)), _1637998)), _1638004)))], (51001 ^ _777864) ^ [_1806693, _1806695, _1806697] : [class_Orderings_Olinorder(_1806693), c_List_Olinorder__class_Osorted(_1806693, _1806695), -(c_List_Olinorder__class_Osorted(_1806693, c_List_OdropWhile(_1806693, _1806697, _1806695)))], (45876 ^ _777864) ^ [_1685259, _1685261, _1685263, _1685265, _1685267, _1685269] : [-(hBOOL(hAPP(hAPP(c_member(_1685259), _1685261), hAPP(c_List_Oset(_1685259), _1685263)))), -(hAPP(hAPP(c_List_Omap(_1685259, _1685265), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1685259, _1685265), _1685267), _1685261), _1685269)), _1685263) = hAPP(hAPP(c_List_Omap(_1685259, _1685265), _1685267), _1685263))], (38130 ^ _777864) ^ [_1493404, _1493406] : [class_Lattices_Obounded__lattice__top(_1493404), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1493404), c_Orderings_Otop__class_Otop(_1493404)), _1493406) = _1493406)], (4540 ^ _777864) ^ [_847262, _847264, _847266, _847268] : [-(c_List_Olexord(_847268, _847264) = c_List_Olexord(_847266, _847262)), _847268 = _847266, _847264 = _847262], (48836 ^ _777864) ^ [_1759471, _1759473] : [-(c_List_Orotate(_1759471, _1759473) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1759471), tc_List_Olist(_1759471)), _1759473), c_List_Orotate1(_1759471)))], (15446 ^ _777864) ^ [_1040686, _1040688] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040686), _1040688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040686), _1040688)))], (33174 ^ _777864) ^ [_1386829, _1386831, _1386833, _1386835, _1386837] : [class_Groups_Ocomm__monoid__mult(_1386829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386831), _1386833)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386831), _1386835)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386831, tc_HOL_Obool)), _1386833), _1386835) = c_Orderings_Obot__class_Obot(tc_fun(_1386831, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386831, _1386829), _1386837), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386831, tc_HOL_Obool)), _1386833), _1386835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386829), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386831, _1386829), _1386837), _1386833)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386831, _1386829), _1386837), _1386835)))], (35786 ^ _777864) ^ [_1443407, _1443409, _1443411] : [class_Orderings_Oorder(_1443407), 35789 ^ _777864 : [(35796 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443407), _1443409), _1443411))), -(c_Orderings_Obot__class_Obot(tc_fun(_1443407, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443407, _1443409), _1443411))], (35790 ^ _777864) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1443407, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443407, _1443409), _1443411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443407), _1443409), _1443411))]]], (2380 ^ _777864) ^ [_812936, _812938, _812940, _812942] : [-(c_Nitpick_Onorm__frac(_812942, _812938) = c_Nitpick_Onorm__frac(_812940, _812936)), _812942 = _812940, _812938 = _812936], (12009 ^ _777864) ^ [_978853, _978855, _978857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _978855), _978857)), -(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, _978853)), _978855)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978853)), _978857))))], (18686 ^ _777864) ^ [] : [-(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)))))], (46066 ^ _777864) ^ [_1689536, _1689538, _1689540] : [hBOOL(hAPP(c_List_Odistinct(_1689536), _1689538)), -(hAPP(c_List_Oset(_1689536), c_List_Oremove1(_1689536, _1689540, _1689538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1689536, tc_HOL_Obool)), hAPP(c_List_Oset(_1689536), _1689538)), hAPP(hAPP(c_Set_Oinsert(_1689536), _1689540), c_Orderings_Obot__class_Obot(tc_fun(_1689536, tc_HOL_Obool)))))], (7054 ^ _777864) ^ [_893717, _893719, _893721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893717), _893719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _893717), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _893721), _893719))))], (41774 ^ _777864) ^ [_1587513, _1587515, _1587517, _1587519, _1587521, _1587523, _1587525, _1587527, _1587529, _1587531] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1587513, _1587515), tc_prod(_1587517, _1587519), tc_prod(_1587521, _1587523), c_Product__Type_Omap__pair(_1587513, _1587517, _1587515, _1587519, _1587525, _1587527)), c_Product__Type_Omap__pair(_1587521, _1587513, _1587523, _1587515, _1587529, _1587531)) = c_Product__Type_Omap__pair(_1587521, _1587517, _1587523, _1587519, hAPP(c_Fun_Ocomp(_1587513, _1587517, _1587521, _1587525), _1587529), hAPP(c_Fun_Ocomp(_1587515, _1587519, _1587523, _1587527), _1587531)))], (580 ^ _777864) ^ [_786812, _786814, _786816, _786818, _786820, _786822] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_786820, _786816, _786812)), c_Hoare__Mirabelle_Ohoare__derivs(_786822, _786818, _786814), _786822 = _786820, _786818 = _786816, _786814 = _786812], (28645 ^ _777864) ^ [_1293953] : [-(c_Wellfounded_Omeasure(_1293953) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1293953), c_Wellfounded_Oless__than))], (43014 ^ _777864) ^ [_1614299, _1614301, _1614303, _1614305, _1614307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614299, _1614299)), hAPP(hAPP(c_Product__Type_OPair(_1614299, _1614299), _1614301), _1614303)), _1614305)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1614299, _1614299)), hAPP(hAPP(c_Product__Type_OPair(_1614299, _1614299), _1614303), _1614307)), c_Transitive__Closure_Otrancl(_1614299, _1614305))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614299, _1614299)), hAPP(hAPP(c_Product__Type_OPair(_1614299, _1614299), _1614301), _1614307)), c_Transitive__Closure_Otrancl(_1614299, _1614305))))], (34379 ^ _777864) ^ [_1415498, _1415500, _1415502, _1415504, _1415506] : [class_Groups_Ocomm__monoid__mult(_1415498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415500), _1415502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1415500, tc_HOL_Obool)), _1415504), _1415502)), 34393 ^ _777864 : [(34396 ^ _777864) ^ [] : [hAPP(_1415506, 34392 ^ [_1415498, _1415500, _1415502, _1415504, _1415506]) = c_Groups_Oone__class_Oone(_1415498)], (34394 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415500), 34392 ^ [_1415498, _1415500, _1415502, _1415504, _1415506]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415500, tc_HOL_Obool)), _1415502), _1415504))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415500, _1415498), _1415506), _1415502) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415500, _1415498), _1415506), _1415504))], (46715 ^ _777864) ^ [_1707450, _1707452, _1707454, _1707456, _1707458, _1707460] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707450), tc_List_Olist(_1707450))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707450), tc_List_Olist(_1707450)), hAPP(hAPP(c_List_Olist_OCons(_1707450), _1707452), _1707454)), hAPP(hAPP(c_List_Olist_OCons(_1707450), _1707456), _1707458))), c_List_Olex(_1707450, _1707460)))), 46716 ^ _777864 : [(46723 ^ _777864) ^ [] : [_1707452 = _1707456, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707450), tc_List_Olist(_1707450))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707450), tc_List_Olist(_1707450)), _1707454), _1707458)), c_List_Olex(_1707450, _1707460)))], (46717 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1707450, _1707450)), hAPP(hAPP(c_Product__Type_OPair(_1707450, _1707450), _1707452), _1707456)), _1707460)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707450)), _1707454) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707450)), _1707458)]]], (44218 ^ _777864) ^ [_1645805, _1645807] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1645805, _1645805), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1645805, _1645807)), c_Relation_OId(_1645805)) = c_Transitive__Closure_Ortrancl(_1645805, _1645807))], (23727 ^ _777864) ^ [_1192382, _1192384, _1192386, _1192388, _1192390, _1192392] : [hAPP(_1192388, hAPP(c_Product__Type_Osnd(_1192386, _1192382), _1192390)) = hAPP(_1192392, hAPP(c_Product__Type_Osnd(_1192386, _1192382), _1192390)), -(hAPP(c_Product__Type_Oapsnd(_1192382, _1192384, _1192386, _1192388), _1192390) = hAPP(c_Product__Type_Oapsnd(_1192382, _1192384, _1192386, _1192392), _1192390))], (1662 ^ _777864) ^ [_801407, _801409] : [-(class_Rings_Osemiring__1(_801407)), _801409 = _801407, class_Rings_Osemiring__1(_801409)], (48103 ^ _777864) ^ [_1741235, _1741237, _1741239] : [hAPP(hAPP(c_List_Oappend(_1741235), _1741237), _1741239) = c_List_Olist_ONil(_1741235), 48106 ^ _777864 : [(48109 ^ _777864) ^ [] : [-(_1741239 = c_List_Olist_ONil(_1741235))], (48107 ^ _777864) ^ [] : [-(_1741237 = c_List_Olist_ONil(_1741235))]]], (50108 ^ _777864) ^ [_1786301, _1786303, _1786305, _1786307, _1786309] : [class_Orderings_Olinorder(_1786301), c_List_Olinorder__class_Osorted(_1786301, hAPP(hAPP(c_List_Omap(_1786303, _1786301), _1786305), _1786307)), -(c_List_Olinorder__class_Osorted(_1786301, hAPP(hAPP(c_List_Omap(_1786303, _1786301), _1786305), c_List_Oremove1(_1786303, _1786309, _1786307))))], (16128 ^ _777864) ^ [_1054446, _1054448, _1054450] : [class_Int_Onumber(_1054446), 16131 ^ _777864 : [(16138 ^ _777864) ^ [] : [_1054450 = hAPP(c_Int_Onumber__class_Onumber__of(_1054446), _1054448), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054446), _1054448) = _1054450)], (16132 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1054446), _1054448) = _1054450, -(_1054450 = hAPP(c_Int_Onumber__class_Onumber__of(_1054446), _1054448))]]], (16950 ^ _777864) ^ [_1070121] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070121) = _1070121)], (27774 ^ _777864) ^ [_1272644, _1272646, _1272648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272644, tc_HOL_Obool)), _1272646), _1272648) = c_Orderings_Obot__class_Obot(tc_fun(_1272644, tc_HOL_Obool))), _1272646 = c_Orderings_Obot__class_Obot(tc_fun(_1272644, tc_HOL_Obool)), _1272648 = c_Orderings_Obot__class_Obot(tc_fun(_1272644, tc_HOL_Obool))], (2140 ^ _777864) ^ [_809186, _809188, _809190, _809192] : [-(c_Divides_OposDivAlg(_809192, _809188) = c_Divides_OposDivAlg(_809190, _809186)), _809192 = _809190, _809188 = _809186], (27710 ^ _777864) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26495 ^ _777864) ^ [_1244647, _1244649] : [_1244649 = c_Orderings_Obot__class_Obot(tc_fun(_1244647, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1244647, tc_HOL_Obool)), _1244649), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1244647, tc_HOL_Obool)), _1244649))))], (30931 ^ _777864) ^ [_1343328, _1343330] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343328, _1343330) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343328), _1343330))], (49492 ^ _777864) ^ [_1773799, _1773801, _1773803] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1773799, tc_HOL_Obool)), hAPP(c_List_Oset(_1773799), hAPP(c_List_Ofilter(_1773799, _1773801), _1773803))), hAPP(c_List_Oset(_1773799), _1773803))))], (48826 ^ _777864) ^ [_1759309, _1759311, _1759313] : [-(_1759309 = c_List_Olist_ONil(_1759311)), -(hAPP(c_List_Otl(_1759311), hAPP(hAPP(c_List_Oappend(_1759311), _1759309), _1759313)) = hAPP(hAPP(c_List_Oappend(_1759311), hAPP(c_List_Otl(_1759311), _1759309)), _1759313))], (22304 ^ _777864) ^ [_1163337, _1163339, _1163341, _1163343] : [_1163337 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1163339), _1163341)), _1163343), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1163337, _1163339), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1163341), _1163343)))), 22311 ^ _777864 : [(22314 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163343), _1163339))], (22312 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163339)))]], 22319 ^ _777864 : [(22322 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163339), _1163343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1163343), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22320 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163339))]]], (51175 ^ _777864) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (47172 ^ _777864) ^ [_1719413, _1719415, _1719417] : [-(hBOOL(hAPP(hAPP(c_member(_1719413), _1719415), hAPP(c_List_Oset(_1719413), _1719417)))), 47173 ^ _777864 : [(47174 ^ _777864) ^ [_1719487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719487), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719413)), _1719417))), hAPP(hAPP(c_List_Onth(_1719413), _1719417), _1719487) = _1719415]]], (18974 ^ _777864) ^ [_1103992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1103992))))], (1958 ^ _777864) ^ [_806365, _806367, _806369, _806371, _806373, _806375] : [-(c_Option_Ooption_Ooption__size(_806375, _806371, _806367) = c_Option_Ooption_Ooption__size(_806373, _806369, _806365)), _806375 = _806373, _806371 = _806369, _806367 = _806365], (41738 ^ _777864) ^ [_1586577, _1586579, _1586581, _1586583, _1586585, _1586587, _1586589] : [-(hAPP(c_Product__Type_Oapfst(_1586577, _1586579, _1586581, _1586583), hAPP(c_Product__Type_Oapfst(_1586585, _1586577, _1586581, _1586587), _1586589)) = hAPP(c_Product__Type_Oapfst(_1586585, _1586579, _1586581, hAPP(c_Fun_Ocomp(_1586577, _1586579, _1586585, _1586583), _1586587)), _1586589))], (26467 ^ _777864) ^ [_1244156] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1244156) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1244156), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (50700 ^ _777864) ^ [_1800508, _1800510, _1800512, _1800514] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800508), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1800508))), _1800510))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800512), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1800508))), c_List_Otranspose(_1800508, _1800510)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1800508))), hAPP(c_List_Ofilter(tc_List_Olist(_1800508), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1800508)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800512)), c_Nat_Osize__class_Osize(tc_List_Olist(_1800508)))), _1800510)))), -(hAPP(hAPP(c_List_Onth(_1800508), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1800508)), c_List_Otranspose(_1800508, _1800510)), _1800512)), _1800514) = hAPP(hAPP(c_List_Onth(_1800508), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1800508)), _1800510), _1800514)), _1800512))], (8646 ^ _777864) ^ [_921403, _921405, _921407] : [class_Groups_Ogroup__add(_921403), 8649 ^ _777864 : [(8656 ^ _777864) ^ [] : [_921405 = _921407, -(hAPP(c_Groups_Ouminus__class_Ouminus(_921403), _921405) = hAPP(c_Groups_Ouminus__class_Ouminus(_921403), _921407))], (8650 ^ _777864) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_921403), _921405) = hAPP(c_Groups_Ouminus__class_Ouminus(_921403), _921407), -(_921405 = _921407)]]], (48878 ^ _777864) ^ [_1760335, _1760337, _1760339, _1760341] : [-(c_List_Olist_Olist__size(_1760335, _1760337, hAPP(hAPP(c_List_Olist_OCons(_1760335), _1760339), _1760341)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1760337, _1760339)), c_List_Olist_Olist__size(_1760335, _1760337, _1760341))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1552 ^ _777864) ^ [_800032, _800034] : [-(class_Groups_Ocomm__monoid__add(_800032)), _800034 = _800032, class_Groups_Ocomm__monoid__add(_800034)], (36806 ^ _777864) ^ [_1465275, _1465277, _1465279, _1465281, _1465283] : [class_Groups_Oab__group__add(_1465275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465277), _1465279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465277, tc_HOL_Obool)), _1465281), _1465279)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465277, _1465275), _1465283), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1465277, tc_HOL_Obool)), _1465279), _1465281)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1465275), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465277, _1465275), _1465283), _1465279)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465277, _1465275), _1465283), _1465281)))], (41374 ^ _777864) ^ [_1577385, _1577387, _1577389, _1577391] : [hBOOL(hAPP(c_Predicate_ODomainP(_1577385, _1577387, hAPP(hAPP(c_COMBC(_1577385, tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_fun(_1577387, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577387, tc_fun(tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_fun(_1577387, tc_HOL_Obool)), _1577385), c_COMBC(_1577387, tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577387, tc_prod(_1577385, _1577387)), tc_fun(_1577387, tc_fun(tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_HOL_Obool)), _1577385), hAPP(c_COMBB(tc_prod(_1577385, _1577387), tc_fun(tc_fun(tc_prod(_1577385, _1577387), tc_HOL_Obool), tc_HOL_Obool), _1577387), c_member(tc_prod(_1577385, _1577387)))), c_Product__Type_OPair(_1577385, _1577387)))), _1577389)), _1577391)), -(hBOOL(hAPP(hAPP(c_member(_1577385), _1577391), hAPP(c_Relation_ODomain(_1577385, _1577387), _1577389))))], (44862 ^ _777864) ^ [_1661374, _1661376, _1661378] : [class_Complete__Lattice_Ocomplete__lattice(_1661374), class_Orderings_Olinorder(_1661374), 44869 ^ _777864 : [(44879 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1661374), _1661376), c_Complete__Lattice_OSup__class_OSup(_1661374, _1661378)))), 44880 ^ _777864 : [(44881 ^ _777864) ^ [_1661680] : [hBOOL(hAPP(hAPP(c_member(_1661374), _1661680), _1661378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1661374), _1661376), _1661680))]]], (44870 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1661374), _1661376), c_Complete__Lattice_OSup__class_OSup(_1661374, _1661378))), 44874 ^ _777864 : [(44877 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1661374), _1661376), 44873 ^ [_1661374, _1661376, _1661378])))], (44875 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661374), 44873 ^ [_1661374, _1661376, _1661378]), _1661378)))]]]]], (3198 ^ _777864) ^ [_826265, _826267, _826269, _826271] : [-(c_Set_Othe__elem(_826271, _826267) = c_Set_Othe__elem(_826269, _826265)), _826271 = _826269, _826267 = _826265], (29149 ^ _777864) ^ [_1305450] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305450), c_Orderings_Obot__class_Obot(tc_fun(_1305450, tc_HOL_Obool)))))], (28936 ^ _777864) ^ [_1300419, _1300421] : [c_Nat__Transfer_Onat__set(_1300419), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1300421), _1300419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300421)))], (43579 ^ _777864) ^ [_1627445, _1627447] : [c_Wellfounded_Owf(_1627445, hAPP(c_Relation_Oconverse(_1627445, _1627445), _1627447)), -(c_Wellfounded_Owf(_1627445, hAPP(c_Relation_Oconverse(_1627445, _1627445), c_Transitive__Closure_Otrancl(_1627445, _1627447))))], (44790 ^ _777864) ^ [_1659611, _1659613, _1659615] : [-(hAPP(c_Relation_ODomain(_1659611, _1659613), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1659611, _1659613), tc_HOL_Obool), _1659615)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1659611, _1659613), tc_HOL_Obool), tc_fun(_1659611, tc_HOL_Obool)), _1659615), c_Relation_ODomain(_1659611, _1659613)))], (17062 ^ _777864) ^ [_1071980, _1071982] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1071980) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071982), 17065 ^ _777864 : [(17068 ^ _777864) ^ [] : [-(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), _1071982))))], (17066 ^ _777864) ^ [] : [-(_1071980 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071982)))]]], (4 ^ _777864) ^ [_777914, _777916] : [_777916 = _777914, -(_777914 = _777916)], (38675 ^ _777864) ^ [_1505955, _1505957, _1505959, _1505961, _1505963] : [class_Groups_Ocomm__monoid__add(_1505955), class_Groups_Ocomm__monoid__mult(_1505955), _1505957 = _1505959, c_Nat__Transfer_Onat__set(_1505959), 38693 ^ _777864 : [(38696 ^ _777864) ^ [] : [hAPP(_1505961, 38692 ^ [_1505955, _1505957, _1505959, _1505961, _1505963]) = hAPP(_1505963, 38692 ^ [_1505955, _1505957, _1505959, _1505961, _1505963])], (38694 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38692 ^ [_1505955, _1505957, _1505959, _1505961, _1505963])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1505955), _1505961), _1505957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1505955), _1505963), _1505959))], (20400 ^ _777864) ^ [_1129129, _1129131, _1129133] : [class_Fields_Ofield__inverse__zero(_1129129), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129129), c_Groups_Oone__class_Oone(_1129129)), hAPP(hAPP(c_Power_Opower__class_Opower(_1129129), _1129131), _1129133)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1129129), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129129), c_Groups_Oone__class_Oone(_1129129)), _1129131)), _1129133))], (30649 ^ _777864) ^ [_1338288, _1338290] : [30650 ^ _777864 : [(30653 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338290), _1338288))], (30651 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338288), _1338290)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338288, _1338290) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24287 ^ _777864) ^ [_1203052] : [class_Orderings_Olinorder(_1203052), -(c_Orderings_Oord_Omax(_1203052, hAPP(c_COMBC(_1203052, _1203052, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1203052))) = c_Orderings_Oord__class_Omin(_1203052))], (38074 ^ _777864) ^ [] : [-(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))))], (44738 ^ _777864) ^ [_1658179, _1658181] : [class_Complete__Lattice_Ocomplete__lattice(_1658179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658179), _1658181)), -(_1658181 = c_Orderings_Obot__class_Obot(tc_fun(_1658179, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1658179, _1658181) = c_Complete__Lattice_OInf__class_OInf(_1658179, _1658181))], (11345 ^ _777864) ^ [_966916, _966918] : [class_Rings_Olinordered__idom(_966916), 11348 ^ _777864 : [(11355 ^ _777864) ^ [] : [_966918 = c_Groups_Ozero__class_Ozero(_966916), -(c_Groups_Osgn__class_Osgn(_966916, _966918) = c_Groups_Ozero__class_Ozero(_966916))], (11349 ^ _777864) ^ [] : [c_Groups_Osgn__class_Osgn(_966916, _966918) = c_Groups_Ozero__class_Ozero(_966916), -(_966918 = c_Groups_Ozero__class_Ozero(_966916))]]], (14266 ^ _777864) ^ [_1019081] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1019081), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16400 ^ _777864) ^ [_1059233, _1059235, _1059237] : [class_Groups_Oordered__ab__group__add__abs(_1059233), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1059233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059233), hAPP(c_Groups_Oabs__class_Oabs(_1059233), _1059235)), hAPP(c_Groups_Oabs__class_Oabs(_1059233), _1059237))), hAPP(c_Groups_Oabs__class_Oabs(_1059233), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059233), _1059237), _1059235)))))], (44905 ^ _777864) ^ [_1662221, _1662223, _1662225, _1662227] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662221, tc_HOL_Obool), hAPP(c_Set_Oimage(_1662223, tc_fun(_1662221, tc_HOL_Obool), _1662225), _1662227)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1662223, tc_fun(_1662221, tc_HOL_Obool)), _1662227), _1662225))], (15158 ^ _777864) ^ [_1035139, _1035141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035139), _1035141)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035139, _1035141) = _1035139)], (41198 ^ _777864) ^ [_1572745, _1572747, _1572749, _1572751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1572745, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1572745, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1572747, _1572745), _1572749)), hAPP(c_Relation_ORange(_1572747, _1572745), _1572751))), hAPP(c_Relation_ORange(_1572747, _1572745), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1572747, _1572745), tc_HOL_Obool)), _1572749), _1572751)))))], (19072 ^ _777864) ^ [_1105735, _1105737] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1105735)), c_Int_OBit1(_1105737)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1105735), _1105737)))], (18036 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41934 ^ _777864) ^ [_1590963, _1590965, _1590967, _1590969, _1590971, _1590973] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1590963, _1590965), _1590965, tc_prod(_1590967, _1590969), c_Product__Type_Osnd(_1590963, _1590965)), c_Product__Type_Omap__pair(_1590967, _1590963, _1590969, _1590965, _1590971, _1590973)) = hAPP(c_Fun_Ocomp(_1590969, _1590965, tc_prod(_1590967, _1590969), _1590973), c_Product__Type_Osnd(_1590967, _1590969)))], (16622 ^ _777864) ^ [_1063597, _1063599, _1063601] : [class_Int_Onumber__ring(_1063597), -(hAPP(c_Int_Onumber__class_Onumber__of(_1063597), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1063599), _1063601)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063597), hAPP(c_Int_Onumber__class_Onumber__of(_1063597), _1063599)), hAPP(c_Int_Onumber__class_Onumber__of(_1063597), _1063601)))], (34747 ^ _777864) ^ [_1422983, _1422985, _1422987, _1422989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1422983), _1422985)), 34750 ^ _777864 : [(34757 ^ _777864) ^ [] : [hAPP(c_Finite__Set_Ocard(_1422987), hAPP(c_Set_Oimage(_1422983, _1422987, _1422989), _1422985)) = hAPP(c_Finite__Set_Ocard(_1422983), _1422985), -(c_Fun_Oinj__on(_1422983, _1422987, _1422989, _1422985))], (34751 ^ _777864) ^ [] : [c_Fun_Oinj__on(_1422983, _1422987, _1422989, _1422985), -(hAPP(c_Finite__Set_Ocard(_1422987), hAPP(c_Set_Oimage(_1422983, _1422987, _1422989), _1422985)) = hAPP(c_Finite__Set_Ocard(_1422983), _1422985))]]], (27860 ^ _777864) ^ [_1274245, _1274247, _1274249, _1274251, _1274253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274245, tc_HOL_Obool)), _1274247), _1274249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274245, tc_HOL_Obool)), _1274251), _1274253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274245, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274245, tc_HOL_Obool)), _1274247), _1274251)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274245, tc_HOL_Obool)), _1274249), _1274253))))], (51357 ^ _777864) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (14612 ^ _777864) ^ [_1024849, _1024851, _1024853] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024849), _1024851)), _1024853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024849), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024851), _1024853))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024849), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024851, _1024853))), _1024853)))], (9460 ^ _777864) ^ [_935755, _935757, _935759] : [class_Rings_Olinordered__semiring__strict(_935755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935755), c_Groups_Ozero__class_Ozero(_935755)), _935757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935755), _935759), c_Groups_Ozero__class_Ozero(_935755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935755), _935757), _935759)), c_Groups_Ozero__class_Ozero(_935755))))], (47552 ^ _777864) ^ [_1728539, _1728541] : [hAPP(c_List_Oset(_1728539), _1728541) = c_Orderings_Obot__class_Obot(tc_fun(_1728539, tc_HOL_Obool)), -(_1728541 = c_List_Olist_ONil(_1728539))], (13670 ^ _777864) ^ [_1008145, _1008147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1008145), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1008147), _1008145)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1008145, _1008147) = _1008145)], (51097 ^ _777864) ^ [_1807986, _1807988] : [class_Orderings_Otop(_1807986), -(class_Orderings_Otop(tc_fun(_1807988, _1807986)))], (40877 ^ _777864) ^ [_1565725, _1565727, _1565729] : [c_Wellfounded_Owf(_1565725, _1565727), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565725, _1565725)), hAPP(hAPP(c_Product__Type_OPair(_1565725, _1565725), _1565729), _1565729)), _1565727))], (30286 ^ _777864) ^ [_1329939, _1329941, _1329943, _1329945, _1329947] : [c_Finite__Set_Ofolding__one(_1329939, _1329941, _1329943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329939), _1329945)), -(_1329945 = c_Orderings_Obot__class_Obot(tc_fun(_1329939, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329939), _1329947)), -(_1329947 = c_Orderings_Obot__class_Obot(tc_fun(_1329939, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329939, tc_HOL_Obool)), _1329945), _1329947) = c_Orderings_Obot__class_Obot(tc_fun(_1329939, tc_HOL_Obool)), -(hAPP(_1329943, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329939, tc_HOL_Obool)), _1329945), _1329947)) = hAPP(hAPP(_1329941, hAPP(_1329943, _1329945)), hAPP(_1329943, _1329947)))], (45626 ^ _777864) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (8838 ^ _777864) ^ [_924869, _924871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924869)), 8841 ^ _777864 : [(8850 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _924869), _924871) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _924869 = c_Groups_Oone__class_Oone(tc_Int_Oint), _924871 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8842 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _924869), _924871) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8845 ^ _777864 : [(8848 ^ _777864) ^ [] : [-(_924871 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8846 ^ _777864) ^ [] : [-(_924869 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (28665 ^ _777864) ^ [] : [-(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))))))], (42275 ^ _777864) ^ [_1599011, _1599013, _1599015, _1599017] : [-(c_New__Random__Sequence_Opos__map(_1599011, _1599013, _1599015, _1599017) = c_New__Random__Sequence_Opos__bind(_1599011, _1599013, _1599017, hAPP(c_Fun_Ocomp(_1599013, 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(_1599013))))), _1599011, c_New__Random__Sequence_Opos__single(_1599013)), _1599015)))], (50895 ^ _777864) ^ [_1804477, _1804479, _1804481] : [hBOOL(hAPP(c_List_Odistinct(_1804477), _1804479)), -(c_List_Oremove1(_1804477, _1804481, c_List_Oremdups(_1804477, _1804479)) = c_List_Oremdups(_1804477, c_List_Oremove1(_1804477, _1804481, _1804479)))], (29179 ^ _777864) ^ [_1305890, _1305892] : [class_Finite__Set_Ofinite(_1305890), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1305890), _1305892)))], (39159 ^ _777864) ^ [_1517513, _1517515, _1517517] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1517513, _1517515), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1517513, _1517515), _1517517), hAPP(c_COMBK(tc_fun(_1517515, tc_HOL_Obool), _1517513), c_Orderings_Otop__class_Otop(tc_fun(_1517515, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1517513, _1517515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1517513, tc_HOL_Obool)), _1517517)), hAPP(c_COMBK(tc_fun(_1517515, tc_HOL_Obool), _1517513), c_Orderings_Otop__class_Otop(tc_fun(_1517515, tc_HOL_Obool)))))], (24333 ^ _777864) ^ [_1203926] : [-(c_Nitpick_Oone__frac(_1203926) = c_Nitpick_OAbs__Frac(_1203926, 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))))], (28028 ^ _777864) ^ [_1277286, _1277288, _1277290] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277286, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277286, tc_HOL_Obool)), _1277288), _1277290)), _1277290) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277286, tc_HOL_Obool)), _1277288), _1277290))], (33694 ^ _777864) ^ [_1398798, _1398800, _1398802, _1398804, _1398806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398798, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398800, tc_fun(_1398798, tc_HOL_Obool)), _1398802), _1398804)), _1398806)), 33697 ^ _777864 : [(33698 ^ _777864) ^ [_1398931] : [hBOOL(hAPP(hAPP(c_member(_1398800), _1398931), _1398802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1398798, tc_HOL_Obool)), hAPP(_1398804, _1398931)), _1398806)))]]], (37290 ^ _777864) ^ [_1476551, _1476553, _1476555, _1476557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476551), _1476553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1476551, tc_HOL_Obool)), _1476553), _1476555)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476551, tc_Nat_Onat), _1476557), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1476551, tc_HOL_Obool)), _1476555), _1476553)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476551, tc_Nat_Onat), _1476557), _1476555)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476551, tc_Nat_Onat), _1476557), _1476553)))], (10009 ^ _777864) ^ [_945137, _945139, _945141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945137), _945139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945141), _945137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945141), _945139))))], (13585 ^ _777864) ^ [_1006745, _1006747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1006747)), -(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, _1006745, _1006747))))], (50759 ^ _777864) ^ [_1802002, _1802004, _1802006] : [-(c_List_OtakeWhile(_1802002, _1802004, _1802006) = hAPP(hAPP(c_List_Otake(_1802002), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802002)), c_List_OtakeWhile(_1802002, _1802004, _1802006))), _1802006))], (51217 ^ _777864) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (27163 ^ _777864) ^ [_1259052, _1259054, _1259056, _1259058] : [hBOOL(hAPP(hAPP(c_member(_1259052), _1259054), _1259056)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259052, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1259052), _1259054), _1259058)), _1259056) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259052, tc_HOL_Obool)), _1259058), _1259056))], (43315 ^ _777864) ^ [_1621431, _1621433, _1621435, _1621437, _1621439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621431, _1621431)), hAPP(hAPP(c_Product__Type_OPair(_1621431, _1621431), _1621433), _1621435)), c_Transitive__Closure_Ortrancl(_1621431, _1621437))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1621431, _1621431)), hAPP(hAPP(c_Product__Type_OPair(_1621431, _1621431), _1621435), _1621439)), c_Transitive__Closure_Otrancl(_1621431, _1621437))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1621431, _1621431)), hAPP(hAPP(c_Product__Type_OPair(_1621431, _1621431), _1621433), _1621439)), c_Transitive__Closure_Otrancl(_1621431, _1621437))))], (50698 ^ _777864) ^ [_1800356, _1800358] : [-(c_List_Oconcat(tc_List_Olist(_1800356), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800356), tc_List_Olist(tc_List_Olist(_1800356))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1800356)), _1800356, c_List_Olist_ONil(tc_List_Olist(_1800356)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1800356), tc_List_Olist(tc_List_Olist(_1800356))), _1800356), hAPP(hAPP(c_COMBC(tc_List_Olist(_1800356), tc_List_Olist(tc_List_Olist(_1800356)), tc_List_Olist(tc_List_Olist(_1800356))), c_List_Olist_OCons(tc_List_Olist(_1800356))), c_List_Olist_ONil(tc_List_Olist(_1800356)))))), _1800358)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1800356), tc_List_Olist(_1800356)), c_List_Otl(_1800356)), hAPP(c_List_Ofilter(tc_List_Olist(_1800356), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1800356)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1800356), tc_List_Olist(_1800356), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1800356)))), _1800358)))], (27756 ^ _777864) ^ [_1272313, _1272315, _1272317, _1272319] : [hBOOL(hAPP(hAPP(c_member(_1272313), _1272315), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272313, tc_HOL_Obool)), _1272317), _1272319))), -(hBOOL(hAPP(hAPP(c_member(_1272313), _1272315), _1272317))), -(hBOOL(hAPP(hAPP(c_member(_1272313), _1272315), _1272319)))], (45077 ^ _777864) ^ [_1666070, _1666072, _1666074, _1666076, _1666078, _1666080] : [-(_1666070 = c_Orderings_Obot__class_Obot(tc_fun(_1666072, tc_HOL_Obool))), 45083 ^ _777864 : [(45086 ^ _777864) ^ [] : [c_Fun_Oinj__on(_1666074, _1666076, _1666078, hAPP(_1666080, 45082 ^ [_1666070, _1666072, _1666074, _1666076, _1666078, _1666080]))], (45084 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666072), 45082 ^ [_1666070, _1666072, _1666074, _1666076, _1666078, _1666080]), _1666070)))]], -(c_Fun_Oinj__on(_1666074, _1666076, _1666078, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666072, tc_fun(_1666074, tc_HOL_Obool)), _1666070), _1666080)))], (45370 ^ _777864) ^ [_1673363, _1673365, _1673367, _1673369, _1673371, _1673373, _1673375, _1673377] : [c_Finite__Set_Ofolding__image__simple__idem(_1673363, _1673365, _1673367, _1673369, _1673371, _1673373), hBOOL(hAPP(c_Finite__Set_Ofinite(_1673365), _1673375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1673365, tc_HOL_Obool)), _1673377), _1673375)), -(hAPP(hAPP(_1673367, hAPP(_1673373, _1673377)), hAPP(_1673373, _1673375)) = hAPP(_1673373, _1673375))], (45340 ^ _777864) ^ [_1672764, _1672766, _1672768, _1672770, _1672772, _1672774, _1672776] : [c_Finite__Set_Ofolding__image__simple__idem(_1672764, _1672766, _1672768, _1672770, _1672772, _1672774), -(hAPP(hAPP(_1672768, _1672776), _1672776) = _1672776)], (40288 ^ _777864) ^ [_1543115, _1543117, _1543119] : [-(c_Map_Odom(_1543115, _1543117, _1543119) = hAPP(c_Set_OCollect(_1543115), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1543115), c_fNot), hAPP(hAPP(c_COMBC(_1543115, tc_Option_Ooption(_1543117), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1543117), tc_fun(tc_Option_Ooption(_1543117), tc_HOL_Obool), _1543115), c_fequal), _1543119)), c_Option_Ooption_ONone(_1543117)))))], (45727 ^ _777864) ^ [_1681494, _1681496, _1681498, _1681500, _1681502, _1681504] : [-(hAPP(hAPP(c_List_Omap(_1681494, _1681496), _1681498), hAPP(hAPP(c_List_Omap(_1681500, _1681494), _1681502), _1681504)) = hAPP(hAPP(c_List_Omap(_1681500, _1681496), hAPP(c_Fun_Ocomp(_1681494, _1681496, _1681500, _1681498), _1681502)), _1681504))], (21302 ^ _777864) ^ [_1145372, _1145374, _1145376, _1145378] : [class_Fields_Olinordered__field(_1145372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145372), _1145374), c_Groups_Ozero__class_Ozero(_1145372))), 21309 ^ _777864 : [(21316 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145372), _1145378), _1145374)), _1145376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145372), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145372), _1145376), _1145374)), _1145378)))], (21310 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145372), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145372), _1145376), _1145374)), _1145378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145372), _1145378), _1145374)), _1145376)))]]], (10518 ^ _777864) ^ [_953532, _953534, _953536, _953538] : [class_Orderings_Opreorder(_953532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953532), _953534), _953536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953532), _953536), _953538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953532), _953534), _953538)))], (37905 ^ _777864) ^ [_1489168, _1489170, _1489172, _1489174, _1489176] : [class_Groups_Oab__semigroup__mult(_1489168), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489168, _1489168, c_Groups_Otimes__class_Otimes(_1489168), _1489170, _1489172), _1489174)), hBOOL(hAPP(hAPP(c_member(_1489168), _1489176), _1489172)), -(hBOOL(hAPP(hAPP(c_member(_1489168), _1489170), _1489172))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489168, _1489168, c_Groups_Otimes__class_Otimes(_1489168), _1489176, hAPP(hAPP(c_Set_Oinsert(_1489168), _1489170), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1489168, tc_HOL_Obool)), _1489172), hAPP(hAPP(c_Set_Oinsert(_1489168), _1489176), c_Orderings_Obot__class_Obot(tc_fun(_1489168, tc_HOL_Obool)))))), _1489174)))], (41173 ^ _777864) ^ [_1572095, _1572097, _1572099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572095, _1572097)), _1572099)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572097), hAPP(c_Relation_ORange(_1572095, _1572097), _1572099))))], (1928 ^ _777864) ^ [_805894, _805896, _805898, _805900, _805902, _805904, _805906, _805908] : [-(c_Com_Ovname_Ovname__rec(_805908, _805904, _805900, _805896) = c_Com_Ovname_Ovname__rec(_805906, _805902, _805898, _805894)), _805908 = _805906, _805904 = _805902, _805900 = _805898, _805896 = _805894], (18942 ^ _777864) ^ [_1103430, _1103432] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1103430)), c_Int_OBit0(_1103432)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1103430), _1103432)))], (36286 ^ _777864) ^ [_1453438, _1453440, _1453442, _1453444, _1453446] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1453438, tc_Option_Ooption(_1453440)), _1453442), _1453444), hAPP(c_Option_Ooption_OSome(_1453440), _1453446)) = hAPP(c_COMBK(tc_Option_Ooption(_1453440), _1453438), c_Option_Ooption_ONone(_1453440))], (19678 ^ _777864) ^ [_1116697] : [-(_1116697 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 19681 ^ _777864 : [(19688 ^ _777864) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1116697, 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, _1116697) = 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), _1116697), 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)))], (19682 ^ _777864) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1116697, 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, _1116697) = 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), _1116697), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (11835 ^ _777864) ^ [_975790, _975792] : [class_Groups_Oordered__ab__group__add(_975790), 11838 ^ _777864 : [(11845 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975790), _975792), c_Groups_Ozero__class_Ozero(_975790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975790), c_Groups_Ozero__class_Ozero(_975790)), hAPP(c_Groups_Ouminus__class_Ouminus(_975790), _975792))))], (11839 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975790), c_Groups_Ozero__class_Ozero(_975790)), hAPP(c_Groups_Ouminus__class_Ouminus(_975790), _975792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975790), _975792), c_Groups_Ozero__class_Ozero(_975790))))]]], (10876 ^ _777864) ^ [_959045, _959047, _959049] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959045), _959047) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _959049), _959047), -(_959045 = _959049), -(_959047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46417 ^ _777864) ^ [_1698749, _1698751, _1698753, _1698755, _1698757] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698749)), _1698751) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698753)), _1698755), 46420 ^ _777864 : [(46427 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1698749), _1698757), hAPP(c_List_Oset(_1698749), _1698751)))), -(hAPP(c_Map_Omap__of(_1698749, _1698753, hAPP(hAPP(c_List_Ozip(_1698749, _1698753), _1698751), _1698755)), _1698757) = c_Option_Ooption_ONone(_1698753))], (46421 ^ _777864) ^ [] : [hAPP(c_Map_Omap__of(_1698749, _1698753, hAPP(hAPP(c_List_Ozip(_1698749, _1698753), _1698751), _1698755)), _1698757) = c_Option_Ooption_ONone(_1698753), hBOOL(hAPP(hAPP(c_member(_1698749), _1698757), hAPP(c_List_Oset(_1698749), _1698751)))]]], (19660 ^ _777864) ^ [_1116385, _1116387] : [class_Int_Onumber__ring(_1116385), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1116385), hAPP(c_Int_Onumber__class_Onumber__of(_1116385), 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)))), _1116387))) = hAPP(c_Int_Onumber__class_Onumber__of(_1116385), c_Int_OMin))], (39816 ^ _777864) ^ [_1532289, _1532291, _1532293, _1532295, _1532297, _1532299] : [hAPP(c_Set_Oimage(_1532289, _1532291, _1532293), c_Orderings_Otop__class_Otop(tc_fun(_1532289, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1532291, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1532295, _1532297, _1532299), c_Orderings_Otop__class_Otop(tc_fun(_1532295, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1532297, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532289, _1532295), tc_prod(_1532291, _1532297), c_Product__Type_Omap__pair(_1532289, _1532291, _1532295, _1532297, _1532293, _1532299)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1532289, _1532295), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1532291, _1532297), tc_HOL_Obool)))], (43227 ^ _777864) ^ [_1619275, _1619277] : [-(hAPP(c_Relation_ORange(_1619275, _1619275), c_Transitive__Closure_Ortrancl(_1619275, _1619277)) = c_Orderings_Otop__class_Otop(tc_fun(_1619275, tc_HOL_Obool)))], (48574 ^ _777864) ^ [_1753760, _1753762, _1753764, _1753766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1753760), _1753762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1753764, tc_HOL_Obool)), hAPP(c_List_Oset(_1753764), hAPP(hAPP(c_List_Odrop(_1753764), _1753762), _1753766))), hAPP(c_List_Oset(_1753764), hAPP(hAPP(c_List_Odrop(_1753764), _1753760), _1753766)))))], (40405 ^ _777864) ^ [_1548454, _1548456, _1548458, _1548460] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548454), hAPP(c_Set_OCollect(_1548454), _1548456))), 40408 ^ _777864 : [(40409 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548458), hAPP(c_Set_OCollect(_1548458), hAPP(hAPP(c_COMBB(tc_fun(_1548454, tc_HOL_Obool), tc_HOL_Obool, _1548458), c_HOL_OEx(_1548454)), hAPP(hAPP(c_COMBB(tc_fun(_1548454, tc_HOL_Obool), tc_fun(_1548454, tc_HOL_Obool), _1548458), hAPP(c_COMBS(_1548454, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548454), c_fconj), _1548456))), _1548460))))), 40412 ^ _777864 : [(40413 ^ _777864) ^ [_1548737] : [hBOOL(hAPP(_1548456, _1548737)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548458), hAPP(c_Set_OCollect(_1548458), hAPP(hAPP(c_COMBC(_1548458, _1548454, tc_HOL_Obool), _1548460), _1548737)))))]]], (40419 ^ _777864) ^ [] : [40421 ^ _777864 : [(40424 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548458), hAPP(c_Set_OCollect(_1548458), hAPP(hAPP(c_COMBC(_1548458, _1548454, tc_HOL_Obool), _1548460), 40420 ^ [_1548454, _1548456, _1548458, _1548460]))))], (40422 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1548456, 40420 ^ [_1548454, _1548456, _1548458, _1548460])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548458), hAPP(c_Set_OCollect(_1548458), hAPP(hAPP(c_COMBB(tc_fun(_1548454, tc_HOL_Obool), tc_HOL_Obool, _1548458), c_HOL_OEx(_1548454)), hAPP(hAPP(c_COMBB(tc_fun(_1548454, tc_HOL_Obool), tc_fun(_1548454, tc_HOL_Obool), _1548458), hAPP(c_COMBS(_1548454, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548454), c_fconj), _1548456))), _1548460))))))]]], (48209 ^ _777864) ^ [_1743357, _1743359, _1743361, _1743363, _1743365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743357), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743359)), _1743361))), -(hAPP(hAPP(c_List_Olist__update(_1743359, hAPP(hAPP(c_List_Oappend(_1743359), _1743361), _1743363)), _1743357), _1743365) = hAPP(hAPP(c_List_Oappend(_1743359), hAPP(hAPP(c_List_Olist__update(_1743359, _1743361), _1743357), _1743365)), _1743363))], (17548 ^ _777864) ^ [_1080843, _1080845] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080843)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1080843)), _1080845) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1080843)), _1080845)))], (41930 ^ _777864) ^ [_1590853] : [-(c_Nitpick_Onum(_1590853) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1590853, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1590853)))], (47654 ^ _777864) ^ [_1730623, _1730625] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1730623), _1730625))), -(c_List_Oupto(_1730623, _1730625) = c_List_Olist_ONil(tc_Int_Oint))], (2360 ^ _777864) ^ [_812638, _812640, _812642, _812644] : [-(c_Nitpick_Onumber__of__frac(_812644, _812640) = c_Nitpick_Onumber__of__frac(_812642, _812638)), _812644 = _812642, _812640 = _812638], (40246 ^ _777864) ^ [_1542093, _1542095, _1542097] : [hBOOL(hAPP(_1542093, _1542095)), -(hAPP(c_Set_OCollect(_1542097), hAPP(hAPP(c_COMBS(_1542097, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542097), c_fconj), hAPP(c_fequal, _1542095))), _1542093)) = hAPP(hAPP(c_Set_Oinsert(_1542097), _1542095), c_Orderings_Obot__class_Obot(tc_fun(_1542097, tc_HOL_Obool))))], (48183 ^ _777864) ^ [_1742805, _1742807, _1742809] : [-(hBOOL(hAPP(c_List_Odistinct(_1742805), hAPP(hAPP(c_List_Oappend(_1742805), _1742807), _1742809)))), hBOOL(hAPP(c_List_Odistinct(_1742805), _1742807)), hBOOL(hAPP(c_List_Odistinct(_1742805), _1742809)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1742805, tc_HOL_Obool)), hAPP(c_List_Oset(_1742805), _1742807)), hAPP(c_List_Oset(_1742805), _1742809)) = c_Orderings_Obot__class_Obot(tc_fun(_1742805, tc_HOL_Obool))], (40210 ^ _777864) ^ [_1541152, _1541154, _1541156] : [-(hAPP(hAPP(c_Set_Oinsert(_1541152), _1541154), _1541156) = hAPP(c_Set_OCollect(_1541152), hAPP(hAPP(c_COMBS(_1541152, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541152), c_fdisj), hAPP(hAPP(c_COMBC(_1541152, _1541152, tc_HOL_Obool), c_fequal), _1541154))), hAPP(hAPP(c_COMBC(_1541152, tc_fun(_1541152, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541152)), _1541156))))], (548 ^ _777864) ^ [_786350, _786352, _786354, _786356] : [-(c_Wellfounded_OwfP(_786354, _786350)), c_Wellfounded_OwfP(_786356, _786352), _786356 = _786354, _786352 = _786350], (31939 ^ _777864) ^ [_1361668, _1361670, _1361672] : [class_Orderings_Olinorder(_1361668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361668), _1361670)), -(_1361670 = c_Orderings_Obot__class_Obot(tc_fun(_1361668, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1361668, c_Orderings_Oord__class_Omin(_1361668), hAPP(hAPP(c_Set_Oinsert(_1361668), _1361672), _1361670)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1361668), _1361672), c_Big__Operators_Olattice_OInf__fin(_1361668, c_Orderings_Oord__class_Omin(_1361668), _1361670)))], (20038 ^ _777864) ^ [_1123292, _1123294, _1123296] : [class_Fields_Olinordered__field(_1123292), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123292), c_Groups_Ozero__class_Ozero(_1123292)), _1123294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123292), _1123296), c_Groups_Ozero__class_Ozero(_1123292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123292), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123292), _1123294), _1123296)), c_Groups_Ozero__class_Ozero(_1123292))))], (1682 ^ _777864) ^ [_801657, _801659] : [-(class_Rings_Omult__zero(_801657)), _801659 = _801657, class_Rings_Omult__zero(_801659)], (35886 ^ _777864) ^ [_1445401, _1445403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1445401), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445403), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445403), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1445401))))), -(_1445401 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1445403), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445403), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1445401))))], (21358 ^ _777864) ^ [_1146471, _1146473, _1146475, _1146477] : [class_Fields_Olinordered__field__inverse__zero(_1146471), class_Int_Onumber(_1146471), 21365 ^ _777864 : [(21366 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146473), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146471), _1146475), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)))), 21369 ^ _777864 : [(21376 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), c_Groups_Ozero__class_Ozero(_1146471)), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)))), 21379 ^ _777864 : [(21386 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)), c_Groups_Ozero__class_Ozero(_1146471)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146473), c_Groups_Ozero__class_Ozero(_1146471))))], (21380 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)), c_Groups_Ozero__class_Ozero(_1146471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146471), _1146473), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)))))]]], (21370 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), c_Groups_Ozero__class_Ozero(_1146471)), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146471), _1146473), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))), _1146475)))]]], (21392 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146473), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146471), _1146475), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))))), 21395 ^ _777864 : [(21398 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146471), _1146473), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))), _1146475))], (21396 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), c_Groups_Ozero__class_Ozero(_1146471)), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))))]], 21399 ^ _777864 : [(21402 ^ _777864) ^ [] : [21403 ^ _777864 : [(21406 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146471), _1146473), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477))))], (21404 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)), c_Groups_Ozero__class_Ozero(_1146471))))]], 21407 ^ _777864 : [(21410 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), _1146473), c_Groups_Ozero__class_Ozero(_1146471)))], (21408 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)), c_Groups_Ozero__class_Ozero(_1146471)))]]], (21400 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146471), c_Groups_Ozero__class_Ozero(_1146471)), hAPP(c_Int_Onumber__class_Onumber__of(_1146471), _1146477)))]]]]], (36052 ^ _777864) ^ [_1449039, _1449041, _1449043, _1449045, _1449047, _1449049] : [-(hBOOL(hAPP(hAPP(c_member(_1449039), _1449041), _1449043))), -(hAPP(c_Set_Oimage(_1449039, _1449045, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1449039, _1449045), _1449047), _1449041), _1449049)), _1449043) = hAPP(c_Set_Oimage(_1449039, _1449045, _1449047), _1449043))], (38222 ^ _777864) ^ [_1495106, _1495108, _1495110] : [class_Orderings_Otop(_1495106), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1495108, _1495106)), _1495110) = c_Orderings_Otop__class_Otop(_1495106))], (28737 ^ _777864) ^ [_1296634, _1296636, _1296638, _1296640] : [-(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), _1296634), _1296636)), 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), _1296638), _1296640)), 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), _1296634), _1296638)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1296636), _1296640))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (8806 ^ _777864) ^ [_924335, _924337, _924339] : [class_Rings_Osemiring__1(_924335), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _924337), _924339)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924335), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924335), _924337)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_924335), _924339)))], (24403 ^ _777864) ^ [_1205321, _1205323, _1205325, _1205327, _1205329, _1205331] : [-(c_Nitpick_Opair__box_OPairBox(_1205321, _1205323, _1205325, _1205327) = c_Nitpick_Opair__box_OPairBox(_1205321, _1205323, _1205329, _1205331)), _1205325 = _1205329, _1205327 = _1205331], (47642 ^ _777864) ^ [_1730350, _1730352, _1730354, _1730356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730350), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730352)), _1730354))), -(hBOOL(hAPP(hAPP(c_member(_1730352), _1730356), hAPP(c_List_Oset(_1730352), hAPP(hAPP(c_List_Olist__update(_1730352, _1730354), _1730350), _1730356)))))], (42629 ^ _777864) ^ [_1606749, _1606751, _1606753, _1606755, _1606757] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1606749, _1606751, _1606753), _1606755), _1606757) = c_HOL_OThe(_1606751, c_Finite__Set_Ofold__graph(_1606749, _1606751, _1606753, _1606755, _1606757)))], (28765 ^ _777864) ^ [_1297628, _1297630] : [c_Relation_Oirrefl(_1297628, _1297630), 28768 ^ _777864 : [(28769 ^ _777864) ^ [_1297710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1297628, _1297628)), hAPP(hAPP(c_Product__Type_OPair(_1297628, _1297628), _1297710), _1297710)), _1297630))]]], (15084 ^ _777864) ^ [_1033680, _1033682, _1033684] : [class_Groups_Oab__group__add(_1033680), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1033680), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033680), _1033682), _1033684)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1033680), _1033684), _1033682))], (28782 ^ _777864) ^ [_1297872, _1297874, _1297876, _1297878] : [-(hAPP(c_Relation_OField(_1297872), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1297872, _1297872)), hAPP(hAPP(c_Product__Type_OPair(_1297872, _1297872), _1297874), _1297876)), _1297878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297872, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1297872), _1297874), hAPP(hAPP(c_Set_Oinsert(_1297872), _1297876), c_Orderings_Obot__class_Obot(tc_fun(_1297872, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1297872), _1297878)))], (24581 ^ _777864) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42330 ^ _777864) ^ [_1600025, _1600027, _1600029] : [-(c_Hilbert__Choice_OEps(tc_prod(_1600025, _1600027), _1600029) = c_Hilbert__Choice_OEps(tc_prod(_1600025, _1600027), hAPP(c_Product__Type_Oprod_Oprod__case(_1600025, _1600027, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1600027, tc_prod(_1600025, _1600027)), tc_fun(_1600027, tc_HOL_Obool), _1600025), hAPP(c_COMBB(tc_prod(_1600025, _1600027), tc_HOL_Obool, _1600027), _1600029)), c_Product__Type_OPair(_1600025, _1600027)))))], (49219 ^ _777864) ^ [_1768288, _1768290, _1768292] : [-(_1768288 = c_List_Olist_ONil(_1768290)), -(c_List_Olast(_1768290, hAPP(hAPP(c_List_Olist_OCons(_1768290), _1768292), _1768288)) = c_List_Olast(_1768290, _1768288))], (19332 ^ _777864) ^ [_1110234, _1110236] : [class_Rings_Olinordered__idom(_1110234), -(hAPP(c_Groups_Oabs__class_Oabs(_1110234), hAPP(hAPP(c_Power_Opower__class_Opower(_1110234), _1110236), 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(_1110234), _1110236), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (2270 ^ _777864) ^ [_811319, _811321, _811323, _811325] : [-(c_Divides_Odivmod__int(_811325, _811321) = c_Divides_Odivmod__int(_811323, _811319)), _811325 = _811323, _811321 = _811319], (6769 ^ _777864) ^ [_889330, _889332] : [6770 ^ _777864 : [(6773 ^ _777864) ^ [] : [_889330 = _889332], (6771 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889330), _889332))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _889330), hAPP(c_Nat_OSuc, _889332))))], (51479 ^ _777864) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (50779 ^ _777864) ^ [_1802361, _1802363, _1802365, _1802367] : [-(hBOOL(hAPP(_1802361, _1802363))), -(c_List_OtakeWhile(_1802365, _1802361, hAPP(hAPP(c_List_Olist_OCons(_1802365), _1802363), _1802367)) = c_List_Olist_ONil(_1802365))], (27269 ^ _777864) ^ [_1262408, _1262410, _1262412, _1262414, _1262416, _1262418, _1262420] : [hBOOL(hAPP(hAPP(c_member(_1262408), _1262410), _1262412)), c_Nitpick_Ofold__graph_H(_1262408, _1262414, _1262416, _1262418, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262408, tc_HOL_Obool)), _1262412), hAPP(hAPP(c_Set_Oinsert(_1262408), _1262410), c_Orderings_Obot__class_Obot(tc_fun(_1262408, tc_HOL_Obool)))), _1262420), -(c_Nitpick_Ofold__graph_H(_1262408, _1262414, _1262416, _1262418, _1262412, hAPP(hAPP(_1262416, _1262410), _1262420)))], (36792 ^ _777864) ^ [_1464914, _1464916, _1464918, _1464920, _1464922] : [class_Groups_Ocomm__monoid__add(_1464914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464916), _1464918)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464916), _1464920)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464914), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464916, _1464914), _1464922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464916, tc_HOL_Obool)), _1464918), _1464920))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464916, _1464914), _1464922), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464916, tc_HOL_Obool)), _1464918), _1464920))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464914), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464916, _1464914), _1464922), _1464918)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464916, _1464914), _1464922), _1464920)))], (23127 ^ _777864) ^ [_1179432, _1179434] : [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(_1179434))), 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)), _1179432))))), -(hAPP(c_Nat_OSuc, _1179432) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179434))], (33521 ^ _777864) ^ [_1394561, _1394563, _1394565, _1394567, _1394569] : [33523 ^ _777864 : [(33529 ^ _777864) ^ [] : [hBOOL(hAPP(_1394569, 33525 ^ [_1394561, _1394563, _1394565, _1394567, _1394569]))], (33527 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394561), 33525 ^ [_1394561, _1394563, _1394565, _1394567, _1394569]), hAPP(_1394567, 33522 ^ [_1394561, _1394563, _1394565, _1394567, _1394569]))))], (33524 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394563), 33522 ^ [_1394561, _1394563, _1394565, _1394567, _1394569]), _1394565)))]], 33530 ^ _777864 : [(33531 ^ _777864) ^ [_1394871] : [hBOOL(hAPP(hAPP(c_member(_1394561), _1394871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394563, tc_fun(_1394561, tc_HOL_Obool)), _1394565), _1394567))), -(hBOOL(hAPP(_1394569, _1394871)))]]], (41740 ^ _777864) ^ [_1586644, _1586646, _1586648, _1586650, _1586652, _1586654, _1586656] : [-(hAPP(c_Product__Type_Oapsnd(_1586644, _1586646, _1586648, _1586650), hAPP(c_Product__Type_Oapsnd(_1586652, _1586644, _1586648, _1586654), _1586656)) = hAPP(c_Product__Type_Oapsnd(_1586652, _1586646, _1586648, hAPP(c_Fun_Ocomp(_1586644, _1586646, _1586652, _1586650), _1586654)), _1586656))], (28440 ^ _777864) ^ [_1289067, _1289069, _1289071, _1289073, _1289075, _1289077] : [28441 ^ _777864 : [(28444 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1289073, _1289069), _1289071))], (28442 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1289067, _1289069), _1289071))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289075, tc_fun(_1289077, tc_HOL_Obool))), _1289073), _1289067), _1289069), _1289071)))], (3396 ^ _777864) ^ [_829368, _829370, _829372, _829374] : [-(c_Predicate_OPowp(_829374, _829370) = c_Predicate_OPowp(_829372, _829368)), _829374 = _829372, _829370 = _829368], (26115 ^ _777864) ^ [_1236691, _1236693, _1236695, _1236697, _1236699] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1236691, _1236693, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1236691)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1236691), hAPP(hAPP(c_COMBC(_1236691, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1236691), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1236691), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1236695))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1236697))), c_Com_Ocom_OWhile(_1236697, _1236699)), _1236695)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1236691), tc_HOL_Obool)))))], (19066 ^ _777864) ^ [_1105616, _1105618] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1105616)), c_Int_OBit0(_1105618)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105616), _1105618)))], (28332 ^ _777864) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (26157 ^ _777864) ^ [_1237791, _1237793, _1237795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1237791), tc_HOL_Obool)), _1237793), _1237795)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1237791, _1237795, _1237793))], (40693 ^ _777864) ^ [_1559470, _1559472, _1559474, _1559476] : [-(c_Product__Type_Oapfst(_1559470, _1559472, _1559474, _1559476) = c_Product__Type_Omap__pair(_1559470, _1559472, _1559474, _1559474, _1559476, c_Fun_Oid(_1559474)))], (7427 ^ _777864) ^ [_900366, _900368, _900370, _900372] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_900366, _900368)), _900370), _900372)), 7431 ^ _777864 : [(7434 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_900368), 7430 ^ [_900366, 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tc_fun(tc_fun(tc_prod(tc_List_Olist(_1697139), tc_List_Olist(_1697139)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1697139)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1697139), tc_List_Olist(_1697139)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1697139), tc_List_Olist(_1697139)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1697139)), c_member(tc_prod(tc_List_Olist(_1697139), tc_List_Olist(_1697139))))), c_Product__Type_OPair(tc_List_Olist(_1697139), tc_List_Olist(_1697139))))), c_List_Olex(_1697139, _1697141)))))))], (51165 ^ _777864) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (7500 ^ _777864) ^ [_901942, _901944, _901946, _901948, _901950] : [c_Com_Ocom_OSemi(_901942, _901944) = c_Com_Ocom_OLocal(_901946, _901948, _901950)], (9188 ^ _777864) ^ [_930902, _930904] : [class_Groups_Olinordered__ab__group__add(_930902), 9191 ^ _777864 : [(9198 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930902), c_Groups_Ozero__class_Ozero(_930902)), _930904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930902), hAPP(c_Groups_Ouminus__class_Ouminus(_930902), _930904)), _930904)))], (9192 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930902), hAPP(c_Groups_Ouminus__class_Ouminus(_930902), _930904)), _930904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930902), c_Groups_Ozero__class_Ozero(_930902)), _930904)))]]], (48290 ^ _777864) ^ [_1745701, _1745703, _1745705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1745701, _1745701), tc_HOL_Obool)), _1745703), _1745705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1745701), tc_List_Olist(_1745701)), tc_HOL_Obool)), c_List_Olistrel1(_1745701, _1745703)), c_List_Olistrel1(_1745701, _1745705))))], (4984 ^ _777864) ^ [_854098, _854100] : [_854100 = _854098, -(c_Groups_Ozero__class_Ozero(_854100) = c_Groups_Ozero__class_Ozero(_854098))], (49584 ^ _777864) ^ [_1775648, _1775650, _1775652] : [-(hAPP(c_List_Oset(_1775648), hAPP(c_List_Ofilter(_1775648, _1775650), _1775652)) = hAPP(c_Set_OCollect(_1775648), hAPP(hAPP(c_COMBS(_1775648, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775648), c_fconj), hAPP(hAPP(c_COMBC(_1775648, tc_fun(_1775648, tc_HOL_Obool), tc_HOL_Obool), c_member(_1775648)), hAPP(c_List_Oset(_1775648), _1775652)))), _1775650)))], (40945 ^ _777864) ^ [_1566986, _1566988, _1566990, _1566992, _1566994, _1566996, _1566998] : [c_Predicate_Opred__comp(_1566986, _1566988, _1566990, _1566992, _1566994, _1566996, _1566998), 40949 ^ _777864 : [(40952 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1566994, 40948 ^ [_1566986, _1566988, _1566990, _1566992, _1566994, _1566996, _1566998]), _1566998)))], (40950 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1566992, _1566996), 40948 ^ [_1566986, _1566988, _1566990, _1566992, _1566994, _1566996, _1566998])))]]], (15624 ^ _777864) ^ [_1044094, _1044096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1044094), _1044096)), -(c_Nat__Transfer_Otsub(_1044096, _1044094) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044096), _1044094))], (19284 ^ _777864) ^ [] : [-(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))))], (50130 ^ _777864) ^ [_1786711, _1786713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1786711), _1786713)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1786711, _1786713)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1786713), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17982 ^ _777864) ^ [_1087702, _1087704] : [class_Rings_Osemiring__1(_1087702), 17985 ^ _777864 : [(17992 ^ _777864) ^ [] : [_1087704 = c_Groups_Ozero__class_Ozero(_1087702), -(c_Int_Oiszero(_1087702, _1087704))], (17986 ^ _777864) ^ [] : [c_Int_Oiszero(_1087702, _1087704), -(_1087704 = c_Groups_Ozero__class_Ozero(_1087702))]]], (40088 ^ _777864) ^ [_1538395, _1538397] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1538395)), 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)), _1538395))), 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, _1538397))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31439 ^ _777864) ^ [_1352251, _1352253, _1352255] : [class_Orderings_Olinorder(_1352251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352251), _1352253)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352251), _1352255)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352251, tc_HOL_Obool)), _1352253), _1352255) = c_Orderings_Obot__class_Obot(tc_fun(_1352251, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352251), c_Big__Operators_Olinorder__class_OMax(_1352251, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352251, tc_HOL_Obool)), _1352253), _1352255))), c_Big__Operators_Olinorder__class_OMax(_1352251, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352251, tc_HOL_Obool)), _1352253), _1352255))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352251), c_Big__Operators_Olinorder__class_OMax(_1352251, _1352253)), c_Big__Operators_Olinorder__class_OMax(_1352251, _1352255)))], (48808 ^ _777864) ^ [_1758902, _1758904] : [hBOOL(hAPP(c_List_Odistinct(_1758902), _1758904)), -(hBOOL(hAPP(c_List_Odistinct(_1758902), hAPP(c_List_Otl(_1758902), _1758904))))], (2908 ^ _777864) ^ [_821584, _821586, _821588, _821590, _821592, _821594, _821596, _821598] : [-(c_New__DSequence_Opos__bind(_821598, _821594, _821590, _821586) = c_New__DSequence_Opos__bind(_821596, _821592, _821588, _821584)), _821598 = _821596, _821594 = _821592, _821590 = _821588, _821586 = _821584], (51359 ^ _777864) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (29898 ^ _777864) ^ [_1320805, _1320807, _1320809, _1320811] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320805, tc_HOL_Obool)), _1320807), _1320809)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320805, tc_HOL_Obool)), _1320809), _1320811))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320805, tc_HOL_Obool)), _1320811), _1320807)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320805, tc_HOL_Obool)), _1320807), _1320809)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320805, tc_HOL_Obool)), _1320809), _1320811))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320805, tc_HOL_Obool)), _1320811), _1320807)))], (37288 ^ _777864) ^ [_1476493, _1476495, _1476497] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476493, tc_Nat_Onat), _1476495), _1476497) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476493, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1476493), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1476495)), _1476497)))], (43993 ^ _777864) ^ [_1639565, _1639567, _1639569, _1639571, _1639573] : [-(_1639565 = c_Orderings_Obot__class_Obot(tc_fun(_1639567, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639569, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639567, tc_fun(_1639569, tc_HOL_Obool)), _1639565), _1639571)), _1639573) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639567, tc_fun(_1639569, tc_HOL_Obool)), _1639565), hAPP(hAPP(c_COMBC(_1639567, tc_fun(_1639569, tc_HOL_Obool), tc_fun(_1639569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639569, tc_HOL_Obool), tc_fun(tc_fun(_1639569, tc_HOL_Obool), tc_fun(_1639569, tc_HOL_Obool)), _1639567), c_Groups_Ominus__class_Ominus(tc_fun(_1639569, tc_HOL_Obool))), _1639571)), _1639573)))], (33156 ^ _777864) ^ [_1386434, _1386436, _1386438, _1386440, _1386442] : [class_Groups_Ocomm__monoid__mult(_1386434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386436), _1386438)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386436), _1386440)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386436, tc_HOL_Obool)), _1386438), _1386440) = c_Orderings_Obot__class_Obot(tc_fun(_1386436, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386436, _1386434), _1386442), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386436, tc_HOL_Obool)), _1386438), _1386440)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386434), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386436, _1386434), _1386442), _1386438)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1386436, _1386434), _1386442), _1386440)))], (22424 ^ _777864) ^ [_1165459] : [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), _1165459))), -(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), _1165459)) = 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), _1165459))))], (45559 ^ _777864) ^ [_1677707, _1677709] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1677707, _1677709) = c_Smallcheck_Ofull__small_H(_1677707, hAPP(c_Code__Numeral_Oint__of, _1677709), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1677709))))], (44303 ^ _777864) ^ [_1647897, _1647899, _1647901] : [44306 ^ _777864 : [(44312 ^ _777864) ^ [] : [44305 ^ [_1647897, _1647899, _1647901] = 44308 ^ [_1647897, _1647899, _1647901]], (44310 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647897, _1647899)), hAPP(hAPP(c_Product__Type_OPair(_1647897, _1647899), 44304 ^ [_1647897, _1647899, _1647901]), 44308 ^ [_1647897, _1647899, _1647901])), _1647901)))], (44307 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647897, _1647899)), hAPP(hAPP(c_Product__Type_OPair(_1647897, _1647899), 44304 ^ [_1647897, _1647899, _1647901]), 44305 ^ [_1647897, _1647899, _1647901])), _1647901)))]], -(c_Relation_Osingle__valued(_1647897, _1647899, _1647901))], (34763 ^ _777864) ^ [_1423267, _1423269, _1423271, _1423273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1423267), hAPP(c_Set_Oimage(_1423269, _1423267, _1423271), _1423273))), hAPP(c_Finite__Set_Ocard(_1423269), _1423273))), c_Fun_Oinj__on(_1423269, _1423267, _1423271, _1423273)], (47824 ^ _777864) ^ [_1734603, _1734605, _1734607, _1734609, _1734611, _1734613, _1734615] : [-(hBOOL(hAPP(hAPP(c_member(_1734603), _1734605), hAPP(c_List_Oset(_1734603), _1734607)))), -(c_Map_Omap__upds(_1734603, _1734609, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1734603, tc_Option_Ooption(_1734609)), _1734611), _1734605), hAPP(c_Option_Ooption_OSome(_1734609), _1734613)), _1734607, _1734615) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1734603, tc_Option_Ooption(_1734609)), c_Map_Omap__upds(_1734603, _1734609, _1734611, _1734607, _1734615)), _1734605), hAPP(c_Option_Ooption_OSome(_1734609), _1734613)))], (46579 ^ _777864) ^ [_1704356, _1704358, _1704360] : [hAPP(hAPP(c_List_Olist_OCons(_1704356), _1704358), _1704360) = _1704360], (44901 ^ _777864) ^ [_1662118] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1662118, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1662118, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1662118, tc_HOL_Obool)))], (7104 ^ _777864) ^ [_894598, _894600, _894602, _894604, _894606, _894608] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_894598, _894600, _894602), _894604, _894606, _894608), 7109 ^ _777864 : [(7112 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_894600, _894604, _894606, _894608))], (7110 ^ _777864) ^ [] : [-(hBOOL(hAPP(_894598, _894604)))]], 7113 ^ _777864 : [(7116 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_894602, _894604, _894606, _894608))], (7114 ^ _777864) ^ [] : [hBOOL(hAPP(_894598, _894604))]]], (20024 ^ _777864) ^ [_1123037, _1123039, _1123041] : [class_Fields_Olinordered__field(_1123037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123037), _1123039), c_Groups_Ozero__class_Ozero(_1123037))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123037), c_Groups_Ozero__class_Ozero(_1123037)), _1123041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123037), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123037), _1123039), _1123041)), c_Groups_Ozero__class_Ozero(_1123037))))], (30180 ^ _777864) ^ [_1327223, _1327225, _1327227, _1327229] : [-(hBOOL(hAPP(hAPP(c_member(_1327223), _1327225), _1327227))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327223, tc_HOL_Obool)), _1327227), hAPP(hAPP(c_Set_Oinsert(_1327223), _1327225), _1327229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327223, tc_HOL_Obool)), _1327227), _1327229))], (34901 ^ _777864) ^ [_1425916, _1425918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425916), _1425918)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1425918, _1425916) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (12826 ^ _777864) ^ [_993183, _993185, _993187, _993189, _993191, _993193] : [class_Rings_Olinordered__semiring__1(_993183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993183), _993185), _993187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993183), _993189), _993187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993183), c_Groups_Ozero__class_Ozero(_993183)), _993191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993183), c_Groups_Ozero__class_Ozero(_993183)), _993193)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993183), _993191), _993193) = c_Groups_Oone__class_Oone(_993183), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993183), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_993183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993183), _993191), _993185)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_993183), _993193), _993189))), _993187)))], (26205 ^ _777864) ^ [_1238676, _1238678, _1238680] : [-(hAPP(hAPP(c_Set_Oinsert(_1238676), _1238678), hAPP(hAPP(c_Set_Oinsert(_1238676), _1238678), _1238680)) = hAPP(hAPP(c_Set_Oinsert(_1238676), _1238678), _1238680))], (6358 ^ _777864) ^ [_882749, _882751, _882753, _882755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882749), _882751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _882753), _882755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882749), _882753)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _882751), _882755))))], (51483 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (50506 ^ _777864) ^ [_1795199, _1795201] : [class_Groups_Ocomm__monoid__add(_1795199), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1795199), hAPP(c_List_Orev(_1795199), _1795201)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1795199), _1795201))], (6258 ^ _777864) ^ [_880949, _880951, _880953, _880955, _880957] : [class_Groups_Oordered__cancel__ab__semigroup__add(_880949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880949), _880951), _880953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880949), _880955), _880957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880949), _880951), _880955)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880949), _880953), _880957))))], (46849 ^ _777864) ^ [_1711720, _1711722] : [class_Groups_Ocomm__monoid__add(_1711720), hBOOL(hAPP(c_List_Odistinct(_1711720), _1711722)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711720), _1711722) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1711720, _1711720), c_COMBI(_1711720)), hAPP(c_List_Oset(_1711720), _1711722)))], (15378 ^ _777864) ^ [_1039405, _1039407] : [class_Groups_Ogroup__add(_1039405), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1039405), c_Groups_Ozero__class_Ozero(_1039405)), _1039407) = hAPP(c_Groups_Ouminus__class_Ouminus(_1039405), _1039407))], (5244 ^ _777864) ^ [_858138, _858140] : [_858140 = _858138, -(c_List_Oembed__list(_858140) = c_List_Oembed__list(_858138))], (15108 ^ _777864) ^ [_1034212, _1034214, _1034216, _1034218, _1034220, _1034222] : [class_Divides_Oring__div(_1034212), c_Divides_Odiv__class_Omod(_1034212, _1034214, _1034216) = c_Divides_Odiv__class_Omod(_1034212, _1034218, _1034216), c_Divides_Odiv__class_Omod(_1034212, _1034220, _1034216) = c_Divides_Odiv__class_Omod(_1034212, _1034222, _1034216), -(c_Divides_Odiv__class_Omod(_1034212, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034212), _1034214), _1034220), _1034216) = c_Divides_Odiv__class_Omod(_1034212, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1034212), _1034218), _1034222), _1034216))], (17626 ^ _777864) ^ [_1081849, _1081851] : [class_Int_Onumber__ring(_1081849), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081849), hAPP(c_Int_Onumber__class_Onumber__of(_1081849), c_Int_OMin)), _1081851) = hAPP(c_Groups_Ouminus__class_Ouminus(_1081849), _1081851))], (33733 ^ _777864) ^ [_1400255, _1400257, _1400259, _1400261, _1400263, _1400265, _1400267] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400255, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400257, tc_fun(_1400255, tc_HOL_Obool)), _1400259), _1400261)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400263, tc_fun(_1400255, tc_HOL_Obool)), _1400265), _1400267)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400257, tc_fun(_1400255, tc_HOL_Obool)), _1400259), hAPP(hAPP(c_COMBB(tc_fun(_1400263, tc_fun(_1400255, tc_HOL_Obool)), tc_fun(_1400255, tc_HOL_Obool), _1400257), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400263, tc_fun(_1400255, tc_HOL_Obool)), _1400265)), hAPP(hAPP(c_COMBC(_1400257, tc_fun(_1400263, tc_fun(_1400255, tc_HOL_Obool)), tc_fun(_1400263, tc_fun(_1400255, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1400255, tc_HOL_Obool), tc_fun(_1400255, tc_HOL_Obool)), tc_fun(tc_fun(_1400263, tc_fun(_1400255, tc_HOL_Obool)), tc_fun(_1400263, tc_fun(_1400255, tc_HOL_Obool))), _1400257), c_COMBB(tc_fun(_1400255, tc_HOL_Obool), tc_fun(_1400255, tc_HOL_Obool), _1400263)), hAPP(hAPP(c_COMBB(tc_fun(_1400255, tc_HOL_Obool), tc_fun(tc_fun(_1400255, tc_HOL_Obool), tc_fun(_1400255, tc_HOL_Obool)), _1400257), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400255, tc_HOL_Obool))), _1400261))), _1400267))))], (47310 ^ _777864) ^ [_1723539, _1723541, _1723543, _1723545] : [hBOOL(hAPP(hAPP(c_member(_1723539), _1723541), hAPP(c_List_Oset(_1723539), hAPP(hAPP(c_List_Otake(_1723539), _1723543), _1723545)))), -(hBOOL(hAPP(hAPP(c_member(_1723539), _1723541), hAPP(c_List_Oset(_1723539), _1723545))))], (48818 ^ _777864) ^ [_1759119, _1759121, _1759123, _1759125] : [-(hAPP(hAPP(c_List_Omap(_1759119, _1759121), _1759123), hAPP(c_List_Otl(_1759119), _1759125)) = hAPP(c_List_Otl(_1759121), hAPP(hAPP(c_List_Omap(_1759119, _1759121), _1759123), _1759125)))], (45840 ^ _777864) ^ [_1684430, _1684432, _1684434, _1684436] : [_1684436 = c_Option_Ooption_ONone(_1684430), -(hAPP(hAPP(c_Option_Omap(_1684430, _1684432), _1684434), _1684436) = c_Option_Ooption_ONone(_1684432))], (19768 ^ _777864) ^ [_1118327, _1118329] : [class_Rings_Odivision__ring__inverse__zero(_1118327), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1118327), _1118329), c_Groups_Ozero__class_Ozero(_1118327)) = c_Groups_Ozero__class_Ozero(_1118327))], (27540 ^ _777864) ^ [_1268302, _1268304] : [class_Int_Onumber__ring(_1268302), -(hBOOL(hAPP(hAPP(c_member(_1268302), hAPP(c_Int_Onumber__class_Onumber__of(_1268302), _1268304)), c_Int_Oring__1__class_OInts(_1268302))))], (19760 ^ _777864) ^ [] : [-(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))], (49420 ^ _777864) ^ [_1772155, _1772157, _1772159, _1772161] : [49421 ^ _777864 : [(49424 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1772155), _1772157), hAPP(c_List_Oset(_1772155), c_List_Obutlast(_1772155, _1772161))))], (49422 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1772155), _1772157), hAPP(c_List_Oset(_1772155), c_List_Obutlast(_1772155, _1772159))))]], -(hBOOL(hAPP(hAPP(c_member(_1772155), _1772157), hAPP(c_List_Oset(_1772155), c_List_Obutlast(_1772155, hAPP(hAPP(c_List_Oappend(_1772155), _1772159), _1772161))))))], (32626 ^ _777864) ^ [_1375402, _1375404, _1375406] : [-(hAPP(c_Finite__Set_Ocard(_1375402), _1375404) = hAPP(c_Nat_OSuc, _1375406)), 32627 ^ _777864 : [(32628 ^ _777864) ^ [_1375502, _1375504] : [_1375404 = hAPP(hAPP(c_Set_Oinsert(_1375402), _1375504), _1375502), -(hBOOL(hAPP(hAPP(c_member(_1375402), _1375504), _1375502))), hAPP(c_Finite__Set_Ocard(_1375402), _1375502) = _1375406, 32639 ^ _777864 : [(32642 ^ _777864) ^ [] : [_1375502 = c_Orderings_Obot__class_Obot(tc_fun(_1375402, tc_HOL_Obool))], (32640 ^ _777864) ^ [] : [-(_1375406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (45469 ^ _777864) ^ [_1675572, _1675574, _1675576, _1675578, _1675580] : [hAPP(c_Map_Omap__add(_1675572, _1675574, _1675576, _1675578), _1675580) = c_Option_Ooption_ONone(_1675574), 45472 ^ _777864 : [(45475 ^ _777864) ^ [] : [-(hAPP(_1675576, _1675580) = c_Option_Ooption_ONone(_1675574))], (45473 ^ _777864) ^ [] : [-(hAPP(_1675578, _1675580) = c_Option_Ooption_ONone(_1675574))]]], (28166 ^ _777864) ^ [_1280105, _1280107, _1280109, _1280111] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280105, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280105, tc_HOL_Obool)), _1280107), _1280109)), _1280111) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280105, tc_HOL_Obool)), _1280107), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280105, tc_HOL_Obool)), _1280109), _1280111)))], (9640 ^ _777864) ^ [_938981] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _938981)), _938981) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19996 ^ _777864) ^ [_1122513, _1122515, _1122517, _1122519] : [class_Fields_Olinordered__field(_1122513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122513), _1122515), _1122517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122513), c_Groups_Ozero__class_Ozero(_1122513)), _1122519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122513), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122513), _1122515), _1122519)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122513), _1122517), _1122519))))], (23301 ^ _777864) ^ [_1183921, _1183923, _1183925] : [-(hAPP(c_Product__Type_Osnd(_1183921, _1183923), _1183925) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183921, _1183923, _1183923), hAPP(c_COMBK(tc_fun(_1183923, _1183923), _1183921), c_COMBI(_1183923))), _1183925))], (45507 ^ _777864) ^ [_1676198, _1676200, _1676202, _1676204, _1676206] : [hBOOL(hAPP(hAPP(c_member(_1676198), _1676200), c_Map_Odom(_1676198, _1676202, _1676204))), -(hAPP(c_Map_Omap__add(_1676198, _1676202, _1676206, _1676204), _1676200) = hAPP(_1676204, _1676200))], (51151 ^ _777864) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (15992 ^ _777864) ^ [_1051937, _1051939] : [_1051937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051937), _1051939) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33719 ^ _777864) ^ [_1399557, _1399559, _1399561, _1399563, _1399565] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399557, tc_fun(_1399559, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399557, tc_HOL_Obool)), _1399561), _1399563)), _1399565) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399559, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399557, tc_fun(_1399559, tc_HOL_Obool)), _1399561), _1399565)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399557, tc_fun(_1399559, tc_HOL_Obool)), _1399563), _1399565)))], (30246 ^ _777864) ^ [_1329014, _1329016, _1329018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329014, tc_HOL_Obool)), _1329016), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1329014, tc_HOL_Obool)), _1329018))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329014, tc_HOL_Obool)), _1329016), _1329018) = c_Orderings_Obot__class_Obot(tc_fun(_1329014, tc_HOL_Obool)))], (15782 ^ _777864) ^ [_1047625, _1047627, _1047629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047625), _1047627)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047629), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047627), _1047625))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047629), _1047625)), hAPP(c_Nat_OSuc, _1047627)))], (32977 ^ _777864) ^ [_1382474, _1382476, _1382478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382474), _1382476)), 32980 ^ _777864 : [(32981 ^ _777864) ^ [] : [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(_1382474, tc_Nat_Onat), _1382478), _1382476))), 32984 ^ _777864 : [(32985 ^ _777864) ^ [_1382642] : [hBOOL(hAPP(hAPP(c_member(_1382474), _1382642), _1382476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1382478, _1382642))))]]], (32991 ^ _777864) ^ [] : [32993 ^ _777864 : [(32996 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1382478, 32992 ^ [_1382474, _1382476, _1382478])))], (32994 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382474), 32992 ^ [_1382474, _1382476, _1382478]), _1382476)))]], -(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(_1382474, tc_Nat_Onat), _1382478), _1382476))))]]], (51375 ^ _777864) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (51315 ^ _777864) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (22693 ^ _777864) ^ [_1170485, _1170487, _1170489, _1170491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1170485, tc_HOL_Obool)), _1170487), _1170489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170485, tc_HOL_Obool)), _1170489), _1170491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1170485, tc_HOL_Obool)), _1170487), _1170491)))], (46450 ^ _777864) ^ [_1699438, _1699440, _1699442] : [hBOOL(hAPP(hAPP(c_member(_1699438), _1699440), hAPP(c_List_Oset(_1699438), _1699442))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699438)), c_List_Oremove1(_1699438, _1699440, _1699442)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699438)), _1699442)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (41776 ^ _777864) ^ [_1587608, _1587610, _1587612, _1587614, _1587616, _1587618, _1587620, _1587622, _1587624, _1587626] : [-(c_Product__Type_Omap__pair(_1587608, _1587610, _1587612, _1587614, hAPP(c_Fun_Ocomp(_1587616, _1587610, _1587608, _1587618), _1587620), hAPP(c_Fun_Ocomp(_1587622, _1587614, _1587612, _1587624), _1587626)) = hAPP(c_Fun_Ocomp(tc_prod(_1587616, _1587622), tc_prod(_1587610, _1587614), tc_prod(_1587608, _1587612), c_Product__Type_Omap__pair(_1587616, _1587610, _1587622, _1587614, _1587618, _1587624)), c_Product__Type_Omap__pair(_1587608, _1587616, _1587612, _1587622, _1587620, _1587626)))], (16550 ^ _777864) ^ [_1062199, _1062201, _1062203, _1062205] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062199), _1062201), _1062203)), hAPP(c_Int_Onumber__class_Onumber__of(_1062199), _1062205)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1062199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062199), _1062201), hAPP(c_Int_Onumber__class_Onumber__of(_1062199), _1062205))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062199), _1062203), hAPP(c_Int_Onumber__class_Onumber__of(_1062199), _1062205)))), class_Int_Onumber(_1062199), class_Rings_Oring(_1062199)], (18110 ^ _777864) ^ [_1089551] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089551), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089551)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1089551)))], (18034 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46861 ^ _777864) ^ [_1711981, _1711983, _1711985, _1711987] : [class_Groups_Ocomm__monoid__add(_1711981), hBOOL(hAPP(c_List_Odistinct(_1711983), _1711985)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711981), hAPP(hAPP(c_List_Omap(_1711983, _1711981), _1711987), _1711985)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1711983, _1711981), _1711987), hAPP(c_List_Oset(_1711983), _1711985)))], (47386 ^ _777864) ^ [_1725230, _1725232, _1725234] : [hAPP(hAPP(c_List_Otake(_1725230), _1725232), _1725234) = c_List_Olist_ONil(_1725230), -(_1725232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1725234 = c_List_Olist_ONil(_1725230))], (23169 ^ _777864) ^ [_1180312, _1180314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1180312)), hAPP(c_Nat_OSuc, _1180314))), -(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(_1180312))), 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)), _1180314)))))], (29026 ^ _777864) ^ [_1302633, _1302635, _1302637] : [29028 ^ _777864 : [(29031 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1302633), 29027 ^ [_1302633, _1302635, _1302637]), c_Wellfounded_Oacc(_1302633, _1302637)))], (29029 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302633, _1302633)), hAPP(hAPP(c_Product__Type_OPair(_1302633, _1302633), 29027 ^ [_1302633, _1302635, _1302637]), _1302635)), _1302637)))]], -(hBOOL(hAPP(hAPP(c_member(_1302633), _1302635), c_Wellfounded_Oacc(_1302633, _1302637))))], (38160 ^ _777864) ^ [_1493999, _1494001] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1493999, _1494001)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1493999, _1494001), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493999), c_Orderings_Otop__class_Otop(tc_fun(_1493999, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494001), c_Orderings_Otop__class_Otop(tc_fun(_1494001, tc_HOL_Obool))))], (17712 ^ _777864) ^ [_1083156] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1083156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1083156))], (16970 ^ _777864) ^ [_1070498, _1070500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1070498), _1070500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070498)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070500))))], (15272 ^ _777864) ^ [_1037227, _1037229, _1037231] : [-(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, _1037227, _1037229)), _1037231), _1037229) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1037227), _1037231), _1037229))], (34 ^ _777864) ^ [_778317, _778319, _778321, _778323] : [-(c_Int_Oiszero(_778321, _778317)), c_Int_Oiszero(_778323, _778319), _778323 = _778321, _778319 = _778317], (23887 ^ _777864) ^ [_1195357, _1195359, _1195361] : [class_Orderings_Olinorder(_1195357), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195357), _1195359), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195357), _1195359), _1195361)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195357), _1195359), _1195361))], (26609 ^ _777864) ^ [_1246960, _1246962, _1246964, _1246966, _1246968, _1246970] : [c_Hoare__Mirabelle_Ohoare__derivs(_1246960, _1246962, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246960)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246960), _1246964), _1246966), _1246968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246960), tc_HOL_Obool)))), 26616 ^ _777864 : [(26619 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1246964, 26614 ^ [_1246960, _1246962, _1246964, _1246966, _1246968, _1246970]), 26615 ^ [_1246960, _1246962, _1246964, _1246966, _1246968, _1246970]))], (26617 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1246970, 26614 ^ [_1246960, _1246962, _1246964, _1246966, _1246968, _1246970]), 26615 ^ [_1246960, _1246962, _1246964, _1246966, _1246968, _1246970])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1246960, _1246962, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246960)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246960), _1246970), _1246966), _1246968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246960), tc_HOL_Obool)))))], (48000 ^ _777864) ^ [_1739072, _1739074, _1739076, _1739078, _1739080] : [hAPP(hAPP(c_List_Oappend(_1739072), _1739074), _1739076) = hAPP(hAPP(c_List_Oappend(_1739072), _1739078), _1739080), 48006 ^ _777864 : [(48009 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1739072), 48003 ^ [_1739072, _1739074, _1739076, _1739078, _1739080]), _1739076) = _1739080)], (48007 ^ _777864) ^ [] : [-(_1739074 = hAPP(hAPP(c_List_Oappend(_1739072), _1739078), 48003 ^ [_1739072, _1739074, _1739076, _1739078, _1739080]))]], 48010 ^ _777864 : [(48013 ^ _777864) ^ [] : [-(_1739076 = hAPP(hAPP(c_List_Oappend(_1739072), 48003 ^ [_1739072, _1739074, _1739076, _1739078, _1739080]), _1739080))], (48011 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1739072), _1739074), 48003 ^ [_1739072, _1739074, _1739076, _1739078, _1739080]) = _1739078)]]], (12668 ^ _777864) ^ [_990652, _990654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _990654)), -(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), _990654), _990652))))], (25943 ^ _777864) ^ [_1233363, _1233365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1233363)), 25946 ^ _777864 : [(25953 ^ _777864) ^ [] : [_1233365 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233365), _1233363)), _1233363)))], (25947 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233365), _1233363)), _1233363)), -(_1233365 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (49148 ^ _777864) ^ [_1766688, _1766690, _1766692] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1766688)), _1766690), c_List_Olists(_1766688, c_Wellfounded_Oacc(_1766688, _1766692)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1766688)), _1766690), c_Wellfounded_Oacc(tc_List_Olist(_1766688), c_List_Olistrel1(_1766688, _1766692)))))], (33549 ^ _777864) ^ [_1395572, _1395574, _1395576, _1395578, _1395580, _1395582, _1395584, _1395586, _1395588, _1395590] : [c_Equiv__Relations_Ocongruent2(_1395572, _1395574, _1395576, _1395578, _1395580, _1395582), hBOOL(hAPP(hAPP(c_member(tc_prod(_1395572, _1395572)), hAPP(hAPP(c_Product__Type_OPair(_1395572, _1395572), _1395584), _1395586)), _1395578)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1395574, _1395574)), hAPP(hAPP(c_Product__Type_OPair(_1395574, _1395574), _1395588), _1395590)), _1395580)), -(hAPP(hAPP(_1395582, _1395584), _1395588) = hAPP(hAPP(_1395582, _1395586), _1395590))], (19534 ^ _777864) ^ [_1113732, _1113734, _1113736] : [class_Rings_Olinordered__idom(_1113732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113732), hAPP(hAPP(c_Power_Opower__class_Opower(_1113732), _1113734), 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(_1113732), _1113736), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1113732)))], (6512 ^ _777864) ^ [_885477, _885479] : [-(_885477 = _885479), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885477), _885479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885479), _885477)))], (31057 ^ _777864) ^ [_1345305, _1345307, _1345309] : [class_Lattices_Olattice(_1345305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345305), _1345307)), -(_1345309 = c_Orderings_Obot__class_Obot(tc_fun(_1345305, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345305, tc_HOL_Obool)), _1345309), _1345307)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1345305), c_Big__Operators_Olattice__class_OInf__fin(_1345305, _1345309)), c_Big__Operators_Olattice__class_OInf__fin(_1345305, _1345307)) = c_Big__Operators_Olattice__class_OInf__fin(_1345305, _1345307))], (24679 ^ _777864) ^ [_1210773, _1210775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1210773), _1210775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1210773)), hAPP(c_Code__Numeral_Onat__of, _1210775))))], (43931 ^ _777864) ^ [_1637576, _1637578, _1637580, _1637582, _1637584] : [-(hAPP(c_Relation_Oconverse(_1637576, _1637578), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637580, tc_fun(tc_prod(_1637576, _1637578), tc_HOL_Obool)), _1637582), _1637584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1637580, tc_fun(tc_prod(_1637578, _1637576), tc_HOL_Obool)), _1637582), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1637576, _1637578), tc_HOL_Obool), tc_fun(tc_prod(_1637578, _1637576), tc_HOL_Obool), _1637580), c_Relation_Oconverse(_1637576, _1637578)), _1637584)))], (47416 ^ _777864) ^ [_1725695, _1725697] : [_1725697 = c_List_Olist_ONil(_1725695), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725695)), _1725697) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5974 ^ _777864) ^ [_876022] : [hAPP(c_Nat_OSuc, _876022) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29840 ^ _777864) ^ [_1319613, _1319615] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319613, tc_HOL_Obool)), _1319615), c_Orderings_Obot__class_Obot(tc_fun(_1319613, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1319613, tc_HOL_Obool)))], (50344 ^ _777864) ^ [_1791420] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1791420)), c_List_Otranspose__rel(_1791420)), c_List_Olist_ONil(tc_List_Olist(_1791420)))), -(c_List_Otranspose(_1791420, c_List_Olist_ONil(tc_List_Olist(_1791420))) = c_List_Olist_ONil(tc_List_Olist(_1791420)))], (30212 ^ _777864) ^ [_1328114, _1328116, _1328118, _1328120] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328114, tc_HOL_Obool)), _1328116), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328114, tc_HOL_Obool)), _1328118), _1328120)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328114, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328114, tc_HOL_Obool)), _1328116), _1328118)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1328114, tc_HOL_Obool)), _1328116), _1328120)))], (40496 ^ _777864) ^ [_1551224, _1551226, _1551228] : [class_Lattices_Odistrib__lattice(_1551224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551224), _1551226)), -(_1551226 = c_Orderings_Obot__class_Obot(tc_fun(_1551224, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551224), _1551228)), -(_1551228 = c_Orderings_Obot__class_Obot(tc_fun(_1551224, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1551224), c_Big__Operators_Olattice__class_OInf__fin(_1551224, _1551226)), c_Big__Operators_Olattice__class_OInf__fin(_1551224, _1551228)) = c_Big__Operators_Olattice__class_OInf__fin(_1551224, hAPP(c_Set_OCollect(_1551224), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_HOL_Obool), tc_HOL_Obool, _1551224), c_HOL_OEx(_1551224)), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool)), tc_fun(_1551224, tc_HOL_Obool), _1551224), hAPP(c_COMBB(tc_fun(_1551224, tc_HOL_Obool), tc_HOL_Obool, _1551224), c_HOL_OEx(_1551224))), hAPP(hAPP(c_COMBC(_1551224, tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool)), tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_fun(tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool))), tc_fun(tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool)), tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool))), _1551224), c_COMBS(_1551224, tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_fun(_1551224, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1551224, tc_fun(tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool))), _1551224), hAPP(c_COMBB(tc_fun(_1551224, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool)), _1551224), c_COMBS(_1551224, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool)), tc_fun(_1551224, tc_fun(_1551224, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1551224), hAPP(c_COMBB(tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1551224), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551224), c_fconj))), hAPP(hAPP(c_COMBC(_1551224, tc_fun(_1551224, tc_fun(_1551224, _1551224)), tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1551224, _1551224), tc_fun(_1551224, tc_HOL_Obool)), tc_fun(tc_fun(_1551224, tc_fun(_1551224, _1551224)), tc_fun(_1551224, tc_fun(_1551224, tc_HOL_Obool))), _1551224), c_COMBB(tc_fun(_1551224, _1551224), tc_fun(_1551224, tc_HOL_Obool), _1551224)), hAPP(hAPP(c_COMBB(tc_fun(_1551224, tc_HOL_Obool), tc_fun(tc_fun(_1551224, _1551224), tc_fun(_1551224, tc_HOL_Obool)), _1551224), c_COMBB(_1551224, tc_HOL_Obool, _1551224)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1551224)))))), hAPP(hAPP(c_COMBC(_1551224, tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1551224, tc_HOL_Obool), tc_fun(_1551224, tc_HOL_Obool)), _1551224), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1551224)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551224), c_fconj), hAPP(hAPP(c_COMBC(_1551224, tc_fun(_1551224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551224)), _1551226)))), hAPP(hAPP(c_COMBC(_1551224, tc_fun(_1551224, tc_HOL_Obool), tc_HOL_Obool), c_member(_1551224)), _1551228))))))))], (33470 ^ _777864) ^ [_1393211, _1393213, _1393215, _1393217, _1393219, _1393221] : [hBOOL(hAPP(hAPP(c_member(_1393211), _1393213), _1393215)), hBOOL(hAPP(hAPP(c_member(_1393217), _1393219), hAPP(_1393221, _1393213))), -(hBOOL(hAPP(hAPP(c_member(_1393217), _1393219), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1393211, tc_fun(_1393217, tc_HOL_Obool)), _1393215), _1393221))))], (24661 ^ _777864) ^ [_1210437] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1210437)) = _1210437)], (40893 ^ _777864) ^ [_1566057, _1566059, _1566061, _1566063] : [c_Wellfounded_Owf(_1566057, _1566059), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566057, _1566057)), hAPP(hAPP(c_Product__Type_OPair(_1566057, _1566057), _1566061), _1566063)), _1566059)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566057, _1566057)), hAPP(hAPP(c_Product__Type_OPair(_1566057, _1566057), _1566063), _1566061)), _1566059))], (17814 ^ _777864) ^ [_1084936] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084936)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084936)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084936))], (25553 ^ _777864) ^ [_1225882, _1225884, _1225886, _1225888, _1225890] : [class_Divides_Osemiring__div(_1225882), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225882), _1225884), _1225886)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225882), _1225888), _1225890)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225882), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225882), _1225886), _1225884)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225882), _1225890), _1225888)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225882), _1225886), _1225890)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225882), _1225884), _1225888)))], (7090 ^ _777864) ^ [_894307, _894309] : [class_Rings_Ocomm__semiring__1(_894307), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894307), c_Groups_Ozero__class_Ozero(_894307)), _894309) = _894309)], (16152 ^ _777864) ^ [_1054828, _1054830, _1054832] : [class_Groups_Oordered__ab__group__add__abs(_1054828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054828), hAPP(c_Groups_Oabs__class_Oabs(_1054828), _1054830)), _1054832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054828), _1054830), _1054832)))], (5424 ^ _777864) ^ [_860816, _860818, _860820, _860822, _860824, _860826] : [-(c_COMBB(_860826, _860822, _860818) = c_COMBB(_860824, _860820, _860816)), _860826 = _860824, _860822 = _860820, _860818 = _860816], (13838 ^ _777864) ^ [_1011189, _1011191] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011189))), -(c_SMT_Oz3mod(_1011191, _1011189) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1011191, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1011189)))], (26313 ^ _777864) ^ [_1240844, _1240846, _1240848, _1240850, _1240852] : [c_Hoare__Mirabelle_Ohoare__derivs(_1240844, _1240846, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1240844)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1240844), _1240848), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1240850))), _1240852)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1240844), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1240844, _1240846, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1240844)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1240844), _1240848), hAPP(c_Com_Ocom_OBODY, _1240850)), _1240852)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1240844), tc_HOL_Obool)))))], (32795 ^ _777864) ^ [_1378963, _1378965, _1378967, _1378969] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1378963), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378965, tc_Nat_Onat), _1378967), _1378969)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1378965, _1378963), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1378963, _1378965), c_Nat_Osemiring__1__class_Oof__nat(_1378963)), _1378967)), _1378969)), class_Groups_Ocomm__monoid__mult(_1378963), class_Rings_Osemiring__1(_1378963)], (1762 ^ _777864) ^ [_802657, _802659] : [-(class_Groups_Oone(_802657)), _802659 = _802657, class_Groups_Oone(_802659)], (30555 ^ _777864) ^ [_1336476, _1336478, _1336480, _1336482, _1336484, _1336486] : [hBOOL(hAPP(hAPP(c_member(_1336476), _1336478), c_SetInterval_Oord_OatLeastLessThan(_1336476, _1336480, _1336482, _1336484, _1336486))), 30558 ^ _777864 : [(30561 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336482, _1336478), _1336486)))], (30559 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336480, _1336484), _1336478)))]]], (7010 ^ _777864) ^ [_893096, _893098, _893100] : [class_Rings_Olinordered__idom(_893096), -(_893098 = _893100), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893096), _893098), _893100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_893096), _893100), _893098)))], (39842 ^ _777864) ^ [_1533020, _1533022, _1533024, _1533026, _1533028, _1533030, _1533032] : [-(hAPP(c_Product__Type_Osnd(_1533020, _1533022), hAPP(c_Product__Type_Omap__pair(_1533024, _1533020, _1533026, _1533022, _1533028, _1533030), _1533032)) = hAPP(_1533030, hAPP(c_Product__Type_Osnd(_1533024, _1533026), _1533032)))], (6414 ^ _777864) ^ [_883753, _883755, _883757] : [class_Groups_Oordered__comm__monoid__add(_883753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883753), c_Groups_Ozero__class_Ozero(_883753)), _883755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883753), c_Groups_Ozero__class_Ozero(_883753)), _883757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_883753), c_Groups_Ozero__class_Ozero(_883753)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_883753), _883755), _883757))))], (38288 ^ _777864) ^ [_1496319, _1496321] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496319), _1496321)), 38291 ^ _777864 : [(38298 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496319), c_Orderings_Otop__class_Otop(tc_fun(_1496319, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496319), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496319, tc_HOL_Obool)), _1496321))))], (38292 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496319), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496319, tc_HOL_Obool)), _1496321))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496319), c_Orderings_Otop__class_Otop(tc_fun(_1496319, tc_HOL_Obool)))))]]], (40260 ^ _777864) ^ [_1542380, _1542382] : [-(hAPP(c_Set_OCollect(_1542380), hAPP(c_fequal, _1542382)) = hAPP(hAPP(c_Set_Oinsert(_1542380), _1542382), c_Orderings_Obot__class_Obot(tc_fun(_1542380, tc_HOL_Obool))))], (25697 ^ _777864) ^ [_1228683, _1228685, _1228687] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228683), _1228685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228683), _1228687))), -(_1228683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228685), _1228687)))], (5982 ^ _777864) ^ [_876171, _876173, _876175] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_876171, _876173, _876175))), -(hBOOL(hAPP(c_Com_OWT, _876175)))], (25921 ^ _777864) ^ [_1232975, _1232977, _1232979] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232975), _1232977)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232975), _1232979))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232975)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232977), _1232979)))], (34239 ^ _777864) ^ [_1412601, _1412603, _1412605, _1412607, _1412609] : [class_Groups_Ocomm__monoid__mult(_1412601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412603), _1412605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412603), _1412607)), 34253 ^ _777864 : [(34256 ^ _777864) ^ [] : [hAPP(_1412609, 34252 ^ [_1412601, _1412603, _1412605, _1412607, _1412609]) = c_Groups_Oone__class_Oone(_1412601)], (34254 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412603), 34252 ^ [_1412601, _1412603, _1412605, _1412607, _1412609]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412603, tc_HOL_Obool)), _1412605), _1412607))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1412601, _1412603, c_Groups_Otimes__class_Otimes(_1412601)), _1412609), c_Groups_Oone__class_Oone(_1412601)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412603, tc_HOL_Obool)), _1412605), _1412607)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412601), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1412601, _1412603, c_Groups_Otimes__class_Otimes(_1412601)), _1412609), c_Groups_Oone__class_Oone(_1412601)), _1412605)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1412601, _1412603, c_Groups_Otimes__class_Otimes(_1412601)), _1412609), c_Groups_Oone__class_Oone(_1412601)), _1412607)))], (48568 ^ _777864) ^ [_1753635, _1753637, _1753639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753635)), _1753639)), _1753637)), -(hAPP(hAPP(c_List_Odrop(_1753635), _1753637), _1753639) = c_List_Olist_ONil(_1753635))], (46581 ^ _777864) ^ [_1704415, _1704417, _1704419, _1704421, _1704423] : [hAPP(hAPP(c_List_Olist_OCons(_1704415), _1704417), _1704419) = hAPP(hAPP(c_List_Olist_OCons(_1704415), _1704421), _1704423), 46584 ^ _777864 : [(46587 ^ _777864) ^ [] : [-(_1704419 = _1704423)], (46585 ^ _777864) ^ [] : [-(_1704417 = _1704421)]]], (42838 ^ _777864) ^ [_1610938, _1610940, _1610942] : [class_Orderings_Olinorder(_1610938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610938), _1610940)), -(c_Big__Operators_Olattice_OInf__fin(_1610938, c_Orderings_Oord__class_Omin(_1610938), hAPP(hAPP(c_Set_Oinsert(_1610938), _1610942), _1610940)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610938, _1610938, c_Orderings_Oord__class_Omin(_1610938)), _1610942), _1610940))], (47267 ^ _777864) ^ [_1722175, _1722177, _1722179, _1722181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1722175), tc_List_Olist(_1722175))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1722175), tc_List_Olist(_1722175)), _1722177), _1722179)), c_List_Olexord(_1722175, _1722181))), 47272 ^ _777864 : [(47275 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1722175), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722175)), _1722177)), _1722179) = _1722177)], (47273 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722175)), _1722177)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722175)), _1722179))))]], 47277 ^ _777864 : [(47282 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1722175, _1722175)), hAPP(hAPP(c_Product__Type_OPair(_1722175, _1722175), hAPP(hAPP(c_List_Onth(_1722175), _1722177), 47276 ^ [_1722175, _1722177, _1722179, _1722181])), hAPP(hAPP(c_List_Onth(_1722175), _1722179), 47276 ^ [_1722175, _1722177, _1722179, _1722181]))), _1722181)))], (47280 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1722175), 47276 ^ [_1722175, _1722177, _1722179, _1722181]), _1722177) = hAPP(hAPP(c_List_Otake(_1722175), 47276 ^ [_1722175, _1722177, _1722179, _1722181]), _1722179))], (47278 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47276 ^ [_1722175, _1722177, _1722179, _1722181]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722175)), _1722177)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722175)), _1722179)))))]]], (6534 ^ _777864) ^ [_885769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _885769), _885769))], (49544 ^ _777864) ^ [_1774783, _1774785, _1774787] : [hBOOL(hAPP(c_List_Odistinct(_1774783), _1774785)), -(hBOOL(hAPP(c_List_Odistinct(_1774783), hAPP(c_List_Ofilter(_1774783, _1774787), _1774785))))], (11245 ^ _777864) ^ [_965235, _965237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _965235), _965237)), 11248 ^ _777864 : [(11251 ^ _777864) ^ [] : [_965235 = _965237], (11249 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _965235), _965237)))]]], (8640 ^ _777864) ^ [_921260, _921262, _921264, _921266] : [class_Groups_Oab__semigroup__mult(_921260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921260), _921262), _921264)), _921266) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921260), _921262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_921260), _921264), _921266)))], (45048 ^ _777864) ^ [_1665289, _1665291, _1665293] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1665289, tc_HOL_Obool)), _1665291)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1665289), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665289, tc_HOL_Obool), _1665291))), 45058 ^ _777864 : [(45061 ^ _777864) ^ [] : [hAPP(c_Finite__Set_Ocard(_1665289), 45057 ^ [_1665289, _1665291, _1665293]) = _1665293], (45059 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1665289, tc_HOL_Obool)), 45057 ^ [_1665289, _1665291, _1665293]), _1665291)))]], 45065 ^ _777864 : [(45069 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1665289, tc_HOL_Obool)), 45067 ^ [_1665289, _1665291, _1665293]), _1665291)))], (45071 ^ _777864) ^ [] : [45064 ^ [_1665289, _1665291, _1665293] = 45067 ^ [_1665289, _1665291, _1665293]], (45073 ^ _777864) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1665289, tc_HOL_Obool)), 45064 ^ [_1665289, _1665291, _1665293]), 45067 ^ [_1665289, _1665291, _1665293]) = c_Orderings_Obot__class_Obot(tc_fun(_1665289, tc_HOL_Obool))], (45066 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1665289, tc_HOL_Obool)), 45064 ^ [_1665289, _1665291, _1665293]), _1665291)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1665293), hAPP(c_Finite__Set_Ocard(tc_fun(_1665289, tc_HOL_Obool)), _1665291)) = hAPP(c_Finite__Set_Ocard(_1665289), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1665289, tc_HOL_Obool), _1665291)))], (12107 ^ _777864) ^ [_980549] : [-(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), _980549))))], (38714 ^ _777864) ^ [_1506719, _1506721, _1506723] : [-(hAPP(c_Set_Ovimage(_1506719, _1506721, _1506723), c_Orderings_Obot__class_Obot(tc_fun(_1506721, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1506719, tc_HOL_Obool)))], (47858 ^ _777864) ^ [_1735605, _1735607, _1735609, _1735611, _1735613] : [-(hAPP(hAPP(c_List_Oappend(_1735605), _1735607), hAPP(hAPP(c_List_Olist_OCons(_1735605), _1735609), c_List_Olist_ONil(_1735605))) = hAPP(hAPP(c_List_Oappend(_1735605), _1735611), hAPP(hAPP(c_List_Olist_OCons(_1735605), _1735613), c_List_Olist_ONil(_1735605)))), _1735607 = _1735611, _1735609 = _1735613], (29982 ^ _777864) ^ [_1323020, _1323022, _1323024, _1323026] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323020, tc_HOL_Obool)), _1323022), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323020, tc_HOL_Obool)), _1323024), _1323026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323020, tc_HOL_Obool)), _1323024), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323020, tc_HOL_Obool)), _1323022), _1323026)))], (40568 ^ _777864) ^ [_1554394, _1554396, _1554398] : [class_Orderings_Olinorder(_1554394), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554394), _1554396)), -(_1554396 = c_Orderings_Obot__class_Obot(tc_fun(_1554394, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1554394), _1554398), c_Big__Operators_Olattice_OInf__fin(_1554394, c_Orderings_Oord__class_Omin(_1554394), _1554396)) = c_Big__Operators_Olattice_OInf__fin(_1554394, c_Orderings_Oord__class_Omin(_1554394), hAPP(c_Set_OCollect(_1554394), hAPP(hAPP(c_COMBB(tc_fun(_1554394, tc_HOL_Obool), tc_HOL_Obool, _1554394), c_HOL_OEx(_1554394)), hAPP(hAPP(c_COMBC(_1554394, tc_fun(_1554394, tc_HOL_Obool), tc_fun(_1554394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1554394, tc_HOL_Obool), tc_fun(_1554394, tc_HOL_Obool)), _1554394), c_COMBS(_1554394, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554394, tc_HOL_Obool), tc_fun(_1554394, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1554394), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554394), c_fconj)), hAPP(hAPP(c_COMBC(_1554394, tc_fun(_1554394, _1554394), tc_fun(_1554394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1554394, tc_HOL_Obool), tc_fun(tc_fun(_1554394, _1554394), tc_fun(_1554394, tc_HOL_Obool)), _1554394), c_COMBB(_1554394, tc_HOL_Obool, _1554394)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1554394), _1554398))))), hAPP(hAPP(c_COMBC(_1554394, tc_fun(_1554394, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554394)), _1554396))))))], (36046 ^ _777864) ^ [_1448830, _1448832, _1448834, _1448836, _1448838, _1448840] : [hBOOL(hAPP(hAPP(c_member(_1448830), _1448832), _1448834)), -(hAPP(c_Set_Oimage(_1448830, _1448836, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1448830, _1448836), _1448838), _1448832), _1448840)), _1448834) = hAPP(hAPP(c_Set_Oinsert(_1448836), _1448840), hAPP(c_Set_Oimage(_1448830, _1448836, _1448838), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1448830, tc_HOL_Obool)), _1448834), hAPP(hAPP(c_Set_Oinsert(_1448830), _1448832), c_Orderings_Obot__class_Obot(tc_fun(_1448830, tc_HOL_Obool)))))))], (20556 ^ _777864) ^ [_1132055, _1132057, _1132059, _1132061] : [class_Fields_Olinordered__field(_1132055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132055), _1132057), _1132059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132055), c_Groups_Ozero__class_Ozero(_1132055)), _1132061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132055), c_Groups_Ozero__class_Ozero(_1132055)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132055), _1132059), _1132057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132055), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132055), _1132061), _1132059)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132055), _1132061), _1132057))))], (38422 ^ _777864) ^ [_1498990, _1498992, _1498994, _1498996] : [c_Fun_Oinj__on(_1498990, _1498992, _1498994, c_Orderings_Otop__class_Otop(tc_fun(_1498990, tc_HOL_Obool))), 38425 ^ _777864 : [(38439 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498992), _1498996), hAPP(c_Set_Oimage(_1498990, _1498992, _1498994), c_Orderings_Otop__class_Otop(tc_fun(_1498990, tc_HOL_Obool)))))), 38440 ^ _777864 : [(38441 ^ _777864) ^ [_1499393] : [_1498996 = hAPP(_1498994, _1499393), 38445 ^ _777864 : [(38448 ^ _777864) ^ [] : [38444 ^ [_1498990, _1498992, _1498994, _1498996, _1499393] = _1499393], (38446 ^ _777864) ^ [] : [-(_1498996 = hAPP(_1498994, 38444 ^ [_1498990, _1498992, _1498994, _1498996, _1499393]))]]]]], (38426 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1498992), _1498996), hAPP(c_Set_Oimage(_1498990, _1498992, _1498994), c_Orderings_Otop__class_Otop(tc_fun(_1498990, tc_HOL_Obool))))), 38430 ^ _777864 : [(38433 ^ _777864) ^ [_1499255] : [_1498996 = hAPP(_1498994, _1499255), -(_1499255 = 38429 ^ [_1498990, _1498992, _1498994, _1498996])], (38431 ^ _777864) ^ [] : [-(_1498996 = hAPP(_1498994, 38429 ^ [_1498990, _1498992, _1498994, _1498996]))]]]]], (5700 ^ _777864) ^ [_869861, _869863, _869865, _869867, _869869] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_869861, _869863, _869865)), _869867), hAPP(hAPP(hAPP(c_Natural_Oupdate, _869869), c_Com_Ovname_OLoc(_869861)), hAPP(hAPP(c_Natural_Ogetlocs, _869867), _869861)))), 5704 ^ _777864 : [(5707 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869865), hAPP(hAPP(hAPP(c_Natural_Oupdate, _869867), c_Com_Ovname_OLoc(_869861)), hAPP(_869863, _869867))), 5703 ^ [_869861, _869863, _869865, _869867, _869869])))], (5705 ^ _777864) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _869869), c_Com_Ovname_OLoc(_869861)), hAPP(hAPP(c_Natural_Ogetlocs, _869867), _869861)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 5703 ^ [_869861, _869863, _869865, _869867, _869869]), c_Com_Ovname_OLoc(_869861)), hAPP(hAPP(c_Natural_Ogetlocs, _869867), _869861)))]]], (32259 ^ _777864) ^ [_1367634, _1367636] : [class_Orderings_Olinorder(_1367634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367634), _1367636)), -(_1367636 = c_Orderings_Obot__class_Obot(tc_fun(_1367634, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1367634), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367634), 32272 ^ [_1367634, _1367636]), 32273 ^ [_1367634, _1367636])), hAPP(hAPP(c_Set_Oinsert(_1367634), 32272 ^ [_1367634, _1367636]), hAPP(hAPP(c_Set_Oinsert(_1367634), 32273 ^ [_1367634, _1367636]), c_Orderings_Obot__class_Obot(tc_fun(_1367634, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1367634), c_Big__Operators_Olattice_OInf__fin(_1367634, c_Orderings_Oord__class_Omin(_1367634), _1367636)), _1367636)))], (10172 ^ _777864) ^ [_947651, _947653, _947655, _947657, _947659] : [class_Orderings_Oord(_947651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947653, _947651)), _947655), _947657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947651), hAPP(_947655, _947659)), hAPP(_947657, _947659))))], (18214 ^ _777864) ^ [_1091205] : [-(c_Int_Osucc(_1091205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1091205), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22616 ^ _777864) ^ [_1168993, _1168995, _1168997, _1168999, _1169001, _1169003] : [-(hAPP(hAPP(c_Product__Type_OPair(_1168993, _1168995), _1168997), _1168999) = hAPP(hAPP(c_Product__Type_OPair(_1168993, _1168995), _1169001), _1169003)), _1168997 = _1169001, _1168999 = _1169003], (40258 ^ _777864) ^ [_1542327, _1542329] : [-(hAPP(c_Set_OCollect(_1542327), hAPP(hAPP(c_COMBC(_1542327, _1542327, tc_HOL_Obool), c_fequal), _1542329)) = hAPP(hAPP(c_Set_Oinsert(_1542327), _1542329), c_Orderings_Obot__class_Obot(tc_fun(_1542327, tc_HOL_Obool))))], (44075 ^ _777864) ^ [_1641793, _1641795, _1641797] : [hAPP(hAPP(c_Relation_Orel__comp(_1641793, _1641793, _1641793), hAPP(c_Relation_Oconverse(_1641793, _1641793), _1641795)), _1641795) = _1641795, hAPP(c_Relation_ODomain(_1641793, _1641793), _1641795) = _1641797, -(c_Equiv__Relations_Oequiv(_1641793, _1641797, _1641795))], (18436 ^ _777864) ^ [_1094943, _1094945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1094943)), c_Int_OBit1(_1094945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094943), _1094945)))], (14111 ^ _777864) ^ [_1016555, _1016557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1016555, _1016557)), _1016555)))], (26039 ^ _777864) ^ [_1234976, _1234978, _1234980, _1234982, _1234984, _1234986, _1234988, _1234990] : [c_Hoare__Mirabelle_Ohoare__derivs(_1234976, _1234978, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1234976)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1234976), _1234980), hAPP(c_Com_Ocom_OBODY, _1234982)), hAPP(hAPP(c_COMBC(_1234976, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1234976), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1234984)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), hAPP(c_Natural_Ogetlocs, _1234986)))), _1234988)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Oloc, tc_Nat_Onat), c_Natural_Ogetlocs), c_Com_ORes))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1234976), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1234976, _1234978, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1234976)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1234976), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1234976), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1234986)))), hAPP(hAPP(c_COMBC(_1234976, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1234976), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1234980)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), c_Natural_Onewlocs))), c_Com_Ovname_OLoc(c_Com_OArg))), _1234990)))), c_Com_Ocom_OCall(_1234988, _1234982, _1234990)), _1234984)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1234976), tc_HOL_Obool)))))], (33318 ^ _777864) ^ [_1390243, _1390245] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1390243, _1390245))))], (12253 ^ _777864) ^ [_982943, _982945] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _982943), _982945)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982943)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982945)))], (27694 ^ _777864) ^ [_1271225, _1271227, _1271229, _1271231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1271225), _1271227)), 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)), _1271229), _1271225)), 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)), _1271231), _1271227)), 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)), _1271229), _1271231)), _1271227)), c_FunDef_Omax__weak)))], (7996 ^ _777864) ^ [_911053, _911055, _911057] : [class_Rings_Olinordered__semidom(_911053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911053), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911053), _911055)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_911053), _911057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _911055), _911057)))], (22867 ^ _777864) ^ [_1174069, _1174071, _1174073, _1174075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1174069, tc_HOL_Obool)), _1174071), _1174073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1174069, tc_HOL_Obool)), _1174073), _1174075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1174069, tc_HOL_Obool)), _1174071), _1174075)))], (5604 ^ _777864) ^ [_867449, _867451, _867453, _867455, _867457] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_867449, _867451, _867453)), _867455), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867457), hAPP(c_Natural_Ogetlocs, _867455))), _867449), hAPP(hAPP(c_Natural_Ogetlocs, _867457), c_Com_ORes)))), 5608 ^ _777864 : [(5611 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _867451)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867455), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_867453, _867455))), 5607 ^ [_867449, _867451, _867453, _867455, _867457])))], (5609 ^ _777864) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _867457), hAPP(c_Natural_Ogetlocs, _867455))), _867449), hAPP(hAPP(c_Natural_Ogetlocs, _867457), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 5607 ^ [_867449, _867451, _867453, _867455, _867457]), hAPP(c_Natural_Ogetlocs, _867455))), _867449), hAPP(hAPP(c_Natural_Ogetlocs, 5607 ^ [_867449, _867451, _867453, _867455, _867457]), c_Com_ORes)))]]], (6494 ^ _777864) ^ [_885148, _885150] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885148), _885150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _885150), _885148))], (43923 ^ _777864) ^ [_1637258, _1637260, _1637262, _1637264, _1637266, _1637268] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637258, tc_fun(_1637260, tc_HOL_Obool)), _1637262), hAPP(hAPP(c_COMBB(_1637264, tc_fun(_1637260, tc_HOL_Obool), _1637258), _1637266), _1637268)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637264, tc_fun(_1637260, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1637258, _1637264, _1637268), _1637262)), _1637266))], (15236 ^ _777864) ^ [_1036440, _1036442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036440), _1036442)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036442), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036442), _1036440)) = _1036440)], (15122 ^ _777864) ^ [_1034495, _1034497] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034495), _1034497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1034497), _1034495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1034495 = _1034497)], (42788 ^ _777864) ^ [_1610003, _1610005, _1610007] : [class_Lattices_Oab__semigroup__idem__mult(_1610003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610003), _1610005)), -(hAPP(c_Finite__Set_Ofold1(_1610003, c_Groups_Otimes__class_Otimes(_1610003)), hAPP(hAPP(c_Set_Oinsert(_1610003), _1610007), _1610005)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610003, _1610003, c_Groups_Otimes__class_Otimes(_1610003)), _1610007), _1610005))], (21048 ^ _777864) ^ [_1140733, _1140735, _1140737] : [class_Fields_Olinordered__field(_1140733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140733), _1140735), _1140737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140733), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140733), _1140735), _1140737)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140733), c_Groups_Oone__class_Oone(_1140733)), c_Groups_Oone__class_Oone(_1140733)))), _1140737)))], (44919 ^ _777864) ^ [_1662500] : [class_Complete__Lattice_Ocomplete__lattice(_1662500), -(c_Complete__Lattice_OSup__class_OSup(_1662500, c_Orderings_Obot__class_Obot(tc_fun(_1662500, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1662500))], (20370 ^ _777864) ^ [_1128645, _1128647, _1128649] : [class_Rings_Odivision__ring(_1128645), -(_1128647 = c_Groups_Ozero__class_Ozero(_1128645)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128645), hAPP(c_Groups_Ouminus__class_Ouminus(_1128645), _1128649)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128645), _1128647)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128645), _1128649), _1128647))], (32031 ^ _777864) ^ [_1363242, _1363244, _1363246] : [class_Orderings_Olinorder(_1363242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363242), _1363244)), -(_1363244 = c_Orderings_Obot__class_Obot(tc_fun(_1363242, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363242), _1363246)), -(_1363246 = c_Orderings_Obot__class_Obot(tc_fun(_1363242, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1363242, c_Orderings_Oord__class_Omin(_1363242), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363242, tc_HOL_Obool)), _1363244), _1363246)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1363242), c_Big__Operators_Olattice_OInf__fin(_1363242, c_Orderings_Oord__class_Omin(_1363242), _1363244)), c_Big__Operators_Olattice_OInf__fin(_1363242, c_Orderings_Oord__class_Omin(_1363242), _1363246)))], (39199 ^ _777864) ^ [_1518770, _1518772, _1518774, _1518776, _1518778] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1518770, _1518772), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518770, tc_HOL_Obool)), _1518774), _1518776)), _1518778) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518770, _1518772), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1518770, _1518772), _1518774), _1518778)), hAPP(hAPP(c_Product__Type_OSigma(_1518770, _1518772), _1518776), _1518778)))], (17980 ^ _777864) ^ [] : [c_Int_OPls = c_Int_OMin], (27087 ^ _777864) ^ [_1257260, _1257262, _1257264, _1257266] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1257260, tc_fun(_1257262, tc_HOL_Obool))), _1257264), _1257266)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1257260, _1257262)), hAPP(hAPP(c_Product__Type_OPair(_1257260, _1257262), _1257264), _1257266)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1257260, _1257262), tc_HOL_Obool)))))], (29750 ^ _777864) ^ [_1317944, _1317946, _1317948, _1317950] : [class_Lattices_Osemilattice__inf(_1317944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317944), _1317946), _1317948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317944), _1317946), _1317950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317944), _1317946), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317944), _1317948), _1317950))))], (22130 ^ _777864) ^ [_1160438, _1160440, _1160442] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1160438, _1160440), _1160442)), 22133 ^ _777864 : [(22134 ^ _777864) ^ [_1160523] : [hBOOL(hAPP(hAPP(_1160440, _1160523), _1160442)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1160438, _1160440), _1160523)))]]], (27400 ^ _777864) ^ [_1265135, _1265137] : [class_Rings_Olinordered__idom(_1265135), hBOOL(hAPP(hAPP(c_member(_1265135), _1265137), c_Int_Oring__1__class_OInts(_1265135))), 27407 ^ _777864 : [(27414 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265135), _1265137), c_Groups_Ozero__class_Ozero(_1265135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265135), c_Groups_Oone__class_Oone(_1265135)), _1265137)), _1265137)), c_Groups_Ozero__class_Ozero(_1265135))))], (27408 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265135), c_Groups_Oone__class_Oone(_1265135)), _1265137)), _1265137)), c_Groups_Ozero__class_Ozero(_1265135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265135), _1265137), c_Groups_Ozero__class_Ozero(_1265135))))]]], (43759 ^ _777864) ^ [_1632387, _1632389, _1632391, _1632393] : [-(hAPP(c_Relation_Oconverse(_1632387, _1632389), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1632387, _1632389), tc_HOL_Obool)), _1632391), _1632393)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1632389, _1632387), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1632387, _1632389), _1632391)), hAPP(c_Relation_Oconverse(_1632387, _1632389), _1632393)))], (40397 ^ _777864) ^ [_1548034, _1548036] : [-(hAPP(c_Set_OPow(_1548034), _1548036) = hAPP(c_Set_OCollect(tc_fun(_1548034, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1548034, tc_HOL_Obool), tc_fun(_1548034, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1548034, tc_HOL_Obool))), _1548036)))], (49308 ^ _777864) ^ [_1769862, _1769864, _1769866] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769862)), _1769864), c_List_Olists(_1769862, _1769866))), -(_1769864 = c_List_Olist_ONil(_1769862)), 49317 ^ _777864 : [(49322 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1769862)), 49316 ^ [_1769862, _1769864, _1769866]), c_List_Olists(_1769862, _1769866))))], (49320 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769862), 49315 ^ [_1769862, _1769864, _1769866]), _1769866)))], (49318 ^ _777864) ^ [] : [-(_1769864 = hAPP(hAPP(c_List_Olist_OCons(_1769862), 49315 ^ [_1769862, _1769864, _1769866]), 49316 ^ [_1769862, _1769864, _1769866]))]]], (27562 ^ _777864) ^ [_1268673, _1268675, _1268677] : [class_Rings_Oring__1(_1268673), hBOOL(hAPP(hAPP(c_member(_1268673), _1268675), c_Int_Oring__1__class_OInts(_1268673))), -(hBOOL(hAPP(hAPP(c_member(_1268673), hAPP(hAPP(c_Power_Opower__class_Opower(_1268673), _1268675), _1268677)), c_Int_Oring__1__class_OInts(_1268673))))], (22448 ^ _777864) ^ [_1165862, _1165864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165864), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165862, _1165864) = 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), _1165862), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1165864)))))], (37604 ^ _777864) ^ [_1483251, _1483253, _1483255, _1483257, _1483259] : [class_Groups_Ocomm__monoid__add(_1483251), class_Groups_Oordered__cancel__ab__semigroup__add(_1483251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1483253), _1483255)), -(_1483255 = c_Orderings_Obot__class_Obot(tc_fun(_1483253, tc_HOL_Obool))), 37622 ^ _777864 : [(37625 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483251), hAPP(_1483257, 37621 ^ [_1483251, _1483253, _1483255, _1483257, _1483259])), hAPP(_1483259, 37621 ^ [_1483251, _1483253, _1483255, _1483257, _1483259])))], (37623 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483253), 37621 ^ [_1483251, _1483253, _1483255, _1483257, _1483259]), _1483255)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483251), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483253, _1483251), _1483257), _1483255)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483253, _1483251), _1483259), _1483255))))], (23037 ^ _777864) ^ [_1177449, _1177451, _1177453, _1177455, _1177457] : [_1177449 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1177451, _1177453, _1177449, _1177455), _1177457) = hAPP(c_Product__Type_OPair(_1177451, _1177453), _1177457))], (11008 ^ _777864) ^ [_961170, _961172, _961174] : [class_Groups_Oordered__ab__group__add(_961170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961170), _961172), _961174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961170), hAPP(c_Groups_Ouminus__class_Ouminus(_961170), _961174)), hAPP(c_Groups_Ouminus__class_Ouminus(_961170), _961172))))], (26553 ^ _777864) ^ [_1245648, _1245650] : [-(_1245648 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26556 ^ _777864 : [(26563 ^ _777864) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1245650) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245648), _1245650)), _1245648)))], (26557 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245648), _1245650)), _1245648)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1245650) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8634 ^ _777864) ^ [_921173] : [class_Rings_Oring__1(_921173), -(hAPP(c_Int_Oring__1__class_Oof__int(_921173), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_921173))], (33545 ^ _777864) ^ [_1395334, _1395336, _1395338, _1395340, _1395342, _1395344] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395334, tc_fun(_1395336, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395338, tc_fun(_1395334, tc_HOL_Obool)), _1395340), _1395342)), _1395344) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395338, tc_fun(_1395336, tc_HOL_Obool)), _1395340), hAPP(hAPP(c_COMBC(_1395338, tc_fun(_1395334, tc_fun(_1395336, tc_HOL_Obool)), tc_fun(_1395336, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1395334, tc_HOL_Obool), tc_fun(tc_fun(_1395334, tc_fun(_1395336, tc_HOL_Obool)), tc_fun(_1395336, tc_HOL_Obool)), _1395338), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1395334, tc_fun(_1395336, tc_HOL_Obool))), _1395342)), _1395344)))], (26595 ^ _777864) ^ [_1246451, _1246453] : [-(c_Set_Othe__elem(_1246451, hAPP(hAPP(c_Set_Oinsert(_1246451), _1246453), c_Orderings_Obot__class_Obot(tc_fun(_1246451, tc_HOL_Obool)))) = _1246453)], (30516 ^ _777864) ^ [_1335640, _1335642] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1335640), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335642))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1335642), _1335640)))], (12888 ^ _777864) ^ [_994301, _994303] : [hAPP(c_Int_Onat, _994301) = _994303, 12891 ^ _777864 : [(12898 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994301))), -(_994303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12892 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994301)), -(_994301 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994303))]]], (5767 ^ _777864) ^ [_871848, _871850, _871852, _871854, _871856, _871858] : [-(c_Natural_Oevaln(c_Com_Ocom_OLocal(_871848, _871850, _871852), _871854, _871856, hAPP(hAPP(hAPP(c_Natural_Oupdate, _871858), c_Com_Ovname_OLoc(_871848)), hAPP(hAPP(c_Natural_Ogetlocs, _871854), _871848)))), 5768 ^ _777864 : [(5769 ^ _777864) ^ [_871969] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _871858), c_Com_Ovname_OLoc(_871848)), hAPP(hAPP(c_Natural_Ogetlocs, _871854), _871848)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _871969), c_Com_Ovname_OLoc(_871848)), hAPP(hAPP(c_Natural_Ogetlocs, _871854), _871848)), c_Natural_Oevaln(_871852, hAPP(hAPP(hAPP(c_Natural_Oupdate, _871854), c_Com_Ovname_OLoc(_871848)), hAPP(_871850, _871854)), _871856, _871969)]]], (15024 ^ _777864) ^ [_1032676, _1032678, _1032680] : [class_Groups_Oab__group__add(_1032676), 15027 ^ _777864 : [(15034 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032676), _1032678), _1032680) = c_Groups_Ozero__class_Ozero(_1032676), -(_1032678 = _1032680)], (15028 ^ _777864) ^ [] : [_1032678 = _1032680, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1032676), _1032678), _1032680) = c_Groups_Ozero__class_Ozero(_1032676))]]], (42088 ^ _777864) ^ [_1594785, _1594787, _1594789, _1594791] : [c_Finite__Set_Ofolding(_1594785, _1594787, _1594789, _1594791), -(hAPP(_1594791, c_Orderings_Obot__class_Obot(tc_fun(_1594785, tc_HOL_Obool))) = c_Fun_Oid(_1594787))], (14710 ^ _777864) ^ [_1026841, _1026843, _1026845] : [-(hBOOL(hAPP(_1026841, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026843), _1026845)))), 14713 ^ _777864 : [(14716 ^ _777864) ^ [] : [hBOOL(hAPP(_1026841, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14714 ^ _777864) ^ [] : [-(_1026845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 14717 ^ _777864 : [(14722 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14720 ^ [_1026841, _1026843, _1026845]), _1026845)))], (14724 ^ _777864) ^ [] : [-(_1026843 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026845), 14719 ^ [_1026841, _1026843, _1026845])), 14720 ^ [_1026841, _1026843, _1026845]))], (14726 ^ _777864) ^ [] : [hBOOL(hAPP(_1026841, 14719 ^ [_1026841, _1026843, _1026845]))], (14718 ^ _777864) ^ [] : [_1026845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (47076 ^ _777864) ^ [_1717120, _1717122, _1717124] : [_1717120 = _1717122, 47079 ^ _777864 : [(47082 ^ _777864) ^ [_1717268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717268), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717124)), _1717120))), -(hAPP(hAPP(c_List_Onth(_1717124), _1717120), _1717268) = hAPP(hAPP(c_List_Onth(_1717124), _1717122), _1717268))], (47080 ^ _777864) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717124)), _1717120) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717124)), _1717122))]]], (44059 ^ _777864) ^ [_1641463, _1641465, _1641467, _1641469, _1641471] : [class_Complete__Lattice_Ocomplete__lattice(_1641463), hBOOL(hAPP(hAPP(c_member(_1641465), _1641467), _1641469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1641463), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641465, _1641463), _1641469), _1641471)), hAPP(_1641471, _1641467))))], (1152 ^ _777864) ^ [_795032, _795034] : [-(class_Int_Oring__char__0(_795032)), _795034 = _795032, class_Int_Oring__char__0(_795034)], (16690 ^ _777864) ^ [_1065087, _1065089] : [class_Rings_Olinordered__idom(_1065087), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065087), c_Groups_Osgn__class_Osgn(_1065087, _1065089)), hAPP(c_Groups_Oabs__class_Oabs(_1065087), _1065089)) = _1065089)], (48306 ^ _777864) ^ [_1746216, _1746218, _1746220, _1746222, _1746224] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746216), tc_List_Olist(_1746216))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746216), tc_List_Olist(_1746216)), _1746218), _1746220)), c_List_Olistrel1(_1746216, _1746222))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1746216), tc_List_Olist(_1746216))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1746216), tc_List_Olist(_1746216)), hAPP(hAPP(c_List_Olist_OCons(_1746216), _1746224), _1746218)), hAPP(hAPP(c_List_Olist_OCons(_1746216), _1746224), _1746220))), c_List_Olistrel1(_1746216, _1746222))))], (43295 ^ _777864) ^ [_1620980, _1620982, _1620984, _1620986, _1620988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620980, _1620980)), hAPP(hAPP(c_Product__Type_OPair(_1620980, _1620980), _1620982), _1620984)), _1620986)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620980, _1620980)), hAPP(hAPP(c_Product__Type_OPair(_1620980, _1620980), _1620984), _1620988)), c_Transitive__Closure_Ortrancl(_1620980, _1620986))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620980, _1620980)), hAPP(hAPP(c_Product__Type_OPair(_1620980, _1620980), _1620982), _1620988)), c_Transitive__Closure_Ortrancl(_1620980, _1620986))))], (24647 ^ _777864) ^ [_1210232, _1210234] : [hAPP(c_Code__Numeral_Onat__of, _1210232) = hAPP(c_Code__Numeral_Onat__of, _1210234), -(_1210232 = _1210234)], (24635 ^ _777864) ^ [_1210041, _1210043] : [hAPP(c_Code__Numeral_Onat__of, _1210041) = hAPP(c_Code__Numeral_Onat__of, _1210043), -(_1210041 = _1210043)], (7084 ^ _777864) ^ [_894212, _894214] : [class_Rings_Ocomm__semiring__1(_894212), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_894212), _894214), c_Groups_Ozero__class_Ozero(_894212)) = _894214)], (32561 ^ _777864) ^ [_1373936, _1373938, _1373940, _1373942] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1373936), _1373938)), hBOOL(hAPP(hAPP(c_member(_1373936), _1373940), _1373938)), -(hBOOL(hAPP(hAPP(c_member(_1373936), _1373940), _1373942))), -(hAPP(c_Finite__Set_Ocard(_1373936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373936, tc_HOL_Obool)), _1373938), hAPP(hAPP(c_Set_Oinsert(_1373936), _1373940), _1373942))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1373936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1373936, tc_HOL_Obool)), _1373938), _1373942))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (37859 ^ _777864) ^ [_1488137, _1488139, _1488141] : [class_Orderings_Oorder(_1488137), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488137, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1488137, _1488139, _1488141)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1488137), _1488141)) = c_Orderings_Obot__class_Obot(tc_fun(_1488137, tc_HOL_Obool)))], (47942 ^ _777864) ^ [_1737454, _1737456, _1737458, _1737460, _1737462] : [-(hAPP(hAPP(c_List_Olist__update(_1737454, hAPP(hAPP(c_List_Oappend(_1737454), _1737456), hAPP(hAPP(c_List_Olist_OCons(_1737454), _1737458), _1737460))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737454)), _1737456)), _1737462) = hAPP(hAPP(c_List_Oappend(_1737454), _1737456), hAPP(hAPP(c_List_Olist_OCons(_1737454), _1737462), _1737460)))], (28462 ^ _777864) ^ [_1289591, _1289593, _1289595, _1289597, _1289599, _1289601] : [hBOOL(hAPP(hAPP(_1289591, _1289593), _1289595)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289597, tc_fun(_1289599, tc_HOL_Obool))), _1289591), _1289601), _1289593), _1289595)))], (22879 ^ _777864) ^ [_1174326] : [-(c_Divides_Odivmod__nat(_1174326, 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)), _1174326))], (40875 ^ _777864) ^ [_1565700] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1565700)))], (27169 ^ _777864) ^ [_1259201, _1259203, _1259205, _1259207] : [-(hBOOL(hAPP(hAPP(c_member(_1259201), _1259203), _1259205))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259201, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1259201), _1259203), _1259207)), _1259205) = hAPP(hAPP(c_Set_Oinsert(_1259201), _1259203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1259201, tc_HOL_Obool)), _1259207), _1259205)))], (41264 ^ _777864) ^ [_1574578] : [-(c_Wellfounded_OwfP(_1574578, hAPP(c_COMBK(tc_fun(_1574578, tc_HOL_Obool), _1574578), hAPP(c_COMBK(tc_HOL_Obool, _1574578), c_fFalse))))], (51197 ^ _777864) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (47762 ^ _777864) ^ [_1732968, _1732970, _1732972, _1732974] : [-(hAPP(c_List_Olist_Olist__case(_1732968, _1732970, _1732972, _1732974), c_List_Olist_ONil(_1732970)) = _1732972)], (22149 ^ _777864) ^ [_1160828, _1160830, _1160832] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1160828, _1160830), _1160832)), 22152 ^ _777864 : [(22153 ^ _777864) ^ [_1160913] : [hBOOL(hAPP(hAPP(_1160830, _1160913), _1160832)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1160828, _1160830), _1160913)))]]], (49966 ^ _777864) ^ [_1784112, _1784114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1784112), _1784114)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1784112, _1784114)) = _1784112)], (15164 ^ _777864) ^ [_1035228, _1035230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035228), _1035230))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035228, _1035230) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035228), _1035230), _1035230))], (12974 ^ _777864) ^ [_995604] : [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, _995604)))))], (33795 ^ _777864) ^ [_1402025, _1402027] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402025, tc_fun(_1402025, tc_HOL_Obool)), _1402027), hAPP(hAPP(c_COMBC(_1402025, tc_fun(_1402025, tc_HOL_Obool), tc_fun(_1402025, tc_HOL_Obool)), c_Set_Oinsert(_1402025)), c_Orderings_Obot__class_Obot(tc_fun(_1402025, tc_HOL_Obool)))) = _1402027)], (38252 ^ _777864) ^ [_1495654, _1495656, _1495658, _1495660] : [-(hBOOL(hAPP(hAPP(c_member(_1495654), hAPP(_1495656, _1495658)), hAPP(c_Set_Oimage(_1495660, _1495654, _1495656), c_Orderings_Otop__class_Otop(tc_fun(_1495660, tc_HOL_Obool))))))], (33859 ^ _777864) ^ [_1403629, _1403631, _1403633, _1403635, _1403637, _1403639, _1403641, _1403643, _1403645] : [c_Equiv__Relations_Oequiv(_1403629, _1403631, _1403633), c_Equiv__Relations_Oequiv(_1403635, _1403637, _1403639), c_Equiv__Relations_Ocongruent2(_1403629, _1403635, tc_fun(_1403641, tc_HOL_Obool), _1403633, _1403639, _1403643), hBOOL(hAPP(hAPP(c_member(_1403635), _1403645), _1403637)), -(c_Equiv__Relations_Ocongruent(_1403629, tc_fun(_1403641, tc_HOL_Obool), _1403633, hAPP(hAPP(c_COMBB(tc_fun(_1403635, tc_fun(_1403641, tc_HOL_Obool)), tc_fun(_1403641, tc_HOL_Obool), _1403629), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403635, tc_fun(_1403641, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403635, _1403635, _1403639), hAPP(hAPP(c_Set_Oinsert(_1403635), _1403645), c_Orderings_Obot__class_Obot(tc_fun(_1403635, tc_HOL_Obool)))))), _1403643)))], (17574 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (40482 ^ _777864) ^ [_1550738, _1550740, _1550742] : [class_Groups_Olinordered__ab__semigroup__add(_1550738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550738), _1550740)), -(_1550740 = c_Orderings_Obot__class_Obot(tc_fun(_1550738, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1550738), _1550742), c_Big__Operators_Olinorder__class_OMin(_1550738, _1550740)) = c_Big__Operators_Olinorder__class_OMin(_1550738, hAPP(c_Set_OCollect(_1550738), hAPP(hAPP(c_COMBB(tc_fun(_1550738, tc_HOL_Obool), tc_HOL_Obool, _1550738), c_HOL_OEx(_1550738)), hAPP(hAPP(c_COMBC(_1550738, tc_fun(_1550738, tc_HOL_Obool), tc_fun(_1550738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550738, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1550738, tc_HOL_Obool), tc_fun(_1550738, tc_HOL_Obool)), _1550738), c_COMBS(_1550738, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550738, tc_HOL_Obool), tc_fun(_1550738, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1550738), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550738), c_fconj)), hAPP(hAPP(c_COMBC(_1550738, tc_fun(_1550738, _1550738), tc_fun(_1550738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550738, tc_HOL_Obool), tc_fun(tc_fun(_1550738, _1550738), tc_fun(_1550738, tc_HOL_Obool)), _1550738), c_COMBB(_1550738, tc_HOL_Obool, _1550738)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1550738), _1550742))))), hAPP(hAPP(c_COMBC(_1550738, tc_fun(_1550738, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550738)), _1550740))))))], (35070 ^ _777864) ^ [_1429840, _1429842, _1429844, _1429846, _1429848, _1429850] : [c_Fun_Oinj__on(_1429840, _1429842, _1429844, _1429846), hAPP(_1429844, _1429848) = hAPP(_1429844, _1429850), hBOOL(hAPP(hAPP(c_member(_1429840), _1429848), _1429846)), hBOOL(hAPP(hAPP(c_member(_1429840), _1429850), _1429846)), -(_1429848 = _1429850)], (46813 ^ _777864) ^ [_1710672, _1710674, _1710676, _1710678, _1710680] : [class_Groups_Ocomm__monoid__add(_1710672), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1710672), hAPP(hAPP(c_List_Omap(_1710674, _1710672), hAPP(hAPP(c_COMBS(_1710674, _1710672, _1710672), hAPP(hAPP(c_COMBB(_1710672, tc_fun(_1710672, _1710672), _1710674), c_Groups_Oplus__class_Oplus(_1710672)), _1710676)), _1710678)), _1710680)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1710672), hAPP(c_List_Omonoid__add__class_Olistsum(_1710672), hAPP(hAPP(c_List_Omap(_1710674, _1710672), _1710676), _1710680))), hAPP(c_List_Omonoid__add__class_Olistsum(_1710672), hAPP(hAPP(c_List_Omap(_1710674, _1710672), _1710678), _1710680))))], (18558 ^ _777864) ^ [_1096956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1096956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1096956))))], (39403 ^ _777864) ^ [_1523303, _1523305, _1523307, _1523309, _1523311, _1523313, _1523315, _1523317] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1523303, _1523305), tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1523303, _1523305), _1523311), hAPP(c_COMBK(tc_fun(_1523305, tc_HOL_Obool), _1523303), _1523313))), hAPP(c_Product__Type_Oprod_Oprod__case(_1523303, _1523305, tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1523303, tc_fun(_1523305, tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool))), tc_fun(_1523305, tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool)), tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool)), tc_fun(tc_fun(_1523305, tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool))), tc_fun(_1523305, tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool))), _1523303), c_COMBB(tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool)), tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool), _1523305)), hAPP(hAPP(c_COMBB(tc_fun(_1523307, tc_HOL_Obool), tc_fun(tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool)), tc_fun(tc_prod(_1523307, _1523309), tc_HOL_Obool)), _1523303), c_Product__Type_OSigma(_1523307, _1523309)), _1523315))), hAPP(hAPP(c_COMBB(tc_fun(_1523309, tc_HOL_Obool), tc_fun(_1523307, tc_fun(_1523309, tc_HOL_Obool)), _1523305), c_COMBK(tc_fun(_1523309, tc_HOL_Obool), _1523307)), _1523317)))) = hAPP(hAPP(c_Product__Type_OSigma(_1523307, _1523309), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523303, tc_fun(_1523307, tc_HOL_Obool)), _1523311), _1523315)), hAPP(c_COMBK(tc_fun(_1523309, tc_HOL_Obool), _1523307), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1523305, tc_fun(_1523309, tc_HOL_Obool)), _1523313), _1523317))))], (16254 ^ _777864) ^ [_1056746, _1056748, _1056750] : [-(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, _1056746, _1056748)), _1056750), _1056748) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1056746), _1056750), _1056748))], (47660 ^ _777864) ^ [_1730681, _1730683, _1730685] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1730681)), -(c_List_Osublist(_1730683, hAPP(hAPP(c_List_Olist_OCons(_1730683), _1730685), c_List_Olist_ONil(_1730683)), _1730681) = hAPP(hAPP(c_List_Olist_OCons(_1730683), _1730685), c_List_Olist_ONil(_1730683)))], (14278 ^ _777864) ^ [_1019343, _1019345] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1019343, _1019345)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019343), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019345)))], (38136 ^ _777864) ^ [_1493499, _1493501] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1493499), c_Orderings_Otop__class_Otop(tc_fun(_1493499, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493501), c_Orderings_Otop__class_Otop(tc_fun(_1493501, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1493499, _1493501)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1493499, _1493501), tc_HOL_Obool)))))], (18418 ^ _777864) ^ [_1094618, _1094620] : [_1094618 = _1094620, -(c_Int_OBit1(_1094618) = c_Int_OBit1(_1094620))], (44210 ^ _777864) ^ [_1645662] : [-(c_Relation_Orefl__on(_1645662, c_Orderings_Otop__class_Otop(tc_fun(_1645662, tc_HOL_Obool)), c_Relation_OId(_1645662)))], (26455 ^ _777864) ^ [_1243938, _1243940, _1243942] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243938), _1243942))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243938, _1243940) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243942, _1243940))], (44722 ^ _777864) ^ [_1657853, _1657855, _1657857] : [class_Complete__Lattice_Ocomplete__lattice(_1657853), -(c_Complete__Lattice_OInf__class_OInf(_1657853, hAPP(hAPP(c_Set_Oinsert(_1657853), _1657855), hAPP(hAPP(c_Set_Oinsert(_1657853), _1657857), c_Orderings_Obot__class_Obot(tc_fun(_1657853, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1657853), _1657855), _1657857))], (48079 ^ _777864) ^ [_1740807, _1740809, _1740811] : [hAPP(hAPP(c_List_Oappend(_1740807), _1740809), _1740811) = _1740811, -(_1740809 = c_List_Olist_ONil(_1740807))], (8758 ^ _777864) ^ [_923349, _923351, _923353, _923355] : [class_Rings_Ocomm__semiring__1(_923349), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923349), _923351), _923353)), _923355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923349), _923351), _923355)), _923353))], (49349 ^ _777864) ^ [_1770761, _1770763, _1770765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1770761), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770763)), _1770765))), -(c_List_Obutlast(_1770763, hAPP(hAPP(c_List_Otake(_1770763), _1770761), _1770765)) = hAPP(hAPP(c_List_Otake(_1770763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1770761), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1770765))], (48580 ^ _777864) ^ [_1753923, _1753925, _1753927] : [-(hAPP(hAPP(c_List_Oappend(_1753923), hAPP(hAPP(c_List_Otake(_1753923), _1753925), _1753927)), hAPP(hAPP(c_List_Odrop(_1753923), _1753925), _1753927)) = _1753927)], (47750 ^ _777864) ^ [_1732344, _1732346, _1732348, _1732350, _1732352] : [-(_1732344 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1732346, _1732348, _1732350, _1732344), _1732352) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1732348), _1732346), tc_prod(_1732348, _1732346), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732348), _1732346), c_List_Olist_ONil(_1732348)), _1732352), hAPP(c_Product__Type_Oprod_Oprod__case(_1732348, _1732346, tc_prod(tc_List_Olist(_1732348), _1732346)), hAPP(hAPP(c_COMBC(_1732348, tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346)), tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1732348), _1732346), tc_prod(tc_List_Olist(_1732348), _1732346)), tc_fun(tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346)), tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346))), _1732348), c_COMBB(tc_prod(tc_List_Olist(_1732348), _1732346), tc_prod(tc_List_Olist(_1732348), _1732346), _1732346)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1732348), tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346))), tc_fun(tc_prod(tc_List_Olist(_1732348), _1732346), tc_prod(tc_List_Olist(_1732348), _1732346)), _1732348), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1732348), _1732346, tc_prod(tc_List_Olist(_1732348), _1732346))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1732348), tc_List_Olist(_1732348)), tc_fun(tc_List_Olist(_1732348), tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346))), _1732348), hAPP(c_COMBB(tc_List_Olist(_1732348), tc_fun(_1732346, tc_prod(tc_List_Olist(_1732348), _1732346)), tc_List_Olist(_1732348)), c_Product__Type_OPair(tc_List_Olist(_1732348), _1732346))), c_List_Olist_OCons(_1732348))))), c_Lazy__Sequence_Oanamorph(_1732346, _1732348, _1732350, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1732344), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1732350, _1732352)))], (440 ^ _777864) ^ [_784640, _784642, _784644, _784646] : [-(c_Predicate_Oreflp(_784644, _784640)), c_Predicate_Oreflp(_784646, _784642), _784646 = _784644, _784642 = _784640], (10041 ^ _777864) ^ [_945703, _945705] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945703), _945705) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945705), _945703))], (23299 ^ _777864) ^ [_1183875, _1183877, _1183879] : [-(hAPP(c_Product__Type_Ofst(_1183875, _1183877), _1183879) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183875, _1183877, _1183875), c_COMBK(_1183875, _1183877)), _1183879))], (29914 ^ _777864) ^ [_1321439, _1321441, _1321443, _1321445] : [class_Lattices_Odistrib__lattice(_1321439), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321439), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321439), _1321441), _1321443)), _1321445) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321439), _1321441), _1321445)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321439), _1321443), _1321445)))], (17048 ^ _777864) ^ [_1071762, _1071764] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071762)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1071764)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071762), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1071764))))], (36040 ^ _777864) ^ [_1448689, _1448691] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1448689), _1448691)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1448691), _1448689)))], (17454 ^ _777864) ^ [_1079253, _1079255, _1079257] : [class_Rings_Olinordered__semidom(_1079253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079253), c_Groups_Ozero__class_Ozero(_1079253)), _1079255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079253), _1079255), c_Groups_Oone__class_Oone(_1079253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079253), _1079255), hAPP(hAPP(c_Power_Opower__class_Opower(_1079253), _1079255), _1079257))), hAPP(hAPP(c_Power_Opower__class_Opower(_1079253), _1079255), _1079257))))], (2112 ^ _777864) ^ [_808736, _808738, _808740, _808742, _808744, _808746, _808748, _808750] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808750, _808746, _808742, _808738) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_808748, _808744, _808740, _808736)), _808750 = _808748, _808746 = _808744, _808742 = _808740, _808738 = _808736], (36434 ^ _777864) ^ [_1456235, _1456237, _1456239] : [class_Orderings_Oorder(_1456235), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456235, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1456235), _1456237)), c_SetInterval_Oord__class_OatLeastAtMost(_1456235, _1456237, _1456239)) = c_Orderings_Obot__class_Obot(tc_fun(_1456235, tc_HOL_Obool)))], (47526 ^ _777864) ^ [_1728077] : [-(hBOOL(hAPP(c_List_Odistinct(_1728077), c_List_Olist_ONil(_1728077))))], (42528 ^ _777864) ^ [_1604607, _1604609, _1604611] : [c_Wellfounded_Owf(_1604607, _1604609), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604607, _1604607)), hAPP(hAPP(c_Product__Type_OPair(_1604607, _1604607), hAPP(_1604611, hAPP(c_Nat_OSuc, 42531 ^ [_1604607, _1604609, _1604611]))), hAPP(_1604611, 42531 ^ [_1604607, _1604609, _1604611]))), _1604609))], (18460 ^ _777864) ^ [_1095389, _1095391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1095389)), c_Int_OBit1(_1095391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095389), _1095391)))], (17808 ^ _777864) ^ [_1084845] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084845))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1084845)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7182 ^ _777864) ^ [_895953, _895955, _895957, _895959, _895961] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895953), _895955), _895957)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895959), _895957), _895961)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_895953, _895959)), _895955), _895961)))], (44348 ^ _777864) ^ [_1648940, _1648942, _1648944, _1648946, _1648948] : [c_Relation_Osingle__valued(_1648940, _1648942, hAPP(c_Relation_Oconverse(_1648942, _1648940), _1648944)), -(hAPP(c_Relation_OImage(_1648942, _1648940, _1648944), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648942, tc_HOL_Obool)), _1648946), _1648948)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1648940, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1648942, _1648940, _1648944), _1648946)), hAPP(c_Relation_OImage(_1648942, _1648940, _1648944), _1648948)))], (12017 ^ _777864) ^ [_979036, _979038] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _979036), hAPP(c_Nat_OSuc, _979038)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _979036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _979036), _979038)))], (45346 ^ _777864) ^ [_1672871, _1672873, _1672875, _1672877, _1672879, _1672881, _1672883, _1672885] : [c_Finite__Set_Ofolding__image__simple__idem(_1672871, _1672873, _1672875, _1672877, _1672879, _1672881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1672873), _1672883)), hBOOL(hAPP(hAPP(c_member(_1672873), _1672885), _1672883)), -(hAPP(hAPP(_1672875, hAPP(_1672879, _1672885)), hAPP(_1672881, _1672883)) = hAPP(_1672881, _1672883))], (45805 ^ _777864) ^ [_1683643] : [-(hAPP(c_Option_Omap(_1683643, _1683643), c_Fun_Oid(_1683643)) = c_Fun_Oid(tc_Option_Ooption(_1683643)))], (34667 ^ _777864) ^ [_1421589, _1421591, _1421593] : [class_Orderings_Oorder(_1421589), _1421591 = _1421593, -(c_SetInterval_Oord__class_OatLeastAtMost(_1421589, _1421591, _1421593) = hAPP(hAPP(c_Set_Oinsert(_1421589), _1421591), c_Orderings_Obot__class_Obot(tc_fun(_1421589, tc_HOL_Obool))))], (24379 ^ _777864) ^ [_1204765, _1204767, _1204769] : [-(c_Nitpick_Oplus__frac(_1204765, _1204767, _1204769) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1204765), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1204765), _1204767), hAPP(c_Nitpick_Odenom(_1204765), _1204769))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1204765), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1204765), tc_Int_Oint), c_Nitpick_Ofrac(_1204765)), 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(_1204765), _1204767))), 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(_1204765), _1204767))))), 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(_1204765), _1204769))), 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(_1204765), _1204769)))))), c_COMBI(tc_Int_Oint))))], (33432 ^ _777864) ^ [_1392363, _1392365, _1392367, _1392369] : [class_Orderings_Oorder(_1392363), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392363, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392363, _1392365, _1392367)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392363, _1392367, _1392369)) = c_Orderings_Obot__class_Obot(tc_fun(_1392363, tc_HOL_Obool)))], (5816 ^ _777864) ^ [_873307, _873309, _873311, _873313, _873315, _873317] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_873307, _873309, _873311, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873307), _873313), _873315), _873317)) = hAPP(hAPP(hAPP(_873311, _873313), _873315), _873317))], (40937 ^ _777864) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (31927 ^ _777864) ^ [_1361442, _1361444] : [class_Orderings_Olinorder(_1361442), -(c_Big__Operators_Olattice_OInf__fin(_1361442, c_Orderings_Oord__class_Omin(_1361442), hAPP(hAPP(c_Set_Oinsert(_1361442), _1361444), c_Orderings_Obot__class_Obot(tc_fun(_1361442, tc_HOL_Obool)))) = _1361444)], (21868 ^ _777864) ^ [_1156107] : [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), _1156107))), 21871 ^ _777864 : [(21878 ^ _777864) ^ [] : [-(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), _1156107))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156107)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156107)), 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), _1156107)))))], (21872 ^ _777864) ^ [] : [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), _1156107)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156107)) = 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), _1156107))))]]], (48772 ^ _777864) ^ [_1758170, _1758172, _1758174] : [-(hAPP(hAPP(c_List_Odrop(_1758170), hAPP(c_Nat_OSuc, _1758172)), _1758174) = hAPP(hAPP(c_List_Odrop(_1758170), _1758172), hAPP(c_List_Otl(_1758170), _1758174)))], (51075 ^ _777864) ^ [_1807699, _1807701] : [-(class_Finite__Set_Ofinite(tc_fun(_1807699, _1807701))), class_Finite__Set_Ofinite(_1807699), class_Finite__Set_Ofinite(_1807701)], (46144 ^ _777864) ^ [_1691088, _1691090] : [-(hAPP(hAPP(c_List_Ozip(_1691088, _1691088), _1691090), _1691090) = hAPP(hAPP(c_List_Omap(_1691088, tc_prod(_1691088, _1691088)), hAPP(hAPP(c_COMBS(_1691088, _1691088, tc_prod(_1691088, _1691088)), c_Product__Type_OPair(_1691088, _1691088)), c_COMBI(_1691088))), _1691090))], (16168 ^ _777864) ^ [_1055096] : [class_Groups_Oordered__ab__group__add__abs(_1055096), -(hAPP(c_Groups_Oabs__class_Oabs(_1055096), c_Groups_Ozero__class_Ozero(_1055096)) = c_Groups_Ozero__class_Ozero(_1055096))], (51205 ^ _777864) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (45797 ^ _777864) ^ [_1683401, _1683403, _1683405, _1683407, _1683409] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1683401), tc_Option_Ooption(_1683403), tc_Option_Ooption(_1683405), hAPP(c_Option_Omap(_1683401, _1683403), _1683407)), hAPP(c_Option_Omap(_1683405, _1683401), _1683409)) = hAPP(c_Option_Omap(_1683405, _1683403), hAPP(c_Fun_Ocomp(_1683401, _1683403, _1683405, _1683407), _1683409)))], (16678 ^ _777864) ^ [_1064865, _1064867] : [class_Int_Onumber__ring(_1064865), -(hAPP(c_Int_Onumber__class_Onumber__of(_1064865), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1064867)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064865), hAPP(c_Int_Onumber__class_Onumber__of(_1064865), _1064867)))], (22378 ^ _777864) ^ [_1164780] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1164780)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1164780)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6222 ^ _777864) ^ [_880252, _880254, _880256, _880258] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_880252), 6225 ^ _777864 : [(6232 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880252), _880256), _880258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880252), _880254), _880256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880252), _880254), _880258))))], (6226 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880252), _880254), _880256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_880252), _880254), _880258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_880252), _880256), _880258)))]]], (8734 ^ _777864) ^ [_922723, _922725] : [class_Groups_Ogroup__add(_922723), -(hAPP(c_Groups_Ouminus__class_Ouminus(_922723), hAPP(c_Groups_Ouminus__class_Ouminus(_922723), _922725)) = _922725)], (50748 ^ _777864) ^ [_1801764, _1801766, _1801768] : [50750 ^ _777864 : [(50753 ^ _777864) ^ [] : [hBOOL(hAPP(_1801766, 50749 ^ [_1801764, _1801766, _1801768]))], (50751 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801764), 50749 ^ [_1801764, _1801766, _1801768]), hAPP(c_List_Oset(_1801764), _1801768))))]], -(c_List_OtakeWhile(_1801764, _1801766, _1801768) = _1801768)], (18668 ^ _777864) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (38569 ^ _777864) ^ [_1503277, _1503279, _1503281, _1503283] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503277, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 38570 ^ [_1503277, _1503279, _1503281, _1503283])), _1503279) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503277, 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), 38570 ^ [_1503277, _1503279, _1503281, _1503283]), _1503281))), _1503283), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503277, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1503279) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1503277, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1503283))], (35802 ^ _777864) ^ [_1443632, _1443634, _1443636, _1443638, _1443640] : [class_Orderings_Olinorder(_1443632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443632, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443632, _1443634), _1443636)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443632, _1443638), _1443640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443632), _1443636), _1443634))), 35813 ^ _777864 : [(35816 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443632), _1443636), _1443640)))], (35814 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443632), _1443638), _1443634)))]]], (32445 ^ _777864) ^ [_1371217, _1371219, _1371221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371217), _1371219)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371217), _1371221)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1371217), _1371219)), hAPP(c_Finite__Set_Ocard(_1371217), _1371221)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1371217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1371217, tc_HOL_Obool)), _1371219), _1371221))), hAPP(c_Finite__Set_Ocard(_1371217), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371217, tc_HOL_Obool)), _1371219), _1371221))))], (18196 ^ _777864) ^ [_1090914, _1090916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090914)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090914), _1090916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090914), c_Int_OPls)))], (43475 ^ _777864) ^ [_1625170, _1625172, _1625174, _1625176, _1625178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625170, _1625170)), hAPP(hAPP(c_Product__Type_OPair(_1625170, _1625170), _1625172), _1625174)), c_Transitive__Closure_Ortrancl(_1625170, _1625176))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1625170, _1625170), tc_HOL_Obool)), _1625176), hAPP(hAPP(c_Product__Type_OSigma(_1625170, _1625170), _1625178), hAPP(c_COMBK(tc_fun(_1625170, tc_HOL_Obool), _1625170), _1625178)))), -(_1625172 = _1625174), -(hBOOL(hAPP(hAPP(c_member(_1625170), _1625172), _1625178)))], (23283 ^ _777864) ^ [_1183398, _1183400, _1183402, _1183404, _1183406, _1183408, _1183410, _1183412] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183398, _1183400, _1183402), _1183404), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183406, _1183408, tc_prod(_1183398, _1183400)), _1183410), _1183412)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1183406, _1183408, _1183402), hAPP(hAPP(c_COMBB(tc_fun(_1183408, tc_prod(_1183398, _1183400)), tc_fun(_1183408, _1183402), _1183406), hAPP(c_COMBB(tc_prod(_1183398, _1183400), _1183402, _1183408), hAPP(c_Product__Type_Oprod_Oprod__case(_1183398, _1183400, _1183402), _1183404))), _1183410)), _1183412))], (27572 ^ _777864) ^ [_1268856, _1268858] : [class_Rings_Oring__1(_1268856), -(hBOOL(hAPP(hAPP(c_member(_1268856), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1268856), _1268858)), c_Int_Oring__1__class_OInts(_1268856))))], (44546 ^ _777864) ^ [_1654080, _1654082, _1654084, _1654086, _1654088] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654080, _1654080)), hAPP(hAPP(c_Product__Type_OPair(_1654080, _1654080), _1654082), _1654084)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1654080, _1654080), tc_HOL_Obool), _1654086), _1654088))), 44551 ^ _777864 : [(44554 ^ _777864) ^ [] : [-(_1654082 = _1654084)], (44552 ^ _777864) ^ [] : [-(_1654086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 44557 ^ _777864 : [(44562 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654080, _1654080)), hAPP(hAPP(c_Product__Type_OPair(_1654080, _1654080), 44555 ^ [_1654080, _1654082, _1654084, _1654086, _1654088]), _1654084)), _1654088)))], (44560 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654080, _1654080)), hAPP(hAPP(c_Product__Type_OPair(_1654080, _1654080), _1654082), 44555 ^ [_1654080, _1654082, _1654084, _1654086, _1654088])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1654080, _1654080), tc_HOL_Obool), 44556 ^ [_1654080, _1654082, _1654084, _1654086, _1654088]), _1654088))))], (44558 ^ _777864) ^ [] : [-(_1654086 = hAPP(c_Nat_OSuc, 44556 ^ [_1654080, _1654082, _1654084, _1654086, _1654088]))]]], (45834 ^ _777864) ^ [_1684327, _1684329, _1684331, _1684333] : [hAPP(hAPP(c_Option_Omap(_1684327, _1684329), _1684331), _1684333) = c_Option_Ooption_ONone(_1684329), -(_1684333 = c_Option_Ooption_ONone(_1684327))], (51129 ^ _777864) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (30741 ^ _777864) ^ [_1340069, _1340071, _1340073] : [class_Lattices_Olattice(_1340069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340069), _1340071)), hBOOL(hAPP(hAPP(c_member(_1340069), _1340073), _1340071)), 30752 ^ _777864 : [(30759 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340069, tc_HOL_Obool)), _1340071), hAPP(hAPP(c_Set_Oinsert(_1340069), _1340073), c_Orderings_Obot__class_Obot(tc_fun(_1340069, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340069, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1340069, _1340071) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1340069), _1340073), c_Big__Operators_Olattice__class_OSup__fin(_1340069, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340069, tc_HOL_Obool)), _1340071), hAPP(hAPP(c_Set_Oinsert(_1340069), _1340073), c_Orderings_Obot__class_Obot(tc_fun(_1340069, tc_HOL_Obool)))))))], (30753 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340069, tc_HOL_Obool)), _1340071), hAPP(hAPP(c_Set_Oinsert(_1340069), _1340073), c_Orderings_Obot__class_Obot(tc_fun(_1340069, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340069, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1340069, _1340071) = _1340073)]]], (17846 ^ _777864) ^ [_1085402, _1085404] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1085402))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1085402)), _1085404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1085404))], (48540 ^ _777864) ^ [_1752981, _1752983, _1752985, _1752987, _1752989] : [-(hAPP(hAPP(c_List_Odrop(_1752981), _1752983), hAPP(hAPP(c_List_Omap(_1752985, _1752981), _1752987), _1752989)) = hAPP(hAPP(c_List_Omap(_1752985, _1752981), _1752987), hAPP(hAPP(c_List_Odrop(_1752985), _1752983), _1752989)))], (23803 ^ _777864) ^ [_1193856, _1193858, _1193860, _1193862] : [class_Orderings_Olinorder(_1193856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193856), _1193858), _1193860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193856), _1193858), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1193856), _1193862), _1193860))))], (43975 ^ _777864) ^ [_1639048, _1639050, _1639052, _1639054, _1639056] : [_1639048 = c_Orderings_Obot__class_Obot(tc_fun(_1639050, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639050, tc_fun(_1639052, tc_HOL_Obool)), _1639048), hAPP(hAPP(c_COMBC(_1639050, tc_fun(_1639052, tc_HOL_Obool), tc_fun(_1639052, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639052, tc_HOL_Obool), tc_fun(tc_fun(_1639052, tc_HOL_Obool), tc_fun(_1639052, tc_HOL_Obool)), _1639050), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639052, tc_HOL_Obool))), _1639054)), _1639056)) = c_Orderings_Otop__class_Otop(tc_fun(_1639052, tc_HOL_Obool)))], (48478 ^ _777864) ^ [_1751500, _1751502] : [-(hAPP(c_List_Orotate1(_1751500), _1751502) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1751500), _1751500, c_List_Olist_ONil(_1751500), hAPP(hAPP(c_COMBB(tc_List_Olist(_1751500), tc_fun(tc_List_Olist(_1751500), tc_List_Olist(_1751500)), _1751500), hAPP(c_COMBC(tc_List_Olist(_1751500), tc_List_Olist(_1751500), tc_List_Olist(_1751500)), c_List_Oappend(_1751500))), hAPP(hAPP(c_COMBC(_1751500, tc_List_Olist(_1751500), tc_List_Olist(_1751500)), c_List_Olist_OCons(_1751500)), c_List_Olist_ONil(_1751500)))), _1751502))], (7096 ^ _777864) ^ [_894402, _894404] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_894402, _894404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _894402)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _894404))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51521 ^ _777864) ^ [_1812065, _1812067] : [-(hAPP(c_COMBI(_1812065), _1812067) = _1812067)], (24275 ^ _777864) ^ [_1202870, _1202872] : [class_Orderings_Olinorder(_1202870), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1202870), _1202872), _1202872) = _1202872)], (5134 ^ _777864) ^ [_856459, _856461] : [_856461 = _856459, -(c_Orderings_Oord__class_Oless(_856461) = c_Orderings_Oord__class_Oless(_856459))], (40188 ^ _777864) ^ [_1540830, _1540832] : [-(hBOOL(hAPP(_1540832, 40189 ^ [_1540830, _1540832]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1540830, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1540830), _1540832))], (24529 ^ _777864) ^ [_1208340, _1208342, _1208344] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1208340, _1208342, _1208344, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1208342)], (35758 ^ _777864) ^ [_1442969, _1442971] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442969), _1442971)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1442969)), hAPP(c_Nat_OSuc, _1442971)))], (6496 ^ _777864) ^ [_885185, _885187] : [class_Groups_Olinordered__ab__group__add(_885185), 6499 ^ _777864 : [(6506 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885185), c_Groups_Ozero__class_Ozero(_885185)), _885187)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885185), c_Groups_Ozero__class_Ozero(_885185)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_885185), _885187), _885187))))], (6500 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885185), c_Groups_Ozero__class_Ozero(_885185)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_885185), _885187), _885187))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_885185), c_Groups_Ozero__class_Ozero(_885185)), _885187)))]]], (38182 ^ _777864) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (39125 ^ _777864) ^ [_1516478, _1516480, _1516482, _1516484, _1516486] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1516478, _1516480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1516478, tc_HOL_Obool)), _1516482), _1516484)), hAPP(c_COMBK(tc_fun(_1516480, tc_HOL_Obool), _1516478), _1516486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1516478, _1516480), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1516478, _1516480), _1516482), hAPP(c_COMBK(tc_fun(_1516480, tc_HOL_Obool), _1516478), _1516486))), hAPP(hAPP(c_Product__Type_OSigma(_1516478, _1516480), _1516484), hAPP(c_COMBK(tc_fun(_1516480, tc_HOL_Obool), _1516478), _1516486))))], (42647 ^ _777864) ^ [_1607161, _1607163, _1607165, _1607167] : [class_Lattices_Osemilattice__inf(_1607161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607161), _1607163)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1607161, _1607161, c_Lattices_Osemilattice__inf__class_Oinf(_1607161)), _1607165), hAPP(hAPP(c_Set_Oinsert(_1607161), _1607167), _1607163)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1607161), _1607167), hAPP(hAPP(c_Finite__Set_Ofold(_1607161, _1607161, c_Lattices_Osemilattice__inf__class_Oinf(_1607161)), _1607165), _1607163)))], (24471 ^ _777864) ^ [_1206633, _1206635, _1206637] : [c_Nitpick_Oless__eq__frac(_1206633, _1206635, _1206637), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1206633), c_Nitpick_Oplus__frac(_1206633, _1206635, c_Nitpick_Ouminus__frac(_1206633, _1206637)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15882 ^ _777864) ^ [_1049999, _1050001] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1049999, _1050001) = 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), _1049999), _1050001) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17316 ^ _777864) ^ [_1076643, _1076645, _1076647, _1076649] : [class_Rings_Olinordered__semidom(_1076643), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076643), hAPP(hAPP(c_Power_Opower__class_Opower(_1076643), _1076645), hAPP(c_Nat_OSuc, _1076647))), hAPP(hAPP(c_Power_Opower__class_Opower(_1076643), _1076649), hAPP(c_Nat_OSuc, _1076647)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076643), c_Groups_Ozero__class_Ozero(_1076643)), _1076649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076643), _1076645), _1076649)))], (51365 ^ _777864) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (45529 ^ _777864) ^ [_1676728, _1676730, _1676732, _1676734] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1676728, tc_HOL_Obool)), c_Map_Odom(_1676728, _1676730, _1676732)), c_Map_Odom(_1676728, _1676730, _1676734)) = c_Orderings_Obot__class_Obot(tc_fun(_1676728, tc_HOL_Obool)), -(c_Map_Omap__add(_1676728, _1676730, _1676732, _1676734) = c_Map_Omap__add(_1676728, _1676730, _1676734, _1676732))], (17638 ^ _777864) ^ [_1082071] : [class_Int_Onumber__ring(_1082071), -(hAPP(c_Int_Onumber__class_Onumber__of(_1082071), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1082071), c_Groups_Oone__class_Oone(_1082071)))], (18950 ^ _777864) ^ [_1103588] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1103588)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1103588)))], (47224 ^ _777864) ^ [_1720733, _1720735, _1720737, _1720739] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1720733), tc_List_Olist(_1720733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720733), tc_List_Olist(_1720733)), _1720735), _1720737)), c_List_Olex(_1720733, _1720739)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1720733), tc_List_Olist(_1720733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1720733), tc_List_Olist(_1720733)), _1720735), _1720737)), c_List_Olexord(_1720733, _1720739))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720733)), _1720735) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720733)), _1720737)], (7560 ^ _777864) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47050 ^ _777864) ^ [_1716472, _1716474, _1716476] : [47052 ^ _777864 : [(47055 ^ _777864) ^ [] : [hBOOL(hAPP(_1716476, 47051 ^ [_1716472, _1716474, _1716476]))], (47053 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1716472), 47051 ^ [_1716472, _1716474, _1716476]), hAPP(c_List_Oset(_1716472), _1716474))))]], 47056 ^ _777864 : [(47057 ^ _777864) ^ [_1716656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1716656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716472)), _1716474))), -(hBOOL(hAPP(_1716476, hAPP(hAPP(c_List_Onth(_1716472), _1716474), _1716656))))]]], (6004 ^ _777864) ^ [_876571, _876573, _876575, _876577, _876579] : [c_Com_Ocom_OAss(_876571, _876573) = c_Com_Ocom_OCall(_876575, _876577, _876579)], (3890 ^ _777864) ^ [_837089, _837091] : [_837091 = _837089, -(c_Relation_OId(_837091) = c_Relation_OId(_837089))], (26091 ^ _777864) ^ [_1236181, _1236183, _1236185] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236181), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236183), _1236185))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236181), _1236185)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1236181), _1236183)))], (49992 ^ _777864) ^ [_1784498, _1784500] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1784498), _1784500) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1784498, _1784500)))], (782 ^ _777864) ^ [_789887, _789889, _789891, _789893, _789895, _789897, _789899, _789901, _789903, _789905, _789907, _789909] : [-(c_Finite__Set_Ofolding__image__simple__idem(_789907, _789903, _789899, _789895, _789891, _789887)), c_Finite__Set_Ofolding__image__simple__idem(_789909, _789905, _789901, _789897, _789893, _789889), _789909 = _789907, _789905 = _789903, _789901 = _789899, _789897 = _789895, _789893 = _789891, _789889 = _789887], (30803 ^ _777864) ^ [_1341267, _1341269] : [class_Orderings_Olinorder(_1341267), -(c_Big__Operators_Olinorder__class_OMax(_1341267, hAPP(hAPP(c_Set_Oinsert(_1341267), _1341269), c_Orderings_Obot__class_Obot(tc_fun(_1341267, tc_HOL_Obool)))) = _1341269)], (41701 ^ _777864) ^ [_1585605, _1585607, _1585609, _1585611, _1585613, _1585615] : [-(hAPP(c_Set_Ovimage(_1585605, tc_prod(_1585607, _1585609), _1585611), hAPP(hAPP(c_Product__Type_OSigma(_1585607, _1585609), _1585613), hAPP(c_COMBK(tc_fun(_1585609, tc_HOL_Obool), _1585607), _1585615))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1585605, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1585605, _1585607, hAPP(c_Fun_Ocomp(tc_prod(_1585607, _1585609), _1585607, _1585605, c_Product__Type_Ofst(_1585607, _1585609)), _1585611)), _1585613)), hAPP(c_Set_Ovimage(_1585605, _1585609, hAPP(c_Fun_Ocomp(tc_prod(_1585607, _1585609), _1585609, _1585605, c_Product__Type_Osnd(_1585607, _1585609)), _1585611)), _1585615)))], (20066 ^ _777864) ^ [_1123802, _1123804, _1123806] : [class_Fields_Olinordered__field__inverse__zero(_1123802), 20069 ^ _777864 : [(20084 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123802), _1123804), _1123806)), c_Groups_Ozero__class_Ozero(_1123802)))), 20085 ^ _777864 : [(20092 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), _1123804), c_Groups_Ozero__class_Ozero(_1123802))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), c_Groups_Ozero__class_Ozero(_1123802)), _1123806))], (20086 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), c_Groups_Ozero__class_Ozero(_1123802)), _1123804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), _1123806), c_Groups_Ozero__class_Ozero(_1123802)))]]], (20070 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1123802), _1123804), _1123806)), c_Groups_Ozero__class_Ozero(_1123802))), 20075 ^ _777864 : [(20078 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), _1123806), c_Groups_Ozero__class_Ozero(_1123802))))], (20076 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), c_Groups_Ozero__class_Ozero(_1123802)), _1123804)))]], 20079 ^ _777864 : [(20082 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), c_Groups_Ozero__class_Ozero(_1123802)), _1123806)))], (20080 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123802), _1123804), c_Groups_Ozero__class_Ozero(_1123802))))]]]]], (44415 ^ _777864) ^ [_1650640, _1650642, _1650644, _1650646] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650640, _1650640), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650642), _1650644)), _1650646) = hAPP(hAPP(c_Relation_Orel__comp(_1650640, _1650640, _1650640), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650640, _1650640), tc_HOL_Obool), _1650642), _1650646)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1650640, _1650640), tc_HOL_Obool), _1650644), _1650646)))], (16174 ^ _777864) ^ [_1055187, _1055189] : [class_Groups_Oordered__ab__group__add__abs(_1055187), 16177 ^ _777864 : [(16184 ^ _777864) ^ [] : [_1055189 = c_Groups_Ozero__class_Ozero(_1055187), -(hAPP(c_Groups_Oabs__class_Oabs(_1055187), _1055189) = c_Groups_Ozero__class_Ozero(_1055187))], (16178 ^ _777864) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1055187), _1055189) = c_Groups_Ozero__class_Ozero(_1055187), -(_1055189 = c_Groups_Ozero__class_Ozero(_1055187))]]], (48860 ^ _777864) ^ [_1760019, _1760021, _1760023] : [-(_1760019 = c_List_Olist_ONil(_1760021)), -(hAPP(hAPP(c_List_Otake(_1760021), hAPP(c_Nat_OSuc, _1760023)), _1760019) = hAPP(hAPP(c_List_Olist_OCons(_1760021), hAPP(c_List_Ohd(_1760021), _1760019)), hAPP(hAPP(c_List_Otake(_1760021), _1760023), hAPP(c_List_Otl(_1760021), _1760019))))], (14215 ^ _777864) ^ [_1018300, _1018302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14218 ^ _777864 : [(14225 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018302), _1018300)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14219 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1018302), _1018300)), 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)), _1018302)))]]], (27316 ^ _777864) ^ [_1263475, _1263477, _1263479, _1263481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1263475, _1263475)), hAPP(hAPP(c_Product__Type_OPair(_1263475, _1263475), _1263477), _1263479)), hAPP(c_Wellfounded_Omeasure(_1263475), _1263481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1263481, _1263477)), hAPP(_1263481, _1263479))))], (4434 ^ _777864) ^ [_845671, _845673, _845675, _845677, _845679, _845681] : [-(c_Big__Operators_Olattice_OInf__fin(_845681, _845677, _845673) = c_Big__Operators_Olattice_OInf__fin(_845679, _845675, _845671)), _845681 = _845679, _845677 = _845675, _845673 = _845671], (42888 ^ _777864) ^ [_1612024, _1612026, _1612028] : [class_Groups_Oab__semigroup__mult(_1612024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612024), _1612026)), -(hBOOL(hAPP(hAPP(c_member(_1612024), _1612028), _1612026))), -(hAPP(c_Finite__Set_Ofold1(_1612024, c_Groups_Otimes__class_Otimes(_1612024)), hAPP(hAPP(c_Set_Oinsert(_1612024), _1612028), _1612026)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612024, _1612024, c_Groups_Otimes__class_Otimes(_1612024)), _1612028), _1612026))], (5687 ^ _777864) ^ [_869618, _869620, _869622] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869618), _869620), _869622)), -(c_Natural_Oevaln(_869618, _869620, 5690 ^ [_869618, _869620, _869622], _869622))], (44686 ^ _777864) ^ [_1656972, _1656974, _1656976] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656972, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1656972, tc_HOL_Obool), tc_HOL_Obool)), _1656974), _1656976)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1656972, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656972, tc_HOL_Obool), _1656974)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656972, tc_HOL_Obool), _1656976)))], (19886 ^ _777864) ^ [_1120526, _1120528, _1120530, _1120532] : [class_Fields_Olinordered__field__inverse__zero(_1120526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120526), _1120528), _1120530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120526), _1120532), c_Groups_Ozero__class_Ozero(_1120526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120526), _1120530), _1120532)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1120526), _1120528), _1120532))))], (24149 ^ _777864) ^ [_1200537, _1200539, _1200541] : [class_Int_Onumber(_1200537), class_Orderings_Oord(_1200537), 24156 ^ _777864 : [(24163 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200537), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200539)), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200541)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200537), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200539)), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200541)) = hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200539))], (24157 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200537), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200539)), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200541))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1200537), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200539)), hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200541)) = hAPP(c_Int_Onumber__class_Onumber__of(_1200537), _1200541))]]], (48288 ^ _777864) ^ [_1745662, _1745664] : [-(c_List_Olistrel(_1745662, c_Transitive__Closure_Ortrancl(_1745662, _1745664)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1745662), c_List_Olistrel1(_1745662, _1745664)))], (22478 ^ _777864) ^ [_1166429] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1166429)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1166429)], (30330 ^ _777864) ^ [_1330829, _1330831, _1330833, _1330835] : [hBOOL(hAPP(hAPP(c_member(_1330829), _1330831), _1330833)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1330829, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1330829, _1330829, _1330835), hAPP(hAPP(c_Set_Oinsert(_1330829), _1330831), c_Orderings_Obot__class_Obot(tc_fun(_1330829, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1330829), _1330833), _1330835))))], (51341 ^ _777864) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (46102 ^ _777864) ^ [_1690223, _1690225, _1690227, _1690229] : [-(c_List_Oremove1(_1690223, _1690225, c_List_Oremove1(_1690223, _1690227, _1690229)) = c_List_Oremove1(_1690223, _1690227, c_List_Oremove1(_1690223, _1690225, _1690229)))], (15614 ^ _777864) ^ [_1043875] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1043875)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1043875)], (7417 ^ _777864) ^ [_900163, _900165, _900167, _900169, _900171] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_900163, _900165), _900167, _900169, _900171)), 7418 ^ _777864 : [(7419 ^ _777864) ^ [_900218] : [c_Natural_Oevaln(_900163, _900167, _900169, _900218), c_Natural_Oevaln(_900165, _900218, _900169, _900171)]]], (15182 ^ _777864) ^ [_1035461, _1035463, _1035465] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035461), _1035463)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035461), _1035465)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1035463), _1035465))], (15794 ^ _777864) ^ [_1047923, _1047925, _1047927, _1047929, _1047931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047923), _1047925)), 15797 ^ _777864 : [(15804 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047925), _1047923)), _1047927)), _1047929)), _1047931)), -(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), _1047925), _1047927)), _1047929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047923), _1047927)), _1047931))))], (15798 ^ _777864) ^ [] : [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), _1047925), _1047927)), _1047929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047923), _1047927)), _1047931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047925), _1047923)), _1047927)), _1047929)), _1047931)))]]], (29730 ^ _777864) ^ [_1317622, _1317624, _1317626] : [class_Lattices_Osemilattice__inf(_1317622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317622), _1317624), _1317626)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317622), _1317624), _1317626) = _1317624)], (48640 ^ _777864) ^ [_1755389, _1755391, _1755393, _1755395, _1755397] : [-(hAPP(hAPP(c_List_Oappend(_1755389), _1755391), _1755393) = hAPP(hAPP(c_List_Oappend(_1755389), _1755395), _1755397)), 48643 ^ _777864 : [(48646 ^ _777864) ^ [] : [_1755391 = hAPP(hAPP(c_List_Otake(_1755389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755391)), _1755395), _1755393 = hAPP(hAPP(c_List_Oappend(_1755389), hAPP(hAPP(c_List_Odrop(_1755389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755391)), _1755395)), _1755397)], (48644 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755391)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755395))))]], 48651 ^ _777864 : [(48654 ^ _777864) ^ [] : [hAPP(hAPP(c_List_Otake(_1755389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755395)), _1755391) = _1755395, hAPP(hAPP(c_List_Oappend(_1755389), hAPP(hAPP(c_List_Odrop(_1755389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755395)), _1755391)), _1755393) = _1755397], (48652 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755391)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755389)), _1755395)))]]], (51517 ^ _777864) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (26975 ^ _777864) ^ [_1254299, _1254301, _1254303] : [hBOOL(hAPP(hAPP(c_member(_1254299), _1254301), _1254303)), -(hBOOL(hAPP(_1254303, _1254301)))], (24139 ^ _777864) ^ [_1200277, _1200279, _1200281, _1200283, _1200285, _1200287] : [hAPP(_1200283, hAPP(c_Product__Type_Ofst(_1200277, _1200281), _1200285)) = hAPP(_1200287, hAPP(c_Product__Type_Ofst(_1200277, _1200281), _1200285)), -(hAPP(c_Product__Type_Oapfst(_1200277, _1200279, _1200281, _1200283), _1200285) = hAPP(c_Product__Type_Oapfst(_1200277, _1200279, _1200281, _1200287), _1200285))], (45477 ^ _777864) ^ [_1675717, _1675719, _1675721, _1675723, _1675725] : [-(hAPP(c_Map_Omap__add(_1675717, _1675719, _1675721, _1675723), _1675725) = c_Option_Ooption_ONone(_1675719)), hAPP(_1675723, _1675725) = c_Option_Ooption_ONone(_1675719), hAPP(_1675721, _1675725) = c_Option_Ooption_ONone(_1675719)], (51543 ^ _777864) ^ [] : [hBOOL(c_fFalse)], (22184 ^ _777864) ^ [_1161500] : [-(_1161500 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1161500), 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)))))], (49978 ^ _777864) ^ [_1784288] : [-(c_List_Oupt(_1784288, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (6639 ^ _777864) ^ [_887423, _887425] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887423)), _887425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _887423), hAPP(c_Nat_OSuc, _887425)))], (25245 ^ _777864) ^ [_1220663, _1220665] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220663), _1220665))), 25246 ^ _777864 : [(25247 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220663), _1220665)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1220665), _1220663)))], (25253 ^ _777864) ^ [] : [_1220663 = _1220665]]], (50380 ^ _777864) ^ [_1792483, _1792485, _1792487] : [-(hAPP(c_List_Orev(_1792483), hAPP(hAPP(c_List_Olist_OCons(_1792483), _1792485), _1792487)) = hAPP(hAPP(c_List_Oappend(_1792483), hAPP(c_List_Orev(_1792483), _1792487)), hAPP(hAPP(c_List_Olist_OCons(_1792483), _1792485), c_List_Olist_ONil(_1792483))))], (6024 ^ _777864) ^ [_877004, _877006, _877008] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _877004))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_877006, _877004, _877008))))], (42958 ^ _777864) ^ [_1613104, _1613106, _1613108] : [class_Orderings_Olinorder(_1613104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613104), _1613106)), -(hBOOL(hAPP(hAPP(c_member(_1613104), _1613108), _1613106))), -(c_Big__Operators_Olattice_OInf__fin(_1613104, c_Orderings_Oord__class_Omin(_1613104), hAPP(hAPP(c_Set_Oinsert(_1613104), _1613108), _1613106)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613104, _1613104, c_Orderings_Oord__class_Omin(_1613104)), _1613108), _1613106))], (29720 ^ _777864) ^ [_1317443, _1317445, _1317447, _1317449] : [class_Lattices_Osemilattice__inf(_1317443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317443), _1317445), _1317447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317443), _1317449), _1317445)), _1317447)))], (23011 ^ _777864) ^ [_1176897, _1176899] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1176897, _1176899), c_Divides_Odivmod__nat(_1176897, _1176899))))], (40124 ^ _777864) ^ [_1539381, _1539383, _1539385, _1539387] : [-(hAPP(c_Set_Ovimage(_1539381, _1539383, _1539385), hAPP(c_Set_OCollect(_1539383), _1539387)) = hAPP(c_Set_OCollect(_1539381), hAPP(hAPP(c_COMBB(_1539383, tc_HOL_Obool, _1539381), _1539387), _1539385)))], (51109 ^ _777864) ^ [_1808144, _1808146] : [class_Orderings_Obot(_1808144), -(class_Orderings_Obot(tc_fun(_1808146, _1808144)))], (13539 ^ _777864) ^ [_1005862, _1005864, _1005866] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005862), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005864, _1005866)), _1005866) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005862), _1005864), _1005866))], (30086 ^ _777864) ^ [_1325208, _1325210] : [c_Nat__Transfer_Onat__set(_1325208), c_Nat__Transfer_Onat__set(_1325210), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1325208), _1325210)))], (7476 ^ _777864) ^ [_901253, _901255, _901257] : [hAPP(c_Com_Ocom_OBODY, _901253) = c_Com_Ocom_OSemi(_901255, _901257)], (26701 ^ _777864) ^ [_1249163, _1249165] : [class_Orderings_Oorder(_1249163), 26708 ^ _777864 : [(26713 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249163), hAPP(_1249165, 26706 ^ [_1249163, _1249165])), hAPP(_1249165, 26707 ^ [_1249163, _1249165])))], (26711 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26707 ^ [_1249163, _1249165]), 26706 ^ [_1249163, _1249165]))], (26709 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 26706 ^ [_1249163, _1249165]), 26707 ^ [_1249163, _1249165])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1249163, 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)))), _1249165))], (22861 ^ _777864) ^ [_1173956, _1173958, _1173960] : [_1173958 = _1173960, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173956, tc_HOL_Obool)), _1173958) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1173956, tc_HOL_Obool)), _1173960))], (33054 ^ _777864) ^ [_1384047, _1384049, _1384051, _1384053, _1384055] : [class_Groups_Ocomm__monoid__mult(_1384047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384049), _1384051)), 33061 ^ _777864 : [(33068 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384049), _1384053), _1384051))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384049, _1384047), hAPP(hAPP(c_COMBC(_1384049, _1384047, _1384047), hAPP(hAPP(c_COMBS(_1384049, _1384047, tc_fun(_1384047, _1384047)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1384047, tc_fun(_1384047, _1384047)), _1384049), c_If(_1384047)), hAPP(hAPP(c_COMBC(_1384049, _1384049, tc_HOL_Obool), c_fequal), _1384053))), _1384055)), c_Groups_Oone__class_Oone(_1384047))), _1384051) = c_Groups_Oone__class_Oone(_1384047))], (33062 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1384049), _1384053), _1384051)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1384049, _1384047), hAPP(hAPP(c_COMBC(_1384049, _1384047, _1384047), hAPP(hAPP(c_COMBS(_1384049, _1384047, tc_fun(_1384047, _1384047)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1384047, tc_fun(_1384047, _1384047)), _1384049), c_If(_1384047)), hAPP(hAPP(c_COMBC(_1384049, _1384049, tc_HOL_Obool), c_fequal), _1384053))), _1384055)), c_Groups_Oone__class_Oone(_1384047))), _1384051) = hAPP(_1384055, _1384053))]]], (39844 ^ _777864) ^ [_1533080, _1533082, _1533084, _1533086, _1533088, _1533090, _1533092] : [-(hAPP(c_Product__Type_Ofst(_1533080, _1533082), hAPP(c_Product__Type_Omap__pair(_1533084, _1533080, _1533086, _1533082, _1533088, _1533090), _1533092)) = hAPP(_1533088, hAPP(c_Product__Type_Ofst(_1533084, _1533086), _1533092)))], (32151 ^ _777864) ^ [_1365450, _1365452, _1365454] : [class_Orderings_Olinorder(_1365450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365450), _1365452)), -(_1365452 = c_Orderings_Obot__class_Obot(tc_fun(_1365450, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365450), _1365454)), -(_1365454 = c_Orderings_Obot__class_Obot(tc_fun(_1365450, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365450, tc_HOL_Obool)), _1365452), _1365454) = c_Orderings_Obot__class_Obot(tc_fun(_1365450, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1365450, c_Orderings_Oord__class_Omin(_1365450), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365450, tc_HOL_Obool)), _1365452), _1365454)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365450), c_Big__Operators_Olattice_OInf__fin(_1365450, c_Orderings_Oord__class_Omin(_1365450), _1365452)), c_Big__Operators_Olattice_OInf__fin(_1365450, c_Orderings_Oord__class_Omin(_1365450), _1365454)))], (11693 ^ _777864) ^ [_973258, _973260, _973262] : [class_Rings_Oordered__cancel__semiring(_973258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973258), c_Groups_Ozero__class_Ozero(_973258)), _973260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973258), _973262), c_Groups_Ozero__class_Ozero(_973258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973258), _973260), _973262)), c_Groups_Ozero__class_Ozero(_973258))))], (45914 ^ _777864) ^ [_1686224, _1686226, _1686228, _1686230] : [-(hBOOL(hAPP(hAPP(c_member(_1686224), _1686230), hAPP(c_Set_Oimage(tc_prod(_1686224, _1686226), _1686224, c_Product__Type_Ofst(_1686224, _1686226)), hAPP(c_List_Oset(tc_prod(_1686224, _1686226)), _1686228))))), -(hAPP(c_Map_Omap__of(_1686224, _1686226, _1686228), _1686230) = c_Option_Ooption_ONone(_1686226))], (16978 ^ _777864) ^ [_1070655, _1070657] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070655)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070657)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1070655), _1070657)))], (14614 ^ _777864) ^ [_1024922, _1024924] : [-(_1024922 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024924), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024922), _1024924))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024922, _1024924)))], (38924 ^ _777864) ^ [] : [-(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))))], (37453 ^ _777864) ^ [_1480198, _1480200, _1480202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1480198, 37454 ^ [_1480198, _1480200, _1480202])), hAPP(_1480200, 37454 ^ [_1480198, _1480200, _1480202]))), -(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), _1480200), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1480202))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1480198), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1480202))) = 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)), _1480200)), _1480198)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1480202)))], (11595 ^ _777864) ^ [_971417, _971419, _971421, _971423] : [class_Rings_Oordered__ring(_971417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971417), _971419), _971421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971417), _971423), c_Groups_Ozero__class_Ozero(_971417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971417), _971421), _971423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971417), _971419), _971423))))], (16248 ^ _777864) ^ [_1056655, _1056657] : [class_Rings_Ocomm__semiring__1(_1056655), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1056655), _1056657), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1056657)], (24295 ^ _777864) ^ [_1203202, _1203204, _1203206] : [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), _1203202), _1203204))), -(hBOOL(hAPP(hAPP(_1203206, _1203202), _1203204))), 24302 ^ _777864 : [(24305 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24301 ^ [_1203202, _1203204, _1203206]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1203206, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24300 ^ [_1203202, _1203204, _1203206])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24301 ^ [_1203202, _1203204, _1203206]))))], (24311 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1203206, 24300 ^ [_1203202, _1203204, _1203206]), 24301 ^ [_1203202, _1203204, _1203206]))], (24303 ^ _777864) ^ [] : [-(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), 24300 ^ [_1203202, _1203204, _1203206]), 24301 ^ [_1203202, _1203204, _1203206]))))]]], (7524 ^ _777864) ^ [_902448, _902450, _902452, _902454] : [class_Rings_Ocomm__semiring__1(_902448), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902448), _902450), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902448), _902452), _902454)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902448), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902448), _902450), _902452)), _902454))], (25729 ^ _777864) ^ [_1229217, _1229219, _1229221] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229217), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1229219), _1229221))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229217), _1229219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1229221), _1229219)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229217), _1229221)))], (32807 ^ _777864) ^ [_1379224, _1379226, _1379228, _1379230, _1379232] : [class_Groups_Ocomm__monoid__mult(_1379224), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379226, _1379224), hAPP(hAPP(c_COMBS(_1379226, _1379224, _1379224), hAPP(hAPP(c_COMBB(_1379224, tc_fun(_1379224, _1379224), _1379226), c_Groups_Otimes__class_Otimes(_1379224)), _1379228)), _1379230)), _1379232) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379224), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379226, _1379224), _1379228), _1379232)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379226, _1379224), _1379230), _1379232)))], (37310 ^ _777864) ^ [_1477010, _1477012, _1477014, _1477016] : [hBOOL(hAPP(hAPP(c_member(_1477010), _1477012), _1477014)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477010, tc_Nat_Onat), _1477016), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477010, tc_HOL_Obool)), _1477014), hAPP(hAPP(c_Set_Oinsert(_1477010), _1477012), c_Orderings_Obot__class_Obot(tc_fun(_1477010, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477010, tc_Nat_Onat), _1477016), _1477014)), hAPP(_1477016, _1477012)))], (29438 ^ _777864) ^ [_1311639] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1311639)), 29442 ^ _777864 : [(29443 ^ _777864) ^ [_1311719] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1311719), _1311639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1311719), 29441 ^ [_1311639])))]]], (42732 ^ _777864) ^ [_1608935, _1608937, _1608939, _1608941] : [class_Lattices_Osemilattice__sup(_1608935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1608935), _1608937)), hBOOL(hAPP(hAPP(c_member(_1608935), _1608939), _1608937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1608935), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1608935), _1608939), _1608941)), hAPP(hAPP(c_Finite__Set_Ofold(_1608935, _1608935, c_Lattices_Osemilattice__sup__class_Osup(_1608935)), _1608941), _1608937))))], (19204 ^ _777864) ^ [_1108041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1108041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1108041))))], (5316 ^ _777864) ^ [_859234, _859236] : [_859236 = _859234, -(c_Orderings_Oord__class_Oless__eq(_859236) = c_Orderings_Oord__class_Oless__eq(_859234))], (35726 ^ _777864) ^ [_1442397, _1442399] : [35734 ^ _777864 : [(35737 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1442399, 35733 ^ [_1442397, _1442399])))], (35735 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35733 ^ [_1442397, _1442399]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1442397))))]], 35727 ^ _777864 : [(35728 ^ _777864) ^ [_1442465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1442465), _1442397)), hBOOL(hAPP(_1442399, _1442465))]]], (50454 ^ _777864) ^ [_1793983, _1793985, _1793987] : [_1793985 = hAPP(hAPP(c_List_Olist_OCons(_1793983), _1793987), c_List_Olist_ONil(_1793983)), -(hAPP(c_List_Orev(_1793983), _1793985) = hAPP(hAPP(c_List_Olist_OCons(_1793983), _1793987), c_List_Olist_ONil(_1793983)))], (12716 ^ _777864) ^ [_991414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991414), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _991414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31687 ^ _777864) ^ [_1356840, _1356842, _1356844] : [class_Orderings_Olinorder(_1356840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356840), _1356842)), -(hBOOL(hAPP(hAPP(c_member(_1356840), _1356844), _1356842))), -(_1356842 = c_Orderings_Obot__class_Obot(tc_fun(_1356840, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1356840, hAPP(hAPP(c_Set_Oinsert(_1356840), _1356844), _1356842)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1356840), _1356844), c_Big__Operators_Olinorder__class_OMin(_1356840, _1356842)))], (49564 ^ _777864) ^ [_1775198, _1775200, _1775202, _1775204] : [hBOOL(hAPP(_1775198, _1775200)), -(hAPP(c_List_Ofilter(_1775202, _1775198), hAPP(hAPP(c_List_Olist_OCons(_1775202), _1775200), _1775204)) = hAPP(hAPP(c_List_Olist_OCons(_1775202), _1775200), hAPP(c_List_Ofilter(_1775202, _1775198), _1775204)))], (25627 ^ _777864) ^ [_1227377, _1227379, _1227381, _1227383] : [class_Rings_Ocomm__semiring__1(_1227377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1227379), _1227381)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227377), hAPP(hAPP(c_Power_Opower__class_Opower(_1227377), _1227383), _1227379)), hAPP(hAPP(c_Power_Opower__class_Opower(_1227377), _1227383), _1227381))))], (33809 ^ _777864) ^ [_1402386, _1402388, _1402390, _1402392, _1402394] : [_1402386 = c_Orderings_Obot__class_Obot(tc_fun(_1402388, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402390, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402388, tc_fun(_1402390, tc_HOL_Obool)), _1402386), _1402392)), _1402394) = _1402394)], (51481 ^ _777864) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (24595 ^ _777864) ^ [_1209330, _1209332] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1209330)), hAPP(c_Code__Numeral_Oof__nat, _1209332)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1209330), _1209332)))], (7508 ^ _777864) ^ [_902150, _902152] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_902150, _902152)], (1432 ^ _777864) ^ [_798532, _798534] : [-(class_Groups_Oordered__comm__monoid__add(_798532)), _798534 = _798532, class_Groups_Oordered__comm__monoid__add(_798534)], (30765 ^ _777864) ^ [_1340575, _1340577, _1340579] : [class_Orderings_Olinorder(_1340575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340575), _1340577)), hBOOL(hAPP(hAPP(c_member(_1340575), _1340579), _1340577)), 30776 ^ _777864 : [(30783 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340575, tc_HOL_Obool)), _1340577), hAPP(hAPP(c_Set_Oinsert(_1340575), _1340579), c_Orderings_Obot__class_Obot(tc_fun(_1340575, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340575, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1340575, _1340577) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1340575), _1340579), c_Big__Operators_Olinorder__class_OMax(_1340575, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340575, tc_HOL_Obool)), _1340577), hAPP(hAPP(c_Set_Oinsert(_1340575), _1340579), c_Orderings_Obot__class_Obot(tc_fun(_1340575, tc_HOL_Obool)))))))], (30777 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340575, tc_HOL_Obool)), _1340577), hAPP(hAPP(c_Set_Oinsert(_1340575), _1340579), c_Orderings_Obot__class_Obot(tc_fun(_1340575, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1340575, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1340575, _1340577) = _1340579)]]], (3712 ^ _777864) ^ [_834386, _834388, _834390, _834392] : [-(c_Lazy__Sequence_Osingle(_834392, _834388) = c_Lazy__Sequence_Osingle(_834390, _834386)), _834392 = _834390, _834388 = _834386], (17596 ^ _777864) ^ [_1081452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1081452)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1081452))], (22649 ^ _777864) ^ [_1169686, _1169688, _1169690] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1169686, tc_HOL_Obool)), _1169688), _1169690))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1169686, tc_HOL_Obool)), _1169688), _1169690)), -(_1169688 = _1169690)], (12346 ^ _777864) ^ [_984608, _984610, _984612] : [class_Groups_Oordered__comm__monoid__add(_984608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984608), _984610), c_Groups_Ozero__class_Ozero(_984608))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984608), _984612), c_Groups_Ozero__class_Ozero(_984608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984608), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984608), _984610), _984612)), c_Groups_Ozero__class_Ozero(_984608))))], (35198 ^ _777864) ^ [_1432219, _1432221, _1432223, _1432225, _1432227, _1432229] : [c_Fun_Oinj__on(_1432219, _1432221, _1432223, _1432225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432219, tc_HOL_Obool)), _1432227), _1432225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432219, tc_HOL_Obool)), _1432229), _1432225)), -(hAPP(c_Set_Oimage(_1432219, _1432221, _1432223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1432219, tc_HOL_Obool)), _1432227), _1432229)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1432221, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432219, _1432221, _1432223), _1432227)), hAPP(c_Set_Oimage(_1432219, _1432221, _1432223), _1432229)))], (34491 ^ _777864) ^ [_1418072, _1418074, _1418076, _1418078, _1418080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1418072, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1418074, _1418072, _1418076), _1418078)), _1418080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1418072, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1418074, tc_HOL_Obool), tc_fun(_1418072, tc_HOL_Obool), c_Set_Oimage(_1418074, _1418072, _1418076)), hAPP(c_Set_OPow(_1418074), _1418078))), hAPP(c_Set_OPow(_1418072), _1418080))))], (27766 ^ _777864) ^ [_1272491, _1272493, _1272495] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272491, tc_HOL_Obool)), _1272493), _1272495) = c_Orderings_Obot__class_Obot(tc_fun(_1272491, tc_HOL_Obool)), 27769 ^ _777864 : [(27772 ^ _777864) ^ [] : [-(_1272495 = c_Orderings_Obot__class_Obot(tc_fun(_1272491, tc_HOL_Obool)))], (27770 ^ _777864) ^ [] : [-(_1272493 = c_Orderings_Obot__class_Obot(tc_fun(_1272491, tc_HOL_Obool)))]]], (16670 ^ _777864) ^ [_1064673, _1064675, _1064677] : [class_Int_Onumber__ring(_1064673), -(hAPP(c_Int_Onumber__class_Onumber__of(_1064673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1064675), _1064677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1064673), hAPP(c_Int_Onumber__class_Onumber__of(_1064673), _1064675)), hAPP(c_Int_Onumber__class_Onumber__of(_1064673), _1064677)))], (5956 ^ _777864) ^ [_875732, _875734, _875736, _875738] : [-(c_Com_Ocom_OAss(_875732, _875734) = c_Com_Ocom_OAss(_875736, _875738)), _875732 = _875736, _875734 = _875738], (10430 ^ _777864) ^ [_951999, _952001, _952003] : [10431 ^ _777864 : [(10434 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952001), _952003))], (10432 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _951999)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951999), _952001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951999), _952003))))], (49787 ^ _777864) ^ [_1780917, _1780919] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780917)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780919)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780917), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1780919)) = c_List_Olist_ONil(tc_Nat_Onat))], (51545 ^ _777864) ^ [] : [-(hBOOL(c_fTrue))], (6556 ^ _777864) ^ [_886102, _886104] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886102), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886104), _886102)))))], (23279 ^ _777864) ^ [_1183144, _1183146, _1183148, _1183150] : [-(c_Nat_Onat_Onat__case(_1183144, _1183146, _1183148, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1183150)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1183144), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1183150))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1183144, _1183144), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1183144, tc_fun(_1183144, _1183144)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1183144, tc_fun(_1183144, _1183144)), tc_Int_Oint), c_If(_1183144)), c_Nat__Numeral_Oneg)), _1183146)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1183144, tc_Int_Oint), _1183148), c_Int_Onat))))], (4404 ^ _777864) ^ [_845224, _845226, _845228, _845230] : [-(c_Big__Operators_Olattice__class_OInf__fin(_845230, _845226) = c_Big__Operators_Olattice__class_OInf__fin(_845228, _845224)), _845230 = _845228, _845226 = _845224], (41138 ^ _777864) ^ [_1571288, _1571290, _1571292, _1571294] : [41140 ^ _777864 : [(41143 ^ _777864) ^ [] : [c_Wellfounded_Owf(_1571290, hAPP(_1571292, 41139 ^ [_1571288, _1571290, _1571292, _1571294]))], (41141 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1571288, 41139 ^ [_1571288, _1571290, _1571292, _1571294])))]], -(c_Wellfounded_Owf(tc_prod(_1571294, _1571290), c_Recdef_Osame__fst(_1571294, _1571290, _1571288, _1571292)))], (49910 ^ _777864) ^ [_1783187, _1783189, _1783191, _1783193] : [class_Orderings_Olinorder(_1783187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1783187), _1783189), _1783191)), c_List_Olinorder__class_Osorted(_1783187, hAPP(hAPP(c_List_Olist_OCons(_1783187), _1783191), _1783193)), -(c_List_Olinorder__class_Osorted(_1783187, hAPP(hAPP(c_List_Olist_OCons(_1783187), _1783189), hAPP(hAPP(c_List_Olist_OCons(_1783187), _1783191), _1783193))))], (41900 ^ _777864) ^ [_1590144, _1590146, _1590148, _1590150, _1590152, _1590154, _1590156] : [c_Fun_Oinj__on(_1590144, _1590146, _1590148, hAPP(c_Set_Oimage(_1590150, _1590144, _1590152), _1590154)), c_Fun_Oinj__on(_1590150, _1590144, _1590152, _1590154), hBOOL(hAPP(hAPP(c_member(_1590146), _1590156), hAPP(c_Set_Oimage(_1590144, _1590146, _1590148), hAPP(c_Set_Oimage(_1590150, _1590144, _1590152), _1590154)))), -(hAPP(c_Fun_Othe__inv__into(_1590150, _1590146, _1590154, hAPP(c_Fun_Ocomp(_1590144, _1590146, _1590150, _1590148), _1590152)), _1590156) = hAPP(hAPP(c_Fun_Ocomp(_1590144, _1590150, _1590146, c_Fun_Othe__inv__into(_1590150, _1590144, _1590154, _1590152)), c_Fun_Othe__inv__into(_1590144, _1590146, hAPP(c_Set_Oimage(_1590150, _1590144, _1590152), _1590154), _1590148)), _1590156))], (18656 ^ _777864) ^ [_1098579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1098579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1098579)))], (12171 ^ _777864) ^ [_981583] : [12172 ^ _777864 : [(12173 ^ _777864) ^ [_981640] : [hBOOL(hAPP(_981583, _981640))]], 12175 ^ _777864 : [(12178 ^ _777864) ^ [] : [-(hBOOL(hAPP(_981583, hAPP(c_Int_Onat, 12174 ^ [_981583]))))], (12176 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 12174 ^ [_981583])))]]], (51393 ^ _777864) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (30450 ^ _777864) ^ [_1333210, _1333212, _1333214, _1333216, _1333218, _1333220] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333210, tc_fun(_1333212, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1333210, tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_fun(_1333212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333212, tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_fun(_1333212, tc_HOL_Obool)), _1333210), c_COMBC(_1333212, tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333212, tc_prod(_1333210, _1333212)), tc_fun(_1333212, tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), _1333210), hAPP(c_COMBB(tc_prod(_1333210, _1333212), tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool), _1333212), c_member(tc_prod(_1333210, _1333212)))), c_Product__Type_OPair(_1333210, _1333212)))), _1333214)), hAPP(hAPP(c_COMBC(_1333210, tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_fun(_1333212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333212, tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_fun(_1333212, tc_HOL_Obool)), _1333210), c_COMBC(_1333212, tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1333212, tc_prod(_1333210, _1333212)), tc_fun(_1333212, tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool)), _1333210), hAPP(c_COMBB(tc_prod(_1333210, _1333212), tc_fun(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool), tc_HOL_Obool), _1333212), c_member(tc_prod(_1333210, _1333212)))), c_Product__Type_OPair(_1333210, _1333212)))), _1333216)), _1333218), _1333220)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1333210, _1333212)), hAPP(hAPP(c_Product__Type_OPair(_1333210, _1333212), _1333218), _1333220)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1333210, _1333212), tc_HOL_Obool)), _1333214), _1333216))))], (28258 ^ _777864) ^ [_1282156, _1282158, _1282160, _1282162] : [hBOOL(hAPP(_1282156, _1282158)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282160, tc_HOL_Obool)), _1282162), _1282156), _1282158)))], (13347 ^ _777864) ^ [_1002038, _1002040, _1002042, _1002044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1002038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1002040), _1002042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1002042), 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), _1002040), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1002044, _1002038))), _1002042)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9126 ^ _777864) ^ [_929575, _929577, _929579, _929581] : [class_Rings_Ocomm__semiring__1(_929575), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929575), _929577), _929579)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929575), _929581), _929579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929575), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929575), _929577), _929581)), _929579))], (20010 ^ _777864) ^ [_1122782, _1122784, _1122786] : [class_Fields_Olinordered__field(_1122782), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122782), _1122784), c_Groups_Ozero__class_Ozero(_1122782))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122782), _1122786), c_Groups_Ozero__class_Ozero(_1122782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122782), c_Groups_Ozero__class_Ozero(_1122782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1122782), _1122784), _1122786))))], (51185 ^ _777864) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (29269 ^ _777864) ^ [_1307467, _1307469, _1307471, _1307473, _1307475] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1307467), _1307469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307471, tc_HOL_Obool)), _1307473), hAPP(c_Set_Oimage(_1307467, _1307471, _1307475), _1307469))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1307471), _1307473)))], (23905 ^ _777864) ^ [_1195768, _1195770, _1195772, _1195774] : [class_Orderings_Olinorder(_1195768), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195768), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195768), _1195770), _1195772)), _1195774) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195768), _1195770), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195768), _1195772), _1195774)))], (34954 ^ _777864) ^ [_1426870, _1426872, _1426874, _1426876] : [c_Fun_Oinj__on(_1426870, tc_fun(tc_fun(_1426870, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1426870, tc_fun(tc_prod(_1426870, _1426870), tc_HOL_Obool), tc_fun(tc_fun(_1426870, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1426870, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1426870, _1426870), tc_HOL_Obool), tc_fun(tc_fun(_1426870, tc_HOL_Obool), tc_HOL_Obool)), _1426870), c_Equiv__Relations_Oquotient(_1426870)), hAPP(hAPP(c_COMBC(_1426870, tc_fun(_1426870, tc_HOL_Obool), tc_fun(_1426870, tc_HOL_Obool)), c_Set_Oinsert(_1426870)), c_Orderings_Obot__class_Obot(tc_fun(_1426870, tc_HOL_Obool))))), _1426872), _1426874), hBOOL(hAPP(hAPP(c_member(_1426870), _1426876), _1426874)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426870, tc_HOL_Obool)), _1426874), hAPP(hAPP(c_Set_Oinsert(_1426870), _1426876), c_Orderings_Obot__class_Obot(tc_fun(_1426870, tc_HOL_Obool))))), _1426872) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1426870, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426870), _1426874), _1426872)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1426870), hAPP(hAPP(c_Set_Oinsert(_1426870), _1426876), c_Orderings_Obot__class_Obot(tc_fun(_1426870, tc_HOL_Obool)))), _1426872)))], (36448 ^ _777864) ^ [_1456553] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1456553)) = 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), _1456553))))], (41545 ^ _777864) ^ [_1581686, _1581688, _1581690] : [41547 ^ _777864 : [(41550 ^ _777864) ^ [] : [hBOOL(hAPP(_1581688, 41546 ^ [_1581686, _1581688, _1581690]))], (41548 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581686), 41546 ^ [_1581686, _1581688, _1581690]), _1581690)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1581686, _1581688), _1581690)))], (36144 ^ _777864) ^ [_1450666, _1450668, _1450670, _1450672, _1450674, _1450676] : [-(_1450666 = _1450668), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1450670, _1450672), _1450674), _1450668), _1450676), _1450666) = hAPP(_1450674, _1450666))], (34555 ^ _777864) ^ [_1419752, _1419754] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1419752, _1419754))))], (4352 ^ _777864) ^ [_844458, _844460] : [_844460 = _844458, -(c_Fun_Oid(_844460) = c_Fun_Oid(_844458))], (39826 ^ _777864) ^ [_1532574, _1532576, _1532578, _1532580, _1532582, _1532584, _1532586, _1532588] : [c_Fun_Oinj__on(_1532574, _1532576, _1532578, _1532580), c_Fun_Oinj__on(_1532582, _1532584, _1532586, _1532588), -(c_Fun_Oinj__on(tc_prod(_1532574, _1532582), tc_prod(_1532576, _1532584), c_Product__Type_Omap__pair(_1532574, _1532576, _1532582, _1532584, _1532578, _1532586), hAPP(hAPP(c_Product__Type_OSigma(_1532574, _1532582), _1532580), hAPP(c_COMBK(tc_fun(_1532582, tc_HOL_Obool), _1532574), _1532588))))], (38589 ^ _777864) ^ [_1503885, _1503887] : [c_Equiv__Relations_Oequiv(_1503885, c_Orderings_Otop__class_Otop(tc_fun(_1503885, tc_HOL_Obool)), _1503887), -(c_Equiv__Relations_Oequivp(_1503885, hAPP(hAPP(c_COMBC(_1503885, tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_fun(_1503885, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503885, tc_fun(tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_fun(_1503885, tc_HOL_Obool)), _1503885), c_COMBC(_1503885, tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503885, tc_prod(_1503885, _1503885)), tc_fun(_1503885, tc_fun(tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_HOL_Obool)), _1503885), hAPP(c_COMBB(tc_prod(_1503885, _1503885), tc_fun(tc_fun(tc_prod(_1503885, _1503885), tc_HOL_Obool), tc_HOL_Obool), _1503885), c_member(tc_prod(_1503885, _1503885)))), c_Product__Type_OPair(_1503885, _1503885)))), _1503887)))], (26517 ^ _777864) ^ [_1245055, _1245057] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1245057), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1245055)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1245055)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1245057))))], (22845 ^ _777864) ^ [_1173590, _1173592, _1173594, _1173596, _1173598] : [hBOOL(hAPP(hAPP(_1173590, _1173592), _1173594)), -(hBOOL(hAPP(hAPP(_1173590, hAPP(c_Product__Type_Osnd(_1173596, _1173598), hAPP(hAPP(c_Product__Type_OPair(_1173596, _1173598), _1173594), _1173592))), hAPP(c_Product__Type_Ofst(_1173596, _1173598), hAPP(hAPP(c_Product__Type_OPair(_1173596, _1173598), _1173594), _1173592)))))], (8494 ^ _777864) ^ [_918653, _918655, _918657] : [class_Rings_Olinordered__semidom(_918653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918653), c_Groups_Oone__class_Oone(_918653)), _918655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918653), c_Groups_Oone__class_Oone(_918653)), _918657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918653), c_Groups_Oone__class_Oone(_918653)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918653), _918655), _918657))))], (15444 ^ _777864) ^ [_1040634, _1040636] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040634), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040634), _1040636)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47696 ^ _777864) ^ [_1731292, _1731294, _1731296] : [-(_1731292 = c_List_Olist_ONil(_1731294)), -(hBOOL(hAPP(hAPP(c_member(_1731294), hAPP(c_Product__Type_Ofst(_1731294, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1731294, _1731292), _1731296))), hAPP(c_List_Oset(_1731294), _1731292))))], (17672 ^ _777864) ^ [_1082554, _1082556] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1082554), _1082556) = c_Groups_Oone__class_Oone(tc_Int_Oint), 17677 ^ _777864 : [(17680 ^ _777864) ^ [] : [-(_1082556 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17678 ^ _777864) ^ [] : [-(_1082554 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 17681 ^ _777864 : [(17684 ^ _777864) ^ [] : [-(_1082556 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (17682 ^ _777864) ^ [] : [-(_1082554 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (45729 ^ _777864) ^ [_1681562, _1681564, _1681566, _1681568, _1681570, _1681572] : [-(hAPP(hAPP(c_List_Omap(_1681562, _1681564), _1681566), hAPP(hAPP(c_List_Omap(_1681568, _1681562), _1681570), _1681572)) = hAPP(hAPP(c_List_Omap(_1681568, _1681564), hAPP(c_Fun_Ocomp(_1681562, _1681564, _1681568, _1681566), _1681570)), _1681572))], (7868 ^ _777864) ^ [_908748, _908750, _908752, _908754] : [class_Orderings_Oorder(_908748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908748), hAPP(_908750, 7873 ^ [_908748, _908750, _908752, _908754])), hAPP(_908750, hAPP(c_Nat_OSuc, 7873 ^ [_908748, _908750, _908752, _908754])))), 7876 ^ _777864 : [(7883 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908752), _908754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908748), hAPP(_908750, _908752)), hAPP(_908750, _908754))))], (7877 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908748), hAPP(_908750, _908752)), hAPP(_908750, _908754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908752), _908754)))]]], (30639 ^ _777864) ^ [_1338127, _1338129] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338127, _1338129) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338127), _1338129)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338129), _1338127)))], (30008 ^ _777864) ^ [_1323661, _1323663, _1323665, _1323667] : [class_Lattices_Osemilattice__inf(_1323661), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323661), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323661), _1323663), _1323665)), _1323667) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323661), _1323663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323661), _1323665), _1323667)))], (5629 ^ _777864) ^ [_868441, _868443, _868445] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _868441))), _868443), _868445)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _868441)), _868443), _868445)))], (35770 ^ _777864) ^ [_1443182, _1443184, _1443186] : [class_Orderings_Oorder(_1443182), 35773 ^ _777864 : [(35780 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443182), _1443184), _1443186))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443182, _1443184), _1443186) = c_Orderings_Obot__class_Obot(tc_fun(_1443182, tc_HOL_Obool)))], (35774 ^ _777864) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443182, _1443184), _1443186) = c_Orderings_Obot__class_Obot(tc_fun(_1443182, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443182), _1443184), _1443186))]]], (9474 ^ _777864) ^ [_936010, _936012, _936014] : [class_Rings_Olinordered__semiring__strict(_936010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936010), c_Groups_Ozero__class_Ozero(_936010)), _936012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936010), c_Groups_Ozero__class_Ozero(_936010)), _936014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936010), c_Groups_Ozero__class_Ozero(_936010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_936010), _936012), _936014))))], (1772 ^ _777864) ^ [_802782, _802784] : [-(class_Rings_Odvd(_802782)), _802784 = _802782, class_Rings_Odvd(_802784)], (19350 ^ _777864) ^ [_1110567, _1110569] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1110567)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1110569))) = 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), _1110567), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1110569))))], (42986 ^ _777864) ^ [_1613681] : [-(c_Transitive__Closure_Otrancl(_1613681, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1613681, _1613681), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1613681, _1613681), tc_HOL_Obool)))], (49582 ^ _777864) ^ [_1775593, _1775595, _1775597] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1775593), tc_List_Olist(_1775593)), c_List_Opartition(_1775593, _1775595, _1775597)) = hAPP(c_List_Ofilter(_1775593, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1775593, c_fNot), _1775595)), _1775597))], (24805 ^ _777864) ^ [_1213374, _1213376, _1213378, _1213380, _1213382] : [class_Rings_Ocomm__semiring__1(_1213374), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213374), _1213376), _1213378)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213374), _1213380), _1213382)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1213374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213374), _1213376), _1213380)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213374), _1213378), _1213382))))], (45888 ^ _777864) ^ [_1685494, _1685496, _1685498, _1685500] : [c_Map_Omap__of(_1685494, _1685496, _1685498) = c_Map_Omap__of(_1685494, _1685496, _1685500), -(hAPP(c_Set_Oimage(tc_prod(_1685494, _1685496), _1685494, c_Product__Type_Ofst(_1685494, _1685496)), hAPP(c_List_Oset(tc_prod(_1685494, _1685496)), _1685498)) = hAPP(c_Set_Oimage(tc_prod(_1685494, _1685496), _1685494, c_Product__Type_Ofst(_1685494, _1685496)), hAPP(c_List_Oset(tc_prod(_1685494, _1685496)), _1685500)))], (47868 ^ _777864) ^ [_1735844, _1735846, _1735848, _1735850, _1735852] : [hAPP(hAPP(c_List_Olist_OCons(_1735844), _1735846), _1735848) = hAPP(hAPP(c_List_Oappend(_1735844), _1735850), _1735852), 47873 ^ _777864 : [(47876 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735844), _1735846), _1735848) = _1735852)], (47874 ^ _777864) ^ [] : [-(_1735850 = c_List_Olist_ONil(_1735844))]], 47878 ^ _777864 : [(47881 ^ _777864) ^ [] : [-(_1735848 = hAPP(hAPP(c_List_Oappend(_1735844), 47877 ^ [_1735844, _1735846, _1735848, _1735850, _1735852]), _1735852))], (47879 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1735844), _1735846), 47877 ^ [_1735844, _1735846, _1735848, _1735850, _1735852]) = _1735850)]]], (7843 ^ _777864) ^ [_908319, _908321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _908319), _908321)), 7847 ^ _777864 : [(7850 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _908319), 7846 ^ [_908319, _908321]) = _908321)], (7848 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7846 ^ [_908319, _908321])))]]], (18670 ^ _777864) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28312 ^ _777864) ^ [_1283507, _1283509, _1283511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1283507, tc_HOL_Obool)), _1283509), _1283511)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283507, tc_HOL_Obool)), _1283509), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1283507, tc_HOL_Obool)), _1283511), _1283509)) = _1283511)], (10182 ^ _777864) ^ [_947836, _947838, _947840] : [class_Orderings_Oorder(_947836), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947836), _947838), _947840)), 10189 ^ _777864 : [(10196 ^ _777864) ^ [] : [_947840 = _947838, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947836), _947840), _947838)))], (10190 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947836), _947840), _947838)), -(_947840 = _947838)]]], (47038 ^ _777864) ^ [_1716179, _1716181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1716179), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1716181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1716181), _1716179)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1716181))))], (36326 ^ _777864) ^ [_1454068] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1454068)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1454068))], (28510 ^ _777864) ^ [_1290753, _1290755, _1290757, _1290759, _1290761] : [-(hBOOL(hAPP(hAPP(c_member(_1290753), _1290755), hAPP(c_Set_Oimage(_1290757, _1290753, _1290759), _1290761)))), 28511 ^ _777864 : [(28512 ^ _777864) ^ [_1290823] : [hBOOL(hAPP(hAPP(c_member(_1290757), _1290823), _1290761)), _1290755 = hAPP(_1290759, _1290823)]]], (33927 ^ _777864) ^ [_1405037] : [-(hAPP(c_Int_Onat, _1405037) = 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, _1405037)), 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)))))))], (5914 ^ _777864) ^ [_875059] : [_875059 = hAPP(c_Nat_OSuc, _875059)], (40292 ^ _777864) ^ [_1543234, _1543236, _1543238, _1543240, _1543242, _1543244, _1543246] : [class_Groups_Ocomm__monoid__add(_1543234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543236), _1543238)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543240), _1543242)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543236, _1543234), hAPP(hAPP(c_COMBS(_1543236, tc_fun(_1543240, tc_HOL_Obool), _1543234), hAPP(hAPP(c_COMBB(tc_fun(_1543240, _1543234), tc_fun(tc_fun(_1543240, tc_HOL_Obool), _1543234), _1543236), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543240, _1543234)), _1543244)), hAPP(hAPP(c_COMBB(tc_fun(_1543240, tc_HOL_Obool), tc_fun(_1543240, tc_HOL_Obool), _1543236), c_Set_OCollect(_1543240)), hAPP(hAPP(c_COMBB(tc_fun(_1543240, tc_HOL_Obool), tc_fun(_1543240, tc_HOL_Obool), _1543236), hAPP(c_COMBS(_1543240, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543240), c_fconj), hAPP(hAPP(c_COMBC(_1543240, tc_fun(_1543240, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543240)), _1543242)))), _1543246)))), _1543238) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543240, _1543234), hAPP(hAPP(c_COMBS(_1543240, tc_fun(_1543236, tc_HOL_Obool), _1543234), hAPP(hAPP(c_COMBB(tc_fun(_1543236, _1543234), tc_fun(tc_fun(_1543236, tc_HOL_Obool), _1543234), _1543240), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543236, _1543234)), hAPP(c_COMBC(_1543236, _1543240, _1543234), _1543244))), hAPP(hAPP(c_COMBB(tc_fun(_1543236, tc_HOL_Obool), tc_fun(_1543236, tc_HOL_Obool), _1543240), c_Set_OCollect(_1543236)), hAPP(hAPP(c_COMBB(tc_fun(_1543236, tc_HOL_Obool), tc_fun(_1543236, tc_HOL_Obool), _1543240), hAPP(c_COMBS(_1543236, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543236), c_fconj), hAPP(hAPP(c_COMBC(_1543236, tc_fun(_1543236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543236)), _1543238)))), hAPP(c_COMBC(_1543236, _1543240, tc_HOL_Obool), _1543246))))), _1543242))], (23557 ^ _777864) ^ [_1189052, _1189054, _1189056] : [class_Orderings_Olinorder(_1189052), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189052), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1189052), _1189054), _1189056)), _1189054)))], (13270 ^ _777864) ^ [] : [-(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))))], (6040 ^ _777864) ^ [_877320] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OLoc(_877320)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15330 ^ _777864) ^ [_1038328, _1038330, _1038332] : [class_Groups_Oordered__ab__group__add(_1038328), 15333 ^ _777864 : [(15340 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038328), _1038330), _1038332)), c_Groups_Ozero__class_Ozero(_1038328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038328), _1038330), _1038332)))], (15334 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038328), _1038330), _1038332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1038328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038328), _1038330), _1038332)), c_Groups_Ozero__class_Ozero(_1038328))))]]], (12710 ^ _777864) ^ [_991327] : [hAPP(c_Int_Onat, _991327) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _991327), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51211 ^ _777864) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51391 ^ _777864) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (43589 ^ _777864) ^ [_1627642, _1627644, _1627646] : [-(hAPP(c_Relation_ORange(_1627642, _1627644), _1627646) = hAPP(c_Relation_ODomain(_1627644, _1627642), hAPP(c_Relation_Oconverse(_1627642, _1627644), _1627646)))], (46060 ^ _777864) ^ [_1689457] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1689457)), -(c_List_Onat__list(_1689457))], (36294 ^ _777864) ^ [_1453597, _1453599, _1453601, _1453603, _1453605, _1453607] : [-(hBOOL(hAPP(hAPP(c_member(_1453597), _1453599), _1453601))), -(hAPP(c_Set_Oimage(_1453597, tc_Option_Ooption(_1453603), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1453597, tc_Option_Ooption(_1453603)), _1453605), _1453599), hAPP(c_Option_Ooption_OSome(_1453603), _1453607))), _1453601) = hAPP(c_Set_Oimage(_1453597, tc_Option_Ooption(_1453603), _1453605), _1453601))], (12530 ^ _777864) ^ [_988124, _988126, _988128, _988130] : [class_Rings_Olinordered__semiring__strict(_988124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988124), _988126), _988128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988124), _988126), _988130))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988124), c_Groups_Ozero__class_Ozero(_988124)), _988126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988124), _988128), _988130)))], (38728 ^ _777864) ^ [_1507007, _1507009, _1507011, _1507013] : [-(hAPP(c_Set_Ovimage(_1507007, _1507009, _1507011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1507009, tc_HOL_Obool)), _1507013)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1507007, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1507007, _1507009, _1507011), _1507013)))], (38304 ^ _777864) ^ [_1496597, _1496599] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496597, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1496597, tc_HOL_Obool)), _1496599)), _1496599) = c_Orderings_Otop__class_Otop(tc_fun(_1496597, tc_HOL_Obool)))], (24443 ^ _777864) ^ [_1206009, _1206011, _1206013] : [-(c_Nitpick_Otimes__frac(_1206009, _1206011, _1206013) = hAPP(hAPP(c_Nitpick_Ofrac(_1206009), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1206009), _1206011)), hAPP(c_Nitpick_Onum(_1206009), _1206013))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1206009), _1206011)), hAPP(c_Nitpick_Odenom(_1206009), _1206013))))], (19436 ^ _777864) ^ [_1112042, _1112044] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1112042), hAPP(c_Int_Onumber__class_Onumber__of(_1112042), _1112044)), 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(_1112042), hAPP(c_Int_Onumber__class_Onumber__of(_1112042), _1112044)), hAPP(c_Int_Onumber__class_Onumber__of(_1112042), _1112044))), class_Groups_Omonoid__mult(_1112042), class_Int_Onumber(_1112042)], (49642 ^ _777864) ^ [_1777584, _1777586, _1777588, _1777590] : [-(c_List_Otranspose(_1777584, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1777586), tc_List_Olist(_1777584)), hAPP(c_List_Omap(_1777586, _1777584), _1777588)), _1777590)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1777586), tc_List_Olist(_1777584)), hAPP(c_List_Omap(_1777586, _1777584), _1777588)), c_List_Otranspose(_1777586, _1777590)))], (51141 ^ _777864) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (19562 ^ _777864) ^ [_1114251, _1114253, _1114255] : [class_Int_Onumber__ring(_1114251), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114251), _1114253), _1114255)), 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(_1114251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114251), hAPP(hAPP(c_Power_Opower__class_Opower(_1114251), _1114253), 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(_1114251), _1114255), 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(_1114251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114251), hAPP(c_Int_Onumber__class_Onumber__of(_1114251), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1114253)), _1114255)))], (9168 ^ _777864) ^ [_930544, _930546, _930548] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _930546), _930548)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930544), _930546)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _930544), _930548)))], (39313 ^ _777864) ^ [_1521614, _1521616, _1521618, _1521620] : [_1521614 = c_Orderings_Obot__class_Obot(tc_fun(_1521616, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1521616, _1521618), _1521618, c_Product__Type_Osnd(_1521616, _1521618)), hAPP(hAPP(c_Product__Type_OSigma(_1521616, _1521618), _1521614), hAPP(c_COMBK(tc_fun(_1521618, tc_HOL_Obool), _1521616), _1521620))) = c_Orderings_Obot__class_Obot(tc_fun(_1521618, tc_HOL_Obool)))], (4308 ^ _777864) ^ [_843774, _843776, _843778, _843780] : [-(c_Transitive__Closure_Ortrancl(_843780, _843776) = c_Transitive__Closure_Ortrancl(_843778, _843774)), _843780 = _843778, _843776 = _843774], (1692 ^ _777864) ^ [_801782, _801784] : [-(class_Orderings_Oorder(_801782)), _801784 = _801782, class_Orderings_Oorder(_801784)], (46120 ^ _777864) ^ [_1690596, _1690598, _1690600, _1690602, _1690604] : [hBOOL(hAPP(hAPP(c_member(_1690596), _1690598), hAPP(c_List_Oset(_1690596), _1690600))), -(hAPP(c_Map_Omap__of(_1690596, _1690602, hAPP(hAPP(c_List_Ozip(_1690596, _1690602), _1690600), hAPP(hAPP(c_List_Omap(_1690596, _1690602), _1690604), _1690600))), _1690598) = hAPP(c_Option_Ooption_OSome(_1690602), hAPP(_1690604, _1690598)))], (46871 ^ _777864) ^ [_1712180, _1712182, _1712184, _1712186] : [class_Groups_Ocomm__monoid__add(_1712180), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1712180), _1712182), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1712184, _1712186))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1712180), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1712180), _1712182), c_List_Oupto(_1712184, _1712186))))], (47960 ^ _777864) ^ [_1737945, _1737947, _1737949, _1737951, _1737953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737947)), _1737949))), -(hAPP(hAPP(c_List_Olist__update(_1737947, hAPP(hAPP(c_List_Oappend(_1737947), _1737949), _1737951)), _1737945), _1737953) = hAPP(hAPP(c_List_Oappend(_1737947), hAPP(hAPP(c_List_Olist__update(_1737947, _1737949), _1737945), _1737953)), _1737951))], (24697 ^ _777864) ^ [_1211089, _1211091] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1211089), _1211091) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211089)), hAPP(c_Code__Numeral_Onat__of, _1211091))))], (16144 ^ _777864) ^ [_1054687, _1054689] : [class_Groups_Oordered__ab__group__add__abs(_1054687), -(hAPP(c_Groups_Oabs__class_Oabs(_1054687), hAPP(c_Groups_Oabs__class_Oabs(_1054687), _1054689)) = hAPP(c_Groups_Oabs__class_Oabs(_1054687), _1054689))], (7002 ^ _777864) ^ [_892940, _892942, _892944] : [-(c_Option_Ooption_Ooption__size(_892940, _892942, hAPP(c_Option_Ooption_OSome(_892940), _892944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_892942, _892944)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43367 ^ _777864) ^ [_1622794, _1622796, _1622798, _1622800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622794, _1622794)), hAPP(hAPP(c_Product__Type_OPair(_1622794, _1622794), _1622796), _1622798)), c_Transitive__Closure_Ortrancl(_1622794, _1622800))), -(_1622796 = _1622798), 43374 ^ _777864 : [(43377 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622794, _1622794)), hAPP(hAPP(c_Product__Type_OPair(_1622794, _1622794), _1622796), _1622798)), c_Transitive__Closure_Otrancl(_1622794, _1622800))))], (43375 ^ _777864) ^ [] : [_1622796 = _1622798]]], (13601 ^ _777864) ^ [_1006993, _1006995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006993), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1006993), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1006995, _1006993))))], (7792 ^ _777864) ^ [_907288, _907290, _907292, _907294, _907296] : [c_Com_Ocom_OWhile(_907288, _907290) = c_Com_Ocom_OCond(_907292, _907294, _907296)], (45652 ^ _777864) ^ [_1679928, _1679930, _1679932, _1679934, _1679936, _1679938, _1679940] : [c_Map_Omap__comp(_1679928, _1679930, _1679932, _1679934, _1679936, _1679938) = hAPP(c_Option_Ooption_OSome(_1679930), _1679940), 45656 ^ _777864 : [(45659 ^ _777864) ^ [] : [-(hAPP(_1679934, 45655 ^ [_1679928, _1679930, _1679932, _1679934, _1679936, _1679938, _1679940]) = hAPP(c_Option_Ooption_OSome(_1679930), _1679940))], (45657 ^ _777864) ^ [] : [-(hAPP(_1679936, _1679938) = hAPP(c_Option_Ooption_OSome(_1679928), 45655 ^ [_1679928, _1679930, _1679932, _1679934, _1679936, _1679938, _1679940]))]]], (18684 ^ _777864) ^ [] : [-(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)))], (5340 ^ _777864) ^ [_859574, _859576] : [_859576 = _859574, -(c_List_Olist_OCons(_859576) = c_List_Olist_OCons(_859574))], (6721 ^ _777864) ^ [_888591, _888593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888591), _888593))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _888591), hAPP(c_Nat_OSuc, _888593))), -(_888593 = _888591)], (35664 ^ _777864) ^ [_1441248, _1441250, _1441252, _1441254, _1441256] : [class_Orderings_Olinorder(_1441248), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441248, _1441250), _1441252) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441248, _1441254), _1441256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441248), _1441250), _1441252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441248), _1441254), _1441256)), -(_1441250 = _1441254)], (19068 ^ _777864) ^ [_1105659] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1105659)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1105659)))], (40803 ^ _777864) ^ [_1563105, _1563107, _1563109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1563105, _1563105), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1563105, _1563105, _1563105), _1563107), _1563109)), _1563107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1563105, _1563107)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1563105, _1563109)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1563105, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1563105, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1563105, tc_HOL_Obool), tc_fun(_1563105, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1563105, _1563107))))], (40921 ^ _777864) ^ [_1566583, _1566585, _1566587] : [c_Wellfounded_Owf(_1566583, _1566585), -(c_Wellfounded_Owf(_1566583, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1566583, _1566583), tc_HOL_Obool)), _1566585), _1566587)))], (51513 ^ _777864) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (15452 ^ _777864) ^ [_1040781, _1040783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040781), _1040783)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040781), _1040783) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9840 ^ _777864) ^ [_942360, _942362] : [class_Rings_Osemiring__1(_942360), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_942360), hAPP(c_Nat_OSuc, _942362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942360), c_Groups_Oone__class_Oone(_942360)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_942360), _942362)))], (24243 ^ _777864) ^ [_1202378, _1202380] : [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), _1202378), _1202380))), 24246 ^ _777864 : [(24253 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202380), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24256 ^ _777864 : [(24265 ^ _777864) ^ [] : [-(c_Nitpick_Onorm__frac(_1202378, _1202380) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1202378), _1202380)), 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), _1202378))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1202380)))), -(_1202378 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1202380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24257 ^ _777864) ^ [] : [24258 ^ _777864 : [(24261 ^ _777864) ^ [] : [_1202380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24259 ^ _777864) ^ [] : [_1202378 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1202378, _1202380) = 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)))]]], (24247 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202380), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1202378, _1202380) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1202378), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1202380)))]]], (45107 ^ _777864) ^ [_1666684, _1666686] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666684, _1666684)), hAPP(hAPP(c_Product__Type_OPair(_1666684, _1666684), 45108 ^ [_1666684, _1666686]), 45108 ^ [_1666684, _1666686])), c_Transitive__Closure_Otrancl(_1666684, _1666686)))), -(c_Wellfounded_Oacyclic(_1666684, _1666686))], (33903 ^ _777864) ^ [_1404633, _1404635] : [hAPP(c_Int_ORep__Integ, _1404633) = hAPP(c_Int_ORep__Integ, _1404635), -(_1404633 = _1404635)], (5382 ^ _777864) ^ [_860199, _860201, _860203, _860205] : [-(tc_sum(_860205, _860201) = tc_sum(_860203, _860199)), _860205 = _860203, _860201 = _860199], (42609 ^ _777864) ^ [_1606380, _1606382, _1606384, _1606386] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1606380, _1606382, _1606384), _1606386), c_Orderings_Obot__class_Obot(tc_fun(_1606380, tc_HOL_Obool))) = _1606386)], (44128 ^ _777864) ^ [_1643161, _1643163, _1643165, _1643167] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1643161, tc_fun(_1643161, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1643161, tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_fun(_1643161, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643161, tc_fun(tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_fun(_1643161, tc_HOL_Obool)), _1643161), c_COMBC(_1643161, tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1643161, tc_prod(_1643161, _1643161)), tc_fun(_1643161, tc_fun(tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_HOL_Obool)), _1643161), hAPP(c_COMBB(tc_prod(_1643161, _1643161), tc_fun(tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool), tc_HOL_Obool), _1643161), c_member(tc_prod(_1643161, _1643161)))), c_Product__Type_OPair(_1643161, _1643161)))), _1643163)), c_fequal), _1643165), _1643167)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643161, _1643161)), hAPP(hAPP(c_Product__Type_OPair(_1643161, _1643161), _1643165), _1643167)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1643161, _1643161), tc_HOL_Obool)), _1643163), c_Relation_OId(_1643161)))))], (44399 ^ _777864) ^ [_1650218, _1650220, _1650222, _1650224] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1650218, _1650220), tc_fun(_1650218, _1650220)), _1650222), c_Fun_Ocomp(_1650220, _1650220, _1650218, _1650224)) = c_Fun_Ocomp(_1650220, _1650220, _1650218, hAPP(hAPP(c_Nat_Ocompow(_1650220, _1650220), _1650222), _1650224)))], (28520 ^ _777864) ^ [_1290971, _1290973, _1290975, _1290977, _1290979] : [hBOOL(hAPP(hAPP(c_member(_1290971), _1290973), _1290975)), -(hBOOL(hAPP(hAPP(c_member(_1290977), hAPP(_1290979, _1290973)), hAPP(c_Set_Oimage(_1290971, _1290977, _1290979), _1290975))))], (36302 ^ _777864) ^ [_1453713] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453713)) = _1453713)], (33438 ^ _777864) ^ [_1392490, _1392492] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1392490, _1392492)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1392492), _1392490))], (18412 ^ _777864) ^ [_1094537, _1094539] : [c_Int_OBit1(_1094537) = c_Int_OBit1(_1094539), -(_1094537 = _1094539)], (17266 ^ _777864) ^ [_1075658, _1075660] : [class_Power_Opower(_1075658), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075658), _1075660), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1075658))], (51187 ^ _777864) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (29291 ^ _777864) ^ [_1308009, _1308011, _1308013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1308009, tc_HOL_Obool), tc_fun(_1308009, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1308009, tc_HOL_Obool), tc_fun(_1308009, tc_HOL_Obool)), _1308011), _1308013)), c_Wellfounded_Ofinite__psubset(_1308009))), 29294 ^ _777864 : [(29297 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1308009), _1308013)))], (29295 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1308009, tc_HOL_Obool)), _1308011), _1308013)))]]], (37018 ^ _777864) ^ [_1470138, _1470140, _1470142, _1470144, _1470146] : [class_Rings_Oring(_1470138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470140), _1470142)), hBOOL(hAPP(hAPP(c_member(_1470140), _1470144), _1470142)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470140, _1470138), _1470146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470140, tc_HOL_Obool)), _1470142), hAPP(hAPP(c_Set_Oinsert(_1470140), _1470144), c_Orderings_Obot__class_Obot(tc_fun(_1470140, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1470138), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470140, _1470138), _1470146), _1470142)), hAPP(_1470146, _1470144)))], (48802 ^ _777864) ^ [_1758793, _1758795, _1758797] : [hBOOL(hAPP(c_List_Odistinct(_1758793), _1758797)), -(hBOOL(hAPP(c_List_Odistinct(_1758793), hAPP(c_List_Orotate(_1758793, _1758795), _1758797))))], (26103 ^ _777864) ^ [_1236401, _1236403, _1236405, _1236407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236401, tc_HOL_Obool)), _1236403), _1236405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1236401, tc_HOL_Obool)), _1236403), hAPP(hAPP(c_Set_Oinsert(_1236401), _1236407), _1236405))))], (24563 ^ _777864) ^ [_1208815, _1208817] : [hAPP(c_Code__Numeral_Oof__nat, _1208815) = hAPP(c_Code__Numeral_Oof__nat, _1208817), -(_1208815 = _1208817)], (41149 ^ _777864) ^ [_1571548, _1571550, _1571552, _1571554, _1571556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571548, _1571550)), hAPP(hAPP(c_Product__Type_OPair(_1571548, _1571550), _1571552), _1571554)), _1571556)), -(hBOOL(hAPP(hAPP(c_member(_1571550), _1571554), hAPP(c_Relation_ORange(_1571548, _1571550), _1571556))))], (4530 ^ _777864) ^ [_847113, _847115, _847117, _847119] : [-(c_List_Olistrel1(_847119, _847115) = c_List_Olistrel1(_847117, _847113)), _847119 = _847117, _847115 = _847113], (25539 ^ _777864) ^ [_1225583, _1225585, _1225587, _1225589] : [class_Divides_Osemiring__div(_1225583), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225583), _1225585), _1225587)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225583), _1225585), _1225589)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225583), _1225587), _1225589)), _1225585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225583), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225583), _1225587), _1225585)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1225583), _1225589), _1225585)))], (9806 ^ _777864) ^ [_941726, _941728, _941730] : [class_Rings_Olinordered__ring(_941726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941726), _941728), _941728)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941726), _941730), _941730))), c_Groups_Ozero__class_Ozero(_941726)))], (44614 ^ _777864) ^ [_1655552, _1655554, _1655556] : [class_Complete__Lattice_Ocomplete__lattice(_1655552), class_Orderings_Olinorder(_1655552), 44621 ^ _777864 : [(44631 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655552), c_Complete__Lattice_OInf__class_OInf(_1655552, _1655554)), _1655556))), 44632 ^ _777864 : [(44633 ^ _777864) ^ [_1655858] : [hBOOL(hAPP(hAPP(c_member(_1655552), _1655858), _1655554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655552), _1655858), _1655556))]]], (44622 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655552), c_Complete__Lattice_OInf__class_OInf(_1655552, _1655554)), _1655556)), 44626 ^ _777864 : [(44629 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1655552), 44625 ^ [_1655552, _1655554, _1655556]), _1655556)))], (44627 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655552), 44625 ^ [_1655552, _1655554, _1655556]), _1655554)))]]]]], (43233 ^ _777864) ^ [_1619409, _1619411, _1619413, _1619415] : [43234 ^ _777864 : [(43237 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619409, _1619409)), _1619411), c_Transitive__Closure_Ortrancl(_1619409, _1619415)))], (43235 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1619409, _1619409)), _1619411), c_Transitive__Closure_Ortrancl(_1619409, _1619413)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1619409, _1619409)), _1619411), c_Transitive__Closure_Ortrancl(_1619409, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1619409, _1619409), tc_HOL_Obool)), _1619413), _1619415)))))], (51051 ^ _777864) ^ [_1807383, _1807385] : [class_Lattices_Olattice(_1807383), -(class_Lattices_Osemilattice__inf(tc_fun(_1807385, _1807383)))], (21848 ^ _777864) ^ [_1155861, _1155863, _1155865] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1155861, _1155863, _1155865, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1155863)], (9794 ^ _777864) ^ [_941510, _941512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941510), hAPP(c_Int_Onat, _941512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _941510)), _941512)))], (43848 ^ _777864) ^ [_1635384, _1635386, _1635388, _1635390] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635384, tc_fun(_1635386, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1635384, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1635386, tc_HOL_Obool), tc_fun(_1635386, tc_HOL_Obool), _1635384), hAPP(c_COMBC(_1635386, tc_fun(_1635386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1635386))), _1635388)), _1635390)), -(hBOOL(hAPP(hAPP(c_member(_1635386), _1635390), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1635384, tc_fun(_1635386, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1635384, tc_HOL_Obool))), _1635388))))], (12149 ^ _777864) ^ [] : [-(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))))], (9672 ^ _777864) ^ [] : [-(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))))], (1722 ^ _777864) ^ [_802157, _802159] : [-(class_Groups_Ominus(_802157)), _802159 = _802157, class_Groups_Ominus(_802159)], (12191 ^ _777864) ^ [_981917] : [hBOOL(hAPP(_981917, 12192 ^ [_981917])), 12195 ^ _777864 : [(12196 ^ _777864) ^ [_982011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982011)), -(hBOOL(hAPP(_981917, hAPP(c_Int_Onat, _982011))))]]], (31357 ^ _777864) ^ [_1350608, _1350610, _1350612] : [class_Lattices_Olattice(_1350608), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350608), _1350610)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350608), _1350612)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350608, tc_HOL_Obool)), _1350610), _1350612) = c_Orderings_Obot__class_Obot(tc_fun(_1350608, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1350608), c_Big__Operators_Olattice__class_OSup__fin(_1350608, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350608, tc_HOL_Obool)), _1350610), _1350612))), c_Big__Operators_Olattice__class_OSup__fin(_1350608, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1350608, tc_HOL_Obool)), _1350610), _1350612))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1350608), c_Big__Operators_Olattice__class_OSup__fin(_1350608, _1350610)), c_Big__Operators_Olattice__class_OSup__fin(_1350608, _1350612)))], (36252 ^ _777864) ^ [_1452701, _1452703, _1452705] : [class_Orderings_Olinorder(_1452701), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452701), _1452703), _1452705)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1452701, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1452701), _1452703)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1452701, _1452703, _1452705)) = hAPP(c_SetInterval_Oord__class_OatMost(_1452701), _1452705))], (47462 ^ _777864) ^ [_1726760, _1726762, _1726764, _1726766] : [class_Orderings_Olinorder(_1726760), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1726762, _1726760, _1726764), _1726766), c_List_Olist_ONil(_1726762)) = hAPP(hAPP(c_List_Olist_OCons(_1726762), _1726766), c_List_Olist_ONil(_1726762)))], (51257 ^ _777864) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (30418 ^ _777864) ^ [_1332625, _1332627] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1332625), 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)))), _1332627))), 30421 ^ _777864 : [(30424 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332625), _1332627))], (30422 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1332627), _1332625)))]]], (28360 ^ _777864) ^ [_1285160, _1285162, _1285164, _1285166, _1285168, _1285170] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285160, tc_fun(_1285162, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1285160, tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_fun(_1285162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285162, tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_fun(_1285162, tc_HOL_Obool)), _1285160), c_COMBC(_1285162, tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285162, tc_prod(_1285160, _1285162)), tc_fun(_1285162, tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), _1285160), hAPP(c_COMBB(tc_prod(_1285160, _1285162), tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool), _1285162), c_member(tc_prod(_1285160, _1285162)))), c_Product__Type_OPair(_1285160, _1285162)))), _1285164)), hAPP(hAPP(c_COMBC(_1285160, tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_fun(_1285162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285162, tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_fun(_1285162, tc_HOL_Obool)), _1285160), c_COMBC(_1285162, tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1285162, tc_prod(_1285160, _1285162)), tc_fun(_1285162, tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool)), _1285160), hAPP(c_COMBB(tc_prod(_1285160, _1285162), tc_fun(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool), tc_HOL_Obool), _1285162), c_member(tc_prod(_1285160, _1285162)))), c_Product__Type_OPair(_1285160, _1285162)))), _1285166)), _1285168), _1285170)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1285160, _1285162)), hAPP(hAPP(c_Product__Type_OPair(_1285160, _1285162), _1285168), _1285170)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1285160, _1285162), tc_HOL_Obool)), _1285164), _1285166))))], (27640 ^ _777864) ^ [_1270204, _1270206, _1270208, _1270210] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270204), _1270206)), 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)), _1270208), _1270204)), 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)), _1270210), _1270206)), 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)), _1270208), _1270210)), _1270206)), c_FunDef_Omax__strict)))], (50907 ^ _777864) ^ [_1804698, _1804700] : [c_List_Oremdups(_1804698, _1804700) = _1804700, -(hBOOL(hAPP(c_List_Odistinct(_1804698), _1804700)))], (49089 ^ _777864) ^ [_1765258, _1765260, _1765262, _1765264] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765258)), hAPP(hAPP(c_List_Oappend(_1765258), _1765260), _1765262)), c_List_Olists(_1765258, _1765264))), 49092 ^ _777864 : [(49095 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765258)), _1765262), c_List_Olists(_1765258, _1765264))))], (49093 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1765258)), _1765260), c_List_Olists(_1765258, _1765264))))]]], (29926 ^ _777864) ^ [_1321757, _1321759, _1321761, _1321763] : [class_Lattices_Odistrib__lattice(_1321757), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321757), _1321759), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321757), _1321761), _1321763)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321757), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321757), _1321759), _1321761)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321757), _1321759), _1321763)))], (24703 ^ _777864) ^ [_1211227, _1211229, _1211231, _1211233, _1211235, _1211237, _1211239] : [-(c_New__Random__Sequence_Opos__decr__bind(_1211227, _1211229, _1211231, _1211233, _1211235, _1211237, _1211239) = c_New__DSequence_Opos__decr__bind(_1211227, _1211229, hAPP(hAPP(hAPP(_1211231, _1211235), _1211237), _1211239), hAPP(hAPP(c_COMBC(_1211227, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1211229))), hAPP(hAPP(c_COMBC(_1211227, 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(_1211229)))), hAPP(hAPP(c_COMBC(_1211227, 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(_1211229))))), _1211233), _1211235)), _1211237)), _1211239)))], (5506 ^ _777864) ^ [_864761, _864763] : [hAPP(_864761, 5507 ^ [_864761, _864763]) = hAPP(_864763, 5507 ^ [_864761, _864763]), -(_864761 = _864763)], (51505 ^ _777864) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (32575 ^ _777864) ^ [_1374216, _1374218, _1374220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1374216), _1374218)), -(hAPP(c_Finite__Set_Ocard(_1374216), hAPP(hAPP(c_Set_Oinsert(_1374216), _1374220), _1374218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1374216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374216, tc_HOL_Obool)), _1374218), hAPP(hAPP(c_Set_Oinsert(_1374216), _1374220), c_Orderings_Obot__class_Obot(tc_fun(_1374216, tc_HOL_Obool)))))))], (7064 ^ _777864) ^ [_893902, _893904] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_893902)), hAPP(c_Option_Ooption_OSome(_893902), _893904)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31011 ^ _777864) ^ [_1344575, _1344577, _1344579] : [class_Lattices_Olattice(_1344575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344575), _1344577)), -(_1344577 = c_Orderings_Obot__class_Obot(tc_fun(_1344575, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1344575, hAPP(hAPP(c_Set_Oinsert(_1344575), _1344579), _1344577)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1344575), _1344579), c_Big__Operators_Olattice__class_OInf__fin(_1344575, _1344577)))], (7386 ^ _777864) ^ [_899601, _899603, _899605] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_899601, _899603, _899605))), 7389 ^ _777864 : [(7392 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _899605)))], (7390 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _899603)))]]], (30102 ^ _777864) ^ [_1325516, _1325518, _1325520, _1325522] : [class_Lattices_Olattice(_1325516), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325516), _1325518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325516), _1325520), _1325522))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1325516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325516), _1325518), _1325520)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325516), _1325518), _1325522)))))], (27019 ^ _777864) ^ [_1255013, _1255015, _1255017, _1255019] : [_1255013 = _1255015, hBOOL(hAPP(hAPP(c_member(_1255017), _1255015), _1255019)), -(hBOOL(hAPP(hAPP(c_member(_1255017), _1255013), _1255019)))], (45573 ^ _777864) ^ [_1677922, _1677924, _1677926] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1677922), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1677924), _1677926)))), 45576 ^ _777864 : [(45583 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1677924), _1677926))), -(c_Smallcheck_Osmall_H(_1677922, _1677924, _1677926) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1677922, _1677924, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1677926), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1677922, _1677926)))], (45577 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1677924), _1677926)), -(c_Smallcheck_Osmall_H(_1677922, _1677924, _1677926) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (15458 ^ _777864) ^ [_1040882, _1040884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040882), _1040884)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040882), _1040884) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11559 ^ _777864) ^ [_970725, _970727, _970729, _970731, _970733] : [class_Rings_Oordered__semiring(_970725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970725), _970727), _970729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970725), _970731), _970733)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970725), c_Groups_Ozero__class_Ozero(_970725)), _970727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970725), c_Groups_Ozero__class_Ozero(_970725)), _970731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970725), _970727), _970731)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_970725), _970729), _970733))))], (46681 ^ _777864) ^ [_1706476, _1706478, _1706480, _1706482, _1706484, _1706486] : [-(_1706476 = _1706478), -(hAPP(c_Map_Omap__of(_1706480, _1706482, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1706480, _1706482)), hAPP(hAPP(c_Product__Type_OPair(_1706480, _1706482), _1706476), _1706484)), _1706486)), _1706478) = hAPP(c_Map_Omap__of(_1706480, _1706482, _1706486), _1706478))], (14177 ^ _777864) ^ [_1017725, _1017727] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1017725, _1017727)) = _1017727, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1017725), _1017727) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43275 ^ _777864) ^ [_1620440, _1620442, _1620444, _1620446, _1620448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620440, _1620440)), hAPP(hAPP(c_Product__Type_OPair(_1620440, _1620440), _1620442), _1620444)), c_Transitive__Closure_Ortrancl(_1620440, _1620446))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620440, _1620440)), hAPP(hAPP(c_Product__Type_OPair(_1620440, _1620440), _1620444), _1620448)), c_Transitive__Closure_Ortrancl(_1620440, _1620446))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620440, _1620440)), hAPP(hAPP(c_Product__Type_OPair(_1620440, _1620440), _1620442), _1620448)), c_Transitive__Closure_Ortrancl(_1620440, _1620446))))], (12740 ^ _777864) ^ [_991774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _991774)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _991774)) = _991774)], (15256 ^ _777864) ^ [_1036833, _1036835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036833), _1036835)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1036835, _1036833) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036835), _1036833), _1036833))], (1282 ^ _777864) ^ [_796657, _796659] : [-(class_Lattices_Osemilattice__inf(_796657)), _796659 = _796657, class_Lattices_Osemilattice__inf(_796659)], (18998 ^ _777864) ^ [_1104405, _1104407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1104405), _1104407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1104405)), c_Int_OBit1(_1104407))))], (32739 ^ _777864) ^ [_1377636, _1377638, _1377640, _1377642] : [-(c_Sum__Type_OPlus(_1377636, _1377638, _1377640, _1377642) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1377636, _1377638), tc_HOL_Obool))), _1377640 = c_Orderings_Obot__class_Obot(tc_fun(_1377636, tc_HOL_Obool)), _1377642 = c_Orderings_Obot__class_Obot(tc_fun(_1377638, tc_HOL_Obool))], (5936 ^ _777864) ^ [_875400, _875402, _875404] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_875400, _875402, _875404))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _875402))))], (49665 ^ _777864) ^ [_1778120, _1778122, _1778124] : [-(c_List_Omap__filter(_1778120, _1778122, _1778124, c_List_Olist_ONil(_1778120)) = c_List_Olist_ONil(_1778122))], (45489 ^ _777864) ^ [_1675951, _1675953, _1675955, _1675957, _1675959, _1675961] : [hAPP(_1675951, _1675953) = hAPP(c_Option_Ooption_OSome(_1675955), _1675957), -(hAPP(c_Map_Omap__add(_1675959, _1675955, _1675961, _1675951), _1675953) = hAPP(c_Option_Ooption_OSome(_1675955), _1675957))], (2424 ^ _777864) ^ [_813604, _813606, _813608, _813610, _813612, _813614, _813616, _813618, _813620, _813622] : [-(c_Nitpick_Opair__box_Opair__box__size(_813622, _813618, _813614, _813610, _813606) = c_Nitpick_Opair__box_Opair__box__size(_813620, _813616, _813612, _813608, _813604)), _813622 = _813620, _813618 = _813616, _813614 = _813612, _813610 = _813608, _813606 = _813604], (48155 ^ _777864) ^ [_1742137, _1742139, _1742141] : [-(c_List_Olist_ONil(_1742137) = hAPP(hAPP(c_List_Oappend(_1742137), _1742139), _1742141)), _1742139 = c_List_Olist_ONil(_1742137), _1742141 = c_List_Olist_ONil(_1742137)], (22444 ^ _777864) ^ [_1165803] : [c_Code__Numeral_OSuc__code__numeral(_1165803) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (28430 ^ _777864) ^ [_1288909, _1288911, _1288913, _1288915, _1288917, _1288919] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288909, tc_fun(_1288911, tc_HOL_Obool))), _1288913), _1288915), _1288917), _1288919)), -(hBOOL(hAPP(hAPP(_1288913, _1288917), _1288919))), -(hBOOL(hAPP(hAPP(_1288915, _1288917), _1288919)))], (40444 ^ _777864) ^ [_1549444] : [-(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)))), _1549444))))], (35288 ^ _777864) ^ [_1434021, _1434023, _1434025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434021)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434023), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1434025)), 35295 ^ _777864 : [(35296 ^ _777864) ^ [_1434229] : [35298 ^ _777864 : [(35304 ^ _777864) ^ [] : [-(_1434229 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35300 ^ [_1434021, _1434023, _1434025, _1434229]), 35297 ^ [_1434021, _1434023, _1434025, _1434229]))], (35302 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35300 ^ [_1434021, _1434023, _1434025, _1434229]), _1434025)))], (35299 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35297 ^ [_1434021, _1434023, _1434025, _1434229]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1434021))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434229), _1434023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434229), _1434021)), _1434023)))]]], (23791 ^ _777864) ^ [_1193599, _1193601, _1193603, _1193605, _1193607, _1193609, _1193611] : [-(hAPP(c_Product__Type_Oapsnd(_1193599, _1193601, _1193603, _1193605), hAPP(c_Product__Type_Oapfst(_1193607, _1193603, _1193599, _1193609), _1193611)) = hAPP(hAPP(c_Product__Type_OPair(_1193603, _1193601), hAPP(_1193609, hAPP(c_Product__Type_Ofst(_1193607, _1193599), _1193611))), hAPP(_1193605, hAPP(c_Product__Type_Osnd(_1193607, _1193599), _1193611))))], (9989 ^ _777864) ^ [_944793, _944795] : [class_Orderings_Opreorder(_944793), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944793), _944795), _944795)))], (38625 ^ 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1486787), _1486791), _1486789)), -(hBOOL(hAPP(hAPP(c_member(_1486787), _1486789), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486787), _1486791))))], (37791 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486787), _1486789), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486787), _1486791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1486787), _1486791), _1486789)))]]], (2318 ^ _777864) ^ [_812021, _812023, _812025, _812027] : [-(c_Orderings_Oord_Omin(_812027, _812023) = c_Orderings_Oord_Omin(_812025, _812021)), _812027 = _812025, _812023 = _812021], (44674 ^ _777864) ^ [_1656765] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1656765, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1656765, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1656765, tc_HOL_Obool)))], (28104 ^ _777864) ^ [_1278642, _1278644, _1278646] : [class_Lattices_Olattice(_1278642), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278642), _1278644), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278642), _1278644), _1278646)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278642), _1278644), _1278646))], (20628 ^ _777864) ^ [_1133445, _1133447, _1133449, _1133451] : [class_Fields_Olinordered__field(_1133445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133445), c_Groups_Ozero__class_Ozero(_1133445)), _1133447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133445), _1133449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133445), _1133451), _1133447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133445), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133445), _1133449), _1133447)), _1133451)))], (23133 ^ _777864) ^ [_1179567] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179567))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1179567)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33448 ^ _777864) ^ [_1392778, _1392780, _1392782, _1392784] : [class_Orderings_Oorder(_1392778), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392778, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1392778, _1392780, _1392782)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1392778, _1392782, _1392784)) = c_Orderings_Obot__class_Obot(tc_fun(_1392778, tc_HOL_Obool)))], (47472 ^ _777864) ^ [_1727034, _1727036, _1727038, _1727040, _1727042] : [-(hAPP(hAPP(c_List_Olist__update(_1727034, hAPP(hAPP(c_List_Olist_OCons(_1727034), _1727036), _1727038)), hAPP(c_Nat_OSuc, _1727040)), _1727042) = hAPP(hAPP(c_List_Olist_OCons(_1727034), _1727036), hAPP(hAPP(c_List_Olist__update(_1727034, _1727038), _1727040), _1727042)))], (7978 ^ _777864) ^ [_910771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _910771)), 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c_Groups_Otimes__class_Otimes(_1411353)), _1411361), c_Groups_Oone__class_Oone(_1411353)), _1411359)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411353), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1411353, _1411355, c_Groups_Otimes__class_Otimes(_1411353)), _1411361), c_Groups_Oone__class_Oone(_1411353)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411355, tc_HOL_Obool)), _1411357), _1411359))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1411353, _1411355, c_Groups_Otimes__class_Otimes(_1411353)), _1411361), c_Groups_Oone__class_Oone(_1411353)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411355, tc_HOL_Obool)), _1411357), _1411359))))], (26953 ^ _777864) ^ [_1253812, _1253814, _1253816, _1253818] : [-(hBOOL(hAPP(hAPP(c_member(_1253812), _1253814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253812, tc_HOL_Obool)), _1253816), _1253818)))), hBOOL(hAPP(hAPP(c_member(_1253812), _1253814), _1253816)), -(hBOOL(hAPP(hAPP(c_member(_1253812), _1253814), _1253818)))], (7408 ^ _777864) ^ [_900009, _900011, _900013, _900015, _900017] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_900009, _900011), _900013, _900015, _900017), 7412 ^ _777864 : [(7415 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_900011, 7411 ^ [_900009, _900011, _900013, _900015, _900017], _900015, _900017))], (7413 ^ _777864) ^ [] : [-(c_Natural_Oevaln(_900009, _900013, _900015, 7411 ^ [_900009, _900011, _900013, _900015, _900017]))]]], (6565 ^ _777864) ^ [_886269, _886271] : [6566 ^ _777864 : [(6567 ^ _777864) ^ [_886322] : [_886271 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _886269), _886322))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _886269), _886271)))], (37460 ^ _777864) ^ [_1480431, _1480433, _1480435, _1480437, _1480439] : [class_Groups_Ocomm__monoid__add(_1480431), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480433), _1480435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480433, tc_HOL_Obool)), _1480437), _1480435)), 37474 ^ _777864 : [(37477 ^ _777864) ^ [] : [hAPP(_1480439, 37473 ^ [_1480431, _1480433, _1480435, _1480437, _1480439]) = c_Groups_Ozero__class_Ozero(_1480431)], (37475 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480433), 37473 ^ [_1480431, _1480433, _1480435, _1480437, _1480439]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1480433, tc_HOL_Obool)), _1480435), _1480437))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480433, _1480431), _1480439), _1480437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480433, _1480431), _1480439), _1480435))], (7032 ^ _777864) ^ [_893375, _893377, _893379] : [_893377 = _893379, -(hAPP(c_Option_Ooption_OSome(_893375), _893377) = hAPP(c_Option_Ooption_OSome(_893375), _893379))], (5978 ^ _777864) ^ [_876092] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _876092)], (13680 ^ _777864) ^ [_1008302, _1008304, _1008306] : [class_Lattices_Oab__semigroup__idem__mult(_1008302), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008302), _1008304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008302), _1008304), _1008306)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008302), _1008304), _1008306))], (40759 ^ _777864) ^ [_1561411, _1561413, _1561415, _1561417, _1561419, _1561421] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1561411, _1561413, _1561415), _1561417), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561413, _1561415), tc_HOL_Obool)), _1561419), _1561421)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561411, _1561415), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1561411, _1561413, _1561415), _1561417), _1561419)), hAPP(hAPP(c_Relation_Orel__comp(_1561411, _1561413, _1561415), _1561417), _1561421)))], (45451 ^ _777864) ^ [_1675156, _1675158, _1675160, _1675162, _1675164, _1675166] : [-(hAPP(c_Map_Omap__add(_1675156, _1675158, _1675160, _1675162), _1675164) = hAPP(c_Option_Ooption_OSome(_1675158), _1675166)), 45452 ^ _777864 : [(45455 ^ _777864) ^ [] : [hAPP(_1675162, _1675164) = c_Option_Ooption_ONone(_1675158), hAPP(_1675160, _1675164) = hAPP(c_Option_Ooption_OSome(_1675158), _1675166)], (45453 ^ _777864) ^ [] : [hAPP(_1675162, _1675164) = hAPP(c_Option_Ooption_OSome(_1675158), _1675166)]]], (24493 ^ _777864) ^ [_1207162, _1207164, _1207166, _1207168] : [-(c_HOL_OThe(tc_prod(_1207162, _1207164), hAPP(c_Product__Type_Oprod_Oprod__case(_1207162, _1207164, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1207162, tc_fun(_1207164, tc_HOL_Obool), tc_fun(_1207164, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1207164, tc_HOL_Obool), tc_fun(_1207164, tc_HOL_Obool)), _1207162), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1207164)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1207162), c_fconj), hAPP(c_fequal, _1207166)))), hAPP(c_fequal, _1207168)))) = hAPP(hAPP(c_Product__Type_OPair(_1207162, _1207164), _1207166), _1207168))], (15894 ^ _777864) ^ [_1050151, _1050153] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1050151, _1050153) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1050151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1050151), _1050153)), _1050153)))], (24029 ^ _777864) ^ [_1197933, _1197935, _1197937, _1197939] : [class_Orderings_Olinorder(_1197933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197933), _1197935), _1197937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197933), _1197939), _1197937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1197933), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1197933), _1197935), _1197939)), _1197937)))], (3722 ^ _777864) ^ [_834535, _834537, _834539, _834541] : [-(c_Wellfounded_Omax__ext(_834541, _834537) = c_Wellfounded_Omax__ext(_834539, _834535)), _834541 = _834539, _834537 = _834535], (49646 ^ _777864) ^ [_1777715, _1777717] : [c_List_Otranspose(_1777715, _1777717) = c_List_Olist_ONil(tc_List_Olist(_1777715)), 49649 ^ _777864 : [(49650 ^ _777864) ^ [_1777810] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777715)), _1777810), hAPP(c_List_Oset(tc_List_Olist(_1777715)), _1777717))), -(_1777810 = c_List_Olist_ONil(_1777715))]]], (30621 ^ _777864) ^ [_1337803, _1337805] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1337803, _1337805), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337803), _1337805)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1337805), _1337803)))], (24747 ^ _777864) ^ [_1212193, _1212195, _1212197, _1212199] : [-(c_New__Random__Sequence_Opos__empty(_1212193, _1212195, _1212197, _1212199) = c_New__DSequence_Opos__empty(_1212193))], (17662 ^ _777864) ^ [_1082437, _1082439] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1082437), _1082439) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1082437 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1082437 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (2616 ^ _777864) ^ [_816714, _816716, _816718, _816720, _816722, _816724, _816726, _816728] : [-(c_Random__Sequence_ORandom(_816728, _816724, _816720, _816716) = c_Random__Sequence_ORandom(_816726, _816722, _816718, _816714)), _816728 = _816726, _816724 = _816722, _816720 = _816718, _816716 = _816714], (47764 ^ _777864) ^ [_1733007, _1733009, _1733011] : [-(c_List_Olistset(_1733007, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1733007, tc_HOL_Obool)), _1733009), _1733011)) = c_List_Oset__Cons(_1733007, _1733009, c_List_Olistset(_1733007, _1733011)))], (4224 ^ _777864) ^ [_842432, _842434, _842436, _842438, _842440, _842442, _842444, _842446] : [-(c_Lazy__Sequence_Oanamorph(_842446, _842442, _842438, _842434) = c_Lazy__Sequence_Oanamorph(_842444, _842440, _842436, _842432)), _842446 = _842444, _842442 = _842440, _842438 = _842436, _842434 = _842432], (43731 ^ _777864) ^ [_1631462, _1631464, _1631466, _1631468, _1631470, _1631472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631462, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1631464, _1631462, _1631466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631468, tc_fun(_1631464, tc_HOL_Obool)), _1631470), _1631472))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1631468, tc_fun(_1631462, tc_HOL_Obool)), _1631470), hAPP(hAPP(c_COMBB(tc_fun(_1631464, tc_HOL_Obool), tc_fun(_1631462, tc_HOL_Obool), _1631468), c_Relation_OImage(_1631464, _1631462, _1631466)), _1631472)))))], (41303 ^ _777864) ^ [_1575288, _1575290, _1575292] : [hAPP(c_Relation_ODomain(_1575288, _1575290), _1575292) = c_Orderings_Obot__class_Obot(tc_fun(_1575288, tc_HOL_Obool)), -(_1575292 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575288, _1575290), tc_HOL_Obool)))], (7929 ^ _777864) ^ [_909899] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _909899) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_909899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44047 ^ _777864) ^ [_1641075, _1641077, _1641079, _1641081, _1641083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641075, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1641077, _1641075, _1641079), _1641081)), _1641083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641077, tc_HOL_Obool)), _1641081), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1641077, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1641075, _1641077, hAPP(c_Relation_Oconverse(_1641077, _1641075), _1641079)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1641075, tc_HOL_Obool)), _1641083))))))], (51295 ^ _777864) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (30681 ^ _777864) ^ [_1338859, _1338861] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338859), _1338861)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338861, _1338859) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (49213 ^ _777864) ^ [_1768236, _1768238, _1768240] : [-(_1768236 = c_List_Olist_ONil(_1768238)), -(c_List_Olast(_1768238, hAPP(hAPP(c_List_Olist_OCons(_1768238), _1768240), _1768236)) = c_List_Olast(_1768238, _1768236))], (5334 ^ _777864) ^ [_859489, _859491] : [_859491 = _859489, -(c_List_Odistinct(_859491) = c_List_Odistinct(_859489))], (24629 ^ _777864) ^ [_1209948, _1209950, _1209952, _1209954, _1209956] : [-(_1209948 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1209950, _1209952, _1209954, _1209956), _1209948) = c_Lazy__Sequence_Obind(_1209950, _1209952, hAPP(_1209954, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1209948), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1209950, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1209952)), _1209956), _1209948)))], (10324 ^ _777864) ^ [_950089, _950091, _950093] : [class_Orderings_Olinorder(_950089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950089), _950091), _950093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950089), _950093), _950091)))], (7582 ^ _777864) ^ [_903592, _903594, _903596, _903598] : [-(hBOOL(hAPP(_903592, _903594))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_903592, _903596), _903594, _903598, _903594))], (44180 ^ _777864) ^ [_1645057] : [-(hAPP(c_Relation_Oconverse(_1645057, _1645057), c_Relation_OId(_1645057)) = c_Relation_OId(_1645057))], (48684 ^ _777864) ^ [_1756476, _1756478, _1756480, _1756482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1756476), _1756478)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756480)), _1756482))), -(hAPP(hAPP(c_List_Otake(_1756480), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1756476), _1756478)), _1756482) = hAPP(hAPP(c_List_Oappend(_1756480), hAPP(hAPP(c_List_Otake(_1756480), _1756476), _1756482)), hAPP(hAPP(c_List_Otake(_1756480), _1756478), hAPP(hAPP(c_List_Odrop(_1756480), _1756476), _1756482))))], (45776 ^ _777864) ^ [_1682821, _1682823, _1682825, _1682827] : [-(hAPP(c_List_Oset(_1682821), hAPP(hAPP(c_List_Omap(_1682823, _1682821), _1682825), _1682827)) = hAPP(c_Set_Oimage(_1682823, _1682821, _1682825), hAPP(c_List_Oset(_1682823), _1682827)))], (40182 ^ _777864) ^ [_1540722, _1540724] : [c_Orderings_Obot__class_Obot(tc_fun(_1540722, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1540722), _1540724), 40185 ^ _777864 : [(40186 ^ _777864) ^ [_1540807] : [hBOOL(hAPP(_1540724, _1540807))]]], (22496 ^ _777864) ^ [_1166663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1166663)), 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), _1166663)) = 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), _1166663))))))], (50150 ^ _777864) ^ [_1787111, _1787113] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1787111), hAPP(c_List_Onth(_1787111), _1787113)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787111)), _1787113))) = _1787113)], (2534 ^ _777864) ^ [_815337, _815339, _815341, _815343, _815345, _815347, _815349, _815351, _815353, _815355] : [-(c_Nitpick_Opair__box_Opair__box__case(_815355, _815351, _815347, _815343, _815339) = c_Nitpick_Opair__box_Opair__box__case(_815353, _815349, _815345, _815341, _815337)), _815355 = _815353, _815351 = _815349, _815347 = _815345, _815343 = _815341, _815339 = _815337], (45360 ^ _777864) ^ [_1673148, _1673150, _1673152, _1673154, _1673156, _1673158, _1673160, _1673162] : [c_Finite__Set_Ofolding__image__simple__idem(_1673148, _1673150, _1673152, _1673154, _1673156, _1673158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1673150), _1673160)), -(hAPP(_1673158, hAPP(hAPP(c_Set_Oinsert(_1673150), _1673162), _1673160)) = hAPP(hAPP(_1673152, hAPP(_1673156, _1673162)), hAPP(_1673158, _1673160)))], (22076 ^ _777864) ^ [_1159463, _1159465] : [-(_1159463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1159465, _1159463) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1159465), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1159463)))], (22833 ^ _777864) ^ [_1173343, _1173345, _1173347, _1173349, _1173351, _1173353] : [hBOOL(hAPP(_1173343, _1173345)), hBOOL(hAPP(_1173347, _1173349)), 22840 ^ _777864 : [(22843 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1173347, hAPP(c_Product__Type_Osnd(_1173351, _1173353), hAPP(hAPP(c_Product__Type_OPair(_1173351, _1173353), _1173345), _1173349)))))], (22841 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1173343, hAPP(c_Product__Type_Ofst(_1173351, _1173353), hAPP(hAPP(c_Product__Type_OPair(_1173351, _1173353), _1173345), _1173349)))))]]], (41786 ^ _777864) ^ [_1587909, _1587911, _1587913, _1587915, _1587917, _1587919] : [c_Fun_Oinj__on(_1587909, _1587911, _1587913, _1587915), 41789 ^ _777864 : [(41796 ^ _777864) ^ [] : [c_Fun_Oinj__on(_1587909, _1587917, hAPP(c_Fun_Ocomp(_1587911, _1587917, _1587909, _1587919), _1587913), _1587915), -(c_Fun_Oinj__on(_1587911, _1587917, _1587919, hAPP(c_Set_Oimage(_1587909, _1587911, _1587913), _1587915)))], (41790 ^ _777864) ^ [] : [c_Fun_Oinj__on(_1587911, _1587917, _1587919, hAPP(c_Set_Oimage(_1587909, _1587911, _1587913), _1587915)), -(c_Fun_Oinj__on(_1587909, _1587917, hAPP(c_Fun_Ocomp(_1587911, _1587917, _1587909, _1587919), _1587913), _1587915))]]], (48528 ^ _777864) ^ [_1752702, _1752704, _1752706] : [hBOOL(hAPP(c_List_Odistinct(_1752702), _1752704)), -(hBOOL(hAPP(c_List_Odistinct(_1752702), hAPP(hAPP(c_List_Odrop(_1752702), _1752706), _1752704))))], (31587 ^ _777864) ^ [_1355248, _1355250] : [class_Orderings_Olinorder(_1355248), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355248), _1355250)), -(_1355250 = c_Orderings_Obot__class_Obot(tc_fun(_1355248, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1355248), c_Big__Operators_Olinorder__class_OMin(_1355248, _1355250)), _1355250)))], (19648 ^ _777864) ^ [_1116143, _1116145] : [class_Rings_Oring__1(_1116143), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1116143), hAPP(c_Groups_Ouminus__class_Ouminus(_1116143), c_Groups_Oone__class_Oone(_1116143))), 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)))), _1116145))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1116143), c_Groups_Oone__class_Oone(_1116143)))], (44005 ^ _777864) ^ [_1639917, _1639919, _1639921, _1639923, _1639925] : [-(_1639917 = c_Orderings_Obot__class_Obot(tc_fun(_1639919, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639919, tc_fun(_1639921, tc_HOL_Obool)), _1639917), hAPP(hAPP(c_COMBC(_1639919, tc_fun(_1639921, tc_HOL_Obool), tc_fun(_1639921, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1639921, tc_HOL_Obool), tc_fun(tc_fun(_1639921, tc_HOL_Obool), tc_fun(_1639921, tc_HOL_Obool)), _1639919), c_Groups_Ominus__class_Ominus(tc_fun(_1639921, tc_HOL_Obool))), _1639923)), _1639925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1639921, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639919, tc_fun(_1639921, tc_HOL_Obool)), _1639917), _1639923)), _1639925))], (20822 ^ _777864) ^ [_1136971, _1136973, _1136975, _1136977] : [class_Fields_Ofield__inverse__zero(_1136971), -(_1136973 = c_Groups_Ozero__class_Ozero(_1136971)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136971), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136971), _1136975), _1136973)), _1136977) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136971), _1136975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136971), _1136977), _1136973))), _1136973))], (47048 ^ _777864) ^ [_1716398, _1716400, _1716402, _1716404] : [-(hAPP(hAPP(c_List_Onth(_1716398), hAPP(hAPP(c_List_Olist_OCons(_1716398), _1716400), _1716402)), hAPP(c_Nat_OSuc, _1716404)) = hAPP(hAPP(c_List_Onth(_1716398), _1716402), _1716404))], (43585 ^ _777864) ^ [_1627552, _1627554, _1627556] : [-(hAPP(c_Relation_ORange(_1627552, _1627554), hAPP(c_Relation_Oconverse(_1627554, _1627552), _1627556)) = hAPP(c_Relation_ODomain(_1627554, _1627552), _1627556))], (41293 ^ _777864) ^ [_1575111, _1575113, _1575115] : [c_Wellfounded_OwfP(_1575111, _1575113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575111, tc_fun(_1575111, tc_HOL_Obool))), _1575115), _1575113)), -(c_Wellfounded_OwfP(_1575111, _1575115))], (7062 ^ _777864) ^ [_893864] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _893864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _893864)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10976 ^ _777864) ^ [_960604, _960606, _960608] : [class_Groups_Oordered__ab__group__add(_960604), 10979 ^ _777864 : [(10986 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960604), hAPP(c_Groups_Ouminus__class_Ouminus(_960604), _960608)), _960606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960604), hAPP(c_Groups_Ouminus__class_Ouminus(_960604), _960606)), _960608)))], (10980 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960604), hAPP(c_Groups_Ouminus__class_Ouminus(_960604), _960606)), _960608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960604), hAPP(c_Groups_Ouminus__class_Ouminus(_960604), _960608)), _960606)))]]], (51569 ^ _777864) ^ [_1812762, _1812764] : [hBOOL(hAPP(hAPP(c_fconj, _1812762), _1812764)), -(hBOOL(_1812762))], (24433 ^ _777864) ^ [_1205818, _1205820, _1205822, _1205824, _1205826, _1205828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205818, tc_fun(_1205820, tc_HOL_Obool))), _1205822), _1205824)), hBOOL(hAPP(hAPP(_1205822, _1205826), _1205828)), -(hBOOL(hAPP(hAPP(_1205824, _1205826), _1205828)))], (44214 ^ _777864) ^ [] : [-(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))))], (40673 ^ _777864) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (18322 ^ _777864) ^ [_1092898, _1092900] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092898), c_Int_OPls))), 18325 ^ _777864 : [(18332 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092900), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092898)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092900)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092898), _1092900)))], (18326 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092900), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092898)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092900)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092898))]]], (51507 ^ _777864) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (30498 ^ _777864) ^ [_1335265, _1335267, _1335269, _1335271] : [hBOOL(hAPP(hAPP(_1335269, _1335267), _1335271)), -(hBOOL(hAPP(hAPP(c_member(_1335265), _1335267), c_SetInterval_Oord_OlessThan(_1335265, _1335269, _1335271))))], (23091 ^ _777864) ^ [_1178731, _1178733] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1178731)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1178733)), hAPP(c_Int_Onat, _1178731)) = hAPP(c_Int_Onat, _1178733))], (10045 ^ _777864) ^ [_945784, _945786] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _945784), _945786), 10048 ^ _777864 : [(10051 ^ _777864) ^ [] : [-(_945786 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10049 ^ _777864) ^ [] : [-(_945784 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (18638 ^ _777864) ^ [_1098272] : [class_Int_Onumber__ring(_1098272), -(c_Groups_Oone__class_Oone(_1098272) = hAPP(c_Int_Onumber__class_Onumber__of(_1098272), c_Int_OBit1(c_Int_OPls)))], (48858 ^ _777864) ^ [_1759964, _1759966, _1759968] : [-(hAPP(c_List_Otl(_1759964), hAPP(hAPP(c_List_Otake(_1759964), _1759966), _1759968)) = hAPP(hAPP(c_List_Otake(_1759964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1759966), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1759964), _1759968)))], (38647 ^ _777864) ^ [_1505321, _1505323] : [-(c_Equiv__Relations_Oequivp(_1505321, _1505323)), 38652 ^ _777864 : [(38655 ^ _777864) ^ [] : [hAPP(_1505323, 38648 ^ [_1505321, _1505323]) = hAPP(_1505323, 38649 ^ [_1505321, _1505323])], (38653 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1505323, 38648 ^ [_1505321, _1505323]), 38649 ^ [_1505321, _1505323])))]], 38656 ^ _777864 : [(38659 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(_1505323, 38648 ^ [_1505321, _1505323]), 38649 ^ [_1505321, _1505323]))], (38657 ^ _777864) ^ [] : [-(hAPP(_1505323, 38648 ^ [_1505321, _1505323]) = hAPP(_1505323, 38649 ^ [_1505321, _1505323]))]]], (6282 ^ _777864) ^ [_881387, _881389, _881391, _881393] : [class_Groups_Ocancel__ab__semigroup__add(_881387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881387), _881389), _881391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_881387), _881389), _881393), -(_881391 = _881393)], (44608 ^ _777864) ^ [_1655421, _1655423, _1655425] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1655421, tc_HOL_Obool)), _1655423), _1655425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1655421, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1655421, tc_HOL_Obool), _1655425)), _1655423)))], (46138 ^ _777864) ^ [_1690967, _1690969, _1690971, _1690973] : [hBOOL(hAPP(c_List_Odistinct(_1690967), _1690969)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1690967, _1690971)), hAPP(hAPP(c_List_Ozip(_1690967, _1690971), _1690969), _1690973))))], (17702 ^ _777864) ^ [_1082964, _1082966, _1082968, _1082970] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1082964, _1082966, _1082968), _1082970), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1082966)], (47020 ^ _777864) ^ [_1715512, _1715514, _1715516, _1715518] : [-(hAPP(c_List_Oset(tc_prod(_1715512, _1715514)), hAPP(hAPP(c_List_Ozip(_1715512, _1715514), _1715516), _1715518)) = hAPP(c_Set_OCollect(tc_prod(_1715512, _1715514)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1715512, _1715514)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1715512, _1715514), 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(_1715512, _1715514)), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_prod(_1715512, _1715514)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(tc_prod(_1715512, _1715514), tc_fun(tc_Nat_Onat, tc_prod(_1715512, _1715514)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1715512, _1715514), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1715512, _1715514)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1715512, _1715514)), c_COMBB(tc_prod(_1715512, _1715514), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1715514, tc_prod(_1715512, _1715514)), hAPP(hAPP(c_COMBB(_1715512, tc_fun(_1715514, tc_prod(_1715512, _1715514)), tc_Nat_Onat), c_Product__Type_OPair(_1715512, _1715514)), hAPP(c_List_Onth(_1715512), _1715516))), hAPP(c_List_Onth(_1715514), _1715518)))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715512)), _1715516)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715514)), _1715518)))))))], (370 ^ _777864) ^ [_783473, _783475, _783477, _783479, _783481, _783483, _783485, _783487] : [-(c_Wellfounded_Omax__extp(_783485, _783481, _783477, _783473)), c_Wellfounded_Omax__extp(_783487, _783483, _783479, _783475), _783487 = _783485, _783483 = _783481, _783479 = _783477, _783475 = _783473], (42669 ^ _777864) ^ [_1607625, _1607627, _1607629, _1607631] : [class_Orderings_Olinorder(_1607625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607625), _1607627)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1607625, _1607625, c_Orderings_Oord__class_Omax(_1607625)), _1607629), hAPP(hAPP(c_Set_Oinsert(_1607625), _1607631), _1607627)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1607625), _1607631), hAPP(hAPP(c_Finite__Set_Ofold(_1607625, _1607625, c_Orderings_Oord__class_Omax(_1607625)), _1607629), _1607627)))], (29764 ^ _777864) ^ [_1318193, _1318195, _1318197, _1318199] : [class_Lattices_Osemilattice__inf(_1318193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318193), _1318195), _1318197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318193), _1318195), _1318199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318193), _1318195), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318193), _1318197), _1318199))))], (20466 ^ _777864) ^ [_1130340, _1130342, _1130344, _1130346, _1130348] : [class_Fields_Olinordered__field(_1130340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130340), c_Groups_Ozero__class_Ozero(_1130340)), _1130342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130340), _1130342), _1130344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130340), c_Groups_Ozero__class_Ozero(_1130340)), _1130346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130340), _1130346), _1130348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130340), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130340), _1130342), _1130348)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130340), _1130344), _1130346))))], (38400 ^ _777864) ^ [_1498574, _1498576] : [class_Lattices_Oboolean__algebra(_1498574), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1498574), _1498576), hAPP(c_Groups_Ouminus__class_Ouminus(_1498574), _1498576)) = c_Orderings_Otop__class_Otop(_1498574))], (24319 ^ _777864) ^ [_1203758, _1203760] : [_1203758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1203760, _1203758) = _1203760)], (30312 ^ _777864) ^ [_1330440, _1330442, _1330444, _1330446, _1330448, _1330450, _1330452, _1330454] : [c_Finite__Set_Ofolding__image__simple(_1330440, _1330442, _1330444, _1330446, _1330448, _1330450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330442), _1330452)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330442), _1330454)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330442, tc_HOL_Obool)), _1330452), _1330454) = c_Orderings_Obot__class_Obot(tc_fun(_1330442, tc_HOL_Obool)), -(hAPP(_1330450, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330442, tc_HOL_Obool)), _1330452), _1330454)) = hAPP(hAPP(_1330444, hAPP(_1330450, _1330452)), hAPP(_1330450, _1330454)))], (43285 ^ _777864) ^ [_1620713, _1620715, _1620717, _1620719, _1620721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1620713, _1620713)), hAPP(hAPP(c_Product__Type_OPair(_1620713, _1620713), _1620715), _1620717)), c_Transitive__Closure_Ortrancl(_1620713, _1620719))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1620713, _1620713)), hAPP(hAPP(c_Product__Type_OPair(_1620713, _1620713), _1620717), _1620721)), _1620719)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1620713, _1620713)), hAPP(hAPP(c_Product__Type_OPair(_1620713, _1620713), _1620715), _1620721)), c_Transitive__Closure_Ortrancl(_1620713, _1620719))))], (21964 ^ _777864) ^ [_1157733, _1157735] : [-(_1157733 = _1157735), -(c_Random_Oinc__shift(_1157733, _1157735) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1157735), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (27053 ^ _777864) ^ [_1255686, _1255688, _1255690, _1255692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1255686, tc_HOL_Obool)), _1255688), _1255690)), hBOOL(hAPP(hAPP(c_member(_1255686), _1255692), _1255688)), -(hBOOL(hAPP(hAPP(c_member(_1255686), _1255692), _1255690)))], (23687 ^ _777864) ^ [_1191505, _1191507, _1191509, _1191511] : [class_Orderings_Olinorder(_1191505), 23690 ^ _777864 : [(23699 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191505), _1191509), _1191511)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), _1191509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), _1191511))], (23691 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1191505), _1191509), _1191511))), 23694 ^ _777864 : [(23697 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), _1191511)))], (23695 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191505), _1191507), _1191509)))]]]]], (26117 ^ _777864) ^ [_1236787, _1236789, _1236791, _1236793, _1236795, _1236797, _1236799] : [c_Hoare__Mirabelle_Ohoare__derivs(_1236787, _1236789, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1236787)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1236787), _1236791), _1236793), _1236795)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1236787), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1236787, _1236789, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1236787)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1236787), _1236795), _1236797), _1236799)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1236787), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1236787, _1236789, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1236787)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1236787), _1236791), c_Com_Ocom_OSemi(_1236793, _1236797)), _1236799)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1236787), tc_HOL_Obool)))))], (41163 ^ _777864) ^ [_1571860, _1571862, _1571864] : [_1571864 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1571860, _1571862), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1571860, _1571862), _1571864) = c_Orderings_Obot__class_Obot(tc_fun(_1571862, tc_HOL_Obool)))], (42018 ^ _777864) ^ [_1593144, _1593146, _1593148, _1593150, _1593152, _1593154] : [c_Finite__Set_Ofolding(_1593144, _1593146, _1593148, _1593150), -(hAPP(c_Fun_Ocomp(_1593146, _1593146, _1593146, hAPP(_1593148, _1593152)), hAPP(_1593148, _1593154)) = hAPP(c_Fun_Ocomp(_1593146, _1593146, _1593146, hAPP(_1593148, _1593154)), hAPP(_1593148, _1593152)))], (29408 ^ _777864) ^ [_1310882, _1310884, _1310886, _1310888, _1310890] : [c_Finite__Set_Ofolding__one(_1310882, _1310884, _1310886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310882), _1310888)), 29415 ^ _777864 : [(29422 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310882, tc_HOL_Obool)), _1310888), hAPP(hAPP(c_Set_Oinsert(_1310882), _1310890), c_Orderings_Obot__class_Obot(tc_fun(_1310882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310882, tc_HOL_Obool))), -(hAPP(_1310886, hAPP(hAPP(c_Set_Oinsert(_1310882), _1310890), _1310888)) = hAPP(hAPP(_1310884, _1310890), hAPP(_1310886, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310882, tc_HOL_Obool)), _1310888), hAPP(hAPP(c_Set_Oinsert(_1310882), _1310890), c_Orderings_Obot__class_Obot(tc_fun(_1310882, tc_HOL_Obool)))))))], (29416 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310882, tc_HOL_Obool)), _1310888), hAPP(hAPP(c_Set_Oinsert(_1310882), _1310890), c_Orderings_Obot__class_Obot(tc_fun(_1310882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310882, tc_HOL_Obool)), -(hAPP(_1310886, hAPP(hAPP(c_Set_Oinsert(_1310882), _1310890), _1310888)) = _1310890)]]], (39964 ^ _777864) ^ [_1535995, _1535997, _1535999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535995, _1535995), tc_HOL_Obool)), _1535997), hAPP(hAPP(c_Product__Type_OSigma(_1535995, _1535995), _1535999), hAPP(c_COMBK(tc_fun(_1535995, tc_HOL_Obool), _1535995), _1535999)))), 39970 ^ _777864 : [(39973 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535995, _1535995)), hAPP(hAPP(c_Product__Type_OPair(_1535995, _1535995), 39969 ^ [_1535995, _1535997, _1535999]), 39969 ^ [_1535995, _1535997, _1535999])), _1535997))], (39971 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535995), 39969 ^ [_1535995, _1535997, _1535999]), _1535999)))]], -(c_Relation_Orefl__on(_1535995, _1535999, _1535997))], (8520 ^ _777864) ^ [_919198, _919200] : [class_Rings_Ocomm__semiring__1(_919198), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919198), _919200), _919200) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919198), c_Groups_Oone__class_Oone(_919198)), c_Groups_Oone__class_Oone(_919198))), _919200))], (40675 ^ _777864) ^ [_1559140, _1559142] : [-(c_Product__Type_Oapsnd(_1559140, _1559140, _1559142, c_Fun_Oid(_1559140)) = c_Fun_Oid(tc_prod(_1559142, _1559140)))], (49386 ^ _777864) ^ [_1771577, _1771579, _1771581] : [_1771577 = c_List_Olist_ONil(_1771579), -(c_List_Obutlast(_1771579, hAPP(hAPP(c_List_Olist_OCons(_1771579), _1771581), _1771577)) = c_List_Olist_ONil(_1771579))], (50207 ^ _777864) ^ [_1788252, _1788254, _1788256, _1788258, _1788260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1788252), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1788254), _1788256))), -(hAPP(hAPP(c_List_Onth(_1788258), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1788258), _1788260), c_List_Oupt(_1788256, _1788254))), _1788252) = hAPP(_1788260, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1788256), _1788252)))], (48097 ^ _777864) ^ [_1741116, _1741118, _1741120] : [_1741120 = c_List_Olist_ONil(_1741116), -(hAPP(hAPP(c_List_Oappend(_1741116), _1741118), _1741120) = _1741118)], (37332 ^ _777864) ^ [_1477585, _1477587, _1477589] : [class_Groups_Ocomm__monoid__add(_1477585), class_Groups_Ocomm__monoid__mult(_1477585), c_Nat__Transfer_Onat__set(_1477587), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1477585), _1477589), _1477587) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477585), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1477585, tc_Nat_Onat), _1477589), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1477587)))], (35868 ^ _777864) ^ [_1444938, _1444940, _1444942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1444938), _1444940)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444940), _1444942)) = 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, _1444938), _1444940)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444940), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444940), _1444942))))], (9002 ^ _777864) ^ [_927542, _927544] : [class_Rings_Ocomm__semiring__1(_927542), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927542), c_Groups_Ozero__class_Ozero(_927542)), _927544) = c_Groups_Ozero__class_Ozero(_927542))], (3208 ^ _777864) ^ [_826414, _826416] : [_826416 = _826414, -(c_Rings_Oinverse__class_Odivide(_826416) = c_Rings_Oinverse__class_Odivide(_826414))], (39997 ^ _777864) ^ [_1536777, _1536779] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1536777), c_Int_OInteg)), hBOOL(hAPP(_1536779, hAPP(c_Int_ORep__Integ, 40002 ^ [_1536777, _1536779]))), -(hBOOL(hAPP(_1536779, _1536777)))], (13076 ^ _777864) ^ [_997321, _997323, _997325, _997327, _997329, _997331] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _997321), _997323)), _997325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _997327), _997329)), _997331), 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), _997327), _997329)), _997331))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _997331), _997327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _997327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997327), _997321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _997323), _997329)))], (36288 ^ _777864) ^ [_1453498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453498)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453498) = 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, _1453498))))], (8164 ^ _777864) ^ [_913434, _913436] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913434) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _913436), -(_913434 = _913436)], (49144 ^ _777864) ^ [_1766560, _1766562] : [-(c_List_Olists(_1766560, _1766562) = hAPP(c_Set_OCollect(tc_List_Olist(_1766560)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1766560), tc_fun(_1766560, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1766560, tc_HOL_Obool), tc_fun(tc_fun(_1766560, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1766560)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1766560, tc_HOL_Obool))), c_List_Oset(_1766560))), _1766562)))], (1702 ^ _777864) ^ [_801907, _801909] : [-(class_Rings_Osemiring(_801907)), _801909 = _801907, class_Rings_Osemiring(_801909)], (1202 ^ _777864) ^ [_795657, _795659] : [-(class_Rings_Oring(_795657)), _795659 = _795657, class_Rings_Oring(_795659)], (27718 ^ _777864) ^ [_1271627, _1271629] : [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), _1271627), _1271629)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1271627), _1271629)))], (19492 ^ _777864) ^ [_1112930, _1112932, _1112934] : [class_Rings_Olinordered__semidom(_1112930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112930), hAPP(hAPP(c_Power_Opower__class_Opower(_1112930), _1112932), 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(_1112930), _1112934), 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(_1112930), c_Groups_Ozero__class_Ozero(_1112930)), _1112934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1112930), _1112932), _1112934)))], (38506 ^ _777864) ^ [_1500913] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1500913), 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, _1500913)) = _1500913)], (17910 ^ _777864) ^ [_1086628, _1086630, _1086632] : [class_Int_Onumber__ring(_1086628), 17913 ^ _777864 : [(17920 ^ _777864) ^ [] : [c_Int_Oiszero(_1086628, hAPP(c_Int_Onumber__class_Onumber__of(_1086628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086630), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086632)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1086628), _1086630) = hAPP(c_Int_Onumber__class_Onumber__of(_1086628), _1086632))], (17914 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1086628), _1086630) = hAPP(c_Int_Onumber__class_Onumber__of(_1086628), _1086632), -(c_Int_Oiszero(_1086628, hAPP(c_Int_Onumber__class_Onumber__of(_1086628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086630), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086632)))))]]], (18430 ^ _777864) ^ [_1094821, _1094823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094821), _1094823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1094821)), c_Int_OBit1(_1094823))))], (7812 ^ _777864) ^ [_907845, _907847] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_907845, _907847)], (15612 ^ _777864) ^ [_1043835, _1043837] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1043835), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1043837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1043835), _1043837))], (20792 ^ _777864) ^ [_1136467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136467)), -(c_Nat__Transfer_Ois__nat(_1136467))], (49436 ^ _777864) ^ [_1772569, _1772571] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772569)), c_List_Obutlast(_1772569, _1772571)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772569)), _1772571)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48496 ^ _777864) ^ [_1752012, _1752014] : [_1752014 = c_List_Olist_ONil(_1752012), -(hAPP(c_List_Orotate1(_1752012), _1752014) = c_List_Olist_ONil(_1752012))], (30581 ^ _777864) ^ [_1336995, _1336997, _1336999, _1337001, _1337003, _1337005] : [hBOOL(hAPP(hAPP(_1336995, _1336997), _1336999)), hBOOL(hAPP(hAPP(_1337001, _1336997), _1336999)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337003, tc_fun(_1337005, tc_HOL_Obool))), _1336995), _1337001), _1336997), _1336999)))], (18600 ^ _777864) ^ [_1097645] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1097645)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1097645))))], (7504 ^ _777864) ^ [_902060, _902062, _902064, _902066, _902068] : [c_Com_Ocom_OLocal(_902060, _902062, _902064) = c_Com_Ocom_OSemi(_902066, _902068)], (13288 ^ _777864) ^ [_1001005, _1001007, _1001009] : [class_Lattices_Oboolean__algebra(_1001005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001005), _1001007), _1001009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001005), hAPP(c_Groups_Ouminus__class_Ouminus(_1001005), _1001009)), hAPP(c_Groups_Ouminus__class_Ouminus(_1001005), _1001007))))], (40240 ^ _777864) ^ [_1541999, _1542001, _1542003] : [-(hBOOL(hAPP(_1541999, _1542001))), -(hAPP(c_Set_OCollect(_1542003), hAPP(hAPP(c_COMBS(_1542003, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542003), c_fconj), hAPP(hAPP(c_COMBC(_1542003, _1542003, tc_HOL_Obool), c_fequal), _1542001))), _1541999)) = c_Orderings_Obot__class_Obot(tc_fun(_1542003, tc_HOL_Obool)))], (51323 ^ _777864) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (14097 ^ _777864) ^ [_1016304, _1016306] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1016304), _1016306)), _1016304)))], (35990 ^ _777864) ^ [_1447569, _1447571, _1447573, _1447575] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447569), _1447571)), 35993 ^ _777864 : [(35994 ^ _777864) ^ [_1447727] : [35996 ^ _777864 : [(36002 ^ _777864) ^ [] : [-(_1447727 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35998 ^ [_1447569, _1447571, _1447573, _1447575, _1447727]), 35995 ^ [_1447569, _1447571, _1447573, _1447575, _1447727]))], (36000 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35998 ^ [_1447569, _1447571, _1447573, _1447575, _1447727]), _1447573)))], (35997 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35995 ^ [_1447569, _1447571, _1447573, _1447575, _1447727]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1447571))))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447727), _1447575)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1447569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1447727), _1447571)), _1447575)))]]], (4346 ^ _777864) ^ [_844373, _844375] : [_844375 = _844373, -(c_List_Orotate1(_844375) = c_List_Orotate1(_844373))], (27081 ^ _777864) ^ [_1256684, _1256686, _1256688, _1256690] : [_1256688 = _1256690, -(hAPP(hAPP(c_COMBC(_1256684, tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_fun(_1256686, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256686, tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_fun(_1256686, tc_HOL_Obool)), _1256684), c_COMBC(_1256686, tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256686, tc_prod(_1256684, _1256686)), tc_fun(_1256686, tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), _1256684), hAPP(c_COMBB(tc_prod(_1256684, _1256686), tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool), _1256686), c_member(tc_prod(_1256684, _1256686)))), c_Product__Type_OPair(_1256684, _1256686)))), _1256688) = hAPP(hAPP(c_COMBC(_1256684, tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_fun(_1256686, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256686, tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_fun(_1256686, tc_HOL_Obool)), _1256684), c_COMBC(_1256686, tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1256686, tc_prod(_1256684, _1256686)), tc_fun(_1256686, tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool)), _1256684), hAPP(c_COMBB(tc_prod(_1256684, _1256686), tc_fun(tc_fun(tc_prod(_1256684, _1256686), tc_HOL_Obool), tc_HOL_Obool), _1256686), c_member(tc_prod(_1256684, _1256686)))), c_Product__Type_OPair(_1256684, _1256686)))), _1256690))], (24709 ^ _777864) ^ [_1211447, _1211449, _1211451, _1211453, _1211455] : [_1211447 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1211449, _1211451, _1211453, _1211455), _1211447) = c_Lazy__Sequence_Ohit__bound(_1211451))], (13541 ^ _777864) ^ [_1005913, _1005915, _1005917] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005913), _1005915), _1005917) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1005913), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1005915, _1005917)), _1005917))], (4196 ^ _777864) ^ [_841990, _841992, _841994, _841996, _841998, _842000] : [-(c_Relation_OImage(_842000, _841996, _841992) = c_Relation_OImage(_841998, _841994, _841990)), _842000 = _841998, _841996 = _841994, _841992 = _841990], (7628 ^ _777864) ^ [_904287, _904289, _904291, _904293] : [c_Com_Ocom_OWhile(_904287, _904289) = c_Com_Ocom_OWhile(_904291, _904293), 7631 ^ _777864 : [(7634 ^ _777864) ^ [] : [-(_904289 = _904293)], (7632 ^ _777864) ^ [] : [-(_904287 = _904291)]]], (23655 ^ _777864) ^ [_1190977, _1190979, _1190981, _1190983] : [class_Orderings_Olinorder(_1190977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190977), _1190979), _1190981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190977), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1190977), _1190983), _1190979)), _1190981)))], (12272 ^ _777864) ^ [] : [-(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)))], (1232 ^ _777864) ^ [_796032, _796034] : [-(class_Orderings_Owellorder(_796032)), _796034 = _796032, class_Orderings_Owellorder(_796034)], (23513 ^ _777864) ^ [_1188309, _1188311, _1188313, _1188315] : [class_Orderings_Olinorder(_1188309), 23516 ^ _777864 : [(23525 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188309), _1188313), _1188315)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), _1188313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), _1188315))], (23517 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1188309), _1188313), _1188315))), 23520 ^ _777864 : [(23523 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), _1188315)))], (23521 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188309), _1188311), _1188313)))]]]]], (41670 ^ _777864) ^ [_1584859, _1584861, _1584863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1584859), c_Map_Odom(_1584859, _1584861, _1584863))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1584859), c_Orderings_Otop__class_Otop(tc_fun(_1584859, tc_HOL_Obool))))), -(hAPP(_1584863, 41677 ^ [_1584859, _1584861, _1584863]) = c_Option_Ooption_ONone(_1584861))], (29974 ^ _777864) ^ [_1322810, _1322812, _1322814, _1322816, _1322818] : [class_Lattices_Olattice(_1322810), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322812, _1322810)), _1322814), _1322816), _1322818) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322810), hAPP(_1322814, _1322818)), hAPP(_1322816, _1322818)))], (38202 ^ _777864) ^ [_1494797, _1494799] : [class_Orderings_Otop(_1494797), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494797), _1494799), c_Orderings_Otop__class_Otop(_1494797))))], (36204 ^ _777864) ^ [_1451720, _1451722, _1451724, _1451726, _1451728] : [c_Fun_Oinj__on(_1451720, _1451722, _1451724, _1451726), hBOOL(hAPP(hAPP(c_member(_1451720), _1451728), _1451726)), -(hAPP(c_Fun_Othe__inv__into(_1451720, _1451722, _1451726, _1451724), hAPP(_1451724, _1451728)) = _1451728)], (32709 ^ _777864) ^ [_1377029, _1377031, _1377033, _1377035] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1377029, _1377031)), c_Sum__Type_OPlus(_1377029, _1377031, _1377033, _1377035))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1377029), _1377033)))], (29660 ^ _777864) ^ [_1316414, _1316416, _1316418] : [class_Lattices_Olattice(_1316414), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316414), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316414), _1316416), _1316418)), _1316418)))], (28014 ^ _777864) ^ [_1277003, _1277005, _1277007, _1277009] : [class_Lattices_Osemilattice__sup(_1277003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277003), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277003), _1277005), _1277007)), _1277009)), 28021 ^ _777864 : [(28024 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277003), _1277007), _1277009)))], (28022 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277003), _1277005), _1277009)))]]], (1192 ^ _777864) ^ [_795532, _795534] : [-(class_Rings_Oring__1(_795532)), _795534 = _795532, class_Rings_Oring__1(_795534)], (38076 ^ _777864) ^ [_1492558, _1492560, _1492562, _1492564, _1492566] : [c_Fun_Oinj__on(_1492558, _1492560, _1492562, c_Orderings_Otop__class_Otop(tc_fun(_1492558, tc_HOL_Obool))), hAPP(_1492562, _1492564) = hAPP(_1492562, _1492566), -(_1492564 = _1492566)], (44718 ^ _777864) ^ [_1657644, _1657646, _1657648, _1657650, _1657652] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657644, tc_fun(_1657646, tc_HOL_Obool)), _1657648), hAPP(hAPP(c_COMBS(_1657644, tc_fun(_1657646, tc_HOL_Obool), tc_fun(_1657646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1657646, tc_HOL_Obool), tc_fun(tc_fun(_1657646, tc_HOL_Obool), tc_fun(_1657646, tc_HOL_Obool)), _1657644), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657646, tc_HOL_Obool))), _1657650)), _1657652)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1657646, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657646, tc_HOL_Obool), hAPP(c_Set_Oimage(_1657644, tc_fun(_1657646, tc_HOL_Obool), _1657650), _1657648))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1657646, tc_HOL_Obool), hAPP(c_Set_Oimage(_1657644, tc_fun(_1657646, tc_HOL_Obool), _1657652), _1657648))))], (10946 ^ _777864) ^ [_960128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _960128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_960128 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41447 ^ _777864) ^ [_1579424, _1579426] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579424, _1579424)), _1579426)), 41450 ^ _777864 : [(41457 ^ _777864) ^ [] : [c_Wellfounded_Oacyclic(_1579424, _1579426), -(c_Wellfounded_Owf(_1579424, _1579426))], (41451 ^ _777864) ^ [] : [c_Wellfounded_Owf(_1579424, _1579426), -(c_Wellfounded_Oacyclic(_1579424, _1579426))]]], (27199 ^ _777864) ^ [_1260299, _1260301, _1260303, _1260305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool)), _1260303), _1260305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260299, tc_fun(_1260301, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1260299, tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_fun(_1260301, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260301, tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_fun(_1260301, tc_HOL_Obool)), _1260299), c_COMBC(_1260301, tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260301, tc_prod(_1260299, _1260301)), tc_fun(_1260301, tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), _1260299), hAPP(c_COMBB(tc_prod(_1260299, _1260301), tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool), _1260301), c_member(tc_prod(_1260299, _1260301)))), c_Product__Type_OPair(_1260299, _1260301)))), _1260303)), hAPP(hAPP(c_COMBC(_1260299, tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_fun(_1260301, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260301, tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_fun(_1260301, tc_HOL_Obool)), _1260299), c_COMBC(_1260301, tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1260301, tc_prod(_1260299, _1260301)), tc_fun(_1260301, tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool)), _1260299), hAPP(c_COMBB(tc_prod(_1260299, _1260301), tc_fun(tc_fun(tc_prod(_1260299, _1260301), tc_HOL_Obool), tc_HOL_Obool), _1260301), c_member(tc_prod(_1260299, _1260301)))), c_Product__Type_OPair(_1260299, _1260301)))), _1260305))))], (1472 ^ _777864) ^ [_799032, _799034] : [-(class_Groups_Ocancel__semigroup__add(_799032)), _799034 = _799032, class_Groups_Ocancel__semigroup__add(_799034)], (23869 ^ _777864) ^ [_1195014, _1195016, _1195018] : [class_Orderings_Olinorder(_1195014), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195014), _1195016), _1195018) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1195014), _1195018), _1195016))], (5124 ^ _777864) ^ [_856310, _856312, _856314, _856316] : [-(c_List_Obutlast(_856316, _856312) = c_List_Obutlast(_856314, _856310)), _856316 = _856314, _856312 = _856310], (39521 ^ _777864) ^ [_1525962, _1525964, _1525966] : [class_Orderings_Olinorder(_1525962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525962), _1525964)), -(_1525964 = c_Orderings_Obot__class_Obot(tc_fun(_1525962, tc_HOL_Obool))), 39532 ^ _777864 : [(39533 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525962), _1525966), hAPP(c_Finite__Set_Ofold1(_1525962, c_Orderings_Oord__class_Omin(_1525962)), _1525964))), 39536 ^ _777864 : [(39537 ^ _777864) ^ [_1526255] : [hBOOL(hAPP(hAPP(c_member(_1525962), _1526255), _1525964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525962), _1525966), _1526255)))]]], (39543 ^ _777864) ^ [] : [39545 ^ _777864 : [(39548 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525962), _1525966), 39544 ^ [_1525962, _1525964, _1525966]))], (39546 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525962), 39544 ^ [_1525962, _1525964, _1525966]), _1525964)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1525962), _1525966), hAPP(c_Finite__Set_Ofold1(_1525962, c_Orderings_Oord__class_Omin(_1525962)), _1525964))))]]], (29502 ^ _777864) ^ [_1312937, _1312939, _1312941, _1312943, _1312945, _1312947] : [c_Equiv__Relations_Oequiv(_1312937, _1312939, _1312941), hBOOL(hAPP(hAPP(c_member(_1312937), _1312943), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312937, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1312937, _1312937, _1312941), hAPP(hAPP(c_Set_Oinsert(_1312937), _1312945), c_Orderings_Obot__class_Obot(tc_fun(_1312937, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1312937, _1312937, _1312941), hAPP(hAPP(c_Set_Oinsert(_1312937), _1312947), c_Orderings_Obot__class_Obot(tc_fun(_1312937, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1312937, _1312937)), hAPP(hAPP(c_Product__Type_OPair(_1312937, _1312937), _1312945), _1312947)), _1312941)))], (18546 ^ _777864) ^ [_1096760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096760), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1096760)), c_Int_OMin)))], (25011 ^ _777864) ^ [_1216921, _1216923] : [_1216921 = _1216923, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216921), _1216923)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1216923), _1216921)))], (40831 ^ _777864) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (35739 ^ _777864) ^ [_1442625, _1442627] : [35747 ^ _777864 : [(35750 ^ _777864) ^ [] : [-(hBOOL(hAPP(_1442627, 35746 ^ [_1442625, _1442627])))], (35748 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35746 ^ [_1442625, _1442627]), _1442625)))]], 35740 ^ _777864 : [(35741 ^ _777864) ^ [_1442693] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1442693), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1442625))), hBOOL(hAPP(_1442627, _1442693))]]], (44965 ^ _777864) ^ [_1663523, _1663525] : [class_Complete__Lattice_Ocomplete__lattice(_1663523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1663523), _1663525)), -(_1663525 = c_Orderings_Obot__class_Obot(tc_fun(_1663523, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1663523, _1663525) = c_Complete__Lattice_OSup__class_OSup(_1663523, _1663525))], (6462 ^ _777864) ^ [_884559, _884561, _884563] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884559), _884561) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _884559), _884563), -(_884561 = _884563)], (40208 ^ _777864) ^ [_1541067, _1541069, _1541071] : [-(hAPP(hAPP(c_Set_Oinsert(_1541067), _1541069), _1541071) = hAPP(c_Set_OCollect(_1541067), hAPP(hAPP(c_COMBS(_1541067, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541067), c_fdisj), hAPP(hAPP(c_COMBC(_1541067, _1541067, tc_HOL_Obool), c_fequal), _1541069))), hAPP(hAPP(c_COMBC(_1541067, tc_fun(_1541067, tc_HOL_Obool), tc_HOL_Obool), c_member(_1541067)), _1541071))))], (47582 ^ _777864) ^ [_1728988, _1728990, _1728992, _1728994, _1728996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728988, tc_HOL_Obool)), hAPP(c_List_Oset(_1728988), _1728990)), _1728992)), hBOOL(hAPP(hAPP(c_member(_1728988), _1728994), _1728992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728988, tc_HOL_Obool)), hAPP(c_List_Oset(_1728988), hAPP(hAPP(c_List_Olist__update(_1728988, _1728990), _1728996), _1728994))), _1728992)))], (51309 ^ _777864) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (36846 ^ _777864) ^ [_1466059, _1466061, _1466063] : [class_Groups_Ocomm__monoid__add(_1466059), hAPP(_1466061, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1466059), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466059), _1466061), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1466063)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466059), _1466061), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1466063)))], (29888 ^ _777864) ^ [_1320602, _1320604, _1320606, _1320608] : [-(hBOOL(hAPP(hAPP(c_member(_1320602), _1320604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320602, tc_HOL_Obool)), _1320606), _1320608)))), hBOOL(hAPP(hAPP(c_member(_1320602), _1320604), _1320606)), hBOOL(hAPP(hAPP(c_member(_1320602), _1320604), _1320608))], (31705 ^ _777864) ^ [_1357077, _1357079, _1357081] : [class_Orderings_Olinorder(_1357077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357077), _1357079)), 31712 ^ _777864 : [(31719 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357077, tc_HOL_Obool)), _1357079), hAPP(hAPP(c_Set_Oinsert(_1357077), _1357081), c_Orderings_Obot__class_Obot(tc_fun(_1357077, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1357077, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1357077, hAPP(hAPP(c_Set_Oinsert(_1357077), _1357081), _1357079)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1357077), _1357081), c_Big__Operators_Olinorder__class_OMin(_1357077, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357077, tc_HOL_Obool)), _1357079), hAPP(hAPP(c_Set_Oinsert(_1357077), _1357081), c_Orderings_Obot__class_Obot(tc_fun(_1357077, tc_HOL_Obool)))))))], (31713 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357077, tc_HOL_Obool)), _1357079), hAPP(hAPP(c_Set_Oinsert(_1357077), _1357081), c_Orderings_Obot__class_Obot(tc_fun(_1357077, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1357077, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1357077, hAPP(hAPP(c_Set_Oinsert(_1357077), _1357081), _1357079)) = _1357081)]]], (29984 ^ _777864) ^ [_1323093, _1323095, _1323097] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323093, tc_HOL_Obool)), _1323095), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323093, tc_HOL_Obool)), _1323095), _1323097)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323093, tc_HOL_Obool)), _1323095), _1323097))], (40642 ^ _777864) ^ [_1557067, _1557069, _1557071, _1557073, _1557075, _1557077, _1557079] : [class_Rings_Osemiring__0(_1557067), c_Fun_Oinj__on(tc_prod(_1557069, _1557071), _1557067, hAPP(c_Product__Type_Oprod_Oprod__case(_1557069, _1557071, _1557067), hAPP(hAPP(c_COMBC(_1557069, tc_fun(_1557071, _1557067), tc_fun(_1557071, _1557067)), hAPP(hAPP(c_COMBB(tc_fun(_1557067, _1557067), tc_fun(tc_fun(_1557071, _1557067), tc_fun(_1557071, _1557067)), _1557069), c_COMBB(_1557067, _1557067, _1557071)), hAPP(hAPP(c_COMBB(_1557067, tc_fun(_1557067, _1557067), _1557069), c_Groups_Otimes__class_Otimes(_1557067)), _1557073))), _1557075)), hAPP(hAPP(c_Product__Type_OSigma(_1557069, _1557071), _1557077), hAPP(c_COMBK(tc_fun(_1557071, tc_HOL_Obool), _1557069), _1557079))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1557067), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557069, _1557067), _1557073), _1557077)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557071, _1557067), _1557075), _1557079)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557067, _1557067), c_Fun_Oid(_1557067)), hAPP(c_Set_OCollect(_1557067), hAPP(hAPP(c_COMBB(tc_fun(_1557069, tc_HOL_Obool), tc_HOL_Obool, _1557067), c_HOL_OEx(_1557069)), hAPP(hAPP(c_COMBB(tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool)), tc_fun(_1557069, tc_HOL_Obool), _1557067), hAPP(c_COMBB(tc_fun(_1557071, tc_HOL_Obool), tc_HOL_Obool, _1557069), c_HOL_OEx(_1557071))), hAPP(hAPP(c_COMBC(_1557067, tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool)), tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557069, tc_fun(tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool))), tc_fun(tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool)), tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool))), _1557067), c_COMBS(_1557069, tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557069, tc_fun(_1557071, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1557069, tc_fun(tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool))), _1557067), hAPP(c_COMBB(tc_fun(_1557071, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool)), _1557069), c_COMBS(_1557071, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool)), tc_fun(_1557069, tc_fun(_1557071, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1557067), hAPP(c_COMBB(tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1557069), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557071), c_fconj))), hAPP(hAPP(c_COMBC(_1557067, tc_fun(_1557069, tc_fun(_1557071, _1557067)), tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1557071, _1557067), tc_fun(_1557071, tc_HOL_Obool)), tc_fun(tc_fun(_1557069, tc_fun(_1557071, _1557067)), tc_fun(_1557069, tc_fun(_1557071, tc_HOL_Obool))), _1557067), c_COMBB(tc_fun(_1557071, _1557067), tc_fun(_1557071, tc_HOL_Obool), _1557069)), hAPP(hAPP(c_COMBB(tc_fun(_1557067, tc_HOL_Obool), tc_fun(tc_fun(_1557071, _1557067), tc_fun(_1557071, tc_HOL_Obool)), _1557067), c_COMBB(_1557067, tc_HOL_Obool, _1557071)), c_fequal))), hAPP(hAPP(c_COMBC(_1557069, tc_fun(_1557071, _1557067), tc_fun(_1557071, _1557067)), hAPP(hAPP(c_COMBB(tc_fun(_1557067, _1557067), tc_fun(tc_fun(_1557071, _1557067), tc_fun(_1557071, _1557067)), _1557069), c_COMBB(_1557067, _1557067, _1557071)), hAPP(hAPP(c_COMBB(_1557067, tc_fun(_1557067, _1557067), _1557069), c_Groups_Otimes__class_Otimes(_1557067)), _1557073))), _1557075)))))), hAPP(hAPP(c_COMBC(_1557069, tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1557071, tc_HOL_Obool), tc_fun(_1557071, tc_HOL_Obool)), _1557069), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1557071)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1557069), c_fconj), hAPP(hAPP(c_COMBC(_1557069, tc_fun(_1557069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1557069)), _1557077)))), hAPP(hAPP(c_COMBC(_1557071, tc_fun(_1557071, tc_HOL_Obool), tc_HOL_Obool), c_member(_1557071)), _1557079))))))))], (14189 ^ _777864) ^ [_1017883, _1017885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017885)), -(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), _1017883), _1017885))))], (1382 ^ _777864) ^ [_797907, _797909] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_797907)), _797909 = _797907, class_Groups_Oordered__ab__semigroup__add__imp__le(_797909)], (33402 ^ _777864) ^ [_1391879, _1391881, _1391883] : [class_Orderings_Oorder(_1391879), 33405 ^ _777864 : [(33412 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391879), _1391881), _1391883))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1391879, _1391881, _1391883) = c_Orderings_Obot__class_Obot(tc_fun(_1391879, tc_HOL_Obool)))], (33406 ^ _777864) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1391879, _1391881, _1391883) = c_Orderings_Obot__class_Obot(tc_fun(_1391879, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391879), _1391881), _1391883))]]], (39227 ^ _777864) ^ [_1519659, _1519661, _1519663, _1519665, _1519667, _1519669] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1519659, _1519661)), hAPP(hAPP(c_Product__Type_OPair(_1519659, _1519661), _1519663), _1519665)), hAPP(hAPP(c_Product__Type_OSigma(_1519659, _1519661), _1519667), _1519669))), -(hBOOL(hAPP(hAPP(c_member(_1519659), _1519663), _1519667)))], (24043 ^ _777864) ^ [_1198182, _1198184, _1198186, _1198188] : [class_Orderings_Olinorder(_1198182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198182), _1198184), _1198186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198182), _1198188), _1198186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1198182), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1198182), _1198184), _1198188)), _1198186)))], (9662 ^ _777864) ^ [_939345, _939347, _939349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _939345), _939347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _939349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939349), _939345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _939349), _939347))))], (46960 ^ _777864) ^ [_1714134, _1714136, _1714138] : [class_Orderings_Olinorder(_1714134), hBOOL(hAPP(hAPP(c_member(_1714134), _1714136), hAPP(c_List_Oset(_1714134), _1714138))), -(c_List_Olinorder__class_Oinsort__insert__key(_1714134, _1714134, c_COMBI(_1714134), _1714136, _1714138) = _1714138)], (14566 ^ _777864) ^ [_1023990, _1023992] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023990), _1023992) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14567 ^ _777864 : [(14576 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023990), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023992), _1023990))], (14570 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023990), _1023992))], (14568 ^ _777864) ^ [] : [_1023992 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (18876 ^ _777864) ^ [_1102340, _1102342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1102340)), c_Int_OBit0(_1102342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102340), _1102342)))], (20962 ^ _777864) ^ [_1139313, _1139315, _1139317, _1139319] : [class_Fields_Ofield__inverse__zero(_1139313), class_Int_Onumber(_1139313), 20969 ^ _777864 : [(20970 ^ _777864) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139313), _1139315), _1139317) = hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319), 20973 ^ _777864 : [(20980 ^ _777864) ^ [] : [_1139317 = c_Groups_Ozero__class_Ozero(_1139313), -(hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319) = c_Groups_Ozero__class_Ozero(_1139313))], (20974 ^ _777864) ^ [] : [-(_1139317 = c_Groups_Ozero__class_Ozero(_1139313)), -(_1139315 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139313), hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319)), _1139317))]]], (20986 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139313), _1139315), _1139317) = hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319)), 20989 ^ _777864 : [(20992 ^ _777864) ^ [] : [_1139315 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139313), hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319)), _1139317)], (20990 ^ _777864) ^ [] : [_1139317 = c_Groups_Ozero__class_Ozero(_1139313)]], 20993 ^ _777864 : [(20996 ^ _777864) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1139313), _1139319) = c_Groups_Ozero__class_Ozero(_1139313)], (20994 ^ _777864) ^ [] : [-(_1139317 = c_Groups_Ozero__class_Ozero(_1139313))]]]]], (8478 ^ _777864) ^ [_918340, _918342] : [-(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, _918340)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _918342))))], (17408 ^ _777864) ^ [_1078327, _1078329, _1078331, _1078333] : [class_Rings_Olinordered__semidom(_1078327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078327), c_Groups_Oone__class_Oone(_1078327)), _1078329)), 17415 ^ _777864 : [(17422 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078331), _1078333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078327), hAPP(hAPP(c_Power_Opower__class_Opower(_1078327), _1078329), _1078331)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078327), _1078329), _1078333))))], (17416 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078327), hAPP(hAPP(c_Power_Opower__class_Opower(_1078327), _1078329), _1078331)), hAPP(hAPP(c_Power_Opower__class_Opower(_1078327), _1078329), _1078333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078331), _1078333)))]]], (17944 ^ _777864) ^ [_1087242, _1087244, _1087246] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087242), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087242)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1087244)), _1087246)) = 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), _1087242), _1087244))), _1087246))], (30961 ^ _777864) ^ [_1343781, _1343783, _1343785] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343781, _1343783) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1343785), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 30964 ^ _777864 : [(30967 ^ _777864) ^ [] : [-(_1343783 = _1343785)], (30965 ^ _777864) ^ [] : [-(_1343781 = _1343783)]]], (32825 ^ _777864) ^ [_1379689, _1379691, _1379693, _1379695] : [class_Rings_Ocomm__semiring__1(_1379689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379691), _1379693)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1379691, _1379689), _1379695), _1379693) = c_Groups_Ozero__class_Ozero(_1379689)), 32834 ^ _777864 : [(32835 ^ _777864) ^ [_1379870] : [hBOOL(hAPP(hAPP(c_member(_1379691), _1379870), _1379693)), hAPP(_1379695, _1379870) = c_Groups_Ozero__class_Ozero(_1379689)]]], (48362 ^ _777864) ^ [_1748091, _1748093, _1748095, _1748097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748091), tc_List_Olist(_1748091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748091), tc_List_Olist(_1748091)), _1748093), _1748095)), c_List_Olistrel1(_1748091, _1748097))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1748091), tc_List_Olist(_1748091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1748091), tc_List_Olist(_1748091)), _1748093), _1748095)), c_List_Olistrel(_1748091, c_Transitive__Closure_Ortrancl(_1748091, _1748097)))))], (51503 ^ _777864) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (25425 ^ _777864) ^ [_1223709, _1223711, _1223713] : [class_Rings_Olinordered__idom(_1223709), hAPP(c_Groups_Oabs__class_Oabs(_1223709), _1223711) = hAPP(c_Groups_Oabs__class_Oabs(_1223709), _1223713), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1223709), _1223711), _1223713)))], (13120 ^ _777864) ^ [_998175, _998177, _998179, _998181, _998183, _998185] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998175), _998177)), _998179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _998181), _998183)), _998185), 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), _998181), _998183)), _998185)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _998179), _998175)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _998181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998181), _998175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _998183), _998177)))], (7782 ^ _777864) ^ [_907080, _907082] : [hBOOL(hAPP(c_Com_OWT, _907080)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_907082, _907080))))], (29990 ^ _777864) ^ [_1323238, _1323240, _1323242, _1323244, _1323246] : [class_Lattices_Olattice(_1323238), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323240, _1323238)), _1323242), _1323244), _1323246) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323238), hAPP(_1323242, _1323246)), hAPP(_1323244, _1323246)))], (9098 ^ _777864) ^ [_928998, _929000, _929002, _929004, _929006] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_928998), 9101 ^ _777864 : [(9102 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929000), _929004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929002), _929006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929000), _929006)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929002), _929004)), -(_929000 = _929002), -(_929004 = _929006)], (9112 ^ _777864) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929000), _929004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929002), _929006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929000), _929006)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928998), _929002), _929004))), 9115 ^ _777864 : [(9118 ^ _777864) ^ [] : [_929004 = _929006], (9116 ^ _777864) ^ [] : [_929000 = _929002]]]]], (33504 ^ _777864) ^ [_1394125, _1394127, _1394129, _1394131, _1394133] : [33506 ^ _777864 : [(33509 ^ _777864) ^ [] : [hBOOL(hAPP(_1394133, 33505 ^ [_1394125, _1394127, _1394129, _1394131, _1394133]))], (33507 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394125), 33505 ^ [_1394125, _1394127, _1394129, _1394131, _1394133]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1394127, tc_fun(_1394125, tc_HOL_Obool)), _1394129), _1394131))))]], 33510 ^ _777864 : [(33511 ^ _777864) ^ [_1394347] : [hBOOL(hAPP(hAPP(c_member(_1394127), _1394347), _1394129)), 33514 ^ _777864 : [(33515 ^ _777864) ^ [_1394444] : [hBOOL(hAPP(hAPP(c_member(_1394125), _1394444), hAPP(_1394131, _1394347))), -(hBOOL(hAPP(_1394133, _1394444)))]]]]], (48774 ^ _777864) ^ [_1758221, _1758223, _1758225] : [-(hAPP(hAPP(c_List_Odrop(_1758221), _1758223), hAPP(c_List_Otl(_1758221), _1758225)) = hAPP(c_List_Otl(_1758221), hAPP(hAPP(c_List_Odrop(_1758221), _1758223), _1758225)))], (10456 ^ _777864) ^ [_952518, _952520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _952520)), 10463 ^ _777864 : [(10470 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952518), _952520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _952518)), hAPP(c_Int_Onat, _952520))))], (10464 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _952518)), hAPP(c_Int_Onat, _952520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _952518), _952520)))]]], (7376 ^ _777864) ^ [_899430, _899432, _899434] : [hBOOL(hAPP(c_Com_OWT, _899430)), hBOOL(hAPP(c_Com_OWT, _899432)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_899434, _899430, _899432))))], (45465 ^ _777864) ^ [_1675464, _1675466, _1675468] : [-(c_Map_Omap__add(_1675464, _1675466, _1675468, hAPP(c_COMBK(tc_Option_Ooption(_1675466), _1675464), c_Option_Ooption_ONone(_1675466))) = _1675468)], (29428 ^ _777864) ^ [_1311364, _1311366, _1311368, _1311370, _1311372, _1311374, _1311376, _1311378] : [c_Finite__Set_Ofolding__image__simple(_1311364, _1311366, _1311368, _1311370, _1311372, _1311374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311366), _1311376)), -(hAPP(_1311374, hAPP(hAPP(c_Set_Oinsert(_1311366), _1311378), _1311376)) = hAPP(hAPP(_1311368, hAPP(_1311372, _1311378)), hAPP(_1311374, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1311366, tc_HOL_Obool)), _1311376), hAPP(hAPP(c_Set_Oinsert(_1311366), _1311378), c_Orderings_Obot__class_Obot(tc_fun(_1311366, tc_HOL_Obool)))))))], (47498 ^ _777864) ^ [_1727556, _1727558, _1727560] : [-(hAPP(c_Map_Omap__of(_1727556, _1727558, c_List_Olist_ONil(tc_prod(_1727556, _1727558))), _1727560) = c_Option_Ooption_ONone(_1727558))], (18158 ^ _777864) ^ [_1090273] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1090273), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090273), c_Int_OPls)))], (50873 ^ _777864) ^ [_1804164, _1804166] : [c_List_Oremdups(_1804164, _1804166) = c_List_Olist_ONil(_1804164), -(_1804166 = c_List_Olist_ONil(_1804164))], (25995 ^ _777864) ^ [_1234274, _1234276, _1234278, _1234280] : [class_Orderings_Oorder(_1234274), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1234274, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234276), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234278), _1234280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234274), hAPP(_1234276, _1234278)), hAPP(_1234276, _1234280))))], (27458 ^ _777864) ^ [_1266539, _1266541, _1266543, _1266545, _1266547, _1266549, _1266551, _1266553] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1266539, _1266541), tc_prod(_1266539, _1266541))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1266539, _1266541), tc_prod(_1266539, _1266541)), hAPP(hAPP(c_Product__Type_OPair(_1266539, _1266541), _1266543), _1266545)), hAPP(hAPP(c_Product__Type_OPair(_1266539, _1266541), _1266547), _1266549))), c_Wellfounded_Olex__prod(_1266539, _1266541, _1266551, _1266553))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1266539, _1266539)), hAPP(hAPP(c_Product__Type_OPair(_1266539, _1266539), _1266543), _1266547)), _1266551))), 27465 ^ _777864 : [(27468 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1266541, _1266541)), hAPP(hAPP(c_Product__Type_OPair(_1266541, _1266541), _1266545), _1266549)), _1266553)))], (27466 ^ _777864) ^ [] : [-(_1266543 = _1266547)]]], (39934 ^ _777864) ^ [_1535414, _1535416, _1535418, _1535420, _1535422] : [c_Relation_Orefl__on(_1535414, _1535416, _1535418), hBOOL(hAPP(hAPP(c_member(tc_prod(_1535414, _1535414)), hAPP(hAPP(c_Product__Type_OPair(_1535414, _1535414), _1535420), _1535422)), _1535418)), -(hBOOL(hAPP(hAPP(c_member(_1535414), _1535422), _1535416)))], (46048 ^ _777864) ^ [_1689258, _1689260] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1689258, _1689260))))], (6140 ^ _777864) ^ [_878842] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _878842))))], (9979 ^ _777864) ^ [_944638, _944640] : [class_Rings_Olinordered__idom(_944638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944638), c_Groups_Ozero__class_Ozero(_944638)), _944640)), -(c_Groups_Osgn__class_Osgn(_944638, _944640) = c_Groups_Oone__class_Oone(_944638))], (38790 ^ _777864) ^ [_1508627, _1508629, _1508631, _1508633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508627), hAPP(c_Set_Ovimage(_1508627, _1508629, _1508631), _1508633))), hAPP(c_Set_Oimage(_1508627, _1508629, _1508631), c_Orderings_Otop__class_Otop(tc_fun(_1508627, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1508629, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1508629), _1508633)))], (19574 ^ _777864) ^ [_1114583, _1114585, _1114587] : [class_Rings_Ocomm__semiring__1(_1114583), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1114583), _1114585), 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)))), _1114587))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114583), _1114585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114583), hAPP(hAPP(c_Power_Opower__class_Opower(_1114583), _1114585), _1114587)), hAPP(hAPP(c_Power_Opower__class_Opower(_1114583), _1114585), _1114587))))], (13487 ^ _777864) ^ [_1004796, _1004798, _1004800, _1004802] : [class_Divides_Osemiring__div(_1004796), -(c_Divides_Odiv__class_Omod(_1004796, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004796), _1004798), _1004800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004796), _1004798), _1004802)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004796), _1004798), c_Divides_Odiv__class_Omod(_1004796, _1004800, _1004802)))], (16976 ^ _777864) ^ [_1070609, _1070611] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070609)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1070611)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1070609), _1070611)))], (7118 ^ _777864) ^ [_894840, _894842, _894844, _894846, _894848, _894850] : [hBOOL(hAPP(_894840, _894842)), c_Natural_Oevaln(_894844, _894842, _894846, _894848), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_894840, _894844, _894850), _894842, _894846, _894848))], (26299 ^ _777864) ^ [_1240545, _1240547] : [_1240547 = c_Orderings_Obot__class_Obot(tc_fun(_1240545, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240545, tc_HOL_Obool)), _1240547), c_Orderings_Obot__class_Obot(tc_fun(_1240545, tc_HOL_Obool)))))], (44200 ^ _777864) ^ [_1645460] : [-(hAPP(c_Relation_ODomain(_1645460, _1645460), c_Relation_OId(_1645460)) = c_Orderings_Otop__class_Otop(tc_fun(_1645460, tc_HOL_Obool)))], (6793 ^ _777864) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (30188 ^ _777864) ^ [_1327386, _1327388, _1327390] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327386, tc_HOL_Obool)), _1327388), _1327390) = c_Orderings_Obot__class_Obot(tc_fun(_1327386, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327386, tc_HOL_Obool)), _1327388), _1327390) = _1327388)], (30835 ^ _777864) ^ [_1341815, _1341817] : [class_Orderings_Olinorder(_1341815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341815), _1341817)), -(_1341817 = c_Orderings_Obot__class_Obot(tc_fun(_1341815, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1341815), c_Big__Operators_Olinorder__class_OMax(_1341815, _1341817)), _1341817)))], (19346 ^ _777864) ^ [_1110486] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1110486)), 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, _1110486, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (47404 ^ _777864) ^ [_1725485, _1725487] : [-(hAPP(hAPP(c_List_Otake(_1725485), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1725487) = c_List_Olist_ONil(_1725485))], (45715 ^ _777864) ^ [_1681255, _1681257, _1681259] : [c_Fun_Oinj__on(_1681255, _1681257, _1681259, c_Orderings_Otop__class_Otop(tc_fun(_1681255, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1681255), tc_List_Olist(_1681257), hAPP(c_List_Omap(_1681255, _1681257), _1681259), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1681255), tc_HOL_Obool))))], (19616 ^ _777864) ^ [_1115443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1115443)), -(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), _1115443), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (33715 ^ _777864) ^ [_1399396, _1399398, _1399400, _1399402, _1399404, _1399406] : [-(hAPP(c_Set_Oimage(_1399396, _1399398, _1399400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399402, tc_fun(_1399396, tc_HOL_Obool)), _1399404), _1399406)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1399402, tc_fun(_1399398, tc_HOL_Obool)), _1399404), hAPP(hAPP(c_COMBB(tc_fun(_1399396, tc_HOL_Obool), tc_fun(_1399398, tc_HOL_Obool), _1399402), c_Set_Oimage(_1399396, _1399398, _1399400)), _1399406)))], (3880 ^ _777864) ^ [_836940, _836942, _836944, _836946] : [-(c_Transitive__Closure_Otrancl(_836946, _836942) = c_Transitive__Closure_Otrancl(_836944, _836940)), _836946 = _836944, _836942 = _836940], (48602 ^ _777864) ^ [_1754480, _1754482, _1754484, _1754486] : [_1754480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1754482), _1754480), hAPP(hAPP(c_List_Olist_OCons(_1754482), _1754484), _1754486)) = hAPP(hAPP(c_List_Olist_OCons(_1754482), _1754484), _1754486))], (44594 ^ _777864) ^ [_1655096, _1655098, _1655100, _1655102] : [hBOOL(hAPP(hAPP(c_member(_1655096), _1655098), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1655096, tc_HOL_Obool), _1655100))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1655096, tc_HOL_Obool)), _1655102), _1655100)), -(hBOOL(hAPP(hAPP(c_member(_1655096), _1655098), _1655102)))], (34889 ^ _777864) ^ [_1425653, _1425655, _1425657, _1425659] : [class_Orderings_Oorder(_1425653), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425653, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1425653, _1425655, _1425657)), c_SetInterval_Oord__class_OatLeastAtMost(_1425653, _1425657, _1425659)) = c_Orderings_Obot__class_Obot(tc_fun(_1425653, tc_HOL_Obool)))], (14532 ^ _777864) ^ [_1023503, _1023505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023503)), 14535 ^ _777864 : [(14542 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023505)), -(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), _1023505), _1023503))))], (14536 ^ _777864) ^ [] : [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), _1023505), _1023503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023505)))]]], (16047 ^ _777864) ^ [_1052973, _1052975, _1052977] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1052973, _1052975) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1052977, _1052975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052977), _1052973)), -(_1052973 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052975), 16054 ^ [_1052973, _1052975, _1052977])))], (16512 ^ _777864) ^ [_1061320, _1061322, _1061324, _1061326] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061320), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061320), _1061322), _1061324)), hAPP(c_Int_Onumber__class_Onumber__of(_1061320), _1061326)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061320), _1061322), hAPP(c_Int_Onumber__class_Onumber__of(_1061320), _1061326))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061320), _1061324), hAPP(c_Int_Onumber__class_Onumber__of(_1061320), _1061326)))), class_Int_Onumber(_1061320), class_Rings_Osemiring(_1061320)], (30573 ^ _777864) ^ [_1336822, _1336824, _1336826, _1336828, _1336830, _1336832] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336822, tc_fun(_1336824, tc_HOL_Obool))), _1336826), _1336828), _1336830), _1336832)), 30576 ^ _777864 : [(30579 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336828, _1336830), _1336832)))], (30577 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(_1336826, _1336830), _1336832)))]]], (28483 ^ _777864) ^ [_1290085, _1290087, _1290089, _1290091, _1290093] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290085, tc_HOL_Obool)), _1290087), hAPP(c_Set_Oimage(_1290089, _1290085, _1290091), _1290093)))), 28484 ^ _777864 : [(28485 ^ _777864) ^ [_1290165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290089, tc_HOL_Obool)), _1290165), _1290093)), _1290087 = hAPP(c_Set_Oimage(_1290089, _1290085, _1290091), _1290165)]]], (15618 ^ _777864) ^ [_1043953, _1043955] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1043953), _1043955)), _1043955) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043953), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1043953, _1043955)))], (17050 ^ _777864) ^ [_1071820, _1071822] : [_1071820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1071822), _1071820) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (40282 ^ _777864) ^ [_1542899, _1542901] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1542899, tc_HOL_Obool)), _1542901) = hAPP(c_Set_OCollect(_1542899), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1542899), c_fNot), hAPP(hAPP(c_COMBC(_1542899, tc_fun(_1542899, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542899)), _1542901))))], (47930 ^ _777864) ^ [_1737148, _1737150, _1737152, _1737154, _1737156, _1737158] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737148)), _1737150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737152)), _1737154), -(c_Map_Omap__upds(_1737148, _1737152, _1737156, hAPP(hAPP(c_List_Oappend(_1737148), _1737150), _1737158), _1737154) = c_Map_Omap__upds(_1737148, _1737152, _1737156, _1737150, _1737154))], (12502 ^ _777864) ^ [_987586, _987588, _987590, _987592] : [class_Rings_Olinordered__semiring__strict(_987586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987586), _987588), _987590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987586), _987592), _987590))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987586), c_Groups_Ozero__class_Ozero(_987586)), _987590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987586), _987588), _987592)))], (16348 ^ _777864) ^ [_1058295, _1058297] : [class_Groups_Oordered__ab__group__add__abs(_1058295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058295), c_Groups_Ozero__class_Ozero(_1058295)), _1058297)), -(hAPP(c_Groups_Oabs__class_Oabs(_1058295), _1058297) = _1058297)], (37763 ^ _777864) ^ [_1486371, _1486373] : [class_Orderings_Olinorder(_1486371), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486371, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1486371), _1486373), c_Orderings_Obot__class_Obot(tc_fun(_1486371, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486371), _1486373)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1486371), _1486373))], (19592 ^ _777864) ^ [_1115029, _1115031] : [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), _1115029))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1115031))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1115029))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115031)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115029)))], (16696 ^ _777864) ^ [_1065194, _1065196] : [class_Rings_Olinordered__idom(_1065194), -(hAPP(c_Groups_Oabs__class_Oabs(_1065194), _1065196) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065194), _1065196), c_Groups_Osgn__class_Osgn(_1065194, _1065196)))], (36744 ^ _777864) ^ [_1463913, _1463915, _1463917, _1463919] : [-(hAPP(c_Map_Orestrict__map(_1463913, _1463915, _1463917, c_Orderings_Obot__class_Obot(tc_fun(_1463913, tc_HOL_Obool))), _1463919) = c_Option_Ooption_ONone(_1463915))], (34639 ^ _777864) ^ [_1421086, _1421088, _1421090, _1421092, _1421094] : [class_Orderings_Oorder(_1421086), 34642 ^ _777864 : [(34655 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1421086, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1421086, _1421088, _1421090)), c_SetInterval_Oord__class_OatLeastAtMost(_1421086, _1421092, _1421094)))), 34656 ^ _777864 : [(34659 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421092), _1421088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421090), _1421094))], (34657 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421088), _1421090)))]]], (34643 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1421086, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1421086, _1421088, _1421090)), c_SetInterval_Oord__class_OatLeastAtMost(_1421086, _1421092, _1421094))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421088), _1421090)), 34650 ^ _777864 : [(34653 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421090), _1421094)))], (34651 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421086), _1421092), _1421088)))]]]]], (34489 ^ _777864) ^ [_1418027, _1418029] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418027, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1418027, tc_HOL_Obool))), hAPP(c_Set_OPow(_1418027), _1418029))))], (1162 ^ _777864) ^ [_795157, _795159] : [-(class_Int_Onumber__ring(_795157)), _795159 = _795157, class_Int_Onumber__ring(_795159)], (49980 ^ _777864) ^ [_1784314, _1784316, _1784318] : [class_Orderings_Olinorder(_1784314), c_List_Olinorder__class_Osorted(_1784314, _1784316), -(c_List_Olinorder__class_Osorted(_1784314, hAPP(hAPP(c_List_Otake(_1784314), _1784318), _1784316)))], (44764 ^ _777864) ^ [_1658819, _1658821, _1658823, _1658825] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1658819, tc_HOL_Obool)), _1658821), _1658823)), hBOOL(hAPP(hAPP(c_member(_1658819), _1658825), _1658821)), -(hBOOL(hAPP(hAPP(c_member(_1658819), _1658825), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1658819, tc_HOL_Obool), _1658823))))], (4336 ^ _777864) ^ [_844224, _844226, _844228, _844230] : [-(c_Nat_Ocompow(_844230, _844226) = c_Nat_Ocompow(_844228, _844224)), _844230 = _844228, _844226 = _844224], (35852 ^ _777864) ^ [_1444631] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444631), hAPP(c_Nat_OSuc, _1444631)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1444631), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (39337 ^ _777864) ^ [_1522046, _1522048] : [class_Lattices_Olattice(_1522046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522046), _1522048)), -(c_Big__Operators_Olattice__class_OInf__fin(_1522046, _1522048) = hAPP(c_Finite__Set_Ofold1(_1522046, c_Lattices_Osemilattice__inf__class_Oinf(_1522046)), _1522048))], (44947 ^ _777864) ^ [_1663117, _1663119, _1663121] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663117, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663117, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1663117, tc_HOL_Obool), tc_HOL_Obool)), _1663119), _1663121))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1663117, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663117, tc_HOL_Obool), _1663119)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1663117, tc_HOL_Obool), _1663121)))))], (6791 ^ _777864) ^ [_889660] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _889660), _889660)))], (36466 ^ _777864) ^ [_1456929, _1456931, _1456933] : [class_Orderings_Olinorder(_1456929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456929), _1456931), _1456933)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456929, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1456929), _1456931)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1456929, _1456931, _1456933)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1456929), _1456933))], (9020 ^ _777864) ^ [_927839, _927841] : [class_Rings_Omult__zero(_927839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927839), _927841), c_Groups_Ozero__class_Ozero(_927839)) = c_Groups_Ozero__class_Ozero(_927839))], (10081 ^ _777864) ^ [_946268, _946270] : [class_Rings_Olinordered__idom(_946268), -(c_Groups_Osgn__class_Osgn(_946268, c_Groups_Osgn__class_Osgn(_946268, _946270)) = c_Groups_Osgn__class_Osgn(_946268, _946270))], (48824 ^ _777864) ^ [_1759273, _1759275, _1759277] : [-(hAPP(c_List_Otl(_1759273), hAPP(hAPP(c_List_Olist_OCons(_1759273), _1759275), _1759277)) = _1759277)], (23395 ^ _777864) ^ [_1186119, _1186121, _1186123, _1186125, _1186127] : [hBOOL(hAPP(hAPP(_1186119, _1186121), _1186123)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186125, _1186127, tc_HOL_Obool), _1186119), hAPP(hAPP(c_Product__Type_OPair(_1186125, _1186127), _1186121), _1186123))))], (24693 ^ _777864) ^ [_1211018, _1211020] : [-(c_Code__Numeral_Onat__of__aux(_1211018, _1211020) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1211018)), _1211020))], (35842 ^ _777864) ^ [_1444397, _1444399, _1444401, _1444403] : [class_Orderings_Oorder(_1444397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1444397, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444397, _1444399), _1444401)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1444397, _1444401), _1444403)) = c_Orderings_Obot__class_Obot(tc_fun(_1444397, tc_HOL_Obool)))], (12904 ^ _777864) ^ [_994493, _994495] : [-(hAPP(c_Int_Onat, _994493) = _994495), 12907 ^ _777864 : [(12910 ^ _777864) ^ [] : [_994493 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994495)], (12908 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994493)))]], 12911 ^ _777864 : [(12914 ^ _777864) ^ [] : [_994495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12912 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _994493))]]], (30657 ^ _777864) ^ [_1338451, _1338453] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1338451, _1338453) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338451), _1338453)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1338453), _1338451)))], (26449 ^ _777864) ^ [_1243825, _1243827, _1243829] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243825, _1243827) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243829, _1243827), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1243827), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243825), _1243829))))], (43682 ^ _777864) ^ [_1629631, _1629633, _1629635, _1629637, _1629639, _1629641] : [hBOOL(hAPP(hAPP(c_member(_1629631), _1629633), _1629635)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629631, tc_fun(_1629637, tc_HOL_Obool)), _1629635), hAPP(hAPP(c_COMBB(tc_fun(_1629637, tc_HOL_Obool), tc_fun(_1629637, tc_HOL_Obool), _1629631), hAPP(c_Set_Oinsert(_1629637), _1629639)), _1629641)) = hAPP(hAPP(c_Set_Oinsert(_1629637), _1629639), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629631, tc_fun(_1629637, tc_HOL_Obool)), _1629635), _1629641)))], (32663 ^ _777864) ^ [_1376204, _1376206, _1376208, _1376210] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1376204, _1376208)), c_Sum__Type_OPlus(_1376204, _1376208, _1376206, _1376210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1376204), _1376206)), hAPP(c_Finite__Set_Ocard(_1376208), _1376210))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376204), _1376206)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376208), _1376210))], (7810 ^ _777864) ^ [_907798, _907800, _907802, _907804] : [c_Com_Ocom_OWhile(_907798, _907800) = c_Com_Ocom_OSemi(_907802, _907804)], (22729 ^ _777864) ^ [_1171150, _1171152, _1171154] : [_1171150 = _1171152, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171154, tc_HOL_Obool)), _1171152), _1171150)))], (33917 ^ _777864) ^ [_1404838, _1404840, _1404842, _1404844, _1404846, _1404848] : [c_Equiv__Relations_Ocongruent(_1404838, _1404840, _1404842, _1404844), hBOOL(hAPP(hAPP(c_member(tc_prod(_1404838, _1404838)), hAPP(hAPP(c_Product__Type_OPair(_1404838, _1404838), _1404846), _1404848)), _1404842)), -(hAPP(_1404844, _1404846) = hAPP(_1404844, _1404848))], (35000 ^ _777864) ^ [_1428247, _1428249, _1428251, _1428253, _1428255] : [c_Fun_Oinj__on(_1428247, _1428249, _1428251, hAPP(hAPP(c_Set_Oinsert(_1428247), _1428253), _1428255)), 35003 ^ _777864 : [(35006 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1428249), hAPP(_1428251, _1428253)), hAPP(c_Set_Oimage(_1428247, _1428249, _1428251), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428247, tc_HOL_Obool)), _1428255), hAPP(hAPP(c_Set_Oinsert(_1428247), _1428253), c_Orderings_Obot__class_Obot(tc_fun(_1428247, tc_HOL_Obool)))))))], (35004 ^ _777864) ^ [] : [-(c_Fun_Oinj__on(_1428247, _1428249, _1428251, _1428255))]]], (13254 ^ _777864) ^ [_1000451, _1000453, _1000455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000451)), 13257 ^ _777864 : [(13264 ^ _777864) ^ [] : [_1000453 = _1000455, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000451), _1000453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000451), _1000455))], (13258 ^ _777864) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000451), _1000453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000451), _1000455), -(_1000453 = _1000455)]]], (5818 ^ _777864) ^ [_873365, _873367, _873369, _873371, _873373, _873375] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_873365, _873367, _873369, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_873365), _873371), _873373), _873375)) = hAPP(hAPP(hAPP(_873369, _873371), _873373), _873375))], (8836 ^ _777864) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9848 ^ _777864) ^ [_942499, _942501] : [-(c_Int_Onat__aux(_942499, _942501) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _942499)), _942501))], (45709 ^ _777864) ^ [_1681128, _1681130, _1681132] : [c_Fun_Oinj__on(tc_List_Olist(_1681128), tc_List_Olist(_1681130), hAPP(c_List_Omap(_1681128, _1681130), _1681132), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1681128), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1681128, _1681130, _1681132, c_Orderings_Otop__class_Otop(tc_fun(_1681128, tc_HOL_Obool))))], (42365 ^ _777864) ^ [_1601034, _1601036, _1601038] : [-(hBOOL(hAPP(hAPP(c_member(_1601034), _1601036), c_Wellfounded_Oacc(_1601034, _1601038)))), 42369 ^ _777864 : [(42372 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1601034), 42368 ^ [_1601034, _1601036, _1601038]), c_Wellfounded_Oacc(_1601034, _1601038)))], (42370 ^ _777864) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601034, _1601034)), hAPP(hAPP(c_Product__Type_OPair(_1601034, _1601034), 42368 ^ [_1601034, _1601036, _1601038]), _1601036)), _1601038)))]]], (11411 ^ _777864) ^ [_968063, _968065, _968067] : [class_Groups_Oordered__comm__monoid__add(_968063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968063), c_Groups_Ozero__class_Ozero(_968063)), _968065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968063), c_Groups_Ozero__class_Ozero(_968063)), _968067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968063), c_Groups_Ozero__class_Ozero(_968063)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968063), _968065), _968067))))], (25567 ^ _777864) ^ [_1226203, _1226205, _1226207, _1226209] : [class_Divides_Osemiring__div(_1226203), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1226203), _1226205), _1226207)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226203), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226203), _1226207), _1226205)), _1226209) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1226203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226203), _1226207), _1226209)), _1226205))], (47458 ^ _777864) ^ [_1726696, _1726698] : [-(c_List_Osublist(_1726696, c_List_Olist_ONil(_1726696), _1726698) = c_List_Olist_ONil(_1726696))], (47899 ^ _777864) ^ [_1736508, _1736510, _1736512, _1736514, _1736516] : [hAPP(hAPP(c_List_Oappend(_1736508), _1736510), _1736512) = hAPP(hAPP(c_List_Olist_OCons(_1736508), _1736514), _1736516), 47904 ^ _777864 : [(47907 ^ _777864) ^ [] : [-(_1736512 = hAPP(hAPP(c_List_Olist_OCons(_1736508), _1736514), _1736516))], (47905 ^ _777864) ^ [] : [-(_1736510 = c_List_Olist_ONil(_1736508))]], 47909 ^ _777864 : [(47912 ^ _777864) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1736508), 47908 ^ [_1736508, _1736510, _1736512, _1736514, _1736516]), _1736512) = _1736516)], (47910 ^ _777864) ^ [] : [-(_1736510 = hAPP(hAPP(c_List_Olist_OCons(_1736508), _1736514), 47908 ^ [_1736508, _1736510, _1736512, _1736514, _1736516]))]]], (41065 ^ _777864) ^ [_1569584, _1569586] : [-(c_FunDef_Oreduction__pair(_1569584, _1569586)), c_Wellfounded_Owf(_1569584, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool), tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool)), _1569586)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1569584, _1569584, _1569584), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool), tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool)), _1569586)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool), tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool)), _1569586))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool), tc_fun(tc_prod(_1569584, _1569584), tc_HOL_Obool)), _1569586)))], (40160 ^ _777864) ^ [_1540139, _1540141, _1540143] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1540139), hAPP(c_Set_OCollect(_1540139), hAPP(hAPP(c_COMBS(_1540139, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540139), c_fdisj), _1540141)), _1540143))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540139), hAPP(c_Set_OCollect(_1540139), _1540141))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540139), hAPP(c_Set_OCollect(_1540139), _1540143)))], (812 ^ _777864) ^ [_790432, _790434] : [-(c_Nat__Transfer_Onat__set(_790432)), _790434 = _790432, c_Nat__Transfer_Onat__set(_790434)], (44778 ^ _777864) ^ [_1659150, _1659152, _1659154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659150, tc_HOL_Obool)), _1659152), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1659150, tc_HOL_Obool), _1659154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1659150, tc_HOL_Obool), tc_fun(_1659150, tc_HOL_Obool)), _1659154), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659150, tc_HOL_Obool)), _1659152)))], (19058 ^ _777864) ^ [_1105466, _1105468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105466), _1105468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1105466)), c_Int_OBit0(_1105468))))], (40399 ^ _777864) ^ [_1548093, _1548095, _1548097, _1548099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1548093), hAPP(c_Set_OCollect(_1548093), _1548095))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548097), hAPP(c_Set_OCollect(_1548097), hAPP(hAPP(c_COMBB(tc_fun(_1548093, tc_HOL_Obool), tc_HOL_Obool, _1548097), c_HOL_OEx(_1548093)), hAPP(hAPP(c_COMBC(_1548097, tc_fun(_1548093, tc_HOL_Obool), tc_fun(_1548093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548093, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1548093, tc_HOL_Obool), tc_fun(_1548093, tc_HOL_Obool)), _1548097), c_COMBS(_1548093, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548093, tc_HOL_Obool), tc_fun(_1548093, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1548097), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548093), c_fconj)), hAPP(hAPP(c_COMBC(_1548097, tc_fun(_1548093, _1548097), tc_fun(_1548093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548097, tc_HOL_Obool), tc_fun(tc_fun(_1548093, _1548097), tc_fun(_1548093, tc_HOL_Obool)), _1548097), c_COMBB(_1548097, tc_HOL_Obool, _1548093)), c_fequal)), _1548099)))), _1548095))))))], (23115 ^ _777864) ^ [_1179165, _1179167] : [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(_1179165))), 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)), _1179167))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179165) = hAPP(c_Nat_OSuc, _1179167))], (34089 ^ _777864) ^ [_1409292, _1409294, _1409296, _1409298, _1409300] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1409292, _1409294, _1409296), _1409298), _1409300), c_Orderings_Obot__class_Obot(tc_fun(_1409294, tc_HOL_Obool))) = _1409300)], (51641 ^ _777864) ^ [] : [-(v_P(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H))))], (47330 ^ _777864) ^ [_1723997, _1723999, _1724001] : [hBOOL(hAPP(c_List_Odistinct(_1723997), _1723999)), -(hBOOL(hAPP(c_List_Odistinct(_1723997), hAPP(hAPP(c_List_Otake(_1723997), _1724001), _1723999))))], (47842 ^ _777864) ^ [_1735066, _1735068, _1735070, _1735072, _1735074, _1735076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735066)), _1735068)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735070)), _1735072))), -(c_Map_Omap__upds(_1735066, _1735070, _1735074, hAPP(hAPP(c_List_Oappend(_1735066), _1735068), hAPP(hAPP(c_List_Olist_OCons(_1735066), _1735076), c_List_Olist_ONil(_1735066))), _1735072) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1735066, tc_Option_Ooption(_1735070)), c_Map_Omap__upds(_1735066, _1735070, _1735074, _1735068, _1735072)), _1735076), hAPP(c_Option_Ooption_OSome(_1735070), hAPP(hAPP(c_List_Onth(_1735070), _1735072), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735066)), _1735068)))))], (4210 ^ _777864) ^ [_842211, _842213, _842215, _842217, _842219, _842221] : [-(c_Set_Oimage(_842221, _842217, _842213) = c_Set_Oimage(_842219, _842215, _842211)), _842221 = _842219, _842217 = _842215, _842213 = _842211], (43635 ^ _777864) ^ [_1628516, _1628518, _1628520, _1628522, _1628524] : [-(_1628516 = c_Orderings_Obot__class_Obot(tc_fun(_1628518, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628520, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628518, tc_fun(_1628520, tc_HOL_Obool)), _1628516), _1628522)), _1628524) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1628518, tc_fun(_1628520, tc_HOL_Obool)), _1628516), hAPP(hAPP(c_COMBC(_1628518, tc_fun(_1628520, tc_HOL_Obool), tc_fun(_1628520, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1628520, tc_HOL_Obool), tc_fun(tc_fun(_1628520, tc_HOL_Obool), tc_fun(_1628520, tc_HOL_Obool)), _1628518), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628520, tc_HOL_Obool))), _1628522)), _1628524)))], (24353 ^ _777864) ^ [_1204209, _1204211, _1204213] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1204209), _1204211), _1204213) = c_Nitpick_OAbs__Frac(_1204209, c_Nitpick_Onorm__frac(_1204211, _1204213)))], (25715 ^ _777864) ^ [_1228978, _1228980, _1228982] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228978), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228980), _1228982))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228978), _1228982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1228982), _1228980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1228978), _1228980)))], (16358 ^ _777864) ^ [_1058450, _1058452] : [class_Groups_Oordered__ab__group__add__abs(_1058450), 16361 ^ _777864 : [(16368 ^ _777864) ^ [] : [-(_1058452 = c_Groups_Ozero__class_Ozero(_1058450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058450), c_Groups_Ozero__class_Ozero(_1058450)), hAPP(c_Groups_Oabs__class_Oabs(_1058450), _1058452))))], (16362 ^ _777864) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058450), c_Groups_Ozero__class_Ozero(_1058450)), hAPP(c_Groups_Oabs__class_Oabs(_1058450), _1058452))), _1058452 = c_Groups_Ozero__class_Ozero(_1058450)]]], (48926 ^ _777864) ^ [_1761450, _1761452, _1761454] : [class_Groups_Omonoid__add(_1761450), -(hAPP(c_List_Ofoldl(_1761450, _1761450, c_Groups_Oplus__class_Oplus(_1761450), _1761452), _1761454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1761450), _1761452), c_List_Ofoldr(_1761450, _1761450, c_Groups_Oplus__class_Oplus(_1761450), _1761454, c_Groups_Ozero__class_Ozero(_1761450))))]], input).
% 45.14/43.94  ncf('1',plain,[v_Q(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s1), hAPP(c_Natural_Ogetlocs, v_s_H))), v_X), hAPP(hAPP(c_Natural_Ogetlocs, v_s1), c_Com_ORes)))],start(51645 ^ 0)).
% 45.14/43.94  ncf('1.1',plain,[-(v_Q(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s1), hAPP(c_Natural_Ogetlocs, v_s_H))), v_X), hAPP(hAPP(c_Natural_Ogetlocs, v_s1), c_Com_ORes)))), 51635 : c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), hAPP(c_Nat_OSuc, v_na), v_s1), 51635 : v_P(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)))],extension(51631 ^ 1,bind([[_1813557, _1813559, _1813643], [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), v_Z, v_s1]]))).
% 45.14/43.94  ncf('1.1.1',plain,[-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, v_pn), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), hAPP(c_Nat_OSuc, v_na), v_s1)), c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), v_na, v_s1)],extension(5531 ^ 4,bind([[_865219, _865221, _865223, _865225], [v_pn, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), v_na, v_s1]]))).
% 45.14/43.94  ncf('1.1.1.1',plain,[-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, v_pn)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H)), v_na, v_s1))],extension(51643 ^ 5)).
% 45.14/43.94  ncf('1.1.2',plain,[-(v_P(v_Z, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, v_s_H), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), v_a(v_s_H))))],extension(51641 ^ 2)).
% 45.14/43.94  %-----------------------------------------------------
% 45.14/43.94  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------